Flood Studies Update Technical Research Report Volume III Hydrograph Analysis Kieran O’Connor, Monomoy Goswami and Duncan Faulkner Derived from Technical Research Reports by NUI Galway and JBA Consulting Volume I Rainfall Frequency Volume II Flood Frequency Estimation Volume III Hydrograph Analysis Volume IV Physical Catchment Descriptors Volume V River Basin Modelling Volume VI Urbanised and Small Catchments Volume III Hydrograph Analysis Abstract This volume presents methods of constructing the hydrograph to accompany a flood peak of given return period at gauged and ungauged sites in Ireland. The peak flow is typically derived by the methods of flood frequency estimation presented in Volume II. The preferred route to constructing the hydrograph is based on the analysis of hydrograph widths. Flood hydrographs are made comparable by characterising them by so-called hydrograph widths. For example, W75 represents the duration in hours over which the flow exceeds 75% of the peak value. Flood hydrographs for many rivers in Ireland typically have a relatively complex shape, with subsidiary peaks and undulations. These reflect the general pattern of successive periods of heavy rainfall leading to the flood but are also moderated by features of the river network. The aim of hydrograph width analysis is to construct a simplified flood hydrograph shape that is characteristic of the catchment. Two approaches are considered. In one, a particular parametric form is imposed on the hydrograph shape. The shape found most useful is a modified version of the Gamma distribution. In the other approach, the characteristic hydrograph is selected by direct analysis (and averaging) of hydrograph widths. Regression-based expressions allow hydrograph descriptors at ungauged sites to be estimated from physical catchment descriptors (PCDs). Using the parametric approach, a flood hydrograph with unit peak is constructed as a continuous curve. This is rescaled by the relevant peak flow to obtain the required design flood hydrograph. A standalone software package, with graphical user interface, called HWA (Hydrograph Width Analysis), was created both as a research tool and as an aid to constructing design flood hydrographs at any site, ideally based on existing or updated flow data. Although some variation of hydrograph width (and hence hydrograph shape) was noted, no systematic pattern of variation with peak flow magnitude, season of occurrence or pre-event flow value could be established. As expected, arterial drainage was typically found to lead to narrower and peakier hydrographs. Urbanised catchments are not well represented in the 89 stations subjected to hydrograph width analysis. This is one of several areas of application where the Interactive Bridge Invoking the Design Event Method extends the reach of FSU methods appreciably. The HWA and IBIDEM software packages are available through the FSU Web Portal. Research on Flood Event Analysis is briefly summarised in Appendix B. ©Office of Public Works 2014 ii Volume III Hydrograph Analysis Further information about the research FSU Technical Research Reports (TRRs) are available in their original form for researchers and practitioners who seek additional information about a method. The original TRRs sometimes document exhaustive application of a method to many catchments. In others, additional options are reported. Inevitably, the relevance of the original TRRs is influenced by OPW decisions on which methods to implement, and how best to arrange and support them. Readers who consult the original TRRs will notice editorial re-arrangements and compressions, and occasional changes in notation and terminology. These were judged necessary to enhance understanding and use of the FSU methods amongst general practitioners. More significant changes are labelled explicitly as editorial notes. iii Volume III Hydrograph Analysis Contents i Abstract ii Contents iv Notation xi Symbols xi Subscripts xii Abbreviations and descriptor names xii Glossary of terms xiii 1 Introduction 1 1.1 Overview 1 1.2 The goal and premise of hydrograph width analysis 2 1.3 Catchment selection 3 1.4 Physical catchment descriptors (PCDs) 4 1.5 The characteristic hydrograph 5 1.6 HWA software 5 2 Processing the flow data for HWA 6 2.1 Data screening and checking 6 2.1.1 Data handling 6 2.1.2 Missing flow data 6 2.1.3 Scrutiny of annual maximum flood peaks 6 2.1.4 Stations affected by arterial drainage 7 2.2 Defining the time-window of the flood hydrograph 7 2.3 Selection of flood hydrographs 8 2.4 Numbering of flood hydrographs 9 2.5 Seasonal distribution of flood events 9 2.6 Filtering of selected hydrographs 10 2.6.1 Desire for broadly unimodal hydrographs 10 2.6.2 Decoupling the main flood response within a complex flood event 10 2.6.3 Discarding the complex segments 10 3 Deriving the characteristic hydrograph at gauged sites 12 3.1 Standardising the flood hydrographs 12 3.2 Calculation of hydrograph widths at particular exceedance levels 12 3.3 Procedures for constructing the characteristic hydrograph 13 3.4 Split-sample and whole-sample calibration 15 3.5 Deriving the median hydrograph 16 3.5.1 Basic method 16 3.5.2 Anomalies in the derived median hydrograph 17 3.5.3 Improving the derived median hydrograph 17 4 The parametric approach 19 4.1 Objectives 19 4.2 General approach 19 4.3 UPO-Gamma model for the characteristic hydrograph 20 4.3.1 Gamma distribution 20 4.3.2 Peak of Gamma distribution 20 iv Volume III Hydrograph Analysis 4.3.3 Gamma model with peak at time zero 20 4.3.4 Gamma model with unit peak at time zero 21 4.3.5 Formulation in terms of hydrograph rise time Tr 21 4.3.6 Families of hydrographs constructed using the model 21 4.3.7 Example application of UPO-Gamma model 22 4.4 UPO-ERR-Gamma model for the characteristic hydrograph 23 4.4.1 Formulation 23 4.4.2 Method of fitting 24 4.5 Method of fitting the parametric model 24 4.5.1 Objective function 25 4.5.2 Optimisation scheme 26 4.5.3 Performance evaluation 27 4.6 Reproduction of flood hydrographs of verification events 28 4.7 Other methods 30 5 Performance of methods at gauged sites 31 5.1 Introduction 31 5.2 Relative performance in verification compared to that in calibration 32 5.3 Complexity of hydrographs at Stations 06011 and 34018 33 5.4 Variability in hydrograph widths at some stations 34 5.5 Attenuated response at some stations 38 5.6 General guidance 38 5.7 Results of whole-sample calibration 39 5.7.1 Derived median hydrograph and its descriptors 39 5.7.2 UPO-ERR-Gamma model and its parameters 40 5.7.3 Stations where the flood hydrograph recedes faster than it rises 43 5.8 Characteristic hydrographs on the River Suir 44 5.9 Hydrograph width analysis at gauged sites – a summary 45 5.10 Flood hydrographs having sustained peaks 46 5.10.1 Where the hydrograph shape reflects the temporal pattern of rainfall 46 5.10.2 Where the hydrograph shape is characteristic of the station 46 6 Constructing the characteristic hydrograph at ungauged sites 48 6.1 Introduction 48 6.1.1 Links with other parts of the FSU 48 6.1.2 Assumptions and difficulties 48 6.2 Selection of dependent variables (DVs) 49 6.3 Selection of independent variables (IVs) 50 6.4 Additional notes 51 6.4.1 Treatment of Gamma shape parameter n 51 6.4.2 Software used for the regression analysis 52 6.5 Correlation studies 52 6.5.1 Inter-correlations between PCDs 52 6.5.2 Individual correlations between DVs and initially selected IVs 56 6.5.3 Choosing a subset of PCDs to use as IVs 56 6.5.4 Checking the Normality of the DVs 57 6.5.5 Final selection of the independent variables; a note on the use of BFI 58 6.6 The regression method used 58 6.7 Illustrative results: Estimating W75 when BFI available 58 v Volume III Hydrograph Analysis 6.7.1 Regression models and their performance evaluation 58 6.7.2 Checking the possible influence of collinearity 60 6.7.3 Checking the logical consistency of the model 60 6.7.4 Additional checks 62 6.8 Recommended models for use at ungauged sites 67 6.8.1 The final models 67 6.8.2 Model performance 69 6.8.3 Additional notes on the regression models 70 7 Ancillary investigations 71 7.1 Variation of hydrograph width with peak flow 71 7.2 Variation of hydrograph width with pre-event minimum flow 73 7.3 Variation of hydrograph width with time of year 74 7.4 Effect of arterial drainage on hydrograph widths 75 8 Constructing the characteristic flood hydrograph 79 8.1 Topics covered 79 8.2 Features of the methods 79 8.3 Allowances in design flood hydrographs for pre-event flow 80 8.3.1 Substitution approach 80 8.3.2 Terminology: baseflow or pre-event flow? 81 8.3.3 Choosing the pre-event flow 81 8.4 Estimation of volume of flow 82 8.4.1 Basic method 82 8.4.2 Non-parametric case 82 8.4.3 Parametric case 82 8.5 Deriving the characteristic hydrograph at a gauged site 83 8.6 Estimating the characteristic hydrograph at an ungauged site 84 8.6.1 Using the UPO-ERR-Gamma model 84 8.6.2 Using the parabolic curves method 84 8.6.3 Using IBIDEM 84 8.7 Parabolic curves method 84 8.7.1 Overview 84 8.7.2 Details of method 85 8.7.3 Examples 86 8.7.4 Application at an ungauged site 86 8.8 Constructing the design flood hydrograph 87 8.9 Software 87 8.10 Selection and use of the pivotal catchment 87 8.10.1 Overview 87 8.10.2 Selection of the pivotal catchment 88 8.10.3 Recommended procedure for data transfer 89 8.10.4 Example 89 8.10.5 Further discussion of choice of method and of pivotal catchment 92 8.10.6 Urbanised catchments 93 9 IBIDEM 94 9.1 The idea of IBIDEM 94 9.1.1 Reminder of hydrograph