Relative merits of different methods for runoff predictions in ungauged catchments

Transcription

1 WATER RESOURCES RESEARCH, VOL. 45,, doi: /2008wr007504, 2009 Relative merits of different methods for runoff predictions in ungauged catchments Yongqiang Zhang 1 and Francis H. S. Chiew 1 Received 5 October 2008; revised 13 February 2009; accepted 8 May 2009; published 14 July [1] There have been numerous regionalization studies on runoff prediction in ungauged catchments. This study evaluates the relative benefits of different methods using two conceptual daily rainfall-runoff models, Xinanjiang and SIMHYD, on 210 relatively unimpacted catchments in southeast Australia. The results show that runoff predictions in ungauged catchments can benefit from a smart selection of donor catchments whose optimized parameter values are used to model runoff in the target ungauged catchment, output averaging of results from multiple-donor catchments and incorporating leaf area index data into the rainfall-runoff models. The biggest benefit comes from an educated selection of donor catchments (compared to a random selection of donor catchments) and output averaging of results from multiple-donor catchments. The difference between the three commonly used approaches for selecting donor catchments is relatively small. The spatial proximity approach (where the geographically closest catchment is used as the donor catchment) performs slightly better than the physical similarity approach (where the catchment with the most similar attributes is used as the donor catchment), and the integrated similarity approach, which combines the spatial proximity and physical similarity approaches, performs only very marginally better than the spatial proximity approach. The incorporation of leaf area index data into the rainfall-runoff models shows marginal improvements to the modeling results, although a more appropriate integration of vegetation and other remotely sensed data may further improve the results. Citation: Zhang, Y., and F. H. S. Chiew (2009), Relative merits of different methods for runoff predictions in ungauged catchments, Water Resour. Res., 45,, doi: /2008wr Introduction [2] Predictions in Ungauged Basins or Catchments (PUB) are regarded as one of the most challenging tasks in surface hydrology. The International Association of Hydrological Sciences (IAHS) launched an initiative, the IAHS Decade on PUB ( ) [PUB_Initiative, available at focusing on formulating and implementing appropriate science programmes to engage and energize the scientific community, in a coordinated manner, towards achieving major advances in the capacity to make reliable predictions in ungauged basins [Sivapalan et al., 2003]. [3] Regionalization is typically used for water quantity studies in PUB, which is referred as the process of transferring parameter values from a gauged catchment to the target ungauged catchment [Bloschl and Sivapalan, 1995]. Three regionalization approaches have been widely used to choose the donor gauged catchment whose optimized parameter values are used to model runoff for the target ungauged catchment: regression; spatial proximity; and physical similarity. The regression approach establishes a relationship between parameter values calibrated on gauged 1 CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, ACT, Australia. Copyright 2009 by the American Geophysical Union /09/2008WR catchments and catchment descriptors or attributes (climatic and physical), and then the parameter values for the ungauged catchments are estimated from its attributes and the established relationship. The spatial proximity approach uses the parameter values from the geographically closest gauged catchment hypothesizing that neighboring catchments should behave similarly owing to similar physical and climatic characteristics. The physical similarity approach transfers the entire set of parameter values from a physically similar catchment whose attributes (climatic and physical) are similar to those of the target ungauged one. [4] The regression approach is popular in regionalization studies [Young, 2006] but it has been strongly criticized [Bardossy, 2007; McIntyre et al., 2005; Oudin et al., 2008b; Parajka et al., 2007]. This is because the cross-correlation between parameters are seldom taken into account and because model calibrations can produce vastly different sets of parameter values that give similar model performance (equifinality problem [Beven and Freer, 2001]). The spatial proximity and physical similarity approaches are very common in many recent regionalization studies [Bardossy, 2007; McIntyre et al., 2005; Merz and Bloschl, 2004; Oudin et al., 2008b; Parajka et al., 2005]. Merz and Bloschl [2004] and Parajka et al. [2005] compare the three regionalization approaches in over 300 Austrian catchments using an 11-parameter HBV model and show that the spatial proximity approach performs best followed by the physical 1of13

2 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 1. Locations of 210 catchments used in this study. similarity approach with the regression approach performing worst. Oudin et al. [2008b] draw the same conclusion using two rainfall-runoff models, GR4J and TOPMO, in 913 French catchments. In their study, they argue that as the spatial proximity approach does not systematically outperform the physical similarity approach, combining the two to select a donor catchment may improve the modeling results, and this is one of the research questions that will be explored in this paper. [5] Various studies, particularly those by McIntyre et al. [2005] and Oudin et al. [2008b] have shown that output averaging can reduce the uncertainty in runoff predictions in ungauged catchments. In output averaging, the target catchment is modeled using parameter values from many donor catchments, rather than one donor catchment, and results from the modeling using the different sets of parameter values from the different donor catchments, are averaged to provide the runoff estimate for the target catchment. The use of output averaging will also be explored in this paper. [6] The use of more information, such as remotely sensed (RS) vegetation data, in rainfall-runoff modeling can improve runoff estimates in ungauged catchments (Y. Q. Zhang and F. H. S. Chiew, Can remote sensing data improve short-term rainfall-runoff simulation?, paper presented at Down Under 2008, Engineers, Adelaide, Australia, April, 2008). Zhang et al. [2008] integrate the Penman-Monteith evapotranspiration (PM-ET) equation which uses MODIS-LAI (the MODerate resolution Imaging Spectrometer mounted on 2of13 the polar-orbiting Terra satellite, Leaf Area Index) data to estimate surface conductance into a lumped rainfall-runoff model and show that the revised model structure significantly improved monthly and daily runoff estimates in ungauged catchments in southeastern Australia. The use of vegetation data in rainfall-runoff modeling will also be explored in this study. [7] The main focus of this paper is to quantify the relative merits of output averaging, different regionalization approaches and the use of MODIS-LAI data to predict daily runoff in ungauged catchments. The specific objectives include: (1) to evaluate the contribution of output averaging from multiple-donor catchments, (2) to investigate four regionalization approaches for selecting the donor catchments: random selection and three educated approaches incorporating spatial proximity, physical similarity and integrated similarity (combination of spatial proximity and physical similarity) and (3) to examine the benefits of using MODIS-LAI time series data in rainfall-runoff modeling. Two lumped conceptual daily rainfall-runoff models, Xinanjiang and SIMHYD, and their revised versions to incorporate the use of MODIS-LAI, are used in this study. The models are applied to 210 relatively unregulated catchments in southeast Australia using data from 1994 to 2006 (Figure 1). [8] The large-scale regionalization study here with Australian data is also unique as most regionalization studies reported in the literature are for European countries [Bardossy, 2007; Goswami et al., 2007; McIntyre et al., 2005; Merz and Bloschl, 2004; Oudin et al., 2008b; Parajka et al., 2005, 2007; Young, 2006]. A regionalization study in Australia is likely to give poorer results compared to the European studies because Australia covers a much larger region than most of the European studies resulting in a larger variation of climatic and catchment physical conditions, and compared to similar regions in Europe, rainfall and streamflow in Australia are more variable due to the function of El Niño-Southern Oscillation and Inter-decade Pacific Oscillation [Chiew et al., 1998; Chiew and McMahon, 2002; Piechota et al., 1998; Post et al., 1998; Power et al., 1999; Verdon et al., 2004], and the density of the stream gauging network is also much lower in Australia than in Europe. 2. Models and Data 2.1. Rainfall-Runoff Models Xinanjiang and SIMHYD Models [9] Xinanjiang and SIMHYD are two lumped conceptual daily rainfall-runoff models. The inputs into the models are daily rainfall and daily potential ET (ET p ), and the models estimate daily runoff. [10] The 14-parameter Xinanjiang model has been widely used, particularly in humid and semi-humid regions in China [Cheng et al., 2002; Gan et al., 1997; Jayawardena and Zhou, 2000; Zhao, 1992; R. J. Zhao et al., The Xinanjiang model, paper presented at Hydrological Forecasting Proceedings Oxford Symposium, IAHS, July, 1980]. The model structure of the Xinanjiang model and the model parameters are shown in Figure 2. The Xinanjiang model has three submodels, ET submodel (3-par: U m, L m and C), runoff generating submodel (3-par: D m, B and

3 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 2. Model structures of Xinanjiang and SIMHYD and their revised versions (the dash-dots show the evapotranspiration submodel, which is modified). I m ) and routing submodel (8-par: S m,e x,k g,k i,c g,c i,c s, L). [11] The version of the SIMHYD model used here has 9 parameters. The structure of the SIMHYD model and the model parameters and algorithms that describe water movement into and out of the storages are shown in Figure 2. SIMHYD has been extensively used for various applications across Australia [Chiew et al., 2002; Siriwardena et al., 2006; Zhang et al., 2008; N. Viney et al., Regionalisation of runoff generation across the Murray-Darling Basin using an ensemble of two rainfall-runoff models, paper presented at Water Down Under 2008, Engineers, Adelaide, Australia, 2008] Revised Versions of the Two Models [12] To use RS-LAI data in the two models, the ET submodels are replaced with the Penman-Monteith (PM-ET) equation to calculate actual ET directly (see Figure 2). [13] The PM-ET equation can be written as: ET ¼ 1 DA e þ r a C p DG a l D þ gð1 þ G a =G s Þ where l is the latent heat of vaporization, D = de*/dt a is the slope of the curve relating saturation water vapor pressure to temperature, D = e*(t a ) e a is the vapor pressure deficit of the air, e*(t a ) is the saturation vapor pressure at air temperature, e a is the actual vapor pressure, g is the psychrometric constant, r a is the air density, C p is the specific heat capacity of air, A e is the available energy, the difference of the net radiation to the soil heat flux ð1þ 3of13 (assumed to be zero here), G a is the aerodynamic conductance and G s is the surface conductance. [14] The terms A e, D, g, r a and D in equation (1) can be calculated from the basic daily meteorological time series and the term G a in equation (1) can be calculated from land cover data [Zhang et al., 2008]. [15] The surface conductance, G s, is the only physiological variable in the PM equation. It is calculated using the algebraic, biophysical two-parameter surface conductance model [Leuning et al., 2008; Zhang et al., 2008]. The daily input data required for the model are LAI and basic meteorological variables. The model has two parameters, the maximum stomatal conductance g sx and the fraction of equilibrium evaporation at the soil surface f. The soil evaporation factor f is directly dependent on moisture status, and the soil wetness modeled by the Xinanjiang and SIMHYD models are used as the estimate for f. The g sx term is considered as a parameter that is optimized together with the other Xinanjiang and SIMHYD model parameters. [16] The revised Xinanjiang model has 12 parameters. The three-layer ET submodel is replaced with a one-layer ET submodel, removing the three parameters, U m, L m and C (see Figure 2). The parameter, f, in the PM model is estimated as the soil wetness W/W M. The parameter g sx is treated as an additional model parameter and optimized together with the remaining eleven parameters. [17] The revised SIMHYD model has 10 parameters (one additional parameter, g sx ). The ET in the evapotranspiration submodel is calculated using the PM model. The parameter, f, in the PM equation is calculated as the soil wetness, SMS/SMSC.

4 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT [18] To distinguish between the revised and original models, the revised models will be referred to as Xinanjiang-ET and SIMHYD-ET Data Runoff Timeseries Data [19] Daily runoff data from 210 relatively unimpacted catchments (50 to 2000 km 2 ) in southeastern Australia (Figure 1) are used. The region includes the most populated and important agricultural areas of Australia. Data from 1994 to 2006 are used in this study, with the data used for model calibration and regionalization assessment of all the four models and the data used for model verification and regionalization assessment for the original Xinanjiang and SIMHYD models. The Xinanjiang- ET and SIMHYD-ET models are not assessed for because the MODIS-LAI data required to drive these revised model is only available from Meteorological Timeseries Data [20] Daily time series of maximum temperature, minimum temperature, incoming solar radiation, actual vapor pressure and precipitation from 1994 to 2006 at (5 km 5 km) grid cells from the SILO Data Drill of the Queensland Department of Natural Resources and Water ( [Jeffrey et al., 2001] are used. The SILO Data Drill provides surfaces of daily rainfall and other climate data interpolated from point measurements made by the Australian Bureau of Meteorology. The rainfall data is required as input to the rainfall-runoff models. The other meteorological data are used to calculate potential ET (ET p ) using the Priestley-Taylor model [Priestley and Taylor, 1972] and to calculate PM-ET for the revised rainfall-runoff models Remote Sensing Data [21] The RS-LAI data required to calculate PM-ET in the revised rainfall-runoff models come from the 8-day composite 1-km resolution MODIS-LAI products (MOD15A2, collection 4) which are obtained from the Land Processes Distributed Active Archive Centre (LPDAAC) ( usgs.gov/dataproducts.asp) for the period Before the application, the MODIS-LAI data are quality controlled and interpolated to a daily time step [Zhang and Wegehenkel, 2006]. However, there still exist the impacts of cloud contamination and atmospheric variability on daily LAI data. Thus the interpolated daily LAI data are then smoothed by the Savitzky-Golay filtering method, a widely used method for obtaining high-quality vegetation index time series [Chen et al., 2004; Fang et al., 2008; Ruffin et al., 2008]. [22] Land cover data required to estimate G a in equation (1) are obtained from the MODIS land cover product, the yearly Land Cover classification product (MOD12Q1) ( The data set has 17 vegetation classes defined according to the International Geosphere-Biosphere Programme. [23] The albedo data required to calculate A e in equation (1) are obtained from an annual average albedo product at a 5-km resolution for Australia [Dilley et al., 2000; Schaaf et al., 2002]. [24] All the remote sensing and meteorological data are reprojected and re-sampled to obtain 1-km gridded data. The gridded data in each catchment are then cut out and 4of13 averaged to obtain aggregate daily data series for model inputs Model Calibration and Verification [25] The Particle Swarm Optimization (PSO) toolbox in MATLAB is used to optimize the parameters of the two rainfall-runoff models. The PSO method is firstly presented by Eberhart and Kennedy, inspired from the behavior of schools of fish or flocks of birds [Eberhart and Kennedy, 1995]. It originates from the swarm paradigm, called particle swarm, and is expected to provide the so-called global or near-global optimum. The PSO method has been successfully used in several rainfall-runoff model parameter optimizations [Chau, 2006; Gill et al., 2006]. [26] The rainfall-runoff models are calibrated to maximize the Nash-Sutcliffe Efficiency (NSE) [Nash and Sutcliffe, 1970] of daily runoff which is defined as: NSE ¼ 1 X N i¼1 X N i¼1 2 Q obs;i Q sim;i ð2þ 2 Q obs;i Q obs where Q sim and Q obs are the simulated daily runoff and observed daily runoff, respectively, Q obs is the arithmetic mean of the observed runoff, i is the ith day and N is the total days sampled. [27] All four models are calibrated against runoff data from 2001 to 2006, with the 2000 data used for model warm up. [28] Two criteria are used for the model assessment: NSE of daily runoff described by equation (2) and absolute Water Balance Error percentage (WBE) which is defined as: WBE ¼ 100 X N i¼1 Q sim;i XN Q obs;i i¼1 X N Q obs;i i¼1 [29] The NSE and WBE results are presented for all four models for the calibration and regionalization assessment against runoff data and for the original two models for the verification and regionalization assessment against runoff data (1994 data are used for model warm up). [30] The model calibration and verification results are summarized in Figure 3 and Tables 2 and 3. The model calibration results for all four models are very similar. The calibrations are generally satisfactory with NSE values greater than 0.6 in 80 percent of the 210 catchments (median value of about 0.8) and WBE of less than 30 percent in 80 percent of the catchments. The calibration results are similar to most rainfall-runoff modeling studies in Australian catchments (Viney et al., presented paper, 2008; W. Boughton and F. Chiew, Estimating runoff in ungauged catchments from rainfall, PET and the AWBM model, paper presented at International Symposium on Environment Software System, Harrisonburg, Virginia, May, 2004). The verification NSE results for the original models are slightly poorer than the calibration results with the ð3þ

5 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 3. Summary of calibrated and verified Nash-Sutcliffe Efficiency (NSE) and absolute Water Balance Error percentage (WBE) values for Xinanjiang and SIMHYD models of the 210 catchments. A good model performance is indicated by large NSE values and small WBE values. averaged NSE values in the model verification generally being 0.1 to 0.2 lower than those in the model calibration. These results will be further discussed in section Modeling Runoff in Ungauged Catchments [31] To assess the model predictions of daily runoff in ungauged catchments, each of the 210 catchments is left out in turn and considered as an ungauged catchment, and the entire set(s) of parameter values from the donor catchment(s) are used to model runoff in the ungauged catchments Single-Donor Catchment Versus Multiple-Donor Catchments [32] In the single donor catchment approach, parameter values from a single donor catchment are used to model runoff in the ungauged catchment. [33] In the multiple-donor catchments approach, multipledonor catchments are used. Parameter values from each donor catchment are used to independently model runoff in the ungauged catchment. Each of the daily runoff time series modeled using parameter sets from each of the donor catchments are then averaged to obtain the daily runoff time 5of13 series for the ungauged catchment, which is called as output averaging method as described by McIntyre et al. [2005] and Oudin et al. [2008b] Selection of Donor Catchment [34] To model runoff in an ungauged catchment, parameter values from a donor catchment are used. Four approaches for choosing the donor catchment are investigated here: random selection; spatial proximity; physical similarity; and integrated similarity Random Selection Approach [35] In the random selection approach, a donor catchment is chosen randomly, using a random integer generator. This approach is taken as a benchmark to evaluate the following three educated or informed approaches Spatial Proximity Approach [36] In the spatial proximity approach, the geographically closest gauged catchment is chosen as the donor catchment. The distance between catchment centroids, D, is used as the distance measure Physical Similarity Approach [37] In the physical similarity approach, the gauged catchment with the closest physical similarity to the target catchment is chosen as the donor catchment.

6 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Table 1. Summary of Catchment Attributes in the 210 Catchments Catchment Characteristics Notation Min 25% Median 75% Max Area A (km 2 ) Aridity index (ET p /P) AI(-) Mean elevation E (m) Mean slope in degree S ( ) Stream length SL (km) Mean Solum thick ST (mm) Plant available water holding capacity PAWC (mm) Mean woody vegetation fraction WF (-) [38] Eight catchment attributes (see Table 1) are considered in this study: (1) catchment Area (A) in km 2, (2) Aridity Index (AI): calculated as the ratio of mean annual ET p to mean annual P, (3) mean catchment Elevation (E) in m: derived from the 9 second DEM for Australia (custodian: Geoscience Australia), (4) catchment Slope (S): derived from the 9 second DEM for Australia (custodian: Geoscience Australia), (5) Stream Length (SL): derived from watercourse lines in the Topo250k Series 3 Hydrography data set (custodian: Geoscience Australia), (6) median Solum Thickness in m(st): derived from the Atlas of Australian Soils, (7) Plant Available Water holding Capacity in solum in mm (PAWC): derived from the Atlas of Australian Soils [McKenzie et al., 2000], and (8) mean Woody vegetation Fraction (WF): derived from the National Carbon Accounting System (NCAS) 2005 Forest Extent data set (custodian: Australian Greenhouse Office). [39] The rank-accumulated similarity is used to select the donor catchment [Oudin et al., 2008b]. For each attribute, the catchment with the most similar attribute to the target catchment is considered rank one, the catchment with the second most similar attribute is considered rank 2, and so on. Where several attributes are used for regionalization, the rank numbers for each of the attributes are added. The catchment with the smallest total rank is chosen as the target catchment. Each attribute used for regionalization is given equal weight in the ranking system [Oudin et al., 2008b] Integrated Similarity Approach [40] In the integrated similarity approach, the spatial proximity and physical similarity measures are considered together. The geographic distance, D, is taken as an attribute together with the other catchment attributes. Like the physical similarity approach, this approach also uses the rank-accumulated similarity to select the donor catchment. therefore there is little meaning in comparing relative negative NSE values), negative NSE values are considered as zero in calculating the average), and the median WBE values. Table 3 summarizes the regionalization results for the two original models in the verification period. Table 4 compares the NSE values between the three educated regionalization approaches, between multiple donors and single donor, and between the integrated similarity approach and random selection for the four models in the calibration period and verification period. Figures 4 to 7 present the distributions of NSE and WBE values respectively obtained for the 210 catchments as whisker plots. [42] The use of one to one hundred donor catchments is explored in this study, and the results show that the optimum number of donor catchments that generally gives the highest NSE and lowest WBE values for the different modeling experiments is about eight to ten (Figure 8). For this reason, the results presented throughout this paper are based on the output averaging of results from eight donor catchments. 4. Regionalization Results [41] The model performances, applied to the ungauged catchments as described in section 3, are summarized as the distributions of NSE and WBE values obtained for the 210 catchments. Table 2 summarizes for the four models (two original rainfall-runoff models and two revised models to integrate MODIS-LAI) for the various methods used to select the donor catchments in the calibration period, the 25th percentile, median and 75th percentile NSE values, the NSE values averaged over the 210 catchments (to avoid the influence of very high negative NSE values (a negative NSE value indicates that the model performs poorer than a mean estimate for every single day and Figure 4. Summary of Nash-Sutcliffe Efficiency (NSE) values for the four regionalization approaches in the calibration period. All the NSE values are from 8-donor catchments except IS1, which is for integrated similarity for one-donor catchment. Whisker plots show 10th, 25th, 50th (median), 75th and 90th results for the 210 catchment. PS, physical similarity; SP, spatial proximity, IS, integrated similarity. The number below each plot means the number of catchments with negative NSE values. 6of13

7 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 5. Summary of absolute Water Balance Error percentage (WBE) values for the four regionalization approaches in the calibration period (see explanation in Figure 4) Regionalization Results Versus Calibration and Verification Results [43] The model regionalization (prediction in ungauged catchments) results are poorer than the model calibration results, with the median NSE values from the best regionalization results (integrated similarity) being about 0.25 to 0.30 lower than the calibration results (Table 2). However, the model regionalization results are similar to the model verification results in the verification period, where the model regionalization and model verification NSE values are similar for the SIMHYD model, and the model regionalization NSE values only about 0.05 lower than the model verification NSE values for the Xinanjiang model (Table 3). The NSE values for the regionalization are about 0.15 to 0.20 lower than the NSE values in the calibration (25th percentile to 75th percentile range of 0.45 to 0.70 in compared to Figure 6. Summary of Nash-Sutcliffe Efficiency (NSE) values for the four regionalization approaches in the verification period (see details in Figure 4). 7of13 Figure 7. Summary of absolute Water Balance Error percentage (WBE) values for the four regionalization approaches in the verification period (see details in Figure 4) to 0.85 in the calibration; Tables 2 and 3) and about 0.05 to 0.10 higher than the NSE values in the regionalization Single-Donor Catchment Versus Multiple-Donor Catchments [44] The output averaging of results from 8-donor catchments are considerably better than the results from a single donor catchment (Tables 2 4 and Figures 4 7). For the integrated similarity approach, which is the best regionalization approach, the 25th percentile, median and average of the NSE values from the 210 catchments from the use of 8-donor catchments compared to the use of a single donor catchment are generally higher by about The 75th percentile NSE values (lower quartile NSE value showing results from the poorer modeled catchments) for 8-donor catchments are 0.15 and 0.23 higher than those for a single donor catchment for the Xinanjiang model and the SIMHYD model, respectively in the calibration period (Table 2 and Figure 4), and 0.14 and 0.15 higher in the verification period (Table 3 and Figure 6). The median WBE values from the 210 catchments from the use of 8-donor catchments are almost same as those from use of a single donor catchment in the calibration period (Figure 5), but are better than those obtained from a single donor catchment in the verification period (Figure 7). The 8-donor catchment NSE values are more than 0.02 higher than the single donor catchment NSE values in catchments, and the single donor catchment NSE values are more than 0.02 higher than the 8-donor catchments NSE values in catchments (IS8-IS1 in Table 4). The comparisons between single donor catchment versus multiple-donor catchments for the random selection, physical similarity and spatial proximity approaches also showed similar results and are not shown here Approaches for Selecting Donor Catchments [45] Tables 2 4 and Figures 4 7 compare the random selection approach and the three educated approaches used to select donor catchments. As expected, the educated or informed selection of donor catchments based on spatial proximity, physical similarity and integrated similarity give

8 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Table 2. Calibration and Regionalization Results for the Four Regionalization Approaches and for the Four Rainfall-Runoff Models in the Calibration Period ( ) Model Indicator Calibration Random8 PS8 SP8 IS8 IS1 Model Indicator Calibration Random8 PS8 SP8 IS8 IS1 Xinanjiang 25th NSE SIMHYD 25th NSE Median NSE Median NSE th NSE th NSE Averaged NSE a Averaged NSE a Median WBE Median WBE Xinanjiang-ET 25th NSE SIMHYD-ET 25th NSE Median NSE Median NSE th NSE th NSE Averaged NSE a Averaged NSE a Median WBE Median WBE a PS, physical similarity; SP, spatial proximity; IS, integrated similarity. All the regionalization results are obtained from eight-donor output averaging except IS1, which is integrated similarity for one-donor catchment. results that are better than donor catchments selected randomly. The median and average of the NSE values from the 210 catchments for the spatial proximity, physical similarity and integrated similarity approaches are generally more than 0.1 higher than the NSE values from the random selection approach (Tables 2 and 3). The median WBE values from the 210 catchments for the spatial proximity, physical similarity and integrated similarity approaches are generally more than 10 percent lower than those from the random selection approach in the calibration period (Table 2), but are similar to those from the random selection approach in the verification period (Table 3). The integrated similarity approach gives better results in of the 210 catchments but the random selection approach gives better results in catchments (IS8-random8 in Table 4). [46] Although expected, the results here are presented to quantify the benefit of an educated selection of donor catchment, with the results indicating that the relative improvement in the modeling results from an educated selection of donor catchment versus a random selection is similar to the relative improvement of output averaging of results from multiple-donor catchments versus using a single donor catchment. The results for the random selection approach may be dependent on the catchment that happened to be selected randomly. To overcome this, the analysis for the random selection approach is repeated for several times to obtain alternative distributions of results presented in Tables 2 and 3 and Figures 4 7. The repeated analysis showed very similar results to those presented here because of the large number of catchments used here. [47] Tables 2 4 and Figures 4 7 also compare the results from the physical similarity, spatial proximity and integrated similarity approaches. For the physical similarity approach, the results shown are for the use of all eight catchment attributes because the use of all eight catchment attributes generally gives the best or very similar to the best results obtained using various combinations of the catchment attributes. [48] The spatial proximity approach generally performs better than the use of a single physically similar catchment attribute, but only marginally better when all eight catchment attributes are used. The use of an integrated similarity approach that combines both the spatial proximity and catchment attributes may lead to a better choice of donor catchments. Because spatial proximity is generally the best single factor for selecting the donor catchments, it is used together with several other catchment attributes in the integrated similarity approach to select the donor catchments. In general, the use of spatial proximity or geographic distance (D) together with the aridity index (AI) and the mean woody vegetation fraction (WF) gives the best results compared to other combinations, and the integrated similarity results presented here are based D, AI and WF. [49] On average, the integrated similarity approach performs marginally better than the spatial proximity approach, which in turn performs better than the physical similarity approach (Tables 2 4 and Figures 4 7). The averages of the NSE values from the 210 catchments are 0.47, 0.45 and 0.42 respectively for the integrated similarity, spatial proximity and physical similarity approaches for the Xinanjiang model and 0.46, 0.43 and 0.42 respectively for the SIM- HYD model in the calibration period (Table 2), and 0.55, 0.54 and 0.53 for the three approaches respectively for the Xinanjiang model and 0.53, 0.52 and 0.52 for the XIMHYD model in the verification period (Table 4). This difference between the three approaches are relatively small compared to the difference between the educated versus random selections of donor catchments and between the use of multiple-donor catchments versus one donor catchment presented earlier. [50] Table 4 shows that the relative improvement of the spatial proximity approach over the physical similarity Table 3. Verification and Regionalization Results for the Four Regionalization Approaches and the Two Original Rainfall-Runoff Models in the Verification Period (See the Meanings of Abbreviations in Table 2) Model Indicator Verification Random8 PS8 SP8 IS8 IS1 Model Indicator Verification Random8 PS8 SP8 IS8 IS1 Xinanjiang 25th NSE SIMHYD 25th NSE Median NSE Median NSE th NSE th NSE Averaged NSE Averaged NSE Median WBE Median WBE of13

9 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Table 4. Comparison Between the Three Educated Regionalization Approaches, Between Multiple Donors and One Donor and Between The Integrated Similarity Approach and Random Selection (See the Meanings of Abbreviations in Table 2) IS8-SP8 IS8-PS8 SP8-PS8 IS8-IS1 IS8-Random8 <0.02 & > 0.02 <= 0.02 <0.02 & > 0.02 <= 0.02 >=0.02 <0.02 & > 0.02 <= 0.02 >=0.02 <0.02 & > 0.02 <= 0.02 >=0.02 <0.02 & > 0.02 <= 0.02 >=0.02 >=0.02 Model Period Xinanjiang Calibration 82 a Xinanjiang-ET SIMHYD SIMHYD-ET Xinanjiang Verification SIMHYD a Catchment number. approach is more significant than the relative improvement of the integrated similarity approach over the spatial proximity approach in the calibration period. The spatial proximity approach outperforms the physical similarity approach in catchments compared to the physical similarity approach outperforming the spatial proximity approach in catchments (SP8-PS8 in Table 4). The number of catchments where the integrated similarity approach outperforms the spatial proximity approach is only slightly more than the number of catchments where the spatial proximity approach outperforms the integrated similarity approach (IS8-SP8 in Table 4). [51] The relative difference between the three regionalization approaches is more significant in the poorer modeled catchments. The 75th percentile of the NSE values from the 210 catchments are 0.27, 0.25 and 0.17 for the Xinanjiang model and 0.24, 0.19, 0.16 for the SIMHYD model (Table 2), and the number of catchments with negative NSE values are 27, 34 and 47 for the Xinanjiang model and 31, 36 and 42 for the SIMHYD model (Figure 4) Revised Models With RS-LAI [52] The revised models with new ET algorithms using remotely sensed LAI time series data generally perform better than the original rainfall-runoff models. However, the improvements in the performance of the revised models are marginal, where the average of the NSE values from the 210 catchments is less than 0.02 higher in the revised-et models compared to the original models (Table 2 and Figure 4). The WBE values for the revised-et and original models are also very similar (Figure 6). However, the revised models give significantly better results compared to the original models in the poorer modeled catchments. The 75th percentile NSE values for the integrated similarity, spatial proximity and physical similarity approaches respectively are 0.33, 0.27 and 0.22 (and 22, 32 and 38 catchments with NSE less than zero) for the Xinanjiang-ET model compared to 0.27, 0.25 and 0.17 (27, 34 and 47) for the original Xinanjiang model. The 75th percentile NSE values for the integrated similarity, spatial proximity and physical similarity approaches respectively are 0.28, 0.22 and 0.08 (and 26, 32 and 48 catchments with NSE less than zero) for the SIMHYD-ET model compared to 0.24, 0.19 and 0.16 (31, 36 and 42) for the original SIMHYD model. 5. Discussion 5.1. Regionalization Results in the Calibration and Verification Periods [53] As expected, the regionalization results are significantly poorer than the calibration results over The relative difference between the model calibration and model regionalization results is slightly greater than that reported in similar studies [Merz and Bloschl, 2004; Oudin et al., 2008b]. First, the calibration period, , is a very dry period. For the 210 catchments used here, runoff coefficient (Q/P) varies in with a median only 0.10 and aridity index (ET p /P) varies in with a median about 1.55 in the calibration period. Compared to the 210 catchments, the 913 French catchments [Oudin et al., 2008b] are much wetter, showing that runoff coefficient varies in with a median 0.34 and aridity index varies in with a median only The UK and 9of13

10 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 8. Averaged regionalization Nash-Sutcliffe Efficiency (NSE) and median absolute Water Balance Error percentage (WBE) for the 210 catchments versus number of donor catchments used for regionalization. Austrian catchments are also wetter than the catchments in this study [Merz and Bloschl, 2009; Oudin et al., 2008a]. Second, the catchments here spread across a large area covering a large range of climates compared to the catchment used in European studies [Bardossy, 2007; Oudin et al., 2008b; Parajka et al., 2007; Young, 2006]. [54] On the other hand, the regionalization results (model parameters calibrated using data from donor catchments used to model data for the target catchment) are only slightly poorer than the verification results (model parameters calibrated using data used to model runoff over for the same catchment). The first reason for this observation is that the regionalization results are compared directly to the best possible results from the calibration, while the regionalization results are compared to the verification results where parameter values used to model runoff come from the model calibration against data and not the data. The second reason is that the period is significantly wetter than the period (90 percent of the catchments are wetter in the period, and averaged across the 210 catchments the period is 30 percent wetter than the period) and modeling results are generally better for wet catchments compared to dry catchments (Figure 9) Output Averaging of Results From Multiple-Donor Catchments [55] The output averaging of results on average gives considerably better daily runoff simulations than the use of Figure 9. Regionalization Nash-Sutcliffe Efficiency (NSE) against observed catchment mean annual rainfall for the Xinanjiang model in the calibration period. 10 of 13

11 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 10. The Nash-Sutcliffe Efficiency (NSE) difference between spatial proximity and physical similarity and between integrated similarity and spatial proximity against mean annual rainfall, the Xinanjiang model in the calibration period. a single donor catchment because it will average out the effect of choosing a poor donor catchment. [56] The optimum number of donor catchments is likely to be different for different models and modeling approaches and considerations (Figure 8), with most studies using five to ten donor catchments [McIntyre et al., 2005; Oudin et al., 2008b; Viney et al., presented paper, 2008]. It is not the focus of this paper to consider the optimum number of donor catchments, but Figure 8 suggests that while eight donor catchments is likely to be close to the optimum number of donor catchments for the spatial proximity and physical similarity approaches, the integrated similarity approach may show better modeling results if more donor catchments are used Regionalization Approaches Educated Approaches Versus Random Selection [57] The daily runoff modeling results from an educated selection of donor catchments (spatial proximity, physical similarity and integrated similarity approaches) are considerably better than the use of randomly selected donor catchments. The improved modeling results from an educated selection of donor catchments are, on average, similar to the improved modeling from output averaging of results from multiple-donor catchments versus the use of a single donor catchment. This observation is important but seldom reported in the literature, where many studies focus on improving and assessing regionalization results using a single donor catchment while the use of multiple-donor catchments versus a single donor catchment can improve the modeling results as much as a smart selection of donor catchments Comparisons Between the Three Educated Regionalization Approaches [58] The difference between the three regionalization approaches considered here, and used in many other studies, is small compared to the improved modeling results from the use of multiple-donor catchments versus a single donor catchment and an educated selection of donor catchments versus a random selection of donor catchments. The spatial proximity approach generally gives better modeling results than the physical similarity approach, which is also reported in other studies [Oudin et al., 2008b; Parajka et al., 2005]. The spatial proximity approach, where the geographically 11 of 13 closest catchments are chosen as the donor catchments, performs reasonably because neighboring catchments are more likely to have similar hydrological characteristics. The physical similarity approach also attempts to select donor catchments with similar climatic and physical characteristics, but it is difficult to define meaningful lumped catchment-average attributes and derive these attributes accurately. [59] The integrated similarity approach, which combines the spatial proximity and physical similarity approaches, only performs very marginally better than the spatial proximity approach. The relative difference between the three regionalization approaches is more significant in the poorer modeled catchments, where the integrated similarity approach outperforms the spatial proximity approach which in turn outperforms the physical similarity approach. However, there is no clear indication of the integrated similarity approach consistently outperforming the spatial proximity approach or the spatial proximity approach consistently outperforming the physical similarity approach in drier/wetter catchments or in specific spatial locations (Figures 10 and 11) Use of RS-LAI in Rainfall-Runoff Modeling [60] The revised rainfall-runoff models with new evapotranspiration algorithms using remotely sensed LAI time series data performs better than the original models. However, like the above differences between the different approaches for selecting donor catchments, this improvement is marginal in the better modeled ungauged catchments, and more significant in the poorer modeled ungauged catchments. This slight improvement is likely due to the use of additional data (in this case, remotely sensed LAI) to constrain the model calibration and because of the important role that vegetation processes play in controlling runoff. [Siriwardena et al., 2006; Yildiz and Barros, 2007; Zhang et al., 2009]. [61] However, unlike the regionalization approaches which have been widely explored in numerous other studies, this is one of few studies that consider the use of leaf area index in conceptual rainfall-runoff models for prediction in ungauged catchments. It is likely that a better integration of vegetation and other remotely sensed data may further improve the modeling results. These may include calibrating the rainfall-runoff models against both

12 ZHANG AND CHIEW: RUNOFF PREDICTIONS IN UNGAUGED CATCHMENT Figure 11. Comparisons of Nash-Sutcliffe Efficiency (NSE) performance between spatial proximity and physical similarity and between integrated similarity and spatial proximity, the Xinanjiang model in the calibration period. runoff and actual evapotranspiration and/or soil moisture [Zhang et al., 2009] from remote sensing and improving model structure to better incorporate remotely sensed information. 6. Conclusions [62] This study evaluates the relative benefits of different regionalization methods for modeling runoff in ungauged catchments, using two conceptual daily rainfall-runoff models, Xinanjiang and SIMHYD, on 210 relatively unimpacted catchments in southeast Australia. The results show that the biggest benefit comes from an educated selection of donor catchments and output averaging of results from multipledonor catchments. The benefit from an educated selection of donor catchment versus a random selection of donor catchment is similar to the benefit of using multiple-donor catchments versus a single donor catchment. [63] The difference between the three commonly used approaches for selecting donor catchments is relatively small. The spatial proximity approach (where the geographically closest catchment is used as the donor catchment) performs slightly better than the physical similarity approach (where the catchment with the most similar attributes is used as the donor catchment). The integrated similarity approach which combines the spatial proximity and physical similarity approaches performs only very marginally better than the spatial proximity approach. The relative difference between the three approaches are more significant in the poorer modeled catchments where the integrated similarity approach performs better than the spatial proximity approach which in turn performs better than the physical similarity approach. [64] The incorporation of LAI data into the rainfall-runoff models only show marginal improvement to the modeling results. However, unlike the regionalization approaches 12 of 13 which have been widely explored in numerous other studies, this is one of few studies that consider the use of LAI in conceptual rainfall-runoff models for prediction in ungauged catchments and a better integration of vegetation and other remotely sensed data may further improve the modeling results. [65] Acknowledgments. The study was supported by the Science Leadership Scheme and the Water Resources Assessment and Accounting Project (WIRADA) in Australian Commonwealth Scientific and Industrial Research Organization (CSIRO). We thank Jenet Austin for calculating the catchment attributes used in this study and Hongxia Li, David Post, and Jai Vaze for helpful discussions. We also thank the three Water Resources reviewers and the Associate Editor whose detailed comments led to significant improvement of the article. References Bardossy, A. (2007), Calibration of hydrological model parameters for ungauged catchments, Hydrol. Earth Syst. Sci., 11, Beven, K., and J. Freer (2001), Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, Bloschl, G., and M. Sivapalan (1995), Scale issues in hydrological modeling A review, Hydrol. Processes, 9, Chau, K. W. (2006), Particle swarm optimization training algorithm for ANNs in stage prediction of Shing Mun River, J. Hydrol., 329, Chen, J., P. Jonsson, M. Tamura, Z. H. Gu, B. Matsushita, and L. Eklundh (2004), A simple method for reconstructing a high-quality NDVI timeseries data set based on the Savitzky-Golay filter, Remote Sens. Environ., 91, Cheng, C. T., C. P. Ou, and K. W. Chau (2002), Combining a fuzzy optimal model with a genetic algorithm to solve multi-objective rainfall-runoff model calibration, J. Hydrol., 268, Chiew, F. H. S., and T. A. McMahon (2002), Global ENSO-streamflow teleconnection, streamflow forecasting and interannual variability, Hydrol. Sci. J., 47, Chiew, F. H. A., T. C. Piechota, J. A. Dracup, and T. A. McMahon (1998), El Niño Southern Oscillation and Australian rainfall, streamflow and drought: Links and potential for forecasting, J. Hydrol., 204, Chiew, F. H. S., M. C. Peel, and A. W. Western (2002), Application and testing of the simple rainfall-runoff model SIMHYD, in Mathematical