ESTIMATION OF THE SPATIO-TEMPORAL HETEROGENEITY OF RAINFALL AND ITS IMPORTANCE TOWARDS ROBUST CATCHMENT SIMULATION, WITHIN A HYDROINFORMATIC ENVIRONMENT.
by K.Umakhanthan School of Civil and Environmental Engineering Faculty of Engineering University of New South Wales Sydney, Australia
June 2002
This thesis is submitted to the University of New South Wales in fulfilment of the requirements for the degree of Doctor of Philosophy UNIVERSITY OF NEW SOUTH WALES Trim page to Thesis/Project Report Sheet guide lines
Surname or Family Name: Umakhanthan First Name: Kanagaratnam Other name/s: Abbreviation for degree as given in the University calendar: PhD School: Civil and Environmental Engineering Faculty: Engineering Title: ESTIMATION OF THE SPATIO-TEMPORAL HETEROGENEITY OF RAINFALL AND ITS IMPORTANCE TOWARDS ROBUST CATCHMENT SIMULATION, WITHIN A HYDROINFORMATIC ENVIRONMENT
Abstract 350 words maximum: Presented in this dissertation is an investigation of the spatial and temporal heterogeneity of rainfall and the influence of this on the robustness of predictions obtained from a Catchment Modelling System (CMS). Proposed in this dissertation is a methodology to investigate the degree of variability of rainfall in the spatial and temporal dimensions. Improved estimates of the spatially distributed with smaller time step hyetographs suited especially the urban catchments were obtained and importance of a more detailed rainfall model is highlighted towards a more robust prediction from CMS.
The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi- variance of gauge records in space and time against distance and time respectively. As the results of the investigation on the developed semi-variogram approach, real storm events were categorised as being High Spatial-High Temporal (HS-HT); High Spatial-Low Temporal; (HS-LT); Low Spatial-High Temporal (LS- HT); and Low Spatial-Low Temporal variability.
A Comparatively detailed rainfall distribution model in space and time was developed within the GIS. The enhanced rainfall representation in both space and time scale is made feasible in the study by the aid of the powerful spatial analytic capability of GIS. From this model, improved estimates of the spatially distributed with smaller time step hyetographs suited for especially the urban catchments could be obtained.
The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error parameters for predictions from CMS using alternate rainfall models, for various degrees of spatio-temporal heterogeneity events. From the investigations made, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event.
The analysis is based on the real events recorded from the Centennial Park Catchment (1.3 km2) and the Upper Parramatta River Catchment (110 km2) in Sydney, Australia.
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REGISTRAR AND DEPUTY PRINCIPAL
THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS This thesis is dedicated to the memory of my beloved father, the late Mr.S.Kanagaratnam (1938-1993)
This is the proper plan of study: Reading, Reflection and Regular application in life.
Study is Work. Inquiry into the value and applicability of what is studied is Worship.
The experience of validity and value of the practice is Wisdom. True education is not for a mere living, but for a fuller and meaningful life.
- Bagawan Sri Sathya Sai Baba CERTIFICATE OF ORIGINALITY
I hereby declare that this submission is my own work and to the best of my knowledge it contains no material previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgment is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis.
I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.
Signature: …………………………………….
Date: …………………………….……… ABSTRACT
Rainfall is a natural process, which has a high degree of variability in both space and time. Information on the spatial and temporal variability of rainfall plays an important role in the process of surface runoff generation. Hence it is important for a variety of applications in hydrology and water resources management. The spatial variability of rainfall can be substantial even for very small catchments and an important factor in the reliability of rainfall-runoff simulations. Catchments in urban areas usually are small, and the management problems often require the numerical simulation of catchment processes and hence the need to consider the spatial and temporal variability of rainfall. A need exists, therefore, to analyse the sensitivity of rainfall-runoff behaviour of catchment modelling systems (CMS) to imperfect knowledge of rainfall input, in order to judge whether or not they are reliable and robust, especially if they are to be used for operational purposes.
Development of a methodology for identification of storm events according to the degree of heterogeneity in space and time and thence development of a detailed spatial and temporal rainfall model within a hydroinformatic environment utilising real-time data has been the focus of this project. The improvement in runoff prediction accuracy and hence the importance of the rainfall input model in runoff prediction is then demonstrated through the application of a CMS for differing variability of real storm events to catchments with differing orders of scale.
The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilised in introducing estimators to measure the degree of heterogeneity of each individual storm events in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. As the results of the investigation on the developed semi-variogram approach, real storm events were categorised as being High Spatial-High Temporal (HS-HT); High Spatial-Low Temporal; (HS-LT); Low Spatial-High Temporal (LS-HT); and Low Spatial-Low Temporal variability.
i Abstract
A comparatively detailed rainfall distribution model in space and time was developed within the Geographical Information Systems (GIS). The enhanced rainfall representation in both space and time scale is made feasible in the study by the aid of the powerful spatial analytic capability of GIS. The basis of this rainfall model is an extension of the rainfall model developed by Luk and Ball (1998) through a temporal discretisation of the storm event. From this model, improved estimates of the spatially distributed with smaller time steps hyetographs suited for especially the urban catchments could be obtained.
The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error parameters for predictions from CMS using alternate rainfall models, for various degrees of spatio- temporal heterogeneity events. Also it is appropriate to investigate whether the degree of this improvement to be dependent on the variability of the storm event which is assessed by the adopted semi-variogram approach. From the investigations made, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event as measured by the proposed semi-variogram approach for assessing this feature of a storm event.
The analysis is based on forty real events recorded from the Centennial Park Catchment (1.3km2) and the Upper Parramatta River Catchment (110km2) in Sydney, Australia. These two case study catchments were selected to ensure that catchment scale effects were incorporated in the conclusions developed during the study.
ii PREFACE
This dissertation is submitted for the degree of Doctor of Philosophy at the University of New South Wales, Sydney, Australia. The work described in the thesis carried out by the candidate during the years 1998-2001 in the School of Civil and Environmental Engineering under the supervision of Associate Professor J.E.Ball and associate supervision of Dr.A.Sharma.
Several papers have been written by the candidate, and the work has been presented at internationally esteemed conferences. At present, a number of papers are still under preparation to be published in selected journals. These papers are listed below. The full versions of the selected papers from the list are amended under Appendix I.
Journal
Umakhanthan, K., Ball, J.E. and Sharma, A., (2001 submitted). Estimation of Spatio-Temporal Heterogeneity of Rainfall on Urban Catchments - A Semi- Variogram Approach, submitted to Journal of Hydrology.
Umakhanthan, K, Ball, J.E. and Sharma, A. Spatio- temporal heterogeneity of rainfall and its importance towards a more robust catchment simulation, to be presented in July 2002, to ASCE Journal of Hydrologic Engineering.
Conference
Umakhanthan, K, and Ball, J.E., Estimation of Rainfall Heterogeneity across space and time scales, 9th ICUD Conference to be held in Portland, Oregon, USA in September 2002.
Umakhanthan, K and Ball, J.E., Importance of rainfall Models in Catchment Simulation, 13th APD-IAHR International conference, Singapore, August 6-8, 2002.
iii Preface
Umakhanthan, K and Ball, J.E., Estimation of spatio- temporal heterogeneity of rainfall and its importance towards a more robust catchment simulation, Int. Conf. on Urban Hydrology for 21st Century (ICUH2002), KL, Malaysia, Oct. 6- 8, 2002.
Umakhanthan, K and Ball, J.E., (2000). Integration of Hydroinformatics with catchment models, 'Hydroinformatics 2000' International Conference, Iowa, USA.
Umakhanthan, K and Ball, J.E., (2000). Influence of spatially variable rainfall on runoff hydrographs. 12th APD-IAHR International conference, Bangkok, Thailand, November 2000, ISBN 974-8202-75-5.
iv ACKNOWLEDGEMENTS
Writing a thesis is singularly hard work, but is far from being a single effort. I would like to take this opportunity to thank a number of people who have made the completion of this thesis possible. First of all, this study would not have been possible without the guidance, inspiration, encouragement and personal support of my primary supervisor, Associate Professor James Edward Ball. I especially thank him for making time for me when he had very little of his own. I am honoured to have studied under his supervision.
I also wish to express my deepest gratitude to my co-supervisor, Dr.Ashish Sharma for his valuable, impressive and insightful suggestions and comments for my study. He led me towards the better exploration of engineering research.
I would like to acknowledge the Department of Employment Education and Training Affairs (DEETYA) of Australia and School of Civil and Environmental Engineering of the UNSW for providing me the financial assistance to this study.
I would like to thank Mr. Stephen Lynch from the Upper Parramatta River Catchment Trust; Mr.Alf Wojcik and Mr.Jim Tilley from the School of Civil and Environmental Engineering at the University of New South Wales; Mr.Stephen Butler from the Department of Land and Water Conservation, for providing the rainfall and flow data and supporting my study.
Furthermore, I wish to thank the staff of Water Research Laboratory (WRL) of the UNSW for providing me the necessary support and for the usage of GIS facilities. Also I am grateful to the academic, computer and the administrative staff and my fellow doctoral students in the school of Civil and Environmental Engineering, who have made my stay here such a pleasant and meaningful experience.
Finally, I wish to express my deep gratitude and love to my dearest wife, Dushy. Her love, patience and encouragement enabled me to complete this study. A special thanks to all my family members for their patience and encouragement.
v TABLE OF CONTENTS
Abstract i
Preface iii
Acknowledgements v
Table of Contents vi
List of Figures xii
List of Tables xviii
Symbols xx
Abbreviations xxi
CHAPTER 1: INTRODUCTION 1
1.1 AN OVERVIEW 1 1.1.1 The role of rainfall in Catchment Modelling Systems 1 1.1.2 The Role of Hydroinformatics in Catchment Management 2 1.1.3 The Role of Catchment Simulation in Hydrology 3
1.2 AUTHOR'S CONTRIBUTIONS 4 1.3 OUTLINE OF THESIS 5
CHAPTER 2: FUNDAMENTAL THEORY AND LITERATURE REVIEW 7
2.1 INTRODUCTION 7
2.2 CATCHMENT MODELLING SYSTEMS 8 2.2.1 Concepts 8 2.2.2 Information Required 11 2.2.3 Rainfall-Runoff process 13 2.2.4 Urban Catchment Modelling Systems 14 2.2.4.1 Concepts 15
vi Table of Contents
2.2.4.2 Stormwater Management Model 16
2.3 INFLUENCE OF RAINFALL IN CATCHMENT MODELLING SYSTEM PREDICTIONS 19 2.3.1 Effect of spatial variability of rainfall 20 2.3.2 Effect of temporal variability of rainfall 22 2.3.3 Effect of Storm movement 23 2.3.4 Effect of averaging rainfall in space and time 24 2.3.4.1 Distributed vs Lumped Modelling 25
2.4 ALTERNATIVE RAINFALL MODELS 27 2.4.1 Concepts of rainfall models 27 2.4.2 Application of alternative rainfall models in hydrology 27 2.4.3 Thiessen Polygon Models 30 2.4.4 Fitting a Spline Surface 31
2.5 CORRELATION ANALYSIS AND SEMI-VARIOGRAM APPROACH IN RAINFALL ANALYSIS 33 2.5.1 General Background 33 2.5.2 Correlation techniques 33 2.5.3 Semi-Variogram approach 34 2.5.3.1 Random Fields and Second Moment Characterisation 35 2.5.3.2 Mean and Covariance Function 36 2.5.3.3 The Variogram 37
2.6 GIS IN CATCHMENT MODELLING SYSTEMS 39 2.6.1 Integration of Hydroinformatics with Catchment Modelling Systems 39 2.6.2 Merits of GIS 40 2.6.2.1 Grid data Model and Structure 41 2.6.2.2 Vector data model and Structure 42 2.6.3 Application of Geographic Information Systems in Hydrology 43
2.7 ASSESSMENT CRITERIA OF CALIBRATION AND VALIDATION PROCESSES 45 2.7.1 Errors in Application of catchment Modelling 45 2.7.2 Assessment Criteria for Runoff Prediction 46
vii Table of Contents
CHAPTER 3: TEST CATCHMENTS 52
3.1 CATCHMENT LOCATION 52
3.2 UPPER PARRAMATTA RIVER CATCHMENT 53 3.2.1 Catchment and drainage description 53 3.2.2 Available Information 55 3.2.2.1 Rainfall Records 55 3.2.2.2 Stream Height Records 58 3.2.3 Subcatchment Details 58
3.3 CENTENNIAL PARK CATCHMENT 61 3.3.1 Catchment and drainage description 61 3.3.2 Available Information 62 3.3.2.1 Rainfall Records 63 3.3.2.2 Flow Records 65 3.3.3 Subcatchment Details 66
CHAPTER 4: ESTIMATION OF SPATIO-TEMPORAL HETEROGENEITY OF RAINFALL 69
4.1 INTRODUCTION 69 4.1.1 Classification of storm events based on their heterogeneity in space and time 71
4.2 METHODOLOGY 74
4.3 SEMI-VARIOGRAM APPROACH; BACKGROUND AND THEORY 74 4.3.1.1 Stationary random field approach 76 4.3.1.2 Intrinsic random field approach 78
4.4 IDENTIFICATION OF SPATIAL VARIOGRAM MODEL 79 4.4.1 Definition of Semi-Variogram 79 4.4.2 Motion of Storm Events 80 4.4.3 Estimation of event based parametric Variogram models 82
4.5 IDENTIFICATION OF TEMPORAL SEMI-VARIOGRAM 83
4.6 APPLICATION ON UPRC 86 4.6.1 Spatial Semi-Variogram plots for UPRC 86
viii Table of Contents
4.6.2 Space Characteristic Parameter ( as ) 90 4.6.3 Impact of time step on spatial variability of rainfall fields 94 4.6.4 Temporal Semi-variogram plots for UPRC 95
4.6.5 Time Characteristic parameter (ts ) 97 4.6.5.1 Impact of time steps on temporal variability of rainfall fields 99 4.6.6 Event categorisation in space and time for UPRC 100
4.7 APPLICATION ON CPC 101 4.7.1 Spatial Semi-variogram plots for CPC 101
4.7.1.1 Space characteristic Parameter ( as ) for CPC 104
4.7.2 Temporal Semi-variogram plots for CPC events 107
4.7.2.1 Time Characteristic Parameter (ts ) for CPC 108 4.7.3 Event Categorisation in space and time for CPC 109
4.8 CONCLUSION 111
CHAPTER 5: IMPLEMENTATION OF THE SPATIO-TEMPORAL RAINFALL MODEL 112
5.1 INTRODUCTION 112
5.2 METHODOLOGY 113
5.3 RESULTS AND DISCUSSION 114 5.3.1 Spatial Variability on total storm. 115 5.3.2 Spatial Variability during the storm event 120 5.3.3 Subcatchment Hyetograph development 123 5.3.4 Comparison of developed spline model with the traditional Thiessen polygon approach. 127 5.3.4.1 Comparisons for the UPRC. 131 5.3.4.2 Comparisons for the CPC 136
5.4 CONCLUSIONS 140
CHAPTER 6: INFLUENCE ON CATCHMENT RESPONSE TO RAINFALL 142
ix Table of Contents
6.1 INTRODUCTION 142
6.2 OBSERVED RAINFALL AND RUNOFF HYDROGRAPH VOLUMES 143
6.3 BEHAVIOUR OF RAINFALL AND RUNOFF DEPTHS 145 6.3.1 At UPRC Outlet 146 6.3.2 At CPC Outlet 148
6.4 INFLUENCE OF SPATIAL HETEROGENEITY ON CATCHMENT SIMULATION 150 6.4.1 Calibration of Events 151 6.4.1.1 Calibration of UPRC Model 151 6.4.1.2 Calibration of CPC Model 153 6.4.2 Validation of Events 157 6.4.2.1 Validation of UPRC Events 157 6.4.2.2 Validation of CPC Events 162 6.4.3 Sensitivity in Catchment Prediction for alternate Rainfall Input 165 6.4.3.1 For events on UPRC 165 6.4.3.2 For events on CPC 169
6.5 CONCLUSIONS. 175
CHAPTER 7: SUMMARY AND CONCLUSIONS 176
7.1 SUMMARY OF RESEARCH 176 7.1.1 Introduction 176 7.1.2 Objectives 176 7.1.3 Estimation of Rainfall heterogeneity in space and time 177 7.1.4 Development of rainfall pattern within a hydroinformatic environment 178 7.1.5 Improvement in prediction of runoff quantity 178
7.2 CONCLUSIONS 179 7.2.1 Estimation of Spatio-temporal heterogeneity of Rainfall 179 7.2.2 Development of rainfall pattern within a hydroinformatic environment 180 7.2.3 Robust prediction of runoff hydrograph 181
7.3 LIMITATIONS AND ASSUMPTIONS 182
REFERENCES 183
x Table of Contents
APPENDICES
Appendix A : Storm Details and Gauge Locations Appendix B1 : Semi-Variogram Models estimated for UPRC events Appendix B2 : Semi-Variogram Models estimated for CPC events Appendix C1 : Estimated Semi-Variogram Model Parameters for UPRC events Appendix C2 : Estimated Semi-Variogram Model Parameters for CPC events Appendix D1 : Estimated spatially varied hyetograph patterns for UPRC events Appendix D2 : Estimated spatially varied hyetograph patterns for CPC events Appendix E1 : Quantitative assessment of spatial variability for UPRC events Appendix E2 : Quantitative assessment of spatial variability for CPC events Appendix F1 : Typical SWMM input data file for UPRC Model Appendix F2 : Typical SWMM input data file for CPC Model Appendix G : Behaviour of rainfall depth vs Observed runoff depth Appendix H1 : Comparison of predicted flow hydrographs at UPRC outlet Appendix H2 : Comparison of predicted flow hydrographs at CPC outlet Appendix I : Publications
xi LIST OF FIGURES
Page
Figure 2-1: Catchment Modelling System, Conceptual Components (after Ball, 1996) 10
Figure 2-2: SWMM program structure (After Huber and Dickinson, 1988) 18
Figure 2-3: Steps involved in 2-D estimation problem in geostatistics. 35
Figure 3-1: Location of Upper Parramatta River Catchment (UPRC) and Centennial Park Catchment (CPC) 52
Figure 3-2: Upper Parramatta River Catchment with Drainage Map 54
Figure 3-3: Rain Gauge Locations within and adjacent to the Catchment 56
Figure 3-4: Schematization of Subcatchments for the Upper Parramatta River Catchment (after the Flood mitigation program by Upper Parramatta River Catchment Trust) 59
Figure 3-5: Centennial Park Catchment with Drainage Map 62
Figure 3-6: Rain Gauge Locations within and adjacent to the Catchment 64
Figure 3-7: Schematization of Subcatchments, of Centennial Park Catchment after Abustan (1997) 67
Figure 4-1: Hypothetical storm patterns represents different categories of storms according to their spatial and temporal heterogeneity. 73
Figure 4-2: Data location randomly scattered in a 2D domain (W) 75
Figure 4-3: Schematic representation of semi-variogram and correlogram for a stationary RF. 78
Figure 4-4: Variation of spatial semi-variogram for lagged rainfall time series from two different gauge locations 81
Figure 4-5: Temporal distributions of three hypothetical storm events. 84
xii List of Figures
Figure 4-6: Typical semi-variogram plots for the different temporal nature of storm events, shown in Figure 4-5. 85
Figure 4-7: Scattered plot of raw variogram estimated for the storm event on July 27, 1996 for UPRC. 87
Figure 4-8: Cumulative rainfall patterns observed from the Gauges of UPRC network for the event on July 27, 1996. (more spatially uniform event compared to event in Figure 4-10) 88
Figure 4-9: Computed experimental semi-variogram model for the event on July 27, 1996 [Spherical model fit is plotted in dotted line with Power function fit for checking the validity of method 2 over 1] 89
Figure 4-10: Cumulative rainfall patterns observed at the Gauges of UPRC for the event on May 2, 1998. (higher spatially heterogeneous event compared to the event in Figure 4-8) 89
Figure 4-11: Computed experimental semi-variogram model for the event on May 2, 1998. Spherical model fit is plotted in dotted line with Power function fit for comparison. 90
Figure 4-12: Experimental semi-variogram plots for the six selected different spatially variable events for UPRC 91
Figure 4-13: Spatial semi-variogram computed between rainfall time series recorded during the event on June 27, 1996 by all gauge pairs of UPRC network. [The different symbols refer to different time intervals] 95
Figure 4-14: Cumulative rainfall patterns observed from the Gauges of UPRC network for the event on August 30, 1996. (more temporally uniform event compared to event in Figure 4-15) 96
Figure 4-15: Cumulative rainfall patterns observed at the Gauges of UPRC for the event on April 11, 1996. (higher temporally heterogeneous event compared to the event in Figure 4-14) 96
Figure 4-16: Typical temporal semi-variogram patterns for the six pre-selected events according to their degree of temporal variability, for UPRC 97
xiii List of Figures
Figure 4-17: Temporal semi-variogram computed between rainfall time series recorded during the event on June 27, 1996 by all gauge pairs of UPRC network. [The different symbols refer to different time intervals] 99
Figure 4-18: Placement of individual storm vents for UPRC, based on their degree of heterogeneity in space and time frame 100
Figure 4-19: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on Jan. 29, 1997. (more spatially uniform event compared to event shown in Figure 4-21) 102
Figure 4-20: Computed raw and experimental semi-variogram model for the event on Jan 29, 1997 for CPC. 102
Figure 4-21: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on April 22, 1997. (Higher spatially heterogeneous event compared to event shown in Figure 4-19) 103
Figure 4-22: Computed raw and experimental semi-variogram model for the event on April 22, 1998 for CPC. 103
Figure 4-23: Experimental semi-variogram plots for the six selected different spatially variable events for CPC. 106
Figure 4-24: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on May 18, 1998. (Higher Temporal heterogeneous event compared to event shown in Figure 4-21) 107
Figure 4-25: Typical temporal semi-variogram patterns for the six pre-selected events according to their degree of temporal variability, for CPC 109
Figure 4-26: Placement of individual storm events for CPC, based on their degree of heterogeneity in space and time frame 110
Figure 5-1: Spatial distribution of total rainfall of an event categorised as ‘HS’ from Upper Parramatta River Catchment (Event on July 14, 1999). 116
Figure 5-2: Spatial distribution of total rainfall of an event categorised as ‘LS’ from Upper Parramatta River Catchment (Event on July 27, 1996). 117
xiv List of Figures
Figure 5-3: Spatial distribution of total rainfall of an event catergoised as ‘HS’ from Centennial Park Catchment (Event on October 9, 1998). 118
Figure 5-4: Spatial distribution of total rainfall of an event categorised as ‘LS’ from Centennial Park Catchment (Event on October 19, 1998) 119
Figure 5-5: Series of rainfall distributions occurred in every five-minute interval for the event categorised as HS-HT from UPRC (Event on July 14, 99) 121
Figure 5-6: Series of rainfall distributions occurred in every five-minute interval for the event categorised as ‘LS-LT’ from UPRC (Event on July 27, 1996) 122
Figure 5-7: Cumulative hyetograph patterns from the developed spatial model for the selected four events (from each classification) from UPRC (Shown for 29 subcatchments) 124
Figure 5-8: Boxplots of Subcatchment Rainfall estimation by the developed model for ten events for UPRC. Events are ordered according to their spatial variability. 125
Figure 5-9: Cumulative hyetograph patterns from the developed spline model for a ‘LS’ event and a ‘HS’ event from CPC (Shown for 42 subcatchments) 126
Figure 5-10: Boxplots of Subcatchment Rainfall estimated by the developed spline model for eight events from CPC. Events are ordered according to their spatial variability. 127
Figure 5-11: Thiessen Polygons for the UPRC with respect to the 29 subcatchment boundaries 129
Figure 5-12: Thiessen Polygons for the CPC with respect to the 42 subcatchment boundaries. 130
Figure 5-13: Comparison of predicted total rainfall (for the overall catchment) of events from UPRC by the developed Spline model and the Thiessen Model 131
xv List of Figures
Figure 5-14: Comparison of predicted subcatchment total rainfall for the ‘LS-LT’ event occurred on 27 July 1996 from UPRC, for each of the 29 subcatchments 132
Figure 5-15: Comparison of predicted subcatchment total rainfall for the ‘HS-HT’ event occurred on 14 July 1999 from UPRC, for each of the 29 subcatchments 133
Figure 5-16: Box-plots of calculated from each of the 29 subcatchments of UPRC ; Events grouped according to their spatial variability. 135
Figure 5-17: Comparison of predicted total rainfall (for the overall catchment) of events from CPC by the developed Spline model and the Thiessen Model 137
Figure 5-18: Comparison of distributions of predicted subcatchment total rainfall and variation from the subcatchment Thiessen total for the various events on CPC 138
Figure 5-19: Box-plots of calculated from each of the 42 subcatchments of CPC ; Events grouped according to their spatial variability. 139
Figure 6-1: Typical Rainfall-Runoff behaviour for the UPRC with the Observed flow at the catchment outlet for the event occurred on April 01, 1999 144
Figure 6-2: Typical Rainfall-Runoff behaviour for the CPC with the Observed flow at the catchment outlet for the event occurred on Feb 11, 1997 145
Figure 6-3: Behaviour of assumed Thiessen rainfall depths against the observed runoff depths from the selected events for UPRC. 147
Figure 6-4: Behaviour of assumed Thiessen rainfall depths against the observed runoff depths from the selected events for CPC. 149
Figure 6-5: The Shape of observed amd Simulated hydrograph for a calibrated events a)- Sep. 9, 1993 ; b ) Sep. 13, 1993 : [Downes (1998)] 153
Figure 6-6: The Shape of observed and Simulated hydrograph for a calibrated events a)- Feb. 28, 1995 ; b ) Oct. 21, 1995 : [Abustan (1997)] 156
xvi List of Figures
Figure 6-7: The shape of the observed and simulated hydrograph for a validation event of UPRC – January 06, 1996 (Event Id. 1b) 160
Figure 6-8: The shape of the observed and simulated hydrograph for a validation event of UPRC - August 30, 1996 (Event Id. 5) 161
Figure 6-9: The shape of the observed and simulated hydrograph for a validation event of UPRC - October 18, 1999 (Event Id. 24). 161
Figure 6-10: The shape of the observed and simulated hydrograph for a validation event - February 11, 1997 164
Figure 6-11: The shape of the observed and simulated hydrograph for a validation event - October 19, 1999 164
Figure 6-12: Prediction of simulated hydrograph from UPRC for a 'HS-HT' event - January 02, 1996 (1a) 166
Figure 6-13: Prediction of simulated hydrograph from UPRC for a 'HS-LT' event - April 09, 1998 166
Figure 6-14: Comparisons between Observed Peak and Simulated Peak (from alternate rainfall input) for the selected events from UPRC 168
Figure 6-15: Comparisons between Observed Volume and Simulated Volume (from alternate rainfall input) for the selected events from UPRC. 169
Figure 6-16: Prediction of simulated hydrograph from CPC for a 'HS-HT' event - October 09, 1999 170
Figure 6-17: Prediction of simulated hydrograph of CPC for a 'HS-HT' event - June 16, 1998 170
Figure 6-18: Prediction of simulated hydrograph of CPC for a 'HS-HT' event - May 18, 1998 171
Figure 6-19: Comparisons between Observed Peak and Simulated Peak (from alternate rainfall input) for the selected events from CPC. 173
Figure 6-20: Comparisons between Observed Peak and Simulated Peak (from alternate rainfall input) for the selected events from CPC. 173
Figure 6-21: Improvement in performance statistics by Spline predicted flow from Thiessen predicted flow ; a) Variance ; b) MSE; c) RMSE 174
xvii LIST OF TABLES
Page Table 2-1: Hydrologic and Hydraulic models in different Urban Modelling Systems 13 Table 2-2: Types of Measurement Criteria and Evaluation of Assessment Criteria 51
Table 3-1: Details of Selected Storm Events from UPRC 57 Table 3-2: Subcatment Description of UPRC 60 Table 3-3: Rainfall Monitoring Stations and Operation Authority 63 Table 3-4: Detailed of Selected Storm Events 66 Table 3-5: Subcatchment Description of CPC 68
Table 4-1: Space and time parameters based on their degree of heterogeneity and the respective classification of events for UPRC. 93 Table 4-2: Space and time parameters based on their degree of heterogeneity and the respective classification of events for CPC. 105
ρ Table 5-1: Comparison summary of coefficient of variation ( s ) from 29 subcatchments of UPRC for different classification of events 136 ρ Table 5-2: Comparison summary of coefficient of variation ( s ) from 42 subcatchments of CPC for different classification of events 139
Table 6-1: Statistical Fit between observed and simulated runoff peak flows for Calibrated Events for UPRC: [Downes (1998)]151 Table 6-2: Statistical Fit between observed and simulated runoff Volume for Calibrated Events for UPRC: [Downes (1998)] 151 Table 6-3: Statistical Fit between observed and simulated runoff peak flows of Calibrated Events for CPC: [Abustan (1997)] 154 Table 6-4: Statistical Fit between observed and simulated runoff depths of Calibrated Events for CPC: [Abustan (1997)] 154 Table 6-5: Parameterset used in rainfall-runoff model available with SWMM for UPRC 158
xviii List of Tables
Table 6-6: Statistical Fit between observed and simulated runoff peak flows of validated Events (Low spatially variable events) for UPRC 158 Table 6-7: Statistical Fit between observed and simulated runoff volume of validated Events (Low spatially variable events) for UPRC 158 Table 6-8: Parameter set used in rainfall-runoff model available with SWMM for CPC 162 Table 6-9: Performance statistics for Validated events for CPC. 163 Table 6-10: Comparison of performance statistics between example events from 'LS-LT’ and 'HS-HT' category events 167 Table 6-11: Comparison of performance statistics between example events from ‘LS’ and 'HS' category events 172
xix Symbols
as Space Characteristic Parameter
Cov(i, j) Covariance Function
E{}Z()x,y Expected Value Operator m()x,y Mean Function
Po Observed Peak Flow
Ps Simulated Peak Flow () Qo i Instantaneous Observed Flow Rate () Qs i Instantaneous Simulated Flow Rate
ts Time Characteristic Parameter
Vo Observed Volume
Vs Simulated Volume
Var{}Z()x,y Variogram Function () Z xk Random Variable at Point xk
ρ()i, j Correlation Coefficient
ρ s Coefficient of Variation
γ ()i, j Semi-variogram Function
γ * ()i, j Standardised Semi-variogram Function
σ Standard Deviation
xx Abbreviations
AAT Arc Attribute Table
AHD Australian Height Datum
AML Arc Macro Language
ARE Absolute Relative Error
BOM Bureau of Meteorology
CBD Central Business District
CDM Camp Dresser & McKee
CMS Catchment Modelling Systems
CPC Centennial Park Catchment
DBMS Data Base Management System
DEM Digital Elevation Model
DLWC Department of Land and Water Conservation
DTM Digital Terrain Model
EPA Environmental Protection Agency
ESRI Environmental System Research Institute
GIS Geographical Information Systems
MAE Mean Absolute Error
MSE Mean Square Error
OSU Oregon State University
PAT Polygon Attribute Table
RE Relative Error
RF Random Field
RMSE Root Mean Square Error
TSM Time Series Manager
SSE Sum of Square Errors
xxi Abbreviations
SWMM Stormwater Management Model
UNSW University of New South Wales
UPRC Upper Parramatta River Catchment
UPRCT Upper Parramatta River Catchment Trust
VAT Value Attribute Table
xxii CHAPTER 1
INTRODUCTION
Presented in this dissertation is an investigation of the spatial and temporal heterogeneity of rainfall and the influence of this on the robustness of predictions obtained from a Catchment Modelling System (CMS). Proposed in this dissertation is a methodology to investigate the degree of variability of rainfall in the spatial and temporal dimensions. Improved estimates of the spatially distributed with smaller time step hyetographs suited especially the urban catchments were obtained and importance of a more detailed rainfall model is highlighted towards a more robust prediction from CMS.
1.1 An Overview
1.1.1 The role of rainfall in Catchment Modelling Systems
Rainfall is a dynamic process, which varies both in space and time. Given the same amount of rainfall, the impact on flow within and from a catchment depends very much on the spatial and temporal patterns of rainfall. Since rainfall drives the runoff formation process in CMS, rainfall provides a rich source of information as well as the primary input in most hydrological systems for understanding and modelling of surface, subsurface water quantity and quality. It is suggested and investigated herein that the variability of rainfall in space and time must be considered in order to provide accurate input for modelling the hydrologic response of a catchment.
Three important problems associated with rainfall information in catchment hydrology are identified as follows :
1. Variability of rainfall in space and time, causing variability in catchment response
2. Rainfall is very difficult to measure accurately across the spatial and temporal scales that are of interest in catchment hydrology, and needs to be inferred from the available information.
1 Chapter 1 Introduction
3. Variability of rainfall is difficult to predict and will cause unpredictability of catchment prediction.
These assertions have given rise to following strong thoughts in formulating this project.
• Ambiguity in definition of spatial rainfall in arid climate regions has been shown to be major factor in failure of conventional rainfall runoff analyses. However, quantitative insight into the different degree of this variability generated by the more typical frontal and convective system is nevertheless lacking. Thus, there is a need for better understanding about the degree of the variability of the events over the urban catchments.
• Information on highly variable rainfall patterns should be essential for good hydrological simulations. Radar precipitation estimates could estimate a two- dimensional rainfall field, however, the space-time resolutions are too coarse compared to the scale of urban catchments that are the interest herein. The point measurements from typical ground based raingauge networks also cannot provide this information accurately. Therefore, there is a strong need for the development of an acceptable two-dimensional rainfall field which could be inferred from these point measurements to the required space-time scale. Despite the fact that several methods proposed for these estimations have long been recognized in the past, there are hardly any studies that have tested the suitability and the robustness of these models in CMS.
• Finally, once detailed patterns of rainfall are available and the variability of events are better understood, it is necessary that methodologies be developed to incorporate spatially and temporally variable rainfall in order to assess the efficiency of the models in reproducing the real response in CMS.
1.1.2 The Role of Hydroinformatics in Catchment Management
Abbott (1993) describes hydroinformatics systems as being concerned with the storage analysis and use of information about the aquatic environment in a computerised format. The concept of hydroinformatics, is that it is a system that deals with electronic processing of information in the hydro sciences. Due to many alternative forms of
2 Chapter 1 Introduction information, the many alternative analyses of information required for catchment management, and the many alternative presentation formats required for the information, it is not possible to devise a single hydroinformatics tool that will meet all the needs of the information incorporated in a hydroinformatics system. Therefore, any software that assists in this regard can be considered to form part of a hydroinformatic system. Consequently, hydroinformatics systems are comprised of a number of tools with Geographical information Systems (GIS), Time Series Managers (TSM) and Catchment Modelling Systems (CMS), being the major hydroinformatics components utilised in the study.
GIS provide an efficient means of accessing the Information databases for the storage, analysis, retrieval and display of spatial and temporal data. Apart from the storage facilities of GIS used in the study, the Arc/Info GIS provided a facility for programming the rainfall model through a macro programming language, Arc Macro Language (AML). In addition to the pre-processing of the rainfall input model by GIS, the spatial and temporal variability of rainfall patterns for various degrees of heterogeneity events are compared with the aid of the post-processing capability of GIS in the study.
A TSM is required for the storage, retrieval and management of temporal data, which is time series data of one water quantity at a specified location. The rainfall and flow data used in the study are stored, retrieved and managed by HYDSYS. HYDSYS is the most commonly used TSM in Australia. Linkage of the time series data with spatial data is an important aspect of the analysis of data prior to development of the hydrological and hydraulic model.
USEPA Stormwater Management Model (SWMM) functioned as an analysis tool of CMS of the present study for simulating the catchment response for alternative rainfall input models to various hydrologic events.
1.1.3 The Role of Catchment Simulation in Hydrology
Hydrology comprises a large number of complex interactions among hydrological inputs and processes that vary in space and time. The increasing hydrological detail that is now available in hydrological data sources and process-based models opens many new opportunities for an improved understanding of hydrology. As the space or time resolution of data sources increases, and when the rainfall processes are more detailed in
3 Chapter 1 Introduction space and time, the impact of the new information on predictions needs to be assessed. In other words, the sensitivity on model predictions of newly introduced input information with the traditionally used methods needs to be assessed. For example, this study assesses the relative importance of the spatio-temporal variability of events and how the alternate distribution of rainfall interacts with the remaining process models in predicting the response of the catchments.
Detailed simulation models driven by detailed space-time data are beginning to play a crucial role in hydrology even though the science underpinning some components of the models remains uncertain at many space scales and time scales [Woods and Sivapalan (1999)]. Detailed computer simulation studies of hydrological variability can provide more detailed and site-specific results than the analytical approaches that are always simplifications and must be recognised as such.
1.2 Author's Contributions
The main contributions made by the author during this research include
1. Investigation of the temporal and spatial dependence of rainfall and consequently categorisation of individual storm events according to their degree of heterogeneity in space and time scale. The estimation technique developed to assess the degree of rainfall variability in space and time, by considering the event semi-variograms is considered an original work. In addition, the model has been developed for real- time operation.
2. Development of a more detailed rainfall model in space and time by the aid the hydroinformatic tool with a view to improving the robustness of catchment prediction. From this approach, improved estimates of the spatially distributed with smaller time steps hyetographs suited for especially the urban catchments have been obtained. The investigation was carried out comparing the developed rainfall model with the traditionally used Thiessen approach carefully and quantitatively assessed the difference and the sensitivity to various degrees of heterogeneous events.
3. The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error
4 Chapter 1 Introduction
parameters for predictions from CMS using alternate rainfall models, for various degrees of spatio-temporal heterogeneity events. The assessment also extended to investigate whether the degree of this improvement to be dependent on the variability of the storm event which is assessed by the adopted semi-variogram approach.
4. Degree of accuracy needed in rainfall representation has been highlighted for different degree of events and catchments with different scale towards the distributed modelling approach.
1.3 Outline of Thesis
Although the importance of spatial variability of rainfall on runoff hydrographs have been understood in the last decade, the development of a technique to identify the different degree of heterogeneity of rainfall, development of more detailed rainfall models by the use of available hydroinformatic tools and its influence on the robust catchment prediction are considered a new research contribution in hydrology. Introductions to general catchment modelling concepts, fundamental theory of Semi- Variogram approach and GIS and general findings on the influence of rainfall in runoff prediction, therefore, are given in Chapter 2. The intention is to provide some background theory of the hydroinformatic tools and the geostatics tools in order to clarify the findings and terminology used in the subsequent chapters and to pave the way for further discussions.
The Upper Parramatta River Catchment of Western Sydney and the The Centennial Park of Central Sydney are used as the experimental catchments for testing the heterogeneity of rainfall and its influence in predicting the catchment response. The catchment characteristics, hydrometric network and available data therefore are described in Chapter 3.
Presented in Chapter 4 is the development of the technique for assessing the degree of heterogeneity of individual events and consequently categorization of events in to classes according to their heterogeneity in space and time dimensions. Furthermore the chapter shows the application of this procedure to two urban test catchments in Sydney, Australia.
5 Chapter 1 Introduction
Presented in Chapter 5 is the development of a spatio-temporal rainfall model towards accurately distributing the rainfall process in space and time, which could replace the traditionally used methods (such as Thiessen method). The developed procedure has been implemented using hydroinformatic tool, particularly the Arc-Info Geographical Information Systems (GIS). Both visual and arithmetic techniques have been established to compare not only the spatial variability of total storm events but also the spatial variability during the storm events suited especially for urban catchments can obtained, along with small time-step hyetographs.
Reported in Chapter 6 have been the results of an investigation into the importance of the rainfall model for robust predictions from CMS. Two alternate rainfall models, namely a Thiessen based rainfall model and a spline surface rainfall model which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model were tested through catchment simulation in assessing the improvement in the predicted hydrographs. The Chapter further investigates whether this improvement to be dependent on the spatial and temporal variability of the storm event as measured in Chapter 4 for assessing this feature.
The main findings and conclusions are summarized in Chapter 7, which is the final chapter of this dissertation. Following that are several appendices providing supplementary information for the study. Finally, the cited publications in this dissertation appear under the bibliography.
6 CHAPTER 2
FUNDAMENTAL THEORY AND LITERATURE REVIEW
2.1 Introduction
Information on the spatial and temporal variability of rainfall plays an important role in the process of surface runoff generation and hence is important for a variety of applications in hydrology and water resources management. However, hardly any work has been done on categorization of the spatial and temporal variability of individual storm events on typical urban catchments derived from ground based raingauge records. Furthermore, despite the findings of the advantages of the dense network rainfall estimate from studies of the spatial variability of rainfall, there have been only a few attempts made to compare the advantage of alternate rainfall estimation from a given network arrangements or in other words the sensitivity analysis of the alternate rainfall representation in estimating the prediction of water quantity from a catchment. Therefore, there is a real need for a holistic approach to understand the importance of spatial and temporal variability of rainfall events and a real time approach towards a more robust estimation of the catchment response by better methods.
The relevant knowledge and theory from the past literature related to the study have been summarized in this Chapter. The importance of the spatial and temporal variability of rainfall can be best explained by the information transfer via the conceptual components of a catchment modelling system and by considering the rainfall runoff process as described in Section 2.2. This section also demonstrates these concepts on urban catchment modelling systems and includes the suitability and advantages of the Storm Water Management Model (SWMM) for the present study. SWMM is the rainfall-runoff model used in this study. Following that in Section 2.3 is the exploration of previous investigations on the influence of rainfall variability in prediction of catchment response. Section 2.3 also summarises other important factors influencing predicted catchment response as well as indicating the limitations on our knowledge from previous research, to be considered in the rainfall variability studies.
7 Chapter 2 Fundamental Theory and Literature Review
The correlation analysis and theory as well as application of semi-variogram techniques in hydrology and in other engineering applications are given in Section 2.4. A semi- variogram technique for spatial and temporal semi-variograms was developed in this study in order to categorise the real storm events in to classes according to their spatial and temporal variability.
Alternative methods and their background theories for inferring the spatial distribution of rainfall from gauge data are discussed in Section 2.5. An alternate rainfall model detailed in space and time dimensions is developed and found appropriate by the spline surface technique in the study. Section 2.6 is an introduction to hydroinformatic system, consisting of geographic information systems (GIS) and its applications in hydrology. A GIS was utilised in this study to develop the alternate spatio-temporal rainfall model. The GIS model was also developed to meet the need for handling vast amount of information regarding the temporal and spatial distribution of rainfall within the study catchments.
Section 2.7 discusses the objective functions used in assessing the accuracy of the numerical simulation results of the study. This section also consists of general introduction on calibration and validation procedures and general criteria for assessment of simulation experiments in the study.
2.2 Catchment Modelling Systems
2.2.1 Concepts
Management of the quantity and quality of water in urban drainage system is a complex task, which has become increasingly important in the last decade. Managers of these systems need to obtain information relevant to the response of the systems vested in their control. Two methodologies by which the desired system information can be obtained are: firstly, through monitoring of the system for stormwater quantity and quality; and secondly, by mathematical simulation of the system, or systems through catchment modelling systems [Ball et al. (1998)]. Where management changes to the drainage system are proposed and it is desired that the impacts of these changes be predicted, it is necessary to use the second methodology; the first methodology can only provide historical information after implementation of the proposed management changes.
8 Chapter 2 Fundamental Theory and Literature Review
Catchment modelling systems are comprised of numerous process models, which simulate pertinent hydrologic and hydraulic processes influencing the quantity and quality of runoff from the catchment. In general, these process models are formulated as a mathematical system, which is amenable to either analytical or numerical evaluation. Following a reductionist philosophy, and reviewing a system of this kind, it is convenient to arbitrarily subdivide the total modelling system into a number of conceptual components with each of these conceptual components consisting of process models simulating pertinent catchment processes. One such conceptual subdivision of a catchment model was presented by Ball (1992) and proposed the following four components to a catchment modelling system.
[1] Generation : The component of the model primarily concerned with the estimation of the spatial and temporal distribution of rainfall over the catchment.
[2] Collection : The component concerned with the accurate prediction of the amount of flow at the entry point to the transport component.
[3] Transport : The component of the model where the prediction of the motion of water routed along the physical drainage system. Generally, this is referred to as the hydraulic component of the model.
[4] Disposal : The component where the prediction of the impact of the discharge of water into the floodplain and receiving waters are made.
Each of these four conceptual components is concerned with different aspects of the catchment modelling system. One of the important concerns of the Generation component is the rainfall model necessary to accurately estimate the spatial and temporal distribution of rainfall over a catchment. Without satisfactory results from the Generation component, accurate predictions from the other components in the Total catchment model will be difficult to achieve.
A schematic arrangement of these four conceptual components is presented as Figure 2-1. Also shown in this figure is the direction of information flow between these conceptual components. A consequence of this information flow is the predictions obtained from any component are a direct reflection of the input information, which comprises both the control parameters for the simulation towards the accuracy of
9 Chapter 2 Fundamental Theory and Literature Review quantity and quality of the catchment prediction. For this reason, the generation component and its model for spatial and temporal variability of rainfall are critical components of a catchment modelling system. GENERATION Spatial and Temporal variation of rainfall Spatial variation of constituents
COLLECTION Simulation of surface runoff Simulation of constituent washoff
TRANSPORT Motion of water and constituents via physical drainage network
DISPOSAL Discharge of runoff and constituents into the receiving waters
Figure 2-1: Catchment Modelling System, Conceptual Components (after Ball, 1996)
It is also important to note that the information flow in Figure 2-1 is in one direction. A successful reproduction of the outlet hydrograph does not imply that all processes that influence the outflow hydrograph are simulated correctly or the selected control parameter values are accurate. Consequently, reverse routing from a discharge hydrograph to an input is theoretically impossible. In essence this problem arises from the number of parameters used in the models for description of the processes, which influence runoff characteristics during any stage in the runoff cycle and the nonlinear mapping of these parameters. Furthermore, the values of many parameters are linked; for example, for a known catchment average depth of rainfall excess, the differences between alternative average depths of rainfall obtained from different spatial rainfall
10 Chapter 2 Fundamental Theory and Literature Review models can be compensated by differences in the parameters used in any other process model.
2.2.2 Information Required
There is a strong feeling expressed in the literature that runoff models and calibration processes of catchment simulations have attained an adequate level of sophistication, and that more emphasis to be placed in developing more accurate rainfall representations, which is the input to runoff models [Obled et al. (1994), Goodrich et al. (1995), O'Loughlin et al. (1996)]. Previous studies recognised the importance of considering the spatial variability of rainfall and demonstrated the need for a dense gauge arrangement. In their description of the development of modelling practice by O'Loughlin et al. (1996), the authors concluded that rainfall-runoff theory has reached a mature stage, and suggested that further research is required in the areas of rainfall variability, scale effects and interfacing between models. The authors further demonstrate that spatial variability of rainfall appears to be the major source of error in modelling and calibration processes, and in design assumptions. This has been studied by researchers in the past. However, there are many unknowns remaining and there is a definite need for further study on several aspects such as spatial and temporal variability of rainfall and their effects on runoff, which is the ultimate objective of the present study.
Furthermore, there have been no studies, which have tested the accuracy of the traditional methods used to develop the rainfall estimate and the impact of these methods on the nature of events and on the robustness of the runoff prediction. Rainfall generation models are rarely an end in them; they are almost always used in conjunction with the subsequent catchment modelling components. The accuracy of the generation component and a more perfect understanding of the influence of the generation component on the end product, therefore, will lead towards a more robust catchment modelling systems.
As discussed previously, one of the methodologies by which the desired system information can be obtained is through the simulation process. There are two main objectives of simulation models [Bevan (1989)]. The first is to explore the implications of making certain assumptions about the nature of the real world system; the second is
11 Chapter 2 Fundamental Theory and Literature Review to predict the behaviour of the real world system under a set of naturally occurring circumstances. It is very important to understand and distinguish between these two objectives. The simulation process of this thesis is primarily concerned with the former with the aim to improve our understanding the impacts of alternate rainfall input assumptions, and also concerned with latter with the aim of predict the behaviour of catchments for naturally different spatio-temporal variability events. Ideally, models would be used, which fully replicate all the processes contributing to runoff and their spatial and temporal variability. In practice however, this does not occur because many processes are so complicated and inter related that a full description is intractably complex and even when a process can be described concisely and completely, the volume of calculations involved is prohibitive. Also, the data available to define the model control parameters are limited in both spatial and temporal dimensions. As a result, simplifying assumptions are made and the real situation is idealized. Alternative idealizations emphasise different processes and require different magnitudes of computational effort. Consequently, instead of one model of reality, alternative models with differing degrees of complexity and computational effort may be developed.
The process models differ from one conceptual component to another. Examples of the use of alternative models for similar processes within alternative catchment modelling systems can be seen by consideration of the process models within the Strom water Management Model [US EPA SWMM Model; Huber and Dickinson (1988)] and the RAFTS Model [WP Software (1991)] for simulation of the routing of flows through the catchment storage; details of the process models in these systems are given below.
12 Chapter 2 Fundamental Theory and Literature Review
Table 2-1: Hydrologic and Hydraulic models in different Urban Modelling Systems
Component RAFTS SWMM
Collection Non-Linear Reservoir Non-Linear Reservoir Kinematic Wave
RUNOFF - Kinematic wave Transport Time-Lag TRANS - Non-Inertial wave Muskingum-Cunge EXTRAN - Dynamic wave PIPENET - Dynamic wav
Based on information presented by WP Software (1991), Huber and Dickinson (1988) and Ball (1996), the process models in RAFTS and SWMM can be categorised in the manner shown in Table 2-1. As can be seen from this table, the process models used in the collection and Transport component differ between RAFTS and SWMM. While this approach is satisfactory from the viewpoint of developing a modelling system capable of simulating the catchment response to a storm event/events, there are problems with this approach when problems requiring development of the catchment modelling system requires consideration of the catchment response at different scales.
2.2.3 Rainfall-Runoff process
Hydrological studies of the rainfall-runoff process provide the basis for estimating the design flows for urban stormwater drainage systems which influences floods and the transport of sediments and pollutants. Runoff from a catchment is a result of surplus rainfall after the abstraction of various losses over the catchment, such as interception by vegetation and infiltration into the soil moisture. The runoff process is very complex because of the spatial and temporal variability of rainfall and the catchment properties. The modeler needs to obtain a perfect understanding of rainfall variability in space and time and the impact of this variability on runoff processes.
Rainfall-runoff models have been one of the central themes of hydrological research for many years. These models can be classified in a number of ways according to a wide range of characteristics. Lumped and Distributed modelling systems are one of the classifications based on the way in which spatial information is handled. Models of
13 Chapter 2 Fundamental Theory and Literature Review simpler type generally characterize the behaviour of a catchment as a lumped system, where the rainfall inputs and internal hydrological processes governing the catchment's behaviour are spatially averaged. Although spatially lumped models can frequently produce runoff simulations of acceptable accuracy for various applications (e.g. real time flood forecasting), the effects of the spatial averaging of rainfall on simulated runoff response are not well understood. As rainfall is measured conventionally at a finite (and sometimes sparse) set of points, the resulting estimate of average rainfall in space is subject to error:
• Because the spatial variability of rainfall has been averaged out;
• Because the accuracy of the resulting average from different methods will be dependent of the heterogeneity of different storm events; and
• Because of sampling errors of recorded rainfall information.
Therefore, efforts have to be made to quantify the accuracy of spatial averaging at the end product (by comparing the observed catchment response with the simulated response from differently averaged rainfall input) using the techniques of statistical analysis. Also the knowledge should be developed towards how this accuracy varies according to the different degrees of variability in various events.
2.2.4 Urban Catchment Modelling Systems
Urban Hydrology will have an increasing role to play in the management of the sustainability of human societies. Growth of urban areas brings significant changes in the physical properties of the land surface. Due to the increasing area of paved surfaces, permeability of soil and infiltration decreases, and surface runoff accelerates. The channeling of natural streams results in rapid catchment response times and high peak flows. Such changes of natural regime on a comparatively small area of a city bring significant, and often disastrous, effects on the whole system within and downstream of the catchment.
Basic urban stormwater runoff models utilise simple hydrologic approaches to estimate total catchment runoff. More elaborate models combine hydrologic models representing subcatchment inputs with more explicit hydraulic routing of flows through drainage
14 Chapter 2 Fundamental Theory and Literature Review systems. Goyen and O'Loughlin (1996) stated that to date, little research has been reported on detailed rainfall input approaches and on the relationships between the accuracy of runoff estimates, the selected subcatchment scale and variations in intra- catchment drainage processes.
2.2.4.1 Concepts
In an ideal situation, urban engineering systems would be designed and analysed with models that fully replicated the physical, chemical and biological processes involved. Computer models provide the ability to mathematically describe the performance of the entire storm water system in much greater detail than was possible using hand calculations. However, computer models are only as good as the data and the model user and their own objectives. They cannot think for the user and also they may not fully replicate the actual processes for the following reasons;
• Processes are so complicated, and involve so many interactions, that a full description may be intractably complex.
• Even when a process can be described concisely and completely, the magnitude and number of calculations involved may be prohibitively large.
• Lack of accurate and comprehensive data on system behaviour.
Therefore, simplifying assumptions must be made and the real situation is idealized to enable economical usage of models. For example, dynamic situations are idealized as being static, three and two-dimensional processes are reduced to one dimension, random processes are analysed as deterministic processes. Consequently, instead of one ultimate model of reality, alternative models of differing degrees of complexity may be utilized based on the needs of the study.
Computer models that generate full hydrographs of flows are replacing methods that produce only peak flow rates in most applications in hydrology and urban stormwater management. RORB, RAFTS, WBNM, ILSAX and SWMM are probably the best known of the hydrograph producing programs commonly used in Australia, but there are many others. These models convert rainfall hyetographs to flow hydrographs by various procedures, defining the flow rates occurring at different time intervals. The
15 Chapter 2 Fundamental Theory and Literature Review deterministic SWMM model is selected for the use in this current study among the other models, for assessing the influence of rainfall models in catchment simulation because the model employs conceptual components as discussed in previous sections. Further it is also easier to simulate subcatchment based distributed rainfall hyetographs from alternate rainfall developments. SWMM is one of the most widely used model in North America [Huber and Heaney (1981) and in Australia [O'Loughlin et al. (1991), Abustan (1997)] and has been continuously developed, updated and documented over the past three decades.
2.2.4.2 Stormwater Management Model
The US Environmental Protection Agency (USEPA), Metcalf and Eddy, Inc., the University of Florida, and Water Resources Engineers, Inc. developed the Storm Water Management Model during 1969-71. It has been updated in 1975, 1981, 1988, 1999 and 2001 and was clearly documented by Huber and Dickinson (1988). SWMM is a large and relatively sophisticated hydrologic, hydraulic and water quality simulation program written in Fortran. SWMM is one of the several operational models suitable for both planning and design analysis of runoff quantity and quality in urban areas. Due to its early development, good documentation, ready availability and user support it has been widely used within the water engineering community. SWMM is not overly difficult to manage and use even though it is not very user friendly [Nix (1994)].
According to the authors it is understood that the researchers who use SWMM as the software for their studies must be knowledgeable of the modelling techniques such as non-linear reservoirs, kinematic waves, St. Venant equations, and buildup-washoff equations with how physical processes may be simulated in a FORTRAN program. The latest upgraded release of SWMM is ‘SWMM4.4h’, dated February, 2001(updated also in March 2002), and includes many enhancements provided by OSU and CDM as well as contributions from users. SWMM 4.4h replaces the last version of SWMM 4.4gu posted in September 2000, included many enhancements by CDM. The primary changes included in the February 2001, 4.4h version relate to new options for overland flow routing in Runoff Block. The executable program, source code and documentation files are available on the Internet via anonymous ftp at Oregon State University at ftp://ftp.engr.orst.edu/pub/swmm/pc.
16 Chapter 2 Fundamental Theory and Literature Review
SWMM simulates real storm events on the basis of rainfall (hyetograph) and other meteorological inputs and system (catchment, conveyance, and storage/treatment) characterisation to predict outcomes in the form of quantity and quality values. Effectiveness can be evaluated by inspection of hydrographs, pollutographs, pollutant loads, and modelled changes in receiving water quality. Since our study objectives are directed towards the investigation of both spatial and temporal variability influences of the storm events, it is essential to have both time series output hydrographs and temporal simulation summaries for different time steps.
The model is structured into ‘blocks’ along the lines of the physical processes that occur in urban hydrology. RUNOFF, TRANSPORT, EXTRAN (Extended Transport) and STORAGE/TREATMENT are the four major computational blocks. In SWMM, output from a block can be used as input for another block. This provides SWMM great flexibility and a staged approach toward modelling complex systems. The Transport, Extran and Storage/Treatment blocks may all use input and provide output to any block, including them selves. The EXTRAN block is the only block that doesn’t simulate water quality. In addition to blocks mentioned above, six service blocks are utilised (Graph, Combine, Rain, Temp, Statistics). The functional details and the linkages between each block were clearly explained in the users manual by Huber and Dickinson, (1988).
An overview of the model structure, indicating the linkages among the computational and service blocks is shown in Figure 2-2. In simplest terms the program is constructed in the forms of 'blocks' as follows.
17 Chapter 2 Fundamental Theory and Literature Review
1. The input sources :
The Runoff Block generates surface and subsurface runoff based on rainfall hyetographs, antecedent conditions, land use and topography.
2. The central cores: The Runoff, Transport and Extended Transport (Extran) Blocks route flows and pollutants through the drainage system. Very sophisticated hydraulic routing may be performed with Extran.
3. The correctional devices: The Storage/Treatment Block characterizes the effects of control devices upon flow and quality. Elementary cost computations are also made.
As indicated in Figure 2-2, in addition to the four computational blocks mentioned, six service blocks are utilized. The Executive Block assigns logical unit numbers to off line files and determines the block or sequence of blocks to be executed. All access to the computational and service blocks and transfers between them must pass through the main program of the Executive Block.
SERVICE BLOCKS COMPUTATIONAL BLOCKS
STATISTICS BLOCK RUNOFF BLOCK
GRAPH BLOCK TRANSPORT EXECUTIVE BLOCK COMBINE BLOCK BLOCK EXTRAN BLOCK RAIN BLOCK STORAGE/TREAT TEMP MENT BLOCK BLOCK
Figure 2-2: SWMM program structure (After Huber and Dickinson, 1988)
In this study, the developed alternate spatial rainfall models are used as the input to either the RUNOFF block or the Rain block, in order to study the spatial influences of the quantity and quality response of the storm event via the simulation process through
18 Chapter 2 Fundamental Theory and Literature Review the RUNOFF and TRANSPORT block. The Runoff block uses input from no other computational block but may receive input from new Rain and Temp blocks for meteorological input, whereas the Transport block receives input from Runoff computational block.
The characteristics and potential limitations of the present version of SWMM, are mainly related with our research work, have to be concerned clearly, and are discussed in this paragraph. The initial study mainly concerned of the spatial and temporal influence in predicting catchment response. Because of that, it is better to summarise the Space and Time properties of SWMM 4.4gu.
Time Properties:
• Both the single and continuous simulation modes have an unlimited number of time steps; Precipitation can be input at arbitrary time intervals for single-event simulation (typically 1-15 Min.) and continuous simulation (typically 1-hr); Variable time step is available in the Runoff block; the time step for the Extran block routing depends on stability criteria and may be as small as few seconds. • Output time intervals can be as required in minutes, hours or days and total summaries for continuous simulation.
Space Properties:
• Small to large multiple catchments can be handled.
• Lumped simulation of surface flow with allowance for up to 200 subcatchments and 10 input hyetographs, up to 200 channel/pipes may be simulated by non-linear reservoir routing. • Catchment area may be desegregated and modelled sequentially for simulation of areas that are too large for present SWMM dimension. • Output from surface, channel/pipe, or storage/treatment simulation may serve as new input for further simulation by same or different blocks.
2.3 Influence of Rainfall in Catchment Modelling System Predictions
Rainfall is a driving force of hydrological processes and it constitutes the most important input to any runoff calculations and modelling procedures. However, because of the usual lack of the rainfall representation of the spatial and temporal variations of
19 Chapter 2 Fundamental Theory and Literature Review the natural rainfall process, the rainfall input is often a weak point in the modelling procedure [Niemczynowicz and Sevruk (1991)]. Still it remains unclear whether the use of distributed rainfall data derived from the different methods of treatments to the rainfall with distributed hydrological models can at present, provide more accurate hydrograph simulations than the use of a lumped approach. The treatment of space and time variability has been a recurrent theme in hydrological research over the past three decades. Several studies from the past reveal that coupled spatial and temporal variation in rainfall can significantly alter predicted hydrographs [Yen and Chow, (1968), Surkan, (1974), James and Drake, (1980), James and Shtifter, (1981)].
Storm events may vary considerably in space and time, and use of data from a single raingauge to represent the rainfall over a whole catchment might not realistically represent the storm’s spatial profile. This is also true of multi-site rainfall distributed by simple traditional methods (such as mean average, Thiessen polygons). Furthermore, rainfall intensity often varies significantly over distances of less than 1 km and a time of less than a few minutes. Therefore, a better understanding of the spatial and temporal variability of rainfall is important in determining the characteristics of stream flow hydrographs.
2.3.1 Effect of spatial variability of rainfall
Variability in the spatial pattern of rainfall has often been proposed as a source of uncertainty that causes errors in predicted runoff hydrographs. This contestation has been supported by a number of modelling studies. A study by Goodrich et al. (1995) showed that the assumption of spatial rainfall uniformity for the considered convective environments at even the small watershed scale of 5 ha appears to be invalid. Saghafian and Julien (1995) showed that the time of concentration is controlled by the spatial pattern of rainfall as well as well as the properties of the catchment, since the most remote point of a catchment to generate runoff depends on the spatial distribution of rainfall during an event. They found that, due to the spatial variability in rainfall, a unique critical duration cannot be defined for a particular catchment and therefore, prediction of runoff is influenced by the spatial pattern of rainfall.
Information on the spatial pattern of rainfall has been difficult to estimate, particularly in the days before sophisticated regression analysis was investigated and made feasible
20 Chapter 2 Fundamental Theory and Literature Review by the use of current hydroinformatic tools, for determination of the rainfall distribution. Studies in the literature have concentrated on the relative abilities of particular gauge networks to sample the spatial variation of rainfall and the representation of this variability by traditional methods, along with the impact of the rainfall representation on catchment outflows. The first authors to do this were Dawdy and Bergam (1969), followed by Obled et al. (1994); Michaud and Sorooshian (1994); Seyfried and Wilcox (1995); Goodrich et al. (1995); Chaubey et al. (1999). Almost all these studies approached the problem by comparing the responses using rainfall fields based on observations from a dense rain gauge network, and from rainfall fields based on the observations from a subset of original network gauges. In the study by Dawdy and Bergman (1969) for example demonstrated that uncertainty was introduced into flood hydrographs by reducing the number of gauges raingauges on a 25 km2 rural catchment from three to one. In other examples Obled et al. (1994), tested two different densities of network (5 or 21 gauges within a 71km2 catchment), showing a significant advantage for the dense network rainfall estimate; Wilson et al. (1979), concluded that errors in the estimation of precipitation input may result in serious errors in predicted runoff hydrographs by comparing the simulated hydrographs using a distributed rainfall (multiple gauge) input with those using rainfall for a single gauge for the same storm.
Colyer (1981), studied twenty-one rainfall events for a 140 ha urban catchment in Europe, and showed that a single rain gauge record could be very unrepresentative of individual storms over smaller catchments. The modelling tests showed that the use of alternative rain gauge records had a significant effect on the simulation of individual rainfall-runoff events. However the study proved that the overall effect of using a composite rainfall profile rather than a single observed profile in a large number of simulations was to reduce runoff discharge by less than 5%.
A study to verify whether the spatial heterogeneity of rainfall influences the hydrologic response of an urban drainage basin was conducted by Brunelle et al. (1994). The study was conducted for a 273 hectare catchment in France. A mathematical model capable of reproducing the hydrologic response was created with a runoff simulation program called CAREDAS. The results showed that differences in the response of the drainage basin for heterogeneous precipitation and homogeneous precipitation events of equal average intensity may be considered significant. Differences of greater than 35% for peak flows and 15 minutes for peak flow response times were observed in certain cases. 21 Chapter 2 Fundamental Theory and Literature Review
Beven et al. (1982) found that, in a relatively homogeneous catchment, the most important effect of rainfall variability was in the timing of the runoff hydrograph. The effect on peak flows was smaller but still significant and that on storm volumes was relatively minor. Numerous field experiments and descriptions of spatial rainfall variability over catchments have also been shown by other authors, for example Moore et al., (1995), Seyfried and Wilcox, (1995) and Merz and Bardassy, (1998).
Furthermore, a recent study by Woods and Sivapalan (1999) developed a theoretical framework that integrates several disparate sources of hydrological variability and a mathematical framework of rainfall, runoff and routing with space-time variability. This study is mainly concentrated on developing the theory and illustrating the possibilities of its application rather than investigating on real site-specific simulation studies, which by their nature can provide more detailed results than a general theory.
2.3.2 Effect of temporal variability of rainfall
Variability in temporal patterns of rainfall between storm events has been recognized as a major cause of variability in urban hydrology. Studies on the impact of the temporal variability of rainfall [Burke et al. (1980); Ward et al. (1980); Lambourne and Stephenson (1987), Niemczynowicz (1991); Schilling (1991); Ball (1994)] approached the problem by comparing the catchment responses to alternate temporal rainfall patterns. For example, Ball (1994) simulated overland flows for different rainfall excess patterns having rectangular, triangular, etc. patterns of rainfall excess and found that the peak flow and time of occurrence depended on the temporal pattern of rainfall excess. The author noted that estimation of the time of concentration for a catchment is dependent on the temporal pattern of the rainfall excess, and may be up to 22% longer or 19% shorter than that predicted using a constant rate of rainfall excess.
Lambourne et al. (1987) investigated this effect for a small urban catchment, 1.42 km2 in area. They simulated runoff peaks and volumes for a series of synthetic 5-year return period storms having rectangular, triangular and bimodal temporal distributions simplified from depth-duration-frequency (DDF) relationships. The storm with a triangular temporal pattern caused 14% more total runoff and a 44% higher peak flow than a storm with the same total rainfall and a uniform temporal pattern. Burke et al. (1980) found that variations between temporal patterns could cause variations of upto a
22 Chapter 2 Fundamental Theory and Literature Review factor of 3 in peak flow on a small urban catchment, 0.49km2 area. Ward et al. (1980) demonstrated for a small rural catchment (1.2 km2) that changes in temporal patterns of rainfall events could result in changes of up to an order of magnitude in peak flow at the catchment outlet.
Stephenson (1984) employed a general triangular shaped rainfall hyetograph with the time of peak 'tp' varying between the start of the time (tp = 0) and the end (tp =1). If the storm intensity peaked in the first part of its duration (tp < 0.5) the peak runoff was less than that for a uniform storm of the same average intensity. This was true for peaks up to 80% of the duration, after the commencement of rain. Only for the peak at the end of the storm ( tp = 1) did the peak runoff exceed that for a uniform intensity storm. In this case, the peak runoff was approximately 10% greater than for a uniform storm of the same duration. When the storm duration was not equal to the time of concentration for a uniform storm, the peak could be higher. When a storm peaked near the end, and the watershed was saturated, the peaks could be up to 30 % greater than for uniform storms [Scheckenberger, (1984)].
Using weather radar for flood forecasting in the Sieve River Basin in Italy, Pessoa et al. (1993) found no significant differences between hydrographs generated from 5, 15 and 30-minute radar rainfall data. However, they noted that a 30-minute time resolution might be inappropriate for stronger storms and/or watersheds with faster response times. The hydrographs were generated using a distributed rainfall-runoff model that extracts topographic information from digital elevation maps.
2.3.3 Effect of Storm movement
The most obvious connection between spatial and temporal patterns of short-term rainfall is that introduced by the movement of storms. The influence of storm movement and its direction on the shape, peak, time to peak and other characteristics of runoff hydrographs has long been recognized by several authors [ Bedient and Springer (1979), Jensen (1984), Niemczynowicz (1984a, 1984b), Watts and Calver (1991), Ogden et al. (1995)]. Generally the studies have shown that storms moving downstream produce significantly larger peak flows than those moving upstream. Watts and Calver (1991) found that for the same rainfall intensity and amount, there was likely to be an under prediction of peak discharge and an over prediction of time to peak for downstream-
23 Chapter 2 Fundamental Theory and Literature Review moving storms, and an over prediction of peak discharge and under prediction of time to peak for upstream or cross-catchment storm directions.
Furthermore, studies have found that the maximum effects occurred for storms that were moving at a speed comparable to the flood wave on the catchment [Niemczynowicz (1984a), Ogden et al. (1995)]. These studies show that the flood wave speed is often less than few kilometers per hour. By contrast, studies using radar rainfall data [ Clarke (1989), Sioutas and Flocas (1996), Seed at al. (1999b)] show that storms typically move at much faster speeds, usually between 20 and 50km/h, in line with the prevailing winds [Niemczynowicz (1987].
Therefore, the literature clearly indicates that there is a need to identify the events with moving nature from the available ground based gauge records, and to assess whether the convective/orographic nature of events does have a practical influence on catchment response.
2.3.4 Effect of averaging rainfall in space and time
The space and time resolutions used for the input variables of a hydrological model have a sufficient impact on the model results. Choice of the resolution depends on the required accuracy, the experimental site and the processes and variables taken into account. A sensitivity analysis of catchment response to space-time resolution was performed by Bruneau et al. (1995) on a 12km2 experimental catchment in France. The authors conclude that the choices of grid size and time step are not independent, and for a large grid size decreasing the time step does not allow the maximum efficiency to be reached. However, the consistency of the modelling appeared to depend more on time step than on grid size for the particular model and catchment considered.
O’Loughlin et al. (1998), studied how the flow rates derived from models may change for different time steps of rainfall input. Examples from the study indicate that peaks can vary in most models. The results further show that it is not worthwhile to reduce the time step beyond a certain point.
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2.3.4.1 Distributed vs Lumped Modelling
The traditional hydrological models of lumped conceptual type are well suited to deal with the main part of current water resources assessment and flood and drought forecasting, but more advanced tools are often required for the remaining problems. Since the heterogeneity effect was clearly understood as a dominant source of uncertainty it has motivated the need of distributed modelling. The first concept of distributed modelling or the outline of the physics based distributed modelling is published by Freeze and Harlan (1969). Thereafter the concepts were discussed and physically based distributed models were developed in recent years by Beven and O’Conell (1982), Abbott et al. (1986), O’Conell (1992), Bathurst (1995), Reffsgaard and Storm (1995), Colver and Wood (1995), Beven (1996). Eventhough, the authors also discuss a couple of the following critiques in their studies on the distributed modelling approach.
The development of distributed modelling lies more in developing sub-grid scale parameterizations based directly on large-scale measurements than on the improvement of the aggregation of small-scale theory and parameter values that underlies. Moreover, it cannot be verified that the distributed modelling is based on the correct equations to describe hydrological reality at the grid scale element. In addition to this, it is very difficult to estimate effective model parameter values for those equations at the grid scale. The measurement techniques do not exist to provide parameter values at the scale required by the model. The parameter values must therefore be estimated or calibrated and over-parameterisation must be avoided.
There have been a number of published applications of models such as SHE and IHDM that have been declared successful in predicting discharges at the catchment scale. However, Beven (1996) critically comments that because most of the measures of assessment of model performance have been those of predicting discharges and the discharge response of hydrological systems at the catchment scale is relatively simple to model. That is why the unit hydrograph technique still survives as an engineering tool after half century of use and criticism as an inadequate representation. The essential difference about distributed models is that they also make predictions of internal state variables at the grid element scale, but there have been very few tests of these predictions.
25 Chapter 2 Fundamental Theory and Literature Review
Variability in within-event rainfall has been found to have a significant impact on the runoff predictions produced by those events. The distribution of rainfall patterns in space and time dimension is complex to model and difficult to measure. It would therefore be attractive to identify an appropriate level of complexity of alternate rainfall representation that will result in prediction with acceptably low levels of bias and uncertainty.
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2.4 Alternative Rainfall Models
2.4.1 Concepts of rainfall models
The measurement of rainfall during a storm event involves determining the time over which an increment of rainfall depth occurs at the defined location. Consequently, the measurement of rainfall is a point measurement of a spatially variable parameter. Information such as the rainfall intensity, at locations other than the measurement locations is not defined by the measurement process and must be inferred from known information.
As discussed earlier, one item of information required for the generation component of a catchment model is the rainfall distribution in space and time. In the study of spatially distributed rainfall-runoff simulations, a two-dimensional rainfall field over the catchment is generally needed. This is repeated for various time intervals that may represent the model time step or a period of uniform rainfall intensity. Consequently, the catchment is divided into sub areas within which rainfall is assumed uniform. Precipitation within each subcatchment can be computed by superimposing the estimated rainfall field on to the catchment and computing areal average within each subcatchment.
2.4.2 Application of alternative rainfall models in hydrology
Many alternative techniques have been developed for the inference of the spatial distribution of rainfall from measured rainfall at a specific location; these alternative techniques are in effect alternative models of the spatial distribution of rainfall. Most of these techniques were developed prior to the availability of the digital computer and subsequent development of hydroinformatic tools.
As discussed in Section 2.2, the rainfall distribution in space and time is a natal component of information required for the generation component of a catchment model. The importance of the rainfall model has been acknowledged previously by Bevan and Hornberger (1982), who stated ' an accurate portrayal of spatial variation in rainfall is a prerequisite for accurate simulation of stream flows'.
27 Chapter 2 Fundamental Theory and Literature Review
Many alternate techniques have developed for the inference of the spatial distribution of rainfall from the measured rainfall at a specific location; these alternative techniques are in effect alternative models of the spatial distribution of rainfall. Thiessen (1911) came up with the first technique to estimate areal average precipitation, which has been commonly applied in hydrology. Another classical work in data analysis is from the foundations of the theory of 2-D interpolation, which is often referred to as Kriging have been established by Krige (1951). The theory has been further developed to great extent by the French geostatistician Matheron (1971). Another method of surface fitting is spline interpolation [Fritsch (1971)].
In the past, studies were undertaken to investigate and compare these different methods used to estimate the spatial distribution of rainfall [Creutin and Obled (1982), Guillermo et al. (1985), Ball and Luk (1998)]. These studies approached the problem either by comparison with an artificially developed rainfall field, or by inferring the rainfall value at a known data point, rather than by comparing the influences of different alternate models by catchment simulation studies. A recent study on an Australian catchment by Ball and Luk (1998) showed that thin plate spline smoothing could spatially interpolate rainfall more accurately than other methods (such as Thiessen, Kriging, and Inverse Distance Methods). The study also highlighted the merits of utilising the spline method on representing the spatial rainfall and shortcomings of the other methods from the spline surface.
Before the development of Geographical Information Systems, various algorithms ranging from the simple arithmetic mean to sophisticated regression analysis were investigated for determination of the rainfall distribution. However, none of these statistical methods were able to fully climatologically and spatially account for the statistical properties of the rainfall field. A lot of studies in the past were undertaken to compare the results from various sophisticated techniques with the formal thiessen polygon and arithmetic mean techniques. From the latest studies, it is clear that sophisticated interpolation techniques better represent the rainfall field spatially, rather than the more commonly used traditional methods. For example, Creutin and Obled (1982) proved that, none of the statistical methods were able to fully account for both climatologically and spatially. Sophisticated techniques provided a much better estimation than the more commonly used techniques. The study clearly showed that the
28 Chapter 2 Fundamental Theory and Literature Review traditionally used Thiessen polygon method was significantly inferior to others, with Kriging and Spline being the better methods.
Guillermo et al. (1985), compared the applicability of various proposed interpolation techniques for estimating annual precipitation. These results indicated that the Kriging and optimal interpolation techniques are superior to the other techniques. However, they showed the multiquadric technique is almost good as those two while the inverse distance interpolation and the Thiessen polygon gave fairly satisfactory results.
Wilson et al. (1979) and Bevan and Hornberger (1982), in their similar studies showed that even if the total depth of rainfall was not in serious error, the spatial distribution of the input might lead to large discrepancies in the volume of the runoff output, when a small number of gauges are used in the study. Wilson et al. (1979) generated synthetic rainfall from their developed mathematical model and used this as the input to a deterministic rainfall-runoff model to show that the spatial distribution of rain and the accuracy of the precipitation input have a marked influence on the outflow hydrograph.
Patrick and Stephenson (1991) found that the inverse distance squared method was especially consistent for a minimal source of data points. They showed that there were seldom enough rain gauges for a high level of accuracy when interpolating storm events, especially when these events have extreme variations in intensity over small distances in most cases, significantly smaller than the distance between gauges. They also note that the distribution of rain gauges in a catchment is not necessarily the optimal arrangement for computer interpolation, and uneven representation can occur.
Thin plate smoothing splines have been shown to be flexible and computationally efficient for the problem of the spatial interpolation of mean rainfall for a standard period from point data, by Hutchinson (1995). A recent study by Ball and Luk (1996), on the development of spatial distribution models for the Upper Parramatta River Catchment, shows the Spline method was the most accurate method for reproducing the rainfall distribution and estimating the subcatchment mean rainfall values. In this study a general comparison was made of five different spatial analysis techniques. The techniques used were: Thiessen Polygon, Inverse Distance Weighted, Kriging, Trend and Spline.
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The importance of the spatial and temporal distribution of rainfall is recognized in the area of catchment modelling. However, still the density of rain gauges on majority of catchments is insufficient to prove very reliable information on spatial modelling of rainfall. Since the direction of storm movement is rarely recorded in urban catchments, one cannot expect a reliable result on the distribution of intensity over the catchment when there are less than three gauges. The pattern of rainfall intensities from real rainfall events over their duration varies radially, both with space and time. Therefore, the number of rain gauges in a catchment has a significant effect on the accuracy of rainfall interpretation.
Fontaine (1991) concludes that gauge density, gauge arrangement and catchment area are significant in getting a reliable interpolated rainfall field. Urbanos et al. (1993) says low-density rain gauge data as input to runoff models results in enormous deviation from field measurements.
2.4.3 Thiessen Polygon Mode ls
Thiessen polygons are probably the most common traditional approach for modelling the spatial distribution of rainfall. The approach is based on defining the area closer to a particular gauge than any alternate gauge and the assumption that the best estimate of rainfall on that area is represented by the point measurement at the gauge [Thiessen (1911)].
A feature of the use of Thiessen polygons, however, is the development of discontinuous functions defining the rainfall depth over the catchment. This feature arises at the boundaries of the polygons where a discrete change in rainfall depth, or intensity occurs. As the basis the model is more on the geometry of the catchment and the gauge network i.e. The Thiessen method determines rainfall over an area in a way that is totally defined by the configuration of the rain gauges, without taking the rainfall values into account. An impact of the use of Thiessen polygons is the development of discontinuous functions defining the rainfall depth over the catchment. This effect is very evident at the boundaries of the polygons where a discrete change in rainfall depth, or intensity, occurs. Implementation of these defined Thiessen polygons within a GIS environment is not that difficult.
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2.4.4 Fitting a Spline Surface
One of the objective analyses in meteorology is the surface fitting methods devised to represent the analysis value as a continuous mathematical function, which fits irregularly spaced observations. Among these methods, polynomial interpolation [Panofsky (1949)] and Splines [Fritsch (1971)] are two well-known techniques to interpolate the meteorological data, especially rainfall.
Among the different methods, thin plate smoothing is widely used method to spatially interpolate hydrological phenomena (such as rainfall and temperature) from point records [Hutchinson (1995), Ball and Luk (1998)]. Spline surfaces are based on interpolation between the given data points using several low-order polynomials, avoiding the computational effort associated with high-order polynomials. Additionally, the spline method prevents the occurrence of undesired maxima and minima between measurement points. Surfaces of this type have been found to be robust spatial interpolation function for many meteorological problems; for example, Hutchinson (1991) applied spline surfaces to long term monthly mean values of daily maximum and minimum temperature across Tasmania, Australia and Ball and Luk (1998) applied the technique to measure the total rainfall of a catchment from Sydney, Australia. However, Ball and Luk (1998) considered only the spatial variation in the total depth of rainfall during the storm event. In contrast, the developed rainfall representation in this study not only considers the spatial variation in total depth but also the spatial variation during the storm event.
The minimum curvature (thin plate smoothing) spline interpolation proposed by Hutchinson (1991) and Ball and Luk (1998) to interpolate between measured rainfall points has the following characteristics:
• The surface exactly passes through the data points.
• The surface consists the minimum curvature (the cumulative sum of the squares of the second derivative terms of the surface, taken over each point on the surface must be a minimum)
The Spline function uses the following formula for the surface interpolation; see Burrough and Rachael (1998) and Ball and Luk (1998).
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N = + λ f (x, y) T (x, y) ∑ i R(ri ) (2.1) i=1
where N = No of data points, λi = weighting coefficients, ri = Distance from the point (x,y) to point i ; while T (x, y) and R(r) are defined as follows
= + + T (x, y) a1 a2 x a3 y (2.2)
ϕ = 1 r r + − + τ ϕ r + + r R(r) ln c 1 K0 c ln (2.3) 2π 4 2τ τ 2π
Where ϕ = The weight attached to the first derivative terms during minimization, τ = The weight of the third derivative terms during minimization, r = The distance between the point and the sample, K0 -The modified Bessel function, c = constant equal to 0.577, ai = coefficients found by the solution of a system linear equations.
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2.5 Correlation Analysis a nd Semi-variogram approach in rainfall analysis
2.5.1 General Background
Statistical techniques such as correlation analysis have been used in the design of raingauge networks [Amorocho et al. (1968), Felgate and Read (1975), Shaw (1983)] and have also been applied to the study of surface rainfall patterns, speed and direction of movement of storm rainfall patterns [Amorocho et al. (1968), Sharon (1972b), Felgate and Read (1975), Marshall (1980), Shaw (1983)]. The commonly used method to track the path of a storm using raingauge data is to derive contours of rainfall in consecutive time intervals and to locate the movement of identifiable features. For this, a reliable contour plotting technique is required. Even if one is available it is often difficult to judge storm motion.
2.5.2 Correlation techniques
In a review of correlation techniques, Sharon (1972a) observes that if the precipitation is cellular in nature, raingauges near each other will record more similar variations than gauges further apart, the similarity depending upon their separations and the cell sizes. The correlation will diminish with increasing gauge separation assuming the cells are randomly distributed in space and time. This will lead to a correlation analysis to provide some measure of storm rainfall patterns on the measurement plane for cellular type storms indicated by closed isohyetal cells.
Correlation analysis has been in use for a considerable time in many fields. Full correlation analysis was initially developed by Briggs et al. (1950) for investigating the fading of radio waves after reflection from the ionosphere and further extended by several authors. These techniques are usually based on the assumption that a high correlation of short-term rainfall measurements indicates that the same cell or precipitation system is affecting both gauges, although it does not necessarily mean that the two stations are receiving similar amounts of rainfall. Full correlation analysis involves the calculation of three ‘cross correlation’ functions between the gauge records taken in pairs. They are coefficients of correlation between two gauges computed as a function of a relative time shift introduced between the two records. Each record is also correlated with itself to provide three autocorrelation functions, which give a measure of
33 Chapter 2 Fundamental Theory and Literature Review the temporal scale of the variations. The correlation analysis does not respond to the spatial variability of precipitation, if it follows persistent patterns. The rate of decay of correlation with distance depends principally on the dimensions of the cell producing the rainfall or more exactly the dimensions of the surface area receiving precipitation from the cell. It is slowest when the cells are largest. Correlation analysis can be therefore, used to calculate some of the properties of the storm pattern such as velocity, spatial scale of the pattern and mean lifetime.
2.5.3 Semi-Variogram approach
The variogram function is the backbone of geostatistical analysis in solving the problem of a 2-D random field with scattered data by Kriging methodology. Estimation of average rainfall over a catchment area from rainfall measurements made at a few measurement stations is an important step in many hydrological applications such as evaluation of hydraulic balances, management of surface water resources, or real-time forecasting of flows. The estimator for the average rainfall is obtained by a straightforward extension of the well-known kriging approach [Krige (1957) , Matheron (1971, 1973), Journal and Huijbregts (1978), Delhome (1978), Bastin (1983), Storm et al. (1989)]. The optimal estimator requires knowledge of the variogram of the rainfall random field as a function of space and time. This thesis utilises the semi-variogram estimation technique as a tool in order to analyse both the spatial and temporal variability of storm events in a rigorous and systematic way, and consequently categorises the individual storm events according to their variability in space and time dimension.
The design of a procedure for the real-time estimation of a variogram model involves choosing a theoretical variogram model, and estimation of its parameters. The estimation and modelling of semi-variograms is well documented in the literature [Armstrong (1971), Omre (1971), Journel and Huijbregts (1978), Bastin et al. (1984), Bastin and Gevers (1985)]. The main steps in the 2-D estimation problem in the geostatistical study are represented schematically in Figure 2-3 after Armstrong (1971).
The formalism of random field (RF) is useful in the modelling of quantities whose variability in space may preclude deterministic prediction, such as rainfall, hydraulic head hydraulic gradient etc [Phillip and Kitanisdis (1989)].
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Data
Experimental / Raw Variogram
Variogram Model
Kriging
Figure 2-3: Steps involved in 2-D estimation problem in geostatistics.
2.5.3.1 Random Fields and Second Moment Characterisation
A one-dimensional random field (RF) Z(X ) ; is a collection of jointly distributed random variables, each associated with a location in a one-dimensional space. A realization of a random field is a collection of values, each a realization of the random variable associated with a point. The definition of a RF expresses the random structured aspects of a regionalized variable; for every set of k points (in n-dimensional space),
X1, X 2 ,...... X k being called support points, there corresponds a k-component
vectorial random variable {Z(X1),Z(X 2 ),...... Z(X k ) }:
I. Locally, at a point X1 , Z(X1) is a random variable
II. Z(X1) is also a RF in the sense that for each pair of points x1 and x1+h , the
corresponding random variables Z(X1 ) , Z(X1+h ) are not, in general, independent but are related by a correlation expressing the spatial structure of the initial variable Z(X ) .
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2.5.3.2 Mean and Covariance Function
A RF may be partially described by its mean function and covariance function. The mean function of a RF specifies the mean of each random variable associated with each point in space. If the distribution function Z(X ) has an expectation (and suppose it has), then this expectation is referred as the mean of the RF, and is generally a function of x . Then the mean ' m(x) ' is:
m(x) = E{}Z(x, y) (2.4) where E is the expected value operator.
The covariance function describes the covariance (or in a sense relatedness) between any two random variables in the space. The covariance function between two random variables Z(X i ) and Z(X j ) can be described as;
= { − − } Cov(i, j) E [Z(xi , yi ) m][Z(x j , y j ) m] (2.5)
In 2-D interpolation problems in typical system engineering applications (such as estimation of rainfall at various points from a small number of observations, estimation of mean mineral grade in geophysics, evaluation of gradient of water level at various points in ground water flow modelling etc.) the following common features were highlighted by Bastin and Gevers (1985);
• Measurements are available in only a very limited number of locations.
• The mean of the RF is almost never zero.
• The mean and the spatial covariance function are seldom known and are hard to estimate precisely since the measure points are few and not evenly spaced.
• The RF is often not wide sense stationary, or at least a wide-sense stationary assumption is hard to validate.
A RF is wide-sense stationary if its mean function is constant and its covariance = − function depends only on the separation vector d X1 X 2 . A stationary RF is
36 Chapter 2 Fundamental Theory and Literature Review isotropic if its covariance function depends only on the separation distance d = d (it does not change with direction).
The presence of a non-zero mean and the non-stationarity of the RF have led the geostaticians to suggest the use of the ‘variogram function’ as an alternative to the covariance for interpolation in RF. This advantage with ‘variogram function’ is utilized in the present study to analyse the spatial and temporal dependence of the Rainfall Field considered as the RF.
2.5.3.3 The Variogram
Another way of describing RF is the Variogram, which is the name given by geostatisticians to the semi-variance of RF increments [Journel and Huijbregts (1978)]. In other words ‘variance’, or more precisely the ‘a priori’ variance of Z(x, y) . When this variance exists, it is defined as the second-order moment about the expectation m(x) of the random variable Z(x, y) and given by
Var{}Z(x, y) = E{}[Z(x, y) − m]2 (2.6)
The variogram function between two random variables Z(x1 ) and Z(x2 ) then can be given as;
γ = − 2 (i, j) Var[Z(xi , yi ) Z(x j , y j )] (2.7)
The function γ (i, j) is then the ‘semi-variogram’ and written by
1 γ (i, j) = E{}[Z(x , y ) − Z(x , y )]2 (2.8) 2 i i j j
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The semi-variogram theory and background knowledge is utilized in developing the technique to estimate the spatio-temporal heterogeneity of rainfall events in our study and is documented in Chapter 4 of this dissertation. The intrinsic nonstationary assumption in the selection of semi-variogram models are compared with the wide- sense stationarity semi-variogram models and included in Chapter 4. The superiority and suitability of intrinsic nonstationarity assumption used in our particular study have also been discussed in this Chapter.
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2.6 GIS in Catchment Modelling Systems
2.6.1 Integration of Hydroinfo rmatics with Catchment Modelling Systems
The term Hydroinformatics was first defined by Abbott (1991) and was generated to describe the application and manipulation of hydrological and hydraulic information within a computerized format. A concise definition of Hydroinformatics is presented by Meynett and Van Zuylen (1994), who state “hydroinformatics deals with the electronic encapsulation of various sources of information related to the hydro sciences.” From this definition it is apparent that hydroinformatics covers a wide range of subject areas which is not limited to the classical hydrological and hydraulic sciences. From the above definitions, any software that assists with various sources of information related to the management of a catchment, can contain the following major components.
• Information databases, for the storage, retrieval and display of spatial and temporal data.
• A model for simulating the catchment response to storm events.
• A decision support system for modelling and data analysis capabilities.
Despite the variability in data needs and usage, it is possible to categorize the information needed into spatial and temporal data. Temporal data are fixed in location and varies with time. Temporally variable data are usually stored in a time series manager. For this study HYDSYS was used as the series manager. Spatial data are fixed in time but vary spatially. Spatially distributed data is usually stored in spatial database. Geographical Information Systems (GIS) provide an efficient means of accessing the spatial database. The hydroinformatics tools used in our study can be listed as:
• Arc/Info GIS: Spatial database, operator for the spatio-temporal rainfall model development, graphical display of rainfall maps • HYDSYS : Time Series Manager • SWMM as Catchment Modelling software for the Hydrologic and Hydraulic Model component.
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2.6.2 Merits of GIS
The use of Geographic Information Systems (GIS) has grown dramatically since the 1980’s. It was popular among geographers initially, but during the last decade engineers found its importance and started to use GIS as a tool in several applications. GIS has the capability to turn spatial data from many different sources into a useful piece of information such as a map for decision-making. In the literature GIS is described as: “An organized collection of computer hardware, software, geographic data, and personnel designed to efficiently capture, store, update, manipulate, analyze, and display all forms of geographically referenced information.” The Environmental Systems Research Institute, Inc (1997), a commercial GIS software development company, offers another following detailed definition; “A GIS is a computer-based tool for mapping and analyzing things that exist and events that happen on Earth. GIS technology integrates common database operations such as query and statistical analysis with the unique visualization and geographic analysis benefits offered by maps. These abilities distinguish GIS from other information systems and make it valuable to a wide range of public and private enterprises for explaining events, predicting outcomes, and planning strategies.
GIS has undergone significant development within the last decade. A powerful spatial analysis tool Arc/Info is included as one of the GIS module. A distinctive advantage of Arc/Info is its programming capability. It provides Arc Macro Language (AML), which allows running sequence of Arc/Info commands. This language capability permits easy repetition of operations and, in consequence, real time operation of the systems. According to the type of study or query, the output from a GIS can be graphical, textual or numerical, in the form of maps, graphs, or tables. Selective display of features is a major capability of a GIS that facilitates decision-making. In addition, the GIS can correlate different layers of information into a single view, discovering relationships, patterns and trends that would otherwise go unnoticed. This can assist decision makers in the evaluation of reliability of proposals and the generation of alternatives. Selective display of features is a major capability of a GIS and this distinguishes a GIS from a computerized map. This relationship between objects and attributes gives GIS powerful capabilities for analysing land and water resources problems.
40 Chapter 2 Fundamental Theory and Literature Review
Hydrological applications require the modelling of the transport of water and materials over the space and time. This may require changes to be signaled in attributes, location and in the form of critical patterns. GIS can be linked with Water Management models as both pre and post processors in the field of quantity and quality. In our studies we use Arc/Info as a preprocessor to develop a rainfall input model for SWMM. We use the algorithm techniques available in the Arc/Info, to interpolate the rainfall values for each subcatchments. A part from that we used Arc/Info as the post processor as well, to visualize the spatial and temporal variability of a particular storm event.
The goal of a GIS is to take observations of the real world and simplify and scale the data into graphical elements to which are related descriptive features termed attributed. The attributes are maintained in a database management system (DBMS). Raster data structure and Vector data structure are two main data structures within a GIS.
2.6.2.1 Grid data Model and Structure
A grid data structure represents an entity as divided into a rectangular grid or matrix of cells. The grid is organized as a set of rows and columns. Each row or column contains a group of cells. Cells have numerical values that represent geographic phenomena; for example rainfall depth, land use type, elevation. Rows and columns are defined in a Cartesian coordinate system, which may have an associated map projection (the map projections available to Arc coverages are also applicable to GRID). Values assigned to each cell may be integer or floating point numbers representing nominal, ordinal, interval, or ratio measurements, null data, such as would exist outside the domain of valid cell values, are assigned NODATA.
When the grid is defined as an integer grid, a Value Attribute Table (VAT) is assigned. Primarily, this comprises a record number, the cell value, and the number of such values in the grid. Each value in the grid corresponds to one record in the VAT. Additionally, the Vat may contain supplemental attributes the use of which may be compared to an Arc Attribute Table (AAT) or a polygon attribute Table (PAT). Supplemental items are not limited to integer values. Grid operations may be performed using a defined item in the VAT but the default item is the cell value. The supplemental attributes must be added to the VAT using standard Arc/Info tabular database procedures; they cannot be
41 Chapter 2 Fundamental Theory and Literature Review added directly from GRID functions assign data to the value and count items of the VAT.
As long as grids are spatially registered, they may be considered as layers between which or on which mathematical or logical operations may be formed. Spatial registration implies that all grids must be in the same map projection. Each grid contains registration information that includes the map projection as well as the location of the grid within the Cartesian coordinate system.
2.6.2.2 Vector data model and Structure
In vector data, the homogeneous units are points, lines and polygons to represent features of any land system. The fundamental primitive for this model is point information, and objects were created by connecting points with straight lines (or arcs) while areas are defined by sets of lines. Vector systems, therefore, have explicit storage for topology and attribute data, and storage information. The advantage of these systems is the mathematical precision and efficiency of vector storage. The advantages of these vector data models are utilized for storing all the relevant and basic informations of the study in vector DBMS and for consequently presenting all the information of study in an understandable manner.
However, modifying the shape of features and linking them to external models in vector structure is relatively difficult. On the other hand, the raster/grid GIS, which the analysis performed in this study is best suited for handling large geographic areas and represent high spatial variations where positional precision is less important than the ability to perform complex mathematical analysis of attribute data. However, attribute data representation can be more efficient in a vector system than a raster system. For example, the value code for a continuous zone of land use must appear in every cell within the zone of a grid. The same zone is represented in a vector system by one polygon and value code. On the other hand, a grid can be completely defined by a point of origin, the cell dimensions, and array size. A vector element requires extensive strings and coordinates.
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2.6.3 Application of Geographic Information Systems in Hydrology
In recent years the description of the environment in digital form has greatly improved in quantity and quality. Further, the tools that are available for analyzing these data have improved as well. This led to an increase in the use of GIS for hydrologic Modelling. Detailed overviews of general GIS applications in Hydrologic Modelling are clearly demonstrated by Maidment (1996), De Vantier and Feldman (1993), Moore (1993).
Recently, there have been attempts to take advantage of GIS capabilities for rainfall modelling [Ball and Luk (1998); Wilk and Anderson (2000); Tsanis and Gad (2001)] and for runoff modelling (Maidment 1993; Olivera 1995; Maidment et al. 1996). Maidment (1993) presents a grid-based methodology for determining a spatially distributed unit hydrograph, assuming a pure translation flow model. A similar methodology, but considering a flow model that accounts for translation and storage effects, is presented by Maidment et al. (1996). The GIS software, Arc/Info-Grid, has proved to be a powerful tool for hydrologic routing modelling and a spatially distributed unit hydrograph is developed based on linear system theory applied to sub areas or cells within a watershed by Olivera and Maidment (1996). The authors in the study kept a unique unit response function for each cell, independent of the functioning of other cells. Convolution of these response functions along cell-to-cell flow paths throughout the watershed produced the runoff response at the outlet from spatially distributed precipitation excess.
Grid-based GIS appears to be a very suitable tool for hydrologic modelling, mainly because raster systems have been used for digital image processing for decades and a mature understanding and technology has been created for that task (Maidment 1993). Grid systems have proven to be ideal for modelling topographically driven flow, because a characteristic of this type of flow is that flow-directions do not depend on any time dependent variable. This characteristic is what makes topographically driven flow easily modeled in a grid environment and, consequently, grid systems include hydrologic functions as part of their capabilities. At present, hydrologic functions, available in grid data structure of GIS, allow one to determine flow direction and drainage area at any location, stream networks, watershed delineation, etc. (Maidment 1993).
43 Chapter 2 Fundamental Theory and Literature Review
Saunders and Maidment (1995) present a simple, yet powerful, grid-based water quantity and quality model for mean annual values, and apply it to the San Antonio - Nueces coastal watershed of Texas, USA. In their model, a relation between precipitation and runoff (both in depth per unit time) is determined. Based on observed runoff values at flow gauging stations and a mean annual precipitation grid, a regression equation gives the expected runoff as a function of precipitation.
DeVantier and Feldman (1993) presented a general review of the connection between GIS and hydrologic modelling, which "summarizes past efforts and current trends in using digital terrain models and GIS to perform hydrologic analysis". The link between GIS and hydrologic modelling has become stronger as the concern about spatially distributed terrain parameters and the use of computers for hydrologic analysis turns more widespread. Digital terrain models (DTM) are the means used by GIS to describe the spatially distributed attributes of the terrain, which are classified as topologic and topographic data; although, strictly speaking, topographic is part of topologic data. Digital elevation models (DEM), in particular, refer to the topographic data, while all other attributes, not related to elevation, constitute the topologic data. It can be expected that, because of the large amount of information required to describe the terrain, GIS is a memory and computationally intensive system. However, storing and handling the data is not necessarily the critical point when working with GIS, because the acquisition and compilation of the information can be an even more difficult task.
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2.7 Assessment Criteria of Calibration and Validation Processes
2.7.1 Errors in Application of catchment Modelling
As discussed in Section 2.2, catchment modelling systems replicate important processes influencing the response of the catchment to storm events with mathematical methods. These systems comprise two components including the theoretical basis of individual process models and the numerical implementation of the process model, and both of these components introduce different forms of errors into simulation. Structural and Numerical errors are the possible source of errors in application of each component of the catchment modelling systems. From the common error free assumption used in the calibration and validation of the modelling system for a particular catchment model, will again introduce further errors such as Systematic and Measurement errors. While it may not be possible to remove all sources of error from the analysis, it is important to be aware of them and interpret data obtained from the modelling system accordingly.
Generally, forecast errors can be either systematic (recurring), or random (due to case specific conditions, such as errors in the meteorological data on which the hydrologic forecast is based). Forecast accuracy is a measure of forecast error, that is, the difference between the amount forecasted and the value that actually occurs. In this comparison, the measured error used is not a direct measure of the inaccuracies incurred in parameter estimation and input conditions but rather it is a measure of the minimum degree of departure between simulated and observed discharges.
Aitken (1973) discussed the criteria for detection of systematic and random errors in model prediction. Although the distinction between random and systematic errors is important in hydrologic modelling, it is quite difficult to distinguish them in practice. The author further demonstrates that random errors occur when the model output shows no tendency to over or under estimate the observed data over successive time intervals, while systematic errors occur when the sign of the error persists over several successive time intervals. The study emphasized the importance of systematic error recognition in the analysis of the model and examined various statistical criteria to distinguish between random and systematic errors.
45 Chapter 2 Fundamental Theory and Literature Review
Lettenmier and Wood (1993) viewed bias and relative bias as measures of systematic error because they measure the degree to which the prediction is consistently above or below the actual values, and considered variance as a random error measure because this is a measure of the variability, or scatter, of a number of predictions about the true values. For measuring both random and systematic errors, they recommended mean square error, mean absolute error, relative mean absolute error and the efficiency coefficient.
Troutman (1983) mainly classified the errors from the assumed stochastic structure of rainfall, in to two components other than the model errors. (1). Error with erroneous rainfall input (2) Error with erroneous Model input. Rather it is only the error associated with different spatio-temporal rainfall input that is of interest here. Since this study is focused on estimating the prediction accuracy from alternate rainfall models, it is appropriate to keep the model errors resulting from the fact that the model itself, only approximates the physical system and the other input errors to be consistent. Therefore, the results given in this thesis cannot be expected to define exactly the errors and biases that are present in actual rainfall runoff modelling applications. Nevertheless, a great deal of insight can be gained in to the nature and relative magnitude of errors caused by the alternate rainfall representation considering the degree of spatio-temporal variability of rainfall.
Though in a couple of studies different stochastic dense gauge informations are used, there is some uncertainty as to what the actual spatial rainfall pattern is. Henceforth, the proposed rainfall models will be taken to represent more accurate input or more realistically, that is in some sense the 'best' input to the model. Since this thesis mainly compare the results from different spatio-temporal rainfall models, some generally used statistical parameters means to be discussed and defined involved in prediction accuracy.
2.7.2 Assessment Criteria for Runoff Prediction
As Lettenmaier and Wood (1993) stated, prediction accuracy is a measure of prediction error, that is the difference between the amount predicted / modeled value and that actually observed. In other words the prediction accuracy is best assessed by retrospective comparison of prediction actually made and the values observed. General
46 Chapter 2 Fundamental Theory and Literature Review objective criteria for assessing the quality of single event modelling are based on differences in runoff volume, peak flow rate and hydrograph shape matches between simulated and observed hydrographs.
Green and Stephenson (1986) reviewed a number of criteria, which can be used for hydrograph comparison in single event modelling and pointed out that no single statistical goodness of fit criteria is sufficient to assess adequately for all purposes the fit between a computed and an observed hydrograph. The similar conclusions were developed by Diskin and Simon (1977) and Refsgaard and Storm (1996).
The prediction accuracy can be defined by widely used statistical parameters, which measure the prediction error. The widely used statistical parameters to measure the forecast efficiency are Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Absolute Relative Error (ARE), Sum of Square Errors (SSE), Bias, Variance, Coefficient of Determination (R2) and Efficiency (E). When () () Qs i is the simulated runoff and Qo i is the observed runoff at time step i and define
M s and M o , the means of the predictions and observations for the simulation period, as follows:
n = 1 M s ∑Qs (i) (2.9) n i=1
n = 1 M o ∑Qo (i) (2.10) n i=1
Then the widely used measures to assess the simulation errors are given as follows
n = 1 []− 2 Mean Square Error MSE ∑ Qo (i) Qs (i) (2.11) n i=1
n = 1 − Mean Absolute Error MAE ∑ Qo (i) Qs (i) (2.12) n i=1
n = 1 []− 2 Root Mean Square Error RMSE ∑ Qo (i) Qs (i) (2.13) n i=1
47 Chapter 2 Fundamental Theory and Literature Review
V −V = o s Absolute Relative Error of Runoff Volume ARErunvol (2.14) Vo
3 where Vo is observed runoff volume (m ) 3 Vs is the simulated runoff volume (m )
P − P = o s Absolute Relative Error of Runoff Peak ARE peak (2.15) Po
3 Where Po is observed peak (m /sec) 3 Ps is simulated peak (m /sec)
= − Bias B M s M o (2.16)
Variance V = MSE − B2 (2.17)
n = []− 2 Sum of Square Error SSE ∑ Qo (i) Qs (i) (2.18) i=1
One of popular measure used in evaluation of model performance is probably the SSE. The value of the sum of squared deviations depends on individual values of runoff generated by the model for the same period of time, which in turn depends on the structure of the model considered and the values of its parameters [Diskin and Simon (1977)]. However, this function gives much more weight to larger differences than the smaller differences, it has been criticized by many authors [Clarke (1973), Sefe Boughton (1982), Green and Stephenson (1986)]. And also it should be noted that since we are interested in assessing the sensitivity of catchment models for alternate rainfall input on individual storm events, it is desirable to reduce the basis of comparison to a dimensionless form regardless of number of data sets. But SSE estimation is dimensional with sum of powered residuals and sum of absolute errors. The value of SSE estimation will, therefore, depend on the number of ordinates used in the data sets. For a meaningful comparison of different models using a number of data sets differing not only in magnitude but also in the number of records contained in the data sets, it is desirable to reduce the basis of comparison to dimensionless form [Green and Stephenson (1986)].
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Instead of SSE many alternatives have been proposed. Another the measure widely used to assess the alternate model performance is the MSE. MSE is the minimum average value of the sum of the squares of the differences between observed and simulated values. The measure also gives greater emphasis to match higher values. The measure is dimensional and the unit of it is the power of used unit of the data.
Another objective function is the MAE, which indicates the absolute departure of a model from observed discharge on average at each time step. MAE gives the same unit as the unit of the data set used. Similar to MAE, RMSE also measures the absolute value of error. The absolute value ensures that positive and negative differences do not and give a false appearance of agreement. It may be preferred for forecasting or the sensitivity analysis of alternate input models, for example, when it is important to be as close as possible to the true discharge at every time step. Lettenmier and Wood (1993) recommended that the MAE and RMSE (absolute error measures) are preferred to MSE (squared error measure) since absolute error measures are less dominated than squared error measures by a small number of large errors, and are thus a more reliable indicator of typical error magnitudes. The authors further suggest that the RMSE is an excellent measure of fit since it also measures both the systematic error and the random error. Legates and Davis (1997) and Legates and McCabe Jr. (1999) strongly recommended the use of absolute error measures such as RMSE or MAE with additional supporting information for complete assessment of model prediction capability.
Bias is an attempt to measure any bias or systematic error in the predicted values. A bias in the predicted values will show as a consistent over or under estimation of the recorded flow. The variance is a measure of the variability or scatter of the predicted values about the recorded value, and is therefore a measure of the random error. The MSE, RMSE, MAE forecast efficiency are all measures that incorporate both systematic and random errors. A perfect forecast exists only if both the bias and variance are zero, which occurs only when all forecasted values are identical to the observations.
Lettenmier and Wood (1993) further suggest that R2 is the square of the correlation coefficient between the observed and forecast values. Although R2 is a widely used measure of forecast accuracy, care must be taken if appreciable bias is present, since R2 evaluates the accuracy of a forecast with respect to random error only. The highest value of R2, 1.0 can be achieved for cases where there is a constant bias in the forecasts;
49 Chapter 2 Fundamental Theory and Literature Review that is, the forecasted value is equal to the observation plus or minus a constant. For this reason, instead of using R2, forecast accuracy is better assessed by using the bias and variance, or the bias and the mean absolute errors.
Presented in Table 2-2 are the summary of Evaluation made on the different objective functions used to assess the simulation results from alternate rainfall input for various degree of heterogeneity events.
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Table 2-2: Types of Measurement Criteria and Evaluation of Assessment Criteria
Assessment Criteria Evaluation Dimension
• Much more weight to large differences than small Mean Square Error differences Dimensional (MSE) • Unbounded measure • Perfect prediction when the value obtained is zero • Measures both systematic and random errors • Better criteria than MSE because absolute error Root Mean Square Error Dimensional measures are less dominated by a small number of (RMSE) large errors, thus a more reliable indicator of typical error magnitudes. • Unbounded measure • Perfect prediction when a value obtained zero • Same as RMSE • In general RMSE > MAE for the range of most Mean Absolute Error Dimensional values and the degree of this differences indicate the (MAE) extent to variance or extreme values existed in the data • Unbounded measure • Perfect prediction when the value obtained is zero
• Relative criteria and the most simple formula Absolute Relative Error • Unbounded measure Dimensionless (ARE) • Perfect prediction when the value obtained is zero • Much more weight to large differences than small differences because of the squared residuals Sum of Square Error Dimensional • Unbounded measure (SSE) • Perfect prediction when the value obtained is zero • Measures the random error only • Describes the proportion of the total variance Dimensionless Coefficient of between the observed and predicted data – evaluates determination (R2) linear relationships between the variables • Limited in standardization of differences between the observed and predicted mean and variances • Insensitive to additive and proportional differences between the model simulations and observation • Sensitive to extreme values than observations near mean • Bounded measure (0< R2<1) • Perfect when the value obtained is one
• Better measure than R2 in a sense of sensitivity for Efficiency (E) differences in the observed and model simulated Dimensionless means and variances. • Overly sensitive to extreme values because of the squared differences • Bounded measure (-1 51 CHAPTER 3 TEST CATCHMENTS 3.1 Catchment Location The Upper Parramatta River Catchment (UPRC) and the Centennial Park Catchment (CPC) were used as case catchments for this project and particularly for categorizing storm events according to their spatio-temporal variability, for developing spatio- temporal rainfall models and for consequently illustrating the influence of the spatio- temporal variability of rainfall in catchment runoff prediction. These two urban catchments are located within the Sydney Metropolitan Area as shown schematically in Figure 3-1. Figure 3-1: Location of Upper Parramatta River Catchment (UPRC) and Centennial Park Catchment (CPC) 52 Chapter 3 Test Catchments This Chapter provides details of the catchment characteristics, hydrometric network, available data and decritization of subcatchments for modelling purposes, of both the UPRC and CPC. Importantly, the selected two catchments were chosen so that they were different in size and in the nature of the response time [UPRC (110 km2) – midsized urban catchment ; CPC (1.3km2) – smallsized urban catchment] and with an entirely different hydrometric network. Consequently the conclusions can be developed regardless of the size of the catchment and the raingauge arrangement. 3.2 Upper Parramatta Rive r Catchment 3.2.1 Catchment and drainage description The first study catchment (UPRC) is located in the western suburbs of Sydney, Australia. The relative location of UPRC with respect to the CBD of Sydney and the study catchment 2 (CPC) is shown in Figure 3-1. The UPRC includes parts of the cities of Blacktown, Holroyd and Parramatta, and the Shire of Baulkham Hills. Covering 110 square kilometers, it is located near the centre of the Sydney metropolitan area and has a population of more than 220,000. It is bounded by Prospect Reservoir to the southwest, Blacktown to the northwest, Castle Hill to the north and Carlingford to the east as shown in Figure 3-2. Considerable development as a result of rapid increases in population and dwellings has occurred within the catchment over the last two decades. At present, the dominant land use within the catchment is typical of an urban environment with mixed residential [houses (72%)], commercial [industrial, shopping (10%)], infrastructure [roads, rails (12%)], open space [parkland, bushland (5%)] and rural (1%) areas. The catchment is rather steep with the confining ridges being 180 meters Australian Height Datum (AHD) at Thompson Corner, Castle Hill, and 100 meters AHD at Prospect, and an overall catchment slope of about 1.2%. The catchment includes the Upper tributaries of the Sydney Harbour Catchment. There are three main tributaries, namely Toongabie Creek (70 km2), Darling Mills Creek (30km2), and Parramatta Creek (10km2). They join about 2.5km as a branch of Parramatta river (at Marsden Weir), upstream of the Charles Street Weir located at the catchment outlet. Parramatta River immediately upstream of the Charles Street Weir passes through part of the Parramatta central business district. The major creeks of all 53 Chapter 3 Test Catchments main tributaries within the catchment are shown in Figure 3-2. More than 80% of the creeks in the catchment remain in a natural or semi natural state, but are fed by hundreds of stormwater drains. The creeks flow through narrow sandstone valleys forming a series of cascading pools. Figure 3-2: Upper Parramatta River Catchment with Drainage Map The effect of urbanization and rapid development has led to an increase in estimates of the peak level for frequently occurring floods. To mitigate the social and economic losses associated with the flood events in this catchment, the Upper Parramatta River Catchment Trust (UPRCT) was established in 1989 with the task of managing flood mitigation measures within the catchment among other duties. The institution of 54 Chapter 3 Test Catchments UPRCT made possible for a continuous monitoring program including rainfall and runoff information with the achievement of other catchment management issues. 3.2.2 Available Information The UPRCT collects rainfall data at 14 stations within UPRC using tipping bucket raingauges, while stream height data is collected by the New South Wales Department of Land and Water Conservation (DLWC) at the Catchment Outlet. A sensor collects the data and sends the information by a radio signal to the Trust office. This provides one of the most intensive data collection systems anywhere in Australia. The data is used by the Trust to validate and refine its detailed computer model of flood behaviour. Figure 3-3 shows the Rain gauge and Stream height gauge locations with respect to the Catchment. 3.2.2.1 Rainfall Records There are fourteen (14) telemeter 0.2mm tipping bucket rain gauges within the UPRC; locations of these gauges are shown in Figure 3-3. The geographical positions of these gauges are tabulated in Appendix A. All these gauges have been installed and maintained by the Upper Parramatta River Catchment Trust (UPRCT) since its formation in 1989. As a result, long-term records are not available from these gauges. Records from fourteen raingauges were obtained in the years from 1996 to 1999. During this period 26 storm events where the event total rainfall was greater than 10mm were extracted. These storms were selected by providing insight in to the different degree of variability generated by the more typical frontal and convective system. A detailed list of selected storm events for the UPRC is given in Table 3-1. Table 3-1 shows the numbers of events extracted for each year, the total number of five-minute time incremental rainfall records for the whole period considered and the event statistics calculated globally. 55 Chapter 3 Test Catchments Figure 3-3: Rain Gauge Locations within and adjacent to the Catchment 56 Chapter 3 Test Catchments Table 3-1: Details of Selected Storm Events from UPRC Storm ID Event date 5 Min. Average Total Average Standard time / (mm) Intensity / Deviation/ increments (mm/hr) (mm/hr) 1a 02/01/1996 54 40.6 9.0 14.3 1b 06/01/1996 112 37.8 4.0 5.8 2a 11/04/1996 56 18.7 4.0 9.9 2b 11/04/1996 77 22.5 3.5 4.8 4 27/07/1996 146 39.9 3.3 4.2 5 30/08/1996 329 96.1 3.5 4.1 6 29/01/1997 323 66.3 2.5 2.5 7 07/10/1997 109 34.0 3.8 4.1 8a 24/01/1998 33 22.0 7.7 15.3 8b 25/01/1998 32 9.3 3.5 5.6 9a 09/04/1998 70 32.3 5.4 16.2 9b 10/04/1998 162 81.9 6.2 9.9 10 21/04/1998 521 46.4 1.1 1.5 11a 02/05/1998 84 20.5 2.9 5.0 11b 04/05/1998 369 39.8 1.3 1.7 12 18/05/1998 325 123.0 4.6 7.7 13 22/06/1998 67 34.4 6.2 7.5 20 01/04/1999 270 37.1 1.7 2.2 21 01/07/1999 41 14.5 4.2 2.5 22a 13/07/1999 83 30.3 4.4 4.4 22b 14/07/1999 56 35.9 7.7 11.0 23 16/09/1999 62 11.4 2.2 4.2 24 18/10/1999 116 33.7 3.5 2.6 25 23/10/1999 224 48.0 2.6 3.3 26a 09/12/1999 38 16.6 5.3 9.6 26b 09/12/1999 24 10.9 5.4 16.8 57 Chapter 3 Test Catchments 3.2.2.2 Stream Height Records The Parramatta River Gauge (Station Number 213004: Marsden Weir) is located on the Parramatta River behind the Parramatta Hospital grounds near the old Nurse's quarters. It is approximately 50 meters upstream of the Charles Street weir. The station was established on 31/01/1979. It is the responsibility of the DLWC - Sydney/South Coast Region for the collection and storage of data from this station. The highest recorded flow gauging is 213 m3/s (1.81m stage height ; Flow=18,478 Megalitres per day) recorded at the site on 30 August 1996. The river stage (height) data is linked to AHD reference, with a Staff Gauge height of 0.000 m equating to an AHD level of 3.733 m. While height and flow data is available from 06/02/1979 to the present, 26 flood events were extracted for the study during the period from 1996 to 1999, with the events selected based on the availability of rainfall information from almost all gauge records and flow records. Transformation of height data to flow data was based on the rating tables developed by DLWC. 3.2.3 Subcatchment Details For Catchment modelling purpose, a conceptual rainfall-runoff model based on the Storm Water Management Model (SWMM) has been developed. For implementation of this catchment modelling system, the total catchment was subdivided into twenty-nine (29) sub-catchments. The complete descritization of UPRC into 29 subcatchments are shown in Figure 3-4. As expected, the area of each of this sub-catchment was not constant but rather different according to the catchment characteristics based on the landuse type. The area of the largest subcatchment was approximately 12km2 while the smallest was approximately 0.5km2. The remaining subcatchments were distributed between these limits. However, for the rainfall modelling purposes, the catchment was modelled using 100 * 100 m pixels in a GIS environment. Details on the number of 100m pixels involved, sizes of individual subcatchments and number of properties within each subcatchment are given in Table 3-2. 58 Chapter 3 Test Catchments Figure 3-4: Schematization of Subcatchments for the Upper Parramatta River Catchment (after the Flood mitigation program by Upper Parramatta River Catchment Trust) 59 Chapter 3 Test Catchments Table 3-2: Subcatment Description of UPRC Subcatch Area - No of Number of Subcatchment Name ment ID Hectares pixels Properties 1 Bellamy Farm Creek 61 61 453 2 Bellbird Creek 161 161 918 3 Bidjigal Creek 262 262 1713 4 Blacktown Creek 732 732 5058 5 Blue Gum Creek 294 294 1872 6 Bogalara Creek 136 136 1405 7 Bowling Club Branch 224 224 1987 8 Brickfield Creek 318 318 2491 9 Christmas Bush Creek 52 52 484 10 Coopers Creek 526 526 4010 11 Darling Mills Creek 797 797 4222 12 Domain Creek 149 149 894 13 Excelsior Creek 243 243 1113 14 Finlaysons Creek 613 613 5739 15 Glenmire Creek 62 62 527 16 Gratham Creek 253 253 2442 17 Greystanes Creek 936 936 4236 18 Hunts Creek 783 783 4709 19 Lalor Creek 730 730 5325 20 Milsons Creek 92 92 541 21 Model Farms Creek 192 192 1414 22 Northmead Gully 322 322 2668 23 Upper Parramatta River 261 261 1050 24 Pendle Hill Creek 550 550 4917 25 Quarry Creek 484 484 3877 26 Rifle Range Creek 149 149 694 27 Sawmill Creek 112 112 855 28 Stevensons Creek 122 122 969 29 Toongabbie Creek 1279 1279 8113 60 Chapter 3 Test Catchments 3.3 Centennial Park Catchment 3.3.1 Catchment and drainage description The second study catchment (CPC) is located in the inner metropolitan Sydney region, approximately 4 km south of the Central Business District and 1 km to the north west of the main campus of the University of New South Wales (UNSW) [Figure 3-1]. The catchment covers the southwestern corner of Waverely Local Government Area and the eastern side of Randwick Local Government Area. The catchment area is 1.32 square kilometers (132 ha) in extent with an overall catchment average slope of 5%. The landuse is primarily open spaces, road surfaces, public buildings, general business and residential areas. The open spaces, which comprise 18 percent of the total catchment, mainly consist of Queens Park and a small part of Centennial Park. Roads and concrete foot-paths occupy about 15 percent of the catchment including 14.9 km of double carrier ways (arterial roads) and 3.6 km of small lanes (alleys). The public building and general business areas comprise 7 percent of the total drainage area contributing to the runoff at the outlet. More than half of the landuse is categorised into different forms of residential lots. The catchment is served and drained by separate sewer and storm water systems. The storm water system consists of a series of pipes, box culverts and open channels, which ultimately discharges into Musgrave Pond in Centennial Park. The complete drainage map of CPC with respect to the road map and catchment boundary is shown in Figure 3-5. The length of stormwater drain studied as shown in Figure 3-5 was approximately 5200m from the upstream of the catchment to the location of the flow gauging station at the Musgrave Avenue pond. Most of the pipe systems outside of Queens’s Park are less than 1000mm in diameter and are operated by the local councils, i.e. Randwick City Council and Waverely Council. Open channels and pipes larger than 1000mm are operated by Sydney Water. The open channels have trapezoidal cross sections with a ‘V’ notch for low or base flows. 61 Chapter 3 Test Catchments Figure 3-5: Centennial Park Catchment with Drainage Map 3.3.2 Available Information Conceptual rainfall-runoff modelling systems require a hyetograph of rainfall depth or intensity versus time for the period of simulation. If multiple gauges exist within the catchment, multiple hyetographs for the catchment could be used for the desired simulations. In most applications for small urban catchments however, a single rainfall pattern or none is available within the catchment. For this catchment, long-term rainfall characteristics are available around the catchment while the flow characteristics monitored at catchment outlet for last few years. Different organizations are responsible for maintaining these rainfall gauges as shown in Table 3-3. 62 Chapter 3 Test Catchments Table 3-3: Rainfall Monitoring Stations and Operation Authority Station No Station Name Operation Authority Period 566002 Avoca Street University of NSW 1977 to date 566003 Storey Street University of NSW 1977 to date 566010 Waverley Public School University of NSW 1995 to date 566032 Paddington Sydney Water 1956 to date MASCOTC Kingsford-Smith Airport Bureau of Meteorology 1960 to date 2132238 Musgrave Avenue Pond University of NSW 1997 to date 3.3.2.1 Rainfall Records Prior to October 1994, there was no rainfall gauging stations existing within the catchment. After realizing the importance of the rainfall modelling in space and time for quantity and quality studies of the Centennial park ponds, a pluviometer was installed by UNSW at Waverley public school in October 94. Another gauging arrangement was installed at the outlet of the catchment with the flow monitoring system, in 1997, in order to better estimation of spatial rainfall pattern. Since the direction of storm movement is rarely recorded in urban catchments, it is not advisable to expect a reliable result on the distribution of intensity over the catchment when there are no more than two gauges. Therefore, four other gauge records adjacent to the catchment were utilized in our study. The locations of the gauging stations are shown with respect to the study catchment in Figure 3-6. 63 Chapter 3 Test Catchments Figure 3-6: Rain Gauge Locations within and adjacent to the Catchment These other pluviometers are located within a radius of 7 km from the study area. All of these gauges are digitally logged 0.2mm tipping bucket pluviometers (except Paddington gauge which is 0.5mm) and have been installed and maintained by different authorities. Among these gauges, the Paddington and Kingsford-Smith Airport Meteorological stations have been operated by Sydney Water and the Bureau of Meteorology (BOM) respectively for approximately forty years. The stations at Avoca and Storey Street have been operated by UNSW for the past 30 years. The rainfall data used for this catchment was extracted from the HYDSYS database in the School of Civil and Environmental Engineering at the UNSW. Events with more than 10mm in total were extracted and used in this study. Based on this approach, thirteen storm events were extracted for analysis. The data were available from 1997 from all gauges and the event records were selected in the years of 1997, 98 and 99. These events were chosen based on their intensity and duration. The details of these 64 Chapter 3 Test Catchments selected storm events are shown in Table 3-4. Table 3-4 shows the number of events extracted for each year and the total number of 5 minute time incremental rainfall records for the whole period considered. The additional details of these events are tabulated in Appendix A. 3.3.2.2 Flow Records A monitoring station was installed at Musgrave Avenue Stormwater Channel in 1997 in order to monitor the quantity as well as the quality of the stormwater for the implementation of catchment management plans. The existing stormwater channel was used to measure the flow. Water levels in the channel were monitored using an ultrasonic probe and converted to flow using a rating curve. This rating curve has been developed by Abustan (1998) after modifying a method developed by Tilley et al. (2000) for gauging rapidly varying discharges. 65 Chapter 3 Test Catchments Table 3-4: Detailed of Selected Storm Events Storm ID Event date 5 Min. time Average Average Standard increments Total / (mm) Intensity / Deviation/ (mm/hr) (mm/hr) 1 29/01/1997 273 78.0 3.4 4.7 2 11/02/1997 339 99.2 3.5 3.6 3 22/04/1998 97 32.6 4.0 4.0 4 04/05/1998 89 16.0 2.1 3.2 5 18/05/1998 85 73.9 10.4 15.2 6 16/06/1998 77 14.3 2.6 7.7 7 09/10/1998 108 9.6 1.0 2.1 8 19/10/1998 115 11.5 1.2 1.8 9 14/08/1999 83 49.0 7.2 6.9 10 18/10/1999 117 33.3 3.4 3.8 11 23/10/1999 102 36.8 4.1 4.9 12 08/11/1999 44 14.2 3.9 7.7 13 09/12/1999 24 18.0 9.1 17.6 3.3.3 Subcatchment Details In order to accurately model the catchment, the catchment was subdivided into 42 subcatchments as shown in Figure 3-7, after the study by Abustan (1997). The size of individual subcatchments ranges from 0.5 ha to 27 ha. Smaller subcatchments were predominantly in the residential areas while the larger subcatchments consisted mainly of open spaces, which have homogeneous landuses. The detailed size of subcatchments and the corresponding types of landuses are listed in Table 3-5. The different types of landuse, the size of drainage conduits and the topographic characteristics were main concerns in the descretization of the catchment into individual subcatchments. Slope was considered also with a flow direction map in discretization of the catchment. The resultant descretization of the Centennial Park Catchment into 42 subcatchments and the corresponding subcatchment ID’s used in the modelling are shown in Figure 3-7. 66 Chapter 3 Test Catchments Figure 3-7: Schematization of Subcatchments, of Centennial Park Catchment after Abustan (1997) 67 Chapter 3 Test Catchments Table 3-5: Subcatchment Description of CPC Subcatch. Area - No of 25 m Subcatch. Area – No of 25 m ID Hectares cells ID Hectares cells processed in processed in rainfall rainfall modelling modelling 1 2.76 43 22 2.17 35 2 1.37 22 23 1.46 23 3 5.14 84 24 2.60 41 4 3.13 48 25 1.80 29 5 6.27 103 26 3.05 48 6 3.39 56 27 1.15 19 7 1.97 31 28 2.60 41 8 1.17 19 29 1.01 16 9 3.17 49 30 3.17 49 10 3.35 57 31 1.76 28 11 3.32 52 32 5.38 87 12 1.56 26 33 0.88 14 13 2.42 39 34 2.58 41 14 1.96 32 35 0.64 10 15 3.21 50 36 1.21 18 16 0.96 17 37 0.50 7 17 1.79 29 38 3.89 65 18 2.91 45 39 1.50 26 19 7.38 119 40 0.53 7 20 4.23 69 41 27.26 439 21 2.45 38 42 3.63 57 68 CHAPTER 4 ESTIMATION OF SPATIO-TEMPORAL HETEROGENEITY OF RAINFALL 4.1 Introduction Urban Hydrology is a special case of hydrology in that it is the study of the water cycle in cities i.e., areas with a very high level of human interference with natural hydrological processes. All hydrological processes in urban areas must be considered in much smaller temporal and spatial scales than those in rural areas due to the smaller scale of the areas of interest. This brings about essential differences with respect to theory, data collection and calculation methods. One of the important hydrological inputs in the generation component of a catchment modelling system as explained in Chapter 2 is the rainfall. The rainfall input is therefore, seldom adequate to provide the information on small spatial scale and short time resolution. However, the selections of spatial and temporal scales as well as the selection of alternate rainfall modelling approaches rely on the degree of heterogeneity of the events occurring in both space and time. However, there have been few, if any attempts to differentiate storm events occurring on urban catchments according to their variability in both the space and time dimensions. Differentiation of events based on their heterogeneity can be used in studying the selection of space and time scales and also on influence of choosing a distributed modelling approach for the rainfall towards improving the robustness of predictions for an urban catchment modelling system. This Chapter illustrates a procedure for assessing the degree of heterogeneity of individual events on urban catchments and consequently shows the categorisation of events, from two urban test catchments in Sydney Australia, according to their heterogeneity in both space and time. The general needs for categorisation of individual events and storm classification based on space-time variability are presented in the next section. The background theory of the adopted semi-variogram tool is explained in the section on the methodology of the 69 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach approach. This adopted methodology is then tested on real events on two different sized urban catchments within the Sydney region. Rainfall is a natural process, which has a high degree of variability in both space and time. Furthermore the measurement of rainfall across the spatial and temporal scales is a complex task. There have been several studies undertaken in the past to show the impact on hydrographs of the spatial and temporal variability of rainfall. The majority of these studies focus on the spatial variability. For example, Obled et al. (1994); Seyfried and Wilcox (1995); Goodrich et al. (1995); Chaubey et al. (1999) approached the problem by comparing the responses using rainfall fields based on observations from a dense rain gauge network, and from rainfall fields based on the observations from a subset of original network gauges. In the study by Obled et al. (1994), for example, two different densities of network were tested (5 or 21 gauges within a 71km2 catchment), showing a significant advantage for the dense network rainfall estimate. Similarly, studies on the impact of the temporal variability of rainfall [Burke et al. (1980); Lambourne and Stephenson (1987), Niemczynowicz (1991); Schilling (1991); Ball (1994)] approached the problem by comparing the responses by considering alternate temporal rainfall patterns. For example, Ball (1994), simulated overland flow for different rainfall excess patterns having rectangular, triangular, etc. patterns of rainfall excess and found that the peak flow and time of occurrence depended on the temporal pattern of rainfall excess. However, in these studies no attempts were made to differentiate the events based on their heterogeneity in space and time scale by utilising available gauge information. There have been few, if any attempts to measure the degree of the heterogeneity of rainfall in the space and time dimensions within the individual storm events occurring on urban catchments. The assessment and measurement of the spatio-temporal heterogeneity of each event is a complex task. Furthermore, there is a need to investigate both the spatial and temporal variability separately since a high spatially heterogeneous event could have a temporal variability. Presented in this chapter will be a technique for assessing the spatial and temporal heterogeneity of individual storm events. The task is achieved by adopting estimators, which measure both the spatial and temporal heterogeneity of different events, by incorporating the semi-variogram approach. 70 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilised in introducing estimators to address the heterogeneous nature of each individual storm event in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. 4.1.1 Classification of storm e vents based on their heterogeneity in space and time Prior to the development of estimation techniques in the subsequent sections, it will be demonstrated how events are defined in the study, according to their variability in space and time. A few hypothetical space-time rainfall patterns (Zi and Zj) from two different spatial positions (i and j) are considered in Figure 4-1 to highlight the categorisation of events based on their spatial and temporal heterogeneity. The proposed estimators that classify different events according to their spatial and temporal variability enable us to categorise all the available individual events into four categories of spatial and temporal variability. • High Spatial heterogeneity ; High Temporal heterogeneity (HS-HT) • High Spatial heterogeneity ; Low Temporal heterogeneity (HS-LT) • Low Spatial heterogeneity ; High Temporal heterogeneity (LS-HT) • Low Spatial heterogeneity ; Low Temporal heterogeneity (LS-LT) A high spatially variable event will be able show the minimum or no dependency between the data obtained from various spatial positions, where a high temporally variable event will not be able to show uniformity along its temporal series of records. The above categorisation divides all the events in to high and low spatially variable events and each of these different spatial nature of events will be categorised again according to their temporal variability into high and low temporally variable events. This will enable the categorization of all the events into four categories listed above. These typical hypothetical patterns represent two sets of records from two different 71 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach spatial locations and which represents the all four categories are illustrated in Figure 4-1. The ranking of events based on these classifications will be used to investigate the impact on the robustness of runoff prediction on above categorised events. Subsequently the above classification of all events considered on typical urban catchments are utilised in order to investigate the influences on prediction errors due to less accurate representation of these categorised rainfall events in space and time. 72 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 1. Category 1: HS-HT (Spatially and temporally varied event) Rainfall Intensity / (mm/hr) / (mm/hr) Intensity Rainfall 12345678 12345678 Time Period Time Period 2. Category 2: HS-LT (Spatially varied but temporally uniform) Rainfall Intensity / (mm/hr) Intensity Rainfall / (mm/hr) Intensity Rainfall 12345678 12345678 Time Period Time Period 3. Category 3: LS-HT (Spatially uniform but temporally varied) Rainfall Intensity / (mm/hr) / Intensity Rainfall (mm/hr) / Intensity Rainfall 12345678 12345678 Time Period Time Period 4. Category 4: LS-LT (Spatially and temporally uniform) Rainfall Intensity / (mm/hr) / Intensity Rainfall (mm/hr) / Intensity Rainfall 12345678 12345678 Time Period Time Period Figure 4-1: Hypothetical storm patterns represents different categories of storms according to their spatial and temporal heterogeneity. 73 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.2 Methodology Ground-based raingauge networks supply a reliable source of precipitation data used in statistical analyses associated with the development of rainfall models. For years various correlation and semi-variogram techniques have been used to evaluate both the temporal and spatial structure of rainfall events. Correlation techniques able to describe the structure and the motion of the storm events by measuring the association among the gauge records were used by Huff (1970), Sharon (1972), Felgate and Read (1975), Marshall (1980). Studies by Felgate and Read (1975) and Marshall (1980) were able to determine the spatial scale, mean lifetime, and velocity of rainfall cells. Investigation by Bastin and Gevers (1985) suggests that in situations where the random field is not necessarily stationary (where the data are so scarce and so scattered in space), the sample covariance function estimates are not so meaningful and therefore, an analytical parametric ‘variogram’ model is used in lieu of the covariance. Also, all of these studies using correlation techniques were not able to distinguish and differentiate the various individual storm events according to their spatial and temporal heterogeneity nature. Apart from correlation techniques, use of a semi-variogram model for two-dimensional (2-D) interpolation using a Kriging approach has been a common practice in different engineering applications in the fields of mining and hydrogeology. By its definition, a semi-variogram function has the capability of estimating the disassociation between measurements from the different gauge locations. In typical engineering applications such as in hydrology, the semi-variogram development has been applied to estimate the mean precipitation over a catchment by a Kriging model by Matheron (1971), Creutin and Obled (1982), Bastin et al. (1984), Guillermo et al. (1985) and Storm et al. (1989). 4.3 Semi-Variogram approach; Background and Theory In reality rainfall measurements are available only at a very limited number of locations, which are randomly scattered and not equi-spaced. This contrasts with 2-D estimation problems where the data points are numerous and located on a grid. The scarcity of the data requires the use of analytic variogram models and consequently the estimation of these models. 74 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Applications of semi-variograms have been numerous in geostatistics for some time; see for example, Journel and Huijbrechts (1978). In the past couple of decades, the theory has been further developed and applied to problems in hydrology by Gevers et al. (1980), Creutin and Obled (1982), Bastin and Gevers (1985), in solving 2-D rainfall interpolation problems using a Kriging technique. The Kriging technique itself was established by Krige (1951), and further developed by Matheron (1971, 1973) and Bastin et al. (1984). 1 2 N 3 i …………… j Figure 4-2: Data location randomly scattered in a 2D domain (Ω) We consider a real-valued Random Field (RF) Z in an (x,y) 2-D Cartesian space coordinate domain (Ω). The locations of the information available are scattered as shown in Figure 4-2. The RF from location ‘i’ denoted by Z(xi , yi ) and from ‘j’ by Z(x j , y j ) . Also the following functions are defined: • The mean (assumed stationary mean) m(x, y) = E{}Z(x, y) (4.1) • The Variance Var{}Z(x, y) = E{[]Z(x, y) − m 2 } (4.2) • The Variogram 75 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach γ = { − } 2 (i, j) Var Z(xi , yi ) Z(x j , y j ) (4.3) where γ (i, j) is the Semi-variogram and given by 1 γ (i, j) = E{}[Z(x , y ) − Z(x , y )]2 (4.4) 2 i i j j • The Covariance = { − − } Cov(i, j) E [Z(xi , yi ) m][Z(x j , y j ) m] (4.5) As particularly in the pioneering work of Matheron (1971) and consequently the work by Bastin and Gevers (1985) the present section follows in the line of Bastin and Gevers (1985), on the identification of two methods of the semi-variogram approach. Method 1 deals with stationary fields while method 2 deals with intrinsic fields. This section compares the two methods and summarises arguments to show that it is preferable to use Method 2 (Intrinsic field approach) in the adopted semi-variogram technique for the rainfall categorisation. 4.3.1.1 Stationary random field approach In addition to the stationary mean assumption, the covariance and semi-variogram are assumed isotropic [i.e. they are only a function of euclidean distance dij between the points (xi , yi ) and (x j , y j ) ] and the covariance is assumed to be stationary. In this case, σ ≈ σ = σ the RF variance is finite and stationary [i.e i j ] and the variogram is by definition, also stationary and related to the covariance as follows: γ = σ 2 − γ = γ (dij ) C(d ij ) where (i, j) (d ij ) (4.6) Similarly the above equation can be written again as γ * = − ρ (dij ) 1 (d ij ) (4.7) ρ where (dij ) is defined as correlation coefficient, which is given by Cov(i, j) ρ(d ) = (4.8) ij σ 2 76 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach and it is defined γ * (i, j ) as Standardised Semi-variogram, which can be related to as a negative correlation coefficient [Messaoud et al. (1990)] and is defined as γ (d ) γ * (d ) = ij (4.9) ij σ 2 Now by definition γ * = ρ = lim (dij ) 1 and lim (dij ) 0 (4.10) d →∞ d →∞ The variogram function and correlogram (Correlation coefficient plotted as a function of separation distance dij ) and their relationship when considering the RF as stationary, are illustrated in Figure 4-3. 77 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 1 * γ (d ij ) Variable Value ρ (d ij ) 0 Separation Distance Figure 4-3: Schematic representation of semi-variogram and correlogram for a stationary RF. 4.3.1.2 Intrinsic random field approach In addition to the stationary mean assumption, the variogram (but not necessarily the covariance) is assumed isotropic and stationary. In this case the RF variance can be infinite, and the variogram can become unbounded; γ = ∞ lim (dij ) (4.11) d →∞ Therefore, the Standardised Semi-variogram equation will be written as shown below γ * = γ * − ρ (dij ) lim (dij ) (dij ) (4.12) d →∞ Bastin and Gevers (1985) demonstrate that it is difficult to validate a stationarity assumption on the variogram. However, since a stationary variogram exists for a wider class of RF than a stationary covariance, it is always safer to adopt the method discussed in this section (method 2) in case of doubt. In other words it is always safer to keep the γ variogram stationary without any condition on lim (dij ) . d →∞ In dealing with random nature of rainfall processes and data availability on real catchments, the range of available distances is often too small to decide whether the variogram would reach a constant value for large dij . In the stationary case (method 1) 78 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach the variogram model would be chosen such that limγ (d) is bounded whereas, in non d →∞ stationary intrinsic RF, the variogram model would be chosen such that limγ (d) is d →∞ unbounded. The experimental variogram figures plotted on real events for different catchments shown in the subsequent sections clearly illustrate this point. Method 2 can be used in all cases where method 1 can be used, but the converse is not true. This makes method 2 makes it a wider class than method 1. 4.4 Identification of Spatial Variogram Model 4.4.1 Definition of Semi-Variogram () = When the temporal distribution of rainfall is denoted P t,Z i , with Z i (xi , yi ) i.e. the location and 't ' the index of the discrete sequence of ∆t -minute depths of rainfall over the ‘T' time intervals. Then the time-invariant estimates of the variogram in the form of a time average over the T time intervals for a particular a rainfall event (Random Field) is written by; T γ = 1 { − }2 (t, Zi , Z j ) ∑ P(t, Z i ) P(t, Z j ) (4.13) 2T t=1 γ Where (t, Zi , Z j ) is the semi-variogram as a function of dij the Euclidean distance between the locations i and j. It will be assumed in this study, that for any t the field P(t, Z) is γ = γ 1. Isotropic, i.e. (t, Z i , Z j ) (d ij ) ; and 2. Fulfils the intrinsic assumption which is a. the mean is space stationary (independent of Z ) b. the variances are not necessarily assumed to be equal to the field variance σ ()≠ σ ( ) ≠ σ Z i Z j It is possible that the variations of the semi-variograms between each event are amplified by differences between the mean rainfall intensity. More specifically, large γ values of (dij ) may be caused by higher rainfall intensities rather than by a truly larger 79 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach spatial variability. In order to avoid this situation a standardised semi-variogram γ * [)(dij ], is introduced with this semi-variogram and given by γ (d ) γ * (d ) = ij (4.14) ij σ ×σ i j 4.4.2 Motion of Storm Events A one-dimensional random variable, for example the temporal rainfall, is directly indicative of the relationship between two time series. Repeated computations for numerous time series reflect the structure of the rainstorm. In the case where the γ * variable is multi-dimensional, (for example the (dij ) calculations of space-time dimensions) the rainfall interpretation is not as simple. A hypothetical example shown in Figure 4-4 is considered to illustrate the tracking the movement of an event, which for example, may be caused by rain cell kinematics. The two time series shown in the figure may exhibit a strong positive dependency in one domain, spatial for example, but variations in the temporal domain can mask this γ * poor dependency or higher (dij ) values. Five graphs with the same base time series were assigned to two stations. This is representative of a moving storm cell whose structure is time invariant. The series at station 2 is then progressively lagged in time γ * γ * and (dij ) is computed. For this specific example (dij ) gradually increases from 0, 0.26, 0.64, 0.94 and 1.20 as the time lag increases from 0 to 4 respectively. Despite the series being identical in structure and showing a high spatial dependence, the time γ * differences result in higher (dij ) values. A similar result was obtained by May, et al. (1998), who showed negative correlations in nature by a similar illustration of time lagging. The illustration not only shows the variability in space and time of a moving rain cell but also demonstrates the ability of the semi-variogram methodology to track the various degrees of motion of the precipitation events. 80 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4 4 Lag = 0 Lag = 1 r* = 0 r* = 0.26 3 Station 1 Station 2 3 Station 1 Station 2 2 2 Let Station 1 and Station 2 time Variable Value series overlap Variable Value each other 1 1 0 0 0246810121402468101214 Time Period Time Period 4 4 Lag = 2 Lag = 3 r* = 0.64 r* = 0.94 3 3 Station 1 Station Station 2 Station 2 2 2 Variable Value Variable Variable ValueVariable 1 1 0 0 0 2 4 6 8 10121402468101214 Time Period Time Period 4 Lag = 4 r* = 1.20 3 Station 1 Station 2 2 Variable Value Variable 1 0 0 2 4 6 8 101214 Time Period Figure 4-4: Variation of spatial semi-variogram for lagged rainfall time series from two different gauge locations: lag = 0 and γ * = 0 ; lag=4 and γ * = 1.20 81 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.4.3 Estimation of event based parametric Variogram models Studies in the past have been able to identify yearly [Guillermo et al. (1985)], monthly [Bastin et al. (1984)] and daily semi-variograms [Storm et al. (1989)] in estimating the average annual, monthly and daily precipitation values respectively for catchments. Despite the fact that these studies in the past considered the seasonal trend when producing the yearly and monthly variograms, they did not take into account the potential spatially variable of different events within the long period considered. By contrast the present approach treats each event separately on their spatial process by identifying spatial event variograms for each event. In reality rainfall measurements are available only at a very limited number of locations, which are randomly scattered and not equi-spaced. This as previously mentioned contrasts with 2-D estimation problems where the data points are numerous and located on a grid. The scarcity of the data requires the use of analytic variogram models and estimation of these models. In modelling practice, semi-variograms describing the spatial structure of a function are formed by combining a small number of simple, mathematically acceptable expressions or models. Kitanidis (1993) lists Gaussian, Exponential and Spherical models as a few of the models accepted to represent stationary semi-variograms. In a similar manner, the Power, Linear and Logarithmic models are acceptable models to represent intrinsic non-stationary semi-variograms. The range of admissible parametric experimental variogram models is of course endless. However, the shape of the experimental variograms obtained from numerous practical applications in hydrology indicates that fairly simple power function models can be used, see for example Bastin et al. (1984), Guillermo and Salas (1985), and Storm and γ * Refsgaard (1989). (dij ) is kept as unbounded based on the non-stationary intrinsic assumption and adopted a simple power function to represent the developed event based γ * semi-variogram model for the study. Therefore, the (dij ) can be written as γ * ()= α β d ij dij (4.15) γ ( ) It is assumed that the semi-variogram t, zi , z j shown in Eq. 4.13 is time invariant during an event, but not necessarily from one event to another. Therefore, the theoretical variogram model is now written as 82 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach γ * ()= γ * = α() β ()s t, zi , z j (s,dij ) s dij (4.16) Where, s is the index of the event to which the ∆t -minute time increments t belongs, α is the scale factor and β is referred to as the shaping factor or spatial auto correlation factor. Combinations of both α and β define the function of the α() β ()s standardised semi-variograms for different events. In this study s dij is computed for each event by a least squares fitting procedure to all rainfall intensities with a 5- minute time step. 4.5 Identification of Temporal Semi-variogram At any point, in a watershed, the rainfall intensity may change during the time intervals. Different shapes of hyetographs are considered in the development of synthetic hyetographs, which often are developed using intensity-frequency-duration curves. In studies on demonstrating the influence on the hydrographs due to different temporal patterns of rainfall, Lambourne and Stephenson. (1987) simulated runoff peaks and volumes by considering design storms having rectangular, triangular and bimodal temporal distribution, Ball (1994) simulated the overland flow on planer surfaces by 10 different hypothetically designed patterns of rainfall excess. Therefore, a need is there to measure the degree of temporal uniformity of the rainfall intensity over the storm duration, in addition to identification of the spatial variability of the storm. The categorisation of the events based on the temporal variability, considered the events with rectangular distribution as low temporal heterogeneous (Uniform distribution) events and events with triangular distribution as high temporal heterogeneous events [as illustrated in Section 4.2]. Therefore, in order to measure how the amount of rainfall varies throughout their time intervals a semi-variogram was calculated as a function of time. The temporal variability analysis from the semi-variogram technique can be again treated in a similar way to the spatial variability analysis discussed previously. γ * () The auto semi-variogram function t k (similar to the auto correlation function) for the time lag k can be written as equation 4.17. Where T is the total number of five- minute time steps at each gauge record, and N is the number of gauges (5 minute records) utilised in the estimation. 83 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 2 1 N 1 T −k γ * ()k = []P(t, z ) − P(t + k, z ) (4.17) t ∑∑ − σ 2 i i N i=1 (T k) i t=1 γ * () The auto semi-variogram [ t k ] plotted against the different time lags, will clearly demonstrate how the storm varies along its temporal scale. When the temporal semi- variogram function rises rapidly towards the value of one after a few lags, it is an indication of small persistence or short memory in the time series, while a slow rise of the semi-variogram is an indication of large persistence or long memory. i.e a time series with a short memory can represents temporally more heterogeneous events where the time series with long memory represent temporally more homogeneous events. This basis will enable us to categorise the events according to their temporal heterogeneous nature in this study. Hypothetical storm events with the same time duration as shown in Figure 4-5, are employed to illustrate tracking of the temporal heterogeneity of events. Storm 1 is represented by a triangular shape temporal distribution in Figure 4-5, can be considered under the category of high temporal heterogeneous event compared to the storm event 2 represented by the rectangular temporal distribution. Storm 3 follows the similar pattern of storm 2, but with higher intensity values. 5 4 Storm 3 3 2 Variable Value Variable Storm 2 Storm 1 1 0 0 2 4 6 8 10 12 14 16 18 20 Time Period Figure 4-5: Temporal distributions of three hypothetical storm events. 84 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 2.0 Storm 1 (High temporal variability) 1.8 Storm 2 (Low temporal variability) 1.6 Storm 3 (Low temporal variability;Higher intensity than 2) 1.4 *(k)] t 1.2 1.0 0.8 Semi-Variogram [r 0.6 0.4 0.2 0.0 0 2 4 6 8 10 12 14 16 18 Time Step (5 Minute time lag) Figure 4-6: Typical semi-variogram plots for the different temporal nature of storm events, shown in Figure 4-5. 85 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-6 shows the corresponding temporal semi-variogram behaviour for the three storms shown in Figure 4-5. It can be seen that the semi-variogram representing Storm 1 has a higher variability or a lower dependency on the intensities in preceding time intervals. The Semi-variogram for storm 1 also has a shorter memory than the semi- variogram for storm 2. This indicates and confirms that storm 1 follows a non-uniform pattern where, storm 2 follows a more uniform temporal pattern. Storm 2 and Storm 3 were considered mainly to check whether similar time varying storm patterns with different magnitudes of rain intensity would produce patterns with similar variability. The similar semi-variogram patterns [shown in Figure 4-6] for the storm 2 and storm 3, indicates that the average intensity doesn’t influence significantly the defining of the temporal heterogeneity of events. 4.6 Application on UPRC 4.6.1 Spatial Semi-Variogram plots for UPRC The semi-variogram function has been computed for time series from every pair of raingauges within the UPRC hydrometric network of 14 gauges. The semi-variogram obtained was plotted against the separation distance of the corresponding gauge pairs in order to form a scatter plot known as a raw variogram for that event (for n gauges, there are n(n-1)/2 such pairs). A typical raw variogram computed for an event occurred on July 27, 1996 from UPRC is shown in Figure 4-7. The raw variogram takes the form of a somewhat extended cluster of scatter points. On the basis of many similar variograms computed for several real events from the catchments, UPRC [example shown in Figure 4-7] and CPC, and in line with common practice in geostatistical literature, we shall fit a very simple power function model [Refer Eq. 4.15] to form the experimental variogram. Note that other forms of theoretical variograms (such as the spherical model) could also be used. However, the following plotted variograms and their illustration clearly demonstrates the suitability of selection of the power function fit and the assumption of an intrinsic RF. 86 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-7: Scattered plot of raw variogram estimated for the storm event on July 27, 1996 for UPRC. Consider the events on July 27, 1996 (Event 4) and event on May 2, 1998 (Event 11) with almost the same average intensity of 3mm/hr. The cumulative rainfall patterns from the individual gauge records are shown in Figure 4-8 and Figure 4-10 respectively. The base duration of these two figures has been kept constant at 10 hours for purposes of the comparison. Using the cumulative rainfall patterns from the gauge records it can be clearly observed that Event 4 shows a lower spatial variability behaviour whereas Event 11 shows a higher spatial variability; the variation between the cumulative rainfall at different gauges during Event 4 is lower than the variation at different gauges during Event 11. For these two events different rainfall generation mechanisms were dominant; Event 4 was influenced by frontal system whereas Event 11 was dominated by a convective system. The scattered raw variogram and the computed power function experimental models for Events 4 and 11 are shown in Figure 4-9 and Figure 4-11 respectively. The plotted raw variograms shows the need of allowing an unlimited capacity for spatial dispersion. [i.e neither the priori variances nor the semi-variogram can be defined]. This again, clearly illustrates the suitability of assuming the intrinsic non-stationary RF approach (method 2) and the selection power function model in computing the experimental variogram. 87 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach The range of available distance is small to ascertain whether the variogram would reach a constant sill value. The plotted experimental variograms and the corresponding power function models are shown in Appendix B for the several events selected for the study. To highlight the non-suitability of the assumption of stationary RF approach (method 1) the spherical model fit is also compared with the power function fit in these figures. The semi-variogram plotted (shown in Figure 4-11) for an event of convective nature, which γ * can be considered as a high spatially variable event shows a much higher (dij ) γ * values. The most significant cause for these higher (dij ) values is due to the progressive spatial displacement of rain cells between the rain gauges. As the rainfall cell moves over the fixed hydrometric network, rain gauges collect rainfall from different positions within the cell. Figure 4-8: Cumulative rainfall patterns observed from the Gauges of UPRC network for the event on July 27, 1996. (more spatially uniform event compared to event in Figure 4-10) 88 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-9: Computed experimental semi-variogram model for the event on July 27, 1996 [Spherical model fit is plotted in dotted line with Power function fit for checking the validity of method 2 over 1] Figure 4-10: Cumulative rainfall patterns observed at the Gauges of UPRC for the event on May 2, 1998. (higher spatially heterogeneous event compared to the event in Figure 4-8) 89 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-11: Computed experimental semi-variogram model for the event on May 2, 1998. Spherical model fit is plotted in dotted line with Power function fit for comparison. 4.6.2 Space Characteristic Parameter ( as ) Almost all computed raw variogram plots from this study catchment indicates that the correlation between Z(i) and Z( j) disappears when the distance dij becomes too large. γ * Very often in practice, a distance has been defined as the range beyond which (dij ) can be considered to be equal to one, which represents the transition from the state where a spatial correlation exists to the state where there is absence of correlation [Journel et al. (1978)]. Based on the observed behaviour of the plotted experimental γ * semi-variograms of the study it is more appropriate to assume that, beyond (dij ) γ * value of one, the semivariogram is less stable (i.e assuming (dij ) =1 represents the γ * null correlation line). Then the separation distance corresponding to (dij ) value of one could be defined as the radius of influence which will be used as the spatial characteristic parameter ( as ) in defining the storm (‘ s ’ is the index representing each individual event) based on its spatial variability. The considered spatial parameter in the study therefore can be defined as the distance by which the storm cluster holds the spatial dependence or the distance by which more or less a stable spatial correlation 90 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach exists. The spatial characteristic parameter ‘ as ’ is derived from the power function γ * representation (from Eq 4.16, when (dij ) value has been equated to one) and is represented mathematically as. 1 β 1 s a = (4.18) s α s Referring to equation 4.16 the variograms were fitted by power function by the least square method for all considered storm events on UPRC. Thence, from the produced power function fits (the fitted alpha and beta values), the space characteristic parameter ‘ as ’ is estimated for all corresponding events. Based on the value of ‘ as ’ all the events were ranked and categorised from high to low spatially heterogeneous events. The fitted power function parametric models for six selected events are compared in Figure 4-12. The estimated parametric models for the complete list of events considered on UPRC are presented in Appendix B1. The relevant power function model parameters are tabulated in Appendix C1, for all 26 events of UPRC. Figure 4-12: Experimental semi-variogram plots for the six selected different spatially variable events for UPRC 91 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach The extent of storm structure relative to the extent of UPRC is considered in dividing the events into low and high spatially heterogeneous events. Once the spatial dependence dissipates within the catchment (diagonal extent of 20km for UPRC), those events are categorised as more non-uniform or higher spatial heterogeneous events. Whereas in the case of the null correlation occurring between points further apart to the extent of the catchment, those events are considered as more uniform or lower spatial heterogeneous events. Now consider the two events mentioned previously. The fitted model for Event 4 produced a radius of influence ( as ) of 21km which means the null spatial correlation could be reached only at a radius of 21km whereas the fitted model for Event 11 produced a radius of influence of 5.5km, which means null spatial correlation could be reached within a shorter distance. This results in, Event 4 and Event 11 holding the ranks of 11 and 25 (out of 26 events) respectively according to their corresponding space characteristic parameter ( as ) values. Consequently the categorisation list Event 4 under the lower spatial heterogeneous (‘LS’) category and Event 11 under the higher spatial heterogeneous (‘HS’) category. The spatial characteristic parameters ( as ), complete ranking and allocated categories on spatial dependence of all 26 events for UPRC are listed in Table 4-1. 92 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Table 4-1: Space and time parameters based on their degree of heterogeneity and the respective classification of events for UPRC. Stor Storm Date Space Ranking – Time Ranking- Category Charac. Spatial Charac. Temporal of Storm m ID Parameter Uniformity Parameter Uniformity / (km) / (5 min. 1a 02/01/1996 18.3 13 8 15 HS-HT 1b 06/01/1996 36.0 6 14 11 LS-HT 2a 11/04/1996 2.8 26 7 17 HS-HT 2b 11/04/1996 75.6 2 18 9 LS-HT 4 27/07/1996 21.1 11 53 4 LS-LT 5 30/08/1996 26.0 9 124 1 LS-LT 6 29/01/1997 62.6 4 53 4 LS-LT 7 07/10/1997 55.1 5 16 10 LS-HT 8a 24/01/1998 25.1 10 5 22 LS-HT 8b 25/01/1998 13.4 20 2 25 HS-HT 9a 09/04/1998 16.3 15 31 7 HS-LT 9b 10/4/1998 9.4 22 13 13 HS-HT 10 21/04/1998 138.0 1 68 2 LS-LT 11a 02/05/1998 5.5 25 6 19 HS-HT 11b 04/05/1998 19.9 12 56 3 LS-LT 12 18/05/1998 14.2 19 14 11 HS-HT 13 22/06/1998 67.7 3 7 17 LS-HT 20 01/04/1999 15.9 16 24 8 HS-LT 21 01/07/1999 28.1 8 12 14 LS-HT 22a 13/07/1999 10.7 21 5 22 HS-HT 22b 14/07/1999 8.1 23 6 19 HS-HT 23 16/09/1999 17.9 14 4 24 HS-HT 24 18/10/1999 32.4 7 8 15 LS-HT 25 23/10/1999 15.5 17 32 6 HS-LT 26a 09/12/1999 14.4 18 6 19 HS-HT 26b 09/12/1999 5.8 24 1 26 HS-HT 93 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.6.3 Impact of time step on spatial variability of rainfall fields Rainfall has a large intrinsic temporal variability especially during thunderstorms. The first and most important parameter to be fixed in this type of modelling problem is the selection of time scale at which the rainfall process is to be represented. Generally in urban sewer and stormwater system designs, the maximum time-step allowed for the rainfall data is 10 minutes in order to obtain an accurate calculation of peak discharge. As an empirical rule, the time-step must be considerably smaller than the concentration time of the system. Therefore, a five-minute time interval was adopted to temporally average the rainfall in order to more accurately model the rainfall in the time dimension. Since rainfall is a space-time phenomenon, it is natural to expect that the physical basis of spatial rainfall be linked to the space-time features of rainfall. Messaud et.al (1990), and May et al. (1998) demonstrated the influence and importance of selection of time interval ‘ ∆t ’over which the rainfall is averaged. They observed that the correlation coefficients and intercorrelation coefficients are much higher over periods greater than ten minutes. There is a need in this study to address the impact of the selected time scale on estimated spatial heterogeneity. The influence of ∆t in estimating the spatial variogram was tested with the variograms estimated with the rainfall records averaged over longer time interval. It was found that semi-variogram values are much lower after time-averaging of the rainfall data over a shorter time resolution (> 10 minute). In other words use of rainfall records averaging over higher time resolution data will under-predict the degree of heterogeneity of the rainfall in the analysis. An example of an experimental semi-variogram from gauge pair in the network plotted against the gauge distance is shown in Figure 4-13, for the event on July 27, 1996 (The event is represented by the gauge record patterns in Figure 4-8). In this figure the different symbols indicate the different time interval ∆t used in the computation of the semi-variogram values. 94 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-13: Spatial semi-variogram computed between rainfall time series recorded during the event on June 27, 1996 by all gauge pairs of UPRC network. [The different symbols refer to different time intervals] 4.6.4 Temporal Semi-variogram plots for UPRC Similar to the procedures explained in spatial semi-variogram estimation, the temporal semi-variogram was calculated for different time lags individually for all events. The semi-variogram was calculated for each gauge record and averaged over all fourteen gauges. The calculated average semi-variogram for a particular event was then plotted against the corresponding time lags in order to estimate the temporal semi-variogram corresponding to that event. 95 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Two events with different convective nature along time have been selected to illustrate the categorisation based on the temporal nature of the events. The recorded cumulative rainfall patterns from the gauges for the selected events, which occured on August 30, 1996 (Event 5) and on April 11, 1996 (Event 2b) are shown in Figure 4-14 and Figure 4-15 respectively. These two events have the same average intensity with this being 3.5mm/hr. Events were selected also so that both have similar degrees of spatial heterogeneity. i.e both the events are selected from ‘LS’ category . Figure 4-14: Cumulative rainfall patterns observed from the Gauges of UPRC network for the event on August 30, 1996. (more temporally uniform event compared to event in Figure 4-15) Figure 4-15: Cumulative rainfall patterns observed at the Gauges of UPRC for the event on April 11, 1996. (higher temporally heterogeneous event compared to the event in Figure 4-14) 96 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Typical semi-variogram patterns for these two events with four other pre-selected events from the whole bunch of twenty-six events are shown in Figure 4-16. 1.4 1.2 1 ] ) ij r*(d 0.8 0.6 Semi-variogram [ Semi-variogram 0.4 Event on Aug 30, 96 (5) Event on April 11, 96 (2b) Event on Jan 29, 97 (6) 0.2 Event on Apr 9, 98 (9) Event on May 4, 98 (11b) Event on May 2, 98 (11) 0 0 5 10 15 20 25 30 Time Lag (5Minute time lags) Figure 4-16: Typical temporal semi-variogram patterns for the six pre-selected events according to their degree of temporal variability, for UPRC 4.6.5 Time Characteristic parameter ( ts ) As demonstrated earlier in Section 4.4, high temporally varied events, such as a triangular shaped event, rapidly decay to the value of one after a few lags, while a slow decay of temporal semi-variogram indicates a more uniform temporal pattern events, such as rectangular shaped event. Therefore, the lower the number of time lags till a null correlation is observed between the rainfall field, the smaller the persistence. Similarly the greater the number of time lags, the larger the persistence. This suggests the number of time lags by which a null correlation is observed between rainfall records, as an indicator, which can be used to rank the events according to their variability along time. The idea identifies this indicator as the Time Characteristic Parameter (ts ). From the plotted temporal variograms for all events considered (six plots shown in Figure 4-16), the respective time characteristic parameter ts are estimated. Then the events are ranked according to the degree of their temporal variability (the highest temporal variability event is ranked 26 and temporally most uniform event is ranked 1). 97 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach The complete list of time characteristic parameter and detailed ranking of all events are included in Table 4-1. The constant gradient of the cumulative patterns of event (5) shown in Figure 4-14 indicates a uniform or a rectangular temporal pattern compared to relatively varying gradient (non uniform or bimodal temporal pattern) of the cumulative pattern of event (2b) shown in Figure 4-15. This varied temporal characteristic of the two events is well tracked from the corresponding modelled temporal variograms represented by the discontinuous lines in Figure 4-16. The pronounced long memory from the semi- variogram of event 5 results in a higher time characteristic parameter of 124, whereas the observed short memory from the semi-variogram of event 2b results in a lower time characteristic parameter of 18. These estimated values of ts from the plotted semi- variograms made event 5 and 2b to rank 1 and 9 respectively. (Rank 1 is for a more uniform temporal pattern where rank 26 is for a more non-uniform temporal pattern). These ranked events were categorised then into two categories namely low and high temporally heterogeneous events. A time characteristic parameter value of twenty (5- minute time lags) is used as the base line to separate the events to low (‘LT’) and high (‘HT’) variable events. The value of 20 time lags was adopted without any physical meaning from the analysis of the histogram patterns of several records from different gauges. In other words if the dependency (memory) of temporal semi-variogram starts to dissipate before hundred minutes in time then those events are categorised as High temporally variable events (HT). In similar manner if the time taken to lose its memory more than hundred minutes then those events are categorised as low temporally varied event (LT). Therefore from the example events, event 5 and 2b will be categorised under ‘LT’ and ‘HT’ categories respectively. A reasonable question is whether the estimated low temporal heterogeneous events (higher temporal characteristic parameter ts ) are influenced by the duration of the event. This will be not true fully, since the estimated temporal heterogeneity is based purely on the rainfall pattern regardless of the extent of the pattern. Events on April 9, 98 (Event 9) and on May 2, 98 can be taken as examples to illustrate this point. Event 9 is a shorter duration storm (6 hours) compared to the duration of Event 11 (7 hours). However, Event 9 shows a longer memory than Event 11 (shown in Figure 4-16). This 98 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach made Event 9 in to more lower (rank 7) in its temporal heterogeneity than the Event 11 (rank 19). 4.6.5.1 Impact of time steps on temporal variability of rainfall fields Similar to the analysis of different time-averaging of rainfall and its impact on the spatial semi-variogram, the impact of different time-averaging of rainfall on temporal semi-variogram is studied in this section. The influence of ∆t on estimating the temporal variogram is tested with the variograms estimated with the rainfall records averaged over shorter time intervals. It was found that semi-variogram values are almost similar for shorter time resolutions (< 10 minute) despite the time-averaging of the rainfall data over a lower time resolution (> 10 minute). In other words the estimated temporal heterogeneity of rainfall will be the same regardless of the time resolution over which the rainfall records are averaged. This result is illustrated well by the semi- variogram plotted in Figure 4-17 for the event on July 27, 1996 (Event 4). 1.4 1.2 ] 1 (t) * r 0.8 5 Minute 10 Minute 0.6 15 Minute Semi-Variogram [ Semi-Variogram 30 Minute 0.4 0.2 0 0 10203040506070 Time steps ( 5 Minute time lag steps) Figure 4-17: Temporal semi-variogram computed between rainfall time series recorded during the event on June 27, 1996 by all gauge pairs of UPRC network. [The different symbols refer to different time intervals] The experimental semi-variograms are plotted versus the distance between the corresponding gauges for the Event 4, which is represented by the gauge record patterns in Figure 4-8, previously. In this figure the different symbols indicate the different time interval ∆t used in the computation of the semi-variogram values. 99 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.6.6 Event categorisation in space and time for UPRC From the plotted spatial as well as temporal semi-variograms and the estimated spatial and temporal characteristic parameters, the selected 26 events were categorised as classified according to their spatial and temporal variability. Based on the space and time characteristic parameters, all the individual events were placed on the space-time frame. The placement of selected events for UPRC, according to their spatio-temporal heterogeneity is shown in Figure 4-18. The complete space and time characteristic parameters and the corresponding ranking based on their degree of heterogeneity are tabulated in Table 4-1. The table also shows the classification types of all events. Based on the calculated degree of heterogeneity in space and time for the events on UPRC there are 11, 7, 4 and 5 no of events, listed under the categories of HS-HT, LS- HT, HS-LT and LS-LT respectively. Figure 4-18: Placement of individual storm vents for UPRC, based on their degree of heterogeneity in space and time frame 100 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.7 Application on CPC 4.7.1 Spatial Semi-variogram plots for CPC The semi-variogram function has been computed for the time series from every pair of raingauges for the CPC hydrometric network of 6 gauges, similarly to the calculation of UPRC Data. The semi-variogram was plotted against the separation distance of the corresponding gauge pairs in order to form the raw variogram for a particular event. Examples of typical raw variograms and computed experimental variograms for events that occurred in January 29, 1997 and on April 22, 98 for CPC are shown in Figure 4-20 and Figure 4-22 respectively. Consider the event in January 29, 1997 (Event 1) and the event in April 22, 1998 (Event 3) had almost the same average intensity (intensity of 3.4mm/hr and 4mm/hr respectively). The cumulative patterns of the rainfall from the gauge records are shown in Figure 4-19 and Figure 4-21 respectively. It is observed that both the events have almost a similar low heterogeneous nature in time (LT category) but with a different degree of spatial heterogeneity. The base duration is kept constant for the both the figures (9 hours) for comparison. Based on the cumulative pattern from gauge records it can be observed that event 1 shows a lower spatial variability behaviour whereas a comparatively higher spatial variability is observed for the event 3 despite the similar convective nature of the events. The scattered raw variogram and the computed power function experimental models for event 1 and 3 shown in Figure 4-20 and Figure 4-22 respectively shows the tracking of the variation of heterogeneity of these events in space. The similar figures for the complete list of events for CPC are shown in Appendix B2. Similar to the analysis with UPRC events the raw variograms for CPC illustrates the need of allowing an unlimited capacity for spatial dispersion. [i.e neither their priori variances nor their semi- variogram can be defined]. This again clearly illustrates the suitability of assuming the intrinsic non-stationary RF approach (method 2) and the selection of power function type model in computing the experimental variogram. Especially for CPC, the range of available distance is too small to decide whether the variogram would reach a constant sill value. 101 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-19: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on Jan. 29, 1997. (more spatially uniform event compared to event shown in Figure 4-21) 1.8 1.6 Scattered Plot 1.4 Power Function fit ] ) ij 1.2 r*(d 1.0 0.8 Semi-Variogram [ Semi-Variogram 0.6 0.4 0.2 0.0 0 4 8 12 16 20 24 28 32 Separation Distance (dij) / (km) Figure 4-20: Computed raw and experimental semi-variogram model for the event on Jan 29, 1997 for CPC. 102 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-21: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on April 22, 1997. (Higher spatially heterogeneous event compared to event shown in Figure 4-19) 1.8 1.6 Scattered Plot Power function fit 1.4 ] ) ij 1.2 r*(d 1.0 0.8 Semi-Variogram [ 0.6 0.4 0.2 0.0 0 4 8 12 16 20 24 28 32 Separation Distance (dij) / (km) Figure 4-22: Computed raw and experimental semi-variogram model for the event on April 22, 1998 for CPC. 103 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.7.1.1 Space characteristic Parameter ( as ) for CPC Referring to Eq 4.16, the variograms were fitted by power function by the least square method for all considered storm events on CPC. Thence, from the produced power function fits (the fitted alpha and beta values) the space characteristic parameter ‘ as ’ is estimated for all corresponding events. Based on the value ‘ a’s all the events were ranked and categorised as high and low spatial heterogeneous events similar to analysis with UPRC events. The fitted models for six selected events are compared in Figure 4-23. The complete ranking and the assigned categories of 13 events from CPC are listed in Table 4-2. The relevant power function model parameters and space-time characteristic parameters are tabulated in Appendix C2, includes results from all 13 events for CPC. 104 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Table 4-2: Space and time parameters based on their degree of heterogeneity and the respective classification of events for CPC. Space Time Ranking – Ranking- Category Stor Storm Date Charac. Charac. Spatial Temporal of Storm m ID Parameter Parameter Uniformity Uniformity / (km) / (5 min. lag) 1 29/01/1997 30.6 2 27 1 LS-LT 2 11/02/1997 15.4 3 17 2 LS-LT 3 22/04/1998 6.3 7 17 2 HS-LT 4 04/05/1998 - 13 10 5 HS-HT 5 18/05/1998 6.6 6 6 8 HS-HT 6 16/06/1998 3.8 8 3 12 HS-HT 7 09/10/1998 1.6 12 4 11 HS-HT 8 19/10/1998 12.2 4 8 7 LS-HT 9 14/08/1999 8.0 5 11 4 LS-LT 10 18/10/1999 94.4 1 6 8 LS-HT 11 23/10/1999 2.5 10 10 5 HS-LT 12 08/11/1999 2.1 11 5 10 HS-HT 13 09/12/1999 2.9 9 2 13 HS-HT 105 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Figure 4-23: Experimental semi-variogram plots for the six selected different spatially variable events for CPC. CPC gauge network extent is considered in dividing the events as low and high spatial heterogeneous events. Once the spatial dependence dissipates within the extent of the study area (diagonal extent of 7.5km for CPC gauge network) then those events are categorised as more non-uniform or higher spatial heterogeneous events. In the case of null correlation occurring between points further apart to the extent of the catchment, the events considered are more uniform or lower spatial heterogeneous events. Now we consider the two events taken as example before. The fitted model for event 1 produces a radius of influence ( as ) of 30.6km (shown in Figure 4-20, Figure 4-23); which means the null spatial correlation could be reached only within the radius of 30.6km. Whereas the fitted model for event 3 produces a radius of influence of 6.3km (shown in Figure 4-22, Figure 4-23) which means the null spatial correlation could be reached within a shorter distance compared to the event 1. Similar to the ranking procedure with UPRC data, this results in event 1 and event 3 taking the ranks of 2 and 7 (out of 13 events) respectively according to their uniformity in space. Consequently this lists, event 1 under the low spatial heterogeneous (LS) category and event 3 under the higher spatial heterogeneous (HS) category. 106 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.7.2 Temporal Semi-variogram plots for CPC events Similarl to the procedure explained for UPRC events, temporal semi-variogram referred in Eq 4.18 is calculated for different time lags, individually for all events from CPC. Apparently the semi-variogram function has been computed for each gauge records and averaged over all six gauges from CPC network. The calculated average semi- variogram for the particular event then plotted against the corresponding time lags in order to estimate the temporal semi-variogram corresponding to that event. An event on May 18, 1998 with a bimodal (triangular and rectangular mode) time varying rainfall pattern is selected to illustrate the categorisation. The cumulative rainfall patterns of all six-gauge records for this event are shown in Figure 4-24. The selected event has the similar degree of spatial heterogeneity of the event (Event 3) shown previously in Figure 4-21 but with a different distribution along its time scale (more uniform rainfall pattern or a rectangular mode of time series). Figure 4-24: Cumulative rainfall patterns observed from the Gauges of CPC network for the event on May 18, 1998. (Higher Temporal heterogeneous event compared to event shown in Figure 4-21) Two of these events with different convective nature along time are selected to illustrate the categorisation based on their temporal heterogeneous nature. The storms with similar storm duration (8 hours) are selected [selected event on April 22, 98 (Event 3; shown in Figure 4-21) and event on April 11, 96 (Event 5; shown in Figure 4-24)]. 107 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach Events are also selected so that both have the similar degree of spatial heterogeneous nature. [i.e both the events are selected from High spatial heterogeneous category (HS)]. 4.7.2.1 Time Characteristic Parameter ( ts ) for CPC From the plotted temporal variograms for all considered events for CPC (six plots, including event 3 and event 5 are shown in Figure 4-23), the respective time characteristic parameter ts are estimated. Then the events are ranked according to the degree of their temporal variability, the highest temporal variability events ranked 13 and temporally the most uniform event ranked 1. The complete list of time characteristic parameter and detailed ranking of all events are given Table 4-2. The constant gradient of the cumulative patterns of event (3) shown in Figure 4-21 indicates a uniform or a rectangular temporal pattern compared to relatively varying gradient (non uniform or bimodal temporal pattern) of the cumulative pattern of event (5) shown in Figure 4-24. This varied temporal character of these two events is well tracked from the corresponding modelled temporal variograms represented by the dotted lines in Figure 4-25. The pronounced long memory from the semi-variogram of event 3 result a higher time characteristic parameter of 17, whereas the observed short memory from the semi-variogram of event 5 results a lower time characteristic parameter of 6. These estimated values of ts from the plotted semi-variograms made event 3 and 5 to rank 2 and 8 respectively. (rank 1 for more uniform temporal variability; rank 13 for more non-uniform temporal variability). 108 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 2 Event on Apr. 22, 98 (3) Event on May 4, 98 (4) 1.8 Event on Jan. 29, 97 (1) Event on Feb 11, 97 (2) 1.6 Event on May 18, 98 (5) Event on June 16, 98 (6) 1.4 ] r*(t) 1.2 1 0.8 Semi-Variogram [ Semi-Variogram 0.6 0.4 0.2 0 0 5 10 15 20 25 30 Time Lag (5Minute time lags) Figure 4-25: Typical temporal semi-variogram patterns for the six pre-selected events according to their degree of temporal variability, for CPC Similar to the base line value selected on UPRC events in categorising the events into low and high temporally heterogeneous events, time characteristic parameter value of twenty (5-minute time lags) is selected for the events on CPC. The values were changed during the investigation to a value more appropriate for the response time of the catchment. This was done based on the assumed space invariant assumption on the temporal heterogeneity nature of each event considered. This has been resulted the event on January 29, 97 (Event 1) under low temporally heterogeneous category (LT) and rest of the all twelve events under high temporally heterogeneous (HT) category. 4.7.3 Event Categorisation in space and time for CPC From the plotted spatial as well as temporal semi-variograms and the estimated spatial and temporal characteristic parameters, it was possible to categorise the selected 13 events similarly to the UPRC events. Based on the space and time characteristic parameters, all the individual events were placed on the space time frame, which scale the spatial and temporal heterogeneity of the rainfall regime respectively. The placement of selected events for CPC, according to their spatio-temporal heterogeneity is shown in Figure 4-26. The complete space and time characteristic parameters and the 109 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach corresponding ranking based on their degree of heterogeneity are tabulated in Table 4-2. The table also shows the classification types of all corresponding events. Based on the calculated degree of heterogeneity in space and time for the events on CPC there are 8, 4, 0 and 1 no of events, listed under the categories of HS-HT, LS-HT, HS-LT and LS-LT respectively. Figure 4-26: Placement of individual storm events for CPC, based on their degree of heterogeneity in space and time frame 110 Chapter 4 Estimation of Spatio-Temporal heterogeneity of rainfall: A Semi-Variogram approach 4.8 Conclusion Within this chapter, the following conclusions have been developed: A methodology for identification of storm events according to their degree of heterogeneity in space and time utilising real-time data has been proposed. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilized in introducing estimators to measure the degree of heterogeneity of each individual event in the spatial and temporal dimension. The proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. Also the application of this technique for the analysis of storm events occurring over Upper Parramatta River and Centennial Park urban catchments within the Sydney urban area were presented. From the estimated spatial and temporal characteristic parameters, all the individual events were placed on the space-time frame. As a result of the analysis, the storms were categorized as having ¾ High spatial and high temporal variability ¾ High spatial and low temporal variability ¾ Low spatial and high temporal variability, and ¾ Low spatial and low temporal variability. The importance and the application of this categorization of events on the selection and importance of more detailed rainfall models towards a more robust catchment modelling systems are well demonstrated in the subsequent Chapters. 111 CHAPTER 5 IMPLEMENTATION OF THE SPATIO-TEMPORAL RAINFALL MODEL 5.1 Introduction The measurement of rainfall during a storm event involves determining the time over which an increment of rainfall depth occurs at defined locations. Consequently the measurement of rainfall is a point measurement of a spatially variable parameter. Information, such as rainfall intensity, at locations other than the measurement locations is not defined by the measurement process and must be inferred from the information recorded at the measurement locations. Many factors affect the spatial distribution of rainfall on the ground and consequently rainfall varies spatially and temporally. The continuous representation of hydrologic process via spatial interpolation permits one to analyse the spatial patterns of variation of such a process. Since these spatial patterns are also constantly changing with time, and since such variability is crucial to modelling rainfall-runoff and flow forecasting [Krzysztofowicz, (1995)], hydrological modelling practice should attempt to consider the spatial and temporal variability of rainfall. Distribution of rainfall process in space and time towards the establishment of an accurate spatio-temporal rainfall model, has been implemented using hydroinformatic tool, particularly the Arc-Info Geographical Information Systems (GIS). The developed model can be an alternate rainfall model to traditionally used rainfall input models such as Thiessen Polygon model. Both visual and arithmetic techniques have been established to compare not only the spatial variability of total storm events but also the spatial variability during storm events. The comparisons have been made on various events from different categories based on their spatial and temporal variability as discussed in Chapter 4. The arithmetic comparisons were based on pixel scale, subcatchment scale, and the catchment scale, using both the total rainfall in the event and 5-minute incremental rainfall patterns. Finally, the variation of rainfall between alternate rainfall estimates has been quantified at the subcatchment scale. The main contributions presented in this chapter are 112 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model • Development of a spatio-temporal rainfall model for storm events, that considers not only the spatial variability of the total event but also the spatial variability during the event. From this model, improved estimates of the spatial distribution of rainfall, suited especially for urban catchments can obtained, along with small time-step hyetographs. • Quantitative assessment of rainfall estimates from the proposed model, and from the traditional Thiessen method are made at different spatial scales for the two study catchments (UPRC and CPC). 5.2 Methodology A detailed rainfall distribution model in space and time was developed, and implemented within the GIS framework. The enhanced rainfall representation in both space and time is made feasible by the aid of the powerful spatial analytic capability of GIS. The basis of this rainfall model is an extension of the rainfall model developed by Ball and Luk (1998) through a temporal discretisation of the storm event. Based on the rainfall recorded at pluviometers within and immediately adjacent to the catchment, the spatial variation of rainfall was ascertained at five-minute increments using the thin plate spline algorithm. Thin plate smoothing is widely used to spatially interpolate hydrological phenomena (such as rainfall and temperature) from point records [Hutchinson (1995), Ball and Luk (1998), Tsanis et.al. (2001)]. A recent study on an Australian catchment by Ball and Luk (1998) showed that thin plate spline smoothing can spatially interpolate rainfall more accurately than other methods (such as Thiessen, Kriging, and Inverse distance methods). However, Ball and Luk (1998) considered only the spatial variation in the total depth of rainfall during the storm event and not the spatial variation during the storm event. A GIS and in particular Arc/Info was used as the software base for implementation of the spatio/temporal rainfall model. In addition to providing basic modelling facilities Arc/Info provides a facility for programming the rainfall model through a macro programming language, Arc Macro Language (AML)[ESRI (1995)]. Use of this programming capability permitted sequencing of Arc/Info commands, which enabled easy repetition of the several operations involved in the creation of five-minute 113 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model incremental patterns of rainfall over the total catchment and the subsequent extraction of five-minute hyetographs for each of the subcatchments. A GIS module is developed to spatially incorporate rainfall data for any number of rain gauges in a geographical reference area. Input consists of rain gauge locations, storm rainfall data extracted for a particular time step (5-minute incremental data), and additional geographical features of the study area (Catchment and Subcatchment boundaries). The module output is in the form of a time series of rainfall intensity maps produced for the required spatial scale. The main objective of the method is to distribute the observed rainfall from the gauge records to a user defined spatial grid, and consequently, to extract the rainfall pattern for the required spatial scale. The methods involves extraction of data from a time series manager (HYDSYS) in Arc-Info format and consequently the development of macro's in Arc-Info Version 8.1.The method can be summarized as follows. 1 for each rainfall gauge, rainfall data is extracted from HYDSYS in an ASCII file. 2 The extracted data are appended and converted to an Arc-Info compatible format. 3 For each time step; o Rainfall data are loaded into Arc-Info and spatially linked to the locations of the gauges. o The spatial distribution of the rainfall intensity is interpolated using the thin-plate spline surface interpolation technique. o Mean rainfall over a subcatchment is determined using the intersection of the GIS layers containing the subcatchments and the spatial distribution of rainfall. 4 The subcatchment rainfall was extracted as time series hyetographs in ASCII format, which will enable to produce the rainfall input in the compatible format of the Catchment Modelling System to be used. 114 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model 5.3 Results and Discussion The developed spatial rainfall patterns for the two study catchments are visually compared for different degree of events. The extracted spatially distributed hyetographs with small time steps are then compared with traditionally used Thiessen rainfall estimates at different spatial scales (at catchment, subcatchment and grid scales) and temporal scales (for total rainfall and for the 5-minute rainfall). Finally, the differences between Thiessen rainfall estimates from spatially distributed estimates are ρ quantitatively assessed by the coefficient of variation ( s ) and the importance is highlighted for the different degree of spatially variable events. 5.3.1 Spatial Variability of Tot al Storm Events. Presented in Figure 5-1 to Figure 5-4 are comparisons of the spatial distribution of the total rainfall to visualise the spatial variability between events in total of its rainfall. Examples of different categories of events based on their spatial heterogeneity are presented in these figures. A spatial distribution pattern for an event categorised as HS- HT (Event on July 14, 1999) from the UPRC is given in Figure 5-1. The pattern is compared with an event categorised as LS-LT (Event on July 27, 1996) is presented in Figure 5-2. Despite the fact that the categorisation of events (as described in Chapter 4) is based on the spatial variability of five minute incremental values within the storm, the patterns created from the spatial variability of the total storm shows how the different events have the different degree of variability in space. Similar comparisons made with the events from CPC. Examples of patterns created from the high spatial variability (HS) event and a Low spatial variability (LS) event for CPC are given in Figure 5-3 and Figure 5-4 respectively. 115 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-1: Spatial distribution of total rainfall of an event categorised as ‘HS’ from Upper Parramatta River Catchment (Event on July 14, 1999). 116 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-2: Spatial distribution of total rainfall of an event categorised as ‘LS’ from Upper Parramatta River Catchment (Event on July 27, 1996). 117 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-3: Spatial distribution of total rainfall of an event catergoised as ‘HS’ from Centennial Park Catchment (Event on October 9, 1998). 118 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-4: Spatial distribution of total rainfall of an event categorised as ‘LS’ from Centennial Park Catchment (Event on October 19, 1998) 119 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model In addition the analysis is further extended to quantify the variability of the total rainfall from the developed spatial rainfall model and to validate the categorization made in Chapter 4. It is possible to determine the rainfall values for the centroid of each pixel within the catchment within the GIS. The spread of the total rainfall value estimated from each pixel show that the events categorised as ‘HS’ do follow a higher spread in their total whereas the ‘LS’ events have a lower spread. However, it was found also that a couple of ‘LS’ events have a high spread. This occurs because the categorisation technique discussed in Chapter 4 considered the spatial variability throughout the storm event while this statistic is based only on the total depth of storm event. It can be observed that these few ‘LS’ events have a high temporal variability. This indicates a high temporal variability of the event can cause a higher variability in the total event, despite the fact that the event has low spatial variability during the majority of the time steps considered. Ranges of the relative total rainfall values obtained for each storm event are presented in Appendix E for both the UPRC and CPC. 5.3.2 Spatial Variability during the storm event Two storm events, which occurred on 14 July 1999 (22b) and 27 July 1996 (4) were selected from UPRC to visualize the spatial distribution of rainfall as it varies with time. The spatial patterns from six five-minute increments are presented in Figure 5-5 and Figure 5-6 respectively. Figure 5-5 shows that event 22b, which was categorised as HS- HT, has a high variability in space throughout the storm duration, similar to the degree of variability in total storm, as shown in Figure 5-1. Figure 5-6 shows that event 4, which was categorised as LS-LT, has a low variability in space throughout the storm duration regardless of its magnitude of intensity. The analysis of total rainfall for this event also followed a similar degree of heterogeneity, as shown in Figure 5-2. Also it can be noted from Figure 5-5 and that the degree of the spatial variability of a high temporally varied event (22b) varies throughout its duration compared to a temporally more uniform event ( 4 ). 120 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-5: Series of rainfall distributions occurred in every five-minute interval for the event categorised as HS-HT from UPRC (Event on July 14, 99) 121 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-6: Series of rainfall distributions occurred in every five-minute interval for the event categorised as ‘LS-LT’ from UPRC (Event on July 27, 1996) 122 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model All these visual comparisons indicate that the degree of spatial variability over the catchment is substantial for events categorised as ‘HS’ and low for events categorised as ‘LS’. In the subsequent sections of this chapter these results will be further validated by statistical measures computed at catchment and subcatchment scales for both the total rainfall estimates and for the 5-minute rainfall estimate. In addition the variations in Thiessen rainfall estimates from the spline rainfall estimates will be quantified for events with different spatial and temporal variability. 5.3.3 Subcatchment Hyetograp h development Implementation of conceptual rainfall-runoff modelling systems requires a hyetograph of rainfall intensities versus time for the time of simulation. If multiple gauges exist within the catchment, multiple hyetographs for the catchment will be able to be used for the desired simulations. However, in most applications for small and medium sized urban catchments, only a single or a few rainfall patterns from gauge records are available within the catchment. Therefore, current modelling practice is that the rainfall patterns are assumed to be uniform within large areas and to represent several subcatchments. Shown in Figure 5-7 are rainfall cumulative hyetographs patterns for each of the twenty-nine subcatchments as developed for the four events out of the selected events for the UPRC. The events are selected to represent each category of heterogeneous nature. The events on 22 June 1998 (13) and 14 July 1999 (22b), which are ‘LS-HT’ and ‘HS-HT’ respectively, are compared together. These two events have relatively similar average intensity of rainfall for the same duration (6 hours) of time. Similarly the events occurred on 27 July 96 (4) and 18 May 1998 (12), which are categorised as ‘LS-LT’ and ‘HS-HT’ respectively are compared together. It should be noted that the total duration has been kept constant at 12 hours for these two events for comparison purposes. 123 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model 60 60 Storm 22b; Event on July 14, 1999 Storm 13; Event on June 22, 1998 50 50 'HS-HT' ) ) 40 'LS-HT' 40 30 30 20 20 Cumulative Rainfall / (mm Rainfall Cumulative Cumulative Rainfall / (mm Rainfall Cumulative 10 10 0 0 1 112131415161 1 112131415161 5-Minute Time Increments 5-Minute Time Increments 60 60 Storm 4; Event on July 27, 1996 Storm 12; Event on May 18, 1998 50 50 ) ) 'LS-LT' 'HS-LT' 40 40 30 30 20 20 Cumulative Rainfall / (mm Rainfall Cumulative Cumulative Rainfall / (mm Rainfall Cumulative 10 10 0 0 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 5-Minute Time Increments 5-Minute Time Increments Figure 5-7: Cumulative hyetograph patterns from the developed spatial model for the selected four events (from each classification) from UPRC (Shown for 29 subcatchments) Use of a spatially variable rainfall model (at subcatchment scale) with spatially more uniform (‘LS’) events resulted in similar hyetograph patterns for all subcatchments. Use of this model with the spatially more variable (‘HS’) events resulted in a high variation of rainfall (approximately 30mm for event 22b and 25mm for event 12) over the catchment. This result is further illustrated by the Figure 5-8, where boxplots are used to show the variation in subcatchment based total rainfall from the average total rainfall of the catchment. The boxplots, as used here, consist of a line in the middle of the box denoting the 50% quantile (median), the edges of the box 25% and 75% quantiles, and whiskers that extend to the 10% and 90% quantiles of the estimated rainfall values. The box plots in Figure 5-8 indicate the distribution of the estimated subcatchment rainfall values for the various events with different degrees of heterogeneity. The ten events presented in Figure 5-8 are ordered according to their spatial variability nature (ranking of the events according to their degree of spatial variability as categorised in the previous Chapter are also given in the brackets). The box plots indicate that the 124 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model variation between the predicted subcatchment total rainfall at different parts of the catchments are higher for the events categorised as ‘HS’ events. However, in few events similar to Event 13 (ranked 3 in Figure 5-8) shows relatively a little higher variation in subcatchment total despite the fact that they follow a more uniform pattern during the majority of the time of its occurrence. Figure 5-8: Boxplots of Subcatchment Rainfall estimation by the developed model for ten events for UPRC. Events are ordered according to their spatial variability. The figures demonstrate the role of multiple hyetographs to more adequately describe a storm event, especially for ‘HS’ events. Furthermore, the rainfall hyetographs for each subcatchment have been shown to enable consideration of the spatial variability in rainfall patterns during the different events. The rainfall hyetographs suggest a ±10% variation in the subcatchment values from the catchment average assumption for ‘LS’ events whereas the variation can be up to ± 50% for ‘HS’ events. 125 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Similar to the development of individual subcatchment hyetographs of the events from UPRC, the patterns have been created for the 42 subcatchments of CPC for the selected events. The cumulative mass curves for the events occurred on 19 October, 1998 (Event 8; classified as ‘LS’) and 9 October, 1998 (Event 7; classified as ‘HS’), are presented in Figure 5-9. Figure 5-9: Cumulative hyetograph patterns from the developed spline model for a ‘LS’ event and a ‘HS’ event from CPC (Shown for 42 subcatchments) The figure highlights the variation of 42 hyetographs developed for each of the subcatchments of CPC. Similar to the box plots shown for UPRC, the box plots are presented in Figure 5-10 for CPC events to show the total impact of the use of a catchment average rainfall input instead of a distributed rainfall input. 126 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model 1.6 1.4 1.2 1.0 0.8 0.6 Subcatchment Total / Mean Total 0.4 0.2 ) ) ) ) ) ) ) ) k 4 k 6 k 7 k 8 k 9 10 11 12 an an an an an nk nk nk (r (r (r (r (r ra a ra 8 5 3 6 13 ( (R 7 ( rm rm rm rm 11 12 to to to to rm m m rm S S S S to or or to S St St S Figure 5-10: Boxplots of Subcatchment Rainfall estimated by the developed spline model for eight events from CPC. Events are ordered according to their spatial variability. The boxplots in Figure 5-10 indicate the range and distribution of the estimated subcatchment total rainfall values for the selected 8 events ordered according to their spatial variability. The results from CPC suggest a ± 8% variation in total for ‘LS’ events whereas the variation can be upto ± 30% for ‘HS’ events, when assuming a single hyetograph assumption instead of a spatially distributed rainfall model. The analysis demonstrates the importance of the need of multiple hyetographs on the different types of storm events utilized in the analysis. Furthermore, the rainfall hyetographs for each subcatchment has been shown to enable consideration of the spatial variability in rainfall patterns during the different events. 5.3.4 Comparison of developed spline model with the traditional Thiessen polygon approach. Despite recognition of the importance of the spatial and temporal variability of rainfall in the past decade, simple traditional methods (for example, Thiessen method) are used regularly in the implementation of the numerical simulation of catchment processes. A need exists therefore for the analysis of traditional methods and the enhanced techniques based on the application of hydroinformatic tools. The purpose of this section is to 127 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model evaluate the spline surface continuous rainfall estimate over a high-resolution grid spacing (100m by 100m for UPRC and 25m by 25m for CPC) and over a high- resolution temporal scale (5-minute) and to compare it to the traditional Thiessen polygon approach. These investigations are important since they will show the difference quantitatively between the developed spline rainfall estimates and the estimates that are currently in use, and consequently highlight the importance of more detailed rainfall models as input to Catchment Modelling Systems. In order to assimilate some of the characteristics of spatially varying rainfall, comparisons have been performed between the obtained spatially continuous rainfall estimates by spline method and the traditionally used Thiessen rainfall estimates. The Thiessen weighting technique, consists of determining the boundary about each gauging station that is halfway between it and surrounding stations. This boundary forms a polygon about the station and the area enclosed by the polygon is taken as the area of influence about the station. As presented by Thiessen (1911), the intersection of this area with the subbasin area determines the station assigned to that particular subcatchment, with the assumption that the best estimate of rainfall on that subcatchment is represented by the point measurement at the gauge. When the modeller is interested in estimating runoff for a particular basin, the raingauge, basin boundaries and Thiessen polygons remained fixed in position regardless of the storm. If the spline surface continuous function is used, the rainfall patterns over the basin are different for each storm. As the basis of the model is the geometry of the catchment, implementation of Thiessen polygons within a GIS environment is not difficult. The implemented Thiessen polygons based on the geometry of the catchment and the gauge network arrangement of UPRC and CPC are shown in Figure 5-11 and Figure 5-12 respectively. 128 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-11: Thiessen Polygons for the UPRC with respect to the 29 subcatchment boundaries It should be noted that the Thiessen diagram for CPC with it’s gauge network as shown in Figure 5-12 indicates that two gauges (Waverley and Musgrave Avenue gauges) within the catchment are important in determining the rainfall estimates for the catchment. However, due to the availability of data, single gauge records from the Waverely gauge was applied as the Thiessen estimate for the CPC catchment by Abustan (1997) previously. After Abustan (1997) the present study also applied the Thiessen rainfall in the similar way whereas the rest of the gauge records have been utilized in the implementation of estimating the continuous rainfall pattern by spline surface technique. 129 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-12: Thiessen Polygons for the CPC with respect to the 42 subcatchment boundaries. 130 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model 5.3.4.1 Comparisons for the UPRC. 5.3.4.1.1 Effect on total rainfall at catchment scale The average areal rainfall depth is often the input parameter for some of the hydrologic studies, such as water balance on watershed and different methods have been proposed to estimate the average areal rainfall of a catchment regularly [Balascio (2001)]. However, when the concern is towards modelling the catchment for water quantity and quality, accurate spatio-temporal rainfall pattern is the interest in calibration, validation and extrapolation of events, which is the great interest of the present study. The relative importance of the areal average rainfall for urban catchments estimated by two different methods was assessed in this section. The representative uniform catchment average rainfall is estimated by both the Thiessen method and the spline method for the UPRC events. Shown in Figure 5-13 are the total rainfall estimates for the entire catchment by both methods for 26 storm events. Figure 5-13: Comparison of predicted total rainfall (for the overall catchment) of events from UPRC by the developed Spline model and the Thiessen Model 131 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model The pattern indicates that there won't be substantial variation in estimating the catchment average rainfall by any method if the gauges are evenly distributed within the catchment, similar to UPRC gauge network. The results therefore, indicate that the selection for a method for the estimation of areal average rainfall depth for a catchment with an evenly distributed gauge network is not that important. 5.3.4.1.2 Effect on total rainfall at subcatchment scale The importance of estimation of the average rainfall estimate by different methods at subcatchment scale was the assessed in this subsection. Estimated representative subcatchment rainfall in total by both the Thiessen method and the developed spline method are compared. The comparison for the event occurred on 27, July 1996 (Event 4), which is categorized as ‘LS-LT’ is shown in Figure 5-14. The figure shows that the estimation of average rainfall at subcatchment scale is relatively similar from both the methods considered for the selected uniform events. Figure 5-14: Comparison of predicted subcatchment total rainfall for the ‘LS-LT’ event occurred on 27 July 1996 from UPRC, for each of the 29 subcatchments 132 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Shown in Figure 5-15 is the comparison for the event occurred on 14, July 1999 (Event 22b), which is categorized as ‘HS-HT’. The comparison suggests that the estimation of average rainfall at subcatchment scale for high variable events are substantially different and has a high variability within subcatchments. Figure 5-15: Comparison of predicted subcatchment total rainfall for the ‘HS-HT’ event occurred on 14 July 1999 from UPRC, for each of the 29 subcatchments 5.3.4.1.3 Evaluation on spatio-temporal variability during an event The rainfall variation for traditionally used Thiessen approach from developed spatial rainfall model for 5-minute temporal data has been evaluated on the line of fictitious point method (cross-validation) used by Delhome (1978), Seaman (1983) and Dirks et. al. (1998). Similar to the error calculation for different rainfall estimate methods, the variation of rainfall from two different methods is compared by the root-mean squared σ variation, s calculated for each and every subcatchment rainfall series and given by N − 2 ∑(rsi rti ) σ = i=1 (5.1) s N 133 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model where rsi is the estimated spline rainfall and rti is the estimated Thiessen rainfall at the‘i th time step ; N is the total number of 5-minute time increments for the particular ρ event. The coefficient of variation s is then defined by σ ρ = s (5.2) s 1 N ∑ rci N i=1 th where rci is the catchment average rainfall at i time step estimated by the spline ρ method. s is used to compare the variation of rainfall by traditional approach from the proposed approach for different storm events regardless of their varying magnitude. The 5-minute rainfall patterns estimated by both the Thiessen method and spline method were treated separately for each subcatchment. Results from each time step for each ρ subcatchment were averaged to estimate s values for all subcatchments in the catchment. ρ Presented in Figure 5-16 are plots of s for the UPRC subcatchments grouped for different classified events. The solid line in the middle of the box plots is the median (50% quantile) value. The two lines form an envelope of ± 25% quantile deviation from the median, and the whiskers extend to the 10% and 90% quantiles of the estimated ρ s values. The figure shows that the amount of variation in Thiessen rainfall from the distributed spline rainfall is substantial and varies considerably more within the subcatchments for classified ‘HS’ events than the ‘LS’ events. ρ The average s function calculated for all 29 subcatchments of UPRC are detailed in ρ Table E-3 of Appendix E. The table summarises the statistics of s for the four categories of events based on their spatial and temporal heterogeneity. The salient points of Table E-3 are summarized in Table 5-1. The salient points are averaged from events listed under each category. Dirks et.al. (1998) compared four interpolation methods using rainfall data from a network of thirteen raingauges on Norfolk Island, New Zealand (area 35km2). They calculated the error, which is defined by coefficient of variation for different integration times (for three years of data). The result suggests that the error coefficient decreases 134 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model substantially with increasing integration time and the error coefficient for Thiessen interpolation estimates for hourly totals is approximately 0.7. The presented values from Table 5-1 show that the coefficient of variation (variation of the Thiessen estimate from the developed spline estimate) for 5-minute total increases substantially with increasing ρ variability of events in space and time. The s values ranged from 0.16 to 0.86 with an average value of approximately 0.4 for ‘LS’ events and ranged from 0.27 to 2.1 with an ρ average of 0.94 for ‘HS’ events. Despite a small variation in s values on temporally different events with similar spatial variability events, they are not substantial as the degree of spatial variability events. ρ Figure 5-16: Box-plots of s calculated from each of the 29 subcatchments of UPRC ; Events grouped according to their spatial variability. 135 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model ρ Table 5-1: Comparison summary of coefficient of variation ( s ) from 29 subcatchments of UPRC for different classification of events Coefficient of Variation (ρ ) Storm s Category Minimum Maximum Median Mean Std. Dev. LS-LT 0.16 0.75 0.39 0.40 0.15 LS-HT 0.14 0.86 0.41 0.42 0.19 HS-LT 0.27 1.74 0.85 0.89 0.38 HS-HT 0.34 2.08 0.84 0.94 0.45 5.3.4.2 Comparisons for the CPC Unlike the gauge network for UPRC, the network of CPC consists of a single gauge within the catchment and five other gauges adjacent to the catchment. Previous catchment studies assume the single gauge record (at Waverely gauge) is the representative rainfall pattern for the entire catchment. However, the present study incorporated the gauges adjacent to the catchment to produce continuous rainfall patterns by a spline surface method and consequently multiple spatial rainfall patterns have been used in representing the rainfall within the catchment. The subsequent sections analyse the variation of the rainfall amounts considered by a single gauge assumption from the spatially distributed rainfall pattern. 5.3.4.2.1 Effect on total rainfall at catchment scale Firstly the total rainfall is estimated for the catchment as a whole, by both approaches for selected events. Results are presented in Figure 5-17. Unlike the results in UPRC, the single gauge assumption by Thiessen approach generally over predicted the amount of rainfall compared to the amount of rainfall estimated by the developed spline model. The slight variation in the behaviour from CPC is mainly caused by the location of the gauge assumed in Thiessen estimate for CPC. This may be because the assumed single gauge is not located at the centroid of the catchment or the gauge was not located at the point where rainfall analogous to the catchment average occured. 136 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-17: Comparison of predicted total rainfall (for the overall catchment) of events from CPC by the developed Spline model and the Thiessen Model 5.3.4.2.2 Effect on total rainfall at subcatchment scale Secondly the amount of rainfall is considered at subcatchment scale. Amount of rainfall from each subcatchment by the assumed uniform rainfall pattern is then compared with the total rainfall estimated for the each subcatchment by the developed spline rainfall model. Shown in Figure 5-18 are the variations of Thiessen rainfall amounts from the developed spline rainfall amounts for the selected events in a box plot format (based on all forty-two subcatchments of CPC). The figure shows that the variation in total rainfall by a single gauge assumption from the developed spline estimation is substantial and the single gauge assumption leads to an over prediction at majority of the subcatchments for CPC. 137 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model Figure 5-18: Comparison of distributions of predicted subcatchment total rainfall and variation from the subcatchment Thiessen total for the various events on CPC 5.3.4.2.3 Evaluation of of spatio-temporal variability during an event Similar to the approach illustrated in 5.3.4.1.3 for UPRC the variation of rainfall between the traditionally used Thiessen approach and the developed spatio-temporal rainfall model for 5-minute temporal data from CPC has been evaluated. Presented in ρ Figure 5-19 are the distributions of s values estimated for the 42 subcatchments of CPC for the selected events. The Low and High spatially variable events are grouped ρ together. The summary of the s values for all the selected events is tabulated in Table E5 of Appendix E and the salient points are presented in Table 5-2. ρ Figure 5-19 shows that CPC gives similar s results to UPRC, for ‘LS’ and “HS’ ρ grouped events. However, compared to the variation of s for ‘LS’ classification events for CPC are considerably substantial compared to the ‘LS’ events from UPRC. This is linked to the single gauge assumption for the entire catchment. It should also be noted 138 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model that the uniformity of the storm event from CPC is considered at a larger scale than the size of the catchment. The presented values in Table 5-2 also show that the coefficient of variation (of Thiessen estimate from the developed spline estimate) for 5-minute rainfall increases ρ substantially with increasing variability of events in space and time. The s values ranged from 0.07 to 1.1 with the average value of approximately 0.6 for Low spatially variable events and ranged from 0.10 to 2.0 with an average of approximately 1.1 for ‘HS’ events. As mentioned before, since, the majority of selected events from CPC falls under higher temporal category it’s hard to generalize the conclusions to track the variation with the degree of temporal variability. ρ Figure 5-19: Box-plots of s calculated from each of the 42 subcatchments of CPC ; Events grouped according to their spatial variability. 139 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model ρ Table 5-2: Comparison summary of coefficient of variation ( s ) from 42 subcatchments of CPC for different classification of events Coefficient of Variation (ρ ) Storm s Category Low High Median Mean Std. Dev. LS-LT 0.07 0.98 0.51 0.52 0.29 LS-HT 0.08 1.35 0.80 0.75 0.42 HS-LT 0.06 1.19 0.62 0.62 0.35 HS-HT 0.12 2.24 1.28 1.22 0.69 5.4 Conclusions Within this chapter, the following conclusions have been developed: A spatio-temporal rainfall distribution model was developed within GIS to transform point rainfall measurements to a spatially distributed rainfall over the catchments at small time-steps. The enhanced rainfall representation in both space and time is made feasible by the aid of the powerful spatial analytic capability of GIS. The basis of this rainfall model is an extension of the rainfall model developed by Ball and Luk (1998) through a temporal discretisation of the storm event. From this model, improved estimates of the spatial distribution with small time step hyetographs can be obtained, which are suited especially for modelling urban catchments. Analysis was performed to assess the difference between rainfall estimates obtained from traditionally used methods (such as Thiessen method) and estimates obtained from the proposed method. The differences were small when considered for the catchment as whole. However, the differences in estimates were significant at the subcatchment scale. The difference significantly increases with the degree of heterogeneity of the events in space and time. The variation between of 5-minute rainfall estimated by Thiessen method from 5-minute rainfall estimated by the proposed method was assessed by the 140 Chapter 5 Implementation of the Spatio-Temporal Rainfall Model ρ introduction of coefficient of variation ( s ). The results suggest that an average of 90% variation can occur between the Thiessen estimate and the proposed spatially distributed spline estimate for ‘HS-HT’ type events on some extreme subcatchments. This variation can go upto an average of 30% on some extreme subcatchments for ‘LS-LT’ type events. The variation between rainfall estimated by the Thiessen method and rainfall estimated by proposed spatially distributed spline method is substantial for highly variable events compared to the low variable events for the UPRC catchment which has an evenly distributed gauge network. However, the variation in the rainfall estimates is more serious for the CPC catchment, which assumes a single rainfall pattern under the Thiessen approach. 141 CHAPTER 6 INFLUENCE ON CATCHMENT RESPONSE TO RAINFALL 6.1 Introduction Management of stormwater runoff from a quantitative and qualitative perspective is a complex task. Information for this task is available from catchment monitoring and from catchment simulation with the latter source increasing in importance since the development of the digital computer. These catchment simulations are based on the catchment modelling systems, which comprise numerous mathematical models of the processes influencing the response of the catchment to storm events and dry periods between storm events. Since a deterministic approach is generally employed, the predicted response of a catchment modelling system will reflect the input data and the process models used for the simulation. Having ascertained the likely variation of estimated rainfall at a subcatchment scale induced by the spatial variation in rainfall demonstrated in previous chapter, it remains to consider the influence of the spatial pattern of the rainfall on a catchment scale. These influences were ascertained by considering rainfall hyetographs determined for the 5- minute time increments for each subcatchment within the catchment. Presented in this chapter are the results from the calibration, validation and extrapolation to different hydrologic events for the test catchments. The results are also of an investigation into the influence of alternative spatial and temporal rainfall models on the robustness of predictions obtained for the test catchments in Sydney, Australia. Before analysis of the calibration, validation and extrapolation of events through a catchment modelling system, it is better to analyse the sensitivity of rainfall-runoff prediction by considering only the observed volume of rainfall and runoff of these catchments. This will lead towards getting a picture of the rainfall observation for the categorised various degree of events, with the absence of a model structure with several assumptions and limitations. 142 Chapter 6 Influence on Catchment Response to Rainfall 6.2 Observed Rainfall and Runoff Hydrograph Volumes It has been argued in the dissertation that research should be focused towards the need to find the spatial distribution of the rainfall throughout the storm event rather than the estimation of the global volume of rainfall falling on the catchment. However, the average rainfall over the catchment is still an important factor for a number of applications in hydrology. Therefore, this section analyses the importance of the catchment average precipitation accuracy on tracking of rainfall-runoff behaviour prior to testing the rainfall redistribution through a CMS. Firstly, the sensitivity of average precipitation accuracy for the different categorised events in space and time dimension has been tested with specific attention given to the volume of observed storm runoff in this section. The observed volume depths are plotted with the total precipitation depth calculated based on the traditional Thiessen approach, to investigate the importance of the need of reasonably perfect rainfall model for different degree of heterogeneous events. Throughout Australia, there are strong regional differences in hydrological response to landscape and climate. However, in general terms, in Australian catchments the flows are typically more peaked, the base flows are of lower proportion, the runoff coefficients are smaller, and the dry periods are longer and more variable, than in the European and North American catchments. Example runoff hydrographs for selected events from the two test catchments UPRC and CPC from Sydney region are shown in Figure 6-1 and Figure 6-2 respectively. The selected 26 events of UPRC produced peak flows ranging from 13 m3/s to 213 m3/s. The highest peak discharge of 213 m3/s (1.81m stage height) was recorded on August 30, 1996. The hydrograph volume ranged from 146 Megaliters to 3000 Megaliters. The time to peak varied from two hours to twenty hours. A typical flood characteristic observed at the UPRC outlet on April 1, 1999 is shown in Figure 6-1 with the 5-minute rainfall hyetograph calculated by the Thiessen method plotted along the secondary ‘X’ axis. The floods had a relatively high velocity of runoff and mainly contributed by the surface runoff (Figure 6-1). 143 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-1: Typical Rainfall-Runoff behaviour for the UPRC with the Observed flow at the catchment outlet for the event occurred on April 01, 1999 Unlike the UPRC flood events the selected hydrographs of 13 events from CPC produced peaks ranged from 0.5 m3/s to 7.1 m3/s. The highest peak discharge of 7.1 m3/s (0.78m stage height) recorded on January 29, 1997. The hydrograph volume ranged from 1.9 Megaliters to 27 Megaliters. The time to peak varied from 60 minutes to several twelve hours. A typical flood characteristic observed at CPC outlet on February 11, 1997 is shown in Figure 6-2 with the 5-minute rainfall hyetograph calculated by the Thiessen method plotted along the secondary ‘X’ axis. The floods from CPC also had a relatively high velocity profile and a lower proportion of base flow. 144 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-2: Typical Rainfall-Runoff behaviour for the CPC with the Observed flow at the catchment outlet for the event occurred on Feb 11, 1997 6.3 Behaviour of rainfall a nd runoff depths In urban catchments, runoff comes from the impervious surfaces, which are connected to the drainage system, often called the effective impervious area. In some comparatively larger storm situations, runoff may also come from pervious surfaces, or from impervious surfaces which are not directly connected and where part of the flow path is over pervious surfaces. The total storm runoff therefore can be considered to consist of an impervious contribution, which is present for all storms, plus a pervious contribution, which is sometimes present depending on the condition of pervious surfaces. The storm events selected for UPRC and CPC for the present study are able to produce runoff from both impervious and pervious area, since the total depth of rainfall events selected are relatively larger than the initial loss of those corresponding catchments. The slope of the straight line plotted with the runoff depth versus the total storm rainfall depth gives the percentage of effective impervious areas of the basin. And the intercept of this straight line on the rainfall axis gives the initial loss, which must be satisfied before runoff occurs. [Huber et. al. (1988), Boyd et. al. (1993), Boyd et.al. (1994), Zaman and Ball (1994), Perrin et. al. (2001)]. 145 Chapter 6 Influence on Catchment Response to Rainfall The study by Boyd et.al (1993), examined the rainfall and runoff depths for 763 storms on 26 urban basins located in 12 countries. The authors found majority of the Australian catchments had significant amounts of runoff from impervious as well as pervious surfaces. The data plotted in the study are closed to straight line on all basins and indicated that the effective impervious areas remained constant for all storm sizes. The data plot has been used to estimate the effective impervious area and the initial losses. A similar approach is used by Zaman and Ball (1994) to estimate the impervious fraction and the depression storage for Upper Salt Pan Creek catchment, which is also within the Sydney region. The authors compared the estimated impervious fraction (40.5%) with the calculated fraction (39.3%), which is obtained by weighting the impervious fraction for each landuse by the proportion of the subcatchment with that land use. 6.3.1 At UPRC Outlet For the selected events from UPRC the observed runoff depths (from the observed hydrographs at UPRC outlet) are plotted against the Thiessen average rainfall of all corresponding events. Thence, the linear rainfall-runoff behaviour is plotted as a straight line from the known parameters of UPRC (percentage of imperviousness of 30% and from the initial loss) as shown in Figure 6-3. The values are obtained from the RAFTS rainfall-runoff model of UPRC developed by Upper Parramatta River Catchment Trust (1997). The complete rainfall depths and corresponding observed flow depth of the events selected are tabulated in Table G.1 of Appendix G. 146 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-3: Behaviour of assumed Thiessen rainfall depths against the observed runoff depths from the selected events for UPRC. It is apparent that the events [such as events on 27/07/1996 (event 4), 30/08/96 (5), 29/01/97 (6), and 04/05/98 (11b)] categorised as Low spatial- low temporal heterogeneous (LS-LT) events follows the rainfall-runoff trend of the UPRC reasonably accurately regardless of their storm magnitude. Whereas the event on 18/05/98 (event 12) and event on 14/07/99 (event 22b), which are categorised as high spatial-high temporal heterogeneous event (HS-HT) considerably deviated from the trend line. This indicates that the assumed total rainfall may under-estimate the actual rainfall amount by up to 30mm despite the different average intensities of 4.5mm/hr and 7.7mm/hr respectively. Boyd et.al. (1998), found that the pervious surfaces themselves have also been observed to generate runoff in large storms in Australia. Therefore, the deviation of these mentioned events may be caused by, the pervious runoff and the misinterpretation of rainfall amount. Event on 10/04/98 (event 9b), which is also categorised as high-spatial-high temporal event (HS-HT) with an average intensity of 6.2mm/hr indicates an over prediction of 10mm on its calculation of the total depth. The event most probably produced runoff from the impervious surfaces alone. It shows the spatial and temporal variability of 147 Chapter 6 Influence on Catchment Response to Rainfall rainfall plays a major role in the accuracy of rainfall amount calculations in determining the rainfall runoff behaviour of a catchment. It is also apparent that different average intensity events may follow the similar degree of spatial and temporal variability whereas events with similar average intensities may not necessarily follow similar degree of spatial and temporal heterogeneity. 6.3.2 At CPC Outlet For the selected events the observed runoff depths (from the observed hydrographs at CPC outlet) are plotted against the Thiessen average rainfall depths of all corresponding events. Thence, the linear rainfall-runoff behaviour is plotted as a straight line from the known parameters of CPC (percentage of imperviousness of 29% and from the initial loss) as shown in Figure 6-4. The complete rainfall depths and corresponding observed flow depth of the events selected are tabulated in Table G.2 of Appendix G. The effective percentage of impervious area (29%) for the CPC was obtained based on the landuse type and weighting the dominant development in the subcatchments from the study by Abustan (1997). The value was also supported by calculating the impervious areas from the detailed orthophoto maps of the catchment. The initial losses that satisfied before runoff occurs are assumed from the calibrated parameters (depression storage and, infiltration losses etc.) of the study by Abustan (1997). 148 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-4: Behaviour of assumed Thiessen rainfall depths against the observed runoff depths from the selected events for CPC. It can be observed that the events [such as events on 29/01/97 (Event 1), 11/02/97 (2), and 14/08/99 (9) and 18/10/99 (10)] categorised as Low spatial heterogeneous events (LS) follow the rainfall-runoff trend of the CPC fairly accurately regardless of their storm magnitude. Whereas the events on 18/05/98 (event 5) and on 23/10/99 (event 11), categorised as high spatial-high temporal heterogeneous event (HS-HT) and high spatial-low temporal heterogeneous event respectively, considerably deviated from the trend line. On an urban catchment, runoff from impervious areas occurs in all storms, so that relative increases in runoff are high. In very large, rare storms, which thoroughly wet a catchment, the runoff rates from pervious surfaces are similar to those from impervious surfaces. However, the event 5 and event 11 (categorised as HS) shows an opposite behaviour due to the imperfect rainfall representation. It is apparent that the runoff production from these two events, are most probably from the impervious surfaces alone. This indicates that the assumed total rainfall is an over-estimate from the actual rainfall amount by 8-20mm. 149 Chapter 6 Influence on Catchment Response to Rainfall The assumed rainfall average for the events on 09/12/99 (event 13), which is also categorised as high spatial – high temporal (HS-HT) heterogeneous events are under predicted by 5mm. Another possible reason for the variation of rainfall-runoff behaviour is due to the combine effect of the flow from pervious surfaces and the misinterpretation of rainfall amount. 6.4 Influence of Spatial He terogeneity on Catchment Simulation To test the possible effects of spatial heterogeneity of rainfall on different events by different sampling methods on simulated hydrological responses, a catchment modelling system has to be used. Such a system must be distributed to a certain extent to not only be capable of responding to spatially variable inputs but also to allow a reasonable understanding of the runoff production processes. There are many alternative theoretical models available for simulation of individual processes influencing the development and transmission of surface runoff through a catchment. As a consequence there are many alternate rainfall-runoff modelling systems with the selection between these alternatives being subjective and highly dependent on the objectives of the modelling process. One model that has been extensively used with some success in several research projects and also used to assess the effect of rainfall input models for events with various degree of heterogeneity in this study is SWMM. The functionality and the components of the SWMM model are well illustrated in Section 2.2. The non-linear reservoir model available within the Runoff block was used together with the Transport block of SWMM in this study to assess hydrological response. The SWMM model simulates the runoff and transport of stormwater through drainage networks, by performing hydrologic and hydraulic analyses of stormwater in the drainage system. The SWMM model provides important and necessary information on the present and future adequacy of the system, see Huber and Dickinson (1988). Presented in the subsequent sections are the results from the calibration, validation and extrapolation to different hydrologic events for the UPRC and CPC. 150 Chapter 6 Influence on Catchment Response to Rainfall 6.4.1 Calibration of Events The first step in running a catchment modelling systems for the study is the calibration process. The calibration process for a gauged catchment involves the minimization of the deviation between recorded information and simulation output by adjusting parameters repeatedly. The present study utilized the relatively well-calibrated models from previous studies for the UPRC [Downes, (1998)], and CPC [Abustan (1997)]. 6.4.1.1 Calibration of UPRC Model The SWMM model of UPRC was calibrated in the study by Downes (1998). The study gave a greater consideration to the arrival at a set of parameters yielding close agreement between measured and predicted storm volumes and peak flow rates over the entire range of storms. In many instances calibration for individual events could have been significantly improved by adjusting the parameters for that event. The success of each calibration run was assessed using the relative and absolute errors for each event. The selected few calibrated events and the calibration statistics for the corresponding events on peak and volume of flows are given in Table 6-1 and Table 6-2 respectively. The average relative and absolute errors for the selected events for UPRC are also presented in the tables. Table 6-1: Statistical Fit between observed and simulated runoff peak flows for Calibrated Events for UPRC: [Downes (1998)] Events for Measured Predicted Relative Abs. Analysis Peak / (m3/s) Peak / (m3/s) Errors (%) Relative Errors (%) Dec. 4, 1992 15.5 17.4 -12.0 12 Mar. 7, 1993 36.8 35.2 4.5 4 July 8, 1993 22.7 21.7 4.5 4 Sep. 9, 1993 8.5 8.3 2.4 2 Sep. 13, 1993 24.7 27.8 12.6 13 Feb. 12, 1994 29.0 32.4 -11.7 12 Average 0.05 7.8 151 Chapter 6 Influence on Catchment Response to Rainfall Table 6-2: Statistical Fit between observed and simulated runoff Volume for Calibrated Events for UPRC: [Downes (1998)] Events for Measured Predicted Relative Abs. Analysis Volume/ Volume / Errors (%) Relative (ML) (ML) Errors (%) Dec. 4, 1992 735.0 655.5 11 11 Mar. 7, 1993 516.0 578.0 -12 12 July 8, 1993 882.3 882.2 0 0 Sep. 9, 1993 273.4 282.0 -3 3 Sep. 13, 1993 415.9 415.7 0 0 Feb. 12, 1994 640.3 716.5 -12 12 Average -2.6 6.3 The observed and predicted hydrographs from the study by Downes (1998) for typical calibration events on September 9, 1993 and Septemeber 13, 1993 are presented in Figure 6-5a and Figure 6-5b respectively. The visual comparisons of calibration of events from the study by Downes (1998) did not show an accurate prediction. This may be mainly due to the scale of the subcatchments selected. The model was developed by creating sixty subcatchments based on their landuse patterns. However, the sizes of a number of subcatchments were larger than the CPC. This will show the major difference in the statistics between UPRC and CPC. For a more accurate UPRC model this scaling should have been increased much more. However, since the objective of the present study is to answer how the prediction of hydrographs could be improved by better representing the rainfall input model, the calibrated model of Downes (1998) was used, after a proper validation process. 152 Chapter 6 Influence on Catchment Response to Rainfall (a) (b) Figure 6-5: The Shape of observed amd Simulated hydrograph for a calibrated events a)- Sep. 9, 1993 ; b ) Sep. 13, 1993 : [Reproduced from Downes (1998)] 6.4.1.2 Calibration of CPC Model The calibration of SWMM for CPC has been performed by Abustan (1997) from events in 1994 and 1995 incorporating the Thiessen rainfall model. The model parameters were calibrated based on the runoff depth, peak flow and the shape of the hydrographs. The statistics of calibration based on the runoff depth and the peak flow for the calibrated events from the study by Abustan are given in Table 6-3 and Table 6-4 respectively. The author concluded that the calibration process was successful for simulation of hydrographs because, the error statistics for all six calibrated events were within the reasonable range. The average relative error (RE) and absolute Relative error (ARE) for 153 Chapter 6 Influence on Catchment Response to Rainfall the runoff depth were -5.2 and 6.7 percent respectively and for the peak flows the values were 2.0 and 10 percent respectively. In developing a relationship between observed and simulated values, a regression coefficient of 0.98 was obtained for both the volume and peak. Table 6-3: Statistical Fit between observed and simulated runoff peak flows of Calibrated Events for CPC: [Abustan (1997)] Events for Observed Simulated RMSE Relative Abs. Analysis Peak Flow Peak Flow (mm) Errors Relative (m3/s) (m3/s) (%) Errors (%) Nov 23, 1975 3.30 2.91 0.39 12 12 Dec 4, 1975 0.14 0.18 0.04 -29 29 Oct 21, 1994 0.76 0.81 0.05 -6.6 6.6 Oct 31, 1994 0.56 0.57 0.01 -1.8 1.8 Jan 2, 1995 0.52 0.46 0.06 12 12 Feb 28, 1995 2.72 2.68 0.04 1.5 1.5 Average 0.10 -2.0 10 Table 6-4: Statistical Fit between observed and simulated runoff depths of Calibrated Events for CPC: [Abustan (1997)] Events for Observed Simulated RMSE Relative Abs. Analysis runoff runoff (mm) Errors Relative (mm) (mm) (%) Errors (%) Nov 23, 1975 1.90 1.93 0.03 -1.6 1.6 Dec 4, 1975 0.18 0.21 0.03 -14 14 Oct 21, 1994 1.87 1.84 0.03 1.6 1.6 Oct 31, 1994 1.20 1.43 0.23 -16 16 Jan 2, 1995 0.51 0.53 0.02 -3.8 3.8 Feb 28, 1995 2.90 2.82 0.08 2.8 2.8 Average 0.07 -5.2 6.7 In the visual comparison, the shape of the hydrograph including the runoff volume and the peak flow of observed values was compared to the simulated value. A visual comparison of two calibrated events from the study by Abustan (1997) on Feb. 28, 1995 and Oct. 21, 1995 are presented in Figure 6-6. 154 Chapter 6 Influence on Catchment Response to Rainfall The visual comparison and the statistical measures showed in the study by Abustan (1997), indicates a fairly reasonable calibrated model for CPC on the small events with single bursts. Therefore, the model has been utilized in our study without any major refinements. However, the sensitive parameters such as pervious and impervious area Manning’s roughness for larger events with multiple peaks have been fine tuned and recalibrated. The recalibrated parameters were then validated with recent events from the study before being utilized for performing the sensitivity analysis for alternate rainfall input. The results on the validating processes are given in the following section. It should be noted that the calibration processes from the study by Abustan and the validation processes of the present study are mainly based on Thiessen rainfall input with the comparatively more uniform events. Furthermore, the 1.32 km2 CPC was discretised into 42 subcatchments, which is a more accurate scaling compared to the calibrated UPRC model. 155 Chapter 6 Influence on Catchment Response to Rainfall (a) (b) Figure 6-6: The Shape of observed and Simulated hydrograph for a calibrated events a)- Feb. 28, 1995 ; b ) Oct. 21, 1995 : [Reproduced from Abustan (1997)] 156 Chapter 6 Influence on Catchment Response to Rainfall 6.4.2 Validation of Events The calibrated models of UPRC and CPC events were then validated with the events used from the present study (events selected during the years of 1996, 1997, 1998 and 1999), in order to reconfirm the accuracy of the models. Spatially uniform events were considered in the validation processes. The rainfall patterns of these events from the Thiessen and Spline calculation follow similar patterns as explained in the previous chapter. The predicted hydrograph patterns from Thiessen and spline rainfall with observed hydrographs are compared and presented in the figures and the summary statistics are tabulated therafter. 6.4.2.1 Validation of UPRC Events The calibrated model of UPRC from the study by Downes (1998) was validated with the selected events, categorized as low uniform events from this present study. The validation process was performed to assess the calibration parameters from using an independent set of data from the present study. The developed five-minute hyetographs were used as input for the SWMM of the catchment. Since the rainfall patterns from Thiessen and Spline model were almost the same for the spatially low variable or more uniform events the validation was considered with the developed Thiessen rainfall. With the exception of the rainfall, all the parameters were based on those obtained from Downes (1998). The calibration statistics from Downes (1998) have been previously presented in Table 6-1 and Table 6-2. The validation accuracy also followed the similar degree as the calibration from the study by Downes (1998). The final SWMM parameter set used in the present study after the calibration and validation processes are presented in Table 6-5. Typical SWMM input file for a validation event on 22, June 1998 is presented in Appendix F1. 157 Chapter 6 Influence on Catchment Response to Rainfall Table 6-5: Parameterset used in rainfall-runoff model available with SWMM for UPRC No of Inlets 60 No of Pipes/Channels 218 Total catchment area 11000 ha Total width of the catchment 16281 m Percentage of Imperviousness 29.8 % Average capillary suction 190 mm/hr Saturated Hydraulic Conductivity 1.7 mm/hr Initial moisture deficit for soil 0.17 Impervious Manning's roughness 0.025 Pervious Manning's roughness 0.028 Impervious area depression storage 1.5 mm Pervious area depression storage 2.5 mm As part of this study the model parameters obtained and listed in Table 6-5 were validated for events, which occurred during 1996, 1997, 1998 and 1999. The events were selected from low spatial heterogeneous category. The performance statistics of prediction of peak and volume from the six validation events are given in Table 6-6 and Table 6-7 respectively. Table 6-6: Statistical Fit between observed and simulated runoff peak flows of validated Events (Low spatially variable events) for UPRC Abs. Measured Predicted Events for Analysis Relative Relative Peak / (m3/s) Peak / (m3/s) Errors (%) Errors (%) Jan. 6, 1996 (1b) 113.2 113.1 0.0 0.0 Apr.11, 1996 (2b) 47.8 44.3 -7.3 7.3 Aug. 30, 1996 (5) 213.9 242.1 13.2 13.2 Oct. 7, 1997 (7) 53.1 51.7 -2.6 2.6 Jun. 22. 1998 (13) 100.5 97.7 -2.8 2.8 Oct. 18, 1999 (24) 34.6 33.5 -3.1 3.1 Average -0.5 4.9 158 Chapter 6 Influence on Catchment Response to Rainfall Table 6-7: Statistical Fit between observed and simulated runoff volume of validated Events (Low spatially variable events) for UPRC Measured Predicted Abs. Events for Analysis Volume / Volume / Relative Relative (ML) (ML) Errors (%) Errors (%) Jan. 6, 1996 (1b) 413.8 326.2 -18.8 21.2 Apr.11, 1996 (2b) 194.7 188.8 -3.0 3.0 Aug. 30, 1996 (5) 1214 1006 -17.1 17.1 Oct. 7, 1997 (7) 193.6 205.5 6.1 6.1 Jun. 22. 1998 (13) 330.8 272.4 -17.7 17.7 Oct. 18, 1999 (24) 240.0 218.9 -8.8 8.8 Average -9.9 12.3 The peak flows of the validation events varied from 34 m3/s to 214 m3/s. The selected events were also from the Low spatially variable (LS) category. Summary of the statistics of the peak flow analysis is presented in Table 6-6. The validation analysis on peak flows shows a close prediction of peak flow by the calibrated UPRC SWMM model. Although the tabulated values are the prediction from the Thiessen rainfall, the prediction from the spline rainfall also followed with an almost similar prediction accuracy. Peak flow validation was successful with average RE and ARE of -0.5 and 4.9 percent respectively. The volume of the validation events varied from 240 ML to 1214 ML Summary statistics of the flow volume analysis is presented in Table 6-7. Flow volume validation was with average RE and ARE of –9.9 and 12.3 percent respectively. The errors were slightly larger than the errors of the validation of peak flow, however, they were acceptable since the average RE was less than ± 10 percent and the average ARE was less than 15 percent [Sriananthakumar (1992); Abustan (1997)]. A visual comparison of the validation for the events that occurred on 06, January 1996, 30, August 1996 and 18, October 1999 are presented in Figure 6-7, Figure 6-8 and Figure 6-9 respectively. The visual comparisons of the hydrograph shape of the observed and the simulated both from the Thiessen rainfall and spline rainfall are presented in these figures. It can be observed that for a low spatially variable event the 159 Chapter 6 Influence on Catchment Response to Rainfall rainfall model doesn’t make much difference in the prediction. The calibration and validation results show the robustness of the UPRC model for predicting the catchment response for Thiessen rainfall and spline rainfall input with low spatially variable events. Figure 6-7: The shape of the observed and simulated hydrograph for a validation event of UPRC – January 06, 1996 (Event Id. 1b) 160 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-8: The shape of the observed and simulated hydrograph for a validation event of UPRC - August 30, 1996 (Event Id. 5) Figure 6-9: The shape of the observed and simulated hydrograph for a validation event of UPRC - October 18, 1999 (Event Id. 24). 161 Chapter 6 Influence on Catchment Response to Rainfall 6.4.2.2 Validation of CPC Events Since, the validation from the study by Abustan considered relatively small events with a single rainfall burst, the calibration parameters were further fine tuned and recalibrated with larger events with multiple bursts. The recalibration of parameters were mainly carried out on the impervious area manning's roughness and impervious are depression storage. The recalibration process was then validated with the recent events from the study. Then, a validation process was performed to assess the calibration parameters from using an independent set of data from the present study. The developed hyetographs were used as input for the SWMM of the catchment. With the exception of the rainfall, all the parameters were based on those obtained from Abustan (1997). The calibration statistics from Abustan (1997) are already given in Table 6-3 and Table 6-4. The final SWMM parameter set used in the present study after the calibration and validation processes are given in Table 6-8. Typical SWMM input file for an occurred on 9, December 1999 is presented in Appendix F2. Table 6-8: Parameter set used in rainfall-runoff model available with SWMM for CPC No of Inlets 48 No of Pipes/Channels 94 Total catchment area 132.7 ha Total width of the catchment 6820 m Percentage of Imperviousness 29 % Horton's Maximum Infiltration rate 250 mm/hr Horton's minimum Infiltration rate 20 mm/hr Horton's decay rate 0.00125sec-1 Impervious Manning's roughness 0.012 Pervious Manning's roughness 0.3 Impervious area depression storage 0.6 mm Pervious area depression storage 2.5 mm 162 Chapter 6 Influence on Catchment Response to Rainfall As part of this study the model parameters obtained and listed in Table 6-8 were validated for events, which occurred during 1997 and 1999. The events were selected from low spatial heterogeneous category. The performance statistics of three validation events are given in Table 6-9. Table 6-9: Performance statistics for Validated events for CPC. Events for MSE RMSE MAE Varianc Bias R2 Analysis (m3/s)2 (m3/s) (m3/s) e (m3/s) (m3/s) Jan 29, 1997 0.009 0.095 0.079 0.006 0.056 0.94 Feb 11, 1997 0.012 0.110 0.075 0.012 0.080 0.92 Oct 19, 1999 0.001 0.032 0.005 0.001 -0.001 0.96 Prediction accuracy as outlined in the study by Lettenmaier and Wood (1993) and as discussed in Chapter 2.7 is a measure of the difference between predicted and observed values and is best assessed by retrospective comparison of the values. Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Variance, Bias and Absolute Errors are some of the statistical measures used in the study to assess the prediction accuracy. The statistics summary shows that the validation results are within the acceptable limit. A visual comparison of the validation for the events that occurred on 11, February 1997 and 19, October 1999 are presented in Figure 6-10 and Figure 6-11 respectively. The calibration and validation results show the robustness of the CPC model for predicting the catchment response for Thiessen rainfall input with low spatially variable events. 163 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-10: The shape of the observed and simulated hydrograph for a validation event - February 11, 1997 Figure 6-11: The shape of the observed and simulated hydrograph for a validation event - October 19, 1999 164 Chapter 6 Influence on Catchment Response to Rainfall 6.4.3 Sensitivity in Catchment Prediction for alternate Rainfall Input In a study of errors in predicted catchment flows arising from rainfall, a study by Troutman (1983) classified errors as those arising from the assumed rainfall input and those arising from errors in either the CMS structure or from the parameter values necessary for operation of the CMS structure. Herein, it is the first source of prediction error that is of interest. In the analysis of prediction errors from the calibration and validation, it has been assumed that SWMM is adequate for simulation of the catchment runoff and that the calibrated parameter values are accurate. A consequence of this assumption, therefore, is that the change in prediction errors arising from changes in the rainfall model can be ascertained. 6.4.3.1 For events on UPRC Shown in Figure 6-12 and Figure 6-13 are the predicted hydrographs obtained using both Thiessen and a spline surface rainfall for the events of May 18, 1998 and September 16, 1999 respectively. These events are categorized as high variability in space dimension. The comparison plots clearly show the variation of simulated hydrographs from different rainfall input and consequently suggests the superiority of the simulated hydrographs from the developed spline rainfall input. In other words the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The similar comparison hydrographs for the events selected from UPRC for the present study are presented in Appendix H1. 165 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-12: Prediction of simulated hydrograph from UPRC for a 'HS-HT' event - January 02, 1996 (1a) Figure 6-13: Prediction of simulated hydrograph from UPRC for a 'HS-LT' event - April 09, 1998 166 Chapter 6 Influence on Catchment Response to Rainfall It is interesting to know whether the degree of this improvement in the predicted hydrograph is dependent on the spatial variability of the storm event as measured in chapter 4. Two events on 7th October 1997 and 9th April 1998, which are from low spatial and high spatial categories respectively, are considered for comparison. The performance statistics of these two events are tabulated in Table 6-10. From the performance criteria results shown in Table 6-10, it can be seen that the storm event of 9th April 1998, which had a higher degree of spatial variability than the storm event of 7th October 1997, predicted the observed event more accurately using the spline rainfall model than the Thiessen rainfall model. On the other hand, the predictions are almost similar and comparatively accurate from both the rainfall models for the 7th October 1997 event. This is consistent with the predictions, for the latter event being improved more than the earlier event. In other words, the performance parameters for predicted hydrographs from the spline rainfall input and from the Thiessen rainfall input are almost similar for the storm event of 7th October 1997. Table 6-10: Comparison of performance statistics between example events from 'LS-LT’ and 'HS-HT' category events Performance Categorised 'LS' event on Categorised 'HS' Event on Statistics 07/10/1997 09/04/1998 Spline Thiessen Improve Spline Thiessen Improve Flow Flow ment Flow Flow ment Rel. RMSE 0.40 0.41 - 0.61 0.66 0.05 Rel. MAE 0.30 0.30 - 0.41 0.44 0.03 Rel. Bias -0.07 -0.07 - 0.27 0.34 0.07 Variation in -3.5 -2.7 - -1.1 9.0 7.9 Peak (%) Variation in 6.1 6.2 - 26.8 32.8 6.0 Volume (%) 167 Chapter 6 Influence on Catchment Response to Rainfall 6.4.3.1.1 Comparison of predicted peak and volume with Observed values The prediction of the peak and the volume of the hydrographs from the alternate rainfall models are then compared and figured in Figure 6-14 and Figure 6-15 respectively for UPRC. The Figure 6-14 shows that the prediction of peak from the spline rainfall input is improved when compared with the prediction from Thiessen rainfall input for the events, which are categorized as high spatially variable events. The prediction accuracy is almost the same for the events categorized as Low spatially variable events. The plot also follows a R2 value of 0.99 for the prediction from Spline surface rainfall input. The prediction of volume of the hydrographs from both the rainfall inputs shown in Figure 6-15, did not show the accuracy as in the prediction of peak. This may be mainly because of the simplicity of the SWMM model used in the study. However, the plot follows a R2 value of 0.95 for the prediction from spline surface rainfall input. Figure 6-14: Comparisons between Observed Peak and Simulated Peak (from alternate rainfall input) for the selected events from UPRC 168 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-15: Comparisons between Observed Volume and Simulated Volume (from alternate rainfall input) for the selected events from UPRC. 6.4.3.2 For events on CPC 6.4.3.2.1 Comparison of simulated hydrographs Shown in Figures from Figure 6-16 to Figure 6-18 are the predicted hydrographs obtained using both Thiessen and a spline surface rainfall for the events of May 18th 1998, 16th June 1998 and 9th October 1999 in order. These events are categorized as high variability in both space and time dimensions. It can be observed that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The simulated hydrographs from all the other events from CPC considered for the present study are compared and presented in Appendix H2. 169 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-16: Prediction of simulated hydrograph from CPC for a 'HS-HT' event - October 09, 1999 Figure 6-17: Prediction of simulated hydrograph of CPC for a 'HS-HT' event - June 16, 1998 170 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-18: Prediction of simulated hydrograph of CPC for a 'HS-HT' event - May 18, 1998 It is interesting to know whether the degree of this improvement in the predicted hydrograph is dependent on the spatial variability of the storm event as measured in chapter 4. Two events on 19th October 1998 and 9th October 1998, which are from low spatial and high spatial categories respectively, are considered for comparison. The performance statistics of these two events are tabulated in Table 6-11. From the performance criteria results shown in Table 6-11, it can be seen that the storm event of 9th October 1998, which had a higher degree of spatial variability than the storm event of 19th October 1998, predicted the observed event more accurately by the spline rainfall model than the Thiessen rainfall model. On the other hand, the prediction are almost similar and comparatively accurate from both the rainfall input models for the 19th October 1998 event. This is consistent with the predictions, for the latter event being improved more than the earlier event. In other words, the performance parameters for predicted hydrographs from the spline rainfall input and from the Thiessen rainfall input are almost similar for the storm event of 19th October. Also hydrographs for the storm event of 19th October did not improve to the same extent as the storm event of 9th October. 171 Chapter 6 Influence on Catchment Response to Rainfall Table 6-11: Comparison of performance statistics between example events from ‘LS’ and 'HS' category events Performance Categorised 'LS' event on Categorised 'HS' Event on Statistics 19/10/1998 09/10/1998 Spline Thiessen Improve Spline Thiessen Improve Flow Flow ment Flow Flow ment MSE (m3/s)2 0.001 0.001 0 0.002 0.011 0.009 RMSE (m3/s) 0.032 0.032 0 0.045 0.105 0.060 MAE (m3/s) 0.024 0.026 0.002 0.025 0.046 0.021 Variance(m3/s)2 0.001 0.001 0 0.002 0.010 0.008 Bias (m3/s) -0.005 -0.001 -0.004 -0.002 0.032 0.030 Variation in 6.5 14.0 7.5 -11.6 42.6 31.0 Peak (%) Variation in -4.1 -0.6 -3.5 -2.1 25.4 23.3 Volume (%) The complete performance statistics for all the selected events from CPC are presented in Appendix H2. The results tabulated from Table H2.1 to H2.7 show the improvement in catchment modelling system predictions arising from the changed rainfall model, therefore, are a function of the spatial variability of the rainfall. Hence, it can be concluded that the more variable the rainfall, the greater the need for a rainfall model which incorporates this variability in space and time. 6.4.3.2.2 Comparison of predicted peak and volume with Observed values Similar to the analysis for the UPRC the prediction of the peak and the volume of the hydrographs from the alternate rainfall models are then compared and presented in Figure 6-19 and Figure 6-20 respectively for CPC. The figure suggests that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted peak and volume of the hydrograph that more closely duplicated the recorded hydrograph peak and volume. 172 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-19: Comparisons between Observed Peak and Simulated Peak (from alternate rainfall input) for the selected events from CPC. Figure 6-20: Comparisons between Observed Volume and Simulated Volume (from alternate rainfall input) for the selected events from CPC. The assessment criteria, which can be used for hydrograph comparison in single event modelling then compared with the hydrographs predicted from the alternate rainfall models. Generally the conclusions were made that the uniform events followed a similar prediction and the non uniform better predicted by the spline rainfall input. The Figure 6-21 shows how the different statistical parameters were improved by the spline rainfall input from the traditionally used rainfall input for the events from CPC. Despite the fact that the improvement did not follow in the order of the degree of the heterogeneity, it was consistent for the highly variable events. 173 Chapter 6 Influence on Catchment Response to Rainfall Figure 6-21: Improvement in performance statistics by Spline predicted flow from Thiessen predicted flow ; a) Variance ; b) MSE; c) RMSE 174 Chapter 6 Influence on Catchment Response to Rainfall 6.5 Conclusions. Reported herein this chapter has been the results of an investigation into the importance of the rainfall model for robust predictions from catchment modelling systems. Two alternate rainfall models, namely a Thiessen based rainfall model and a spline surface rainfall model, were considered. The following conclusions have been developed from the simulation studies: The rainfall model significantly influenced the predicted hydrographs obtained from a catchment modelling system. Furthermore, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event as measured by the semi-variaogram approach developed in Chapter 4 for assessing this feature of a storm event. The hydrograph prediction accuracy can be the same from a simple Thiessen rainfall input model as a more detailed spline rainfall model for rainfall events where there is a lower variability in the space and time dimensions. The simulated hydrographs more closely duplicated the recorded hydrographs with the introduction of a more detailed rainfall input model than a simple Thiessen rainfall model for the more highly variable events in the space and time dimensions. The improvement in the modelling system predictions followed the categorization of events. However, the degree of improvement obtained did not correspond directly with the order of events when sorted according to their degree of spatial and temporal variability. 175 CHAPTER 7 SUMMARY AND CONCLUSIONS This section summarises the approached methodologies, outcomes from the research and lists the major conclusions and recommendations for further research. 7.1 Summary of Research 7.1.1 Introduction This study investigated the importance of the rainfall model during a storm event for robust prediction of catchment runoff. As part of this investigation, it was necessary to develop a methodology for considering the variability of rainfall in space and time. Improved estimates of the spatially distributed rainfall fields with individual subcatchment hyetographs were also obtained within a GIS. These developments were necessary to relate improvements in the flow prediction to different storm characteristics. The importance of a more detailed rainfall model towards more robust prediction from Catchment Modelling Systems (CMS) was highlighted through application of these spatially distributed hyetographs. The study also proves the value of using distributed rainfalls to improve hydrological predictions in the sense that was foreseen. 7.1.2 Objectives The purpose of this dissertation was to improve the understanding and measurement of the variability of rainfall over the urban catchments, improve the robustness of prediction from a CMS by better representing the rainfall in space and time, and to highlight the importance of the rainfall input model in catchment simulation. The specific objectives of this dissertation therefore were: • to develop a methodology to categorize storm events according to the within- event heterogeneity in both space and time dimensions; 176 Chapter 7 Summary and Conclusions • to develop a more detailed rainfall model by the aid of hydroinformatic tools towards improving the runoff prediction; and • to analyse the importance of the rainfall model in catchment simulation and to assess the sensitivity of alternate rainfall models to various degrees of heterogeneous events. A summary of the approaches used to address these three objectives are given in the subsequent Sections 7.1.3, 7.1.4 and 7.1.5. Specific conclusions relating to the three objectives are given in Sections 7.2.1, 7.2.2. and 7.2.3 respectively. 7.1.3 Estimation of Rainfall heterogeneity in space and time For years, various correlation and semi-variogram techniques have been used to evaluate both the temporal and spatial structure of rainfall events. Correlation techniques are able to describe the structure and the motion of the storm events by measuring the association among the gauge records. However, past studies suggest that in situations where the random field is not necessarily stationary (where the data are so scarce and so scattered in space), the sample covariance function estimates are not meaningful and therefore, an analytical parametric ‘variogram’ model should be used in lieu of the covariance. On the other hand, by its definition, a semi-variogram function has the capability of estimating the disassociation between measurements from the different gauge locations. In typical engineering applications such as in hydrology, the semi-variogram development has been applied to estimate the mean precipitation over a catchment by a Kriging model. In order to investigate both the spatial and temporal variability separately since a high spatially heterogeneous event could have a temporal variability, a semi-variogram approach was used as a tool to achieve the first objective of the study. A technique for assessing the spatial and temporal heterogeneity of individual storm events was developed. The task was achieved by adopting estimators, which measure both the spatial and temporal heterogeneity of different events, by incorporating the semi- variogram approach. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilised in introducing estimators to address the heterogeneous nature of each individual storm 177 Chapter 7 Summary and Conclusions event in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. 7.1.4 Development of rainfall pattern within a hydroinformatic environment Information, such as rainfall intensity, at locations other than the measurement locations is not defined by the measurement process and must be inferred from the information recorded at the measurement locations. The powerful spatial analysis hydroinformatic tool particularly the Arc/Info GIS was used to achieve the second objective of the study. A detailed rainfall distribution model in space and time was developed, and implemented within the GIS framework. The enhanced rainfall representation in both space and time was made feasible with the aid of the powerful spatial analytic capability of the GIS. The basis of this rainfall model was an extension of the rainfall model developed by Ball and Luk (1998) through a temporal discretisation of the storm event. Based on the rainfall recorded at pluviometers within and immediately adjacent to the catchment, the spatial variation of rainfall was ascertained at five-minute increments using the thin plate spline algorithm. A GIS and in particular Arc/Info was used as the software base for implementation of the spatio/temporal rainfall model. In addition to providing basic modelling facilities Arc/Info provides a facility for programming the rainfall model through a macro programming language, Arc Macro Language (AML). Use of this programming capability permitted sequencing of Arc/Info commands, which enabled easy repetition of the several operations involved in the creation of five-minute incremental patterns of rainfall over the total catchment and in the subsequent extraction of five-minute hyetographs for each of the subcatchments. 7.1.5 Improvement in prediction of runoff quantity Having ascertained the likely variation of estimated rainfall at a subcatchment scale induced by the spatial variation in rainfall demonstrated, it remains to consider the influence of the spatial pattern of the rainfall on a catchment scale. These influences were ascertained by considering rainfall hyetographs determined for 5-minute time increments for each subcatchment within the catchment. The Calibration, validation and 178 Chapter 7 Summary and Conclusions extrapolation to different hydrologic events for the test catchments were performed in this section. The results served to further investigate the influence of alternative spatial and temporal rainfall models on the robustness of predictions obtained for the test catchments in Sydney, Australia. The importance of the detailed space-time rainfall model in improving the robustness of runoff prediction of CMS was investigated by comparing error parameters for predictions from CMS using alternate rainfall models, for various degrees of spatio-temporal heterogeneity events. Also it is appropriate to investigate whether the degree of this improvement is dependent on the variability of the storm event as assessed by the semi-variogram approach. The SWMM models of UPRC and CPC for the approach were utilized from the earlier studies by Downes (1998) and Abustan (1997) respectively. The reasonably calibrated models were then validated with the events from the present study. These events used for validation were from the categorized Low variable events. The validated model was then tested for its sensitivity with alternate rainfall inputs for the events categorized as high variable events. 7.2 Conclusions 7.2.1 Estimation of Spatio-temporal heterogeneity of Rainfall A methodology for identification of storm events according to their degree of heterogeneity in space and time utilizing real-time data has been proposed. The study has identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilized in introducing estimators to measure the degree of heterogeneity of each individual event in the spatial and temporal dimension. The proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. Also the application of this technique for the analysis of storm events occurring over Upper Parramatta River and Centennial Park urban catchments within the Sydney urban area were presented. 179 Chapter 7 Summary and Conclusions From the estimated spatial and temporal characteristic parameters, all the individual events were placed on the space-time frame. As a result of the analysis, the storms were categorized as having • High spatial and high temporal variability (HS-HT) • High spatial and low temporal variability (HS-LT) • Low spatial and high temporal variability (LS-HT), and • Low spatial and low temporal variability (LS-LT). 7.2.2 Development of rainfall pattern within a hydroinformatic environment A spatio-temporal rainfall distribution model was developed within GIS to transform point rainfall measurements to a spatially distributed rainfall over the catchments at small time-steps. The enhanced rainfall representation in both space and time was made feasible with the aid of the powerful spatial analytic capability of GIS through a temporal discretisation of the storm event. From this model, improved estimates of the spatial distribution of rainfall with small time step hyetographs were obtained. The approach and the rainfall model developed were suited especially for modelling of urban catchments. Analysis was performed to assess the difference between rainfall estimates obtained from traditionally used methods (such as Thiessen method) and estimates obtained from the proposed method. The differences were small when considered for the catchment as a whole. However, the differences in estimates were significant at the subcatchment scale. The difference was found to significantly increase with the degree of heterogeneity of the event in the space and time dimensions. The variation between the 5-minute rainfall estimated by Thiessen method and the 5- minute rainfall estimated by the proposed method was assessed by the introduction of ρ coefficient of variation ( s ). The results suggested that an average of 90% variation has occurred between the Thiessen estimate and the proposed spatially distributed spline estimate for ‘HS-HT’ type events on some extreme subcatchments. In comparison, for LS-LT type events, variation has gone up to an average of 30% on some extreme subcatchments. 180 Chapter 7 Summary and Conclusions The variation between rainfall estimated by the Thiessen method and rainfall estimated by proposed spatially distributed spline method was substantial for highly variable events when compared to the less variable events for the UPRC catchment which has an evenly distributed gauge network. However, the variation in the rainfall estimates is more serious for the CPC catchment, which assumes a single rainfall pattern under the Thiessen approach. 7.2.3 Robust prediction of runoff hydrograph Reported herein are the results of an investigation into the importance of the rainfall model for robust predictions from catchment modelling systems. Two alternate rainfall models, namely a Thiessen based rainfall model and a spline surface rainfall model, were considered. The following conclusions have been developed from the simulation studies. The rainfall model significantly influenced the predicted hydrographs obtained from a catchment modelling system. Furthermore, it was found that the spline surface rainfall model, which considered the spatial and temporal variability of the rainfall in greater detail than the Thiessen rainfall model resulted in predicted hydrographs that more closely duplicated the recorded hydrograph for the same parameter set. The degree of this improvement in the predicted hydrograph was found to be dependent on the spatial and temporal variability of the storm event as measured by the semi- variogram approach developed in Chapter 4 for assessing this feature of a storm event. In other words, the accuracy of a predicted hydrograph depends on the spatial and temporal variability of the rainfall. When the spatial and temporal variability of the rainfall is low, the rainfall model, as discussed earlier in Section 6.4.3 does not significantly influence the predicted runoff. On the other hand, when the spatial and temporal variability of rainfall is high, the rainfall model, as discussed in Section 6.4.3, singnificantly influences the predicted runoff. 181 Chapter 7 Summary and Conclusions 7.3 Limitations and assumptions During the progress of this study, a number of limitations arising for the need to adopt assumptions necessary for completion of the project. While these assumptions are not considered to impact on the results obtained for the study, there is a need to further validate the basis of these assumptions. Principal among these assumptions are: Definition of appropriate dimensional parameters to delineate High Spatial (HS) & Low Spatial (LS) and High Temporal (HT) & Low Temporal (LT) events. Within the current study, it was assumed that the appropriate measures were the diagonal distance of the respective catchments and the average time to peak of the observed hydrographs. There is a need to further investigate these measures to develop generic approaches to apriori determine them with minimal knowledge of the storm radius and of the catchment response. Furthermore, there is a need to investigate the interaction between the dimensional measures. Semi-Variogram assumption. There is a need to validate the adopted model over a wider range of catchments with different scales from different climatic regions. 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Simulation of small events in an Urban Catchment, Proceedings of Hydrology and Water Resources Symposium, Water Down ’94, Adelaide, Australia, 353-358. 194 Appendix A Storm Details and gauge Locations APPENDIX A Storm Details and Gau ge Locations Appendix A Storm Details and gauge Locations Table A.1: Real storm events of UPRC No Storm ID Event date Start Time End Time Remarks 1 1a 02/1/1996 12:25 16:50 all data available 2 1b 06/1/1996 3:00 12:15 all data available 3 2a 11/04/1996 14:00 18:35 7255 missing 4 2b 11/04/1996 22:50 5:10 all data available 5 4 27/07/1996 13:40 1:50 7253 missing 6 5 30/08/1996 4:15 7:35 7299 Missing 7 6 29/01/1997 15:35 18:25 all data available 8 7 07/10/1997 7:45 16:45 all data available 9 8a 24/01/1998 15:05 17:45 7273 missing 10 8b 25/01/1998 9:25 9:30 7273 missing 11 9a 09/04/1998 17:30 23:15 7273 missing 12 9b 10/4/1998 10:30 23:55 7273 missing 13 10 21/04/1998 21:30 16:50 all data available 14 11a 02/05/1998 11:55 18:50 all data available 15 11b 04/05/1998 19:45 2:25 all data available 16 12 18/05/1998 3:40 6:40 all data available 17 13 22/06/1998 17:15 22:45 7273 missing 18 20 01/04/1999 18:50 17:15 7273 missing 19 21 01/07/1999 16:15 19:35 all data available 20 22a 13/07/1999 12:10 19:00 all data available 21 22b 14/07/1999 1:50 6:25 all data available 22 23 16/09/1999 21:20 2:25 7299 missing 23 24 18/10/1999 18:50 4:25 all data available 24 25 23/10/1999 9:00 3:35 all data available 25 26a 09/12/1999 13:30 16:35 7253 missing 26 26b 09/12/1999 22:40 0:35 all data available Appendix A Storm Details and gauge Locations Table A.2: Real storm details of CPC No Storm ID Event date Start Time End Time Remarks 1129/01/1997 18:00 30/01/ all data available 2211/02/1997 10:30 14:40 all data available 3322/04/1998 16:05 0:05 all data available 4404/05/1998 9:00 16:40 all data available 5518/05/1998 22:10 5:10 all data available 6616/06/1998 14:20 20:40 No Paddington Data 7709/10/1998 21:50 6:45 all data available 8819/10/1998 8:30 18:00 all data available 9914/08/1999 18:00 0:50 No Mascot Data 10 10 18/10/1999 19:05 4:45 No Mascot Data 11 11 23/10/1999 19:00 3:25 No Mascot Data 12 12 08/11/1999 15:25 19:00 all data available 13 13 09/12/1999 13:45 15:40 all data available Appendix A Storm Details and gauge Locations Table A.3: Storm Event Statistics calculated globally for UPRC Storm ID Event date 5 Min. Average Total Average Standard time / (mm) Intensity / Deviation/ increments (mm/hr) (mm/hr) 1a 02/01/1996 54 40.6 9.0 14.3 1b 06/01/1996 112 37.8 4.0 5.8 2a 11/04/1996 56 18.7 4.0 9.9 2b 11/04/1996 77 22.5 3.5 4.8 4 27/07/1996 146 39.9 3.3 4.2 5 30/08/1996 329 96.1 3.5 4.1 6 29/01/1997 323 66.3 2.5 2.5 7 07/10/1997 109 34.0 3.8 4.1 8a 24/01/1998 33 22.0 7.7 15.3 8b 25/01/1998 32 9.3 3.5 5.6 9a 09/04/1998 70 32.3 5.4 16.2 9b 10/04/1998 162 81.9 6.2 9.9 10 21/04/1998 521 46.4 1.1 1.5 11a 02/05/1998 84 20.5 2.9 5.0 11b 04/05/1998 369 39.8 1.3 1.7 12 18/05/1998 325 123.0 4.6 7.7 13 22/06/1998 67 34.4 6.2 7.5 20 01/04/1999 270 37.1 1.7 2.2 21 01/07/1999 41 14.5 4.2 2.5 22a 13/07/1999 83 30.3 4.4 4.4 22b 14/07/1999 56 35.9 7.7 11.0 23 16/09/1999 62 11.4 2.2 4.2 24 18/10/1999 116 33.7 3.5 2.6 25 23/10/1999 224 48.0 2.6 3.3 26a 09/12/1999 38 16.6 5.3 9.6 26b 09/12/1999 24 10.9 5.4 16.8 Appendix A Storm Details and gauge Locations Table A.4: Storm Event Statistics calculated globally for CPC Storm ID Event date 5 Min. time Average Average Standard increments Total / Intensity / Deviation/ (mm) (mm/hr) (mm/hr) 1 29/01/1997 273 78.0 3.4 4.7 2 11/02/1997 339 99.2 3.5 3.6 3 22/04/1998 97 32.6 4.0 4.0 4 04/05/1998 89 16.0 2.1 3.2 5 18/05/1998 85 73.9 10.4 15.2 6 16/06/1998 77 14.3 2.6 7.7 7 09/10/1998 108 9.6 1.0 2.1 8 19/10/1998 115 11.5 1.2 1.8 9 14/08/1999 83 49.0 7.2 6.9 10 18/10/1999 117 33.3 3.4 3.8 11 23/10/1999 102 36.8 4.1 4.9 12 08/11/1999 44 14.2 3.9 7.7 13 09/12/1999 24 18.0 9.1 17.6 Appendix A Storm Details and gauge Locations Table A.5: The Gauging Locations of UPRC Gauge ID Gauge Name Easting Northing 7273 Westmead Hosp. @ Redbank Rd 299124.8 6258567.9 7299 DWR Macquarie Tower 300481.0 6256500.5 7261 Toongabbie Bowling Club 295409.5 6260325.5 7251 Greystanes (Cumberland GC) 294502.4 6256167.5 7253 Baulkham Hills (Swimming Pool) 299148.5 6264748.9 7255 Kings Langly (NSW Soccor Fed.) 294882.8 6265155.6 7257 Cumberland State Forest 303346.9 6264546.6 7259 Blacktown (Dog Pound) 290844.4 6258455.9 7263 Merrylands West (Canal Road) 295924.4 6254477.8 7265 Seven Hills (2WS) 292916.1 6260272.9 7267 North Rocks (Muirfield GC) 301727.0 6262354.7 7269 Baulkham Hills South (Balcombe 298284.1 6262290.4 Hts) 7283 Northmead (Bowling Club) 299477.2 6260563.7 7285 North Parramatta (Burnside) 301557.4 6259484.8 213004 Marsden Wier- Flow Gauge 300050.4 6257318.1 Appendix A Storm Details and gauge Locations Table A.6: The Gauging Locations of UPRC Gauge ID Gauge Name Easting Northing 566002 Avoca Steet 338544.8 6244099.5 566003 Storey Street 339096.5 6243616.5 566010 Waverely Public School 338230.5 6247547.5 566032 Paddington 336682.7 6248375.0 MASCOTC Kingsford Smith Airport 333786.1 6243065.0 2132238 Musgrave Avenue Pond 337475.5 6247167.5 Appendix B1 Estimated Semi-Variograms for UPRC Events APPENDIX B1 Experimental and Para meteric Semi-Variogram Models estimated for UPRC events Appendix B1 Estimated Semi-Variograms for UPRC Events Figure B1.1: Semi-Variogram plot for Event ID. 1a : 2 Jan 1996 Figure B1.2: Semi-Variogram plot for Event No. 1b : 6 Jan 1996 Figure B1.3: Semi-Variogram plot for Event No. 2b : 11 Apr 1996 Appendix B1 Estimated Semi-Variograms for UPRC Events Figure B1.4: Semi-Variogram plot for Event ID. 4 : 27 Jul 1996 Figure B1.5: Semi-Variogram plot for Event ID. 5 : 30 Aug 1996 Figure B1.5: Semi-Variogram plot for Event ID. 6 : 29 Jan 1997 Appendix B1 Estimated Semi-Variograms for UPRC Events Figure B1.7: Semi-Variogram plot for Event ID. 8a : 24 Jan 1998 Figure B1.8: Semi-Variogram plot for Event ID. 9b : 10 Apr 1998 Figure B1.9: Semi-Variogram plot for Event ID. 12 : 18 May 1998 Appendix B1 Estimated Semi-Variograms for UPRC Events Figure B1.10: Semi-Variogram plot for Event ID. 13 : 22 June 1998 Figure B1.11: Semi-Variogram plot for Event ID. 22 : 13 Jul 1999 Figure B1.12: Semi-Variogram plot for Event ID. 24 : 18 Oct 1999 Appendix B1 Estimated Semi-Variograms for UPRC Events Figure B1.13: Semi-Variogram plot for Event ID. 25 : 23 Oct 1999 Appendix B2 Estimated Semi-Variograms for CPC Events APPENDIX B2 Experimental and Para meteric Semi-Variogram Models estimated for CPC events Appendix B2 Estimated Semi-Variograms for CPC Events Figure B2.1: Semi-Variogram plot for Event ID. 1 : 29 Jan 1997 Figure B2.2: Semi-Variogram plot for Event No. 2 : 11 Feb 1997 Figure B2.3: Semi-Variogram plot for Event No. 3 : 22 Apr 1998 Appendix B2 Estimated Semi-Variograms for CPC Events Figure B2.4: Semi-Variogram plot for Event ID. 5 : 18 May 1998 Figure B2.6: Semi-Variogram plot for Event ID. 7 : 09 Oct 1998 Figure B2.6: Semi-Variogram plot for Event ID. 8 : 19 Oct 1998 Appendix C1 Selected Parameters and Categorization of storm events for UPRC APPENDIX C1 Estimated Model Parameters and Categorisation of Storm Events for UPRC Appendix C1 Selected Parameters and Categorization of storm events for UPRC Table C1.1: Estimated Parameter set from spatial and temporal semi-variograms Spatial Variogram Temporal Variogram No Storm ID Power Power Space Time function fit function fit characteristic characteristic (α) (β) parameter parameter (km) (timelag) 11a 0.08 0.88 18.3 8 21b 0.16 0.52 36.0 14 32a 0.65 0.42 2.8 7 42b 0.07 0.62 75.6 18 54 0.11 0.72 21.1 53 65 0.06 0.88 26.0 124 76 0.09 0.58 62.6 53 87 0.11 0.54 55.1 16 98a 0.09 0.76 25.1 5 10 8b 0.22 0.59 13.4 2 11 9a 0.12 0.75 16.3 31 12 9b 0.35 0.47 9.4 13 13 10 0.34 0.22 138.0 68 14 11a 0.36 0.60 5.5 6 15 11b 0.16 0.62 19.9 56 16 12 0.23 0.56 14.2 14 17 13 0.08 0.59 67.7 7 18 20 0.25 0.50 15.9 24 19 21 0.17 0.53 28.1 12 20 22a 0.31 0.50 10.7 5 21 22b 0.38 0.47 8.1 6 22 23 0.03 1.19 17.9 4 23 24 0.11 0.63 32.4 8 24 25 0.14 0.71 15.5 32 25 26a 0.12 0.79 14.4 6 26 26b 0.12 1.23 5.8 1 Appendix C1 Selected Parameters and Categorization of storm events for UPRC Table C1.2: Ranking and Categorisation of Events in Space and Time Dimension Ranking – Ranking – Category No Storm ID Event date Spatial Temporal Uniformity Uniformity 1 1a 02/1/1996 13 15 HS-HT 2 1b 06/1/1996 6 11 LS-HT 3 2a 11/04/1996 26 17 HS-HT 4 2b 11/04/1996 2 9 LS-HT 5 4 27/07/1996 11 4 LS-LT 6 5 30/08/1996 9 1 LS-LT 7 6 29/01/1997 4 4 LS-LT 8 7 07/10/1997 5 10 LS-HT 9 8a 24/01/1998 10 22 LS-HT 10 8b 25/01/1998 20 25 HS-HT 11 9a 09/04/1998 15 7 HS-LT 12 9b 10/4/1998 22 13 HS-HT 13 10 21/04/1998 1 2 LS-LT 14 11a 02/05/1998 25 19 HS-HT 15 11b 04/05/1998 12 3 LS-LT 16 12 18/05/1998 19 11 HS-HT 17 13 22/06/1998 3 17 LS-HT 18 20 01/04/1999 16 8 HS-LT 19 21 01/07/1999 8 14 LS-HT 20 22a 13/07/1999 21 22 HS-HT 21 22b 14/07/1999 23 19 HS-HT 22 23 16/09/1999 14 24 HS-HT 23 24 18/10/1999 7 15 LS-HT 24 25 23/10/1999 17 6 HS-LT 25 26a 09/12/1999 18 19 HS-HT 26 26b 09/12/1999 24 26 HS-HT Appendix C2 Selected Parameters and Categorization of storm events for CPC APPENDIX C2 Estimated Model Parameters and Categorisation of Storm Events for CPC Appendix C2 Selected Parameters and Categorization of storm events for CPC Table C2.1: Estimated Parameter set from spatial and temporal semi-variograms Temporal Spatial Variogram Variogram No Storm ID Power Power Space Time function fit function fit characteristic characteristic (α) (β) parameter / Parameter (km) (time lag) 11 0.24 0.42 30.6 27 22 0.35 0.38 15.4 17 33 0.47 0.40 6.3 17 44 No spatial dependence 10 55 0.28 0.68 6.6 6 66 0.47 0.57 3.8 3 77 0.87 0.28 1.6 4 88 0.76 0.11 12.2 8 99 0.46 0.37 8.0 11 10 10 0.33 0.24 94.4 6 11 11 0.48 0.81 2.5 10 12 12 0.60 0.68 2.1 5 13 13 0.31 1.11 2.9 2 Appendix C2 Selected Parameters and Categorization of storm events for CPC Table C2.2: Ranking and Categorisation of Events in Space and Time Dimension Ranking – Ranking – No Storm Event Date Spatial Temporal Category ID Uniformity Uniformity 1129/01/1997 2 1 LS-LT 2211/02/1997 3 2 LS-HT 3322/04/1998 7 2 HS-HT 4404/05/1998 13 5 HS-HT 5518/05/1998 6 8 HS-HT 6616/06/1998 8 12 HS-HT 7709/10/1998 12 11 HS-HT 8819/10/1998 4 7 LS-HT 9914/08/1999 5 4 HS-HT 10 10 18/10/1999 1 8 LS-HT 11 11 23/10/1999 10 5 HS-HT 12 12 08/11/1999 11 10 HS-HT 13 13 09/12/1999 9 13 HS-HT Appendix D1 Estimated 5-minute hyetograph patterns for UPRC APPENDIX D1 Estimated five-minute spatially varied cumulative hyetographs patterns for UPRC (based from 29 subcatchments) Appendix D1 Estimated 5-minute hyetograph patterns for UPRC Appendix D1 Estimated 5-minute hyetograph patterns for UPRC Appendix D1 Estimated 5-minute hyetograph patterns for UPRC Appendix D1 Estimated 5-minute hyetograph patterns for UPRC Appendix D2 Estimated 5-minute hyetograph patterns for CPC APPENDIX D2 Estimated five-minute spatially varied cumulative hyetograph patterns for CPC (based from 42 subcatchments) Appendix D2 Estimated 5-minute hyetograph patterns for CPC Appendix D2 Estimated 5-minute hyetograph patterns for CPC Appendix E1 Assessment of Spatial Variability for UPRC APPENDIX E1 Quantitative assessment of Spatial variability of Events for UPRC Appendix E1 Assessment of Spatial Variability for UPRC Table E1.1: Range of relative variation in estimated rainfall (total) at individual Pixels on UPRC No Storm Category of Rainfall Total / (mm) event ID Low High Mean Std. Dev. 11aHS-HT 22.2 73.0 40.0 9.6 21bLS-HT 17.0 55.6 36.8 9.3 32aHS-HT 19.0 45.6 19.0 11.7 42bLS-HT 0 29.8 21.4 5.2 54 LS-LT 33.0 49.0 39.9 3.6 66 LS-LT 24.3 86.5 62.3 12.4 77 LS-HT 21.5 85.4 36.4 12.7 88aLS-HT 8.1 36.5 22.0 5.6 98bHS-HT 3.2 15.3 9.0 2.7 10 9a HS-LT 14.2 51.3 31.9 6.2 11 9b HS-HT 49.0 167.0 82.6 24.0 12 11a HS-HT 3.5 27.3 19.4 4.9 13 11b LS-LT 6.8 57.0 37.0 10.1 14 12 HS-HT 4.0 122.0 63.0 24.5 15 13 LS-HT 15.7 41.2 33.3 4.8 16 20 HS-LT 14.1 57.2 35.6 9.7 17 21 LS-HT 3.0 17.0 14.0 2.0 18 22a HS-HT 18.3 44.8 29.4 4.7 19 22b HS-HT 0.0 54.0 34.3 9.4 20 23 HS-HT 7.7 18.6 12.1 2.1 21 24 LS-HT 14.3 42.5 32.7 4.8 22 25 HS-LT 39.4 63.0 47.7 3.7 23 26a HS-HT 0.0 24.2 14.6 4.7 24 26b HS-HT 1.3 20.5 9.9 4.4 Appendix E1 Assessment of Spatial Variability for UPRC ρ Table E1.2: Comparison summary of coefficient of variation ( s ) from 29 subcatchments of UPRC for different classification of events Category Storm ID Event Coeffiecient of Variation Date Low High Media Mean Std. n Dev. Event 4 27/07/96 0.17 0.99 0.45 0.45 0.19 Event 5 30/08/96 0.14 0.57 0.29 0.31 0.12 LS-LT Event 6 29/01/97 0.14 0.52 0.28 0.29 0.09 Event 11b 04/05/98 0.18 0.91 0.52 0.55 0.21 Event 1b 06/01/96 0.13 0.98 0.56 0.52 0.20 Event 2b 11/04/96 0.17 0.61 0.34 0.36 0.13 Event 7 07/10/97 0.09 0.64 0.28 0.31 0.14 Event 8a 24/01/98 0.29 1.43 0.74 0.75 0.31 LS-HT Event 13 22/06/98 0.10 1.46 0.50 0.58 0.34 Event 21 01/07/99 0.08 0.39 0.19 0.21 0.07 Event 24 18/10/99 0.09 0.49 0.23 0.24 0.09 Event 9a 09/04/98 0.26 3.07 1.56 1.54 0.73 Event 12 18/05/98 0.32 1.42 0.64 0.73 0.31 HS-LT Event 20 01/04/99 0.26 1.51 0.61 0.69 0.30 Event 25 23/10/99 0.23 0.96 0.60 0.59 0.19 Event 1a 02/01/96 0.11 0.95 0.41 0.45 0.20 Event 2a 11/04/96 0.35 3.52 1.01 1.22 0.76 Event 8b 25/01/98 0.17 1.57 0.84 0.85 0.37 Event 9b 10/04/98 0.26 2.20 1.06 1.08 0.56 Event 11a 02/05/98 0.38 1.96 0.88 0.95 0.47 HS-HT Event 22a 13/07/99 0.20 1.09 0.40 0.49 0.23 Event 22b 14/07/99 0.24 1.55 0.61 0.69 0.32 Event 23 16/09/99 0.79 1.47 1.15 1.15 0.15 Event 26a 09/12/99 0.63 2.75 1.27 1.46 0.60 Event 26b 09/12/99 0.28 3.77 0.84 1.10 0.86 Appendix E2 Assessment of Spatial Variability for CPC APPENDIX E2 Quantitative assessment of Spatial variability of Events for CPC Appendix E2 Assessment of Spatial Variability for CPC Table E2.1: Range of relative variation in estimated rainfall (total) at individual Pixels on CPC Storm Category of Rainfall Total / (mm) event ID Low High Mean Std. Dev. 1LS-LT 0.0 180.0 58.2 33.2 2LS-HT64.8 231.2 103.4 34.1 3HS-HT 0.0 85 41 14.4 4HS-HT 0.0 103.0 14.7 23.0 5HS-HT 4.4 115.0 83.0 20.8 6HS-HT 0.0 45.1 13.6 10.6 7HS-HT 0.0 36.4 7.2 9.0 8LS-HT 7.2 21.5 12.1 2.6 9HS-HT 0.0 126.2 34.2 32.0 10 LS-HT 0.0 87.2 23.5 21.6 11 HS-HT 0.0 99.8 23.6 25.6 12 HS-HT 0.0 61.2 17.5 12.1 13 HS-HT 1.5 83.1 19.2 17.4 Appendix E2 Assessment of Spatial Variability for CPC ρ Table E2.2: Comparison summary of coefficient of variation ( s ) from 42 subcatchments of CPC for different classification of events. Event ρ Category Storm ID Coeffiecient of Variation ( s ) Date Low High Median Mean Std. Dev. Event 1 29/01/97 0.10 0.92 0.49 0.50 0.26 LS-LT Event 2 11/02/97 0.05 0.92 0.51 0.50 0.28 Event 9 14/08/99 0.06 1.09 0.53 0.55 0.32 Event 8 19/10/98 0.09 1.57 0.99 0.91 0.50 LS-HT Event 10 18/10/99 0.06 1.12 0.61 0.59 0.34 Event 3 22/04/98 0.05 1.23 0.69 0.66 0.37 HS-LT Event 11 23/10/99 0.07 1.14 0.55 0.58 0.33 Event 4 04/05/98 0.08 2.03 1.39 1.26 0.69 Event 5 18/05/98 0.09 1.48 0.92 0.84 0.44 HS-HT Event 6 16/06/98 0.19 3.86 2.00 1.98 1.20 Event 7 09/10/98 0.10 2.59 1.36 1.36 0.81 Event 12 08/11/99 0.10 1.65 1.05 0.92 0.46 Event 13 09/12/99 0.13 1.84 0.94 0.97 0.53 Appendix F1 Typical SWMM input file for UPRC APPENDIX F1 Typical SWMM input data file for UPRC : Storm Event on July 27, 1996 ; with spatially distributed rainfall input Appendix F1 Typical SWMM input file for UPRC SW 2 0 8 8 0 MM 7 1 2 3 10 11 12 13 $ANUM $RUNOFF A1 'Validation of UPRC model- Event 13: on 22/06/1998' A1 'K.Umakhanthan, Run performed 23/06/2001; output : spli13out' * METRIC ISNOW NRGAG INFILM KWALTY IVAP NHR NMN NDAY MONTH ITRSTR B1 1 0 29 1 0 1 17 15 22 6 98 * IPRN(1) IPRN(2) IPRN(3) B2 0 1 0 * WET WETDRY DRY LUNIT LONG B3 60 60 3600 2 48 * PCTZER REGEN B4 0.0 0.01 * ROPT D1 0 * KTYPE KINC KPRINT KTHIS KTIME KPREP NHISTO THISTO TZRAIN E1 0 67 0 0 0 1 67 5 1035 E3 0.02 0.00 0.00 0.00 0.00 0.09 0.29 0.32 0.30 0.27 0.63 0.38 0.59 0.50 0.48 0.45 0.41 0.43 0.28 0.24 0.08 0.08 0.08 0.08 0.09 0.52 0.41 0.18 0.21 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.02 0.06 0.50 0.44 0.30 0.32 0.31 0.24 0.21 0.23 0.26 0.31 0.33 1.61 1.22 0.83 1.02 0.96 0.91 0.68 0.67 3.61 3.44 2.06 0.95 1.05 0.08 0.06 0.02 0.01 0.02 E3 0.02 0.08 0.17 0.12 0.08 0.13 0.31 0.40 0.40 0.33 0.53 0.52 0.48 0.57 0.46 0.42 0.42 0.46 0.28 0.22 0.13 0.12 0.11 0.11 0.09 0.31 0.18 0.26 0.14 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.29 0.40 0.72 0.39 0.34 0.32 0.33 0.32 0.23 0.19 0.29 0.33 0.33 1.03 0.83 0.93 0.88 1.38 1.07 1.77 1.81 3.00 2.68 1.47 0.68 0.88 0.15 0.08 0.11 0.13 0.04 E3 0.02 0.07 0.25 0.23 0.15 0.18 0.28 0.46 0.44 0.39 0.48 0.70 0.30 0.39 0.43 0.42 0.52 0.47 0.18 0.20 0.13 0.13 0.12 0.12 0.13 0.20 0.05 0.25 0.08 0.09 0.09 0.09 0.10 0.09 0.09 0.09 0.80 0.92 1.13 0.18 0.35 0.33 0.37 0.34 0.23 0.16 0.27 0.29 0.28 0.64 1.31 0.70 0.53 1.40 1.44 2.93 3.04 2.68 2.49 0.75 0.53 0.77 0.30 0.06 0.13 0.11 0.03 E3 0.02 0.19 0.22 0.23 0.28 0.38 0.44 0.37 0.53 0.42 0.33 0.51 0.53 0.51 0.37 0.28 0.28 0.29 0.38 0.23 0.17 0.18 0.28 0.43 0.36 0.27 0.14 0.13 0.13 0.12 0.12 0.21 0.29 0.28 0.23 0.22 0.43 0.53 0.61 0.42 0.31 0.36 0.37 0.47 0.23 0.14 0.15 0.21 0.30 0.23 0.36 0.75 2.08 1.13 1.11 1.43 1.63 2.40 1.89 0.74 0.53 0.58 0.48 0.28 0.20 0.14 0.03 E3 0.02 0.02 0.03 0.00 0.00 0.08 0.34 0.39 0.28 0.24 0.53 0.40 0.89 0.73 0.53 0.44 0.38 0.52 0.38 0.21 0.08 0.08 0.08 0.08 0.08 0.54 0.63 0.33 0.27 0.13 0.13 0.13 0.14 0.13 0.13 0.13 0.00 0.12 0.68 0.70 0.28 0.29 0.28 0.26 0.33 0.32 0.28 0.29 0.35 1.33 1.32 1.78 1.83 1.33 0.84 0.49 0.48 3.20 3.81 2.43 0.96 1.00 0.30 0.18 0.10 0.08 0.04 E3 0.11 0.11 0.20 0.23 0.23 0.21 0.29 0.34 0.45 0.45 0.33 0.60 0.98 0.48 0.43 0.32 0.32 0.47 0.28 0.26 0.20 0.30 0.26 0.24 0.30 0.33 0.26 0.27 0.09 0.08 0.08 0.12 0.23 0.09 0.09 0.11 0.33 0.88 0.89 0.68 0.42 0.20 0.18 0.23 0.27 0.33 0.32 0.31 0.27 0.20 0.56 1.43 1.28 1.03 1.52 1.90 2.52 3.27 2.45 1.25 0.70 0.72 0.38 0.32 0.21 0.11 0.10 E3 0.00 0.11 0.15 0.15 0.27 0.57 0.45 0.22 0.33 0.28 0.26 0.71 0.27 0.39 0.25 0.28 0.28 0.32 0.41 0.22 0.16 0.09 0.33 0.42 0.36 0.22 0.08 0.07 0.11 0.09 0.09 0.23 0.28 0.32 0.23 0.22 0.69 0.52 0.47 0.38 0.16 0.40 0.45 0.41 0.02 0.07 0.13 0.26 0.41 0.20 0.33 1.02 2.47 1.42 1.20 1.63 1.53 2.73 1.63 0.39 0.47 0.53 0.54 0.22 0.16 0.13 0.00 Appendix F1 Typical SWMM input file for UPRC E3 0.02 0.00 0.01 0.08 0.08 0.13 0.30 0.45 0.34 0.30 0.31 0.46 1.05 1.08 0.51 0.40 0.38 0.58 0.40 0.13 0.08 0.09 0.09 0.08 0.10 0.34 0.58 0.41 0.24 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.12 0.50 0.81 0.78 0.23 0.23 0.23 0.23 0.34 0.37 0.30 0.27 0.28 0.45 0.98 2.33 2.23 1.38 1.04 0.95 0.85 2.13 3.95 2.52 0.79 0.72 0.66 0.32 0.14 0.05 0.03 E3 0.01 0.09 0.23 0.16 0.13 0.15 0.33 0.48 0.43 0.36 0.43 0.69 0.85 0.72 0.46 0.40 0.46 0.55 0.34 0.19 0.18 0.13 0.11 0.11 0.13 0.33 0.38 0.26 0.09 0.06 0.06 0.06 0.05 0.06 0.06 0.06 0.29 0.83 1.12 0.53 0.31 0.27 0.31 0.35 0.34 0.28 0.28 0.28 0.30 0.50 1.73 1.99 1.07 1.70 1.32 1.77 2.18 2.82 2.66 1.47 0.72 0.76 0.47 0.23 0.23 0.23 0.05 E3 0.06 0.08 0.13 0.26 0.28 0.28 0.32 0.32 0.42 0.46 0.35 0.54 0.68 0.44 0.45 0.33 0.31 0.41 0.24 0.26 0.15 0.20 0.20 0.30 0.31 0.29 0.20 0.22 0.11 0.10 0.10 0.11 0.16 0.16 0.16 0.13 0.44 0.83 0.72 0.65 0.43 0.30 0.22 0.24 0.41 0.33 0.32 0.30 0.38 0.26 0.43 0.98 1.01 1.18 1.46 1.80 2.33 3.04 2.78 1.33 0.77 0.68 0.38 0.28 0.18 0.06 0.10 E3 0.02 0.08 0.18 0.12 0.08 0.13 0.32 0.41 0.40 0.34 0.42 0.53 0.80 0.76 0.48 0.39 0.36 0.53 0.37 0.20 0.15 0.13 0.11 0.11 0.10 0.33 0.36 0.34 0.16 0.09 0.09 0.09 0.08 0.09 0.09 0.09 0.11 0.48 0.77 0.67 0.32 0.26 0.28 0.30 0.29 0.28 0.32 0.33 0.33 0.73 0.80 1.87 1.44 1.59 1.05 1.40 1.60 2.98 2.75 1.79 0.73 0.82 0.32 0.19 0.18 0.18 0.06 E3 0.01 0.00 0.03 0.20 0.23 0.23 0.20 0.28 0.43 0.44 0.32 0.55 0.68 0.71 0.40 0.36 0.35 0.49 0.23 0.23 0.13 0.11 0.13 0.15 0.20 0.20 0.18 0.18 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.07 0.43 0.82 0.65 0.53 0.30 0.26 0.21 0.17 0.21 0.29 0.33 0.33 0.34 0.24 0.59 1.33 0.90 0.92 1.46 1.73 2.07 2.98 2.98 1.56 0.73 0.62 0.48 0.23 0.09 0.00 0.01 E3 0.02 0.08 0.22 0.18 0.11 0.16 0.28 0.41 0.43 0.37 0.52 0.58 0.33 0.47 0.43 0.42 0.46 0.45 0.23 0.22 0.13 0.13 0.11 0.11 0.11 0.24 0.08 0.23 0.10 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.51 0.58 0.83 0.27 0.35 0.33 0.35 0.33 0.21 0.16 0.28 0.33 0.31 0.90 0.91 0.68 0.60 1.35 1.21 2.30 2.37 2.92 2.47 1.10 0.60 0.83 0.16 0.06 0.11 0.12 0.03 E3 0.03 0.01 0.03 0.23 0.28 0.28 0.40 0.33 0.44 0.42 0.33 0.52 0.59 0.70 0.54 0.40 0.36 0.39 0.27 0.28 0.14 0.15 0.19 0.32 0.28 0.28 0.24 0.15 0.10 0.09 0.09 0.09 0.10 0.09 0.09 0.08 0.41 0.72 0.57 0.60 0.48 0.43 0.27 0.21 0.51 0.43 0.33 0.30 0.79 0.31 0.49 0.80 0.73 1.23 1.33 1.53 1.93 2.65 3.60 1.65 0.93 0.60 0.51 0.37 0.18 0.06 0.09 E3 0.02 0.00 0.00 0.02 0.18 0.46 0.26 0.31 0.28 0.31 0.43 1.04 1.08 0.31 0.35 0.39 0.56 0.56 0.24 0.22 0.18 0.13 0.15 0.14 0.28 0.57 0.69 0.00 0.05 0.07 0.07 0.05 0.05 0.05 0.05 0.05 0.44 1.15 1.39 0.48 0.22 0.20 0.22 0.29 0.34 0.36 0.21 0.22 0.21 0.56 3.67 2.45 0.74 1.26 1.85 1.27 2.17 3.87 3.23 1.41 1.05 0.82 0.68 0.28 0.15 0.03 0.01 E3 0.05 0.18 0.22 0.23 0.27 0.30 0.46 0.36 0.34 0.35 0.36 0.47 0.62 0.43 0.35 0.28 0.28 0.28 0.41 0.23 0.18 0.25 0.37 0.43 0.41 0.32 0.11 0.13 0.10 0.10 0.10 0.23 0.38 0.33 0.26 0.24 0.48 0.57 0.59 0.46 0.35 0.36 0.38 0.35 0.21 0.18 0.17 0.23 0.30 0.19 0.15 0.43 1.99 1.21 1.27 1.53 1.62 2.43 2.13 0.89 0.58 0.67 0.40 0.30 0.18 0.18 0.07 E3 0.06 0.24 0.31 0.35 0.36 0.36 0.41 0.43 0.48 0.48 0.38 0.41 0.58 0.47 0.39 0.28 0.26 0.28 0.37 0.22 0.16 0.23 0.23 0.42 0.36 0.28 0.09 0.18 0.14 0.13 0.13 0.18 0.27 0.33 0.31 0.23 0.32 0.53 0.57 0.53 0.42 0.31 0.28 0.47 0.48 Appendix F1 Typical SWMM input file for UPRC 0.19 0.22 0.23 0.13 0.26 0.10 0.42 1.41 1.38 1.13 1.38 1.73 2.19 1.98 1.21 0.58 0.68 0.26 0.23 0.18 0.17 0.13 E3 0.02 0.03 0.05 0.03 0.02 0.07 0.38 0.46 0.28 0.23 0.39 0.45 1.15 0.94 0.59 0.43 0.37 0.60 0.43 0.16 0.07 0.08 0.08 0.08 0.07 0.51 0.83 0.50 0.32 0.08 0.08 0.09 0.09 0.08 0.08 0.09 0.02 0.32 0.90 0.95 0.25 0.27 0.26 0.25 0.42 0.41 0.30 0.27 0.36 0.91 1.34 2.73 2.66 1.65 0.87 0.64 0.64 2.70 4.19 2.68 0.93 0.89 0.60 0.32 0.19 0.12 0.07 E3 0.04 0.05 0.12 0.14 0.34 0.98 0.38 0.19 0.16 0.18 0.22 1.18 0.53 0.26 0.23 0.32 0.43 0.46 0.35 0.20 0.19 0.27 0.33 0.32 0.31 0.31 0.29 0.12 0.13 0.13 0.12 0.13 0.18 0.13 0.12 0.13 0.72 0.69 0.78 0.61 0.23 0.21 0.25 0.37 0.21 0.24 0.27 0.32 0.33 0.35 1.34 1.92 1.58 1.78 1.51 1.88 2.08 3.09 2.30 1.04 0.69 0.68 0.46 0.23 0.10 0.08 0.05 E3 0.03 0.00 0.04 0.19 0.22 0.22 0.20 0.25 0.43 0.47 0.32 0.61 0.70 0.52 0.41 0.35 0.33 0.50 0.18 0.25 0.13 0.13 0.14 0.17 0.23 0.23 0.21 0.22 0.08 0.07 0.07 0.07 0.08 0.06 0.06 0.07 0.50 0.96 0.77 0.61 0.32 0.26 0.20 0.15 0.21 0.31 0.34 0.34 0.35 0.23 0.64 1.50 1.00 0.94 1.58 2.00 2.52 3.47 2.80 1.28 0.74 0.64 0.48 0.23 0.13 0.00 0.03 E3 0.07 0.05 0.04 0.06 0.18 0.31 0.30 0.35 0.35 0.35 0.41 0.81 1.33 0.53 0.41 0.36 0.44 0.53 0.34 0.23 0.22 0.23 0.21 0.19 0.30 0.57 0.68 0.08 0.07 0.08 0.08 0.08 0.14 0.06 0.07 0.08 0.06 0.91 1.15 0.68 0.30 0.16 0.18 0.28 0.38 0.41 0.24 0.23 0.23 0.47 2.65 2.41 1.04 1.20 1.61 0.78 1.73 3.71 2.98 1.75 1.04 0.83 0.56 0.37 0.21 0.13 0.06 E3 0.02 0.10 0.22 0.13 0.15 0.18 0.31 0.40 0.43 0.38 0.37 0.69 1.12 0.78 0.44 0.36 0.37 0.58 0.39 0.21 0.21 0.14 0.13 0.13 0.17 0.38 0.49 0.23 0.08 0.04 0.04 0.04 0.04 0.05 0.04 0.04 0.03 0.79 0.98 0.74 0.30 0.20 0.24 0.31 0.33 0.34 0.31 0.31 0.30 0.37 1.57 2.56 1.23 1.68 1.33 1.20 1.90 3.28 2.43 1.69 0.81 0.74 0.48 0.30 0.27 0.25 0.06 E3 0.01 0.01 0.05 0.19 0.20 0.20 0.21 0.35 0.42 0.41 0.32 0.50 0.78 0.89 0.40 0.36 0.35 0.51 0.30 0.18 0.13 0.11 0.12 0.12 0.15 0.20 0.23 0.23 0.11 0.07 0.07 0.07 0.06 0.07 0.07 0.07 0.29 0.67 0.63 0.56 0.26 0.23 0.22 0.20 0.22 0.28 0.32 0.32 0.25 0.27 0.55 1.56 1.22 1.06 1.28 1.47 1.63 2.55 3.05 1.88 0.70 0.63 0.48 0.23 0.09 0.01 0.01 E3 0.10 0.18 0.24 0.33 0.34 0.33 0.38 0.41 0.42 0.46 0.38 0.46 0.73 0.44 0.43 0.29 0.28 0.33 0.33 0.23 0.17 0.28 0.25 0.38 0.36 0.31 0.15 0.21 0.13 0.13 0.13 0.15 0.26 0.26 0.25 0.19 0.33 0.66 0.66 0.62 0.47 0.28 0.23 0.35 0.49 0.28 0.27 0.26 0.18 0.26 0.20 0.55 1.12 1.29 1.32 1.54 1.98 2.48 2.47 1.43 0.69 0.73 0.26 0.27 0.17 0.13 0.15 E3 0.02 0.01 0.04 0.06 0.15 0.28 0.28 0.38 0.34 0.35 0.45 0.90 1.05 0.43 0.40 0.40 0.53 0.56 0.26 0.21 0.18 0.12 0.13 0.13 0.24 0.50 0.61 0.08 0.05 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.41 1.13 1.39 0.47 0.25 0.23 0.25 0.30 0.35 0.34 0.22 0.23 0.23 0.51 3.23 2.28 0.79 1.32 1.74 1.47 2.28 3.58 3.10 1.38 0.96 0.80 0.64 0.27 0.19 0.10 0.02 E3 0.02 0.11 0.22 0.10 0.06 0.10 0.38 0.48 0.39 0.30 0.36 0.53 0.98 0.95 0.54 0.40 0.35 0.58 0.45 0.18 0.14 0.13 0.10 0.10 0.07 0.35 0.53 0.47 0.22 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.00 0.43 0.86 0.85 0.32 0.26 0.29 0.33 0.38 0.33 0.33 0.32 0.37 0.64 0.79 2.48 2.05 1.93 0.91 1.22 1.33 2.59 3.02 2.11 0.73 0.80 0.44 0.28 0.25 0.26 0.08 E3 0.01 0.07 0.20 0.17 0.13 0.17 0.31 0.48 0.43 0.38 0.44 0.75 0.73 0.57 0.44 0.41 0.51 0.53 0.28 0.18 0.16 0.12 0.11 0.11 0.16 0.32 0.32 0.23 0.08 0.06 0.06 0.06 0.06 0.07 Appendix F1 Typical SWMM input file for UPRC 0.06 0.06 0.52 0.98 1.25 0.39 0.31 0.28 0.33 0.34 0.33 0.26 0.26 0.27 0.28 0.49 2.00 1.68 0.88 1.57 1.47 2.18 2.58 2.82 2.75 1.19 0.69 0.76 0.49 0.19 0.21 0.18 0.04 E3 0.01 0.09 0.21 0.13 0.13 0.15 0.33 0.46 0.43 0.36 0.41 0.71 1.01 0.76 0.46 0.39 0.44 0.57 0.38 0.19 0.19 0.12 0.10 0.11 0.14 0.38 0.48 0.24 0.08 0.04 0.05 0.05 0.03 0.05 0.05 0.05 0.17 0.83 1.12 0.61 0.29 0.24 0.28 0.33 0.36 0.32 0.28 0.28 0.30 0.46 1.93 2.34 1.14 1.72 1.33 1.43 1.98 3.01 2.67 1.62 0.79 0.77 0.51 0.27 0.25 0.24 0.05 E3 0.08 0.07 0.12 0.15 0.23 0.41 0.31 0.33 0.35 0.35 0.35 0.83 1.00 0.43 0.38 0.34 0.42 0.50 0.29 0.23 0.20 0.26 0.24 0.23 0.29 0.42 0.43 0.17 0.09 0.09 0.08 0.10 0.18 0.08 0.08 0.09 0.37 0.89 1.04 0.63 0.33 0.18 0.20 0.28 0.30 0.34 0.28 0.28 0.25 0.35 1.70 1.88 1.18 1.23 1.58 1.58 2.23 3.34 2.73 1.38 0.83 0.75 0.48 0.31 0.18 0.10 0.07 * JAN FEB MARCH APRIL MAY JUNE JULY AUG SEP OCT NOV DEC F1 5.8 5.1 4.2 3.2 2.1 1.8 2.0 2.6 3.0 4.3 5.3 6.5 * NAMEG NGTO NPG GWIDTH GLEN G3 GS1 GS2 G6 DFULL GDEPTH G1 92.00C L20-10 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 L20-10 9.010J 1 3 240 0.0083333 2 2 0.035 2 0 G1 9.000C L10-80 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 L10-80 9.010J 1 3 850 0.01117652 2 2 0.035 2 0 G1 9.010J L10-70 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 L10-70 9.020C 1 3 550 0.0072727 2 2 0.035 2 0 G1 9.020C L10-60 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 L10-60 9.030T 1 3 980 0.0059592 2 2 0.035 2 0 G1 66.00C G17-10 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 G17-10 65.01J 1 3 750 0.0046667 2 2 0.045 2 0 G1 65.00C G16-10 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 G16-10 65.01J 1 3 300 0.01 2 2 0.045 2 0 G1 65.01J G16-20 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 G16-20 65.02L 1 3 1080 0.0032407 2 2 0.045 2 0 G1 13.00C NMG4-0 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 NMG4-0 13.01T 1 3 1400 0.0147857 1 1 0.035 2 0 G1 2.000C D3-500 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D3-500 2.010j 1 3 220 0.0136364 1 1 0.05 3 0 G1 21.00C D4-100 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D4-100 2.010j 1 3 350 0.0071429 1 1 0.05 3 0 G1 2.010j D3-450 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D3-450 2.020J 1 3 600 0.0075 1 1 0.05 3 0 G1 23.00C D5-100 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D5-100 2.020J 1 3 400 0.025 1 1 0.05 3 0 G1 2.020J D3-400 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D3-400 2.030C 1 3 720 0.0180556 1 1 0.05 3 0 G1 2.030C D3-350 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D3-350 2.040J 1 3 50 0.037 1 1 0.05 3 0 G1 25.00C D7-100 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D7-100 25.01J 1 3 50 0.02 1 1 0.05 3 0 G1 24.00C D6-100 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D6-100 25.01J 1 3 50 0.02 1 1 0.05 3 0 G1 25.01J D7-200 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D7-200 25.02L 1 3 1250 0.028 1 1 0.05 3 0 G1 25.02L D7-300 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 D7-300 2.040J 1 3 50 0.027 1 1 0.05 3 0 G1 3.000C H9-100 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 H9-100 3.010T 1 3 2600 0.0053846 1 1 0.014 2 0 G1 48.00C BF45-2 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 G1 BF45-2 45.00T 1 3 1850 0.0102703 2 2 0.045 3 0 Appendix F1 Typical SWMM input file for UPRC * SUBCATCHMENT CHARACTERISTICS * JK NAMEW NGTO WIDTH WAREA IMP WSLOP IRGH PRGH ISTOR PSTOR WLMX WLMN DECAY H1 25 1.000T 1.000T 297. 172.5 34.6 2.6 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 25 1.010L 1.010L 511. 456.1 29.12 2.9 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 29 95.00T 95.00T 320. 226.8 26.5 3.5 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 21 18.01T 18.01T 207. 147.9 30.3 2.9 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 29 1.020L 1.020L 132. 163.2 23.7 3.7 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 29 1.030L 1.030L 224. 218.4 47.3 2.7 0.025 0.028 1.5 2.5 227.38 1.7 0.17 1 H1 19 9.000C 9.000C 320. 206.1 8.7 2.2 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 19 92.00C 92.00C 291. 150.8 20.0 2.3 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 19 9.020C 9.020C 215. 154.1 40. 2.0 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 19 9.030T 9.030T 152. 130.0 30. 2.1 0.025 0.028 1.5 2.5 207.75 1.7 0.17 1 H1 19 9.040L 9.040L 176. 92.5 38.2 1.6 0.025 0.028 1.5 2.5 200.62 1.7 0.17 1 H1 4 8.000C 8.000C 550. 289.1 21.8 4.0 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 4 8.010T 8.010T 160. 107.1 27.3 3.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 4 8.020L 8.020L 176. 103.6 27.3 2.9 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 7 82.00T 82.00T 320. 121.1 38.4 2.2 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 7 8.030L 8.030L 68. 95.9 26.4 2.3 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 16 10.00T 10.00T 312. 179.6 20.9 2.6 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 16 10.01L 10.01L 144. 72.7 22.8 3.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 4 8.050L 8.050L 288. 141.2 23.7 1.9 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 4 1.050L 1.050L 176. 77.9 30.0 1.2 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 17 65.00C 65.00C 240. 148.3 15.4 3.1 0.025 0.028 1.5 2.5 166.40 1.7 0.17 1 H1 17 66.00C 66.00C 219. 139.8 4.1 3.1 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 17 65.02L 65.02L 256. 294.1 31.9 2.3 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 17 65.03L 65.03L 272. 263.2 33.7 1.7 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 17 65.04L 65.04L 456. 59.9 39.1 1.9 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 24 6.000T 6.000T 368. 181.4 33.7 2.4 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 24 6.010L 6.010L 268. 167.7 38.2 3.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 24 6.020L 6.020L 219. 119.5 37.6 2.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 24 6.030L 6.030L 176. 96. 35.0 1.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 6 1.070L 1.070L 161. 178.1 33.5 2.6 0.025 0.028 1.5 2.5 197.24 1.7 0.17 1 H1 29 1.080L 1.080L 320. 354.1 25.7 2.4 0.025 0.028 1.5 2.5 193.03 1.7 0.17 1 H1 22 13.00C 13.00C 288. 185.5 28.2 2.9 0.025 0.028 1.5 2.5 220.0 1.7 0.17 1 H1 22 13.01T 13.01T 192. 143. 24.6 4.2 0.025 0.028 1.5 2.5 220.0 1.7 0.17 1 H1 29 1.090L 1.090L 240. 120.2 29.5 2.7 0.025 0.028 1.5 2.5 214.8 1.7 0.17 1 H1 10 5.000T 5.000T 580. 217.6 31. 1.9 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 10 5.010L 5.010L 160. 152.2 36.3 2.6 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 10 5.020L 5.020L 160. 59.9 34.2 0.8 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 14 4.000T 4.000T 271. 287.9 33.1 2.2 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 14 4.010L 4.010L 160. 174.8 32. 2.1 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 14 4.020L 4.020L 248. 127.9 36.4 1.8 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 20 51.00T 51.00T 255. 82.2 23.9 2.2 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 29 1.110L 1.110L 216. 118.3 29.5 3.2 0.025 0.028 1.5 2.5 175.5 1.7 0.17 1 H1 5 2.000C 2.000C 335. 264. 29.5 4.4 0.025 0.028 1.5 2.5 179.8 1.7 0.17 1 H1 1 21.00C 21.00C 527. 320. 26.4 4.0 0.025 0.028 1.5 2.5 222.1 1.7 0.17 1 H1 2 23.00C 23.00C 400. 145. 23.3 5.1 0.025 0.028 1.5 2.5 193.4 1.7 0.17 1 H1 26 2.030C 2.030C 254. 149. 14.7 4.3 0.025 0.028 1.5 2.5 178.8 1.7 0.17 1 H1 13 24.00C 24.00C 383. 188.9 28.6 4.9 0.025 0.028 1.5 2.5 220.0 1.7 0.17 1 H1 3 25.00C 25.00C 140. 262. 26. 3.5 0.025 0.028 0.35 2.5 227.0 1.7 0.17 1 H1 27 25.02L 25.02L 365. 217. 32.1 4.5 0.025 0.028 1.5 2.5 225.70 1.7 0.17 1 H1 11 34.00T 34.00T 280. 142. 26.1 4.7 0.025 0.028 1.5 2.5 206.0 1.7 0.17 1 H1 28 2.050L 2.050L 320. 255.3 25.9 4.8 0.025 0.028 1.5 2.5 212.7 1.7 0.17 1 H1 11 2.060L 2.060L 225. 213.3 33.7 2.8 0.025 0.028 1.5 2.5 190.0 1.7 0.17 1 H1 18 3.000C 3.000C 432. 410. 42.3 2.8 0.025 0.028 1.5 2.5 191.8 1.7 0.17 1 H1 8 3.010T 3.010T 432. 342. 24.5 3.2 0.025 0.028 1.5 2.5 191.8 1.7 0.17 1 H1 23 2.080L 2.080L 136. 111.4 46.4 4.8 0.025 0.028 1.5 2.5 130.5 1.7 0.17 1 H1 12 52.00T 52.00T 320. 26.2 28.8 1.5 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 H1 23 1.140L 1.140L 200. 108.8 37.6 1.5 0.025 0.028 1.5 2.5 199.3 1.7 0.17 1 Appendix F1 Typical SWMM input file for UPRC H1 8 48.00C 48.00C 208. 79.9 37.1 2.5 0.025 0.028 1.5 2.5 167.3 1.7 0.17 1 H1 8 45.00T 45.00T 320. 225.2 32.8 2.4 0.025 0.028 1.5 2.5 178.3 1.7 0.17 1 H1 23 1.160L 1.160L 240. 163.8 39.7 1.8 0.025 0.028 1.5 2.5 169.9 1.7 0.17 1 M1 1 1 * NDET STARTP STOPPR M2 1 980622 980624 * IPRNT M3 1.140L $ANUM $TRANSPORT A1 'TRANSPORT BLOCKS BEGINS – Event 13: on 22/06/2998' A1 'K.Umakhanthan Run performed : 23/06/2001 – Spline Rainfall Input' * Control Data * NDT NINPUT NNYN NNPE(J2) NOUTS(H1) NPRINT NPOLL NITER IDATEZ METRIC INTPRT B1 576 0 0 1 0 0 0 4 980622 1 1 * DT EPSIL DWDAYS TZERO GNU TRIBA B2 300 0.0001 1 17.25 0.01 11000 * NCNTRL NINFIL NFILTH NDESN B3 0 0 0 0 * NKALSS KPRINT C1 0 0 * NOE NUE(1) NUE(2) NUE(3) NTYPE DIST GEOM(1) SLOP ROUGH GEOM(2) BARR GEOM(3) KGEOM E1 '1.000T' '' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T53-5' '1.000T' '' '' 16 292.5 0 1.36752 0 0 1 0 ' ' E1 'T53.3' 'T53-5' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T53-3' 'T53.3' '' '' 16 200.7 0 1.25495 0 0 2 0 ' ' E1 'T53.0' 'T53-3' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T53-0' 'T53.0' '' '' 16 334.5 0 1.96712 0 0 3 0 ' ' E1 'T52.3' 'T53-0' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T52-3' 'T52.3' '' '' 16 260 0 2.09615 0 0 4 0 ' ' E1 'T52.1' 'T52-3' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T52-1' 'T52.1' '' '' 16 201 0 0.88557 0 0 5 0 ' ' E1 'T51.8' 'T52-1' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T51-8' 'T51.8' '' '' 16 273 0 1.03663 0 0 6 0 ' ' E1 'T51.6' 'T51-8' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T51-6' 'T51.6' '' '' 16 219 0 0.76256 0 0 7 0 ' ' E1 'T51.4' 'T51-6' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T51-4' 'T51.4' '' '' 16 325 0 0.64615 0 0 8 0 ' ' E1 '95.00T' '' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T58-5' '95.00T' '' '' 16 269 0 0.72119 0 0 9 0 ' ' E1 'T58.3' 'T58-5' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T58-3' 'T58.3' '' '' 16 345.2 0 1.1993 0 0 10 0 ' ' E1 'T57.7' 'T58-3' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T57-7' 'T57.7' '' '' 16 257 0 1.07393 0 0 11 0 ' ' E1 'T57.3' 'T57-7' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T57-3' 'T57.3' '' '' 16 217 0 1.40092 0 0 12 0 ' ' E1 '1.010L' 'T57-3' 'T51-4' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T51-0 ' '1.010L' '' '' 16 151.7 0 1.07449 0 0 13 0 ' ' E1 'T50.90' 'T51-0' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T50-90' 'T50.90' '' '' 16 406 0 0.69212 0 0 14 0 ' ' E1 'T50.50' 'T50-90' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T50-50' 'T50.50' '' '' 16 209 0 0.2823 0 0 15 0 ' ' E1 'T50.30' 'T50-50' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'T50-30' 'T50.30' '' '' 16 137 0 0.57664 0 0 16 0 ' ' E1 'T50.10' 'T50-30' '' '' 19 0 0 0 0 0 1.0 0 ' ' * >>>>>>>>>>>>>>>>>>>>>>>>>>>es. E1 '1.140L' 'P12-00' '' '' 22 0 0 0 0 0 1.0 0 ' ' E1 'P10-00' '1.140L' '' '' 16 273 0 0.50916 0 0 209 0 ' ' E1 'P9.100' 'P10-00' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P9-100' 'P9.100' '' '' 16 260 0 0.13 0 0 210 0 ' ' Appendix F1 Typical SWMM input file for UPRC E1 'P9.000' 'P9-100' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P9-000' 'P9.000' '' '' 16 210 0 0.13 0 0 211 0 ' ' E1 'P8.900' 'P9-000' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P8-900' 'P8.900' '' '' 16 245 0 0.16 0 0 212 0 ' ' E1 'P8.300' 'P8-900' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P8-200' 'P8.300' '' '' 16 321 0 0.16 0 0 213 0 ' ' E1 'P7.000' 'P8-200' '' '' 22 0 0 0 0 0 1.0 0 ' ' E1 'P6-100' 'P7.000' '' '' 16 139 0 0.3 0 0 214 0 ' ' E1 'P4.000' 'P6-100' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P2-900' 'P4.000' '' '' 16 345.6 0 0.13 0 0 215 0 ' ' E1 '45.00T' '' '' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'BF45-1' '45.00T' '' '' 16 67 0 0.35821 0 0 216 0 ' ' E1 'P2.180' 'BF45-1' 'P2-900' '' 19 0 0 0 0 0 1.0 0 ' ' E1 'P2-180' 'P2.180' '' '' 16 242 0 0.19008 0 0 217 0 ' ' E1 '1.160L' 'P2-180' '' '' 22 0 0 0 0 0 1.0 0 ' ' E1 'P1-000' '1.160L' '' '' 16 161 0 0.6087 0 0 218 0 ' ' E1 'P1.000' 'P1-000' '' '' 19 0 0 0 0 0 1.0 0 ' ' * Channel Cross Section Data NC 0.0600 0.0600 0.0400 ' ' X1 1 14 35 47 0.0 0.0 292.5 0.0 0.0 GR 80, 0, 76, .1, 75, 12.5, 74, 21, 73, 25, GR 72, 26, 71, 31, 70, 35, 69, 40.5, 70, 47, GR 71, 50, 72, 51.5, 73, 57, 80, 57.1, NC 0.0550, 0.0550, 0.0400, X1 2, 19, 24.5, 35, 0.0, 0.0, 200.7, 0.0, 0.0, , , , , GR 75, 0, 73, .1, 72, 3.2, 71, 8, 70, 15, GR 69, 18.5, 68, 20, 67, 23.5, 66, 24.5, 65, 29, GR 66, 35, 67, 38.5, 68, 42.5, 69, 46.5, 70, 49, GR 71, 54, 72, 61.5, 73, 79, 75, 79.1, NC 0.0550, 0.0550, 0.0350, X1 3, 15, 44.8, 51, 0.0, 0.0, 334.5, 0.0, 0.0, , , , , GR 73, 0, 68, .1, 67, 25, 66, 35, 65, 39, GR 64, 44.8, 63, 45, 62.59, 47, 63, 49, 64, 51, GR 65, 53, 66, 56, 67, 70, 68, 81, 73, 81.1, NC 0.0550, 0.0550, 0.0350, X1 4, 21, 11.5, 22.2, 0.0, 0.0, 260, 0.0, 0.0, , , , , GR 70, 0, 65, .1, 64, .8, 63, 1.8, 62, 3, GR 61, 4, 60, 6, 59, 7, 58, 8.8, 57, 11.5, GR 56.03, 15.8, 57, 22.2, 58, 29, 59, 33, 60, 35, GR 61, 37.5, 62, 42, 63, 46, 64, 54, 65, 61.5, GR 70, 61.6, NC 0.0600, 0.0600, 0.0400, X1 5, 25, 29.8, 41, 0.0, 0.0, 201, 0.0, 0.0, , , , , GR 65, 0, 61, .1, 60, 8, 59, 14, 58, 16.5, GR 57, 19.5, 56, 22, 55, 23.5, 54, 25, 53, 28, GR 52, 29.8, 51, 32, 50.58, 34, 51, 37, 52, 41, GR 53, 43, 54, 47, 55, 49.8, 56, 51.1, 57, 53.5, GR 58, 54.8, 59, 61, 60, 64, 61, 71, 65, 71.1, NC 0.0700, 0.0700, 0.0500, X1 6, 27, 79.2, 91.2, 0.0, 0.0, 273, 0.0, 0.0, , , , , GR 65, 0, 60, .1, 59, 13, 58, 22, 57, 35, GR 56, 41, 55, 45, 54, 49.5, 53, 53.2, 52, 59.5, GR 51, 68.5, 50, 79.2, 49, 81, 48, 84, 49, 89, GR 50, 91.2, 51, 93, 52, 94.5, 53, 97, 54, 98, GR 55, 100, 56, 103.5, 57, 115, 58, 118.5, 59, 123, GR 60, 126, 65, 126.1, NC 0.0700, 0.0700, 0.0500, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Channel Cross Section Data Continues X1 218, 14, 11, 63, 0.0, 0.0, 161, 0., 0., , , , , Appendix F1 Typical SWMM input file for UPRC GR 20, 0, 6, .001, 4, 3, 2.8, 3.1, 2.7, 11, GR .35, 13, -.3, 17, -.5, 31, -.3, 37, -.6, 57, GR .3, 63, 7, 92, 6, 104, 20, 104.001, *Storage Data * Storage Element Data G1 0 G2 0.0, , 0.0, 0.0, G2 0.8, , 748., 6.3, G2 1.27, , 2085.15, 10., G2 1.8, , 3593., 15.7, G2 2.2, , 5993., 20., G2 2.8, , 9593., 31.88, G2 3.21, , 14611., 40., G2 3.8, , 21833., 52.3, G2 4.17, , 29904.5, 60.0, G2 4.8, , 43648., 74., G2 5.07, , 52551., 80., G2 5.8, , 76623., 91.9, G2 6.3, , 99553.0, 100., G2 6.8, , 122483., 108.3, G2 7.51, , 165630., 120., G2 9.1, , 287044., 315., G5 0.0 * Storage Element Data G1 0, G2 0.0, , 0.0, 0.0, G2 0.2, , 10., 0.9, G2 0.5, , 100., 1.8, G2 0.7, , 500., 2.7, G2 1.0, , 2500., 5.4, G2 1.5, , 3750., 10.8, G2 2.0, , 5000., 22., G2 3.0, , 5500., 90., G2 4.0, , 6000., 300., * Initial Storage Conditions G5 0.0, >>>>>>>>>>>>>>>>>> Storage Data Continues * Outflow Transfer Node List *H1,'1.140L', * Hydrograph Input Print Node List *J1 ,'1.140L', * Hydrograph Output Print Node List J2,'1.140L' $ENDPROGRAM Appendix F2 Typical SWMM input file for CPC APPENDIX F2 Typical SWMM input data file for CPC : Storm Event on December 9, 1999 ; with spatially distributed rainfall input Appendix F2 Typical SWMM input file for CPC SW 2 0 8 8 0 MM 7 1 2 3 10 11 12 13 $RUNOFF A1 'Runoff generation from the CPC, for distributed rainfall pattern for the storm on 09/12/99 (13)' A1 'K.Umakhanthan, 14/08/2000' * METRIC ISNOW NRGAG INFILM KWALTY IVAP NHR NMN NDAY MONTH ITRSTR B1 1 0 42 0 0 1 13 45 9 12 99 * IPRN(1) IPRN(2) IPRN(3) B2 0 1 0 * WET WETDRY DRY LUNIT LONG B3 60 300 86400 2 4 * PCTZER REGEN B4 0.0 0.01 * ROPT D1 0 * KTYPE KINC KPRINT KTHIS KTIME KPREP NHISTO THISTO TZRAIN E1 0 23 0 0 0 1 24 5 825 E3 0.0 0.0 0.0 0.2 2.1 8.5 1.4 1.2 1.2 1.0 0.5 0.8 2.2 1.5 0.8 0.6 0.3 0.9 0.5 0.5 0.1 0.2 0.1 E3 0.0 0.0 0.0 0.1 1.9 9.2 1.6 1.5 1.3 1.1 0.5 0.8 2.2 1.6 0.9 0.6 0.3 0.9 0.5 0.5 0.1 0.2 0.2 E3 0.0 0.0 0.0 0.1 1.8 10.4 1.7 1.6 1.4 1.4 0.5 0.8 2.4 1.7 1.0 0.6 0.3 0.9 0.5 0.6 0.2 0.2 0.2 E3 0.0 0.0 0.0 0.1 1.9 11.3 1.4 1.0 1.6 1.5 0.4 0.8 2.6 1.8 1.0 0.5 0.4 1.0 0.6 0.7 0.1 0.2 0.2 E3 0.0 0.0 0.0 0.0 1.5 12.3 2.0 1.7 1.7 1.7 0.4 0.8 2.7 2.0 1.2 0.6 0.4 1.0 0.6 0.8 0.2 0.2 0.2 E3 0.0 0.0 0.0 0.0 1.1 14.4 2.5 2.3 2.0 2.1 0.3 0.8 3.0 2.3 1.5 0.7 0.4 1.0 0.7 1.0 0.3 0.2 0.3 E3 0.0 0.0 0.0 0.0 1.3 14.1 2.1 1.8 2.0 2.0 0.4 0.8 3.0 2.2 1.4 0.7 0.4 1.0 0.6 0.9 0.2 0.2 0.2 E3 0.0 0.0 0.0 0.0 1.5 13.6 1.8 1.4 1.9 1.9 0.4 0.8 2.9 2.1 1.3 0.6 0.4 1.0 0.6 0.9 0.2 0.2 0.2 E3 0.0 0.0 0.0 0.0 1.7 13.2 1.5 0.9 1.9 1.9 0.4 0.8 2.9 2.0 1.2 0.5 0.4 1.0 0.6 0.8 0.2 0.2 0.2 E3 0.0 0.0 0.0 0.0 1.3 14.8 2.0 1.6 2.1 2.2 0.3 0.8 3.1 2.3 1.4 0.6 0.5 1.1 0.7 1.0 0.2 0.2 0.2 E3 0.0 0.0 0.1 0.1 2.0 12.5 1.0 0.3 1.8 1.8 0.4 0.8 2.8 1.8 1.1 0.4 0.4 1.0 0.6 0.7 0.1 0.2 0.1 E3 0.0 0.0 0.1 0.1 1.9 13.2 0.9 0.1 1.9 2.0 0.4 0.8 2.9 1.9 1.1 0.4 0.4 1.0 0.6 0.8 0.1 0.2 0.1 E3 0.0 0.0 0.1 0.1 1.8 13.8 1.1 0.3 2.0 2.1 0.4 0.8 3.0 2.0 1.2 0.4 0.5 1.0 0.6 0.8 0.1 0.2 0.1 E3 0.0 0.0 0.1 0.2 2.1 12.9 0.7 0.0 1.8 2.0 0.4 0.8 2.9 1.8 1.1 0.3 0.4 1.0 0.6 0.7 0.1 0.2 0.1 E3 0.0 0.0 0.2 0.2 2.3 12.0 0.4 0.0 1.7 2.0 0.5 0.8 2.8 1.7 1.0 0.3 0.4 1.0 0.6 0.6 0.1 0.2 0.0 E3 0.0 0.0 0.1 0.3 2.5 10.7 0.2 0.0 1.5 1.7 0.5 0.8 2.6 1.5 0.8 0.3 0.4 0.9 0.5 0.5 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.3 2.5 11.0 0.0 0.0 1.6 2.0 0.5 0.8 2.6 1.5 0.9 0.2 0.4 0.9 0.5 0.6 0.0 0.3 0.0 E3 0.0 0.0 0.1 0.4 2.7 9.1 0.0 0.0 1.3 1.4 0.5 0.8 2.3 1.3 0.7 0.2 0.3 0.9 0.5 0.4 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.4 2.7 9.6 0.0 0.0 1.4 1.7 0.5 0.8 2.4 1.3 0.7 0.2 0.4 0.9 0.5 0.4 0.0 0.2 0.0 E3 0.0 0.0 0.3 0.5 2.7 9.5 0.0 0.0 1.4 1.9 0.5 0.8 2.4 1.3 0.7 0.1 0.4 0.9 0.5 0.5 0.0 0.3 0.0 E3 0.0 0.0 0.1 0.4 2.7 8.9 0.1 0.0 1.3 1.3 0.5 0.8 2.3 1.3 0.6 0.3 0.3 0.9 0.5 0.4 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.5 2.9 8.2 0.0 0.0 1.2 1.3 0.6 0.8 2.2 1.2 0.6 0.2 0.3 0.9 0.5 0.3 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.5 2.9 8.0 0.0 0.0 1.2 1.5 0.6 0.8 2.2 1.1 0.6 0.1 0.3 0.8 0.5 0.3 0.0 0.3 0.0 E3 0.0 0.0 0.2 0.6 3.0 7.2 0.0 0.0 1.0 1.4 0.6 0.8 2.1 1.0 0.5 0.1 0.3 0.8 0.4 0.3 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.5 3.0 7.5 0.0 0.0 1.1 1.2 0.6 0.8 2.1 1.1 0.5 0.2 0.3 0.8 0.4 0.3 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.6 3.1 6.3 0.0 0.0 0.9 1.3 0.6 0.8 1.9 0.9 0.4 0.1 0.3 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.4 2.9 7.3 0.0 0.0 1.0 1.0 0.6 0.8 2.1 1.1 0.5 0.3 0.3 0.8 0.4 0.3 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.5 3.0 6.9 0.0 0.0 1.0 1.0 0.6 0.8 2.0 1.0 0.4 0.2 0.3 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.6 3.2 6.0 0.0 0.0 0.9 1.1 0.6 0.8 1.9 0.9 0.4 0.1 0.3 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.3 0.7 3.3 5.0 0.0 0.0 0.7 1.1 0.6 0.8 1.7 0.7 0.3 0.1 0.3 0.7 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.5 3.0 6.3 0.0 0.0 0.9 0.9 0.6 0.8 1.9 1.0 0.4 0.2 0.2 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.2 0.6 3.2 5.3 0.0 0.0 0.8 1.0 0.6 0.8 1.8 0.8 0.3 0.1 0.2 0.7 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.0 0.5 3.0 5.8 0.1 0.0 0.8 0.7 0.6 0.8 1.8 1.0 0.4 0.3 0.2 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.0 0.5 3.0 5.5 0.0 0.0 0.8 0.6 0.6 0.8 1.8 0.9 0.3 0.3 0.2 0.8 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.5 3.1 5.5 0.0 0.0 0.8 0.7 0.6 0.8 1.8 0.9 0.3 0.2 0.2 0.8 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.6 3.2 5.0 0.0 0.0 0.7 0.7 0.6 0.8 1.7 0.8 0.3 0.2 0.2 0.8 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.5 3.1 5.1 0.0 0.0 0.7 0.6 0.6 0.8 1.7 0.8 0.3 0.3 0.2 0.8 0.4 0.1 0.0 0.2 0.0 E3 0.0 0.0 0.1 0.6 3.3 4.4 0.0 0.0 0.6 0.7 0.7 0.8 1.6 0.7 0.2 0.2 0.2 0.7 0.4 0.0 0.0 0.2 0.0 E3 0.0 0.0 0.0 0.4 2.8 6.4 0.4 0.0 0.9 0.7 0.6 0.8 1.9 1.1 0.4 0.4 0.2 0.8 0.4 0.2 0.0 0.2 0.0 E3 0.0 0.0 0.0 0.4 2.7 6.8 0.4 0.1 1.0 0.8 0.6 0.8 2.0 1.1 0.5 0.4 0.2 0.8 0.4 0.3 0.0 0.2 0.0 E3 0.0 0.0 0.0 0.3 2.4 9.6 0.6 0.2 1.4 1.3 0.5 0.8 2.4 1.4 0.8 0.4 0.3 0.9 0.5 0.5 0.1 0.2 0.1 E3 0.0 0.0 0.0 0.3 2.5 6.4 0.9 0.6 0.9 0.7 0.6 0.8 1.9 1.2 0.5 0.5 0.2 0.8 0.4 0.3 0.1 0.2 0.1 * Evaporation data (mm/day) Appendix F2 Typical SWMM input file for CPC * JAN FEB MARCH APRIL MAY JUNE JULY AUG SEP OCT NOV DEC F1 8.70 6.80 4.80 4.10 3.90 2.30 2.40 4.00 5.40 6.20 6.90 7.20 * Pipe data * NAMEG NGTO NPG GWIDTH GLEN G3 GS1 GS2 G6 DFULL GDEPTH G1 101 100 1 3.658 121.9 0.0035 0.25 0.25 0.012 5 0 G1 102 41 1 1.524 117.5 0.0091 0 0 0.012 1.17 0 G1 103 42 2 0.375 210.0 0.0300 0 0 0.012 0 0 G1 104 42 1 1.524 48.4 0.0091 0 0 0.012 1.17 0 G1 105 43 2 0.900 234.0 0.0080 0 0 0.012 0 0 G1 106 43 1 1.067 225.9 0.0167 0 0 0.012 1.14 0 G1 107 1 2 0.450 80.7 0.0213 0 0 0.012 0 0 G1 108 1 2 0.45 72.6 0.0210 0 0 0.012 0 0 G1 109 44 1 1.372 153.3 0.0050 0 0 0.012 1.07 0 G1 110 48 1 0.990 88.7 0.0333 0 0 0.012 0.914 0 G1 150 4 2 0.600 137.2 0.1110 0 0 0.012 0 0 G1 151 5 2 0.600 80.7 0.1110 0 0 0.012 0 0 G1 111 5 2 0.400 161.4 0.1110 0 0 0.012 0 0 G1 112 50 2 0.450 104.9 0.1110 0 0 0.012 0 0 G1 113 50 2 0.450 121.0 0.1110 0 0 0.012 00 G1 114 48 2 0.600 121.0 0.0370 0 0 0.012 0 0 G1 115 9 2 0.450 210.0 0.0420 0 0 0.012 0 0 G1 116 44 1 1.220 177.5 0.0139 0 0 0.012 1.07 0 G1 117 45 2 0.600 113.0 0.0300 0 0 0.012 0 0 G1 118 45 2 0.900 129.1 0.0286 0 0 0.012 0 0 G1 119 46 2 0.550 129.1 0.0300 0 0 0.012 0 0 G1 120 46 2 0.600 121.0 0.0300 0 0 0.012 0 0 G1 121 46 2 0.600 113.0 0.0300 0 0 0.012 0 0 G1 122 14 2 0.600 80.7 0.0680 0 0 0.012 0 0 G1 123 12 2 0.450 145.2 0.0450 0 0 0.012 0 0 G1 124 15 2 0.375 137.2 0.0640 0 0 0.012 0 0 G1 125 41 1 1.219 56.5 0.0300 0 0 0.012 1.22 0 G1 126 21 2 1.200 24.2 0.0170 0 0 0.012 0 0 G1 127 21 2 0.600 40.3 0.0390 0 0 0.012 0 0 G1 128 32 2 0.600 137.2 0.0180 0 0 0.012 0 0 G1 129 36 2 0.600 72.6 0.0180 0 0 0.012 0 0 G1 130 36 2 0.400 56.5 0.0650 0 0 0.012 0 0 G1 131 38 2 0.600 56.5 0.0110 0 0 0.012 0 0 G1 132 37 2 0.450 40.3 0.0110 0 0 0.012 0 0 G1 133 28 2 1.200 113.0 0.0170 0 0 0.012 0 0 G1 134 29 2 1.200 56.5 0.0420 0 0 0.012 0 0 G1 135 47 2 0.900 215.2 0.0420 0 0 0.012 0 0 G1 136 47 2 0.900 56.5 0.0420 0 0 0.012 0 0 G1 137 18 2 0.900 32.3 0.0570 0 0 0.012 0 0 G1 138 26 2 0.600 104.9 0.0580 0 0 0.012 0 0 G1 139 23 2 0.600 80.7 0.0670 0 0 0.012 0 0 G1 140 27 2 0.600 40.3 0.0670 0 0 0.012 0 0 G1 141 30 2 0.600 129.1 0.0870 0 0 0.012 0 0 G1 142 27 2 0.450 32.3 0.0420 0 0 0.012 0 0 G1 143 25 2 0.450 137.2 0.0400 0 0 0.012 0 0 G1 144 34 2 0.400 153.3 0.0500 0 0 0.012 0 0 * SUBCATCHMENT CHARACTERISTICS * JK NAME NGTO WIDTH AREA IMP SLOP IRGH PRGH ISTOR PSTOR LMX LMN DECAY H1 1 201 1 156 2.76 30 0.021 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 2 202 2 158.3 1.37 30 0.036 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 3 203 3 156 5.14 30 0.067 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 4 204 4 90.5 3.13 30 0.037 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 5 205 5 345.3 6.27 40 0.111 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 6 206 6 120 3.39 45 0.059 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 7 207 7 138 1.97 50 0.065 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 Appendix F2 Typical SWMM input file for CPC H1 8 208 8 100.5 1.17 45 0.050 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 9 209 9 152.8 3.17 50 0.042 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 10 210 10 85.1 3.35 50 0.041 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 11 211 11 177.3 3.32 40 0.056 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 12 212 12 122.9 1.56 45 0.045 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 13 213 13 98 2.42 50 0.05 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 14 214 14 83.4 1.96 45 0.068 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 15 215 15 237.6 3.21 40 0.064 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 16 216 16 196.5 0.96 40 0.083 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 17 217 17 107.3 1.79 40 0.038 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 18 218 18 92 2.91 40 0.057 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 19 219 19 263.4 7.38 40 0.050 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 20 220 20 156 4.23 45 0.046 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 21 221 21 60.1 2.45 40 0.045 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 22 223 23 157.2 2.17 40 0.067 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 23 224 24 117.3 1.46 45 0.05 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 24 225 25 156.5 2.60 40 0.04 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 25 226 26 116.6 1.80 40 0.058 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 26 227 27 101.3 3.05 45 0.067 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 27 228 28 190.5 1.15 30 0.017 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 28 229 29 123.8 2.60 30 0.042 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 29 230 30 61.4 1.01 45 0.087 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 30 231 31 144.6 3.17 45 0.044 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 31 232 32 96.8 1.76 30 0.04 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 32 233 33 183.8 5.38 50 0.065 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 33 234 41 47.8 0.88 30 0.039 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 34 235 32 92.6 2.58 30 0.018 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 35 236 36 118.1 0.64 30 0.018 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 36 237 37 100.2 1.21 30 0.083 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 37 238 38 103.9 0.50 30 0.011 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 38 239 39 134.4 3.89 40 0.092 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 39 240 41 117.3 1.50 30 0.05 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 40 241 41 161 0.53 0 0.023 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 41 242 41 1089 27.3 0 0.030 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 H1 42 200 22 216 3.63 55 0.025 0.021 0.3 0.03 2.5 250.0 20.0 0.00125 M1 1 1 * NDET STARTP STOPPR M2 1 991209 991209 * IPRNT M3 100 $TRANSPORT A1 'TRANSPORT BLOCKS BEGINS' A1 '14/08/2000' * NDT NINPUT NNYN NNPE NOUTS NPRINT NPOLL NITER IDATEZ METRIC INTPRT B1 240 0 0 1 0 0 0 4 991209 1 1 * DT EPSIL DWDAYS TZERO GNU TRIBA B2 60 0.0001 2 13.25 0.01 132.7 * NCNTRL NINFIL NFILTH NDESN B3 0 0 0 0 * NKALSS KPRINT C1 0 0 * NOE NUE(1) NUE(2) NUE(3) NTYPE DIST GEOM(1) SLOPE ROUG GEOM(2) BARREL GEOM(3) E1 1001010019000001.00 E1 101 41 0 0 13 121.9 1.259 0.35 0.012 3.658 1.0 0.25 E1 41102125019000001.00 E1 102 42 0 0 2 177.5 1.17 0.91 0.012 1.524 1.0 0 E1 42103104019000001.00 E1 103 22 0 0 1 210.0 0.375 3.00 0.012 0 1.0 0 E1 2200019000001.00 E1 104 43 0 0 2 48.4 1.17 0.91 0.012 1.524 1.0 0 Appendix F2 Typical SWMM input file for CPC E1 43105106019000001.00 E1 1051001234.0 0.900 0.80 0.012 1.524 1.0 0 E1 1107108019000001.00 E1 107200180.70.4502.10.01201.00 E1 200019000001.00 E1 108300172.60.4502.10.01201.00 E1 300019000001.00 E1 106 44 0 0 2 225.9 1.14 1.67 0.012 1.067 1.0 0 E1 44109116019000001.00 E1 109 48 0 0 2 153.3 1.07 5.0 0.012 1.372 1.0 0 E1 48110114019000001.00 E1 110400288.70.9143.30.0120.9901.00 E1 41500019000001.00 E1 1505001137.2 0.600 1.11 0.012 0 1.0 0 E1 5111151019000001.00 E1 1118001161.4 0.400 1.11 0.012 0 1.0 0 E1 800019000001.00 E1 151 50 0 0 1 80.7 0.600 1.11 0.012 0 1.0 0 E1 50112113019000001.00 E1 1127001104.9 0.450 1.11 0.012 0 1.0 0 E1 700019000001.00 E1 1136001121.0 0.450 1.11 0.012 0 1.0 0 E1 600019000001.00 E1 1149001121.0 0.600 3.7 0.012 0 1.0 0 E1 91150019000001.00 E1 115 10 0 0 1 210.0 0.450 4.2 0.012 0 1.0 0 E1 1000019000001.00 E1 116 45 0 0 2 177.5 1.067 1.4 0.012 1.220 1.0 0 E1 45117118019000001.00 E1 117 11 0 0 1 113.0 .600 3.0 0.012 0 1.0 0 E1 1100019000001.00 E1 118 46 0 0 1 129.1 0.900 2.9 0.012 0 1.0 0 E1 4611912012119000001.00 E1 119 16 0 0 1 129.1 0.550 3.0 0.012 0 1.0 0 E1 1600019000001.00 E1 120 15 0 0 1 120.0 0.600 3.0 0.012 0 1.0 0 E1 151240019000001.00 E1 124 17 0 0 1 137.2 0.375 6.8 0.012 0 1.0 0 E1 1700019000001.00 E1 121 14 0 0 1 113.0 0.600 3.0 0.012 0 1.0 0 E1 141220019000001.00 E1 122 12 0 0 1 80.0 0.600 6.8 0.012 0 1.0 0 E1 121230019000001.00 E1 123 13 0 0 1 145.2 0.450 4.5 0.012 0 1.0 0 E1 1300019000001.00 E1 125 21 0 0 2 56.5 1.220 3.9 0.012 1.22 1.0 0 E1 21126127019000001.00 E1 126 28 0 0 1 24.1 1.200 1.7 0.012 0 1.0 0 E1 127 32 0 0 1 40.3 0.600 3.9 0.012 0 1.0 0 E1 321280019000001.00 E1 128 36 0 0 1 137.2 0.600 1.8 0.012 0 1.0 0 E1 36129130019000001.00 E1 129 38 0 0 1 72.6 0.600 1.8 0.012 0 1.0 0 E1 130 33 0 0 1 56.5 0.400 6.5 0.012 0 1.0 0 E1 3300019000001.00 E1 381310019000001.00 E1 131 37 0 0 1 56.5 0.600 1.1 0.012 0 1.0 0 E1 371320019000001.00 E1 132 39 0 0 1 40.3 0.450 1.1 0.012 0 1.0 0 Appendix F2 Typical SWMM input file for CPC E1 3900019000001.00 E1 281330019000001.00 E1 133 29 0 0 1 113.0 1.200 1.7 0.012 0 1.0 0 E1 291340019000001.00 E1 134 47 0 0 1 56.5 1.200 4.2 0.012 0 1.0 0 E1 47135136019000001.00 E1 135 27 0 0 1 258.2 0.900 4.2 0.012 0 1.0 0 E1 136 18 0 0 1 56.5 0.900 4.2 0.012 0 1.0 0 E1 27140142019000001.00 E1 140 30 0 0 1 40.3 0.600 6.7 0.012 0 1.0 0 E1 142 25 0 0 1 32.3 0.450 4.2 0.012 0 1.0 0 E1 301410019000001.00 E1 141 31 0 0 1 129.1 0.600 8.7 0.012 0 1.0 0 E1 3100019000001.00 E1 251430019000001.00 E1 143 24 0 0 1 137.2 0.450 4.0 0.012 0 1.0 0 E1 241440019000001.00 E1 144 20 0 0 1 153.3 0.400 5.0 0.012 0 1.0 0 E1 2000019000001.00 E1 181370019000001.00 E1 137 26 0 0 1 32.3 0.900 5.7 0.012 0 1.0 0 E1 261380019000001.00 E1 138 23 0 0 1 104.9 0.600 5.8 0.012 0 1.0 0 E1 231390019000001.00 E1 139 19 0 0 1 80.7 0.600 6.7 0.012 0 1.0 0 E1 1900019000001.00 H1 100 J1 13 20 * Hydrograph output print node list J2 100 $ENDPROGRAM Appendix F2 Typical SWMM input file for CPC Appendix G Behaviour of Rainfall-Runoff depth APPENDIX G Behaviour of Rainfall depth vs Observed runoff depth for the different classes of events Appendix G Behaviour of Rainfall-Runoff depth Table G.1: Average rainfall depth vs the observed runoff depth for the events from UPRC Observed Runoff at the No Storm ID Event date Thiessen Catchment Outlet Average Rainfall Runoff Volume Runoff Depth / Depth / (mm) / (m3) (mm) 1 1a 02/01/1996 40.6 740722 6.7 2 1b 06/01/1996 37.8 1003284 9.1 3 2 11/04/1996 41.2 749482 6.8 4 4 27/07/1996 39.9 972301 8.8 5 5 30/08/1996 100.6 3169550 28.8 6 6 29/01/1997 66.2 2714144 24.7 7 7 07/10/1997 34.0 484073 4.4 8 8 24/01/1998 22.0 559136 5.1 9 9a 09/04/1998 32.3 404301 3.7 10 9b 10/04/1998 81.9 2164782 19.7 11 10 21/04/1998 46.4 990587 9.0 12 11a 02/05/1998 20.5 342401 3.1 13 11b 04/05/1998 39.8 1326653 12.1 14 12 18/05/1998 123.0 5881437 53.5 15 13 22/06/1998 34.4 777054 7.1 16 20 01/04/1999 37.1 530648 4.8 17 21 01/07/1999 14.5 343911 3.1 18 22a 13/07/1999 30.3 917456 8.3 19 22b 14/07/1999 35.9 1966081 17.9 20 23 16/09/1999 11.4 146623 1.3 21 24 18/10/1999 33.7 578044 5.3 22 25 23/10/1999 48.0 1418166 12.9 23 26a 09/12/1999 27.9 362230 3.3 Appendix G Behaviour of Rainfall-Runoff depth Table G.2: Average rainfall depth vs the observed runoff depth for the events from CPC Observed Runoff at the Thiessen Catchment Outlet No Storm ID Event date Average Rainfall Depth / (mm) Runoff Volume Runoff Depth / / (m3) (mm) 1 1 29/01/1997 78.2 30853 23.4 2 2 11/02/1997 86.4 27184 20.6 3 3 22/04/1998 29.9 9074 6.9 4 4 04/05/1998 17.5 1886 1.4 5 5 18/05/1998 80.6 18128 13.7 6 6 16/06/1998 19.4 4333 3.3 7 7 09/10/1998 13.1 2352 1.8 8 8 19/10/1998 13.1 2461 1.9 9 9 14/08/1999 45.4 12001 9.1 10 10 18/10/1999 36.0 6078 4.6 11 11 23/10/1999 42.4 8494 6.4 12 12 08/11/1999 16.0 2586 2.0 13 13 09/12/1999 25.0 5089 3.9 Appendix H1 Predicted Hydrographs at UPRC Outlet APPENDIX H1 Comparison of Predicted hydrographs from alternate rainfall input with the observed flow hydrographs at UPRC outlet Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.1: Predicted Hydrographs for the Storm Event on 6th January 1996 Figure H1.2: Predicted Hydrographs for the Storm Event on 2nd January 1996 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.3: Predicted Hydrographs for the Storm Event on 23rd October 1999 Figure H1.4: Predicted Hydrographs for the Storm Event on 7th October 1997 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.5: Predicted Hydrographs for the Storm Event on 30th August 1996 Figure H1.6: Predicted Hydrographs for the Storm Event on 29th January 1997 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.7: Predicted Hydrographs for the Storm Event on 22nd June 1998 Figure H1.8: Predicted Hydrographs for the Storm Event on 18th October 1999 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.9: Predicted Hydrographs for the Storm Event on 27th July 1996 Figure H1.20: Predicted Hydrographs for the Storm Event on 9th April 1998 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.11: Predicted Hydrographs for the Storm Event on 1st April 1999 Figure H1.12: Predicted Hydrographs for the Storm Event on 11th April 1996 Appendix H1 Predicted Hydrographs at UPRC Outlet Figure H1.33: Predicted Hydrographs for the Storm Event on 10th April 1998 Figure H1.44: Predicted Hydrographs for the Storm Event on 18th May 1998 Appendix H1 Predicted Hydrographs at UPRC Outlet Table H2.1: Variation in Relative Bias : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Relative Bias Category Storm ID Event Date Spline Thiessen Rainfall rainfall Event 5 30/08/1996 -0.17 -0.19 LS-LT Event 6 29/01/1997 -0.36 -0.32 Event 1b 06/01/1996 -0.21 -0.22 Event 2b 11/04/1996 -0.03 -0.03 LS-HT Event 7 07/10/1997 -0.07 -0.07 Event 13 22/06/1998 -0.16 -0.20 Event 24 18/10/1999 -0.12 -0.09 Event 9a 09/04/1998 0.27 0.34 HS-LT Event 12 18/05/1998 -0.41 -0.39 Event 20 01/04/1999 -0.10 -0.15 Event 1a 02/01/1996 -0.27 -0.22 Event 2a 11/04/1996 0.44 0.54 HS-HT Event 9b 10/04/1998 -0.07 -0.17 Event 26 09/12/1999 0.05 0.06 Appendix H1 Predicted Hydrographs at UPRC Outlet Table H2.2: Variation in Relative Mean Absolute Error : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Relative MAE Category Storm ID Event Date Spline Thiessen Rainfall rainfall Event 5 30/08/1996 LS-LT Event 6 29/01/1997 Event 1b 06/01/1996 Event 2b 11/04/1996 LS-HT Event 7 07/10/1997 Event 13 22/06/1998 Event 24 18/10/1999 Event 9a 09/04/1998 HS-LT Event 12 18/05/1998 Event 20 01/04/1999 Event 1a 02/01/1996 Event 2a 11/04/1996 HS-HT Event 9b 10/04/1998 Event 26 09/12/1999 Appendix H1 Predicted Hydrographs at UPRC Outlet Table H2.3: Variation in Peak flow : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Peak (%) Category Storm ID Event Date Spline Thiessen Rainfall rainfall Event 5 30/08/1996 15.9 13.2 LS-LT Event 6 29/01/1997 -0.9 4.5 Event 1b 06/01/1996 0.3 0.0 Event 2b 11/04/1996 -7.3 -7.8 LS-HT Event 7 07/10/1997 -3.5 -2.6 Event 13 22/06/1998 4.0 -2.8 Event 24 18/10/1999 -4.7 -3.1 Event 9a 09/04/1998 -1.1 9.0 HS-LT Event 12 18/05/1998 -3.0 -7.2 Event 20 01/04/1999 13.6 11.1 Event 1a 02/01/1996 10.4 22.0 Event 2a 11/04/1996 12.4 14.3 HS-HT Event 9b 10/04/1998 28.0 -6.5 Event 26 09/12/1999 1.7 4.1 Appendix H1 Predicted Hydrographs at UPRC Outlet Table H2.4: Variation in Hydrograph Volume : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Volume (%) Category Storm ID Event Date Spline Thiessen Rainfall rainfall Event 5 30/08/1996 -17.1 -18.8 LS-LT Event 6 29/01/1997 -36.4 -32.6 Event 1b 06/01/1996 -21.2 -21.8 Event 2b 11/04/1996 -3.0 -2.7 LS-HT Event 7 07/10/1997 6.1 6.2 Event 13 22/06/1998 -16.2 -20.2 Event 24 18/10/1999 -11.8 -8.8 Event 9a 09/04/1998 26.8 32.8 HS-LT Event 12 18/05/1998 -41.0 -39.0 Event 20 01/04/1999 -9.5 -15.4 Event 1a 02/01/1996 -23.0 -27.0 Event 2a 11/04/1996 44.8 55.4 HS-HT Event 9b 10/04/1998 -6.8 -17.6 Event 26 09/12/1999 0.5 3.0 Appendix H2 Predicted Hydrographs at CPC Outlet APPENDIX H2 Comparison of Predicted hydrographs from alternate rainfall input with the observed flow hydrographs at CPC outlet Appendix H2 Predicted Hydrographs at CPC Outlet Figure H1.1: Predicted Hydrographs for the Storm Event on 19th October 1998 Figure H2.2: Predicted Hydrographs for the Storm Event on 9th October 1998 Appendix H2 Predicted Hydrographs at CPC Outlet Figure H2.3: Predicted Hydrographs for the Storm Event on 18th October 1999 Figure H2.4: Predicted Hydrographs for the Storm Event on 11th February 1997 Appendix H2 Predicted Hydrographs at CPC Outlet Figure H2.5: Predicted Hydrographs for the Storm Event on 14th August 1999 Figure H2.6: Predicted Hydrographs for the Storm Event on 22nd April 1998 Appendix H2 Predicted Hydrographs at CPC Outlet Figure H2.7: Predicted Hydrographs for the Storm Event on 23rd October 1999 Figure H2.8: Predicted Hydrographs for the Storm Event on 9th December 1999 Appendix H2 Predicted Hydrographs at CPC Outlet Figure H2.9: Predicted Hydrographs for the Storm Event on 8th November 1999 Figure H2.10: Predicted Hydrographs for the Storm Event on 18th May 1998 Appendix H2 Predicted Hydrographs at CPC Outlet Figure H2.11: Predicted Hydrographs for the Storm Event on 16th June 1998 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.1: Variation of 'Mean Square Error (MSE)' : Comparison of observed flow with model flows from different spatial averaging rainfall input. MSE (m3/s)2 Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 0.021 0.009 LS-LT Event 2 11/02/1997 0.017 0.012 Event 9 14/08/1999 0.039 0.087 Event 8 19/10/1998 0.001 0.001 LS-HT Event 10 18/10/1999 0.011 0.035 Event 3 22/04/1998 0.033 0.159 HS-LT Event 11 23/10/1999 0.022 0.046 Event 5 18/05/1998 0.110 0.253 Event 6 16/06/1998 0.074 0.131 HS-HT Event 7 09/10/1998 0.002 0.011 Event 12 08/11/1999 0.038 0.131 Event 13 09/12/1999 0.317 0.970 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.2: Variation of 'Mean Absolute Error (MAE)' : Comparison of observed flow with model flows from different spatial averaging rainfall input. MAE (m3/s) Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 0.104 0.079 LS-LT Event 2 11/02/1997 0.089 0.075 Event 9 14/08/1999 0.460 0.200 Event 8 19/10/1998 0.024 0.026 LS-HT Event 10 18/10/1999 0.084 0.138 Event 3 22/04/1998 0.137 0.263 HS-LT Event 11 23/10/1999 0.100 0.143 Event 5 18/05/1998 0.239 0.331 Event 6 16/06/1998 0.128 0.256 HS-HT Event 7 09/10/1998 0.025 0.046 Event 12 08/11/1999 0.413 0.756 Event 13 09/12/1999 0.373 0.526 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.3: Variation of 'Bias (B)' : Comparison of observed flow with model flows from different spatial averaging rainfall input. Bias (m3/s) Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 -0.097 -0.056 LS-LT Event 2 11/02/1997 -0.075 0.079 Event 9 14/08/1999 -0.025 -0.096 Event 8 19/10/1998 -0.005 -0.001 LS-HT Event 10 18/10/1999 0.055 0.123 Event 3 22/04/1998 -0.084 0.083 HS-LT Event 11 23/10/1999 -0.001 -0.092 Event 5 18/05/1998 -0.101 0.100 Event 6 16/06/1998 -0.010 0.033 HS-HT Event 7 09/10/1998 -0.002 0.032 Event 12 08/11/1999 0.084 0.184 Event 13 09/12/1999 0.025 0.315 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.4: Variation of 'Root Mean Square Error (RMSE)' : Comparison of observed flow with model flows from different spatial averaging rainfall input. RMSE (m3/s) Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 0.145 0.095 LS-LT Event 2 11/02/1997 0.130 0.110 Event 9 14/08/1999 0.197 0.295 Event 8 19/10/1998 0.032 0.032 LS-HT Event 10 18/10/1999 0.105 0.187 Event 3 22/04/1998 0.182 0.399 HS-LT Event 11 23/10/1999 0.148 0.214 Event 5 18/05/1998 0.332 0.503 Event 6 16/06/1998 0.272 0.362 HS-HT Event 7 09/10/1998 0.045 0.105 Event 12 08/11/1999 0.195 0.362 Event 13 09/12/1999 0.563 0.985 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.5: Variation of Variance : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variance (m3/s)2 Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 0.011 0.006 LS-LT Event 2 11/02/1997 0.011 0.012 Event 9 14/08/1999 0.038 0.078 Event 8 19/10/1998 0.001 0.001 LS-HT Event 10 18/10/1999 0.008 0.020 Event 3 22/04/1998 0.026 0.152 HS-LT Event 11 23/10/1999 0.022 0.037 Event 5 18/05/1998 0.100 0.243 Event 6 16/06/1998 0.074 0.131 HS-HT Event 7 09/10/1998 0.002 0.010 Event 12 08/11/1999 0.031 0.097 Event 13 09/12/1999 0.316 0.871 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.6: Variation in Peak flow : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Peak (%) Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 -20.3 -7.2 LS-LT Event 2 11/02/1997 -23.7 -3.0 Event 9 14/08/1999 3.7 33.1 Event 8 19/10/1998 6.5 14.0 LS-HT Event 10 18/10/1999 -0.2 40.9 Event 3 22/04/1998 1.3 38.0 HS-LT Event 11 23/10/1999 -11.2 19.3 Event 5 18/05/1998 23.1 33.7 Event 6 16/06/1998 -3.3 46.4 HS-HT Event 7 09/10/1998 -11.6 42.6 Event 12 08/11/1999 28.0 65.9 Event 13 09/12/1999 17.4 46.3 Appendix H2 Predicted Hydrographs at CPC Outlet Table H2.1: Variation of total volume of flow : Comparison of observed flow with model flows from different spatial averaging rainfall input. Variation in Volume (%) Category Storm ID Event Date Spline Thiessen Rainfall Rainfall Event 1 29/01/1997 -31.9 -18.5 LS-LT Event 2 11/02/1997 -17.2 -1.9 Event 9 14/08/1999 -3.4 11.6 Event 8 19/10/1998 -4.1 -0.6 LS-HT Event 10 18/10/1999 17.2 38.7 Event 3 22/04/1998 -11.6 11.5 HS-LT Event 11 23/10/1999 -0.4 18.9 Event 5 18/05/1998 -8.1 8.2 Event 6 16/06/1998 -3.7 10.9 HS-HT Event 7 09/10/1998 -2.1 25.4 Event 12 08/11/1999 29.1 63.9 Event 13 09/12/1999 2.1 32.7 Appendix I Publications APPENDIX I Publications 1. Estimation of Rainfall Heterogeneity Across Space and Time Scale 2. Importance of Rainfall Models in Catchment Simulation 3. Integration of Hydroinformatics with Catchment Models 4. The influence of Spatially Variable Rainfall on Runoff Hydrographs 45 9th International Conference on Urban Drainage, September 8-13, 2002, Portland, Orgeon, USA Estimation of Rainfall heterogeneity across space and time scale K.Umakhanthan* and James E. Ball** * PhD. Student, Water Research Laboratory, School of Civil and Environmental Engineering, The University of NSW, 110 King Street, Manly Vale NSW 2093, Australia, PH 61-2-99494488 ; [email protected] **Associate Professor, Water Research Laboratory, School of Civil and Environmental Engineering, The University of NSW, 110 King Street, Manly Vale NSW 2093, Australia, PH 61-2-99494488 ; [email protected] Abstract Over the last decade, it has been recognized that the spatial and temporal variability of rainfall is a significant influence on the robustness of predictions from catchment modelling systems. However, there have been few, if any, attempts to differentiate storm events occurring on urban catchments according to their variability in both the space and time dimensions. Presented in this paper will be a technique for assessing the spatial and temporal heterogeneity of individual storm events. Also presented will be the application of this technique for the analysis of storm events occurring over urban catchments within the Sydney urban area. This analysis will be based on five-minute rainfall records extracted from the 14 pluviometers within Upper Parramatta River (110 km2) and from the 6 pluviometers in and around the Centennial Park (1.3km2) catchments within Sydney, Australia. As a result of the analysis, the storms were categorized as having · High spatial and high temporal variability (HS-HT), · High spatial and low temporal variability (HS-LT), · Low spatial and high temporal variability (LS-HT), and · Low spatial and low temporal variability (LS-LT). This categorization was undertaken as part of an investigation into the importance of alternate rainfall models for application in Catchment Modelling Systems. Introduction Rainfall is a natural process, which has a high degree of variability in both space and time. Information on the spatial and temporal variability of rainfall plays an important role in the process of surface runoff generation and hence for a variety of applications in Hydrology and Water resources management. There have been several studies undertaken in the past to show the impact on hydrographs of the spatial and temporal variability of rainfall. The majority of these studies focusing on the spatial variability, [Obled et al.(1994); Seyfried et al.(1995); Goodrich et al.(1995); Chaubey et al.(1999)] approached the problem by comparing the responses using rainfall fields based on observations from a dense rain gauge network, and from rainfall fields based on the observations from a subset of original network gauges. In the study by Obled et al.(1994), for example, two different densities of network were tested (5 or 21 gauges within a 71km2 catchment, showing a significant advantage for the dense network rainfall estimate. Similarly, studies on the impact of the temporal variability of rainfall [Burke et al.(1980); Lambourne and Stephenson (1987), Ball (1994)] approached the problem by comparing the responses by considering alternate temporal rainfall patterns. For example, Ball (1994), simulated overland flows for different rainfall excess patterns having rectangular, triangular, etc. patterns of rainfall excess and found that the peak flow and time of occurrence depended on the temporal pattern of rainfall excess. However, in these studies no attempts were made to differentiate the events based on their heterogeneity in space and time scale by utilizing available gauge information. Therefore, attempts should be made to estimate the degree of the heterogeneity of rainfall in the space and time dimensions within the individual storm events occurring on urban catchments, since the measurement of rainfall across the spatial and temporal scale is a complex task. This paper illustrates a procedure for assessing the degree of heterogeneity of individual events on urban catchments and consequently shows the categorization of events, from two urban test catchments in Sydney Australia, according to their heterogeneity in both space and time. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilized in introducing estimators to address the heterogeneous nature of each individual storm event in their space and time scale. Also, the proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. Classification of storm events based on their heterogeneity in space and time Prior to the development of estimation techniques in the subsequent sections, it will be demonstrated how events are defined in the study, according to their variable nature in space and time. The proposed estimators that classify different events according to their spatial and temporal variability enable us to categories all the available individual events into four categories of spatial and temporal variability. High Spatial heterogeneity ; High Temporal heterogeneity ('HS-HT') High Spatial heterogeneity ; Low Temporal heterogeneity ('HS-LT') Low Spatial heterogeneity ; High Temporal heterogeneity ('LS-HT') Low Spatial heterogeneity ; Low Temporal heterogeneity ('LS-LT') A high spatially variable event will be able show the minimum or no dependency between the data obtained from various spatial positions, where a high temporally variable event will be able to show uniformity along its temporal series of records. The above categorization divides all the events in to high and low spatially variable events and each of these different spatial nature of events, will be categorized again according to their temporal variability into high and low temporally variable events. This will enable the categorization of all the events into four classes as listed above. 2 Methodology Ground-based raingauge network supply a reliable source of precipitation data used in statistical analyses associated with the development of rainfall models. For years various correlation and Semi-Variogram techniques have been used to evaluate both the temporal and spatial structure of rainfall events. Correlation techniques able to describe the structure and the motion of the storm events by measuring the association among the gauge records were used by Huff (1970), Sharon (1972a), Felgate and Read (1975), Marshall (1980). Studies by Felgate and Read (1975) and Marshall (1980) were able to determine the spatial scale, mean lifetime, and velocity of rainfall cells. Investigation by Bastin and Gevers (1985) suggests that in situations where the random field is not necessarily stationary (where the data are so scarce and so scattered in space), the sample covariance function estimates are not so meaningful and therefore, an analytical parametric ‘variogram’ model is used in lieu of the covariance. Also, all of these studies using correlation techniques were not able to distinguish and differentiate the various individual storm events according to their spatial and temporal heterogeneity nature. Apart from correlation techniques, use of a Semi-Variogram model for two-dimensional (2-D) interpolation using a Kriging approach has been a common practice in different engineering applications in the fields of mining and hydrogeology. By its definition, a semi-variogram function has the capability of estimating the disassociation between measurements from the different gauge locations. In typical engineering applications such as in hydrology, the Semi- variogram development has been applied to estimate the mean precipitation over a catchment by a Kriging model by Matheron (1971), Creutin and Obled (1982), Bastin et al. (1984), Guillermo et al. (1985), Storm et al. (1989). Semi-Variogram approach; Background and Theory Applications of semi-variograms have been numerous in geostatistics for some time [see for example, Journel and Huijbrechts (1978)]. In the past couple of decades, the theory has been further developed and applied to problems in hydrology by Lebel et al. (1987), Creutin and Obled (1982), Bastin and Gevers (1985) in solving 2-D rainfall interpolation problems using a Kriging technique. The Kriging technique itself was established by Krige (1951), and further developed by Matheron (1971) and Bastin et al. (1984). Consider a real-valued Random Field (RF) Z in an (x,y) 2-D Cartesian space coordinate domain. The locations of the information available are scattered. The RF from location ‘i’ denoted by Z(xi , yi ) and from ‘j’ by Z(x j , y j ) . Also the following semi-variogram functions are defined The Variogram 2γ (i, j) = Var[Z(xi , yi ) − Z(x j , y j )] (1) where γ (i, j) is the Semi-Variogram and given by 1 2 γ (i, j) = E{[Z(xi , yi ) − Z(x j , y j )]} (2) 2 The work by Bastin and Gevers (1985) identified of two methods of the semi-variogram approach. Method 1 deals with stationary fields while method 2 deals with intrinsic fields. The authors summarize the superiority of method 2 especially in rainfall applications. This paper also 3 identified and compared the two methods and found the superiority and preferabality of method 2 (Intrinsic field approach) in the adopted semi-variogram technique for the rainfall categorization. Identification of Spatial Variogram Model Definition of Spatial Semi-Variogram When the temporal distribution of rainfall is denoted P(t,Zi ) , with Z(xi , yi ) i.e. the location and 't ' the index of the discrete sequence of ∆t -minute depths of rainfall over the 'T ' time intervals. Then the time-invariant estimates of the variogram in the form of a time average over the 'T ' time intervals for a particular rainfall event (Random Field) is written by; 1 T 2 γ (t,Zi ,Z j ) = ∑{P(t,Zi ) − P(t,Z j )} (3) 2T t =1 Where γ (t,Zi ,Z j ) is the Semi-variogram as a function of dij , the Euclidean distance between the locations i and j. It will be assumed in this study, that for any t , the field P(t,Z) is [1] Isotropic, i.e. γ (t,Zi ,Z j ) = γ (dij ) ; and [2] Fulfils the intrinsic assumption which is a. the mean is space stationary (independent of Z ) b. the variances are not necessarily assumed to be equal to the field variance σ (Zi ) ≠ σ (Z j ) ≠ σ It is possible that the variations of the semi-variograms between each event are amplified by differences between the mean rainfall intensity. More specifically, large values of γ (dij ) may be caused by higher rainfall intensities rather than by a truly larger spatial variability. In order to * avoid this situation a standardized semi-variogram [γ (dij ) ], which can be related to as a negative correlation coefficient [Messaoud et.al (1990)] and is defined as is introduced with this semi-variogram and given by * γ (dij ) γ (dij ) = (4) σ i ×σ j In addition to the stationary mean assumption, the variogram (but not necessarily the covariance) is assumed isotropic and stationary. In this case the RF variance can be infinite, and the * variogram can become unbounded; i.e. limγ (dij ) = ∞ . Bastin et al.(1985) demonstrates that it is d →∞ difficult to validate a stationary assumption on the variogram. However, since a stationary variogram exists for a wider class of RF than a stationary covariance, it is always safer to adopt the method discussed in this section (method 2) in case of doubt. In other words it is always safer * to keep the variogram stationary without any condition on limγ (dij ) . Especially, when dealing d →∞ with random nature of rainfall processes and data availability on real catchments, the range of available distances is often too small to decide whether the variogram would reach a constant value for large dij . 4 Estimation of event based parametric variogram models Studies in the past have been able to identify yearly [Guillermo et al. (1985)], monthly [Bastin et al. (1984)] and daily semi-variograms [Storm et al. (1989)] in estimating the average annual, monthly and daily precipitation values respectively for catchments. Despite the fact that these studies in the past considered the seasonal trend when producing the yearly and monthly variograms, they did not take into account the potential spatial variability of different events within the long period considered. By contrast the present approach treats each event separately on their spatial process by identifying event variograms for each event. In reality rainfall measurements are available only at a very limited number of locations, which are randomly scattered and not equi-spaced. The scarcity of the data requires the use of analytic variogram models and estimation of these models. In modelling practice, semi-variograms describing the spatial structure of a function are formed by combining a small number of simple, mathematically acceptable expressions or models. Kitanidis (1993), list Gaussian, Exponential and Spherical models as a few of the models accepted to represent stationary semi-variograms. In a similar manner, the Power, Linear and Logarithmic models are acceptable models to represent intrinsic non-stationary semi-variograms. The range of admissible parametric experimental variogram models is of course endless. However, the shape of the experimental variograms obtained from numerous practical applications in hydrology indicates that fairly simple power function models can be used, see for example Bastin et al. (1984), Guillermo et al. (1985), and Storm et al. (1989). * γ (dij ) is kept as unbounded based on the non-stationary intrinsic assumption and adopted a simple power function to represent the developed event based semi-variogram model for the study. It is assumed that the semi-variogram γ (t, zi , z j ) shown in equation 3 is time invariant during an event, but not necessarily from one event to another. Therefore, the theoretical variogram model is now written as * * β (s) γ ()t, zi , z j = γ (s,dij ) = α()s dij (5) Where, s is the index of the event to which the ∆t -minute time increments t belongs, α is the scale factor and β is referred to as the shaping factor or spatial auto correlation factor. Combinations of both α and β define the function of the standardized semi-variograms for β (s) different events. In this study α()s dij is computed for each event by a least squares fitting procedure to all rainfall intensities with a 5-minute time step. Identification of Temporal Semi-variogram At any point, in a catchment, the rainfall intensity may change during the time intervals. Different shapes of hyetographs are considered in the development of synthetic hyetographs, which often are developed using intensity-frequency-duration curves. In studies on demonstrating the influence on the hydrographs due to different temporal patterns of rainfall, Lambourne et al. (1987) simulated runoff peaks and volumes by considering design storms having rectangular, triangular and bimodal temporal distribution, Ball (1994) simulated the overland flow on planer surfaces by 10 different hypothetically designed patterns of rainfall excess. Therefore, still a need is there to measure the degree of temporal uniformity of the rainfall intensity over the storm 5 duration, in addition to identification of the spatial variability of the storm. The categorization of the events based on the temporal variability, considered the events with rectangular distribution as low temporal heterogeneous (Uniform distribution) events and events with triangular distribution as high temporal heterogeneous events. Hence, in order to measure how the amount of rainfall varies throughout their time intervals a semi-variogram was calculated as a function of time. The temporal variability analysis from the semi-variogram technique can be again treated in a similar way to the spatial variability analysis discussed, previously. * The auto semi-variogram function γ t (k) (similar to the auto correlation function) for the time lag k can be written as equation 6. Where T is the total no of five-minute time steps at each gauge record, and N is the number of gauges (5 minute records) utilized in the estimation. 2 1 N 1 T −k γ * k = P(t, z ) − P(t + k, z ) (6) t () ∑∑ 2 [i i ] N i=1 (T − k)σ i t=1 * The auto semi-variogram [γ t (k)] plotted against the different time lags, will clearly demonstrate how the storm varies along its temporal scale. When the temporal semi-variogram function rises rapidly towards the value of one after a few lags, it is an indication of small persistence or short memory in the time series, while a slow rise of the semi-variogram is an indication of large persistence or long memory. i.e a time series with a short memory can represents temporally more heterogeneous events where the time series with long memory represent temporally more homogeneous events. This basis will enable us to categorize the events according to their temporal heterogeneous nature in this study. Test Catchments Two Urban catchments, which are different in size and with entirely different raingauge network configurations, were selected for the study. The Upper Parramatta River Catchment (UPRC) and the Centennial Park Catchment (CPC) were used as case catchments for this project. These two urban catchments are located within the metropolitan area of Sydney as shown schematically in Fig. 1a. Upper Parramatta River Catchment (UPRC) The UPRC is located in the western suburbs of Sydney, Australia. Covering 110 square kilometers, it is located near the geographic center of the Sydney metropolitan area and has a population of more than 220,000. It is bounded by Prospect Reservoir to the southwest, Blacktown to the northwest, Castle Hill to the north and Carlingford to the east as shown in Fig. 1b. There are fourteen telemetered rain gauges within the UPRC; locations of these gauges are shown in Fig. 1b. All of these gauges have been installed and maintained by the Upper Parramatta River Catchment Trust (UPRCT) since its formation in 1989. As a result, long-term records are not available from these gauges. Operationally, a sensor collects the rainfall data and sends the information by a radio signal to the Trust office. This provides one of the most intensive data collection systems anywhere in Australia. The data is used by the Trust to validate and refine its detailed computer model of flood behaviour. Records from fourteen raingauges 6 (a) (b) (c) Figure 1. Study Catchment Details: (a). Location of study Catchments with respect to the Sydney Metropolitan; (b). Raingauge details of Upper Parramatta River Catchment; (c). Raingauge details of Centennial Park Catchment were obtained for the years from 1996 to 1999. During this period 26 storm events where the event total rainfall was greater than 10mm were extracted. The details of selected events from UPRC with their event statistics are tabulated in Table 1. Centennial Park Catchment (CPC) The second study catchment (CPC) is located within the Sydney metropolitan region, approximately 4 km south of the Central Business District and 1 km to the north west of the main campus of the University of New South Wales (UNSW). The catchment is 132 ha (1.32 km2) in extent. Prior to October 1994, there was no rainfall gauging stations existing within the catchment. After realizing the importance of rainfall for quality studies of the Centennial park ponds, a pluviometer was installed by UNSW at Waverley public school in October 94. Another rain gauge was installed at the outlet of the catchment with the flow monitoring system, in 1997. Four other gauges around the outskirts of the CPC were among the six gauges considered in the study. These four other pluviometers are located within a radius of 7 km from the study area. The locations of the gauging stations are shown with respect to the study catchment in Fig. 1c. All of these gauges are digitally logged 0.2mm tipping bucket (except Paddington gauge with 0.5mm) pluviometers. The rainfall data used for this study was extracted from the HYDSYS database in the School of Civil and Environmental Engineering at UNSW. The gauge readings were utilized as the point rainfall input data in developing the rainfall surface. Events, with more than 10mm in total were used in this study. Based on this approach, 13 events from 1997 to 1999 were extracted for analysis and listed in Table 2 with the event statistics. 7 Table 1 Summary UPRC case studies and event statistics calculated globally Storm ID Event date 5 Min. time Average Total Average Standard increments / (mm) Intensity / Deviation/ (mm/hr) (mm/hr) 1a 02/01/96 54 40.6 9.0 14.3 1b 06/01/96 112 37.8 4.0 5.8 2a 11/04/96 56 18.7 4.0 9.9 2b 11/04/96 77 22.5 3.5 4.8 4 27/07/96 146 39.9 3.3 4.2 5 30/08/96 329 96.1 3.5 4.1 6 29/01/97 323 66.3 2.5 2.5 7 07/10/97 109 34.0 3.8 4.1 8a 24/01/98 33 22.0 7.7 15.3 8b 25/01/98 32 9.3 3.5 5.6 9a 09/04/98 70 32.3 5.4 16.2 9b 10/04/98 162 81.9 6.2 9.9 10 21/04/98 521 46.4 1.1 1.5 11a 02/05/98 84 20.5 2.9 5.0 11b 04/05/98 369 39.8 1.3 1.7 12 18/05/98 325 123.0 4.6 7.7 13 22/06/98 67 34.4 6.2 7.5 20 01/04/99 270 37.1 1.7 2.2 21 01/07/99 41 14.5 4.2 2.5 22a 13/07/99 83 30.3 4.4 4.4 22b 14/07/99 56 35.9 7.7 11.0 23 16/09/99 62 11.4 2.2 4.2 24 18/10/99 116 33.7 3.5 2.6 25 23/10/99 224 48.0 2.6 3.3 26a 09/12/99 38 16.6 5.3 9.6 26b 09/12/99 24 10.9 5.4 16.8 Table 2 - Summary of CPC case studies and event statistics calculated globally Average Total Average Standard Storm ID Event date 5 Min. time / (mm) Intensity / Deviation/ increments (mm/hr) (mm/hr) 1 29/01/1997 273 78.0 3.4 4.7 2 11/02/1997 339 99.2 3.5 3.6 3 22/04/1998 97 32.6 4.0 4.0 4 04/05/1998 89 16.0 2.1 3.2 5 18/05/1998 85 73.9 10.4 15.2 6 16/06/1998 77 14.3 2.6 7.7 7 09/10/1998 108 9.6 1.0 2.1 8 19/10/1998 115 11.5 1.2 1.8 9 14/08/1999 83 49.0 7.2 6.9 10 18/10/1999 117 33.3 3.4 3.8 11 23/10/1999 102 36.8 4.1 4.9 12 08/11/1999 44 14.2 3.9 7.7 13 09/12/1999 24 18.0 9.1 17.6 8 Application on Urban test catchments Spatial Semi-Variogram plots The semi-variogram function has been computed for time series from every pair of raingauges within the UPRC and CPC hydrometric network of 14 and 6 gauges respectively. The semi- variogram obtained was plotted against the separation distance of the corresponding gauge pairs in order to form a scatter plot known as a raw variogram for that event (for n gauges, there are n(n-1)/2 such pairs). Typical raw variograms computed for events occurred on July 27, 1996 and May 2, 1998 from UPRC are shown in Figure 2. The raw variogram takes the form of a somewhat extended cluster of scatter points. On the basis of many similar variograms computed for several real events from the catchments, UPRC and CPC, and in line with common practice in geostatistical literature, we shall fit a very simple power function model [Refer Eq. 5] to form the experimental variogram. Note that other forms of theoretical variograms (such as the spherical model) could also be used. However, the following plotted variograms and their illustration clearly demonstrates the suitability of selection of the power function fit and the assumption of an intrinsic RF. Consider the events from UPRC on July 27, 1996 (Event 4) and event on May 2, 1998 (Event 11) with almost the same average intensity of 3mm/hr. Based on the cumulative rainfall patterns and mass curves drawn from the gauge records it can be clearly observed that Event 4 shows a lower spatial variability behaviour whereas Event 11 shows comparatively a higher spatial variability. Event 4 was influenced by a frontal system whereas Event 11 was dominated by a convective system or is subject to pronounced orographic effect. The scattered raw variogram and the computed power function experimental models for Events 4 and 11 are shown in Figure 2a and Figure 2b respectively. The plotted raw variograms shows the need of allowing an unlimited capacity for spatial dispersion. [i.e neither the priori variances nor the semi-variogram can be defined]. This again, clearly illustrates the suitability of assuming the intrinsic non-stationary RF approach (method 2) and the selection power function model in computing the experimental variogram. The range of available distance is small to ascertain whether the variogram would reach a constant sill value. (a) (b) Figure 2. Computed experimental semi-variogram model for the events on (a). July 27, 1996 ; ( b). May 2, 1998 [Spherical model fit is plotted in dotted line with Power function fit for checking the validity of intrinsic assumption] 9 To highlight the non-suitability of the assumption of stationary RF approach (method 1) the spherical model fit is also compared with the power function fit in these figures. The semi- variogram plotted (shown in Figure 2b) for an event of convective nature, which can be * considered as a high spatially variable event shows a much higher γ (dij ) values. The most significant cause for these higher values is due to the progressive spatial displacement of rain cells between the rain gauges. As the rainfall cell moves over the fixed hydrometric network, rain gauges collect rainfall from different positions within the cell. Space Characteristic Parameter ( as ) Almost all computed raw variogram plots from these study catchments indicate that the correlation between Z(i) and Z( j) disappears when the distance dij becomes too large. Very * often in practice, a distance has been defined as the range beyond which γ (dij ) can be considered to be equal to one, which represents the transition from the state where a spatial correlation exists to the state where there is absence of correlation [Journel et al. (1978)]. Based on the observed behaviour of the plotted experimental semi-variograms of the study it is more * appropriate to assume that, beyond γ (dij ) value of one, the semivariogram is less stable (i.e * assuming γ (dij ) =1 represents the null correlation line). Then the separation distance * corresponding to γ (dij ) value of one could be defined as the radius of influence which will be used as the spatial characteristic parameter ( as ) in defining the storm (‘ s ’ is the index representing each individual event) based on its spatial variability. The considered spatial parameter in the study therefore can be defined as the distance by which the storm cluster holds the spatial dependence or the distance by which more or less a stable spatial correlation exists. * as is derived from the power function representation (from Eq. 5, when γ (dij ) value has been equated to one) and is represented mathematically as. 1 1 β s as = (7) αs Based on the value of ‘ as ’ all the events were ranked and categorized from high to low spatially heterogeneous events. The fitted power function parametric models for some selected events from UPRC and CPC are compared in Figure 3a and Figure 3b respectively. The relevant power function model parameters are tabulated in Table 3 and Table 4 for all 26 events of UPRC and all 13 events of CPC respectively. The extent of storm structure relative to the extent of the catchments is considered in divisionning the events into low and high spatially heterogeneous. Once the spatial dependence dissipates within the catchment (diagonal extent of 20km for UPRC and 7.5km for CPC), those events are categorized as more non-uniform or higher spatial heterogeneous events. Whereas in the case of the null correlation occurring between points further apart to the extent of the catchment, those events are considered as more uniform or lower spatial heterogeneous events. Now consider the two events from UPRC mentioned previously. The fitted model for Event 4 produced a radius of influence ( as ) of 21km which means the null spatial correlation could be reached only at a radius 10 of 21km whereas the fitted model for Event 11 produced a radius of influence of 5.5km, which means null spatial correlation could be reached within a shorter distance. This results in, Event 4 and Event 11 holding the ranks of 11 and 25 (out of 26 events) respectively according to their corresponding space characteristic parameter ( as ) values. Consequently the categorization list Event 4 under the lower spatial heterogeneous (‘LS’) category and Event 11 under the higher spatial heterogeneous (‘HS’) category. The space characteristic parameters values, complete ranking and allocated categories on spatial dependence of all 26 events for UPRC and CPC are included in Table 3 and Table 4 respectively. (a) (b) Figure 3. Experimental semi-variogram plots for the selected six different spatially variable events: (a). for UPRC hydrometric network; (b). for CPC hydrometric network Temporal Semi-variogram plots Similar to the procedures explained in spatial semi-variogram estimation, the temporal semi- variogram was calculated for different time lags individually for all events. The semi-variogram was calculated for each gauge record and averaged over all gauges from the corresponding catchments. The calculated average semi-variogram for a particular event was then plotted against the corresponding time lags in order to estimate the temporal semi-variogram corresponding to that event. Typical semi-variogram patterns for the selected events from UPRC and CPC are shown in Figure 4a and Figure 4b respectively. (a) (b) Figure 4. Typical temporal semi-variogram patterns for the selected events according to their degree of temporal variability, (a). for UPRC ; (b). for CPC 11 Table 3. Space and Time parameters based on their degree of heterogeneity and the respective classification of events for UPRC Storm Storm Space Ranking – Time Ranking- Categoriza ID Date Charac. Spatial Charac. Temporal tion of Parameter / Variability Parameter / Variability storm (km) (5 min. lag) 1a 02/01/1996 18.3 13 8 15 HS-HT 1b 06/01/1996 36.0 6 14 11 LS-HT 2a 11/04/1996 2.8 26 7 17 HS-HT 2b 11/04/1996 75.6 2 18 9 LS-HT 4 27/07/1996 21.1 11 53 4 LS-LT 5 30/08/1996 26.0 9 124 1 LS-LT 6 29/01/1997 62.6 4 53 4 LS-LT 7 07/10/1997 55.1 5 16 10 LS-HT 8a 24/01/1998 25.1 10 5 22 LS-HT 8b 25/01/1998 13.4 20 2 25 HS-HT 9a 09/04/1998 16.3 15 31 7 HS-LT 9b 10/04/1998 9.4 22 13 13 HS-HT 10 21/04/1998 138.0 1 68 2 LS-LT 11 02/05/1998 5.5 25 6 19 HS-HT 11a 04/05/1998 19.9 12 56 3 LS-LT 12 18/05/1998 14.2 19 14 11 HS-HT 13 22/06/1998 67.7 3 7 17 LS-HT 20 01/04/1999 15.9 16 24 8 HS-LT 21 01/07/1999 28.1 8 12 14 LS-HT 22a 13/07/1999 10.7 21 5 22 HS-HT 22b 14/07/1999 8.1 23 6 19 HS-HT 23 16/09/1999 17.9 14 4 24 HS-HT 24 18/10/1999 32.4 7 8 15 LS-HT 25 23/10/1999 15.5 17 32 6 HS-LT 26a 09/12/1999 14.4 18 6 19 HS-HT 26b 09/12/1999 5.8 24 1 26 HS-HT Time Characteristic parameter (t)s As demonstrated earlier, highly temporally varied events, such as a triangular shaped event, rapidly decay to the value of one, after a few lags while a slow decay of temporal semi-variogram indicates a more uniform temporal pattern (events, such as rectangular shaped event). Therefore, the lower the number of time lags till a null correlation is observed between the rainfall fields the smaller the persistence. Similarly the greater the number of time lags, the larger the persistence. This suggests the number of time lags by which a null correlation is observed between rainfall records, as an indicator, which can be used to rank the events according to their variability along time. The idea identifies this indicator as the Time Characteristic Parameter (ts ). 12 From the plotted temporal variograms for all events considered (plots for 12 events are shown in Figure 4), the respective time characteristic parameters ts are estimated. Then the events are ranked according to the degree of their temporal variability (the highest temporal variability event is ranked 26 and temporally most uniform event is ranked 1 for UPRC and highest ranking for CPC is 13. The complete list of time characteristic parameter and detailed ranking of all events for UPRC and CPC are also included in Table 3 and Table 4 respectively. These ranked events were categorized then into two categories namely low and high temporally heterogeneous events. A time characteristic parameter value of twenty and ten (5-minute time lags) are used as the base line to separate the events to low (‘LT’) and high (‘HT’) variable events for UPRC and CPC respectively. In other words if the dependency (memory) of temporal semi- variogram starts to dissipate before hundred minutes in time (for UPRC) then those events are categorized as High temporally variable events (HT). In similar manner if the time taken to lose its memory more than hundred minutes then those events are categorized as low temporally varied event (LT). Therefore from the example events, event 5 and 2b will be categorized under ‘LT’ and ‘HT’ categories respectively. The base value of 20 and 10 for UPRC and CPC respectively was adopted from the analysis of the catchment response times of several flow records of the corresponding catchments. Table 4. Space and Time parameters based on their degree of heterogeneity and the respective classification of events for CPC Storm Storm Space Ranking – Time Ranking- Categoriza ID Date Charac. Spatial Charac. Temporal tion of Parameter / Variability Parameter / Variability storm (km) (5 min. lag) 1 29/01/1997 30.6 2 27 1 LS-LT 2 11/02/1997 15.4 3 17 2 LS-HT 3 22/04/1998 6.3 7 17 2 HS-HT 4 04/05/1998 - 13 10 5 HS-HT 5 18/05/1998 6.6 6 6 8 HS-HT 6 16/06/1998 3.8 8 3 12 HS-HT 7 09/10/1998 1.6 12 4 11 HS-HT 8 19/10/1998 12.2 4 8 7 LS-HT 9 14/08/1999 8.0 5 11 4 LS-HT 10 18/10/1999 94.4 1 6 8 LS-HT 11 23/10/1999 2.5 10 10 5 HS-HT 12 08/11/1999 2.1 11 5 10 HS-HT 13 09/12/1999 2.9 9 2 13 HS-HT A reasonable question is whether the estimated low temporal heterogeneous events (higher temporal characteristic parameter) are influenced by the duration of the event. This will be not 13 true fully, since the estimated temporal heterogeneity is based purely on the rainfall pattern regardless of the extent of the pattern. Events on April 9, 98 (Event 9) and on May 2, 98 from UPRC can be taken as examples to illustrate this point. Event 9 is a shorter duration storm (6 hours) compared to the duration of Event 11 (7 hours). However, Event 9 shows a longer memory than Event 11 (shown in Figure 4a). This made Event 9 in to lower (rank 7) in its temporal heterogeneity than the Event 11 (rank 19). Event categorization in space and time From the plotted spatial as well as temporal semi-variograms and the estimated spatial and temporal characteristic parameters, the selected 26 and 13 events from UPRC and CPC respectively were categorised as classified according to their spatial and temporal variability. Based on the space and time characteristic parameters, all the individual events were placed on the space-time frame. The placement of selected events for UPRC and CPC, according to their spatio-temporal heterogeneity is shown in Figure 5a and Figure 5b respectively. The complete space and time characteristic parameters and the corresponding ranking based on their degree of heterogeneity for the events from UPRC and CPC are tabulated in Table 3 and Table 4 respectively. The tables also show the classification types of all events. (a) (b) Figure 5. Placement of Individual storm events based on their degree of heterogeneity in space and time frame: (a). Events from UPRC ; (b). Events from CPC [respective event ID. Numbers are given in the brackets] Conclusions A methodology for identification of storm events according to their degree of heterogeneity in space and time utilizing real-time data has been proposed. The study identified both spatial and temporal semi-variograms, which were produced by plotting the semi-variance of gauge records in space and time against distance and time respectively. These semi-variograms were utilized in introducing estimators to measure the degree of heterogeneity of each individual event in the spatial and temporal dimension. The proposed estimators use ground based gauge records of the real storm events and do not rely on delicate meteorological interpretations. Also the application of this technique for the analysis of storm events occurring over Upper Parramatta River and Centennial Park urban catchments within the Sydney urban area were presented. 14 From the estimated spatial and temporal characteristic parameters, all the individual events were placed on the space-time frame. As a result of the analysis, the storms were categorized as having High spatial and high temporal variability High spatial and low temporal variability Low spatial and high temporal variability, and Low spatial and low temporal variability. The importance and the application of this categorization of events on the selection and importance of more detailed rainfall models towards a more robust catchment modeling systems are well demonstrated by Umakhanthan and Ball (2002). Acknowledgements The authors wish to acknowledge the Upper Parramatta River catchment Trust and the hydrology division of School of Civil and Environmental Engineering of the University of New South Wales for providing the raw rainfall data for the study. References Ball, J.E., (1994). “The influence of storm temporal patterns on catchment response”, Journal of Hydrology, 158:285-303. Bastin, G., Lorent, B., Duque, C. and Gevers, M., (1984). “Optimal estimation of the average rainfall and optimal selection of rain gauge locations”, Water Resources Research, 20(4):463- 470. Bastin, G. and Gevers, M., (1985). “Identification and optimal estimation of random fields from scattered point-wise data”, Autamatica, 21(2):139-155. Chaubey, I, Haan, C.T., Grunwald, S. and Salisbury, J.M., (1999). “Uncertainty in the model parameters due to spatial variability of rainfall”, Journal of Hydrology, 220:48-61. Creutin, J.D. and Obled, C., (1982). “Objective Analyses and Mapping Techniques for Rainfall Fields”, Water Resources Research, Vol. 18(2):413-431 Felgate, D.G. and Read, D.G., (1975). “Correlation analysis of the cellular structure of storms observed by raingauges”, Journal of Hydrology, 24:191-200. Goodrich, D.C., Faures, J., Woolhiser, D.A., Lane, L.J. and Sorooshian, S., (1995). “Measurement and analysis of small-scale convective storm rainfall variability”, Journal of Hydrology, 173:283-308 Guillermo, Q., Tabios III and Salas, J.D., (1985). “A comparative analysis of techniques for spatial interpolation of precipitation”, Water Resources Bulletin, 21(3):365-380 Huff, F.A., (1970). “Spatial distribution of rainfall rates”, Water Resources Research, 6(1):254- 259. Journel, A.G. and Huijbregts, (1978). “Mining Geostatistics”, New York Academic Press. 15 Kitanidis, P.K., “Geostatistics”, Handbook of Hydrology, Ed. Maidment, DR, McGraw-Hill Inc., NY, USA. Krige, D.G., (1951). “A statistical approach to some mine valuations and allied problems on the Witwatersrand”, Master's thesis, Uni. Of Witwatersrand. Lambourne, J.J. and Stephenson, D., (1987). “Model study of the effect of storm temporal distributions on peak discharges and volumes”, Hydrological Sciences Journal, 32:215-226. Lebel, T., Bastin, G., Obled, C., and Creutin, J.D., (1987). “On the accuracy of areal rainfall estimation:A case study”, Water Resources Research, 23(11):2123-2134 Marshall, R.J., (1980). “The estimation and distribution of storm movement and storm structure, using a correlation analysis technique and rain gauge data”, Journal of Hydrology, 48:19-39. Matheron, G., (1971). “Theory of regionalized Variables and its applications”, Ecole des Mines, Cahier 5, 211 pp Messaoud, M and Pointin, Y.B., (1990). “Small time and space measurements of the mean rainfall rate made by a gauge network and by a dual-polarization radar”, Journal of Applied Meteorology, 29:830-841. Obled, Ch., Wendling, J., and Beven, K., (1994). “The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data”, Journal of Hydrology, 159:305-333. Seyfried, M.S. and Wilcox, B.P., (1995). “Scale and nature of spatial variability: Field examples having implications for spatial variability”, Water Resources Research, 31(3):173-184. Sharon, D., (1972a). “Spatial analysis of rainfall data from dense networks”, Bulletin Int. Assoc. of Hydrolo. Sci., XVII(3): 291-300 Storm, B., Jensen, K.H. and Refsgaard, J.C., (1989). “Estimation of catchment rainfall uncertainty and its influence on runoff prediction”, Nordic Hydrology, 19:77-88 Umakhanthan, K. and Ball, J.E., (2001submitted). “Importance of Rainfall Models in catchment simulation”, 13th APD-IAHR Congress, August 6-8, 2002, Singapore. 16 Thirteenth Congress of the APD-IAHR, August 6-8, 2002, NUS, Singapore IMPORTANCE OF RAINFALL MODELS IN CATCHMENT SIMULATION K.UMAKHANTHAN Water Research Laboratory, The University of New South Wales, Sydney, Australia JAMES E BALL Water Research Laboratory, The University of New South Wales, Sydney, Australia e-mail : [email protected] Abstract Implementation of a catchment the development of a detailed rainfall distribution model modelling system requires three steps, which are the in space and time, through implementation of a spline calibration of the system, the validation of the surface technique within a GIS. The enhanced spline calibration, and the extrapolation of the system to surface rainfall representation is then quantitatively different hydrologic events and catchment conditions. compared with the traditionally used Thiessen rainfall The robustness of the simulations when this extrapolation is undertaken is related to the calibration representation. Finally the alternate rainfall and validation of the catchment modeling system, and representations were tested through a catchment will reflect the more detailed representation of rainfall modeling system (CMS) to assess the prediction input. Within the generation conceptual component, an accuracy on events with different degree of spatial important aspect is the model used to transform the variability. point rainfall measurements into a spatially distributed rainfall over the catchment. There have been many II. STUDY CATCHMENTS alternative models proposed for this transformation. Presented herein is an analysis of the influence of Two Urban catchments, which are different in size alternative rainfall models on the simulated hydrograph and with entirely different raingauge network and hence the influence on the system calibration. An configurations, were selected for the study. The Upper enhanced rainfall representation in both space and time Parramatta River Catchment (UPRC) and the Centennial scale is made feasible by the application of the Park Catchment (CPC) were used as case catchments hydroinformatic tool Arc/Info-GIS. The analysis will be for this project and particularly for developing detailed based on real events recorded over the Upper Parramatta River catchment (110km2) and the Centennial Park rainfall representations in space and time, and for catchment (1.3km2) in Sydney, Australia. Based on the quantitatively assessing the influences of differences in comparisons of runoff predictions with the recorded rainfall estimation. The catchment simulation model runoff at the outlet of the Centennial Park catchment, it used was the Stormwater Management Model (SWMM) will be shown that the prediction error is related to the while the observed flow at the catchment outlet were rainfall model and the spatial variability of the storm utilized in assessing the improvement in catchment event. prediction through an enhanced rainfall representation. These two urban catchments are located within the metropolitan area of Sydney as shown schematically in I. INTRODUCTION FIG. 1a. Rainfall is a natural process, which has a high degree of variability in both space and time. There have been A. Upper Parramatta River Catchment (UPRC) several studies undertaken in the past to show the The UPRC is located in the western suburbs of Sydney, impact on hydrographs of the spatial and temporal Australia. Covering 110 square kilometers, it is located near variability of rainfall. The majority of these studies [11], the geographic center of the Sydney metropolitan area and has [12], [7] and [3] focused on the spatial variability and a population of more than 220,000. It is bounded by Prospect approached the problem by comparing the responses Reservoir to the southwest, Blacktown to the northwest, using rainfall fields based on observations from a dense Castle Hill to the north and Carlingford to the east as shown in rain gauge network, and from rainfall fields based on FIG. 1b. For a detailed rainfall modeling in space the the observations from a subset of original network catchment was subdivided into 29 subcatchments. gauges. In the study by Obled et.al. [9], for example, two different densities of network were tested (5 or 21 There are fourteen telemetered rain gauges within the 2 gauges within a 71km catchment, showing a significant UPRC; locations of these gauges are shown in FIG. 1b. All of advantage for the dense network rainfall estimate. These these gauges have been installed and maintained by the Upper studies, however, were based on ideal gauging Parramatta River Catchment Trust (UPRCT) since its arrangements and rainfall patterns were developed from formation in 1989. As a result, long-term records are not traditional approaches such as Thiessen Polygons. Apart available from these gauges. Operationally, a sensor collects from these simulation studies rainfall models from, the rainfall data and sends the information by a radio signal to alternate rainfall techniques have been compared in the Trust office. This provides one of the most intensive data studies [4],[8],[2] and [6]. However, there have been collection systems anywhere in Australia. The data is used by few, if any attempts made to compare the alternate the Trust to validate and refine its detailed computer model of rainfall representations of a storm event with a flood behaviour. catchment modeling system. This paper also describes ( a ) ( b ) ( c ) Fig. 1. Study Catchment Details: a) Location of study Catchments ; b) Raingauge details of Upper Parramatta River Catchment ; c) Raingauge details of Centennial Park Catchment Records from fourteen raingauges were obtained for All of these gauges are digitally logged 0.2mm tipping the years from 1996 to 1999. During this period 26 bucket (except Paddington gauge with 0.5mm) pluviometers. storm events where the event total rainfall was greater The rainfall data used for this study was extracted from the than 10mm were extracted. HYDSYS database in the School of Civil and Environmental Engineering at UNSW. The gauge readings were utilized as B. Centennial Park catchment (CPC) the point rainfall input data in developing the rainfall surface. The second study catchment (CPC) is located within the Events, with more than 10mm in total were used in this study. Sydney metropolitan region, approximately 4 km south of the Based on this approach, 13 events from 1997 to 1999 were Central Business District and 1 km to the north west of the extracted for analysis. main campus of the University of New South Wales (UNSW). The catchment is 132 ha (1.32 km2) in extent. For III. IMPLEMENTATION OF SPATIO-TEMPORAL catchment modeling purposes, a conceptual rainfall-runoff RAINFALL MODEL model based on the Storm Water Management Model A detailed rainfall distribution model in space and (SWMM) has been developed. In-order to accurately model time was developed, which is implemented within the the catchment, it was subdivided into 42 subcatchments after GIS framework. The enhanced rainfall representation in Abustan [1]. both space and time is made feasible by the aid of the powerful spatial analytic capability of GIS. The basis of Since this study is aimed at improving the this rainfall model is an extension of the rainfall model representation of actual rainfall and to test the developed in [2] through a temporal discretisation of the representation for catchment simulation, rainfall storm event in [15]. Based on the rainfall recorded at information is obtained from the gauging arrangements pluviometers within and immediately adjacent to the within and adjacent to the catchments. Therefore, four catchment, the spatial variation of rainfall was other gauges around the outskirts of the CPC were ascertained at five-minute increments using the thin among the six gauges considered in the study. These four plate spline algorithm. Thin plate smoothing is widely other pluviometers are located within a radius of 7 km from used to spatially interpolate hydrological phenomena the study area. Prior to October 1994, there were no (such as rainfall and temperature) from point records as rainfall gauging stations existing within the catchment. in [9], [2] and [14]. After realizing the importance of rainfall for quality studies of the Centennial park ponds, a pluviometer was A GIS module is developed after [15] to spatially installed by UNSW at Waverley public school in incorporate rainfall data for any number of rain gauges October 94. Another rain gauge was installed at the in a geographical reference area. Input consists of outlet of the catchment with the flow monitoring rainfall station locations, storm rainfall data extracted system, in 1997. The locations of the gauging stations for a particular time step (5-minute incremental data), are shown with respect to the study catchment in FIG. and additional geographical features of the study area 1c. (Catchment and Subcatchment boundaries). The module output is in the form of a time series of rainfall intensity where r is the catchment average rainfall at i th time maps produced for the required spatial scale. ci step estimated by the spline method. ρs is used to The main objective of the method is to distribute the compare the variation of rainfall between the Thiessen observed rainfall from the gauge records to a user approach and the proposed approach for different storm defined spatial grid, and consequently, to extract the events regardless of their magnitude. 5-minute rainfall rainfall pattern for the required spatial scale. The patterns estimated by both the Thiessen method and methods involve extraction of data from a time series spline method were treated separately for each manager (HYDSYS) in Arc-Info format and the subcatchments. Results from each time steps for each development of suitable macros in Arc-Info. The subcatchment were averaged to estimate values for all method can be summarized as follows. subcatchments of the entire catchment. Presented in Fig. 2a and Fig. 2b are box-plots of 1 For each rainfall gauge, rainfall data were calculated ρ values for all the UPRC and CPC extracted from HYDSYS. s 2 The extracted data were appended and converted to subcatchments respectively, grouped for different an Arc-Info compatible format. classified events. The events were classified as low and 3 For each time step; high spatial variable events from the method proposed a. Rainfall data were loaded into Arc-Info and in [16]. The solid line in the middle of the box plots is spatially linked to the locations of the gauges. the median (50% quantile) value. The two lines form an b. A rainfall grid was interpolated from the current envelope ± 25% of quantile deviation from the median, rainfall intensities using a thin plate spline and the whiskers extend to the 10% and 90% quantiles surface interpolation technique. of the estimated values. c. Subcatchment grids were combined with the rainfall grid to produce the mean rainfall within subcatchment boundary. 4 The subcatchment rainfall were extracted as time (a) series hyetographs to produce the rainfall input in a compatible format for the Catchment Modelling System to be used. A. Evaluation on spatio-temporal variability during an event The rainfall variation between the traditionally used Thiessen approach and the spatial rainfall approach for 5- minute temporal data has been evaluated on the line of fictitious point method (cross-validation) used by [5] and [6]. Similar to the error calculation for different rainfall estimation methods, the variation of rainfall from two different methods is compared by the root- mean squared variation, σ s calculated for each and (b) every subcatchment rainfall series. This parameter is given by N 2 ∑(rsi − rti ) σ = i=1 (1) s N where rsi is the estimated spline rainfall and rti is the Fig. 2. Box-plots of ρs : a) Calculated from each of the 29 th estimated Thiessen rainfall at the i time step ; N is subcatchments of UPRC; b) Calculated from each of the 42 the total number of 5-minute time increments for the subcatchments of CPC - events grouped according to the spatial variability particular event. The coefficient of variation ρs is then defined by The figure shows that the amount of variation in σ ρ = s (2) Thiessen rainfall from the distributed spline rainfall is s 1 N substantial and varies considerably within the r N ∑ ci subcatchments for those events classified as highly i=1 spatially variable ('HS'). The events were grouped based on the semi-variogram approach proposed in [16]. The study [6] compared four interpolation methods Prediction accuracy, as outlined in [10], is a measure using rainfall data from a network of thirteen raingauges of the difference between predicted and observed values on Norfolk Island, New Zealand (area 35km2). The and is best assessed by retrospective comparison of the Authors calculated the error, which is defined by values. Mean Square Error (MSE), Root Mean Square coefficient of variation for different integration times Error (RMSE), Mean Absolute Error (MAE), Variance, from three years of data. This results suggest that the Bias and Absolute Errors are some of the statistical error coefficient decreases substantially with increasing measures used in the study to assess the prediction integration time with the error coefficient for Thiessen accuracy. interpolation estimates for hourly totals being approximately 0.7. The ρ values from the present TABLE I s STATISTICAL FIT BETWEEN OBSERVED AND SIMULATED study show that the coefficient of variation (variation of PEAK OF CALIBRATED EVENTS FOR CPC: [ABUSTAN (1997)] the Thiessen estimate from the developed spline Events for RMSE Relative Abs. Relative estimate) for 5-minute rainfall totals increases Analysis (m3/s) Errors (%) Errors (%) substantially with increasing spatial variability of Nov23, 1975 0.39 12 12 events. The values ranged from 0.16 to 0.86 with an Dec 4, 1975 0.04 -29 29 average value of approximately 0.4 for ‘LS’ events and ranged from 0.27 to 2.1 with an average of 0.94 for Oct 21, 1994 0.05 -6.6 6.6 ‘HS’ events. Oct 31, 1994 0.01 -1.8 1.8 Jan 2, 1995 0.06 12 12 Feb 28, 1995 0.04 1.5 1.5 NFLUENCE ON ATCHMENT IMULATION IV. I C S Average 0.10 -2.0 10 Having ascertained the likely variation in estimated rainfall at a subcatchment scale induced by the spatial variation in rainfall, it remains to consider the influence B. Validation of CPC Events of the spatial pattern of the rainfall on a catchment As part of this study the model parameters obtained in scale. These influences were ascertained by considering [1] were validated for events, which occurred during rainfall hyetographs determined for 5-minute time 1997 and 1998. The events were selected from 'LS'. The increments for each subcatchment within the catchment. performance statistics of three validation events are The results from the calibration, validation and given in TABLE II. A visual comparison of the extrapolation to different hydrologic events for the CPC validation for the event that occurred on 11 February is presented in the subsequent sections of this paper. 1997 is presented in Fig. 3. The calibration and validation results show the robustness of the CPC model The storm water system of CPC consists of a series of for predicting the catchment response for Thiessen pipes, box culverts and open channels, which ultimately rainfall input with low spatially variable events. discharge into Musgrave Pond in Centennial Park. The length of stormwater drain studied was approximately 5200m from TABLE II the upstream of the catchment to the location of the flow PERFORMANCE STATISTICS FOR VALIDATED EVENTS gauging station at the Musgrave Avenue pond. In-order to Events for MSE RMSE MAE Varian. Bias R2 accurately model the catchment, it was subdivided into 42 3 2 3 3 3 3 Analysis (m /s) (m /s) (m /s) (m /s) (m /s) subcatchments after [1]. The size of individual subcatchments ranges from 0.5 ha to 27 ha. The different forms of landuse Jan.29, 97 0.009 0.095 0.079 0.006 0.056 0.94 and catchment slope were the main concern in performing the Feb.11, 97 0.012 0.110 0.075 0.012 0.080 0.92 discretisation of catchment into subcatchments. The average Oct.19, 98 0.001 0.032 0.005 0.001 -0.001 0.96 slope of the catchment is 5%. A. Calibration of CPC events The calibration process for a gauged catchment involves minimization of the deviation between recorded information and simulation output by adjusting parameters repeatedly. The calibration of SWMM for CPC was performed by Abustan [1] from events in 1994 and 1995 incorporating the Thiessen rainfall model. Then, a validation process was performed to assess the calibration parameters from [1] using an independent set of data from the present study. The developed hyetographs were used as input for the SWMM of the catchment. With the exception of the rainfall, all the parameters were based on those obtained from [1]. The calibration statistics from [1] are given in Fig. 3. The shape of the observed and simulated hydrograph for a TABLE I. validation event - February 11, 1997 C. Improvement in Prediction by the alternate rainfall model (a) In a study of errors in predicted catchment flows arising from rainfall, study [13] classified errors as those arising from the assumed rainfall input and those arising from errors in either the CMS structure or from the parameter values necessary for operation of the CMS structure. Herein, it is the first source of prediction error that is of interest. In the analysis of prediction errors from the calibration validation, it has been assumed that SWMM is adequate for simulation of the catchment runoff and that the calibrated parameter values are accurate. A consequence of this assumption, therefore, is that the change in prediction errors arising from changes in the rainfall model can be ascertained. (b) Shown in Fig. 4 and Fig. 5 are the predicted hydrographs obtained using both Thiessen polygons and a spline surface rainfall for the storm events of 9th October 1998 and 18th October 1999. The improvement in predicting the peak discharge and the volume of the hydrographs for the events considered in the study are given in Fig. 6b. As shown in these figures, the spline surface rainfall model consistently resulted in a better fit to the recorded event than the Thiessen rainfall model. Fig. 6. Comparisons between (a) Volume; and (b) Peak of predicted hydrographs from alternate rainfall input, and observed hydrographs for the selected events It can be seen that prediction of peak discharge as shown in Fig. 6b is not that accurate for two events with higher peak flow even from the spatially distributed spline rainfall input. This may be due to the much larger values for these two events in comparison with the events used for calibration and validation. However, a better prediction is obtained using the spline rainfall input than the Thiessen rainfall input. Fig. 4. The shape of the observed and simulated hydrograph for the It is interesting to know whether the degree of this event on October 09, 1998 improvement in the predicted hydrograph is dependent on the spatial variability of the storm event as measured in [16]. From the performance criteria results shown in th TABLE III, it can be seen that the storm event of 19 October 1998 had a lower degree of spatial variability than the storm event of 9th October 1998. This is consistent with the predictions, for the latter event being improved more than the earlier event. Furthermore, the performance parameters for predicted hydrographs from the spline rainfall input and from the Thiessen rainfall input are almost similar for the storm event of 19th October. Also hydrographs for the storm event of 19th October were found not to improve to the same extent as the storm event of 9th October. The improvement in the catchment modeling system Fig. 5. The shape of the observed and simulated hydrograph for the predictions arising from the changed rainfall model, event on October 18, 1999 therefore, are a function of the spatial variability of the rainfall. Hence, it can be concluded that the more variable the rainfall, the greater the need for a rainfall model which incorporates this variability in space and REFERENCES time. [1] Abustan, I. (1997) "Modeling of Phosphorus Transport in Urban Storm water Runoff”, PhD. Dissertation, UNSW, TABLE III COMPARISON OF PERFORMANCE STATISTICS BETWEEN Australia. EXAMPLE EVENTS FROM ‘LS’ AND ‘HS’ CATEGORY [2] Ball, J.E. and Luk, K.C. (1998) “Modeling Spatial EVENTS variability of Rainfall over a catchment”, Journal of Hydrologic Engineering, Vol. 3, No. 2, 122-130 Categorised ‘LS’ event on Categorised ‘HS’Event on Statistics 19/10/1998 09/10/1998 [3] Chaubey, I, Haan, C.T., Grunwald, S. and Salisbury, J.M. Spline Thies. Improv Spline Thies. Improv (1999) "Uncertainty in the model parameters due to Flow Flow ement Flow Flow ement spatial variability of rainfall", Journal of Hydrology, MSE 0.001 0.001 0 0.002 0.011 0.009 220:48-61. 3 2 (m /s) [4] Creutin, J.D. and Obled, C., (1982) "Objective Analyses RMSE 0.032 0.032 0 0.045 0.105 0.060 and Mapping Techniques for Rainfall Fields”, Water 3 (m /s) Resources Research, Vol. 18(2):413-431 MAE 0.024 0.026 0.002 0.025 0.046 0.021 [5] Delhomme, J.P. (1978) "Kriging in hydrosciences, 3 (m /s) Advances in Water Resources", 1(5):251-266 Variance 0.001 0.001 0 0.002 0.010 0.008 3 2 [6] Dirks, K.N., Hay, J.E., Stow, C.D. and Harris, D. (1998) (m /s) "High-resolution studies of rainfall on Norfolk Island part Bias -0.005 -0.001 -0.004 -0.002 0.032 0.030 11 : Interpolation of rainfall data", Journal of Hydrology, (m3/s) 208:187-193. Variation 6.5 14.0 7.5 -11.6 42.6 31.0 [7] Goodrich, D.C., Faures, J., Woolhiser, D.A., Lane, L.J. Peak(%) and Sorooshian, S. (1995) "Measurement and analysis of small-scale convective storm rainfall variability", Journal of Hydrology, 173:283-308 V. CONCLUSIONS [8] Guillermo, Q., Tabios III and Salas, J.D. (1985) "A comparative analysis of techniques for spatial Reported herein have been the results of an interpolation of preceipitation”, Water Resources investigation into the importance of the rainfall model Bulletin, Vol. 21, No. 3,:365-380 for robust predictions from catchment modelling [9] Hutchinson, M.F. (1995) “Interpolating mean rainfall systems. Two alternate rainfall models, namely a using thin plate smoothing splines”, International Journal Thiessen based rainfall model and a spline surface of GIS, Vol. 9, No. 4. rainfall model, were considered. It was found that the [10] Lettenmaier, D.P. and Wood, E.F. (1993) "Hydrologic rainfall model significantly influenced the predicted Forecasting", Handbook of Hydrology , Ed. Maidment, hydrographs obtained from a catchment modelling DR, McGraw-Hill Inc., NY, USA. [11] Obled, Ch., Wendling, J., and Beven, K. (1994) "The system. Furthermore, it was found that the spline sensitivity of hydrological models to spatial rainfall surface rainfall model, which considered the spatial and patterns: an evaluation using observed data", Journal of temporal variability of the rainfall in greater detail than Hydrology, 159:305-333. the Thiessen rainfall model resulted in predicted [12] Seyfried, M.S. and Wilcox, B.P. (1995) "Scale and hydrographs that more closely duplicated the recorded nature of spatial variability: Field examples having hydrograph for the same parameter set. The degree of implications for spatial variability", Water Resources, this improvement in the predicted hydrograph was Research., Vol. 31, 173-184. found to be dependent on the spatial and temporal [13] Troutman, B. M. (1983) "Runoff prediction errors and variability of the storm event as measured by [16] for bias in parameter estimation induced by spatial variability of precipitation", Water Resources Research, Vol. 19, No. assessing this feature of a storm event. 3. [14] Tsanis, I.K. and Gad, M.A. (2001) "A GIS precipitation VI. ACKNOWLEDGMENT method for analysis of storm kinematics", Environmental The authors wish to acknowledge the Upper Modelling & Software, 16:273-281 [15] Umakhanthan, K. and Ball, J.E. (2000) "Integration of Parramatta River catchment Trust and the hydrology Hydroinformatics with catchment models", division of School of Civil and Environmental Hydroinformatics 2000 conference proceedings, Iowa, Engineering of the University of New South Wales for USA providing the raw rainfall data and the flow data for the [16] Umakhanthan, K., Ball, J.E. and Sharma, A. (submitted study. 2001, unpublished). "Estimation of Spatio-Temporal Heterogeneity of Rainfall and the need for rainfall redistribution for urban catchment", Journal of Hydrology Hydroinformatics 2000, July 23-27 2000, Iowa, USA Integration of Hydroinformatics with Catchment models. K. Umakhanthan The University of New South Wales, Sydney, Australia James E Ball The University of New South Wales, Sydney, Australia ABSTRACT : The spatial variability of rainfall can be substantial even for very small catchments and an important factor in the reliability of rainfall-runoff simulations. Catchments in urban areas usually are small and the management problems often require the numerical simulation of catchment processes and hence the consideration of the spatial and temporal variability of rainfall. A need exists therefore for the analysis of the influence of traditional methods (for example, Thiessen method) and enhanced techniques based on the application of hydroinformatic tools. Over the past decade, hydroinformatic tools have been used for the extraction and manipulation of information for the modelling of storm water systems. This paper mainly describes the application of a hydroinformatic tool, in this case the GIS - Arc/Info, in developing a spatially variable rainfall model for a small-urbanised catchment based on temporally variable rainfall records stored in a time series database. The 132ha Centennial Park catchment that is located within the eastern suburbs of the Sydney metropolitan region is used as a case study for this investigation. Based on the rainfall recorded at six pluviometers within and immediately adjacent to the catchment, the spatial variation of rainfall was ascertained at five minute increments using a thin-plate spline algorithm developed previously by Ball and Luk (1996). From these spatial patterns of rainfall, it was possible to develop individual hyetographs for each of the 42 subcatchments within this catchment. Presented in this paper is an analysis of the spatial and temporal variability in rainfall obtained through this approach. Also presented is an analysis of the likely impacts of this variability on runoff hydrographs. 1 INTRODUCTION leads to various uncertainties along the passage of the above information cycle Ball et al. Fundamental to hydroinformatic system is the (1998). Therefore, developing accurate rainfall management of information and its passage series with sufficient temporal and spatial from the time is generated to the time when it resolution is vital and attracts much attention in ultimately is presented to interested parties. In modelling the quantity and quality of catchment Catchment management practice, the runoff. Eventually the developed rainfall series information can be considered to pass through should be in a form that can be easily integrated conceptual components such as hydrological, with the catchment model. hydraulic, transport and receiving models. The Numerous field experiments and descriptions passage of information through these of spatial rainfall variability over catchments components is not linear but rather is random were clearly shown by several authors, for and in a nonuniform manner. In essence, the example Obled et al. (1995), Seyfried and variation in modelling the rainfall input could Wilcox (1995), Chaubey et al. (1999). The importance of spatial rainfall variability and the event and not the spatial variation during the short response time involved in urban storm event. Presented in this paper is the use of catchments has been well documented by the spline surface technique available in Niemczynowicz (1991), Schilling (1991). Arc/Info-GIS to consider the spatial variation Furthermore, a recent study by Woods and during the storm event. The effects on the Sivapalan (1999) developed a theoretical hydrographs produced from the developed framework, that integrates several disparate subcatchment averaged rainfall series are also sources of hydrological variability and a presented. mathematical framework of rainfall with space- time variability. However, Woods and 2 BACKGROUND THEORY Sivapalan (1999) concentrated on developing the theory and illustrating the possibilities of its The Arc/Info minimum curvature (thin plate application rather than investigating on real site smoothing) spline interpolation proposed by specific simulation studies, which by their Ball and Luk (1998) and Hutchinson (1991) to nature can provide more detailed results than a interpolate between measured rainfall points has general theory. Ball (1994) noted that the following two characteristics: estimation of the time of concentration for a • catchment is dependent on the temporal pattern The surface exactly passes through the data of rainfall excess and vary by around + 20% points. • from that predicted using a constant rate of The surface consists the minimum rainfall excess. Moreover O’Loughlin (1998) curvature (the cumulative sum of the utilised data from Sydney urban catchments and squares of the second derivative terms of showed that using a longer time steps in the the surface, taken over each point on the model decreased the calculated flows by as surface must be a minimum) much as 50%. Shown in this brief literature The Spline function uses the following review is the importance of modelling the formula for the surface interpolation, see rainfall with sufficient spatial and temporal Burrough and Rachael (1998) and Ball and Luk resolution for modelling of the quantity and (1998). N quality of stormwater runoff. The attainment of = + λ f ( x , y ) T ( x , y ) ∑ i R ( ri ) (1) this resolution in the rainfall model is possible i = 1 with the aid of hydroinformatic tools rather than the assumption of uniform spatial and temporal where N - No of data points, λi -weighting pattern based on traditional method such as the coefficients, ri - Distance from the point (x,y) to Thiessen method. point I; while T (x, y) and R(r) are defined There were several methods proposed in last as follows = + + decade to represent the spatial variability of T (x, y) a1 a2 x a3 y (2) rainfall over a catchment, such as thin plate smoothing splines and the radar information and technique, etc. Thin plate smoothing is widely ϕ r r + − used to spatially interpolate hydrological ln c 1 phenomena (such as rainfall and temperature) 1 4 2τ R(r) = (3) from point records. [Hutchinson (1995), Ball π 2 ϕ r r and Luk (1998)]. Recent study on an Australian +τ K +c+ln catchment by Ball and Luk (1998) showed that 0 τ π 2 thin plate spline smoothing can spatially ϕ interpolate rainfall accurately than other Where -The weight attached to the first methods. (such as Thiessen, Kriging, and derivative terms during minimization, τ -The Inverse distance methods). However, Ball and weight of the third derivative terms during Luk (1998) considered only the spatial variation minimization, r -The distance between the in the total depth of rainfall during the storm point and the sample, K0 -The modified Bessel function, c - constant equal to 0.577215, a - the different forms of landuse. The slope was i also considered in discretisation of the coefficients found by the solution of a system catchment. The average slope of the catchment linear equations. is 5%. 3 CATCHMENT DESCRIPTION AND 3.2 Gauging Details GAUGING DETAILS Prior to October 1994, there were no rainfall 3.1 Description of Centennial Park Catchment gauging stations existing within the catchment. After realising the importance of the rainfall for The study catchment is located within the quality studies of the Centennial park ponds, a Sydney metropolitan region, approximately 4 pluviometer was installed by UNSW at km south of the Central Business District and 1 Waverley public school in October 94. Another km to the north west of the main campus of the gauging arrangement was installed at the outlet University of New South Wales (UNSW). The of the catchment with the flow monitoring catchment covers the southwestern corner of system, in 1997, in order to study the spatial Waverely Local Government Area and the variability of rainfall. Since the direction of eastern side of Randwick. The catchment is 132 storm movement is rarely recorded in urban ha (1.32 km2) in extent. The catchment is served catchments, it is not advisable to expect a and drained by separate sewer and storm water reliable result on the distribution of intensity systems. The storm water system consists of a over the catchment when there is no more than series of pipes, box culverts and open channels two gauges. Four other gauge records adjacent which ultimately discharge into Musgrave Pond to the catchment therefore were utilised in our in Centennial Park. study. The locations of the gauging stations are shown with respect to the study catchment in Figure 2. Figure 1 - Schematisation of subcatchments of Centennial Park Catchment after Abustan (1997) In order to accurately model the catchment, it was subdivided into 42 subcatchments (Figure 1). The size of individual subcatchments ranges from 0.5 ha to 27 ha. The Figure 2. Rainfall Gauges within and adjacent discretisation was made mainly by considering, to the Catchment. These other pluviometers are located within a previously by Ball and Luk (1998). A GIS and radius of 7 km from the study area. All of these in particular Arc/Info was used as the software gauges are digitally logged 0.2mm tipping base for implementation of the spatio/temporal bucket (except Paddington gauge with 0.5mm) rainfall model. In addition to providing basic pluviometers and have been installed and modelling facilities Arc/Info provides a facility maintained by different authorities. Among for programming the rainfall model through a these gauges, the Paddington and Kingsford- macro programming language, Arc Macro Smith Airport Meteorological stations have Language (AML). Use of this programming been operated by Sydney Water and the Bureau capability permitted sequencing of Arc/Info of Meteorology (BOM) respectively for commands, which enabled easy repetition of the approximately forty years. The stations at several operations involved in the creation of Avoca and Storey Street have been operated by five minute incremental patterns of rainfall over UNSW for the past 30 years. the total catchment and the subsequent extraction of five minute hyetographs for each of the 42 subcatchments. 4 IMPLEMENTAION OF RAINFALL MODELLING The rainfall patterns from this spatial rainfall model were then compared with those from the Conceptual rainfall-runoff modelling systems Thiessen model. Table 1 shows the comparison require a hyetograph of rainfall intensities of developed spatial rainfall series versus time for the time of simulation. If (subcatchment based) with the uniform rainfall multiple gauges exist within the catchment, pattern produced by the Thiessen model. multiple hyetographs for the catchment will be Lettenmaier and Wood (1992) suggest that able to be used for the desired simulations. In Mean Absolute Error is preferred to squared most applications for small urban catchments, error measures because, when compared to however, a single rainfall pattern or none is squared error measures, absolute error measures available within the catchment. This are less dominated by a small number of large investigation is aimed at improving the errors, and are thus a more reliable indicator of representation of actual rainfall from the typical error magnitudes. The Variation (V) in gauging arrangements within and adjacent to total and Mean Absolute Variation (MAV) of the catchments, and hence to assess how the spline rainfall prediction from the Thiessen assumption of uniform rainfall influences rainfall prediction for each individual simulation results from catchment modelling subcatchments were calculated using; applications. = − (4) The rainfall data used for this study was Variation Ts Tt extracted from the HYDSYS database in the School of Civil and Environmental Engineering Where T - Average subcatchment total from at the University of New South Wales. The s gauge readings were utilised as the point developed model, Tt - Thiessen total for the rainfall input data in developing the rainfall storm event surface. Events where more than 20mm in total were recorded were used in this study. Based on 1 n MAV = − this approach, ten storm events in 1998 were ∑ Rs (i) Rt (i) (5) n = extracted for analysis. The results presented in i 1 this paper are from the four of these events. Based on the rainfall recorded at six Where Rs - five minute Simulated rainfall pluviometers within and immediately adjacent value from developed spline model, R - five to the catchment, the spatial variation of rainfall t was ascertained at five minute increments using minute rainfall value from Thiessen model, n - the thin plate spline algorithm developed Number of observations in the time series. Table 1. Variation in prediction and Mean Absolute Variation of developed subcatchment averaged rainfall from the Thiessen averaged method Storm No of Thiessen Variation in Highest Date Duration data total total (mm) MAV (min.) points (mm) (mm) Storm 1 22/06/98 160 32 33.4 -18 to +4 0.64 Storm 2 10/04/98 240 48 43.2 -11 to +4 0.90 Storm 3 22/04/98 490 98 42.6 -16 to +4 0.28 Storm 4 18/05/98 425 85 101.4 -26 to +8 0.74 40 50 ) Storm 1 Storm 3 ) 40 30 30 20 20 10 10 Cumulative rainfall (mm Cumulative rainfall (mm Cumulative rainfall 0 0 11121311 21416181 5 minute time increments 5 minute time increments 100 60 Storm 4 ) ) Storm 2 80 40 60 40 20 20 Cumulative (mm Rainfall Cumulative rainfall (mm 0 0 1 11213141 1 21416181 5 minute time Increments 5 minute time increments Figure 3. Cumulative rainfall patterns from the developed spatial model for the selected four events (shown for 42 subcatchments) 'Variation' in prediction is calculated for the The non-liner reservoir model available total rainfall and a range (range of variation in within the Runoff block of SWMM was used in total rainfall for different subcatchments) is this study to assess hydrological response. The given to show how the ascertained rainfall SWMM model simulates the runoff and pattern varies from subcatchment to transport of stormwater through drainage subcatchment. The highest MAV value in networks, by performing hydrologic and Table 1 gives the extreme effect of the spatial hydraulic analyses of stormwater in the variation for a storm event on a particular drainage system. The SWMM model provides subcatchment. The cumulative rainfall patterns important and necessary information on the for different storm events for each of the 42 present and future adequacy of the system, see subcatchments are shown in Figure 3. Huber et al. (1988). Consideration this figure shows how the rainfall Five-minute incremental rainfall series patterns at different parts of the catchment developed for each subcatchment within the varies and how different storms have different study catchment were used in the model characteristics. Storm event 1 has a together with a Thiessen weighted uniform homogeneous nature but even this event has rainfall for comparison. A 5ha, small spatial variations in the depth of rainfall; use of impervious hypothetical catchment was used to the spatially variable rainfall model results in a show the spatial variability effect of rainfall on rainfall depth variation of approximately 22 mm hydrographs. This was mainly to consider across the catchment. However, the variable within an area of the catchment with finer pattern of storm can leads to variation upto resolution, than considering at catchment scale. 15mm to 34mm in total within two extreme The results from this hypothetical catchment subcatchment rainfall. On the other hand storm will highlight the effect of uncertainty of 3 has a high spatial heterogeneity, along its time rainfall input on a subcatchment scale. series, even though it doesn't have much Hydrographs obtained from two extreme variation in total rainfall, when compared to the rainfalls obtained at subcatchment 6 and 30 other storm events. Eventhough, the total were shown in Figure 4. The hydrograph rainfall of storm 4 is 2.5 times than the total of obtained by inputting Thiessen rainfall also storm 2, both follow almost the same spatially added for comparison. It shows a considerable variable nature along their time series. variation in predicting the peak and volume while accurately predicting the time to peak. 5 INFLUENCE OF SPATIAL RAINFALL However, in multiple peak events (storm 2) the ON HYDROGRAPHS. predicted time to peak also showed a considerable variation from subcatchment to To study the impact of spatially variable rainfall subcatchment. Results of the peak flow and the on simulated hydrological responses, volume of the hydrograph obtained from unfortunately, a rainfall-runoff modelling simulating the spatially variable hyetographs on system has to be used. There are many a hypothetical subcatchment for the four events alternative theoretical models available for considered are tabulated in Table 2. A visual simulation of individual processes influencing comparison of the simulation results for the the development and transmission of surface event of 22/04/98 is presented as Figure 4. runoff through a catchment. As a consequence The study is further extended to calibrate and there are many alternative rainfall-runoff validate the model for the developed spatially modelling systems with the selection between varied rainfall pattern. Consequently it is these alternatives being subjective and highly needed to clarify whether the above dependent on the objectives of the modelling subcatchment scale effect will be compensated process. in producing the total outflow hydrograph. Table 2. Comparison of Peak and Volume discharges between developed spatial rainfall and Thiessen rainfall pattern Hydrograph Peak (m3/s) Hydrograph Volume * 102 (m3) Event From From spatially developed From From spatially developed Thiessen model Thiessen model r/f r/f SC. 6 r/f SC. 30 r/f SC. 6 r/f SC. 30 r/f 1.50 0.31 15.8 17.7 7.55 Storm 1 1.24 (+21.0%)* (-75.0%) (+12.0%) (-52.0%) Storm 2 0.82 1.11 1.04 20.8 22.7 21.4 (+35.4%) (+26.8%) (+9.1%) (+2.9%) 0.46 0.17 19.8 21.8 11.5 Storm 3 0.40 (+15.0%) (-57.5%) (+10.1%) (-41.9%) 1.35 0.97 40.9 45.0 27.8 Storm 4 1.28 (+5.5%) (-24.2%) (+10.0%) (-32.0%) *The percentage values showed in the brackets are the variation with the results from Thiessen rainfall input, SC. refers to Subcatchment Number, and r/f refers to Rainfall. 0.5 Flow for the thiessen rainfall Storm 3 0.4 Flow for the rainfall from the model (Subcatchment 30) 0.3 Flow for the rainfall from the model (Subcatchment 6) /s) 3 0.2 Flow (m 0.1 0 1 112131415161718191101111 Time increments (2.5minutes) Figure 4. Comparison of hydrographs from two different subcatchment (6, 30) rainfall pattern and Thiessen averaged rainfall for the storm event on 22/04/1998 catchment hydrographs have long been 6 DISCUSSION AND CONCLUSIONS recognised Singh (1997), Obled et al. (1994). However, the majority of studies were carried The importance of the spatial variability of out for large catchments with dense gauging rainfall and the effect of this variability on the arrangements, or by using radar information with 2-5 km spatial resolution and 15minute- Burrough, PA and Rachael, AM, “Principles of 1hr. time resolution. This study aimed at geographic systems”, Oxford University assessing the potential for use of available Press, 1998. hydroinformatic tools in modelling the spatial Chaubey, I, Haan, CT, Grunwald, S and and temporal variation of the rainfall over a Salisbury, JM, “Uncertainty in the model small urban catchment with the records from a parameters due to spatial variability of typical rainfall gauging arrangement within and rainfall”, Journal of Hydrology, Vol. 220, adjacent to the catchment. Individual 5-minute pp.48-61, 1999. hyetographs for each of the 42 subcatchments Huber, WC & Dickinson, RE, “Storm water within the catchment have been produced from Management Model”, Version 4, Users the approach. The results from the development Manual, 1988. of a rainfall pattern using this approach can Hutchinson, MF, “Interpolating mean rainfall produce a 0.9mm average variation (From the using thin plate smoothing splines”, Thiessen rainfall) in a 5-minute incremental International Journal of GIS, Vol. 9, No. 4, rainfall at some subcatchments. pp.385-403, 1995. The study also considered the impacts of this Lettenmaier, DP and Wood, EF, "Hydrologic spatial variability of rainfall in the prediction of Forecasting", Handbook of Hydrology , Ed. hydrographs by integrating the results with Maidment, DR, McGraw-Hill Inc., NY, catchment modeling software SWMM. It was USA. shown that using the above developed Niemczynowicz, J and Sevruk, K, “Introduction hyetographs in a conceptual rainfall-runoff and workshop conclusions”, Atmospheric model can result in variations of +20 to –50% in Research, Vol. 27, pp 1-4, 1991. the peak runoff rate when compared with the O’Loughlin, G, Stack, B and Wilkinson, A, hydrograph peak from the hyetograph produced “Effects of varying time steps in urban using a Thiessen model. rainfall-runoff models”, Hyrdastorm ’98, Adelaide, Australia, pp.57-62, 1998. Obled, Ch., Wendling, J., and Beven, K., “The REFERENCES sensitivity of hydrological models to spatial rainfall patterns: an evaluation using Abustan, I., "Modelling of Phosphorus observed data”, Journal of Hydrology, Vol. Transport in Urban Storm water Runoff”, 159, pp.305-333, 1994. PhD. Dissertation, UNSW, Australia, 1997. Schilling, W, “Rainfall data for urban Ball, JE and Luk, KC, "Determination of the hydrology: What do we need?”, Rainfall Distribution over a Catchment Atmospheric Research, Vol. 27, pp 5-21, using Hydroinformatics Tools", Proc. 2nd 1991. Int. Conf. on Hydroinformatics, Zurich, Seyfried, MS and Wilcox, BP, “Scale and Switzerland, pp.369 - 376, 1996. nature of spatial variability: Field examples Ball, JE and Luk, KC, "Modelling spatial having implications for spatial variability”, variability of rainfall over a catchment", Water Res. Res., Vol. 31, pp.173-184, 1995. Journal of Hydrologic Engineering, Vol. 3, Singh, VP, “Effect of spatial and temporal No. 2, pp.122-130, (1998). variability in rainfall and watershed Ball, JE, “The influence of storm temporal characteristics on stream flow hydrographs”, patterns on catchment response”, Journal of Hydrological Processes Journal, Vol. 11, Hydrology, Vol. 158, pp.285-303, 1994. pp.1649-1669, 1997. Ball, JE, Coates, A and Waite, TD, Woods, R and Sivapalan, M. (1999), “A “Application of information systems in synthesis of space-time variability in storm catchment management, Proc. 2nd response: Rainfall, runoff generation, and International Conference. On Environmental routing.” Water Resources Research, 35(8), Management, Wollongong, Australia, pp.573-582, 1998 pp.2469-2485. THE INFLUENCE OF SPATIALLY VARIABLE RAINFALL ON RUNOFF HYDROGRAPHS K Umakhanthan 1 and James E Ball 2 1Research Student, Water Research Laboratory, School of Civil Engineering, The University of New South Wales, 110 King Street Manly Vale, NSW 2093, Australia. 2Associate Professor, Water Research Laboratory, School of Civil Engineering, The University of New South Wales, 110 King Street Manly Vale, NSW 2093, Australia. Abstract The application of conceptual rainfall-runoff models for assessment of the quantity and quality of stormwater runoff requires a knowledge of the many influencing factors or input data. One of these data items is the rainfall intensity or depth over a defined time increment. There are many alternative methodologies for assessment of the spatial distribution of the rainfall over the catchment of interest. Historically, however, these methodologies have considered only the spatial variation in the total depth of rainfall during the storm event and not the spatial variation during the storm event. Presented in this paper will be the results of an investigation into the influence of the spatial and temporal variation in rainfall over a catchment on the predicted runoff hydrographs. Based on the rainfall recorded at six (6) pluviometers around and in the Musgrave Avenue Stormwater Channel Catchment, five (5) minute hyetographs were developed using the thin plate spline algorithm of Luk and Ball (1998) for ten different storm events recorded during 1998 at the centroids of the 42 subcatchments used by Abustan (1998) in his modelling of the catchment using SWMM. It will be shown in the paper that using these hyetographs in a conceptual rainfall-runoff model could result in variations of up to +50% in the peak runoff rate when compared with use of the hyetograph recorded at the nearest pluviometer. INTRODUCTION Numerous field experiments and descriptions of spatial rainfall variability over catchments were clearly shown by several authors, for example [13], [15], and [7]. The importance of spatial rainfall variability and the short response time involved in urban catchments has been well documented by [11], [14]. Furthermore, a recent study from [18] developed a theoretical framework, that integrates several disparate sources of hydrological variability and a mathematical framework of rainfall with space-time variability. However, Woods and Sivapalan (1999) in [18] concentrated on developing the theory and illustrating the possibilities of its application rather than investigating on real site specific simulation studies, which by their nature can provide more detailed results than a general theory. Study [4] noted that estimation of the time of concentration for a catchment is dependent on the temporal pattern of rainfall excess and vary by around + 20% from that predicted using a constant rate of rainfall excess. Moreover case study [12] utilised data from Sydney urban catchments and showed that using longer time steps in the model decreased the calculated flows by as much as 50%. Shown in this brief literature review it is clear that in Catchment management practice, the information can be considered to pass through conceptual components such as hydrological, hydraulic, transport and receiving models. The passage of information through these components is not linear but rather is random and in a nonuniform manner. In essence, the variation in modelling the rainfall input could leads to various uncertainties along the passage of the above information cycle [5]. Therefore, developing accurate rainfall series with sufficient temporal and spatial resolution is vital and attracts much attention in modelling the quantity and quality of catchment runoff. Eventually the developed rainfall series should be in a form that can be easily integrated with the catchment model. The attainment of this resolution in the rainfall model is possible with the aid of hydroinformatic tools rather than the assumption of uniform spatial and temporal pattern based on traditional method such as the Thiessen method. There were several methods proposed in last decade to represent the spatial variability of rainfall over a catchment, such as thin plate smoothing splines and the radar information technique, etc. Thin plate smoothing is widely used to spatially interpolate hydrological phenomena (such as rainfall and temperature) from point records, [9], [3]. Recent study on an Australian catchment from [3] showed that thin plate spline smoothing could spatially interpolate rainfall accurately than other methods. (Such as Thiessen, Kriging, and Inverse distance methods). However, study [3] considered only the spatial variation in the total depth of rainfall during the storm event and not the spatial variation during the storm event. This paper mainly aimed on the followings. • Development of five minute's incremental spatial rainfall pattern to consider the spatial variation during the storm event, by the spline surface technique available in Arc/Info- GIS. • Investigate the effects of the above-developed subcatchment averaged rainfall series on the hydrographs at the outlet of the catchment. Also the comparisons were made with the hydrogrphs produced from the Thiessen rainfall input. CATCHMENT DESCRIPTION AND GAUGING DETAILS The study catchment is located within the Sydney metropolitan region, approximately 4 km south of the Central Business District and 1 km to the north west of the main campus of the University of New South Wales (UNSW). The catchment covers the southwestern corner of Waverely Local Government Area and the eastern side of Randwick. The catchment is 132 ha (1.32 km2) in extent. The catchment is served and drained by separate sewer and storm water systems. The storm water system consists of a series of pipes, box culverts and open channels which ultimately discharge into Musgrave Pond in Centennial Park as shown in Figure 1. The length of stormwater drain studied was approximately 5200m from the upstream of the catchment to the location of the flow gauging station at the Musgrave Avenue pond. In-order to accurately model the catchment, it was subdivided into 42 subcatchments. The size of individual subcatchments ranges from 0.5 ha to 27 ha. The discretisation was made mainly by considering, the different forms of landuse. The slope was also considered in discretisation of the catchment. The average slope of the catchment is 5%. Gauging Details Prior to October 1994, there were no rainfall gauging stations existing within the catchment. After realising the importance of the rainfall for quality studies of the Centennial park ponds, a pluviometer was installed by UNSW at Waverley public school in October 94. Another gauging arrangement was installed at the outlet of the catchment with the flow monitoring system, in 1997, in order to study the spatial variability of rainfall. Since the direction of storm movement is rarely recorded in urban catchments, it is not advisable to expect a reliable result on the distribution of intensity over the catchment when there is no more than two gauges. Four other gauge records adjacent to the catchment therefore were utilized in our study. The locations of the gauging stations are shown with respect to the study catchment in Figure 2 Catchment Outlet Figure 1: Schematisation of Figure 2: Rainfall Gauges within and subcatchments, Pipes and Channels of adjacent to the Catchment. Centennial Park Catchment after Abustan (1997) These other pluviometers are located within a radius of 7 km from the study area. All of these gauges are digitally logged 0.2mm tipping bucket (except Paddington gauge with 0.5mm) pluviometers and have been installed and maintained by different authorities. Among these gauges, the Paddington and Kingsford-Smith Airport Meteorological stations have been operated by Sydney Water and the Bureau of Meteorology (BOM) respectively for approximately forty years. The stations at Avoca and Storey Street have been operated by UNSW for the past 30 years. IMPLEMENTAION OF RAINFALL MODELLING Conceptual rainfall-runoff modelling systems require a hyetograph of rainfall intensities versus time for the time of simulation. If multiple gauges exist within the catchment, multiple hyetographs for the catchment will be able to be used for the desired simulations. In most applications for small urban catchments, however, a single rainfall pattern or none is available within the catchment. This investigation is aimed at improving the representation of actual rainfall from the gauging arrangements within and adjacent to the catchments, and hence to assess how the assumption of uniform rainfall influences simulation results from catchment modelling applications. The rainfall data used for this study was extracted from the HYDSYS database in the School of Civil and Environmental Engineering at the University of New South Wales. The gauge readings were utilised as the point rainfall input data in developing the rainfall surface. Events where more than 20mm in total were recorded were used in this study. Based on this approach, ten storm events in 1998 were extracted for analysis. Among the selected ten storm events four were focused for the analysis on this paper. These events were chosen based on their intensity, duration and their nature on forming the peak. The details of these storm events were shown in Table 1. Table 2: The details of selected four storm events Storm Storm No of Thiessen categorization Date duration data total (mm) (min.) points High Intensity Storm 1 short duration 22/06/98 160 32 33.4 single peak High Intensity Storm 2 short duration 10/04/98 240 48 43.2 multiple peak Low Intensity Storm 3 long duration 22/04/98 490 98 42.6 multiple peak High Intensity Storm 4 long duration 18/05/98 425 85 92.4 multiple peak Based on the rainfall recorded at six pluviometers within and immediately adjacent to the catchment, the spatial variation of rainfall was ascertained at five minute increments using the thin plate spline algorithm developed previously by Ball and Luk (1998). A GIS and in particular Arc/Info was used as the software base for implementation of the spatio/temporal rainfall model. In addition to providing basic modelling facilities Arc/Info provides a facility for programming the rainfall model through a macro programming language, Arc Macro Language (AML). Use of this programming capability permitted sequencing of Arc/Info commands, which enabled easy repetition of the several operations involved in the creation of five minute incremental patterns of rainfall over the total catchment and the subsequent extraction of five minute hyetographs for each of the 42 subcatchments. The detail analysis of the developed subcatchment based rainfall series and the related comparisons on different storm events were clearly shown from the study [17], with the Background theory on Spline surface technique available with Arc/Info-GIS. INFLUENCE OF SPATIAL RAINFALL ON HYDROGRAPHS To study the impact of spatially variable rainfall on simulated hydrological responses, unfortunately, a rainfall-runoff modelling system has to be used. There are many alternative theoretical models available for simulation of individual processes influencing the development and transmission of surface runoff through a catchment. As a consequence there are many alternative rainfall-runoff modelling systems with the selection between these alternatives being subjective and highly dependent on the objectives of the modelling process. The non-liner reservoir model available within the Runoff block was used combinely with the Transport block of SWMM in this study to assess hydrological response. The SWMM model simulates the runoff and transport of stormwater through drainage networks, by performing hydrologic and hydraulic analyses of stormwater in the drainage system. The SWMM model provides important and necessary information on the present and future adequacy of the system, see Huber et al. (1988). The ascertained five-minute's spatial rainfall pattern was inserted into rainfall-runoff model of SWMM. This was carried out in order to analyse the impact of this spatially variable rainfall pattern on the temporal variability of the catchment response from currently used Thiessen rainfall input approach. The catchment parameters, with the other modelling parameters including infiltration parameters were utilised from the study [1]. These parameters from [1] were based on the calibration and validation of the events from 1994 and 1995, are given in Table 2. Exactly the similar input conditions were used other than the rainfall input conditions. The runs were implemented with the Thiessen uniform rainfall and developed spatially varied rainfall, aimed on predicting the uncertainty from the above different rainfall inputs. The above mentioned runs were performed for the differently categorised four storm events. The peak, volume and time to peak were concerned on the developed hydrographs from the two different rainfall pattern. The performance results were tabulated in Table 3. The performance variation on the consideration of uniform rainfall input from the temporally varied rainfall was tried to be correlated with the different character of the storm events. Table 2: Parameter set used in rainfall-runoff model available with SWMM No of Inlets 48 No of Pipes/Channels 94 Total catchment area 132.7 ha Total width of the catchment 6820 m Percentage of Imperviousness 68.86 % Horton's Maximum Infiltration rate 250 mm/hr Horton's minimum Infiltration rate 20 mm/hr Horton's decay rate 0.00125 Impervious Manning's roughness 0.012 Pervious Manning's roughness 0.3 Table 3: Performance details of Hydrographs produced from two different rainfall input, for the four different storm events Storm 1 Storm 2 Storm 3 Storm 4 Date 22/06/1998 10/04/1998 22/04/1998 18/05/1998 Storm Start time 20:45 07:10 16:05 22:15 Total rainfall range from spatial 15.9 - 37.8 31.5 - 53.6 25.4 - 46.1 61.9 - 92.2 model / (mm) Average Spatial r/f input 0.647 1.261 0.425 0.911 Flow / (m3/s) Thiessen r/f input 0.835 1.199 0.520 1.077 Std. Spatial r/f input 0.066 0.088 0.016 0.057 Deviation of Flow Thiessen r/f input 0.096 0.088 0.022 0.070 Peak Flow / Spatial r/f input 5.831 5.533 2.426 7.959 (m3/s) Thiessen r/f input 8.732 6.329 3.369 8.719 Varition of peak from spatially +49.8 +14.4 +38.9 +9.5 variable r/f input / (%) Volume * Spatial r/f input 10.9 17.0 14.0 30.1 103 / (m3/s) Thiessen r/f input 14.0 18.0 17.2 35.6 Variation in Volume from +28.4 +5.6 +22.9 +18.2 spatially variable r/f input / (%) DISCUSSION AND CONCLUSIONS The importance of the spatial variability of rainfall and the effect of this variability on the catchment hydrographs have long been recognised for example [16], [13]. However, the majority of studies were carried out for large catchments with dense gauging arrangements, or by using radar information with 2-5 km spatial resolution and 15minute-1hr. time resolution. There were fewer studies in proposing a more accurate method with the available typical gauging arrangements on small urban catchments. This study aimed at assessing the potential for use of available hydroinformatic tools in modelling the spatial and temporal variation of the rainfall over a small urban catchment with the records from a typical rainfall gauging arrangement within and adjacent to the catchment. Individual 5-minute hyetographs for each of the 42 subcatchments within the catchment have been produced from the approach. The results from the development of a rainfall pattern using this approach can produce a 0.9mm average variation (From the Thiessen rainfall) in a 5-minute incremental rainfall at some subcatchments. The impact on the use of uniform Thiessen rainfall input on predicting the temporal pattern of hydrographs at the catchment outlet was studied. The detail results on the prediction for both the uniform and spatially variable rainfall input for differently categorised four events were shown in Table 3. Figures 3,4, and 5 show the rainfall pattern of storm 2 for 42 subcatchments, comparison of the temporal variation of hydrographs produced from the particular event, and deviation of discharges created from the Thiessen uniform r/f input with developed r/f input respectively. The Figures 6, 7, and 8 were the repetition of the same sequence for the storm event 4. Apparently the figures show the total variation in rainfall is higher for storm 4 among the 42 subcatchment series than the storm 2. However, The storm 2 shows a higher variation of uncertainty on hydrograph prediction by considering a uniform rainfall pattern. This shows the importance of not only considering the spatial variation in the total depth during the storm event but also the spatial variation during the storm event. The results further show the importance of considering the spatial variability during storm event even for a small catchment (132ha). The investigation show that, the usage of Thiessen uniform rainfall input in the model prediction could vary in hydrograph peak by as much as 50% compared with the peak predicted from the temporally varied spatial rainfall input in some heterogeneous storm situations. Figures 4 and 5 implicates how these temporal discharge pattern deviate and how it delayed in predicting the peak for a heterogeneous moving storm event. Moreover Figures 7 and 8 shows a different nature of the prediction of hydrographs on storm event 4 for both the rainfall input pattern. The results from the figures and flow analysis on Table 3 clearly indicates the need of corporating the spatial variation of rainfall during the storm event. The study been further extended on assigning the calibration parameters and how the accommodation of spatial variability of rainfall can improve the calibration process in catchment modelling practice. 60 Storm 2 40 20 Cummulative rainfall rainfall Cummulative 0 1 11213141 5 minute time Increments Figure 3: Cumulative (5 minute temporally varied) pattern from the developed rainfall model for the storm 2 (shown for 42 subcatchments) 8 Simulated flow for sptially variable r/f Simulated flow for the 6 T hiessen r/f 4 Flow / (m3/s) / Flow 2 0 0 50 100 150 200 250 Time Increments / 1 minute Figure 4: Comparison of flow from Thiessen rainfall and spatially variable rainfall input for storm 2 6 5 /s) 3 4 3 2 rainfall input(m / 1 Discharges from Thiessen uniform uniform from Thiessen Discharges 0 0123456 Discharges from spatially distributed rainfall input / (m3/s) Figure 5: Scattered plots to show the deviation of Thiessen r/f-runoff from the spatially distributed r/f runoff 100 ( Storm 4 80 60 40 20 Cummulative Rainfall / Rainfall Cummulative 0 1 21416181 5 minute time increments Figure 6: Cumulative (5 minute temporally varied) pattern from the developed rainfall model for the storm 2 (shown for 42 subcatchments) 10 Simulated flow for sptially variable r/f 8 Simulated flow for the T hiessen r/f 6 4 Flow / (m3/s) / Flow 2 0 0 50 100 150 200 250 300 350 400 450 Time Increments / 1 minute Figure 7: Comparison of flow from Thiessen rainfall and spatially variable rainfall input for storm 4 10 8 /s) 3 6 4 rainfall input(m / 2 Discharges from Thiessen uniform uniform from Thiessen Discharges 0 0246810 Discharges from spatially distributed rainfall input / (m3/s) Figure 8: Scattered plots to show the deviation of Thiessen r/f-runoff from the spatially distributed r/f runoff REFERENCES 1. 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