Application of a Macroscale Hydrologic Model to Estimate Streamflow across Southeast Australia

Fangfang Zhao CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, Australian Capital Territory, Australia

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Francis H. S. Chiew CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, Australian Capital Territory, Australia

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Lu Zhang CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, Australian Capital Territory, Australia

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Jai Vaze CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, Australian Capital Territory, Australia

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Jean-Michel Perraud CSIRO Water for a Healthy Country National Research Flagship, CSIRO Land and Water, Canberra, Australian Capital Territory, Australia

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Ming Li CSIRO Mathematics Informatics and Statistics, Perth, Western Australia, Australia

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Abstract

Reliable predictions of water availability and streamflow characteristics, and the impact of climate and land use change on water availability, are central to water resources planning and management. This paper assesses the application of the widely used macroscale hydrologic model, the three-layer Variable Infiltration Capacity model (VIC-3L), to estimate daily streamflow in 191 unregulated catchments across southeast Australia and evaluates the regionalization of model parameters to predict streamflow in ungauged catchments. The parameter values in the VIC-3L model are estimated using three methods: default values, optimized values based on model calibration, and regionalized values based on spatial proximity method. The modeled streamflows from VIC-3L are assessed against the observed streamflows from the catchments. The authors discuss the model performance based on different parameter estimation methods and the effects of rainfall regimes on streamflow prediction. Also the implication of using a priori estimates of parameter values versus optimizing parameter values against observed streamflow to predict the impact of climate and land use change on streamflow is discussed. The VIC-3L model can simulate the streamflow in the catchments across southeast Australia reasonably well, with comparable results to those reported for the same region using conceptual rainfall-runoff models. The model performed better in summer-dominant rainfall catchments and wet catchments than in other catchments. The regionalization based on spatial proximity method performed reasonably well, which demonstrated the potential of VIC-3L model to predict streamflow in ungauged catchments in Australia.

Corresponding author address: Fangfang Zhao, CSIRO Land and Water, GPO Box 1666, Canberra ACT 2601, Australia. E-mail: fangfang.zhao@csiro.au

Abstract

Reliable predictions of water availability and streamflow characteristics, and the impact of climate and land use change on water availability, are central to water resources planning and management. This paper assesses the application of the widely used macroscale hydrologic model, the three-layer Variable Infiltration Capacity model (VIC-3L), to estimate daily streamflow in 191 unregulated catchments across southeast Australia and evaluates the regionalization of model parameters to predict streamflow in ungauged catchments. The parameter values in the VIC-3L model are estimated using three methods: default values, optimized values based on model calibration, and regionalized values based on spatial proximity method. The modeled streamflows from VIC-3L are assessed against the observed streamflows from the catchments. The authors discuss the model performance based on different parameter estimation methods and the effects of rainfall regimes on streamflow prediction. Also the implication of using a priori estimates of parameter values versus optimizing parameter values against observed streamflow to predict the impact of climate and land use change on streamflow is discussed. The VIC-3L model can simulate the streamflow in the catchments across southeast Australia reasonably well, with comparable results to those reported for the same region using conceptual rainfall-runoff models. The model performed better in summer-dominant rainfall catchments and wet catchments than in other catchments. The regionalization based on spatial proximity method performed reasonably well, which demonstrated the potential of VIC-3L model to predict streamflow in ungauged catchments in Australia.

Corresponding author address: Fangfang Zhao, CSIRO Land and Water, GPO Box 1666, Canberra ACT 2601, Australia. E-mail: fangfang.zhao@csiro.au

1. Introduction

Hydrological processes occur at a wide range of spatial and temporal scales, and the dominant controls of key processes are scale dependent (Klemeš 1983). As a result, a number of hydrological models have been developed depending on conceptualization of dominant processes and scales of interest. It is generally accepted that hydrological models are simplifications of real world catchments regardless of how complex they are. From this point of view, no hydrological model is perfect. Nevertheless, hydrological models are useful tools in our attempts to understand catchment behaviors and impact of climate and land use changes on the water balance. In fact, in many cases, hydrological models are the only tools available to use and they are increasingly used for operational purposes and scientific investigations.

In general, hydrologic models represent catchments using state variables and parameters. The state variables define functional relationships between fluxes and storages of catchments and form the basic frameworks of hydrologic models, while model parameters quantify the relationships of the various model components and are usually considered time invariant. Parameter estimation has been an important part of hydrologic research for decades and much effort has been directed toward the improvement of model accuracy. Application of hydrological models requires estimation of model parameters. In gauged catchments, model calibration is commonly used to obtain parameter values. The accuracy of a model in simulating fluxes, such as streamflow, depends on how well the model can be calibrated against observed streamflow. It is obvious that the model accuracy is determined by how well it represents the key processes that control catchment water balance. In ungauged catchments, the reliable streamflow estimation has remained a largely unsolved problem (Wagener and Wheater 2006). There is an increasing need for predictions in ungauged catchments. In this case, model parameter values have to be estimated using other means (Post and Jakeman 1999; Fernandez et al. 2000; Wagener and Wheater 2006). Attempts have been made to derive model parameters for ungauged catchments using the spatial proximity method whereby the calibrated model parameters from the nearest gauged catchments are used to simulate streamflow in the ungauged catchment (Vandewiele and Elias 1995). Many studies have confirmed the value of the spatial proximity method as a regionalization technique (Merz and Blöschl 2004; Oudin et al. 2008; Parajka et al. 2005; Zhang and Chiew 2009). Other approaches of regionalization include a hydrologic similarity method in which a similarity index is defined based on catchment characteristics (e.g., slope and stream density) and the calibrated model parameters from the most similar gauged catchment are used in the ungauged catchment (McIntyre et al. 2005; Reichl et al. 2009). Probably the most common regionalization approach is to establish statistical relationships between model parameters and catchment characteristics and various statistical techniques have been used (Fernandez et al. 2000; Vogel 2005; Wagener and Wheater 2006).

A number of studies have shown that catchment water balance is controlled by climate and catchment characteristics. The degree of control exerted by these factors varies with the spatial and temporal scales of the processes modeled. At mean annual scale, the water balance is dominated by climatic factors such as average precipitation and potential evapotranspiration. Hence, one can ignore the effect of catchment soil moisture storage. At shorter time scales, other factors become important in controlling water balance and one has to take into consideration the effects of soil moisture dynamics and other rainfall characteristics on catchment responses; hence, increased model complexity is required (Zhang et al. 2008). Catchments often exhibit strong spatiotemporal dynamics in water balance components such as soil moisture.

The hydrological behaviors of a catchment are the result of complex interactions among soil, vegetation, and climate. Peel et al. (2001) showed that hydrological characteristics of a catchment are climate dependent. As a result, catchments can be classified based on climatic and vegetation conditions. They showed that Australian catchments are different from the catchments in other parts of the world in several aspects. Australian catchments tend to show greater variability and are more sensitive to changes in climatic variables (e.g., rainfall). Vaze et al. (2011a) applied six hydrological models to Australian catchments and showed that they are capable of simulating historical streamflow. The models used by Vaze et al. were developed for hydrological applications with a focus on streamflow. These models are more suited to small to medium-sized catchments.

Liang et al. (1994, 1996a) developed a macroscale hydrological model—the three-layer Variable Infiltration Capacity model (VIC-3L)—that included water balance and energy balance. It is designed for hydrological investigations and it can also be used as a land surface model for global climate modeling. The VIC model has been widely tested and used in the United States and other countries (Abdulla et al. 1996; Bowling et al. 2000; Lohmann et al. 1998; Nijssen et al. 1997, 2001; Shi et al. 2008; Su et al. 2005; Wood et al. 1997; Zhu and Lettenmaier 2007). It has also been included in several large international projects such as the Project for Intercomparison of Land-Surface Parameterization Schemes (PILPS) (Liang et al. 1998; Wood et al. 1998) and North America Land Data Assimilation (NLDAS) (Lohmann et al. 2004; Schaake et al. 2004). Unlike most lumped conceptual hydrological models, the VIC-3L model considers both water balance and energy balance and it also explicitly represents soil and vegetation information in simulating streamflow. One of the attractive features of the VIC model is the representation of subgrid variability of precipitation and infiltration.

There are only a few studies that investigate the application of the VIC model in Australian catchments. Sivapalan and Woods (1995) made a preliminary attempt to evaluate the impact of subgrid variability of rainfall in one catchment in southwest Western Australia. Kalma et al. (1995) investigated the concept of a catchmentwide soil moisture index based on limited field measurements in a small catchment in southeast Australia. Both studies used the earlier version of the VIC model with a single soil layer (Wood et al. 1992). There is no study in Australian catchments since Liang et al. (1994) generalized the two-layer VIC model (VIC-2L) to include the multiple soil layer and spatially varying vegetation and evaporation within a grid cell. This is the first study that investigates the applicability of VIC-3L using data from a large number of catchments spread across southeast Australia.

A macroscale hydrologic model (i.e., the VIC) is usually applied at continental- or subcontinental-scale catchments with large-scale spatial resolution. For example, Abdulla et al. (1996) and Abdulla and Lettenmaier (1997a,b) used the VIC model to simulate the water balance of the Red–Arkansas basin at 1° × 1° grids, and there are a number of studies where the model was applied at spatial resolutions ranging from 0.125° to 2° (Lohmann et al. 1998; Wood et al. 1997; Nijssen et al. 1997, 2001; Xie et al. 2007). In comparison with above published studies, this paper is one of few studies applying a macroscale hydrologic model at high spatial resolution scale (0.05° × 0.05°), and it is the first study conducting macroscale hydrologic modeling using a large number of small to medium-sized catchments across southeast Australia.

The hydrologic characteristics of the catchments in Australia are very different from catchments in the United States and other countries (McMahon et al. 2007). Australian catchments have a lower runoff coefficient and much larger hydroclimatic variability compared to similar catchments across the world (Peel et al. 2004). These catchments show significant variability in streamflow and even ephemeral flow regime. Occurrence of very low flows or zero flows makes it challenging for any hydrological model to accurately simulate streamflow for these catchments. Therefore, it is necessary to evaluate the applicability of hydrological models to Australian catchments, although these models may have been successfully applied to catchments elsewhere.

The purpose of this study is to assess the application of the VIC-3L model to estimate daily streamflow in unregulated catchments across southeast Australia and to evaluate the regionalization of parameters in the VIC-3L model to predict streamflow in ungauged catchments.

2. Catchment description and data

a. Catchments and streamflow data

The study area (Fig. 1) is in southeast Australia and includes the Murray–Darling basin and the Southeast Coast drainage divisions (the Great Dividing Range separates these two drainage divisions). In total, 191 catchments that have at least 10 complete years of unregulated daily streamflow data and a catchment area between 50 and 2000 km2 were used in this study. All catchments are located in the upland areas in southeast Australia and along the east coast where most of the runoff is generated (see Fig. 1). The streamflow data were obtained from the relevant state government agencies, and additional checks were carried out to ensure data quality for use in large-scale hydrological modeling (Vaze et al. 2011a). Unregulated streamflow is defined as streamflow that is not subject to regulation or diversion. The mean annual streamflow across the catchments ranges from 11 to 1421 mm.

Fig. 1.
Fig. 1.

Locations in the study area and selected catchments representing summer-dominant rainfall, nonseasonal rainfall, and winter-dominant rainfall.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Table 1 gives the summary of catchment characteristics. Southeast Australia covers large geographic and climatic regions and spans a variety of climates from temperate near the coast to semiarid and arid farther inland toward the northwest and west (Vaze et al. 2011a). Across the catchments the mean annual rainfall varies from 441 to 2034 mm and the proportion of mean annual rainfall that becomes runoff ranges from 2% to 86%, representing diverse hydrological conditions. There are clear east–west rainfall and streamflow gradients with higher values in the southeast and along the east coast and lower values in the west (Chiew et al. 2009). Rainfall seasonality is important for the water balance of Australian catchments and the selected catchments in this study were classified based on seasonal rainfall and potential evapotranspiration as described in Potter et al. (2005) and Hickel and Zhang (2006). Three groups of catchments with different rainfall seasonality were considered: winter-dominant rainfall, summer-dominant rainfall, and nonseasonal rainfall. The vegetation in the catchments includes native woodlands, open forests, rain forests, eucalyptus, various species of pine trees, native and managed grass, and dryland agricultural crops. The catchments cover soil types from sand through loams to clays with large differences in soil properties such as saturated hydraulic conductivity and water holding capacity.

Table 1.

Summary of catchment information.

Table 1.

b. Meteorological forcing data

The meteorological data (rainfall and temperature) were used as driving variables for the VIC-3L model. Daily rainfall and maximum and minimum temperatures over 0.05° grids were obtained from the “SILO Data Drill” of the Queensland Department of Natural Resources and Water (http://www.longpaddock.qld.gov.au/silo/; Jeffrey et al. 2001). The SILO Data Drill data were interpolated from point measurements made by the Australian Bureau of Meteorology.

c. Vegetation and soil dataset

The vegetation types and land cover information at 0.05° × 0.05° grid resolution were obtained from the University of Maryland (UMD) land cover data at a 1 × 1 km2 global resolution on the basis of Advanced Very High Resolution Radiometer data (Hansen et al. 2000), with fractional subgrid cover allowing for multiple types of land cover in one grid cell. The soil texture information and soil bulk densities at 0.05° × 0.05° grid resolution were derived from the 5-min Food and Agriculture Organization dataset (FAO 1998). In the VIC-3L model application in this study, 11 vegetation types such as grassland and cropland and 12 soil types were considered.

3. Methods

a. Model description

The Variable Infiltration Capacity, VIC-3L, model (Liang et al. 1994, 1996a,b) is a large-scale distributed hydrologic model that solves the coupled water and energy balances at the land surface. One of the key characteristics of the model is the representation of subgrid spatial variability in precipitation and infiltration capacity. It also explicitly represents multiple land covers (i.e., different vegetation covers and bare soil) and subgrid variability of topography using elevation bands. In the VIC configuration, the soil column is typically divided into three layers: top layer, upper layer, and lower layer. The top soil layer is generally a thin soil layer that allows for quick bare soil evaporation to take place. The upper soil layer is designed to represent the dynamic response of soil to rainfall events, and the lower layer is used to characterize seasonal soil moisture behavior. Exchange of soil moisture between the soil layers is modeled based on soil moisture content and hydraulic conductivity. The VIC model calculates canopy evaporation, vegetation transpiration, and soil evaporation separately using canopy interception capacity, canopy resistance, infiltration capacity, and potential evaporation. Total runoff is modeled as the sum of direct runoff and subsurface runoff, which is represented by the Arno model formulation (Franchini and Pacciani 1991).

The VIC-3L model (version 4.0.6) was applied to the study catchments at 0.05° × 0.05° grid spatial resolution and 24-h time step. This study is for water balance modeling, so only the water balance mode was chosen. In the VIC model, each grid cell is modeled independently without horizontal water flow. The routing of flows was not included because the catchments are relatively small.

b. Model parameters

There are a number of parameters in the VIC-3L model (Liang et al. 1994, 1996b) and they are primarily related to soil texture and vegetation types. The principal parameters and their estimation methods are summarized in Table 2. The soil parameters include porosity (ρ), saturated soil water potential (ψs), saturated hydraulic conductivity (Ks), and an exponential unsaturated hydraulic conductivity curve (c). In ideal cases, these parameter values can be obtained by fitting experimental data to specified functions. When no such data are available, the parameter values can be estimated based on soil texture and particle size distribution. It should be noted that some of the soil parameters listed in Table 2 are unique to the VIC model and include thicknesses of the three soil layers (d1, d2, and d3); the infiltration parameter (b), which controls the shape of the spatial distribution of soil moisture storage capacity over a grid; and three parameters related to the baseflow scheme. The baseflow parameters are the maximum baseflow that can occur from the lowest soil layer (Dsmax), the fraction of the maximum baseflow where nonlinear baseflow begins (Ds), and the fraction of the maximum soil moisture of the lowest soil layer where nonlinear baseflow occurs (Ws). These parameter values are generally obtained by model calibration based on the agreement between simulated and observed hydrographs.

Table 2.

VIC-3L model parameters and their estimating methods.

Table 2.

The vegetation parameters of the VIC-3L model are used to describe the energy balance, canopy transpiration, and interactions between soil and vegetation. Most of the vegetation parameters can be obtained from published literature. Canopy albedo (α) is considered as a constant for a given vegetation type. Roughness length (z0) and zero-plane displacement (d0) affect the turbulence transport of water between canopy and the atmosphere and they are estimated from the height of vegetation canopy (Brutsaert 1982). Architectural resistance (rarc) and minimum stomata resistance (rmin) control vegetation transpiration and they were estimated from the Land Data Assimilation Systems developed by the National Aeronautics and Space Administration (http://ldas.gsfc.nasa.gov/).

c. Parameter estimation

Parameter estimation is a critical step in application of hydrological models to catchments as model parameter values quantify partitioning of rainfall into runoff and evapotranspiration. Of the VIC-3L parameters listed in Table 2, some can be estimated a priori based on soil and vegetation characteristics, and others have to be determined by model calibration. In this study, for each grid cell within a catchment the vegetation parameters were estimated primarily from the Land Data Assimilation Systems (http://ldas.gsfc.nasa.gov/) and the soil parameters were determined from the FAO soil texture maps and Cosby et al. (1984) and Rawls et al. (1998). There are seven parameters in the VIC-3L model that need to be optimized: they are b, Ds, Dsmax, Ws, d1, d2, and d3 (Su et al. 2005). In this study, the thickness of top soil layer (d1) was set to 10 cm for every grid cell, following Liang et al. (1996b). The other six sensitive parameters were considered uniform across a catchment and estimated using three methods: default parameter values, model calibration, and spatial proximity method in the case of predictions of ungauged catchments.

1) Default parameter values

Macroscale hydrological models and land surface models are typically applied to large spatial scales. Applications of these models require a priori estimates of model parameters (Duan et al. 2006). As a macroscale hydrological model, the VIC-3L model has a number of parameters. Some of them are related to vegetation characteristics and soil properties and these parameters are generally obtained from published literatures. The other model parameters have to be estimated by model calibration. However, model calibration is possible only in regions with measured streamflow data. In this study, we are also interested in predictions of streamflow in ungauged catchments and want to know if the model parameters estimated from other studies can be applied to Australian catchments. There has been a number of studies to examine the model parameters of the VIC-3L model and the parameter values obtained from these studies may be considered as a priori estimates of the model parameters for Australian catchments. In the default parameter experiment here, the six sensitive soil parameters were set to values of b = 0.3, Ds = 0.02, Dsmax = 10, Ws = 0.8, d2 = 0.5, and d3 = 2.0 following Xie et al. (2007).

2) Optimized parameter values based on model calibration

The six sensitive model parameter values (b, Ds, Dsmax, Ws, d2, and d3) were obtained by calibrating the VIC-3L model against 1975–85 observed daily streamflow. A combination of a “global search” (shuffled complex evolution) (Duan et al. 1992) and a “steepest gradient” (Rosenbrock 1960) method was applied for parameter optimization, with multiple starting parameter sets to increase the likelihood of locating the global optimum (Vaze et al. 2011b). In the model calibration, the model parameters were optimized to maximize the E-bias objective function, which is a weighted combination of daily Nash–Sutcliffe (Nash and Sutcliffe 1970) efficiency and a logarithmic function of bias given by
e1
where E is the Nash–Sutcliffe efficiency of daily streamflow and B is the bias (total prediction error divided by total observed streamflow) (Viney et al. 2009a). The coefficients of this equation control the severity and shape of the bias constraint penalty.

The split-sample test was applied where the observed streamflow was divided into two roughly equal parts for calibration and validation (Klemeš 1986; Refsgaard and Knudsen 1996). On the basis of this test, the periods 1975–85 and 1986–95 were selected as the calibration and validation periods, respectively.

3) Regionalized parameter values based on spatial proximity method

To assess the model prediction in ungauged catchments, the regionalization based on spatial proximity was used. In the spatial proximity method the entire set of calibrated parameters is transferred from closest neighboring catchments to the ungauged catchments. The method is based on the rationale that catchments close to each other should have similar behavior since climate and other catchment conditions should have little difference in space (Oudin et al. 2008). The same 191 gauged catchments are used in this study but with each catchment, in turn, treated as ungauged (termed as “pseudo ungauged”) for the purpose of assessment. The selection of the donor catchments is based on the proximity of the ungauged catchments to the gauged ones; that is, the geographically closest gauged catchment is chosen as the donor catchment. The distance measure is regarded as the distance between catchment centroids. To ensure the representativeness of potential donor catchments, only catchments with E values greater than 0.4 are used as donor catchments, while all catchments whether poorly or well modeled are considered in turn to be ungauged.

4. Results

a. Model performance with default parameter values

The VIC model was first applied to all of the selected catchments with default parameter values to simulate daily streamflow, and the results are shown in Fig. 2. Maximum E value is 0.55 and 13% of the catchments have E values greater than 0.3. The bias in the simulated daily streamflow is also large. It is clear that the model with default parameter values is not able to accurately simulate daily streamflow in most of the catchments. The default parameters used in this study are based on published literature using Chinese catchments (Xie et al. 2007). The variability of hydroclimatic characteristics is much larger in Australian catchments (McMahon et al. 2007). This suggests that other methods are needed to estimate model parameter values in order to simulate the observed daily streamflow in Australian catchments.

Fig. 2.
Fig. 2.

Summary of model simulations with default parameter values and summary of model calibration and validation for all catchments: (a) percentage of catchments (a) with E value greater than or equal to a given E value and (b) where bias value exceeded. A good model performance is indicated by high E values and low B values.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

b. Model performance with parameter optimization

1) Overall model performance

Results of model calibration and validation at a daily time step are also shown in Fig. 2. It is clear that the model can be well calibrated against the daily streamflow for a large number of catchments. The majority of catchments have values of the coefficient of efficiency ranging between 0.30 and 0.95 with less than 8% of the catchments having calibration E values less than 0.30 in the calibration period. The validation results are slightly poorer than the calibration results with averaged E value in the validation period generally being 0.09 lower than that in the calibration period. The E values for the validation period have been plotted versus the E values for the calibration period in Fig. 3. The points mostly cluster around the 1:1 line, so the performances of the calibration and validation periods are similar, which confirms the successful application of the VIC-3L model in the southeast Australian catchments. The validation E values in some of the catchments are higher than the corresponding calibration E values. A possible reason for this could be higher rainfall and streamflow during the validation periods in these catchments.

Fig. 3.
Fig. 3.

Summary of model efficiencies for the calibration and validation periods.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Detailed results of the model performance in the calibration and validation periods are summarized in Table 3. The 25th percentile, median, and 75th percentile E values for all catchments in the calibration period are 0.73, 0.59, and 0.45, respectively. The averaged E value is 0.57 and the median absolute bias is 4%. As a measure of scatter, the scatter of E values (i.e., difference of 25% and 75% quantiles of efficiencies) and |B| values are 0.31 and 5%. These results show that the VIC-3L model can be well calibrated for most Australian catchments at the daily time step. The validation results shown in Fig. 2 and Table 3 indicate that 75% of the catchments have E values greater than 0.35, over 50% of the catchments have E values greater than 0.51, and over 25% of the catchments have E values greater than 0.67. The averaged E value is 0.48 for all catchments with the median absolute bias of 13%. The decrease of model performance when moving from the calibration period to the validation period is termed the temporal loss in model efficiencies (Merz and Blöschl 2004). So, the temporal loss in model efficiencies is 0.08 based on median efficiency decreases from 0.59 to 0.51 for the calibration and validation periods.

Table 3.

Results of model calibration, validation and regionalization.

Table 3.

2) Model performance in catchments with different rainfall regimes

Rainfall seasonality is an important factor controlling catchment-scale water balance (Potter et al. 2005). The performances of the VIC-3L model in the catchments with different rainfall seasonality are evaluated to better understand the seasonality effect on streamflow. Results of model calibration and validation for catchments with different rainfall regimes are shown in Fig. 4. It is clear that the model performed best (i.e., high E values and low B values) in the catchments with summer-dominant rainfall in both calibration and validation periods. The results in the catchments with winter-dominant rainfall are slightly better than those in the catchments with nonseasonal rainfall.

Fig. 4.
Fig. 4.

Summary of model calibration and validation for catchments with different rainfall regimes: percentage of catchments (a) with E value greater than or equal to a given E value and (b) where bias value exceeded. A good model performance is indicated by high E values and low B values.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Figure 5 shows the results of model performance for the calibration period in three selected catchments representing the three rainfall regimes. Apart from different rainfall regime, average annual rainfall in these catchments ranged from 873 mm (catchment 221210) to 1535 mm (catchment 208015). It can be noted that the first two catchments (i.e., 208015 and 221210) are flashy with large streamflows following heavy rainfall events and the catchments showed little baseflow components. On the other hand, the third catchment exhibits hydrological features of a wet catchment with sustained baseflow, but the magnitude of the streamflow is much lower compared with catchment 208015, which has similar average annual rainfall and runoff ratio. Despite the differences in streamflow characteristics, the model was able to simulate daily streamflow time series well with both high flows and low flows accurately simulated. The E values for the three catchments are 0.92, 0.81, and 0.84 and the bias is less than 3%. No systematic error has been found in the simulated daily streamflow (Fig. 5). The points cluster around the 1:1 line in the scatterplots of observed and simulated daily streamflow.

Fig. 5.
Fig. 5.

(a) Scatterplots of observed and simulated daily streamflow for the period of 1975–85 for three selected catchments representing summer-dominant rainfall (208015), nonseasonal rainfall (221210), and winter-dominant rainfall (405209); (b) time series of observed (red dash line) and simulated (black solid line) daily streamflow and daily rainfall (blue column) for the same catchments.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Figure 6 shows comparisons of the simulated and observed daily flow duration curves for the three selected catchments. As discussed above, these catchments exhibit different streamflow characteristics. Catchments 208015 and 221210 showed higher streamflow variability compared with catchment 405209 and experienced zero flows. The ephemeral nature of the streamflow in these two catchments presents a challenge for the VIC model. The results shown in Fig. 6 demonstrate that the VIC model provides a good fit to the observed flow duration curves. The model is considered capable of accurately simulating daily streamflow regime.

Fig. 6.
Fig. 6.

Comparison of observed and simulated daily flow duration curves in the selected catchments for calibration period and validation period.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

3) Model performance in catchments with different average annual rainfall

Climatic factors such as mean annual rainfall can significantly affect catchment water balance (Zhang et al. 2008). The model performances in the catchments with different mean annual rainfall are investigated to better understand the hydrological characteristics of the catchments. Figure 7 shows the results of model calibration and validation for catchments with different mean annual rainfall. It is obvious that the model performed better in the catchments with higher mean annual rainfall in both calibration and validation periods. These results support the conclusion that hydrological models usually perform better in higher rainfall catchments (Gallart et al. 2007; Gan et al. 1997; Hughes 1997; Lidén and Harlin 2000; Perrin et al. 2007; Vaze et al. 2010).

Fig. 7.
Fig. 7.

Summary of model calibration and validation: percentage of catchments (a) with E value greater than or equal to a given E value and (b) where bias value exceeded for different rainfall ranges. A good model performance is indicated by high E values and low B values.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

c. Parameter distribution

Figure 8 shows the distribution of the calibrated model parameter values for catchments with different rainfall regimes. Of the six model parameters, b and d2 showed large differences across the catchments with different rainfall seasonality, and other parameter values are more consistent.

Fig. 8.
Fig. 8.

Distribution of calibrated model parameter values for catchments with different rainfall regimes.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Parameter b ranges from 0.0001 to 0.40 and most of the winter-dominant catchments tend to have b value less than 0.15. The summer-dominant and nonseasonal catchments showed a wider range in b value. Parameter d2 ranges from 0.13 to 1.5 m. The summer-dominant catchments had d2 in the range of 0.13 to 1.0 m with 35% of the catchments having d2 value in a narrow range of 0.6 to 0.75 m. The winter-dominant and nonseasonal catchments showed similar distributions in d2 with the majority of catchments having d2 value in the range from 0.75 to 1.5 m. Other model parameters (i.e., Ds, Dsmax, Ws, and d3) showed consistent distributions across all three rainfall regimes. Parameters Ds and Ws showed strong bimodal distributions with most of the catchments having either small or large values. Parameter Dsmax also showed some degrees of bimodal distribution with the majority of catchments having Dsmax in the range from 27 to 30. Most of the catchments had d3 values in a narrow range (0.1 to 0.15 m). It can be noted that some of the model parameters reached their maximum and minimum values recommended by the model developer (http://www.hydro.washington.edu/Lettenmaier/Models/VIC/).

d. Predictions in ungauged catchments

The model performances using regionalized parameters are shown in Fig. 9 together with the results of model calibration and validation. The coefficient of efficiencies using regionalized parameters are plotted in Fig. 10 against the model efficiencies using calibrated parameters in the calibration period (1975–85) and validation period (1986–95). As expected, the model performance using regionalized parameters decreased compared to calibration results, consistent with the conclusions of Merz and Blöschl (2004) and Zhang and Chiew (2009). However, the degradation here is smaller than that of Vaze et al. (2010) for similar southeast Australian catchments.

Fig. 9.
Fig. 9.

Summary of model calibration (solid lines), validation (dash lines), and regionalization (dotted lines): percentage of catchments (a) with E value greater than or equal to a given E value and (b) where bias value exceeded. A good model performance is indicated by high E values and low B values.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Fig. 10.
Fig. 10.

Summary of model efficiencies of regionalized vs calibrated parameters for the periods of (a) calibration (1975–85) and (b) validation (1986–95).

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Figure 10a shows scatterplots of model efficiencies of regionalized and calibrated parameters in the calibration period. It is clear that most points are below the 1:1 line, so for most of the catchments the model efficiencies based on regionalized parameters are lower than those based on calibrated parameters. However, in some catchments the efficiencies of model regionalization are higher than those of the model calibration. This is because of the volumetric constraint used in model calibration that is not there in model regionalization. Table 3 summarizes the regionalization results in the calibration period. The 25th percentile, median percentile, and 75th percentile E values for the regionalization results are 0.17, 0.16, and 0.18 lower than the calibration results. The averaged E values from regionalization results are 0.16 lower than that from calibration results, with median percentile absolute bias 0.24 higher. The scatter of E values based on regionalized parameters are similar to that based on calibrated parameters, but the scatter of absolute bias is larger. The above findings are not surprising as the objective function in the calibration procedure is closely related to the E value and bias value.

The E values of the model regionalization are lower compared with the validation results as shown in Figs. 9 and 10b. The averaged E values and median percentile absolute bias from regionalization results are 0.11 lower and 0.15 higher than that from validation results (Table 3). The scatters of the E values in the model regionalization are similar to those in the validation period. However, the scatters of absolute B values are higher than those in the validation period. This is expected as the parameters are transferred to a different catchment in regionalization compared to validation where the parameters are used for a different period but for the same catchment.

The results of model regionalization for catchments with different rainfall regimes and different mean annual rainfall in the calibration period are shown in Figs. 11 and 12. Similar results using regionalized parameters are shown with the results using calibrated parameters among catchments with different rainfall regimes and different mean annual rainfall. The model performed best in the catchments with summer-dominant rainfall and performed slightly better in the catchments with winter-dominant rainfall than in the catchments with nonseasonal rainfall. Meanwhile, the model using regionalized parameters exhibits better performance in the catchments with high mean annual rainfall.

Fig. 11.
Fig. 11.

Summary of model regionalization for catchments with different rainfall regimes. (a) Percentage of catchments with E value greater than or equal to a given E value and (b) percentage of catchments where bias value exceeded. A good model performance is indicated by high E values and low B values.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

Fig. 12.
Fig. 12.

As in Fig. 11 but with different mean annual rainfall.

Citation: Journal of Hydrometeorology 13, 4; 10.1175/JHM-D-11-0114.1

5. Discussion

a. How do results compare with outputs from other hydrological models?

Figures 27 showed that the VIC-3L model can be successfully applied to catchments across southeast Australia with different rainfall regimes and mean annual rainfall. The successful application of the VIC-3L model to Australian catchments suggests that the model is capable of representing hydrological processes in Australian catchments.

However, the results from this study are not as good as those reported for the same regions by Chiew et al. (2009), Li et al. (2009), Reichl et al. (2009), Vaze et al. (2011a), and Zhang and Chiew (2009) using different rainfall–runoff models. This may be due to several reasons. The VIC-3L model is not focused solely on simulating daily streamflow and it aims to simulate other water balance components (e.g., soil evaporation and vegetation transpiration). Much better model performances are derived by accumulating the simulated daily to monthly streamflow and comparing this to the observed monthly streamflow. The median percentile E values for all catchments at monthly time scale in the calibration and validation periods are 0.79 and 0.77, respectively. The VIC-3L model used in this study does not include an infiltration excess runoff mechanism, which can be important in some of the Australian catchments, especially in the catchments with low mean annual rainfall. Potter et al. (2005) discussed the effects of infiltration excess runoff on streamflow in some Australian catchments and argued that lack of infiltration excess runoff in the probabilistic water balance model may explain some of the differences between observed and simulated runoff. The infiltration excess runoff occurs when the rainfall rate is larger than the infiltration capacity and usually requires high resolution input (mostly hourly) in the model (Liang and Xie 2001). The VIC-3L model is run at a daily time step in this study, which is difficult to represent the runoff generation mechanism with infiltration excess.

Potter et al. (2005) and Hickel and Zhang (2006) showed that rainfall seasonality is important for the water balance of Australian catchments. Catchments with the same mean annual rainfall may have different streamflow because of different rainfall distribution (Hickel and Zhang 2006). The summer-dominant rainfall catchments tend to have a higher average annual runoff coefficient compared to the winter-dominant rainfall and nonseasonal rainfall catchments. This may partly explain better model performance observed in the summer-dominant rainfall catchments.

The VIC-3L model performs better in the wetter catchments, as shown in Fig. 7, and this highlights the difficulty in simulating streamflow from catchments under dry climatic conditions. It is known that most of our hydrological models were developed for catchments in humid regions where saturation excess runoff is likely to be the dominant runoff generation mechanism. For catchments in arid regions the infiltration excess runoff may play an important role in runoff generation and baseflow is generally a small component of total runoff. Dry catchments also have more cease-to-flow days, making flow predictions more difficult. One of the other features of catchments in arid regions is more variable rainfall distribution in space and time (Pilgrim et al. 1988). The combined effect of these features means that runoff simulation for dry catchments is generally associated with larger uncertainty. Better model performance observed in catchments with a higher rainfall/runoff ratio may be attributed to the fact that the relative errors in both rainfall and runoff are lower and also these catchments generally contain enough high flows to adequately calibrate model parameters responsible for simulating high flows. Gupta et al. (1999) showed that hydrological model performance tends to improve with flow levels with higher coefficient of efficiency and lower percent bias in simulating the above-mean flow. Houghton-Carr (1999) reported that better model performances tended to be shown in baseflow-dominated catchments and the probable reason was that the flow regime showed smaller variability in the baseflow-dominated catchments. Hughes (1997) offered an explanation for better model performance in wetter catchments and suggested that flow data from wetter catchments contain more “information” that helps to improve model calibration. Lidén and Harlin (2000) showed that the model performance increased with increased catchment wetness and the risk of obtaining a model with poor volume performance characteristics increased with increasing dryness of the catchment. The results shown in Fig. 7 support the conclusions of Gupta et al. (1999), Hughes (1997), Houghton-Carr (1999), and Lidén and Harlin (2000).

In general, model performance is dependent on the quality of input data, model structure, calibration methods, and choice of calibration periods (Lidén and Harlin 2000; Vaze et al. 2010). For most of the catchments in this study, the VIC-3L model performed better in the calibration period. However, in a few catchments the model performed better in the validation period. A closer examination of the rainfall and runoff data in these catchments revealed some interesting results. Rainfall is higher in the validation period compared to the calibration period for these catchments. Streamflow also showed stronger correlation with rainfall in the validation period, making it easier to model streamflow. To verify this, further cross-validations were carried out for these catchments, and the results showed that the validation period (i.e., 1986–95) had higher E values than the calibration period (i.e., 1975–85) regardless of whether the model was calibrated on the former period or validated on it.

b. What relationships exist between parameter distributions and their physical meanings?

The parameters Ds, Dsmax, Ws, and d3 are broadly consistent for catchments with different rainfall regimes (Fig. 8). This suggests that these parameters are not strongly dependent on the rainfall regimes in different catchments. The parameters b and d2, however, showed strong dependence on the rainfall regimes.

The values of infiltration parameter (b) and thickness of second soil layer (d2) are more broadly distributed in the ranges of possible values, but the values of other parameters (three baseflow parameters Ds, Dsmax, and Ws, and thickness of the third soil layer d3) are more concentrated in smaller ranges. These results imply that parameters b and d2 are more sensitive in the model calibration than other parameters, which supports the conclusions of Nijssen et al. (2001) and Su et al. (2005); that is, parameters b and d2 require intensive calibration, but other parameters only need minor adjustments.

The infiltration parameter (b) controls the partitioning of rainfall into infiltration and direct runoff with higher b values giving lower infiltration and yielding higher surface runoff (Nijssen et al. 2001; Su et al. 2005). The majority of catchments across southeast Australia have b values less than 0.20. This indicates that a smaller proportion of the grid cell is saturated and more rainfall is partitioned into infiltration, yielding less surface runoff and more evapotranspiration in southeast Australian catchments. For example, b value for catchment 204017 is 0.4; the ratio of surface runoff to baseflow is 1.12 with the ratio of mean annual evapotranspiration to rainfall is 0.44. For catchment 204041, the b value is 0.1 and the ratios are 0.51 and 0.73, respectively. Therefore, lower b values will yield lower surface runoff and higher evapotranspiration.

Soil thickness affects the maximum soil water storage available for transpiration. A thicker soil layer will dampen seasonal peak flows and increase the loss due to evapotranspiration. In this study, the majority (72%) of winter-dominant rainfall catchments have high d2 values in the range 1.0–1.5 m (Fig. 8), which means that more rainfall is evapotranspired in the winter-dominant rainfall catchments than in other catchments. The results are consistent with Potter et al. (2005); that is, the observed evapotranspiration ratios (Q/P) for the Australian catchments are more likely to be higher in the winter-dominant rainfall catchments than in other catchments.

c. How well does the model regionalization perform?

The regionalization based on spatial proximity performs reasonably well considering that only one donor catchment was used for each ungauged catchment. Selection of donor catchments is one of the important optimal settings for the spatial proximity approach. Oudin et al. (2008) discussed whether poorly modeled catchments should be kept for regionalization purposes and pointed out that the answer to this question was not straightforward. They used a threshold on model efficiency (in calibration mode) to select the donor catchments: a donor catchment was not used to predict streamflow for an ungauged catchment if the model calibration efficiency is below the threshold (i.e., E = 0.7). The calibration E values in Australian catchments are always lower than those reported for European catchments because of the larger hydroclimatic variability in Australian catchments. In this study, there are 80% of 191 catchments with the coefficient of efficiency more than 0.4 (Fig. 2). It is reasonable to select the threshold on model efficiency of 0.4 for the catchments across southeast Australia, which was also used by Chiew et al. (2009) for the same region. Figure 10 showed that some catchments exhibited higher E values using the regionalized parameter values. However, this does not mean more accurate estimates of streamflow as these catchments are also associated with larger bias.

Another important optimal setting when using the spatial proximity method is selecting single or multiple donor catchments. A number of studies reported that regionalization results using multidonor catchments were slightly better than using a single donor catchment (especially for poorly simulated catchments) because it will eliminate the effect of choosing a poor donor catchment (McIntyre et al. 2005; Oudin et al. 2008; Viney et al. 2009b; Zhang and Chiew 2009). However, use of multidonor catchments is beyond the scope of the current study. It may result in slightly better regionalization results using multiple donor catchments than using a single donor catchment. However, the performance of model calibration should be the main reason impacting regionalization results. The calibration results of the VIC model were not as good as those of other rainfall–runoff models (as described in section 5a), which might affect the regionalization results of the VIC model. This may be one possible reason that the regionalization results in this study are not as good as those in former studies for the same region (e.g., Reichl et al. 2009 and Zhang and Chiew 2009).

The regionalization performance differs with the hydrologic regime of the catchments (Merz and Blöschl 2005). In general, the regionalization method performs better in wet than in dry catchments. The results shown in Fig. 12 support this conclusion. This can possibly be explained by rainfall characteristics. In wet catchments rainfall tends to be more uniformly distributed in space and time and a larger proportion of rainfall generally becomes streamflow.

Predictions in ungauged basins or catchments (PUB) are regarded as one of the most challenging tasks in surface hydrologic modeling (Sivapalan et al. 2003). Large uncertainties exist in regionalization research. The main sources of these uncertainties include model structural error, lack of parameter identifiability during calibration, and a lack of reliable relationships between observable catchment characteristics and model parameters (Wagener and Montanari 2011). This paper assessed the model prediction in ungauged catchments based on the spatial proximity method. The method calculates an objective function using catchment outlet streamflow based on transferred parameter values from the nearest neighbor catchment. The use of streamflow limited the assessment of spatial variability in runoff. Troy et al. (2008) overcome this drawback by calibrating individual grid cells against monthly runoff ratio other than streamflow because the monthly runoff ratio is a spatially continuous field that can be derived from an irregular network of small catchment observations. The regionalization may perform better using the runoff ratio as “observations” calculating objective function than using streamflow. The spatial proximity method transferred calibrated parameters from geographically closest gauged catchments to the ungauged catchments, hypothesizing that neighboring catchments should behave similarly owing to similar physical and climatic characteristics (Zhang and Chiew 2009). However, gauged catchments are not always uniformly distributed. Use of the spatial proximity method is restricted in large regions with less gauged catchments. Yuan et al. (2008) applied a Gaussian mixture model (GMM) clustering method to classify continental-scale areas into several zones according to soil and climate characteristics. The clustering method can reflect to some extent macroscale spatial variability of physical characteristics of the catchments. The parameters regionalized based on the clustering method may result in better predictions in ungauged catchments.

6. Conclusions

Streamflow is an important component of the surface water balance. Accurate simulation and prediction of streamflow are important not only for water resources studies, but also for the studies that investigate the impact of climate change and land use change on water balance. This paper assesses application of the VIC-3L model to estimate streamflow using data from 191 unregulated catchments across southeast Australia and evaluates the regionalization of model parameters based on the spatial proximity method to predict streamflow in ungauged catchments. For most of the hydrological models, parameter estimation is a critical step for streamflow simulation and prediction. In the VIC-3L model, six sensitive parameters (b, Ds, Dsmax, Ws, d2, and d3) were estimated using three methods: default parameter values, optimized parameter values based on model calibration, and regionalized parameter values based on spatial proximity method.

The results showed that use of the VIC-3L model with default parameter values yields poor estimates of daily streamflow for most of the catchments in southeast Australia, indicating the need for other parameter estimation methods. Based on the automated search procedure, the VIC-3L model can be well calibrated against the water balance criteria for the majority of catchments and is capable of reproducing observed daily streamflow. The effect of mean annual rainfall on streamflow was investigated, and the results confirmed previous observations that high model performance is usually shown in high mean annual rainfall catchments, probably because of the high rainfall in these catchments. The model performances with different rainfall seasonality were also evaluated and showed that better performance was in summer-dominant catchments. The analysis of calibrated model parameter value distributions showed that the parameters b and d2 exhibited large differences for catchments with different rainfall regimes, with other parameter values being more consistent across the rainfall regimes. The regionalization based on spatial proximity performed reasonably well, which illustrated the potential use of VIC-3L model to predict streamflow in ungauged catchments.

Acknowledgments

This study was supported by the CSIRO OCE Postdoctoral Fellowship Program and Water for a Healthy Country National Research Flagship. We thank Professor Xu Liang and her group in University of Pittsburgh for providing useful comments about the application of VIC-3L model and Professor Murugesu Sivapalan from University of Illinois at Urbana–Champaign for discussions around catchment classification and parameter regionalization in ungauged catchments. We thank Dr. Nick Potter for grouping the catchments based on rainfall regimes and thank Dr. Yongqiang Zhang and Dr. Fengge Su for helpful discussions. We also thank Dr. Cuan Petheram, Dr. David Post, and the three anonymous reviewers for their constructive comments, which led to improvements in this paper.

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