A Regionalisation of Tasmanian Catchments
Donald Hine and Bryce Graham Water Assessment and Planning Branch Water Resources Division DPIWE Technical Report WRA 03/02 February 2003 Acknowledgments
This study has been conducted under the Natural Heritage Trust as part of the project "Tasmanian Environmental Flows" (NRC13182) and has received funding from the Commonwealth Government and the Department of Primary Industries, Water and Environment.
The authors would like to thank Martin Read, Ian Tye, Abbie Foley and David Fuller for their assistance and comments.
Copyright Notice:
Material contained in the report provided is subject to Australian copyright law. Other than in accordance with the Copyright Act 1968 of the Commonwealth Parliament, no part of this report may, in any form or by any means, be reproduced, transmitted or used. This report cannot be redistributed for any commercial purpose whatsoever, or distributed to a third party for such purpose, without prior written permission being sought from the Department of Primary Industries, Water and Environment, on behalf of the Crown in Right of the State of Tasmania.
Disclaimer:
Whilst DPIWE has made every attempt to ensure the accuracy and reliability of the information and data provided, it is the responsibility of the data user to make their own decisions about the accuracy, currency, reliability and correctness of information provided.
The Department of Primary Industries, Water and Environment, its employees and agents, and the Crown in the Right of the State of Tasmania do not accept any liability for any damage caused by, or economic loss arising from, reliance on this information.
Preferred Citation:
Hine, D. and Graham, B. (2003) A Regionalisation of Tasmanian Catchments. Department of Primary Industries, Water and Environment, Hobart Technical Report No. WRA 03/02
ISBN: 07246 6964 7
ISSN: 1448-1626
The Department of Primary Industries, Water and Environment
The Department of Primary Industries, Water and Environment provides leadership in the sustainable management and development of Tasmania’s resources. The Mission of the Department is to advance Tasmania’s prosperity through the sustainable development of our natural resources and the conservation of our natural and cultural heritage for the future.
The Water Resources Division provides a focus for water management and water development in Tasmania through a diverse range of functions including the design of policy and regulatory frameworks to ensure sustainable use of the surface water and groundwater resources; monitoring, assessment and reporting on the condition of the State’s freshwater resources; facilitation of infrastructure development projects to ensure the efficient and sustainable supply of water; and implementation of the Water Management Act 1999 , related legislation and the State Water Development Plan. Table of contents
SUMMARY...... 1
INTRODUCTION ...... 2
THE REGIONALISATION PROCESS ...... 2 REVIEW OF PREVIOUS TASMANIAN STUDIES ...... 2 CURRENT STUDY...... 3
METHODS ...... 3 CATCHMENT SELECTION ...... 3 HYDROLOGICAL DATA ...... 4 BIOPHYSICAL DATA ...... 4 GROUPING ...... 4
HYDROLOGICAL CLUSTERING ...... 4 BIOPHYSICAL CLUSTERING ...... 14 DISCRIMINANT FUNCTION ANALYSIS ...... 17 CLASSIFICATION MODELS ...... 25 ANDREWS CURVES ...... 26 DISCUSSION...... 27
CURRENT STUDY RESULTS ...... 27 COMPARISON WITH PREVIOUS STUDY METHODS AND RESULTS ...... 30 CONCLUSIONS ...... 38 BIBLIOGRAPHY...... 39
APPENDICES...... 40
A1: 52 STATIONS USED TO FORM INITIAL HYDROLOGICAL CLUSTERS ...... 40 A2: K MEANS GROUPING OF 51 STATIONS BY HYDROLOGICAL VARIABLE AND CLASSIFICATIONS TRANSFERRED TO CATCHMENTS ...... 42 A2 CONTINUED ...... 43 A3: H YDROLOGICAL DATA . 52 STATIONS ...... 45 A3 CONTINUED ...... 46 B1: 51 CATCHMENT CLUSTER MEMBERSHIP PROBABILITIES BY QUADRATIC DISCRIMINANT ANALYSIS ...... 47 B1 CONTINUED ...... 48 B2: 74 CATCHMENTS FINAL CLASSIFICATION PROBABILITIES ...... 49 B2 CONTINUED ...... 50 B3: B IOPHYSICAL DATA 74 CATCHMENTS ...... 51 B3 CONTINUED ...... 52 C: C LUSTER METHODS , RESULTS COMPARISON ...... 53 C CONTINUED ...... 54 D: H UGHES (1987,1989) HYDROLOGICAL CLASSIFICATION INDEXES ...... 55 E: A B RIEF EXPLANATION OF ANALYSIS METHODS ...... 56 Summary
The project objective was to produce a broad classification model of Tasmanian catchments based on biophysical characteristics, describing a set of climatic, physical and vegetation conditions within catchments. The model can then be used to classify ungauged catchments into hydrologically similar catchment groups. Once a model of each group's hydrological behaviour has been developed it is expected that the assignment of ungauged catchments to one of these groups on the basis of biophysical similarity will provide a generalised description of the ungauged streams hydrological behaviour. Development of hydrological behaviour models for the groups was not undertaken for this study.
Three hydrological groupings were derived from a hydrological data set of 52 gauged catchments using a complete linkage hierarchical cluster analysis and K means clustering. The classifications were then applied to the catchment biophysical variables. These variables were then reduced to those providing the greatest discrimination between groups using manual stepwise discriminant analysis techniques. The most significant variables were then selected to form a final classification set.
Due to the non equality of the selected variables covariance matrix a quadratic rather than a linear classification model was derived and applied to 51 catchments (one catchment was removed due to incomplete data) together with 23 previously unclassified catchments. This process resulted in the prediction of three groups from a total of 74 catchments which were then mapped.
1 Introduction
The Regionalisation Process
Regionalisation requires the application of flow characteristics of a catchment where records are available to those of another where the record is incomplete or unavailable. There is an underlying assumption that streams in hydrologically homogeneous regions or “families”, which may or may not be geographically contiguous, will have similar flow characteristics and that it is possible to produce a generalised model of flows in these regions.
The approach taken in this study is to establish groups of hydrologically similar streams for which data is available, and assign ungauged streams to these groups on the basis of catchment biophysical similarity. It is expected that hydrological similarity will follow from biophysical similarity.
A number of approaches have been used in the past and the major techniques and associated problems have been reviewed in Nathan and McMahon (1990), Burn and Goel (2000) and Bates (1994). Hughes (1987) reviewed Tasmanian work and currently recommended procedures are detailed in ARR (2001).
Establishing similarity between catchments and the relationship between catchment characteristics and hydrological model parameters are fundamental to effective regionalisation. This study is restricted to investigating and producing a classification model, which uses a number of hydrological characteristics from of a set of gauging stations to determine an initial classification. The classification is then transferred to a set of biophysical variables describing a set of climatic, physical and vegetation conditions within the catchments containing the gauging stations, to produce an optimised model for the broad classification of ungauged catchments. The study provides a basis for further investigation of the links between hydrological behaviour and catchment biophysical characteristics in Tasmania.
Review of Previous Tasmanian Studies
Major problems for regionalisation are the lack of a substantial number of long term records and the existence of unimpacted gauged water courses. Gauging tends to occur in areas which are subject to:
• land use change with implications for run-off volume;
• extraction for human consumption;
• irrigation;
• where some measure of control is established eg. for hydro electricity production.
In Tasmania Knighton (1987) examined 13 gauged sites in N.E. Tasmania (Figure 18) with the study focusing on flood flows. Rivers were grouped into two hydrogeographic regions on the basis of the ratio
Q2/Qma where: Q2 = median maximum annual discharge, Qma = mean maximum annual discharge.
These values were derived from a minimum record length of 10 years (and in one case seven years). This period may be too short for a reliable estimate of model parameters (which Knighton acknowledges) however the ratio Q2/Qma could be a useful characteristic in testing and establishing similarity by other means.
The only physiographic characteristic used in this study was catchment area, which was used to derive an equation for mean annual discharge (Qma) for the individual regions.
2 Hughes (1987) classified 77 gauged sites in 69 catchments into four regions using principle coordinates and cluster analysis (Figure 17, Table 8). Catchment area, mean annual run-off and coefficient of variance of annual flows were used in this study to derive 12 catchment indexes for the gauged sites (Appendix F). Hughes asserts these groups show a spatial distribution related to the annual precipitation distribution for Tasmania (Figure 16). Hughes also demonstrated the use of catchment area as a surrogate for mean annual discharge. Only uncontrolled streams with a record greater than 15 years were used in the study.
A similar method was used by Dyer et al. (1994)(Figure 19) with the added technique of Andrews- Fourier curve analysis, (Andrews, 1972; Grayson et al., 1996) to produce a graphical representation of similar catchment groups. This catchment signature could then be used to refine groups. Dyer et al. (1994) found a total of 4 Northern Tasmania catchments were grouped with 9 from Eastern Victoria and 1 from North Queensland in developing regional parameters for the RORB model. RORB is a runoff and streamflow routing model used for calculating flood hydrographs from rainfall and other channel inputs (Pilgrim, 2001).
This project has employed established methods of cluster and discriminant analysis to analyse the longer hydrological data sets available compared to those of Hughes (1987) and Knighton (1987). The groupings indicated could form the basis for further work in catchment model development.
Current Study
Methods
This regionalisation consists of the process of assigning ungauged catchments to groups of physiographically similar gauged catchments. The expectation is that hydrological characteristics will be similar and therefore generally predictable given suitable modelling.
This project consists of the following stages in that process:
• initial catchment selection;
• catchment data acquisition, collation and transformation;
• initial grouping using hydrological variables to perform cluster analysis and K means grouping to optimise the groups and variables set;
• group classification testing, and optimising biophysical variables by discriminant analysis and Andrews-Fourier curves based on a matrix of biophysical data.
A large amount of data was available and the formation of matrices for hydrological cluster and subsequent discriminant analysis was initially a subjective choice of characteristics believed to be most helpful in differentiating between potential groupings eg. the use of wettest and driest flow periods. The choice of biophysical data was also influenced by the ability to extract variables from existing data sources for later testing purposes.
All hydrological data used in the project are available within the Hydrol data base maintained by DPIWE. Biophysical data was derived from the ANUCLIM data base (Hutchinson et al., 1999) by the GIS section within DPIWE. Data analysis was carried out using Systat 10, SPSS (2000).
Catchment selection
The initial selection of catchments was identified in earlier DPIWE exploratory studies as being a priority based on actual or potential human impacts. Selected gauging stations within these catchments were those located on unregulated streams having a record length greater than 15 years. Where multiple stations were present on a stream the lowest station with the longest record was used. Catchment numbers were assigned from 1999 digital catchment maps developed within the then Land and Water Assessment Branch of DPIWE. 3 Hydrological data
Streamflow data were derived from the Hydrol state water resources data base maintained by DPIWE. Eighty two stations were identified as potentially useful. This list was reduced to 52, then 51 on the basis of record completeness and availability of biophysical data. These data are described in Table 2 and detailed in Appendix A. Stations are listed and mapped in Table 1 and Figure 4 together with individual record lengths and the station identification code used in the Hydrol data base.
Biophysical Data
Data for 76 priority catchments were acquired from the 1:25000 mapping of Tasmania by DPIWE and GIS Section data generated from the ANUCLIM data base (Hutchinson et al., 1999). These data are described in Table 3 and detailed in Appendix B.
Grouping
Hydrological Clustering
The probability plots of hydrological data are given overleaf. Figure 1 shows a heavy tailed (highly skewed) data distribution for almost all variables. A natural log transform was applied and the resulting probability plot is given in Figure 2.
An exploratory cluster analysis was carried out on the transformed hydrological data from 52 gauging stations (Appendix A) using complete linkage hierarchical clustering. This indicated the potential for three group clusters (Figure 3). Further examination by K means clustering, specifying four groups, indicated an unacceptable degree of overlap between groups while specifying three groups produced reasonable group separation. A cluster profile of the final grouping is shown in Figure 5 which plots the Z scores for the variables in each group. Figure 6 provides a comparison of group means. Figure 7 shows the effect of specifying 4 groups during the initial classification and variables selection process. The untransformed data for this analysis is provided in Appendix A3.
Specifying 3 groups using the K means clustering method showed that the groups could be represented by a minimal set of 6 variables compared with a large initial set of 15 variables . Selection of variables was determined by those variables with an F ratio value greater than 100 indicating the largest contributions to between clusters discrimination. The clusters were designated groups 1, 2 and 3 and are given in Figure 4 and Table 1.
4 3 3 3 3
2 2 2 2
1 1 1 1
0 0 0 0
-1 -1 -1 -1
-2 -2 -2 -2 Expected ValueNormal for Distribution Expected Value for Normal Distribution -3 -3 Expected Value for Normal Distribution -3 Expected Value for Normal Distribution -3 0 1000 2000 3000 0 100 200 300 400 500 0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 MARO SDARO MCPRO SDCPRO
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Expected Value for Normal Distribution -3 Expected Value for Normal Distribution -3 Expected Value for Normal Distribution -3
0 10 20 30 40 50 60 ValueExpected Normal for Distribution -3 0 50 100 150 200 250 0 50 100 150 200 250 AVFLMO1 0 10 20 30 40 AVFLMO7 AVFLMO8 AVFLMO2
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Expected ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 0 0 50 100 150 200 0 10 20 30 40 50 60 70 80 90 100 0 50 100 150 1000000 2000000 3000000 4000000 5000000 AVFLMO9 AVFLMO12 AVANFLOW AVANYIELD
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Expected Value Normal for Distribution -3 Expected Value Normal for Distribution -3 Expected Value Normal for Distribution -3 1000000 2000003000004000005000006000007000008000009000001000000 0 500 1000 1500 2000 0 1 2 3 4 5 6 7 8 AVMAXFLOW AVMINFLOW AVCPYIELD
Figure 1. Probability plot of raw hydrological data.
5 3 3 3 3
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Expected ValueExpected for Normal Distribution -3 ValueExpected for Normal Distribution -3 ValueExpected for Normal Distribution -3 ValueExpected for Normal Distribution -3 3 4 5 6 7 8 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 LNMARO LNSDARO LNMCPRO VLNSDCPRO
3 3 3 3
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1 1 1 1
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Expected ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 ValueExpected Normal for Distribution -3 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 -1 0 1 2 3 4 5 6 -1 0 1 2 3 4 5 6 LNAVFLMO1 LNAVFLMO2 LNAVFLMO7 LNAVFLMO8
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Expected Value Normal for Distribution -3 Expected Value Normal for Distribution -3 Expected Value Normal for Distribution -3 Expected Value Normal for Distribution -3 -1 0 1 2 3 4 5 6 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 LNAVFLMO9 LNAVFLMO12 LNAVANFLOW LNAVANYIELD
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Expected ValueExpected for NormalDistribution -3 ValueExpected for NormalDistribution -3 ValueExpected for NormalDistribution -3 6 7 8 9 10 11 12 13 14 2 3 4 5 6 7 8 -10 -5 0 5 LNAVCPYIELD LNAVMAXFLOW LNAVMINFLOW
Figure 2. ln transformed hydrological data , normal probability plot.
6 WELCOME RIVE RUBICON RIVE FRANKLIN RIV TOMAHAWK RIV ANDERSONS CR PIPERS RIVER SUPPLY RIVER MOUNTAIN RIV BROWNS RIVER SNUG RIVULET ORIELTON RIV COAL RIVER JORDAN RIVER SWAN RIVER SCAMANDER RI BREAK O"DAY ANSONS RIVER APSLEY RIVER CARLTON RIVE MEREDITH RIV DON RIVER MONTAGU RIVE BRID RIVER EMU RIVER ESPERANCE RI NILE RIVER GREAT MUSSEL GREAT FOREST FLOWERDALE R INGLIS RIVER CAM RIVER NIVE RIVER TYENNA RIVER DUCK RIVER NORTH ESK RI BLACK RIVER MACQUARIE RI GEORGE RIVER RINGAROOMA R MEANDER RIVE LEVEN RIVER WHYTE RIVER FORTH RIVER GORDON RIVER MACKINTOSH R SOUTH ESK KING RIVER DAVEY RIVER FRANKLIN RIV MURCHISON RI ARTHUR RIVER PIEMAN RIVER 0 1 2 3 4 5 6 Distances
Figure 3. Clusters formed by transformed data shown in Figure 1 (complete linkage hierarchical clustering).
7 Figure 4. Location of gauging stations used to form initial clusters.
8 Table 1. K means grouping of 51 stations by hydrological variable.
Group 1. Group 2 . Group 3 . site RIVER K means CLUSTER site RIVER K means CLUSTER site RIVER K means CLUSTER 25 NILE RIVER 1 46 GORDON RIVER 2 116 PIPERS RIVER 3 30 RINGAROOMA 1 78 KING RIVER 2 2200 SWAN RIVER 3 76 NORTH ESK 1 145 FRANKLIN 2 2208 MEREDITH RIV 3 191 BREAK O"DAY 1 148 MURCHISON 2 2209 CARLTON RIVE 3 497 NIVE RIVER 1 149 MACKINTOSH 2 2211 ORIELTON RIVER 3 499 TYENNA RIVER 1 154 PIEMAN RIVER 2 3201 COAL RIVER 3 2204 APSLEY RIVER 1 159 ARTHUR RIVER 2 4201 JORDAN RIVER 3 2205 GEORGE RIVER 1 181 SOUTH ESK 2 5200 BROWNS RIVER 3 2206 SCAMANDER 1 350 WHYTE RIVER 2 5202 SNUG RIVULET 3 2210 GREAT MUSSEL 1 450 FORTH RIVER 2 6200 MOUNTAIN RIVER 3 2214 ANSONS RIVER 1 473 DAVEY RIVER 2 14219 EMU RIVER 3 7200 ESPERANCE 1 852 MEANDER RIVER 2 14223 WELCOME RIVER 3 14200 MONTAGU RIVER 1 14207 LEVEN RIVER 2 16200 DON RIVER 3 14210 INGLIS RIVER 1 17200 RUBICON RIVER 3 14212 CAM RIVER 1 17201 FRANKLIN RIVER 3 14213 BLACK RIVER 1 18200 ANDERSONS 3 14214 DUCK RIVER 1 18201 SUPPLY RIVER 3 14215 FLOWERDALE 1 19200 BRID RIVER 3 18312 MACQUARIE 1 19202 TOMAHAWK 3 19201 GREAT FORESTER 1
9 The group classifications arrived at by K means were retained and used as the initial classification of catchments containing the gauging stations. This classification is shown in Appendix A2. A listing of the initial hydrological variable set is given in Table 2, the final variables set members together with their F values are indicated in Table 3.
Table 2. Hydrological variables used in hierarchical clustering with complete linkage. (*) indicates those variables showing greatest F ratios (>100) in K means analysis and used to identify hydrological groups.
Variable Description AVCPYIELD* Average critical period yield (Ml) (critical period = Dec-Mar) AVMAXFLOW Average annual maximum flow (m 3/s) AVMINFLOW Average annual minimum flow (m 3/s) MARO Mean annual run off (Ml/km 2) SDARO Standard deviation annual run off (Ml/km2) MCPRO Mean critical period run off (Ml/km2) (critical period = Dec-Mar) SDCPRO Standard deviation CP run off (Ml/km2) AVFLMO1* Average flow month 1 (m 3/s) AVFLMO2* Average flow month 2 (m 3/s) AVFLMO7 Average flow month 7 (m 3/s)) AVFLMO8 Average flow month 8 (m 3/s) AVFLMO9* Average flow month 9 (m 3/s) AVFLMO12* Average flow month 12 (m 3/s) AVANFLOW* Average annual flow (m 3/s)
Table 3. K means clustering variables.
Variable Between SS Df Within SS df F-ratio LNAVFLMO1 125.517 2 20.436 49 150.475 LNAVFLMO2 111.881 2 17.960 49 152.619 LNAVFLMO9 91.913 2 18.638 49 120.821 LNAVFLMO12 80.539 2 11.475 49 171.965 LNAVANFLOW 108.906 2 22.428 49 118.967 LNAVCPYIELD 127.683 2 29.208 49 107.101 * TOTAL * 646.439 12 120.146 294
10 Cluster Parallel Coordinate Plots
1 2
LNAVFLMO12 LNAVFLMO12
LNAVFLMO2 LNAVFLMO2
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Figure 5. Z scores of final hydrological variables for each cluster (lines are cluster members).
11 Cluster Profile Plots
1 2
LNAVFLMO12 LNAVFLMO12
LNAVFLMO2 LNAVFLMO2
LNAVFLMO1 LNAVFLMO1
LNAVFLMO9 LNAVFLMO9
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3
LNAVFLMO12
LNAVFLMO2
LNAVFLMO1
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Figure 6. Hydrological cluster means.
12 Cluster Profile Plots
1 2
LNAVCPYIELD LNAVCPYIELD LNAVFLMO1 LNAVFLMO1 LNAVFLMO2 LNAVFLMO2 LNAVFLMO12 LNAVFLMO12 LNAVMINFLOW LNAVMINFLOW LNAVANFLOW LNAVANFLOW LNAVANYIELD LNAVANYIELD LNAVFLMO8 LNAVFLMO8 LNMCPRO LNMCPRO LNMARO LNMARO VLNSDCPRO VLNSDCPRO
3 4
LNAVCPYIELD LNAVCPYIELD LNAVFLMO1 LNAVFLMO1 LNAVFLMO2 LNAVFLMO2 LNAVFLMO12 LNAVFLMO12 LNAVMINFLOW LNAVMINFLOW LNAVANFLOW LNAVANFLOW LNAVANYIELD LNAVANYIELD LNAVFLMO8 LNAVFLMO8 LNMCPRO LNMCPRO LNMARO LNMARO VLNSDCPRO VLNSDCPRO
Figure 7. K means clustering, 4 groups specified, 11 variables.
13 Biophysical Clustering
A very large data set of biophysical characteristics of the catchments was assembled. These are listed below in Table 4. Examination of the raw data normal probability plot showed this data to be highly skewed (Figure 8) and a log transform was applied (Figure 9).
Table 4. Biophysical characteristics. Variable Description MAINSL Main stream length DRNDENSY Drainage density (km/km 2) CATAREA Catchment area (km 2) WQTRRF_MIN Wettest quarter minimum rainfall (mm) WQTRF_MAX Wettest quarter max rainfall (mm) WQTRFAVE Wettest quarter average rainfall (mm) WQTR_SD Wettest quarter standard deviation rainfall (mm) WQTRCOV Wettest quarter coefficient of variation rainfall (sd/mean) WQTRMIN Wettest quarter minimum temperature DQTRMAX Driest quarter max rainfall (mm) DQTRAVE Driest quarter average rainfall (mm) DQTR_SD Driest quarter standard deviation rainfall (mm) DQTRCOV Driest quarter coefficient of variation rainfall (sd/mean) MAXSLOPE Maximum catchment slope MEANSLOPE Mean catchment slope SD_SLOPE Standard deviation catchment slope COV_SLOPE Coefficient of variation of catchment slope(sd/mean) AVANT Average annual temperature AVETRAN Average annual temperature range VEGNV Non native veg percentage HW_ELEV Head waters elevation ANRFMIN Annual rainfall minimum (mm) ANRFMAX Annual rainfall maximum (mm) ANRFMEAN Mean annual rainfall(mm) ANRFSD Annual rainfall standard deviation (mm) OG_AREA Old growth vegetation area
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x 0 50 100 150 200 x 0.0 0.1 0.2 0.3 0.4 0.5 x 0 100 200 300 400 x 100 200 300 400 500 600 700 x 100 200 300 400 500 600 x 0 10 20 30 40 50 60 70 80 90 E WQTR_SD E WQTRCOV E WQTRMIN E DQTRMAX E DQTRAVE E DQTR_SD
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x 0 100 200 300 400 500 600 x 0 100200300400500600700800 E ANRFSD E OG_AREA
Figure 8. Untransformed biophysical data probability plot.
15 n n n n n n
o o o o o o
i i i i i i
t t t t t t
u 3 u 3 u 3 u 3 u 3 u 3
b b b b b b
i i i i i i
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s s s s s s i 2 i 2 i 2 i 2 i 2 i 2
D D D D D D
l l l l l l a 1 a 1 a 1 a 1 a 1 a 1
m m m m m m
r r r r r r
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N N N N N N 0 0 0 0 0 0
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o o o o o o
f f f f f f
e e e e e e
u -1 u -1 u -1 u -1 u -1 u -1
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V V V V V V -2 -2 -2 -2 -2 -2
d d d d d d
e e e e e e
t t t t t t
c c c c c c
e -3 e -3 e -3 e -3 e -3 e -3
p p p p p p
x 2 3 4 5 6 x 0.0 0.5 1.0 1.5 x 3 4 5 6 7 8 x 4 5 6 7 x 5.0 5.5 6.0 6.5 7.0 x 5.0 5.5 6.0 6.5 7.0 E LNMAINSL E LNDRNDENSY E LNCATAREA E LNWQTRRF_MIN E LNWQTRF_MAX E LNWQTRFAVE
n n n n n n
o o o o o o
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s s s s s s i 2 i 2 i 2 i 2 i 2 i 2
D D D D D D
l l l l l l a 1 a 1 a 1 a 1 a 1 a 1
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V V V V V V -2 -2 -2 -2 -2 -2
d d d d d d
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p p p p p p
x 2 3 4 5 6 x -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 x 4.5 5.0 5.5 6.0 x 5.0 5.5 6.0 6.5 x 4.5 5.0 5.5 6.0 6.5 x 2 3 4 5 E LNWQTR_SD E LNWQTRCOV E LNWQTRMIN E LNDQTRMAX E LNDQTRAVE E LNDQTR_SD
n n n n n n
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D D D D D D
l l l l l l a 1 a 1 a 1 a 1 a 1 a 1
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u u u u u u
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V V V V V V -2 -2 -2 -2 -2 -2
d d d d d d
e e e e e e
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e -3 e -3 e -3 e -3 e -3 e -3
p p p p p p
x -3.0 -2.5 -2.0 -1.5 -1.0 x -1.5 -1.0 -0.5 0.0 x -4 -3 -2 -1 x -4.0 -3.5 -3.0 -2.5 -2.0 x -5.5 -5.0 -4.5 -4.0 x 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 E LNDQTRCOV E LNMAXSLOPE E LNMEANSLOPE E LNSD_SLOPE E LNCOV_SLOPE E LNAVANT
n n n n n n
o o o o o o
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D D D D D D
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N N N N N N 0 0 0 0 0 0
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e -1 e -1 e -1 e -1 e -1 e -1
u u u u u u
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V V V V V V -2 -2 -2 -2 -2 -2
d d d d d d
e e e e e e
t t t t t t
c c c c c c
e -3 e -3 e -3 e -3 e -3 e -3
p p p p p p
x 2.6 2.7 2.8 2.9 3.0 3.1 x -3 -2 -1 0 x 4 5 6 7 8 x 6.0 6.5 7.0 7.5 8.0 x 6.5 7.0 7.5 8.0 8.5 x 6.0 6.5 7.0 7.5 8.0 E LNAVETRAN E LNVEGNV E LNHW_ELEV E LNANRFMIN E LNANRFMAX E LNANRFMEAN
n n
o o
i i
t t
u 3 u 3
b b
i i
r r
t t
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l l a 1 a 1
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r r
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e e
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l l
a a
V V -2 -2
d d
e e
t t
c c
e -3 e -3
p p
x 3 4 5 6 7 x -5 0 5 10 E LNANRFSD E LN_OG_AREA
Figure 9. Transformed biophysical data.
16 Discriminant Function Analysis
Cluster designations determined from the hydrological hierarchical cluster and K means clustering analysis were assigned to the 51 catchments containing the gauging stations. One catchment was removed due to incomplete data.
A discriminant analysis was then carried out to investigate the accuracy of the initial K means classification and to identify the biophysical variables which maximised the discrimination between clusters (ie. which variables best separated the groups). This was achieved by using a stepwise iterative process of discriminant analysis together with a cross validation where data was split 80:20 between a learning set and a test set. At the completion of each run five outputs were available to assess the usefulness of variables in maximising the percentage of correct classifications and thus discrimination between groups (Box 1 and 2). These were :
• between groups F matrix;
• learning set % correct classification;
• test set % correct classification;
• jack-knifed % correct classification;
• a canonical scores plot providing a graphical indication of group membership.
Three factors were used to assess variables. Those variables retained met the following criteria:
• maximised the learning set percentage classified correctly;
• minimised the differences in percentages correctly classified between the three classification outputs;
• maximised the between groups F values.
This resulted in the retention of the five variables shown in Box 1 and the classification matrix in Box 2.
Box 1. Retained biophysical variables.
Finally an inspection of the scatter plot matrix (SPLOM/ Figure 10). for the grouped variables was carried out. The SPLOM indicated that the condition of equal covariance matrices for a linear discriminant model was not met (Engelman, 1998), and a quadratic discriminant analysis of groups was carried out using the retained variables. The quadratic model was then optimised by manual re-allocation of misclassified catchments based on their model probabilities (Appendix B1) and re-run resulting in the output in Box 3.
17 Box 2. Initial classification matrix, biophysical variables. Classification matrix (cases in row categories classified into columns
Group 1 2 3 %correct 1 18 0 0 100 2 2 10 0 83 3 3 0 14 82 Total 23 10 14 89
Classification of cases with zero weight or frequency Group 1 2 3 %correct 1 2 0 0 100 2 0 0 0 0 3 1 0 1 50 %correct 3 0 1 75
Jackknifed classification matrix Group 1 2 3 %correct 1 15 0 3 83 2 2 10 0 83 3 6 0 11 65 Total 23 10 14 77
1.000 2.000
L L
S S
N N
I I
A A
M M
N N
L L
D D
S S
_ _
R R
T T
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E E
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P P
O O
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_ _
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_ _
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_ _
N N L LNMAINSL LNWQTR_SDLNSD_SLOPELNANRFMAXLN_OG_AREA L LNMAINSL LNWQTR_SDLNSD_SLOPELNANRFMAXLN_OG_AREA
3.000
L
S
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A
M
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L
D
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_
R
T
Q
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_
G
O
_
N L LNMAINSL LNWQTR_SDLNSD_SLOPELNANRFMAXLN_OG_AREA
Figure 10. Scatter Plot Matrix (SPLOM) for three groups described by five variables.
18 Box 3. Classification matrix of manually reallocated catchments .
Classification matrix (cases in row categories classified into column 1 2 3 %correct 1 26 0 0 100 2 0 10 0 100 3 0 0 15 100 Total 26 10 15 100
Jackknifed classification matrix 1 2 3 %correct 1 26 0 0 100 2 0 10 0 100 3 1 0 14 93 Total 27 10 14 98
Canonical Scores Plot
7
3
FACTOR(2) -1 ADJCLUSTER 1 2 -5 3 -5 -1 3 7 FACTOR(1) . Figure 11. Clusters based on 51 catchments.
The resulting group membership is shown in the canonical scores plot above (Figure 11) and tabulated in Appendix B2 together with final group membership. Variables are described previously in Table 4 and Box 1.
After reassignment of the misclassified catchments was completed a further 23 previously unused catchments were added to the analysis matrix. The quadratic analysis was then repeated.
These unclassified catchments were not used in constructing the model and so acted as a test of the 51 case model. This process produced a probability for membership of each cluster for these 23 previously un- allocated catchments. The 23 additional catchments were then classified on the basis of these probabilities and the analysis re-run, resulting in a final classification model based on the total 74 catchments.
19 Appendix B1. shows the final grouping of the original 51 catchments together with their probabilities. The canonical scores plot in Figure 11 summarises the clusters based on 51 catchments, Figure 12 after the previously un-allocated catchments had been added and Figure 13 after assignment of catchments to their clusters based on the probabilities indicated in Appendixes B2.
Canonical Scores Plot
7
) 3
2
(
R
O
T
C
A F -1 ADJ_CLUSTER 1 2 -5 3 -5 -1 3 7 FACTOR(1)
Figure 12. Three groups based on 51 catchments plus 23 previously unclassified catchments.
Canonical Scores Plot
6.0
3.8
)
2
( 1.6
R
O
T
C
A -0.6
F
ADJ_CLUSTER -2.8 1 2 -5.0 3 -5.0 -2.8 -0.6 1.6 3.8 6.0 FACTOR(1)
Figure 13. Complete classification of 74 catchments.
20 Map 1. Final grouping of 74 catchments using a quadratic discriminant analysis indicating the spatial distribution of the catchment groupings. (Comparison of the original K means classification and the final classification of catchments can be made by reference to Table 5 overleaf).
21 Table 5. Complete classification of 74 catchments. (River in Bold and Blanks are stations not included in initial K means classification ) CATCHMENT_IDENTIFICATION RIVER NEWKCLUSTER Quad predicted cluster 31 MONTAGU RIVER 1 1 35 DUCK RIVER 1 1 36 GREAT MUSSELROE RIVER 1 1 37 BLACK RIVER 1 1 39 TOMAHAWK RIVER 3 1 40 RINGAROOMA RIVER 1 1 43 BOOBYALLA RIVER 1 44 FLOWERDALE RIVER 1 1 45 INGLIS RIVER 1 1 47 GREAT FORESTER RIVER 1 1 48 ANSONS RIVER 1 1 49 BRID RIVER 3 1 50 PIPERS RIVER 3 1 55 CAM RIVER 1 1 56 EMU RIVER 3 1 58 BLYTHE RIVER 1 63 NELSON BAY RIVER 1 71 GEORGE RIVER 1 1 79 NORTH ESK RIVER 1 1 83 SOUTH ESK RIVER 2 1 84 SCAMANDER RIVER 1 1 85 MEANDER RIVER 2 1 93 NILE RIVER 1 1 95 BREAK O"DAY RIVER 1 1 96 MACQUARIE RIVER 1 1 98 ST. PAULS RIVER 1 102 LAKE RIVER 1 103 Great Lake 1 105 OUSE 1 106 APSLEY RIVER 1 1 107 NIVE RIVER 1 1
22 Table 5. continued. 117 CLYDE RIVER 1 142 TYENNA RIVER 1 1 170 CROOKS RIVULET 1 52 ARTHUR RIVER 2 2 61 LEVEN RIVER 2 2 69 HELLYER RIVER 2 70 FORTH RIVER 2 2 74 MERSEY RIVER 2 82 SAVAGE RIVER 2 86 WHYTE RIVER 2 2 90 HUSKISSON RIVER 2 91 PIEMAN RIVER 2 2 94 MACKINTOSH RIVER 2 2 104 MURCHISON RIVER 2 2 112 HENTY RIVER 2 114 KING RIVER 2 2 115 DERWENT RIVER 2 119 FRANKLIN RIVER 2 2 131 GORDON RIVER 2 2 159 Lake Pedder 2 160 HUON RIVER 2 190 ESPERANCE RIVER 1 2 29 WELCOME RIVER 3 3 53 CURRIES RIVULET 3 64 ANDERSONS CREEK 3 3 67 GAWLER RIVER 3 68 DON RIVER 3 3 72 JOHNSTON CREEK 3 75 FRANKLIN RIVER 3 3 76 SUPPLY RIVER 3 3 78 RUBICON RIVER 3 3 128 JORDAN RIVER 3 3 134 COAL RIVER 3 3
23 Table 5. continued.
136 PROSSER RIVER 3 146 ORIELTON RIVER 3 3 150 CARLTON RIVER 3 3 163 MOUNTAIN RIVER 3 3 164 NORTH WEST BAY RIVULET 3 169 SNUG RIVULET 3 3 172 BROWNS RIVER 3 3
24 Classification Models
The classification model for each group resulting from the discriminant analysis is: f = a+bx 1+cx 2+dx 3+ex 4+fx 5 +gx 1x2+hx 1x3+ix 1x4+jx 1x5 +kx 2x3+lx 2x4+mx 2x5 +nx 3x4+ox 3x5 2 2 2 2 2 +px 4x5+qx 1 +rx 2 +sx 3 +tx 4 +ux 5
where ; x1 = LNARFMAX, x 2 = LNMAINSL, x 3 = LNWQTR_SD, x 4 = LNAREA_OG, x5= LNSDSLOPE
and have the values shown in Appendix B2
Group 1 model f = -1496.36+452.17x 1+6.96x 2-151.62x 35.87x 4+130.91x 5 +0.03x 1x2+13.45x 1x3-0.43x 1x4-9.68x 1x5 +0.07x 2x3+0.42x 2x4+1.30x 2x5 +0.04x 3x4+6.37x 3x5 2 2 2 2 2 +0.08x 4x5+-35.58x 1 -1.98x 2 -8.48x 3 -0.5x 4 -14.26x 5
Group 2 model f =-1599 - 420.16x 1+45.91x 2- 16.84x 3- 35.06x 4-26.57x 5 -2.28x 1x2 +2.23x 1x3 +2.41x 1x4+21.04x 1x5 +1.12x 2x3+0.88x 2x4-2.34x 2x5 -0.23x 3x4-0.02x 3x5 2 2 2 2 2 +0.64x 4x5-34.07x 1 +-2.22x 2 -2.87x 3 -1.07x 4 -65.53x 5
Group 3 model f = - 4328.93+1405.64x 1-77.90x 2- 470.04x 3+22.14x 4+277.6x 5 +7.49x 1x2+39.99x 1x3-1.85x 1x4-21.30x 1x5 -2.68x 2x3+0.38x 2x4+1.02x 2x5 +0.42x 3x4+8.31x 3x5 2 2 2 2 2 -0.22x 4x5-115.78x 1 -2.24x 2 -16.46x 3 -0.16 x 4 -10.05 x 5
25 Andrews curves
Andrews curves (Andrews, 1972) of the complete cluster families are shown below for comparison with the three cluster means. (Figures 14 and 15).
Curves are calculated from the following equation
f (t) = x /1 2 + x2sin(t) + x3cos(t) + x4sin(2t) + x5cos(2t)...
where x1 x2… are the retained catchment characteristics and t is a value between negative and positive values of Pi .
Andrews curves demonstrate graphically the cluster characteristics based on the variables selected. Use of the variables mean values for each cluster can be used as a group signature to rapidly assign an unknown station to a group or to refine existing groups. The order in which the variables are entered in the Andrews equation is important. The leading catchment characteristics have the greatest influence on the resulting curves (Grayson et al., 1996). In this case the order was determined by the final F ratio value of the retained variables, entered in descending order. Standardised variables were employed for this examination rather than the log transform used earlier. The plots show a high degree of similarity with minimal phase difference. Major differences are limited to the amplitude of the group plots.
1 2 grp1 grp2
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-2 -2 -1 -1 -180 -90 0 90 180 -180 -90 0 90 180 -180 -90 0 90 180 -180 -90 0 90 180 Degrees Degrees Degrees Degrees 3 grp3
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Figure 14. Complete grouping Andrews curves. Figure 15. Group means Andrews curves.
26 Discussion
Current study results
The methodology employed was largely determined by the availability of existing or easily obtainable data. An initial classification by complete linkage hierarchical clustering (Krzanovski, 1988) was an attempt to produce an unbiased initial classification using hydrological variables which were assumed to be dependant on the biophysical conditions within the catchment. After the initial complete linkage cluster analysis which suggested three reasonably distinct groups, further investigation was undertaken to find the set of hydrological variables which best represented the classification. This was done by K means clustering, (Wilkinson et al. , 2000) where the number of groups is specified in advance. This method attempts to maximise F values between groups and this approach was used to identify the variables producing values greater than 100 and thus better discriminate between groups.
Specifying 4 groups, splitting by K means analysis of hydrological variables showed a potential fourth grouping containing a majority of eastern coastal rivers. Further analysis by complete linkage indicated this group to be a sub set of the larger Group 1 classification. Examination of the associated cluster profiles when four groups were specified showed considerable overlap between groups. However when the number of groups was reduced to three the overlap was reduced enhancing group discrimination. Once the number of variables included in the analysis was reduced by reference to the F ratio the group discrimination was further enhanced and classification was fixed into three groups. Thus the number of groups was determined by hydrological variables. The use of variables with stronger F ratios reduced the number of potential clusters and increased discrimination between clusters. Comparison of Figure 6 and Figure 7 illustrates this point showing poor separation of groups where four groups are specified with a relatively large number of variables.
There were minimal changes made to the hydrological classifications when transferred to catchment biophysical characteristics. Subsequent changes that were made were based on the probability associated with the stepwise discriminant function analysis, (Table 5, Appendix A2 and A3) applied to the biophysical variables . A total of seven catchments representing 9.5% of the total were reclassified compared with their original hydrological classification. Summary statistics for the final classification are given in Table 6 and Table 7.
Table 6. Summary statistics, hydrological variables, 51 catchments. Group 1 AVFLMO1 AVFLMO2 AVFLMO9 AVFLMO12 AVANFLOW AVCPYIELD Mean 2.15 1.43 8.48 3.64 5 30675.8 Standard Error 0.47 0.31 1.72 0.7 1.02 6384.29 Standard Deviation 2.34 1.53 8.61 3.5 5.09 31921.47 Minimum 0.15 0.11 1.25 0.4 0.82 2237.95 Maximum 11.93 7.59 40.95 18.51 24.81 165867.95
Group 2 AVFLMO1 AVFLMO2 AVFLMO9 AVFLMO12 AVANFLOW AVCPYIELD Mean 15.35 10.98 53.92 26.14 38.22 265244.32 Standard Error 4.33 2.96 14.86 7.38 10.76 75789.08 Standard Deviation 14.37 9.83 49.27 24.48 35.68 251363.96 Minimum 2.14 1.32 6.79 4.09 4.11 31427.27 Maximum 53.78 36.54 184.59 92.18 133.44 938626
Group 3 AVFLMO1 AVFLMO2 AVFLMO9 AVFLMO12 AVANFLOW AVCPYIELD Mean 0.279 0.23 1.733 0.858 0.914 5778.354 Standard Deviation 0.196 0.175 1.271 0.316 0.68 10150.405 Standard Error 0.051 0.045 0.328 0.082 0.176 2620.823 Minimum 0.073 0.105 0.455 0.404 0.109 574.724 Maximum 0.62 0.674 4.608 1.424 2.299 41783.544
27 Table 7. Summary statistics, biophysical variables from 74 classified catchments. Group 1 area ARFMAX MainSL WQTR_SD SDslope area_og Mean 566.91 1720.15 64.79 79.03 6.50 55.84 Standard Error 89.93 51.92 7.97 5.12 0.25 9.39 Standard Deviation 524.36 302.73 46.49 29.86 1.47 54.76 Minimum 68.82 982.00 13.15 27.62 3.19 2.38 Maximum 2340.01 2337.00 240.05 155.90 9.26 194.48
Group 2 area ARFMAX MainSL WQTR_SD SDslope area_og Mean 947.32 2846.26 78.07 93.88 9.53 280.66 Standard Error 158.36 100.71 11.09 10.28 0.23 50.16 Standard Deviation 690.26 438.98 48.35 44.83 0.99 218.63 Minimum 173.18 1932.00 25.07 40.28 7.76 40.05 Maximum 2607.36 3546.00 174.59 195.64 11.06 742.92
Group 3 area ARFMAX MainSL WQTR_SD SDslope area_og Mean 267.73 1203.00 36.81 32.86 6.99 41.05 Standard Error 67.57 47.98 6.71 3.59 0.36 16.30 Standard Deviation 309.66 219.86 30.74 16.43 1.63 74.68 Minimum 23.48 743.00 10.22 13.32 2.66 0.03 Maximum 1244.50 1570.00 145.28 64.02 9.10 300.24
Use of Andrews curves as a rapid classification tool was also examined. Andrews curves are plots of variables as Fourier curves which allow the multi-dimensional relationship between catchment variables to be presented as a two dimensional curve which can be visually inspected for similarity (Grayson et al. , 1996). Two plots were produced, (Figure 14 and Figure 15) showing the complete groupings and group means as potential signature plots for comparison with previously unclassified catchment plots. The curves function as an illustration of the broad nature of the classification arrived at by discriminant analysis. They also indicate the potential to further refine the classification or produce smaller sub regions by the presence of coherent group banding together with some apparent outliers. As a classification tool within this study it appears to have limited value given the low level of rapid visual discrimination.
Graphical examination of the classification (Map1) shows there is some broad geographic grouping into western (W), central to north east (NE) and south east (SE) regions. The clusters of catchments generally show a dependence on catchment size, relief, and mean annual rainfall.
Group1, comprising the central and northeasterly catchments is bounded in the west by the 1200mm average annual rainfall isohyet and in the north by the 900mm isohyet (Figure16). The south easterly group (Group3) is largely contained within the boundary of the 400mm isohyet and is notable for its relatively small catchments (Map1) particularly the detached catchments along the central northern and north west coast. The northern part of the main southeastern group, centred on the Swan River, makes up Knighton's (1987) southern group (Figure 18).
Group 2 is the most contiguous cluster, intuitively expected to be the most distinctive of the groups given its high rainfall, high relief and large catchment areas. This is shown to be the case by its almost complete containment within the 1200mm isohyet (Map1 and Figure16). The exception is its northwestern boundary which has retreated to the 1800mm isohyet probably due to the influence of the small, low lying cathments to the north classified as Group 1 catchments.
28 average annual rainfall(mm) BoM (2001)
Figure 16. Average annual rainfall.
29 Comparison with previous study methods and results
A comparison table of Hughes's (1987) station clusters and the current study is shown in Table 9. Several rivers are classified into more than one group under the Hughes methodology caused by the use of multiple gauging stations on a single stream. These multiple classifications are indicated in Table 9. Individual stations are identified in Table 8.
Hughes's (1987) study aimed to classify solely on the basis of basic hydrological variables and a number of indexes derived from them (Appendix D). No relationships were derived between hydrological and catchment physiographic characteristics other than a log 10 based relationship between catchment area and annual flows.
The major focus of the study was to examine where Tasmanian rivers fit in the Australian context, concluding that for the four groups identified:
• Groups 1 and 4 were temperate in nature
• the dry south east region (Group 2) was similar to drier Australian mainland regions
• the wettest region (Group 3) had no Australian analogue
• the groupings corresponded broadly with rainfall distribution (Figure 16).
Hughes's Group 1 and 4 (Figure 17 below) correspond largely to the current study Group 1(NE) (Map 1.) while Hughes Group 2 corresponds to Group 3 (SE) in the current study. Group 2 (W) in the current study broadly covers Group 3 of Hughes's classification being the wettest and most distinct grouping .
Figure 17. Hughes (1987) Classification of gauging stations.
30 Table 8. Hughes (1987) Classification of gauging stations. Group H number River 1 47 MONTAGU RIVER 1 61 SEABROOK CREEK 1 9 CAM RIVER 1 28 GAWLER RIVER 1 12 CLAYTONS RIVULET 1 11 CLAYTONS RIVULET 1 20 DON RIVER 1 46 MERSEY RIVER 1 60 RUBICON RIVER 1 1 ANDERSON'S CREEK 1 56 PIPERS RIVER 1 58 QUE RIVER 1 70 TOMAHAWK RIVER 1 30 GREAT MUSSELROE RIVER 1 77 MEANDER RIVER 1 65 SOUTH ESK RIVER 1 64 SOUTH ESK RIVER 1 38 LAKE RIVER 1 45 MEREDITH RIVER 1 8 BROWNS RIVER 1 52 NORTH WEST BAY RIVER 1 62 SNUG RIVER 1 29 GEORGE RIVER 2 14 CLYDE RIVER 2 22 DULVERTON RIVER 2 5 BIRRALEE CREEK 2 40 LITTLE SWANPORT RIVER 2 69 SWAN RIVER 2 2 APSLEY RIVER 2 42 MACLAINES CREEK 2 57 PROSSER RIVER 2 15 COAL RIVER 2 17 COAL RIVER 2 53 ORIFLTON RIVULET 2 35 IRON CREEK 2 10 CARLTON RIVER 2 36 JORDAN RIVER
31 Table 8. continued
2 13 CLYDE RIVER 2 19 DERWENT RIVER 3 31 HELLYER RIVER 3 58 QUE RIVER 3 73 WHYTE RIVER 3 55 PIEMAN RIVI R 3 32 HENTY RIVER 3 37 KING RIVER 3 75 FRANKLIN RIVER 3 27 FRANKLIN RIVER 3 74 GORDON RIVER 3 72 TYENNA RIVER 3 33 HUON RIVER 3 24 ESPERANCE RIVER 3 18 DAVEY RIVER 3 71 FLORENTINE RIVER 3 50 NIVE RIVER 3 3 ARM RIVER 3 26 FORTH RIVER 3 44 MEANDER RIVER 4 21 DUCK RIVER 4 4 ARTHUR RIVER 4 25 FLOWERFDALE RIVER 4 6 BLACK RIVER 4 34 INGLIS RIVER 4 67 SULPHUR CREEK 4 54 PET RIVER 4 23 EMU RIVER 4 41 LOUDWATER RIVER 4 43 MEANDER RIVER 4 63 SOUTH ESK RIVER 4 51 NORTH ESK RIVER 4 7 BRID RIVER 4 59 RINGAROOMA RIVER 4 49 MOUNTAIN RIVER 4 49 MONTAGU RIVER
32 The major differences between the two studies are:
• the combining in the current study of Hughes's two temperate regions into a single group (NE) ;
• the absence in Hughes's study of any catchments classified as belonging to the SE group along the central north coast.
Knighton's (1987) study shows a division between northern and southern classifications which is approximately that of the northern limit of the southeastern region found in the current study and in Hughes (1987). Knighton's northern region falls within the NE (group1) and Hughes' temperate (group 1) NE region.
River ID Group Great Musselroe GM n Tomahawk T n Brid B n Pipers P n Curries CU unused Lauriston Creek LC n Great Forester GF unused Ringarooma R unused Cascade C unused Ransom RA unused George G n South Esk (Perth) SEp n North Esk NE n South Esk (llewellyn) SEl n Macquarie MA unused Apsley A s Swan S s Goatrock creek GC s Meredith ME s
Figure 18. Classification of regional flood flows in north east Tasmania (after Knighton (1987)).
33 Dyer's (1994) classification (Figure 19) only contains four stations two of which are on the North Esk River. This grouping straddles the northern division between northeastern and western groupings falling equally into both. Since this grouping was part of a national clustering study rather than an exclusively Tasmanian study there appears to be no value in this grouping to the current study.
Station Name lat long
315002 Cethana R 41.23 146.13
316201 Fisher Rv 41.41 146.24
318010 North Esk 41.30 147.23
318031 North Esk 41.29 147.14
Figure 19. Four Tasmanian sites used in a national regionalisation (after Dyer (1994)).
34 A comparison of the current regionalisation (Map 1) with a biogeographical regionalisation (Figure 20) carried out by Peters & Thackay (1998) shows the western and southeastern regions as broadly equivalent. Looking at the Hughes (1987) classification shows the Group 1 and Group 4 classes as roughly equivalent to the Peters & Thackay (1998) Northern Slopes and Ben Lomond classification.
Figure 20. Peters and Thackay (1998) Biogeographical regionalisation.
35 Table 9. Classification comparisons. CATCH_ID RIVER Hydrological K CLUSTER Biophys Quad Model Cluster Hughes number Hughes class 58 BLYTHE RIVER 1 43 BOOBYALLA RIVER 1 170 CROOKS RIVULET. 1 53 CURRIES RIVER 3 103 GREAT LAKE RIVER 1 90 HUSKISSON RIVER 2 72 JOHNSTON CK. RIVER 3 159 LAKE PEDDER RIVER 2 63 NELSON BAY RIVER 1 105 OUSE RIVER 1 82 SAVAGE RIVER 2 98 ST. PAULS RIVER 1 127 SWANPORT RIVER 3 48 ANSONS RIVER 1 1 95 BREAK O"DAY RIVER 1 1 47 GREAT FORESTER RIVER 1 1 96 MACQUARIE RIVER 1 1 93 NILE RIVER 1 1 84 SCAMANDER RIVER 1 1 94 MACKINTOSH RIVER 2 2 104 MURCHISON RIVER 2 2 75 FRANKLIN RIVER 3 3 163 MOUNTAIN RIVER 3 3 49 29 WELCOME RIVER 3 3 67 GAWLER RIVER 3 28 1 102 LAKE RIVER 1 38 1 74 MERSEY RIVER 2 46 1 164 NORTHWEST BAY RIVULET 3 52 1 55 CAM RIVER 1 1 9 1 71 GEORGE RIVER 1 1 29 1 36 GREATMUSSELROE RIVER 1 1 30 1 31 MONTAGU RIVER 1 1 48 1 64 ANDERSONS CREEK 3 3 1 1 172 BROWNS RIVER 3 3 8 1 68 DON RIVER 3 3 20 1 122 MEREDITH RIVER 3 3 45 1 50 PIPERS RIVER 3 1 56 1 78 RUBICON RIVER 3 3 60 1 169 SNUG RIVULET 3 3 62 1
36 Table 9 continued. CATCH_ID RIVER Hydrological K CLUSTER Biophys Quad Model Cluster Hughes number Hughes class 76 SUPPLY RIVER 3 3 68 1 39 TOMAHAWK RIVER 3 1 70 1 117 CLYDE RIVER 1 13 2 136 PROSSER RIVER 3 57 2 106 APSLEY RIVER 1 1 2 2 150 CARLTON RIVER 3 3 10 2 134 COAL RIVER 3 3 15 2 128 JORDAN RIVER 3 3 36 2 146 ORIELTON RIVER 3 3 53 2 108 SWAN RIVER 3 3 69 2 115 DERWENT RIVER 2 19 3 69 HELLYER RIVER 2 31 3 112 HENTY RIVER 2 32 3 160 HUON RIVER 2 33 3 190 ESPERANCE RIVER 1 2 24 3 107 NIVE RIVER 1 1 50 3 142 TYENNA RIVER 1 1 72 3 52 ARTHUR RIVER 2 2 4 3 70 FORTH RIVER 2 2 26 3 119 FRANKLIN RIVER 2 2 27 3 131 GORDON RIVER 2 2 74 3 114 KING RIVER 2 2 37 3 91 PIEMAN RIVER 2 2 55 3 86 WHYTE RIVER 2 2 73 3 37 BLACK RIVER 1 1 6 4 35 DUCK RIVER 1 1 21 4 44 FLOWERDALE RIVER 1 1 25 4 45 INGLIS RIVER 1 1 34 4 79 NORTH ESK RIVER 1 1 51 4 40 RINGAROOMA RIVER 1 1 59 4 61 LEVEN RIVER 2 2 39 4 49 BRID RIVER 3 1 7 4 56 EMU RIVER 3 1 23 4 83 SOUTH ESK RIVER 2 1 66 4 and 1 85 MEANDER RIVER 2 1 44 4, 1, 3
37 Conclusions
The classification of 74 catchments (Map 1) represents 39% of Tasmania's 189 catchments ( as defined in 1999 from one of a suite of catchment mapping definitions available) with an approximately 10% error rate. The result for this sample size gives confidence to the applicability of this classification. Further qualitative confidence can be gained from comparison with Hughes's (1987) classification which did not reveal major discrepancies between the two results. In addition examination of the sub regions studied by Knighton (1987) lends weight to the boundary delineated between northeastern and southeastern groups. The clusters of catchments generally show a dependence on catchment relief, size and mean annual rainfall illustrated by comparing Appendix B and Figure 16.
Small scale analysis has not allowed a localised outcome. The results are broadly applicable and any new ungauged catchment classification will fall into a category with a wide range of catchment characteristics. There are indications however that some marginal refinement of groups or the establishment of sub regions may be possible eg. Hughes' division of temperate catchments into two zones and the coherent banding and potential outliers indicated by the Andrews curves.
38 Bibliography
Andrews, D.F. (1972) Plots of High Dimensional Data. Biometrics, 28 :125-136.
ARR (2001) Australian Rainfall and Runoff, V.1, A guide to Flood Estimation. The Institution of Engineers, Australia. Barton, ACT.
Bates, B.C. (1994) Regionalisation of Hydrologic Data: A Review: A report as part of Project D2: regionalisation and scaling of hydrologic data. Cooperative Research Centre for Catchment Hydrology, Clayton, Victoria.
Burn, D.H. and Goel, N.K. (2000) The formation of groups for regional flood frequency analysis, Hydrological Sciences , 45 (1), pp 97-112.
Dyer, B.G., Nathan, R.J., McMahon, T.A. and O'Neill, I.C. , (1994) Development of Regional Prediction Equations for the RORB Run-off Routing Model, Cooperative Research Centre for Catchment Hydrology Report 94/1 . Pp 48-54. Clayton, Victoria..
Engelman, L., (1998) Systat 8, Statistics , p245-296, SPSS, Chicago.
Grayson, R.B., Argent, R.M., Nathan, RJ., McMahon, T.A., and Mein, R.G., (1996) Hydrological Recipes: Estimation Techniques in Australian Hydrology , Cooperative Research Centre for Catchment Hydrology, Clayton, Victoria. Pp 89-97.
Hughes, J.M.R. (1987) Hydrological Characteristics and Classification of Tasmanian Rivers, Australian Geographical Studies , 25 (1): pp61-82.
Hughes, J.M.R., and James, B., (1989) A Hydrological Regionalisation of Streams in Victoria, Australia with implications for Stream Ecology, Australian Journal of Marine and Freshwater Research, 40 , pp303-26.
Hutchinson, M.F., Houlder, D.J., Nix, H.A. and McMahon, J.P. (1999) ANUCLIM User Guide, Version 5.0. Centre for Resource and Environmental Studies, Australian National University, Canberra. (http://cres.anu.edu.au/software.html).
Knighton, A.D. (1987) Streamflow Characteristics of Northeastern Tasmania: 1. Regional Flood Flows, Papers and Proceedings of the Royal Society of Tasmania , 121, pp23-33.
Krzanowski, W.J. (1988) Principles of Multivariate Analysis, A Users Perpective . Clarendon Press, Oxford.
Nathan, R.J., and McMahon, T.A. (1990) Identification of homogeneous regions for the purposes of regionalisation, Journal of Hydrology , 121 , pp217-238.
Peters, D. and Thackway, R. (1998) A New Biogeographic Regionalisation for Tasmania , Tasmanian Parks and Wildlife Service. Hobart.
Pilgrim, D.H., (2001) Australian Rainfall and Runoff, A guide to Flood Estimation. V1., Book 5 , Runoff Routing Methods, Institution of Engineers Australia, Barton, ACT.
Tasmanian Land Use Commission (1996a) Tasmanian-Commonwealth Regional Forest Agreement, Environment and Heritage Report Vol. 1, Background Report Part C, p 159-161, Hobart.
Tasmanian Land Use Commission (1996b) Tasmanian-Commonwealth Regional Forest Agreement, Environment and Heritage Report Vol. 2, Background Report Part C, p 129-139, 163-171, Hobart.
Wilkinson, L., Engleman, L., Corter, J. and Coward, M., (2000) Systat 10 , Statistics I SPSS Inc, Chicago P1-(60-68). 39 Appendices
A1: 52 stations used to form initial hydrological clusters.
Site Name Elevation Easting Northing Record length(1999) 25 NILE RIVER AT DEDDINGTON 243.8 538200.04 5397199.40 14.5 30 RINGAROOMA RIVER AT MOORINA 110 572700.00 5446650.00 22.7 46 GORDON RIVER BELOW HUNTLEY 441 447900.00 5276400.00 26.2 76 NORTH ESK AT BALLROOM 325 532500.00 5406100.00 77.0 78 KING RIVER AT CROTTY 174 388349.99 5331500.10 71.9 116 PIPERS RIVER AT UNDERWOOD 230 517050.27 5428649.60 41.3 145 FRANKLIN RIVER AT Mt.FINCHAM TRACK 220 398400.00 5322500.00 44.2 148 MURCHISON RIVER ABOVE STERLING 138 385500.00 5375550.00 28.4 149 MACKINTOSH RIVER BELOW SOPHIA 147 386300.00 5380700.00 26.8 154 PIEMAN RIVER ABOVE HEEMSKIRK 36 353350.00 5370800.00 31.0 159 ARTHUR RIVER BELOW RAPID 46 338600.00 5445700.00 41.3 181 SOUTH ESK AT SYMMONS PLAINS 150 522100.00 5390500.00 56.7 191 BREAK O DAY RIVER AT KILLYMOON 243.84 588000.00 5394500.00 16.5 350 WHYTE RIVER ABOVE ROCKY CREEK 55 348800.00 5390250.00 32.1 473 DAVEY RIVER B/L CROSSING RIVER 35 414600 5222900 35.7 497 NIVE RIVER AT GOWAN BRAE 800 451682.00 5346402.00 33.1 499 TYENNA RIVER AT NEWBURY 170 476100.00 5271600.00 35.8 852 MEANDER RIVER AT STRATHBRIDGE 160 492625.00 5406875.00 14.5 2200 SWAN RIVER AT THE GRANGE 10 588900.00 5344500.00 35.8 2204 APSLEY RIVER UPSTREAM COLES BAY ROAD BRIDGE 10 602400.00 5356100.00 24.1 2205 GEORGE RIVER AT ST.HELENS WATER SUPPLY INTAKE 45 601800.00 5428200.00 28.5 2206 SCAMANDER RIVER UPSTREAM SCAMANDER WATER SUPPLY INTAKE 5 598400 5410900 28.5 2208 MEREDITH RIVER AT SWANSEA 15 585900.00 5336100.00 29.9 2209 CARLTON RIVER AT TIDAL LIMIT 5 557500.00 5253700.00 27.8 2210 GREAT MUSSELROE RIVER 6.5 km UPSTREAM OF MOUTH 10 591900.00 5473900.00 24.3 2211 ORIELTON RIVULET UPSTREAM BRINKTOP ROAD 10 544100 5265600 24.3 2214 ANSONS RIVER DOWNSTREAM BIG BOGGY CREEK 15 602200.00 5455200.00 17.4
40 A1. Continued.
3201 COAL RIVER AT CRAIGBOURNE ROAD 140 532900.00 5288500.00 19.5 4201 JORDAN RIVER AT MAURICETON 150 510100.00 5291400.00 34.3 5200 BROWNS RIVER AT SUMMERLEAS ROAD BRIDGE 90 521800.00 5244000.00 29.1 5202 SNUG RIVULET UPSTREAM SNUG TIERS ROAD BRIDGE 60 519200.00 5231000.00 34.5 6200 MOUNTAIN RIVER DOWNSTREAM GRUNDYS CREEK 140 510800.00 5245800.00 28.1 7200 ESPERANCE RIVER AT DOVER WATER SUPPLY INTAKE 5 497100.00 5201900.00 28.3 14200 MONTAGU RIVER AT MONTAGU ROAD BRIDGE 5 325400.00 5483000.00 34.6 14207 LEVEN RIVER AT BANNONS BRIDGE 60 423700.00 5432800.00 21.7 14210 INGLIS RIVER ABOVE FLOWERDALE RIVER JUNCTION 30 384400 5459800 21.7 14212 CAM RIVER UPSTREAM SOMERSET WATER SUPPLY INTAKE 20 402200.00 5454000.00 29.2 14213 BLACK RIVER AT SOUTH FOREST 10 356400.00 5473900.00 31.6 14214 DUCK RIVER UPSTREAM SCOTCHTOWN ROAD 5 341399.19 5473598.60 33.9 14215 FLOWERDALE RIVER AT MOORLEAH 35 382900.00 5463700.00 33.8 14219 EMU RIVER DOWNSTREAM COMPANION DAM 295 394600 5426300 28.6 14223 WELCOME RIVER AT WOOLNORTH 10 310500.00 5483300.00 18.6 16200 DON RIVER UPSTREAM OLD BASS HIGHWAY 5 442400.00 5439600.00 23.2 17200 RUBICON RIVER AT TIDAL LIMIT 5 463700.00 5432600.00 32.7 17201 FRANKLIN RIVULET 1.5 km UPSTREAM TIDAL LIMIT 15 467200 5431800 19.1 18200 ANDERSONS CREEK UPSTREAM KELSO ROAD 2 480700.00 5442500.00 26.3 18201 SUPPLY RIVER 0.5 km UPSTREAM TAMAR RIVER 20 494800.00 5432700.00 19.1 18312 MACQUARIE RIVER DOWNSTREAM ELIZABETH RIVER JUNCTION 170 532400.00 5359800.00 34.6 19200 BRID RIVER 2.6 km UPSTREAM TIDAL LIMIT 10 531300 5458800 34.6 19201 GREAT FORESTER RIVER 2 km UPSTREAM FORESTER ROAD BRIDGE 45 551300.00 5448400.00 30.0 19202 TOMAHAWK RIVER AT TIDAL LIMIT 10 563300.00 5472800.00 22.4
41 A2: K means grouping of 51 stations by hydrological variable and classifications transferred to catchments. Group 1
Site CATCH_ID RIVER K means CLUSTER Quad predicted cluster 25 93 NILE RIVER 1 1 30 40 RINGAROOMA RIVER 1 1 76 79 NORTH ESK RIVER 1 1 191 95 BREAK O"DAY RIVER 1 1 497 107 NIVE RIVER 1 1 499 142 TYENNA RIVER 1 1 2204 106 APSLEY RIVER 1 1 2205 71 GEORGE RIVER 1 1 2206 84 SCAMANDER RIVER 1 1 2210 36 GREAT MUSSELROE 1 1 2214 48 ANSONS RIVER 1 1 7200 190 ESPERANCE RIVER 1 2 14200 31 MONTAGU RIVER 1 1 14210 45 INGLIS RIVER 1 1 14212 55 CAM RIVER 1 1 14213 37 BLACK RIVER 1 1 14214 35 DUCK RIVER 1 1 14215 44 FLOWERDALE RIVER 1 1 18312 96 MACQUARIE RIVER 1 1 19201 47 GREAT FORESTER RIVER 1 1
42 A2. continued Group 2
Site CATCH_ID RIVER K means CLUSTER Quad predicted cluster 46 131 GORDON RIVER 2 2 78 114 KING RIVER 2 2 145 119 FRANKLIN RIVER 2 2 148 104 MURCHISON RIVER 2 2 149 94 MACKINTOSH RIVER 2 2 154 91 PIEMAN RIVER 2 2 159 52 ARTHUR RIVER 2 2 181 83 SOUTH ESK RIVER 2 1 350 86 WHYTE RIVER 2 2 450 70 FORTH RIVER 2 2 473 DAVEY RIVER 2 852 85 MEANDER RIVER 2 1 14207 61 LEVEN RIVER 2 2 Group 3 Site CATCH_ID RIVER K means CLUSTER Quad predicted cluster 116 50 PIPERS RIVER 3 1 2200 108 SWAN RIVER 3 3 2208 122 MEREDITH RIVER 3 3 2209 150 CARLTON RIVER 3 3 2211 146 ORIELTON RIVER 3 3 3201 134 COAL RIVER 3 3 4201 128 JORDAN RIVER 3 3 5200 172 BROWNS RIVER 3 3 5202 169 SNUG RIVULET 3 3 6200 163 MOUNTAIN RIVER 3 3 14219 56 EMU RIVER 3 1 14223 29 WELCOME RIVER 3 3 16200 68 DON RIVER 3 3 17200 78 RUBICON RIVER 3 3 17201 75 FRANKLIN RIVER 3 3 18200 64 ANDERSONS CREEK 3 3 18201 76 SUPPLY RIVER 3 3 19200 49 BRID RIVER 3 1 19202 39 TOMAHAWK RIVER 3 1
43
A3: Hydrological Data. 52 stations SITE RIVER CATCH_ID AVFLMO1 AVFLMO2 AVFLMO9 AVFLMO12 AVANFLOW AVCPYIELD 14200 MONTAGU RIVE 31 0.57 0.40 7.87 1.59 3.95 8527.92 14214 DUCK RIVER 35 1.52 1.19 10.88 2.85 5.87 21753.72 2210 GREAT MUSSEL 36 1.12 0.82 4.91 2.71 2.95 17291.59 14213 BLACK RIVER 37 1.55 1.09 11.42 3.22 6.42 30156.84 19202 TOMAHAWK RIV 39 0.15 0.13 1.91 0.88 0.82 2237.95 30 RINGAROOMA R 40 3.72 2.45 15.37 5.54 8.60 49028.50 14215 FLOWERDALE R 44 1.28 1.10 6.27 2.32 3.76 19733.72 14210 INGLIS RIVER 45 1.24 0.96 7.55 2.64 4.24 19138.63 19201 GREAT FOREST 47 1.21 0.87 4.42 2.03 2.65 16057.45 2214 ANSONS RIVER 48 1.36 0.45 3.04 3.00 1.88 14602.51 19200 BRID RIVER 49 0.62 0.51 2.73 1.21 1.44 8482.76 116 PIPERS RIVER 50 0.17 0.11 1.34 0.40 0.93 3517.49 14212 CAM RIVER 55 1.55 1.10 8.66 2.71 5.03 21660.89 14219 EMU RIVER 56 0.46 0.46 1.25 0.90 0.99 20452.46 2205 GEORGE RIVER 71 2.97 2.45 8.31 5.47 6.30 51309.78 76 NORTH ESK RI 79 2.17 1.84 9.47 3.24 5.53 30644.22 181 SOUTH ESK 83 11.93 7.59 40.95 18.51 24.81 165867.95 2206 SCAMANDER RI 84 1.55 1.00 2.54 2.70 1.92 20117.21 852 MEANDER RIVE 85 4.69 3.75 25.77 6.36 14.65 64429.83 25 NILE RIVER 93 2.11 0.81 6.87 3.28 3.68 25985.15 191 BREAK O"DAY 95 1.93 0.47 2.61 2.36 1.68 17546.47 18312 MACQUARIE RI 96 4.03 2.03 6.74 6.82 3.55 44088.55 2204 APSLEY RIVER 106 1.28 0.98 2.03 2.62 2.09 24086.28 497 NIVE RIVER 107 2.20 1.33 10.53 3.93 6.00 32905.50 499 TYENNA RIVER 142 2.44 1.94 8.48 3.78 5.22 37271.70 159 ARTHUR RIVER 52 17.45 13.18 82.33 28.55 56.25 291056.07 14207 LEVEN RIVER 61 5.63 4.24 25.43 8.82 16.40 87297.43 450 FORTH RIVER 70 6.07 3.84 23.65 9.36 14.74 96293.28 350 WHYTE RIVER 86 6.27 4.38 22.27 9.74 15.00 100366.95 154 PIEMAN RIVER 91 53.78 36.54 184.59 92.18 133.44 938626.00 149 MACKINTOSH R 94 10.09 7.78 34.47 19.42 26.50 184756.11 148 MURCHISON RI 104 17.18 12.25 69.54 35.95 49.58 355611.49 78 KING RIVER 114 17.49 14.92 45.70 24.40 32.90 277363.87 145 FRANKLIN RIV 119 23.75 16.05 67.98 35.90 48.05 378873.25 46 GORDON RIVER 131 9.03 6.26 30.40 19.16 23.46 176015.74 7200 ESPERANCE RI 190 2.14 1.32 6.79 4.09 4.11 31427.27 14223 WELCOME RIVE 29 0.09 0.16 3.43 0.80 1.65 1431.28 18200 ANDERSONS CR 64 0.09 0.12 1.38 0.69 0.66 1871.83
45 A3 continued 16200 DON RIVER 68 0.31 0.25 3.46 0.63 2.12 5598.32 17201 FRANKLIN RIV 75 0.13 0.12 2.20 1.03 1.10 4595.32 18201 SUPPLY RIVER 76 0.21 0.23 2.68 0.97 1.38 3074.30 17200 RUBICON RIVE 78 0.20 0.25 4.61 0.82 2.30 3931.79 2200 SWAN RIVER 108 0.54 0.15 0.67 0.90 0.44 41783.54 2208 MEREDITH RIV 122 0.47 0.22 0.79 1.33 0.56 5650.16 4201 JORDAN RIVER 128 0.41 0.15 1.35 0.48 0.68 3634.00 3201 COAL RIVER 134 0.32 0.13 1.23 0.40 0.71 3153.39 2211 ORIELTON RIV 146 0.07 0.11 0.45 0.80 0.11 1351.20 2209 CARLTON RIVE 150 0.55 0.67 1.35 1.36 0.87 7313.15 6200 MOUNTAIN RIV 163 0.62 0.61 1.30 1.42 0.81 574.72 5202 SNUG RIVULET 169 0.09 0.16 0.60 0.68 0.18 1573.78 5200 BROWNS RIVER 172 0.08 0.11 0.48 0.55 0.14 1138.51 473 DAVEY RIVER 161 23.08 18.80 58.14 32.74 44.81 384038.72
46 B1: 51 catchment cluster membership probabilities by quadratic discriminant analysis ADJCLUSTER RIVER$ PREDICTD MISCLASS PROB(1) PROB(2) PROB(3) $ 3 WELCOME RIVE 3 0 0.074 0.000 0.926 1 MONTAGU RIVE 1 0 1.000 0.000 0.000 1 DUCK RIVER 1 0 0.900 0.000 0.100 1 GREAT MUSSEL 1 0 0.987 0.000 0.013 1 BLACK RIVER 1 0 0.997 0.000 0.003 1 TOMAHAWK RIV 1 0 1.000 0.000 0.000 1 RINGAROOMA R 1 0 1.000 0.000 0.000 1 FLOWERDALE R 1 0 0.990 0.000 0.010 1 INGLIS RIVER 1 0 0.963 0.000 0.037 1 GREAT FOREST 1 0 1.000 0.000 0.000 1 ANSONS RIVER 1 0 0.992 0.000 0.008 1 BRID RIVER 1 0 1.000 0.000 0.000 1 PIPERS RIVER 1 0 1.000 0.000 0.000 2 ARTHUR RIVER 2 0 0.000 1.000 0.000 1 CAM RIVER 1 0 0.979 0.000 0.021 1 EMU RIVER 1 0 1.000 0.000 0.000 2 LEVEN RIVER 2 0 0.008 0.992 0.000 3 ANDERSONS CR 3 0 0.001 0.000 0.999 3 DON RIVER 3 0 0.000 0.000 1.000 2 FORTH RIVER 2 0 0.001 0.999 0.000 1 GEORGE RIVER 1 0 0.997 0.000 0.003 3 FRANKLIN RIV 3 0 0.029 0.000 0.971 3 SUPPLY RIVER 3 0 0.001 0.000 0.999 3 RUBICON RIVE 3 0 0.008 0.000 0.992 1 NORTH ESK RI 1 0 1.000 0.000 0.000 1 SOUTH ESK 1 0 1.000 0.000 0.000 1 SCAMANDER RI 1 0 0.706 0.000 0.294 1 MEANDER RIVE 1 0 0.998 0.000 0.002 2 WHYTE RIVER 2 0 0.000 1.000 0.000 2 PIEMAN RIVER 2 0 0.000 1.000 0.000 1 NILE RIVER 1 0 0.999 0.000 0.001 2 MACKINTOSH R 2 0 0.000 1.000 0.000 1 BREAK O"DAY 1 0 0.770 0.000 0.230 1 MACQUARIE RI 1 0 1.000 0.000 0.000 2 MURCHISON RI 2 0 0.000 1.000 0.000
47 B1 continued 1 APSLEY RIVER 1 0 0.810 0.000 0.190 1 NIVE RIVER 1 0 0.999 0.000 0.001 3 SWAN RIVER 3 0 0.044 0.000 0.956 2 KING RIVER 2 0 0.000 1.000 0.000 2 FRANKLIN 2 0 0.000 1.000 0.000 3 MEREDITH RIV 3 0 0.000 0.000 1.000 3 JORDAN RIVER 3 0 0.002 0.000 0.998 2 GORDON RIVER 2 0 0.000 1.000 0.000 3 COAL RIVER 3 0 0.001 0.000 0.999 1 TYENNA RIVER 1 0 0.997 0.000 0.003 3 ORIELTON RIV 3 0 0.000 0.000 1.000 3 CARLTON RIVE 3 0 0.000 0.000 1.000 3 MOUNTAIN RIV 3 0 0.197 0.000 0.803 3 SNUG RIVULET 3 0 0.000 0.000 1.000 3 BROWNS RIVER 3 0 0.009 0.000 0.991 1 ESPERANCE RI 1 0 1.000 0.000 0.000
48 B2: 74 catchments final classification probabilities ADJ_CLUSTER CATCH_ID PREDICTD MISCLASS PROB(1) PROB(2) PROB(3) 3 29.000 3.000 0.000 0.228 0.000 0.772 1 31.000 1.000 0.000 0.978 0.000 0.022 1 35.000 1.000 0.000 0.923 0.000 0.077 1 36.000 1.000 0.000 0.992 0.000 0.008 1 37.000 1.000 0.000 0.996 0.000 0.004 1 39.000 1.000 0.000 0.983 0.000 0.017 1 40.000 1.000 0.000 0.879 0.121 0.000 1 43.000 1.000 0.000 0.972 0.000 0.028 1 44.000 1.000 0.000 0.954 0.000 0.046 1 45.000 1.000 0.000 0.971 0.026 0.002 1 47.000 1.000 0.000 0.992 0.005 0.002 1 48.000 1.000 0.000 0.975 0.000 0.025 1 49.000 1.000 0.000 0.972 0.000 0.028 1 50.000 1.000 0.000 0.989 0.000 0.011 2 52.000 2.000 0.000 0.000 1.000 0.000 3 53.000 3.000 0.000 0.186 0.000 0.814 1 55.000 1.000 0.000 0.975 0.006 0.018 1 56.000 1.000 0.000 0.959 0.041 0.000 1 58.000 1.000 0.000 0.976 0.024 0.000 2 61.000 2.000 0.000 0.006 0.994 0.000 1 63.000 1.000 0.000 0.991 0.000 0.009 3 64.000 3.000 0.000 0.002 0.000 0.998 3 67.000 3.000 0.000 0.001 0.000 0.999 3 68.000 3.000 0.000 0.000 0.000 1.000 2 69.000 2.000 0.000 0.000 1.000 0.000 2 70.000 2.000 0.000 0.000 1.000 0.000 1 71.000 1.000 0.000 0.965 0.031 0.004 3 72.000 3.000 0.000 0.000 0.000 1.000 2 74.000 2.000 0.000 0.002 0.998 0.000 3 75.000 3.000 0.000 0.046 0.000 0.954 3 76.000 3.000 0.000 0.002 0.000 0.998 3 78.000 3.000 0.000 0.021 0.000 0.979 1 79.000 1.000 0.000 0.961 0.039 0.000 2 82.000 2.000 0.000 0.000 1.000 0.000 1 83.000 1.000 0.000 0.961 0.039 0.000 1 84.000 1.000 0.000 0.756 0.004 0.241 1 85.000 1.000 0.000 0.934 0.066 0.000 2 86.000 2.000 0.000 0.000 1.000 0.000 2 90.000 2.000 0.000 0.000 1.000 0.000 2 91.000 2.000 0.000 0.000 1.000 0.000 1 93.000 1.000 0.000 0.842 0.000 0.158 2 94.000 2.000 0.000 0.000 1.000 0.000
49 B2 continued ADJ_CLUSTER$ CATCH_ID PREDICTD MISCLASS PROB(1) PROB(2) PROB(3) 1 95.000 1.000 0.000 0.748 0.000 0.252 1 96.000 1.000 0.000 0.998 0.000 0.002 1 98.000 1.000 0.000 0.994 0.000 0.006 1 102.000 1.000 0.000 0.988 0.000 0.012 1 103.000 1.000 0.000 0.986 0.000 0.014 2 104.000 2.000 0.000 0.000 1.000 0.000 1 105.000 1.000 0.000 0.998 0.002 0.000 1 106.000 1.000 0.000 0.654 0.000 0.346 1 107.000 1.000 0.000 1.000 0.000 0.000 3 108.000 3.000 0.000 0.168 0.000 0.832 2 112.000 2.000 0.000 0.000 1.000 0.000 2 114.000 2.000 0.000 0.000 1.000 0.000 2 115.000 2.000 0.000 0.015 0.985 0.000 1 117.000 1.000 0.000 0.896 0.000 0.104 2 119.000 2.000 0.000 0.000 1.000 0.000 3 122.000 3.000 0.000 0.001 0.000 0.999 3 127.000 3.000 0.000 0.000 0.000 1.000 3 128.000 3.000 0.000 0.019 0.000 0.981 2 131.000 2.000 0.000 0.000 1.000 0.000 3 134.000 3.000 0.000 0.013 0.000 0.987 3 136.000 3.000 0.000 0.000 0.000 1.000 1 142.000 1.000 0.000 0.952 0.044 0.004 3 146.000 3.000 0.000 0.000 0.000 1.000 3 150.000 3.000 0.000 0.001 0.000 0.999 2 159.000 2.000 0.000 0.000 1.000 0.000 2 160.000 2.000 0.000 0.029 0.971 0.000 3 163.000 3.000 0.000 0.169 0.000 0.831 3 164.000 3.000 0.000 0.000 0.000 1.000 3 169.000 3.000 0.000 0.000 0.000 1.000 1 170.000 1.000 0.000 0.902 0.000 0.097 3 172.000 3.000 0.000 0.009 0.000 0.991 2 190.000 2.000 0.000 0.290 0.710 0.000
50 B3: Biophysical Data 74 catchments. CATCH_ID RIVER area ARFMAX MainSL WQTR_SD SDslope area_og 31 MONTAGU RIVER 317.46 1567.00 39.63 29.33 3.98 47.17 35 DUCK RIVER 392.71 1558.00 29.23 45.13 5.27 21.23 36 GREAT MUSSEL 368.90 1790.00 38.19 79.27 5.29 29.34 37 BLACK RIVER 335.35 1790.00 55.29 51.16 5.56 46.02 39 TOMAHAWK RIVER 139.07 1610.00 28.57 79.73 4.24 12.03 40 RINGAROOMA RIVER 912.93 1832.00 119.00 113.79 8.15 111.43 43 Boobyalla 249.63 1610.00 32.30 67.99 4.79 20.36 44 FLOWERDALE R 172.73 1871.00 60.87 80.96 5.92 5.32 45 INGLIS RIVER 326.19 1887.00 60.36 77.11 7.07 42.64 47 GREAT FOREST 517.93 1681.00 67.80 92.22 7.28 31.17 48 ANSONS RIVER 237.12 1588.00 32.66 36.42 4.18 40.54 49 BRID RIVER 149.04 1588.00 63.20 87.90 6.73 2.94 50 PIPERS RIVER 375.82 1628.00 56.10 78.95 5.98 13.20 55 CAM RIVER 239.85 1861.00 47.06 71.46 7.42 10.19 56 EMU RIVER 242.12 2337.00 61.44 87.71 6.93 26.77 58 Blythe 272.56 2069.00 51.22 87.48 6.96 33.72 63 Nelson Bay 68.82 2030.00 38.78 54.15 3.19 7.05 71 GEORGE RIVER 522.47 1817.00 36.64 113.37 8.14 61.57 79 NORTH ESK RI 1065.50 1739.00 95.69 115.62 7.66 96.88 83 SOUTH ESK 2340.01 1751.00 240.05 117.53 9.03 183.84 84 SCAMANDER RI 296.06 1642.00 34.35 70.89 9.26 13.94 85 MEANDER RIVE 1334.19 2087.00 116.52 90.89 6.97 52.98 93 NILE RIVER 323.20 1739.00 46.64 104.16 7.88 2.38 95 BREAK O"DAY 230.09 1487.00 33.47 60.72 7.46 14.50 96 MACQUARIE RI 1558.02 982.00 178.30 28.99 5.94 194.48 98 St. Pauls 521.46 1384.00 52.09 75.59 7.83 154.06 102 Lake 815.48 1575.00 55.90 73.45 6.83 121.64 103 Great Lake 396.37 1762.00 13.15 107.96 4.85 35.35 105 Ouse 1646.98 2227.00 130.22 155.90 6.02 69.06 106 APSLEY RIVER 231.07 1239.00 46.75 44.26 7.40 90.71 107 NIVE RIVER 1089.29 2312.00 76.39 120.30 5.90 177.82 117 Clyde 1117.52 1030.00 93.78 27.62 5.85 42.07 142 TYENNA RIVER 336.45 1786.00 51.99 99.35 8.44 72.90 170 Crooks Rt. 132.58 1629.00 19.42 59.80 6.55 13.17 52 ARTHUR RIVER 1502.92 2571.00 174.59 82.74 8.60 742.92 61 LEVEN RIVER 563.16 2743.00 95.30 129.30 9.37 60.64 69 Hellyer 327.15 2622.00 53.34 46.86 7.76 52.79 70 FORTH RIVER 1110.22 2858.00 100.98 160.03 10.73 201.56 74 Mersey 1710.63 2655.00 149.80 144.74 9.44 197.31 82 Savage 303.02 2376.00 80.80 40.28 9.46 207.34
51 B3 continued CATCH_ID RIVER area ARFMAX MainSL WQTR_SD SDslope area_og 86 WHYTE RIVER 386.78 2940.00 64.74 56.24 9.01 188.36 90 Huskisson 509.01 2779.00 37.94 46.02 9.41 309.35 91 PIEMAN RIVER 979.65 3280.00 34.38 88.12 9.03 421.81 94 MACKINTOSH R 534.38 2952.00 25.57 100.45 10.66 264.24 104 MURCHISON RI 794.45 3339.00 42.91 73.43 10.44 323.36 112 Henty 375.68 3509.00 51.46 140.14 9.53 98.77 114 KING RIVER 812.97 3546.00 25.07 76.59 11.06 111.21 115 Derwent 2027.15 2661.00 154.95 195.64 7.88 523.41 119 FRANKLIN 1656.27 3352.00 127.96 59.52 10.63 601.90 131 GORDON RIVER 2607.36 3198.00 108.01 104.26 10.15 684.32 159 Lake Pedder 262.51 2457.00 27.15 43.18 10.45 55.79 160 Huon 1362.49 2309.00 100.86 128.58 9.34 247.44 190 ESPERANCE RI 173.18 1932.00 27.45 67.56 8.15 40.05 29 WELCOME RIVE 292.15 1367.00 48.35 26.73 2.66 25.65 53 Curries 82.23 1122.00 14.68 26.66 3.81 5.79 64 ANDERSONS CR 49.51 1278.00 15.76 43.60 9.10 4.07 67 Gawler 86.90 1570.00 16.28 45.07 6.38 0.30 68 DON RIVER 129.76 1346.00 38.81 39.03 6.04 0.08 72 Johnston Ck. 61.43 1093.00 14.95 15.42 6.32 0.13 75 FRANKLIN RIV 132.59 1256.00 25.82 35.55 6.96 7.48 76 SUPPLY RIVER 134.89 1240.00 29.66 30.86 6.67 1.71 78 RUBICON RIVE 262.63 1249.00 46.33 22.53 4.74 4.51 108 SWAN RIVER 659.36 1257.00 41.42 43.38 8.05 300.24 122 MEREDITH RIV 96.70 978.00 24.66 22.23 8.35 52.42 127 Swanport 605.82 976.00 58.10 14.63 7.10 132.96 128 JORDAN RIVER 1244.50 1180.00 145.28 21.60 7.27 85.32 134 COAL RIVER 541.56 940.00 83.33 19.86 7.76 51.43 136 Prosser 686.88 963.00 45.28 15.65 7.14 158.99 146 ORIELTON RIV 49.68 743.00 13.35 13.32 7.53 5.66 150 CARLTON RIVE 141.42 927.00 33.60 17.54 7.27 16.94 163 MOUNTAIN RIV 187.06 1456.00 27.37 63.28 9.01 6.48 164 North WestBa 95.68 1456.00 27.37 64.02 8.48 0.13 169 SNUG RIVULET 23.48 1423.00 10.22 54.99 8.46 0.03 172 BROWNS RIVER 58.15 1443.00 12.30 54.03 7.62 1.68
52 C: Cluster Methods, results comparison CATCH_ID RIVER Hydrological K CLUSTER Biophys Quad Model Cluster Hughes number Hughes class 58 Blythe 1 43 Boobyalla 1 170 Crooks Rt. 1 53 Curries 3 103 Great Lake 1 90 Huskisson 2 72 Johnston Ck. 3 159 Lake Pedder 2 63 Nelson Bay 1 105 Ouse 1 82 Savage 2 98 St. Pauls 1 127 Swanport 3 48 ANSONS RIVER 1 1 95 BREAK O"DAY 1 1 47 GREAT FOREST 1 1 96 MACQUARIE RIVER 1 1 93 NILE RIVER 1 1 84 SCAMANDER RIVER 1 1 94 MACKINTOSH RIVER 2 2 104 MURCHISON RIVER 2 2 75 FRANKLIN RIVER 3 3 163 MOUNTAIN RIVER 3 3 49 29 WELCOME RIVER 3 3 67 Gawler 3 28 1 102 Lake 1 38 1 74 Mersey 2 46 1 164 North WestBa 3 52 1 55 CAM RIVER 1 1 9 1 71 GEORGE RIVER 1 1 29 1 36 GREAT MUSSEL 1 1 30 1 31 MONTAGU RIVER 1 1 48 1 64 ANDERSONS CREEK 3 3 1 1 172 BROWNS RIVER 3 3 8 1 68 DON RIVER 3 3 20 1 122 MEREDITH RIVER 3 3 45 1 50 PIPERS RIVER 3 1 56 1 78 RUBICON RIVER 3 3 60 1 169 SNUG RIVULET 3 3 62 1 76 SUPPLY RIVER 3 3 68 1
53 C continued CATCH_ID RIVER Hydrological K CLUSTER Biophys Quad Model Cluster Hughes number Hughes class 39 TOMAHAWK RIV 3 1 70 1 117 Clyde 1 13 2 136 Prosser 3 57 2 106 APSLEY RIVER 1 1 2 2 150 CARLTON RIVER 3 3 10 2 134 COAL RIVER 3 3 15 2 128 JORDAN RIVER 3 3 36 2 146 ORIELTON RIVER 3 3 53 2 108 SWAN RIVER 3 3 69 2 115 Derwent 2 19 3 69 Hellyer 2 31 3 112 Henty 2 32 3 160 Huon 2 33 3 190 ESPERANCE RIVER 1 2 24 3 107 NIVE RIVER 1 1 50 3 142 TYENNA RIVER 1 1 72 3 52 ARTHUR RIVER 2 2 4 3 70 FORTH RIVER 2 2 26 3 119 FRANKLIN 2 2 27 3 131 GORDON RIVER 2 2 74 3 114 KING RIVER 2 2 37 3 91 PIEMAN RIVER 2 2 55 3 86 WHYTE RIVER 2 2 73 3 37 BLACK RIVER 1 1 6 4 35 DUCK RIVER 1 1 21 4 44 FLOWERDALE RIVER 1 1 25 4 45 INGLIS RIVER 1 1 34 4 79 NORTH ESK RIVER 1 1 51 4 40 RINGAROOMA 1 1 59 4 61 LEVEN RIVER 2 2 39 4 49 BRID RIVER 3 1 7 4 56 EMU RIVER 3 1 23 4 83 SOUTH ESK 2 1 66 4 and 1 85 MEANDER RIVER 2 1 44 4, 1, 3
54 D: Hughes (1987,1989)hydrological classification indexes.
Hughes (1987)
Derived 12 indexes from 4 flows, the flows were: annual, monthly, peak flow, low flow. Indexes were:
Annual COV (Cv)
Mean Annual Runoff (mm),
Coefficient of Skewness(Cs)
Serial Correlation of Annual Flows (ra)
Monthly flow COV(Cv monthly)
Monthly Peaks COV(Cv monthQmax)
Monthly low COV(Cv monthQlow)
Specific mean Peak Annual discharge(Qmax/m 3/s/k 2)
Index of variability of log peak flows(ly)
Coefficient of Skewness of log peak flows(g)
Specific Mean Low Annual Discharge(Qlow/m 3/s/k 2)
Index of Variability of Low Flows(lv)
A minimum record length of 15 years was used.
Matrix analysis was by principal coordinates and complete linkage cluster analysis with a stopping rule to give optimum number of groups.
Hughes 1989
In addition to the twelve variables used in the 1987 study four additional variables were derived for the 1989 study of Victorian catchments, these were:
Monthly Flow Duration Index (Dr) flow>=95% time/mean monthly flow
Spells/Year(Sy) total number low flow spells/record length (years) thv=5% mean daily flow
Mean Low Flow Spell duration(Sd)= sum of spell durations(days)/total number spells
Mean spell Severity(Ss) = mean deficit volume/mean threshold volume
Method was principle components analysis (with varimax rotation) and average linkage analysis
55 E: A Brief Explanation of Analysis Methods.
Cluster Analysis
Cluster analysis is a multivariate procedure for detecting natural groupings in data. It resembles discriminant analysis in one respect--the researcher seeks to classify a set of objects into subgroups although neither the number nor members of the subgroups are known. (SPSS, 2000)
This project employed clustering as investigative tools to:
• determine possible group numbers ( Hierarchical, complete linkage clustering)
• assign an initial classification to catchments based on hydrological variables (K-means clustering)
Hierarchical, Complete Linkage Clustering.
Hierarchical clustering produces clusters that are displayed in a tree. Initially, each object (case or variable) is considered a separate cluster. SYSTAT begins by joining the two "closest" objects as a cluster and continues (in a stepwise manner) joining an object with another object, an object with a cluster, or a cluster with another cluster until all objects are combined into one cluster.
Complete linkage uses the most distant pair of objects in two clusters to compute between- cluster distances. This method tends to produce compact, globular clusters.
Both hierarchical clustering and k-means clustering allow you to select the type of distance metric to use between objects. (SPSS, 2000)
K-means Clustering
K-means clustering splits a set of objects into a selected number of groups by maximising between-cluster variation relative to within-cluster variation. It is similar to doing a one-way analysis of variance where the groups are unknown and the largest F value is sought by reassigning members to each group.
K-means starts with one cluster and splits it into two clusters by picking the case farthest from the centre as a seed for a second cluster and assigning each case to the nearest centre. It continues splitting one of the clusters into two (and reassigning cases) until a specified number of clusters are formed. K-means reassigns cases until the within-groups sum of squares can no longer be reduced. (SPSS, 2000)
In the current project the number of groups to specify was selected by examination of the Hierarchical Cluster dendrogram.
Discriminant Analysis
Discriminant analysis is related to both multivariate analysis of variance and multiple regression. The cases are grouped in cells like a one-way multivariate analysis of variance and the predictor variables form an equation like that for multiple regression. In discriminant analysis, Wilks’ lambda, the same test statistic used in multivariate ANOVA, is used to test the equality of group centroids. Discriminant analysis can be used not only to test multivariate differences among groups, but also to explore which variables are most useful for discriminating among groups (SPSS, 2000)
56 In the current study the discriminant function is the model which describes each group via the contribution of the variables identified as the most significant. ie. those which best separate the pre defined groups.
The group model which provides the highest score in terms of the selected variables and model coefficients provides the classification for any previously unclassified catchment.
57