REG75 — A tool to estimate mean annual flow for the South West of Western

Department of Water

Surface Water Hydrology

October 2007 REG75 Surface Water Hydrology, no. 25

Department of Water 168 St Georges Terrace 6000

Telephone +61 8 6364 7600 Facsimile +61 8 6364 7601

For more information about this report, contact Water Resource Management Division, Department of Water.

ISBN 978-1-921094-68-2

October 2007

ii Department of Water Surface Water Hydrology, no. 25 REG75

Contents Contents ...... iii Summary ...... 1 1 Introduction...... 2 2 REG6 ...... 5 3 A simple water balance model...... 7 4 Data requirements...... 10 4.1 Catchment areas and surface water management areas and sub-areas...... 10 4.2 Rainfall...... 10 4.3 Evaporation...... 12 4.4 Clearing...... 12 4.5 Streamflow...... 13 5 Application to WA...... 16 6 Modified water balance model...... 20 6.1 Why don’t the Zhang curves work for WA?...... 20 6.2 Groupings/regions ...... 21 6.3 Calibration and application ...... 23 6.3.1 Modified Zhang — one group ...... 28 6.4 Model prediction and accuracy...... 29 6.4.1 Errors...... 29 6.4.2 Factors...... 31 6.4.3 Model validation...... 32 6.4.4 Sustainable yields and allocation limits...... 33 6.5 Comparison to REG6 ...... 35 7 Conclusions...... 36 Appendices...... 37 References ...... 50 Contributors...... 52

Appendices

Appendix A — ANUSPLIN fitting characteristics ...... 38 Appendix B — Streamflow gauges ...... 39 Appendix C — Spatial distribution of streamflow gauges ...... 48 Appendix D — Statistics ...... 49

Department of Water iii REG75 Surface Water Hydrology, no. 25

Figures

Figure 1 Estimation of sustainable yield with increasing use/demand...... 2 Figure 2 Runoff-rainfall relationship with respect to clearing in the REG6 model .6 Figure 3 Runoff-rainfall with respect to clearing for the period 1975 to 2003...... 6 Figure 4 Ratio of mean annual evapotranspiration to rainfall as a function of the index of dryness (E o/P) and Zhang curves for forest and pasture ...... 8 Figure 5 Mean annual rainfall isohyets (1975 to 2003)...... 11 Figure 6 Extent of native vegetation (NLWRA, 2001)...... 13 Figure 7 Comparison of modelled and observed mean annual flow for application of the Zhang model to south-west WA...... 17 Figure 8 Comparison of modelled and calculated evapotranspiration for application of the Zhang model to south-west WA ...... 17 Figure 9 Relationship between annual evapotranspiration and rainfall for south- west WA with Zhang curves for forested and grassed catchments overlain...... 18 Figure 10 Ratio of mean annual actual evapotranspiration to rainfall as a function of the index of dryness (E o/P) with Zhang curves overlain ...... 20 Figure 11 Modified Zhang curves for forest and pasture ...... 21 Figure 12 Pan evaporation E o versus mean annual actual evaporation grouped by hydrographic basins ...... 22 Figure 13 Group 1 and Group 2 based on hydrographic basins...... 22 Figure 14 Comparison of observed and modelled mean annual flow (Group 1)...24 Figure 15 Comparison of observed and modelled mean annual runoff (Group 1) 24 Figure 16 Comparison of observed and modelled mean annual flow (Group 2)...25 Figure 17 Comparison of observed and modelled mean annual runoff (Group 2) 25 Figure 18 Residuals plot of the mean annual flow data against catchment area..26 Figure 19 Spatial distribution of difference in observed and modelled values ...... 29 Figure 20 Residuals plot of the mean annual flow data for the gauging station locations across the south west of WA...... 30 Figure 21 Example of the development of factors for surface water management sub-areas using the difference in observed to modelled mean annual flow at each gauging station...... 31 Figure 22 Allocation limits (AL) corresponding to level of use, mean annual flow and sustainable yield...... 33 Figure 23 Sites where the REG75 allocation limit exceeds the observed sustainable yield and mean annual flow...... 34

iv Department of Water Surface Water Hydrology, no. 25 REG75

Tables

Table 1 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the Zhang application to south west WA...... 18 Table 2 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application to Group 1 ...... 27 Table 3 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application to Group 2 ...... 27 Table 4 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application as one group ...... 28 Table 5 Percent difference of REG75 estimates and observed mean annual flow for validation catchments...... 32 Table 6 Error margins between observed and modelled mean annual flows for REG75 and REG6...... 35 Table 7 Comparison between REG75 and REG6 approaches...... 35

Department of Water v

Surface Water Hydrology, no. 25 REG75

Summary

The sustainable yield is the maximum quantity of water available for abstraction from a surface water resource after environmental water requirements have been satisfied. In areas where the level of surface water use is low, estimates of the notional sustainable yield are based on regional models and have typically been estimated as a function of the mean annual flow. The Department of Water has developed a simple regional model to determine the mean annual flow, and hence the notional sustainable yields, for systems in the south west of Western Australia with low levels of surface water use.

REG75 is a simple regional mean annual flow model that provides an estimate of mean annual flow from a catchment, for the period 1975 to 2003, based on land clearing and rainfall data for the same period. REG75 is based on a model developed by Zhang, Dawes and Walker (1999, 2001) which was developed and calibrated against research-catchment data from around the world. The Zhang model was modified to suit the vegetation and soil profile characteristics of south west Western Australian catchments. The REG75 model replaces the widely used REG6 model and can be used to determine the notional sustainable yields for surface water management areas from Esperance to .

Department of Water 1 REG75 Surface Water Hydrology, no. 25

1 Introduction

In Western Australia, the Department of Water outlines the processes to be used in determining sustainable yields from surface water resources. The sustainable yield is the maximum quantity of water available for abstraction from a surface water resource after environmental water requirements have been satisfied.

The National Land and Water Resources Audit (2001) identified levels of resource investigation (R1 to R4) based on the level of use (C1 to C4). In areas where the level of surface water use is low (C1), estimates of sustainable yield are based on regional models and the term ‘notional sustainable yield’ is used. The notional sustainable yield for the south west of WA has been estimated as 60% of the mean annual flow. As the level of surface water use increases towards highly allocated systems, then so too does the intensity of investigations required to determine the sustainable yield (Figure 1).

Mean Annual Flow

Uncertainty in sustainable yield

Sustainable Yield Volume

C1 C2 C3 C4

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% Proportion of sustainable yield allocated

Figure 1 Estimation of sustainable yield with increasing use/demand

The Department of Water has been working to identify the priorities associated with surface water management in Western Australia. This process has led to the endorsement of a standard, 28-year data period (1975 to 2003) for surface water management decisions in the south west of WA as defined in the water resource allocation note: Adoption of a standard data period for hydrologic studies that guide surface water allocation decisions in the south west of Western Australia (Loh, 2004). This accounts for the reduction in rainfall and subsequent reduction in runoff that has been observed in the south west over this period in comparison to long-term averages. There is evidence of a further reduction in rainfall in more recent years, as of approximately 1997 onwards. The period for which we have data however is insufficient to justify if this period is statistically significant for incorporation into

2 Department of Water Surface Water Hydrology, no. 25 REG75

surface water management decisions. In addition, new surface water management areas and sub-areas have been developed throughout the whole State. The areas are primarily based on hydrological boundaries and have been determined in conjunction with the Department of Water’s regional officers, who are responsible for surface water licensing, to address their operational requirements. The demand for water resource assessment occurs largely in the south west of WA and hence the majority of work has focused on this area. In terms of water resource assessment, the south west of WA covers an area from Australian Water Resources Council (AWRC) basin 601 – 619, the South West Drainage Division, to AWRC basin 701, the Drainage Basin, i.e. Esperance to Geraldton.

Until now the Department of Water uses REG6, an internally-developed regional model, to estimate annual sustainable yields for the south west of WA. REG6 was calibrated using: • mean annual flows from 1962 to 1996; • long-term isohyet rainfall from 1907 to 1979; • clearing estimates based on topographic maps.

With an increasing demand for water resource use it was intended that REG6 be replaced by a more defensible process for the period 1975 to 2003 that still provided quick and conservative estimates of sustainable yield. It was anticipated that this would be an interim procedure while more detailed regional models were being developed.

To this end, REG75 was developed to predict mean annual flows in ungauged catchments in the south west land division of Western Australia (AWRC basins 601- 701) for the standard time period 1975 to 2003. REG75 is a simple regional model based on a model developed by Zhang et al. (1999, 2001) and modified to suit south west Western Australian catchments. The Zhang et al. (1999, 2001) model was originally developed to assess the effect of vegetation changes on the water balance but the authors identified its potential for water yield modelling.

Mean annual flow (ML/a) data from as many unregulated streamflow gauging stations as possible was summarised for the standard time period. A new rainfall surface was developed for this period. Reference information was collated on the catchment characteristics. This included: • centroidal catchment rainfall: the average annual rainfall in mm taken at the catchment centroid; • catchment area: total catchment area in square kilometres; • catchment clearing: estimated percentage of clearing in the catchment.

Catchment runoff (mm) was then calculated by dividing the mean annual flow by the catchment area.

Department of Water 3 REG75 Surface Water Hydrology, no. 25

The model is appropriate for catchments in basins 601–701 that do not have internally draining sub-catchments within them. The model was calibrated using a range of catchment characteristics. The calibration data set consisted of catchments ranging in size from 0.1 to 18,700 km2. The catchments varied from 100% cleared to fully forested. Rainfall ranged from 1200 mm at the coast decreasing to 260 mm inland. Recorded mean annual flows varied from 0.5 ML to 527,000 ML and mean annual runoffs ranged from 0.04 mm to 406 mm. As REG75 is based on observed data it has the advantage that the input data (mean annual rainfall and percentage of catchment cleared) required to model flow is readily available at the required catchment scale. The 10 and 90 percentile differences between the estimated mean annual flows and the measured mean annual flows are -39–187% respectively. In order to reduce this error, factors were produced by comparing the observed runoff at the gauges to the modelled runoff.

4 Department of Water Surface Water Hydrology, no. 25 REG75

2 REG6

REG6 was developed by plotting catchment runoff against centroidal rainfalls (Figure 2). Clear divisions based on catchment clearing could be seen and from these a non- linear relationship was developed.

This plot was re-created using runoff, rainfall and clearing values for the period 1975 to 2003 (Figure 3). The divisions based on catchment clearing were not as apparent for this time period, particularly for low levels of clearing. Therefore a decision was made to produce a simple water balance model for the south west of Western Australia.

Department of Water 5 REG75 Surface Water Hydrology, no. 25

500

450 Clearing (%) 0 400 1-5 350 6-25 26-60 300 65-100 250

200

150 Mean Annual Runoff (mm) Mean Annual Runoff 100

50

0 0 200 400 600 800 1000 1200 1400 1600 Rainfall

Figure 2 Runoff-rainfall relationship with respect to clearing in the REG6 model

500

450 Clearing (%) 0 400 1-5 350 6-25 26-60 300 61-100 250

200

150 Mean Annual Runoff (mm) Mean Annual Runoff 100

50

0 0 200 400 600 800 1000 1200 1400 1600 Rainfall

Figure 3 Runoff-rainfall with respect to clearing for the period 1975 to 2003

6 Department of Water Surface Water Hydrology, no. 25 REG75

3 A simple water balance model

In order to predict mean annual flows (MAF) in ungauged catchments a simple, annual, water balance model was required. Bari, Smettem and Sivapalan (2005) inferred that relatively simple equations are sufficient to capture the most important processes of catchment hydrologic response on an annual time-step. At this spatial and temporal scale a simple method needs to be used to capture the overall response of a catchment based on the analysis and interpretation of observed data rather than using a complicated physically based modelling approach.

By assuming that the change in catchment soil water storage over time is negligible, the mean annual streamflow is calculated as the difference between the mean annual rainfall and the mean annual evapotranspiration. The evapotranspiration component therefore accounts for all losses in the system. This simplified water balance for a catchment can be written as:

Q = R – ET Equation 1

Where Q is streamflow, R is rainfall and ET is evapotranspiration.

Evapotranspiration is an important component of the hydrological cycle. The physics of this complex process are well understood, however the challenge lies in simplifying this process for modelling to allow the practical prediction of evapotranspiration values at the catchment scale.

A number of relationships have been developed based on the following two assumptions:

1. Under very dry conditions, evapotranspiration is limited by water availability (i.e. rainfall). Potential evapotranspiration exceeds precipitation and annual actual evapotranspiration equals annual precipitation.

2. Under very wet conditions, evapotranspiration is limited by available energy (i.e. potential evaporation). Annual precipitation exceeds annual potential evapotranspiration and actual evapotranspiration asymptotically approaches potential evapotranspiration.

Budyko (1958; as cited in Zhang et al., 2001) translated these relationships into the limits shown in Figure 4.

Department of Water 7 REG75 Surface Water Hydrology, no. 25

1

0.8

0.6 ET/P 0.4

Budyko Limits 0.2 Zhang - Evaporation (forest) Zhang - Evaporation (pasture)

0 0 2 4 6 8 10 E /P o Figure 4 Ratio of mean annual evapotranspiration to rainfall as a function of the index of dryness (E o/P) and Zhang curves for forest and pasture

On the basis of these considerations, Zhang et al. (1999, 2001) developed a simple, two-parameter model that can be used to estimate the mean annual evapotranspiration (ET):

E 1+ w o ET = P Equation 2 P E P 1+ w o + P Eo where: ET is annual evapotranspiration (mm)

Eo is potential evapotranspiration (rainfall scaling parameter)

P is long-term annual rainfall (mm)

w is the plant available water coefficient

Zhang et al. (1999, 2001) posits that applying the above formula for forested and grassed catchments encapsulates the range of possible land uses. The overall equation for evapotranspiration then becomes:

ET = fET f + (1-f)ET h Equation 3

Where ET is total annual evapotranspiration (mm), f is percentage forest cover, ET f is evapotranspiration from forests (mm) and ET h is evapotranspiration from herbaceous

8 Department of Water Surface Water Hydrology, no. 25 REG75

plants (cleared areas – generally pasture) (mm). The potential evapotranspiration and plant-available water coefficient are constants based on a worldwide data set however the values are different for forested and herbaceous vegetation. The two ‘Zhang curves’ for forested and herbaceous data are plotted in Figure 4.

The mean annual water balance model as described in Zhang et al. (1999, 2001) is then the simplified water balance (Eqn 1) with the mean annual evapotranspiration component estimated using the simple, two-parameter evapotranspiration model by Zhang et al. (1999, 2001) (Eqn 2). For the purpose of this report, this combination of equations has been termed the ‘Zhang model’.

The Zhang model was calibrated to over 250 catchments worldwide and shows that for a given forest cover the mean annual evapotranspiration can be predicted at the catchment scale. For evapotranspiration, the mean absolute error (MAE) between the observed and modelled was 4%. The correlation coefficient was 0.92 and the best-fit slope through the origin was 1.04. The MAE in the ratio of evapotranspiration to rainfall (ET/P) between the observed and modelled was 5% and the root mean square error (RMSE) was 6%. A scatterplot of the data resulted in most of the forested catchments plotted around the upper curve in Figure 4 and grassed catchments plotted around the lower curve with mixed vegetation catchments in the middle.

The estimated ET can then be changed into a runoff estimate, by assuming that the mean annual runoff is equal to the mean annual rainfall minus the mean annual ET as per the simple water balance equation described previously (Eqn 1). Bradford, Zhang and Hairsine (2001) used the Zhang model to estimate the impact of land-use changes on catchment water yield in the Murray–Darling Basin, and produced an R 2 of 0.643 with the best fit slope through the origin of 1.03. There was large scatter in the results with a tendency for the model to overestimate water yield in low rainfall catchments. The error in estimated runoff as a percentage of mean annual rainfall ranged between 5–16%.

On an annual time scale, Bari et al. (2005) posited that the gross hydrological behaviour of catchments is realistically encapsulated in the Zhang curves (1999, 2001) as they are derived from observed data. Two Western Australian catchments (Salmon and Wights) were part of the data set used in developing the Zhang curves. Bari et al. (2005) undertook an analysis of the hydrological response of 10 catchments in Western Australia and this showed that Zhang et al’s (1999, 2001) ‘world forest curve’ significantly underestimated evapotranspiration in comparison to the observed evapotranspiration data for forested catchments. This may be accounted for because Jarrah is extremely deep rooted (~30 m) and has access to deep soil moisture over the summer dry period (Silberstein, 1999, as cited in Bari et al., 2005). This is unaccounted for in the plant available water coefficient ( w). This study indicates that there may be subtle departures from the gross world curve that are important for describing local hydrological phenomena.

Department of Water 9 REG75 Surface Water Hydrology, no. 25

4 Data requirements

To calibrate the water balance model to catchments in the south west of WA and estimate catchment runoff, spatial datasets of rainfall, evaporation and forest cover were required. Mean annual streamflow data was also required. 4.1 Catchment areas and surface water management areas and sub-areas

Hydrographic gauging station catchment boundaries within the 12 drainage basins of the south west were delineated prior to this study. The gauging station catchments are a summation of all the upstream hydrographic sub-catchments that contribute flow every year.

Surface water management areas and sub-areas had also been derived, based on hydrographic catchment boundaries and grouped by similar management issues, to easily address operational requirements. The sub-areas were derived by identifying areas with high management needs due to either current, or the potential for future, large allocation demand or environmental issues. The surface water management sub-area data was developed in order to give a clear understanding of surface water availability and to provide management tools to make sound water allocation and natural resources management decisions. REG75 was used to derive mean annual flow for each sub-area. 4.2 Rainfall

To account for the observed step change in rainfall in the south west of WA, new mean annual rainfall isohyets were developed. Previously long-term rainfall isohyets (1909–1979) were used. To develop the isohyets, a three-dimensional spline surface was fitted to mean annual SILO rainfall values at 776 rainfall stations, averaged over the period 1975–2003. The SILO Patched Point Dataset is a dataset combining original Bureau of Meteorology daily rainfall measurements for a particular meteorological station with infilling of any gaps in the record using interpolation methods. Mapping the isohyets of rainfall over WA allowed for the calculation of the rainfall estimates at locations other than the existing stations. A grid was fitted to the SILO rainfall points using the ANUSPLIN program suite Version 4.2 developed by Hutchinson (2003). As part of the surface fitting approach, two independent spline variables, latitude and longitude, were used. Rainfall is generally influenced by factors such as elevation and distance from the coast. Therefore elevation was used as an independent covariate in the fitting as recommended by Hutchinson (2003). This was used to obtain improved rainfall estimates in areas where there was a low density of stations. An appropriate grid size was trialled to adequately describe the spatial variation of annual rainfalls. This resulted in a 0.1 degree resolution digital elevation model being used (approximately 11 km grid spacing) with the data specified at the grid centre. The surface fitting procedure was optimised based on the

10 Department of Water Surface Water Hydrology, no. 25 REG75

guidelines provided in Appendix A. The surfaces were converted to grids for use in the Geographic Information System, ArcGIS and then isohyets were defined at 10 mm and 50 mm intervals. In some cases, the rainfall isohyets were manually manipulated to best fit the most likely rainfall patterns of the area, based on surrounding Bureau of Meteorology station data for the period 1975–2003, where the density of SILO stations was low or the ANUSPLIN fitting did not produce enough definition. An objective average for each catchment was generated in ArcGIS. This technique of ‘data smoothing’ resulted in values at point locations differing slightly from actual recorded SILO values in high-density rain gauge areas but provided a useful means to estimate rainfall in data-sparse areas. The resulting 50 mm isohyets are shown in Figure 5.

Figure 5 Mean annual rainfall isohyets (1975 to 2003)

To calibrate REG75, centroidal rainfall (mm) was calculated for the hydrographic catchments for each gauging station. For application of the REG75 model, centroidal rainfall was calculated at each Surface Water Management Sub-area.

Department of Water 11 REG75 Surface Water Hydrology, no. 25

4.3 Evaporation

Zhang et al. (1999, 2001) identified E o as potential evapotranspiration and calculated this using the equation of Priestley and Taylor (1972, as cited in Zhang et al., 1999, 2001). The index of dryness is calculated as E o/P and it is common for E o to be interchangeably referred to as either pan evaporation, potential evaporation or potential evapotranspiration. For this study, values of E o, and subsequently the index of dryness, were calculated using two methods.

1. Bureau of Meteorology areal potential evapotranspiration derived for the period 1961–1990

2. Mean annual pan evaporation isopleths derived for the period 1975–2003 using mean annual SILO pan evaporation values for the same 776 rainfall stations as used in the rainfall analysis. The same ANUSPLIN fitting procedure was used as for the rainfall isohyets but with elevation as an independent variable and a 0.008 degree resolution digital elevation model.

Mean annual pan evaporation values (mm) were then identified at the centroid of each hydrographic gauging station catchment for use in calibration (Section 6.1). 4.4 Clearing

Clearing information was obtained from the extent of native vegetation mapping reported in the National Land and Water Resources Audit 2001 (NLWRA, 2001) (Figure 6). The data set mapped remnant vegetation in Western Australia and was originally derived from 1995 Landsat TM satellite imagery. The imagery was corrected using digital aerial photography from 1996 to 1999 and was checked against field survey records. The aerial photography is accurate to +/- 3.13 m. The NLWRA extent of native vegetation did not cover the whole of Basins 601-701 (Figure 6), however the eastern edge where the coverage ended was generally remnant vegetation, and therefore it was assumed that any area beyond the coverage was 100% forested. It was also assumed that the level of clearing was constant from 1975 to 2003. For calibration purposes, the percentage of area cleared was estimated for the hydrographic catchments for each gauging station and for application of the REG75 model, clearing values were estimated for each Surface Water Management Sub-area.

12 Department of Water Surface Water Hydrology, no. 25 REG75

Figure 6 Extent of native vegetation (NLWRA, 2001) 4.5 Streamflow

Mean annual flow was required at as many gauging stations that are not affected by regulation as possible. A regulated river refers to the section of river that is downstream of a major storage area from which supply of water to irrigators or other users can be regulated or controlled. In WA these water stores are typically operated by the Water Corporation. An unregulated river implies no storage, however if the storage is significantly smaller than the annual flow the river is assumed to be unregulated. This includes those rivers where the flow is controlled by minor dams or weirs.

Flow is defined as a volume of water that passes a point over a period of time (e.g. ML/a or m 3/s). Flow is usually measured as a water velocity multiplied by a cross sectional area. Mean annual flow is the average or mean yearly flow in a stream. This is the arithmetic mean of a data set (sum of annual flows divided by the number of years).

Department of Water 13 REG75 Surface Water Hydrology, no. 25

A total of 287 streamflow stations were identified for the analysis. Infilling of monthly flow data was undertaken for small gaps in the record from 1975 onwards by correlating with a physically close station. If a gap covered the period from May to July, or more than one year, it was generally not filled as it was considered that these estimates would contain a significant amount of uncertainty.

At some stations, the record period was less than the standard 1975–2003 time period. Therefore the data was extended so it could be analysed for the standard period. The data was assumed to be stationary (i.e. no trends for change in water yield over the period of record). Mean annual flow is required for the analysis so it was not necessary to actually construct the extended data series from 1975 to 2003. Rather record augmentation was used by cross correlating a short record with a longer nearby station with which observations in the short record were highly correlated. This also had the effect of eliminating the bias between high flow/low flow years in short-term records. The Matalas-Jacobs augmented record estimator of the mean is (Stedinger, Vogel and Foufoula-Georgiou, 1993):

n µˆ = y + 2 b(x − x ) 1 + 2 1 n1 n2

Valid when: n1 >= 4; and, the cross correlation is 0.70 or greater.

Where:

x is the mean flow record at the long-record site

y is the mean flow record at the short-record site

subscript 1 denotes the sample mean calculated for the period of concurrent record

subscript 2 denotes the sample mean for the long record site x calculated using only the observations for which there is no corresponding y

n1 is the number of concurrent observations

n2 is the number of additional observations available at the long record site x; and,

 s  =  y1  b rho xy    sx1 

Where:

rho is the correlation coefficient

s is the standard deviation (square root of variance)

14 Department of Water Surface Water Hydrology, no. 25 REG75

The variance was also calculated, in order to estimate the standard deviation, using the Matalas-Jacob augmented record estimator of the variance as shown below:

n variance = s 2 + 2 b 2 ()s 2 − s 2 y1 + x2 x1 n1 n2

Valid when: n1 > 6; and, the cross correlation is greater than 0.85.

This resulted in 244 stations with six years or more data for which the record augmentation was performed. Of these stations, 79 stations (32%) had a full period of record from 1975 to 2003. Appendix B details the stations used in the analysis, their length of record from 1975 to 2003 (whole years of data only with gaps filled), and the station used for record augmentation. The spatial distribution of the stations is shown in Appendix C.

The mean annual runoff for each catchment was then determined where mean annual runoff (mm) = mean annual flow (ML) / catchment area (km 2).

Department of Water 15 REG75 Surface Water Hydrology, no. 25

5 Application to WA

The Zhang model was directly applied to catchments in the south west of WA where the mean annual streamflow was known so that the model could be validated before its application in ungauged areas. Information on catchment area, centroidal rainfall and clearing were used as inputs to the model.

The original parameter values of Zhang et al. (1999, 2001) were used for calculating the evapotranspiration for forested and cleared catchments. To provide a comparison between the direct application to WA and to Zhang et al’s (1999, 2001) original development of the model, the mean absolute error (MAE) in the ratio of evapotranspiration to rainfall (ET/P) between the observed and modelled was 8% and the root mean square error (RMSE) was 9%. For evapotranspiration, the MAE between the observed and modelled was 58 mm. The correlation coefficient was 0.92 and the best fit slope through the origin was 0.94.

The estimate of ET was then changed into a mean annual runoff and mean annual flow estimate as per the simple water balance equation (Eqn 1) described previously. The comparison between observed and modelled values shows that the Zhang model is not suitable for direct application to Western Australia. With mean annual flow as an example, the model produced an R 2 of 0.85 which implies a strong relationship between observed and modelled flows. However the best-fit slope through the origin of 1.9 shows that the R 2 value is insensitive to proportional differences, with the modelled flows effectively twice that of the observed values (Figure 7). There was large scatter in the results with a tendency for the model to underestimate evapotranspiration (Figure 8) and overestimate flow, particularly in highly cleared areas, across all rainfall zones (Figure 9).

16 Department of Water Surface Water Hydrology, no. 25 REG75

1200

y = 1.90x 1000 R2 = 0.88

800

600 1:1 line

400

Modelled Modelled annual mean flow (GL) 200

+/-10% Confidence Limits 0 0 100 200 300 400 500 600 Observed mean annual flow (GL)

Figure 7 Comparison of modelled and observed mean annual flow for application of the Zhang model to south-west WA

1200 1:1 line

1000

800 y = 0.94x R2 = 0.92 600

400

200 Modelled evapotranspiration (mm) evapotranspiration Modelled

0 0 200 400 600 800 1000 1200 Calculated evapotranspiration (observed rainfall less runoff) (mm)

Figure 8 Comparison of modelled and calculated evapotranspiration for application of the Zhang model to south-west WA

Department of Water 17 REG75 Surface Water Hydrology, no. 25

1400

Evapotranspiration = Rainfall 1200

1000

800

600

400 Zhang Curve Forest Zhang Curve Pasture

(observed rainfall less runoff) (mm) runoff) less rainfall (observed 200 1:1 line

Calculated mean annual evapotranspiration evapotranspiration annual mean Calculated South-west WA data 0 0 200 400 600 800 1000 1200 1400 Mean annual rainfall (mm)

Figure 9 Relationship between annual evapotranspiration and rainfall for south-west WA with Zhang curves for forested and grassed catchments overlain

To confirm that direct application of the Zhang model is unsuitable, several other statistics were assessed, including the coefficient of efficiency ( ε) (Nash and Sutcliffe, 1970; as cited in Legates and McCabe, 1999), index of agreement (d) (Willmot, 1984; as cited in Legates and McCabe, 1999), the mean absolute error (MAE) and the root mean square error (RMSE) (Appendix C). The mean and standard deviations of the observed and modelled values were also compared (Table 1).

Table 1 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the Zhang application to south west WA

Mean Annual Runoff (mm) Mean Annual Flow (GL) Observed Modelled Observed Modelled Average 94 137 27 58 Standard Deviation 89 74 62 124 Coefficient of Determination (r 2) 0.69 0.88 Mean Absolute Error (MAE) 58 32 Root Mean Square Error (RMSE) 68 78 Coefficient of Efficiency ( ε) 0.41 -0.57 Modified Coefficient of Efficiency ( ε 1) 0.23 -0.25 Index of Agreement (d) 0.83 0.83 Modified Index of Agreement (d 1) 0.59 0.64

18 Department of Water Surface Water Hydrology, no. 25 REG75

The misleading r2 value for the mean annual flow is more sensitive to outliers (Figure 7) than to observations near the mean (Table 1) with the modelled average flow twice that of the observed average. The MAE and RMSE, which measure the average size of the prediction errors, are extremely large for the mean annual flow and more than half the average for the mean annual runoff. Particularly in the mean annual flow the RMSE is significantly greater than the MAE indicating that there is large variance in the differences between observed and modelled flows. The coefficient of efficiency (ε) and index of agreement (d) are also low indicating that the model is not a good predictor. The negative value of ε calculated for the mean annual flow is due to the RMSE being significantly greater than the observed standard deviation (a model with no variability would have an RMSE equal to the observed standard deviation). Owing to the squared differences (Legates and McCabe, 1999), these two measures are also sensitive to outliers, so modified measures were also calculated ( ε 1 and d 1) by replacing squared terms with absolute values. Overall these measures were lower confirming again that the direct application of the Zhang model does not produce favourable results.

Interestingly, other studies throughout Australia have encountered poor fits to the Zhang curves. Yee Yet and Silburn (as cited in Evans, Gilfedder and Austin, 2004) concluded that the curves overestimate ET for forests with large scatter about the curve and significantly underestimate ET for native grasses. Evans et al. (2004) concluded that for catchments in NSW with rainfall less than 700 mm/yr, Zhang provides reasonable estimates of evapotranspiration, however, the estimates diverge as rainfall increases. Nordblom et al. (2005) showed that the Zhang curves under predicted ET where annual rainfall was low, as in many Australian settings. Suitable estimates of catchment water yield were achieved by Nordblom et al. (2005) by adjusting to Australian data the parameters of Zhang et al’s (1999, 2001) evapotranspiration equation (Eqn 2).

It is determined that using the Zhang curves ‘as is’ will introduce a potentially large source of error into the process of estimating sustainable yields. The results show that although there may be similarities with the Zhang curves within the range of data used in the worldwide dataset there appears to be departures between the Zhang curves and modelled outputs where specific information has been used as Bari et al. (2005) predicted.

Department of Water 19 REG75 Surface Water Hydrology, no. 25

6 Modified water balance model 6.1 Why don’t the Zhang curves work for WA?

For each gauging station the mean annual actual evapotranspiration was determined (where ET is centroidal rainfall minus mean annual runoff). The ratio of actual evapotranspiration to rainfall (ET/P) was then derived. The dryness index (E o/P) was calculated (using the evaporation contours derived from SILO data and the Bureau of Meteorology areal potential evapotranspiration, both divided by rainfall). A plot of ET/P versus E o/P for south-west WA was created and the Zhang curves overlain (Figure 10).

1.00

0.80

0.60 ET/P 0.40 Data (Eo = areal potential evapotranspiration) Data (Eo = SILO pan evaporation) 0.20 Budyko (1985) Limits of Evapotranspiration Zhang (1999) Evapotranspiration (forest) Zhang (1999) Evapotranspiration (pasture) 0.00 0 2 4 6 8 10 E /P o Figure 10 Ratio of mean annual actual evapotranspiration to rainfall as a function of the index of dryness (E o/P) with Zhang curves overlain

Budyko (1974; as cited in Milly, 1994, Zhang et al., 1999, 2001) noted that scatter around curves, such as Zhang’s model, is considerable. A number of empirical relationships have been developed for estimating annual evapotranspiration (Schreiber, 1904, Pike, 1964, Budyko, 1974; all as cited in Zhang et al., 1999, 2001) all of which are in agreement with each other but can not account for the large scatter. It appears that not only is there a large amount of scatter about the curve for the Western-Australian data but the Zhang curves tend to underestimate the ratio of ET/P, particularly for cleared catchments. There also appears to be a cluster of data (denoted in the green oval in Figure 10) that is poorly described by Zhang et al’s function (Eqn 2). This clustering is due to the number of sites that fall within a similar Eo/P band with high values of actual evapotranspiration. Similar results were

20 Department of Water Surface Water Hydrology, no. 25 REG75

apparent using both the SILO pan evaporation data and the Bureau of Meteorology areal potential evapotranspiration. As many of the data points fall outside the range of the two curves it is evident that a large number of points are misrepresented. Nordblom et al. (2005) adjusted the parameter values of Zhang et al. (1999) to capture as many data points as possible while minimising the residuals. This approach is considered unsatisfactory due to the large scatter in the data. Therefore to encompass the range of data it was necessary to introduce a step change with a transition from linear to the modified Zhang curves (e.g. Figure 11). It was decided to use the SILO pan evaporation data to calibrate the Zhang model to south-west WA as they were derived for the period 1975–2003 and exhibited only minor differences from the areal potential evapotranspiration.

1

0.8

0.6

ET/P Data 0.4 Zhang (1999) Evaporation (forest)

Modified evaporation (forest)

0.2 Zhang (1999) Evaporation (pasture)

Modified evaporation (pasture) 0 0 2 4 6 8 10 E /P o Figure 11 Modified Zhang curves for forest and pasture

6.2 Groupings/regions

Recorded SILO pan evaporation (Eo) versus mean annual actual evapotranspiration (ET) was plotted by the AWRC hydrographic drainage basins (Figure 12). This showed two distinct groupings; one with 157 stations across the south coast, south- west and inland regions (Group 1) and the other with 87 stations from a western- coastal group (Group 2) (Figure 13). Hydrographic basin 614 was divided between both groups as per the demarcation of the surface water management areas.

Department of Water 21 REG75 Surface Water Hydrology, no. 25

1200

1000 601 602 603 604 800 605 606 607 608

600 609 610 611 612

400 613 614 (rain -runoff) (mm) 615 616 617 701 200 ETmean annual evapotranspiration

0 0 500 1000 1500 2000 2500 3000

Eo SILO pan evaporation (mm)

Figure 12 Pan evaporation E o versus mean annual actual evaporation grouped by hydrographic basins

Figure 13 Group 1 and Group 2 based on hydrographic basins

22 Department of Water Surface Water Hydrology, no. 25 REG75

6.3 Calibration and application

The modified Zhang model was re-calibrated using Western-Australia data (as derived in Chapter 3). Estimation of model parameter values of plant available water coefficient and potential evapotranspiration were obtained by a least-squares fit to the data for both groups for forested and cleared areas. The modelled values using the modified Zhang model appeared to be in better agreement with the observed values than the direct application of the Zhang model (Chapter 5).

Again, to provide a comparison to the Zhang et al. (1999, 2001) model and the application of the Zhang model to Western Australia, error statistics in the ratio of evapotranspiration to rainfall (ET/P) between the observed and modelled were calculated. The mean absolute error (MAE) was 4% and the root mean square error (RMSE) was 5% for both Group 1 and Group 2. For evapotranspiration for Group 1, the MAE between the observed and modelled was 32 mm. The correlation coefficient was 0.90 and the best-fit slope through the origin was 0.989. For evapotranspiration for Group 2, the MAE between the observed and modelled was 34 mm. The correlation coefficient was 0.95 and the best-fit slope through the origin was 0.997.

The estimate of ET was then changed into a mean annual flow and mean annual runoff estimate as per Zhang et al’s (1999, 2001) simple water balance equation described previously. The comparison between observed and modelled values (Figure 14 and 15 – Group 1 and Figure 16 and 17 – Group 2) shows that the modified Zhang model is a much better fit than a direct application of the Zhang model (Chapter 5).

Department of Water 23 REG75 Surface Water Hydrology, no. 25

600 1:1 line

500

y = 0.73x 400 R2 = 0.89

300

200

Modelled mean annual flow (GL) 100 +/-10% Confidence Limits 0 0 100 200 300 400 500 600 Observed mean annual flow (GL)

Figure 14 Comparison of observed and modelled mean annual flow (Group 1)

500

450 1:1 line 400 y = 0.98x 350 R2 = 0.77 300

250

200

150

100

Modelled mean annual runoff (mm) 50 +/-10% Confidence Limits 0 0 50 100 150 200 250 300 350 400 450 Observed mean annual runoff (mm)

Figure 15 Comparison of observed and modelled mean annual runoff (Group 1)

24 Department of Water Surface Water Hydrology, no. 25 REG75

450 1:1 line 400

350

300 y = 0.72x R2 = 0.88 250

200

150

100 Modelled mean annual flow (GL) 50 +/-10% Confidence Limits 0 0 50 100 150 200 250 300 350 400 450 Observed mean annual flow (GL)

Figure 16 Comparison of observed and modelled mean annual flow (Group 2)

350 1:1 line

300 y = 0.84x 250 R2 = 0.78

200

150

100

Modelled mean annual runoff (mm) 50 +/-10% Confidence Limits 0 0 50 100 150 200 250 300 350 Observed mean annual runoff (mm)

Figure 17 Comparison of observed and modelled mean annual runoff (Group 2)

Department of Water 25 REG75 Surface Water Hydrology, no. 25

The model appears to demonstrate a bias toward under predicting mean annual flow in larger catchments and over predicting mean annual flow in small catchments (Figure 14 and Figure 16) however exhibits less bias in terms of predicting mean annual runoff (Figure 15 and Figure 17). The plot of mean annual flow residuals versus catchment area shows that the model is biased for large catchments (Figure 18). This indicates that the model should ideally be used for predicting mean annual flow in catchments with areas less than approximately 3000 km 2.

250

200

150

100

50

0 Mean annual flow residuals annual Mean (GL) -50

-100 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Area (km 2)

Figure 18 Residuals plot of the mean annual flow data against catchment area

Using mean annual flow as a comparison, the model produced r2 values (Table 2) which were more favourable than the direct application of Zhang. There was still large scatter in the results.

In order to evaluate if the modification was a significant improvement over the direct application of the Zhang model several statistics were assessed. Again, this included the coefficient of efficiency ( ε) (Nash and Sutcliffe, 1970; as cited in Legates and McCabe, 1999), index of agreement (d) (Willmot, 1984; as cited in Legates and McCabe, 1999), the mean absolute error (MAE) and the root mean square error (RMSE) (Appendix B). The mean and standard deviations of the observed and modelled values were also compared (Table 2 – Group 1 and Table 3 – Group 2).

26 Department of Water Surface Water Hydrology, no. 25 REG75

Table 2 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application to Group 1

Mean Annual Runoff (mm) Mean Annual Flow (GL) Observed Modelled Observed Modelled Average 107 111 28 27 Standard Deviation 95 98 58 42 Coefficient of Determination (r 2) 0.77 0.89 Mean Absolute Error (MAE) 32 16 Root Mean Square Error (RMSE) 50 33 Coefficient of Efficiency ( ε) 0.72 0.83 Modified Coefficient of Efficiency ( ε 1) 0.47 0.58 Index of Agreement (d) 0.93 0.94 Modified Index of Agreement (d 1) 0.80 0.85

Best fit slope through the origin 0.98 0.73

Table 3 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application to Group 2

Mean Annual Runoff (mm) Mean Annual Flow (GL) Observed Modelled Observed Modelled Average 71 71 24 23 Standard Deviation 74 66 69 51 Coefficient of Determination (r 2) 0.78 0.88 Mean Absolute Error (MAE) 34 10 Root Mean Square Error (RMSE) 49 27 Coefficient of Efficiency ( ε) 0.56 0.84 Modified Coefficient of Efficiency ( ε 1) 0.34 0.60 Index of Agreement (d) 0.94 0.95 Modified Index of Agreement (d 1) 0.76 0.84

Best fit slope through the origin 0.84 0.72

The r 2 values and comparison of the modelled and observed averages indicates that the model closely replicates the observed data. Of note is the match between the modelled and observed mean annual runoff of 71 mm for Group 2 which indicates that the model produces reasonably good estimates. However, the difference between the standard deviations is large and the value of the MAE is more than a third of the average annual yield indicating large prediction errors. Again for the mean annual flow the RMSE is significantly greater than the MAE indicating that there is large variance in the differences between observed and modelled flows. The high values of the index of agreement (d ranges from 0.93 to 0.95) provide the impression that the model is able to replicate observed values well. The modified index of agreement (d 1 ranges from 0.76 to 0.85), where the squared terms are replaced by absolute values, allows a more realistic interpretation of the model. This measure (d 1), the coefficient of efficiency ( ε) and the modified efficiency measure ( ε 1), are relatively low indicating that the model is only a reasonable predictor. Overall the

Department of Water 27 REG75 Surface Water Hydrology, no. 25

modified Zhang model for Group 1 has a better ‘goodness of fit’ to the observed data than the model produced for Group 2.

6.3.1 Modified Zhang — one group

Even though this study identified two distinct groups (Figure 12 and 13), the hypothesis of using the south west of WA as one group was tested. The model was re-calibrated to test the south-west as one group as opposed to two. The statistics show that although there is an improvement in comparison to the second group the model does not predict as effectively for the area covered by Group 1 (Table 4). As the area covered by Group 1 will be the primary user of the model it was decided to use two groups.

Table 4 Statistics comparing the observed and modelled mean annual runoff and mean annual flow results of the modified Zhang application as one group

Mean Annual Runoff (mm) Mean Annual Flow (GL) Observed Modelled Observed Modelled Average 94 91 27 23 Standard Deviation 89 87 62 43 Coefficient of Determination (r 2) 0.71 0.89 Mean Absolute Error (MAE) 39 10 Root Mean Square Error (RMSE) 57 27 Coefficient of Efficiency ( ε) 0.59 0.81 Modified Coefficient of Efficiency ( ε 1) 0.36 0.56 Index of Agreement (d) 0.89 0.93 Modified Index of Agreement (d 1) 0.73 0.83

28 Department of Water Surface Water Hydrology, no. 25 REG75

6.4 Model prediction and accuracy

The modified Zhang model, termed REG75, can be used to predict the mean annual flow at ungauged catchments provided the level of clearing, catchment area and centroidal rainfall are known. The mean annual flow generated from the application of REG75 allows comparison against the observed streamflow which can be used to verify the accuracy of the model.

6.4.1 Errors

The difference between the estimated mean annual flow and the measured mean annual flow for the 10 and 90 percentiles are -39–187%. REG75 tends to over predict estimates of mean annual flow in wheatbelt catchments however these catchments are typically saline with a low demand for surface water use. Overall there is no consistent spatial pattern in whether the REG75 estimates are an under or over prediction of the observed values (Figure 19). This is confirmed with the random pattern generated in the plot of mean annual flow residuals versus gauging station location (Figure 20).

Figure 19 Spatial distribution of difference in observed and modelled values

Department of Water 29 REG75 Surface Water Hydrology, no. 25

250

200

150

100

50

0 Mean annual flow residuals (GL) residuals flow annual Mean -50

-100 Gauging station AWRC no. (in numerical order from Basin 601 - Basin 701)

Figure 20 Residuals plot of the mean annual flow data for the gauging station locations across the south west of WA

The large error could be partly attributed to the REG75 model being parsimonious in terms of data inputs and model parameters. This simplicity is required to enable the practical application of the REG75 model. In the first instance, at the mean annual scale, the water balance is dominated by rainfall and evapotranspiration. However the variability and deviations from the curves could be due to effects of climate and catchment characteristics that are not incorporated in the simple regional model.

It is assumed that the change in catchment soil water storage over time is minimal however Farmer et al., (2003) and Evans et al., (2004) indicate that soil water storage may be important, even over a longer time step. For example, the Lefroy catchment is known to have a high summer baseflow contribution and the REG75 model does not accurately predict the mean annual runoff in this area.

Budyko (1958; as cited in Zhang et al., 2001) also noted that deviations from the curve are often in response to seasonal variations in rainfall. Normally this is only incorporated into water balance models at finer time scales.

30 Department of Water Surface Water Hydrology, no. 25 REG75

6.4.2 Factors

The error margin around the mean annual flow output may be substantially greater than first thought for REG75, and other simple regional models. The large error necessitates the introduction of factors to scale the calculated mean annual flow to the observed mean annual flow. A generic scaling factor for each Surface Water Management Sub-area has been calculated primarily based on the gauging station factors within the Sub-area and those surrounding the area (e.g. Figure 21). The factors are to be applied to the mean annual runoff/flow value estimated from REG75.

It is important to note that despite the factors significantly reducing the model error at the gauging station the intention is for REG75 to be used in estimating mean annual flow, and hence the sustainable yield, for ungauged catchments. Due to unknown factors and climate conditions at ungauged locations, the estimation of factors is hard to achieve and hence the estimation of error margins is unknown.

Figure 21 Example of the development of factors for surface water management sub-areas using the difference in observed to modelled mean annual flow at each gauging station

Department of Water 31 REG75 Surface Water Hydrology, no. 25

6.4.3 Model validation

The REG75 model was tested at nine gauged catchments in order to validate the model performance with the factors applied. The nine catchments were independent to the calibration of the model.

The validation data set consisted of catchments ranging in size from 1.7 km 2 to 3,760 km 2. The catchments varied from 6% cleared to 90% cleared. Rainfall ranged from 500 mm to 920 mm.

The majority of the stations had a record length of only five years, however some were longer term stations. Record augmentation was performed to calculate the observed mean annual flow for the period 1975–2003. Observed mean annual flows varied from 49 ML to 98,900 ML and mean annual runoffs ranged from 26 mm to 370 mm.

Factors were applied to the mean annual runoff/flow values estimated from REG75 based on the surrounding calibrated gauging station factors. Once the factors were applied, the 10 and 90 percentile error margins were reduced from -27 to 48% (Table 5).

Table 5 Percent difference of REG75 estimates and observed mean annual flow for validation catchments

Mean Annual Flow (GL) % difference Observed REG75 estimated to observed Torbay (Main) Drain – Meenwood Road 12.9 13.1 2% extended Torbay Townsite 603-(012)/025 Frankland River – Trappers Road 605-013 98.9 94.0 -5% Chowerup Brook – Stretches Farm 607- 3.85 2.87 -26% 024 Balingup Brook Tributary – Padbury Road 0.05 0.04 -11% 609-011 Gnowergerup Brook – Jayes Road 17.2 17.2 0% 609-028 – Lowden 611-009 20.3 20.3 0% East – Buckingham 612-038 40.8 27.1 -34% Main Drain – Hope Valley 614-013 1.57 2.12 35% Nambeelup Brook – Kielman 614-063 13.2 26.7 102%

32 Department of Water Surface Water Hydrology, no. 25 REG75

6.4.4 Sustainable yields and allocation limits

In areas where the level of surface water use is low, estimates of sustainable yield are based on regional models such as REG75. The notional sustainable yield is calculated as 60% of the mean annual flow for the period 1975–2003.

Despite the possibility that the error margin for the estimate of mean annual flow and thus sustainable yield may be quite large, the risk to the environment is considered to be low. This is based on the assumption that REG75 will only be used to determine notional sustainable yields for sub-areas where the level of surface water use is low (less than 30% of the sustainable yield).

However, given the uncertainty in error it raises the issue of allocation limits. It is proposed that an allocation limit would be set at less than the notional sustainable yield (e.g. for C1 areas (low level of surface water use), the allocation limit would be set at 30% of the sustainable yield) (Figure 22).

Mean Annual Flow

Uncertainty in sustainable yield

Sustainable Yield Volume AL2

AL1 C1 C2 C3 C4

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% Proportion of sustainable yield allocated Figure 22 Allocation limits (AL) corresponding to level of use, mean annual flow and sustainable yield

This approach triggers the need for a more detailed investigation into the estimation of sustainable yield earlier in the allocation process and aims to reduce the possibility of over allocation of the surface water resource.

If REG75 underestimates the true mean annual flow, then the allocation limit is set at a conservative level, limiting the negative consequences for the environment. If REG75 overestimates the true mean annual flow, then the allocation limit will be set at a level higher than expected. The allocation limit calculated by REG75 has the potential to exceed the true allocation limit, the true sustainable yield or even the true mean annual flow. This could possibly exacerbate negative consequences to the

Department of Water 33 REG75 Surface Water Hydrology, no. 25

environment with the greatest risk to the environment occurring when the calculated allocation limit exceeds the true mean annual flow. Therefore, this risk was quantified using data from the existing gauged catchments and assuming an allocation limit of 18% of mean annual flow.

REG75 calculated allocation limits that exceeded the true sustainable yield at 9% of sites. Two thirds of these also exceeded the true mean annual flow. These sites typically have low surface water demand (e.g. experimental catchments and saline wheatbelt catchments) and were considered outliers (Figure 23).

Removing the outliers from the analysis, the probability that the calculated allocation limit exceeds the true allocation limit is 49%. This risk is considered acceptable as the calculated allocation limit is less than the true sustainable yield, satisfying the environmental water requirements.

Figure 23 Sites where the REG75 allocation limit exceeds the observed sustainable yield and mean annual flow

34 Department of Water Surface Water Hydrology, no. 25 REG75

6.5 Comparison to REG6

Error margins were calculated between the observed and modelled mean annual flows for the gauging stations that were common to the development of both REG6 and REG75 (135 stations). For the calculations, it was assumed that no scaling factors were applied. The REG6 errors were also calculated using the same data inputs and time period as REG75 (Table 6).

Table 6 Error margins between observed and modelled mean annual flows for REG75 and REG6

REG75 REG6 REG6* Minimum -87% -70% -95% 5 percentile -46% -33% -83% 10 percentile -39% -22% -71% 90 percentile 187% 292% 188% 95 percentile 540% 631% 363% Maximum 27692% 8598% 17705% *with REG75 rainfall isohyets and clearing levels applied

The large maximum errors occur in a catchment with a mean annual flow very close to zero, but for which REG75 predicted a large mean annual flow. It is not unexpected that there are differences between the estimates due to the differences in the development of the two approaches (Table 7). Although both approaches have significant error margins, it is recommended the REG75 model be used as it has a more defensible approach and is calibrated for the standard period 1975–2003.

Table 7 Comparison between REG75 and REG6 approaches

Criteria REG75 REG6 Period of flow record 1975 to 2003 1962 to 1996

Hydrometeorological 1975 to 2003 1907 to 1979 information SILO data

Clearing Information Estimated using GIS – NLWRA Estimated by hand using extent of native vegetation 1995 topographic maps (various dates)

Model Based on Zhang et al. (1999, 2001) Non-linear regression

In order to demonstrate that REG75 has ‘skill’ over REG6, the reduction of variance (Appendix D; Bureau of Meteorology, 2007) was calculated. The skill score of 0.7 indicates the relative improvement in accuracy of the mean annual flow estimates produced using REG75 over the REG6 estimates (a score of 0 indicates equal accuracy; a score of 1 indicates the model has perfect accuracy).

Department of Water 35 REG75 Surface Water Hydrology, no. 25

7 Conclusions

REG75 is a simple regional mean annual flow model that provides an estimate of mean annual flow from a catchment, calibrated for the period 1975–2003, and using land clearing and rainfall data for the same period. REG75 is based on a model developed by Zhang et al. (1999, 2001) and has been modified to suit south-west WA catchments.

The following data is required for input into the model; centroidal catchment rainfall (mm), catchment area (km 2) and catchment clearing (%).

It has been noted that deficiencies in the REG75 model may arise from effects of climate and catchment characteristics that are not addressed in this simple model. This has led to the development of factors based on observed mean annual flow records at gauging stations.

The REG75 model replaces the widely used REG6 model and will be used to estimate the notional sustainable yields for surface water management areas from Esperance to Geraldton for areas with a low level of surface water use.

36 Department of Water Surface Water Hydrology, no. 25 REG75

Appendices

Department of Water 37 REG75 Surface Water Hydrology, no. 25

Appendix A — ANUSPLIN fitting characteristics

A number of statistical indicators are provided in the ANUSPLIN output files so the optimum fitted surface can be assessed. The best goodness of fit is achieved when (Hutchinson 2003): • The generalised cross validation (GCV) is minimised. A very low GCV indicates the surface is representing the spatial trends in the rainfall process well. • The root mean square error divided by the mean is less than 10% • The signal is approximately half the number of data points. If the signal is very high, the data becomes exactly interpolated and the spline model is considered unstable and requires more data to explain finer scale variability. • The signal divided by the noise (error) is less than 1 (the error has to be equal to or greater than the signal). The error and the signal sum should equal the number of data points. • Rho (the smoothing parameter) is maximised. A higher rho value represents a smoother surface with rho close to 0 implying an exact interpolation. • There are no large residuals from the fitted surface (as large residuals often indicate errors in data positions or values).

38 Department of Water Surface Water Hydrology, no. 25 REG75

Appendix B — Streamflow gauges

Length of record of streamflow gauges used in the development of REG75 (from 1975 to 2003, whole years of data only with gaps filled). Y-axis shows gauging station name, gauging station number and [gauging station used for record augmentation].

Young River — Neds Corner 601-001

Lort River — Fairfield 601-004

Young River — Cascades 601-005 [601-006]

Young River — Munglinup 601-006

Coramup Creek — Myrup Road 601-008 [601-001]

Bandy Creek — Fisheries Road 601-009 [601-001]

Young River — Melaleuka 601-600

Robinson Road Drain & Munster Hill Drain Confluence 602-(007)/009 [602-199]

Pallinup River — Bull Crossing 602-001

Jackitup Creek — Wellards 602-003

Kalgan River — Stevens Farm 602-004

Chelgiup Creek — Anderson Farm 602-005 [602-199]

King River — Billa Boya Reserve 602-014 [603-001]

Mill Brook — Warren Road 602-015 [603-001]

Waychinicup Creek — Cheynes Beach Road 602-031

Angove Creek — Pumping Station 602-187 [602-031]

Goodga River — Black Cat 602-199

Jackitup Creek Tributary — Hinkleys Farm 602-600 [602-003]

Marbellup Brook — Elleker 603-001

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

Department of Water 39 REG75 Surface Water Hydrology, no. 25

Denmark River — Kompup 603-003 Hay River — Sunny Glen 603-004 [603-190] Mitchell River — Beigpiegup 603-005 [603-136] Sleeman River — Sleeman Road Bridge 603-007 [603-136] Upper Hay Tributary — Pardelup Prison Farm 603-008 [603-190] Upper Hay Tributary — Barrama 603-009 [603-190] Upper Hay Tributary — Willmay 603-010 [603-190] Cuppup River — Eden Road 603-013 [603-001] Seven Mile Creek — Gunn Road 603-018 [603-001] Little River — Ocean Beach Road 603-020 [604-053] Sunny Glen Creek — Girrawheen 603-022 [603-001] Scotsdale Brook — Pipehead 603-023 [603-190] Seven Mile Creek — Wonton Hills Farm Road 603-024 [602-199] — Mount Lindesay 603-136 Yate Flat Creek — Woonanup 603-190 — Rocky Glen 604-001 [604-053] Kent River — Styx Junction 604-053 Frankland River — Mount Frankland 605-012 Deep River — Teds Pool 606-001 — Wattle Block 606-002 [606-195] Shannon River — Dog Pool 606-185 [606-195] Weld River — Ordnance Road Crossing 606-195 Gardner River — Baldania Creek Confluence 606-218 [606-195] Lefroy Brook — Pemberton Weir & Rainbow Trail 607-(009)/013 Smiths Brook — Middlesex & Picketts Pond 607-(017)/020 [607-144] Lefroy Brook — Channybearup 607-002 [607-009/013] Warren River — Wheatley Farm 607-003 Perup River — Quabicup Hill 607-004 Yerraminnup Creek — North Catchment 607-005 [607-004] Yerraminnup Creek — South Catchment 607-006 [607-004]

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

40 Department of Water Surface Water Hydrology, no. 25 REG75

Tone River — Bullilup 607-007 [607-003] Six Mile Brook Tributary — March Road Catchment 607-010 [607-144] Quininup Brook Tributary — April Road North 607-011 [607-144] Quininup Brook Tributary — April Road South 607-012 [606-001] Four Mile Brook — Netic Road 607-014 [607-009/013] Scabby Gully — Rock Bar Road 607-016 [607-009/013] Perup River Tributary — Topanup 607-018 [607-004] Smiths Brook Tributary — Keegan's Road 607-019 [607-009/013] Lefroy Brook — Cascades 607-022 [607-220] Wilgarup River — Quintarrup 607-144 Dombakup Brook — Malimup Track 607-155 [607-009/013] Warren River — Barker Road Crossing 607-220 Smiths Brook Tributary — Manjimup Research Station 607-600 [607-009/013] Barlee Brook — Upper Iffley 608-001 [608-151] Carey Brook — Staircase Road 608-002 Easter Brook Tributary — Lewin North 608-004 [608-151] Easter Brook Tributary — Lewin South 608-005 [608-151] Carey Brook — Lease Road 608-006 [608-002] Record Brook — Boundary Road 608-007 [607-009/013] Donnelly River — Strickland 608-151 Fly Brook — Boat Landing Road 608-171 [608-002] — Darradup & Hut Pool 609-(025)/ 019 Scott River — Brennans Ford 609-002 St Paul Brook — Cambray 609-003 [610-003] St Paul Brook — Dido Road 609-004 [610-003] Balgarup River — Mandelup Pool 609-005 Weenup Creek — Balgarup 609-006 [609-005] Apostle Brook — Millbrook 609-008 [611-111] Northern Arthur River — Lake Toolibin Inflow 609-010 [609-005] Blackwood River — Winnejup 609-012

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

Department of Water 41 REG75 Surface Water Hydrology, no. 25

Arthur River — Mount Brown 609-014 [609-012] — Manywaters 609-015 [609-012] Hester Brook — Hester Hill 609-016 [609-025/019] Balingup Brook — Brooklands 609-017 [609-025/019] St John Brook — Barrabup Pool 609-018 [611-111] Narrogin — Walker Road 609-020 [609-012] Coblinine River — Bibikin Road Bridge 609-021 [609-012] Chapman Brook — White Elephant Bridge 609-022 [609-025/019] Chapman Brook — Forest Grove 609-023 [609-025/019] — Willmots Farm 610-001 — Chapman Hill 610-003 — Happy Valley 610-005 [611-111] Wilyabrup Brook — Woodlands 610-006 Ludlow River — Claymore 610-007 [611-111] Margaret River North — 610-008 [610-003] Ludlow River — Ludlow 610-009 [610-003] — Capel Railway Bridge 610-010 [611-221] Vasse Diversion Drain — D-S Hill Rd 610-014 [610-001] — Lennox Vineyard 610-015 [610-001] — Wonnerup Siding 610-016 [610-003] Capel River — Yates Bridge 610-219 [611-221] Preston River — Boyanup Bridge 611-004 [611-111] Ferguson River — 611-007 [611-221] Thompson Brook — Woodperry Homestead 611-111 Coolingutup Brook — Persconeri's Farm 611-221 Collie River East Branch — Coolangatta Farm 612-001 Collie River — Mungalup Tower 612-002 Hamilton River — Worsley 612-004 Stones Brook — Mast View 612-005 [612-004] Bingham River Tributary — Dons Catchment 612-007

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

42 Department of Water Surface Water Hydrology, no. 25 REG75

Bingham River Tributary — Ernies Catchment 612-008 Salmon Brook — Wights Catchment 612-010 Salmon Brook — Salmon Catchment 612-011 [611-111] Bingham River — Palmer 612-014 Batalling Creek — Maxon Farm 612-016 Harris River — Tallannalla Road 612-017 [612-014] Bussull Brook — Duces Farm 612-019 [612-010] Bingham River — Stenwood 612-021 [612-014] Brunswick River — Sandalwood 612-022 [613-002] Lunenburgh River — Silver Springs 612-023 [613-002] Camballan Creek — James Well 612-025 [612-001] Mairdebing Creek — Maringee 612-026 [612-001] Brunswick River — Cross Farm 612-032 [612-004] Collie River — South Branch 612-034 Wellesley River — Juegenup 612-039 [612-004] Brunswick River — Olive Hill 612-152 [613-002] Collie River East Tributary — James Crossing 612-230 Harvey River — Dingo Road 613-002 Tallanalla Creek — Blackbutt Point 613-005 [613-002] Bancell Brook — Waterous 613-007 Falls Brook — Dee Tee 59 613-008 [613-002] Samson North Drain — Somers Road 613-014 [613-007] Yalup Brook — Springton North 613-015 [613-007] McKnoes Brook — Urquharts 613-018 [613-007] Samson Brook — Mt William 613-020 [613-007] South Coolup Main Drain — Yackaboon 613-027 [614-003] Caris Drain — Greenlands Road 613-029 [614-003] Mayfield Drain — Old Bunbury Road 613-031 [614-044] Harvey River — Clifton Park 613-052 [613-007] Meredith Drain — Johnston Road 613-053 [613-146]

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

Department of Water 43 REG75 Surface Water Hydrology, no. 25

Mayfield Drain (Sub G) — Mayfield 613-054 [614-044] Clarke Brook — Hillview Farm 613-146 Marrinup Brook — Brookdale Siding 614-003 Dirk Brook — Kentish Farm 614-005 [614-003] Murray River — Baden Powell Water Spout 614-006 South Tributary — Del Park 614-007 Tributary — Falls Farm 614-008 [614-224] Mooradung Brook Tributary — Tunnel Road 614-011 [614-006] North Dandalup River — Scarp Road Damsite 614-016 [614-021] Little Dandalup River Tributary — Warren Catchment 614-017 [614-007] Little Dandalup River Tributary — Bennetts Catchment 614-018 [614-007] Little Dandalup River Tributary — Hansens Catchment 614-019 [614-021] Little Dandalup River Tributary — Higgens Catchment 614-020 [614-021] Wilson Brook Tributary — Lewis Catchment 614-021 North Dandalup Tributary — Jones Catchment 614-024 [614-021] Marrinup Brook Tributary — Umbucks Catchment 614-025 [614-003] Dirk Brook — Hopelands Road 614-028 [614-003] Serpentine Drain — Dog Hill 614-030 [614-003] 39 Mile Brook — Jack Rocks 614-031 [614-044] Serpentine River — River Road 614-035 [614-006] North Dandalup River — North Road 614-036 [614-021] Big Brook — O'Neil Road 614-037 [614-006] Big Brook — West Cameron 614-038 [614-044] Wuraming — Yarragil Tributary 614-041 [614-006] Tributary — Pindalup 614-043 [614-006] Yarragil Brook — Yarragil Formation 614-044 Swamp Oak Brook Tributary — Chadoora 614-045 [614-044] Yarragil Brook Tributary — Yarragil North 614-046 [614-044] Davis Brook — Murray Valley Plantation 614-047 [614-044] Yarragil Brook Tributary — Yarragil 4x 614-048 [614-044]

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

44 Department of Water Surface Water Hydrology, no. 25 REG75

Yarragil Brook Tributary — Yarragil 6c 614-049 [614-044] Yarragil Brook Tributary — Yarragil East 614-050 [614-044] Yarragil Brook Tributary — 4l Sub Catchment 614-057 [614-044] South Dandalup River Tributary — Skeleton Road 614-059 [614-006] South Dandalup River Tributary — Gordon Catchment 614-060 [614-006] Little Dandalup River Tributary — Bates Catchment 614-062 [614-007] Big Brook Tributary — Cameron West 614-064 [614-006] Murray River — Pinjarra 614-065 [614-006] Big Brook Tributary — Cameron Central 614-066 [614-006] Gooralong Brook — Mundlimup 614-073 [614-007] Big Brook — Jayrup 614-093 [614-006] Hotham River — Pumphrey's Bridge 614-105 [614-224] Chalk Brook — Quindanning Road 614-123 [614-196] Williams River — Saddleback Road Bridge 614-196 Hotham River — Marradong Road Bridge 614-224 Avon River — Brouns Farm & Balladong Street 615-(014)/024 — Waterhatch Bridge & Brookton Highway 615-(027)/222 Mooranoppin Creek — Mooranoppin Rock 615-011 Lockhart River — Kwolyn Hill 615-012 North — Frenches 615-013 Yilgarn River — Gairdeners Crossing 615-015 Lake Ace Creek — Spencers Farm 615-016 [615-012] Lake Ace Creek — Hatters Hill 615-017 [615-012] Mooranoppin Creek — McLellans Farm 615-019 [615-011] Mortlock River — O'Driscolls Farm 615-020 Avon River — Beverley Bridge 615-025 [615-011] Avon River — Stirling Terrace Toodyay 615-026 [615-020] Avon River — Yenyening Confluence 615-029 [615-011] Avon River — Northam Weir 615-062 [615-020] Wooroloo Brook — Karl's Ranch 616-001

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

Department of Water 45 REG75 Surface Water Hydrology, no. 25

Darkin River — Pine Plantation 616-002 Wooroloo Brook — Noble Falls 616-005 [616-001] — Tanamerah 616-006 [616-019] Rushy Creek — Byfield Road 616-007 [616-012] Pickering Brook — Slavery Lane 616-009 [616-002] Little Darkin River — Hairpin Bend Road 616-010 [616-002] Swan River — Walyunga 616-011 Helena Brook — Trewd Road 616-012 — Ngangaguringuring 616-013 Piesse Gully — Furfaros Orchard 616-014 [616-178] Brockman River — Yalliawirra 616-019 Seldom Seen Creek — Travellers Arms 616-021 More Seldom Seen Creek — Ceriani Farm 616-022 Waterfall Gully — Mount Curtis 616-023 East — Rocky Valley 616-025 [616-002] 31 Mile Brook — 31 Mile Road 616-026 [616-023] Stinton Creek — Moondyne Hollow 616-029 [616-022] Canning River — Millars Road 616-039 [616-002] Susannah Brook — Gilmours Farm 616-040 [616-178] Wungong Brook — Vardi Road 616-041 [616-021] Neerigen Brook — Abbey Road 616-044 [616-021] Wungong Brook — Cobiac 616-058 [616-021] Canning River — Glen Eagle 616-065 [616-002] Swan River — Great Northern Highway 616-076 [616-011] Southern River — Anaconda Drive 616-092 [616-178] Susannah Brook — River Road 616-099 [616-001] Jane Brook — National Park 616-178 — Railway Parade 616-189 Helena River — Poison Lease 616-216 — Quinns Ford 617-001

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

46 Department of Water Surface Water Hydrology, no. 25 REG75

Hill River — Hill River Springs 617-002 Gingin Brook — Bookine Bookine 617-003 Gingin Brook — Gingin 617-058

Lennard Brook — Molecap Hill 617-165 [616-019] Berkshire Valley — Experimental Catchment 617-600 [617-001] Greenough River — Karlenew Peak 701-002 Nokanena Brook — Wootachooka 701-003 [701-007] East Tributary — Narra Tarra Homestead 701-004 [701-007] — Robb Crossing 701-005 [701-007] Buller River — Buller 701-006 [701-007] Chapman River — Utakarra 701-007 Greenough River — Pindarring Rocks 701-008

Irwin River — Mountain Bridge 701-009 [701-002] Hutt River — Yerina 701-010 [701-007] Nokanena Brook Catchment — Wearbe 701-601 [701-007]

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003

Department of Water 47 REG75 Surface Water Hydrology, no. 25

Appendix C — Spatial distribution of streamflow gauges

48 Department of Water Surface Water Hydrology, no. 25 REG75

Appendix D — Statistics

O represents the observed data point, P the simulated data point and N the total number of observations.

Statistic Formula

= 1 Observed mean O ∑Oi N

= 1 Predicted mean P ∑ Pi N − 2 ∑(Oi O ) Standard deviation s = N −1 = − 2 Squared deviation from the observed mean SOO ∑ (Oi O ) = − 2 Squared deviation from the predicted mean S PP ∑(Pi P) = − − Sum of the cross products of deviations SOP ∑(Oi O )( Pi P) S r = OP Correlation coefficient SOO SPP

2 2 Coefficient of determination R = r range of 0 to 1; perfect score 1

= 1 − MAE ∑ Oi Pi Mean absolute error N range of 0 to infinity; perfect score 0

= 1 − 2 RMSE ∑(Oi Pi ) Root mean squared error N range of 0 to infinity; perfect score 0 = 1 − 2 MSE ∑(Pi Oi ) Mean squared error N range of 0 to infinity; perfect score 0 − 2 ∑(Oi Pi ) ε = 1− − 2 Coefficient of efficiency ∑(Oi O ) range of negative infinity to 1; perfect score 1

− 2 ∑(Oi Pi ) d = 1− − + − 2 Index of agreement ∑( Pi O Oi O )

range of 0 to 1; perfect score of 1

Skill Score Score forecast Skill Score =1−

Score reference Reduction of Variance (Score = MSE) 0 indicates no improvement over reference; perfect score 1

Department of Water 49 REG75 Surface Water Hydrology, no. 25

References

Bari, M.A., Smettem, K.R.J., and Sivapalan, M., 2005, ‘Understanding changes in annual runoff following land use changes: a systematic data-based approach’, Hydrological Processes , vol. 19, pp. 2463–2479.

Bradford, A., Zhang, L., and Hairsine, P., 2001, Implementation of a mean annual water balance model within a GIS framework and application to the Murray- Darling Basin, Cooperative Research Centre for Catchment Hydrology Technical Report 01/8.

Bureau of Meteorology, 2007, Forecast Verification – Issues, Methods and FAQ , , accessed 24 April 2007.

Evans, R., Gilfedder, M., and Austin, J., 2004, Application of the Biophysical Capacity to Change (BC2C) model to the Little River (NSW) , CSIRO Land and Water Technical Report No 16/04.

Farmer, D., Sivapalan, M., and Jothityangkoon, C., 2003, ‘Climate, soil, and vegetation controls upon the variability of water balance in temperate and semiarid landscapes: Downward approach to water balance analysis’, Water Resources Research , vol. 39, no. 2, pp. 1035–1055.

Hutchinson, M.F., 2003, ANUSPLIN Version 4.2 User Guide, Centre for Resource and Environmental Studies, The Australian National University, Canberra.

Legates, D.R., and McCabe Jr., G.J., 1999, ‘Evaluating the use of ‘goodness-of-fit’ measures in hydrologic and hydroclimatic model validation’, Water Resources Research, vol. 35, no. 1, pp. 233–241.

Milly, P.C.D., 1994, ‘Climate, soil water storage, and the average annual water balance’, Water Resources Research , vol. 30, no. 7, pp. 2143–2156.

National Land and Water Resources Audit (NLWRA), 2001, Current Extent of Native Vegetation, Conservation and Land Management and Department of Agriculture.

Nordblom, T., Hume, I., Bathgate, A., Hean, R., and Reynolds, M., 2005, ‘Towards a market: geophysical-bioeconomic targeting of plant-based land use change for management of stream water yield and salinity’, Economics and Environment Network (EEN) National Workshop , Canberra, May 5-6, 2005.

Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E., 1993, ‘Frequency Analysis of Extreme Events’, in Handbook of Hydrology , ed D.R. Maidment, McGraw-Hill, Inc., United States of America.

50 Department of Water Surface Water Hydrology, no. 25 REG75

Loh, I., 2004, ‘Adoption of a standard data period for hydrologic studies that guide surface water allocation decisions in the south west of Western Australia’, Internal Water Resource Allocation Note.

Zhang, L., Dawes, W.R., and Walker, G.R., 1999, Predicting the effect of vegetation changes on catchment average water balance, Cooperative Research Centre for Catchment Hydrology Technical Report 99/12.

Zhang, L., Dawes, W.R., and Walker, G.R., 2001, ‘Response of mean annual evapotranspiration to vegetation changes at catchment scale’, Water Resources Research , vol. 37, no. 3, pp.701–708.

Department of Water 51 REG75 Surface Water Hydrology, no. 25

Contributors

This report was prepared by Jacqueline Durrant from the Water Resource Management Division, Department of Water. The technical assistance of Mark Pearcey (Water Resource Management Division, Department of Water) and review by Dr Phillip Jordan (Sinclair Knight Merz) is recognised.

52 Department of Water