There are different views on the selection of hydrological model structural complexity for streamflow prediction in ungauged basins. Some studies suggest that complex models are better than simple models due to the former's prediction capability; whereas some studies favor parsimonious model structures to overcome a risk of over-parameterization. The Xinanjiang (XAJ) model, the most widely used hydrological model in China, has two different versions, as follows: (1) the simple version with seven parameters (XAJ7) and (2) the complex version with 14 parameters (XAJ14). In this study, the two versions of the XAJ model were comprehensively evaluated for streamflow prediction in ungauged basins based on their efficiency, parameter identifiability, and independence. The results showed that the complex XAJ14 model was more flexible than the simple XAJ7 in calibration mode; while the two models have similar performance in validation and regionalization modes. Lack of parameter identifiability and the presence of parameter interdependence most likely explain why the complex XAJ14 cannot consistently outperform the XAJ7 in different modes. Therefore, the simple XAJ7 is a better choice than XAJ14 for streamflow prediction in ungauged basins.

INTRODUCTION

Streamflow observation records are important for hydrological research and practices, such as flooding forecasting, hydraulic engineering design, drought risk assessment, and water resources planning and management. However, streamflow observations are not always available in many parts of the world, and the publicly available streamflow records are often incomplete or very brief (Sivapalan 2003; Wagener et al. 2004a). Missing or incomplete streamflow observations have greatly impeded the operation of hydrological research and practices. Some methods can be used to reconstruct the streamflow time series, including statistic-based methods, artificial intelligence-based methods, and process-based hydrological models (Wagener et al. 2004b; Besaw et al. 2010; Benito 2012). However, these methods often become invalid, unable to reproduce streamflow given the limited observed data for calibration. Consequently, reliable streamflow prediction in ungauged basins is a great challenge for hydrological research (Sivapalan et al. 2003; Seibert & Beven 2009). The International Association of Hydrological Sciences (IAHS) launched the Scientific Decade of IAHS (2003–2012), entitled Predictions in Ungauged Basins (PUB), which focuses on improving scientific understanding and simulation of hydrological processes in ungauged basins (Sivapalan et al. 2003; Blöschl et al. 2013; Hrachowitz et al. 2013).

Several methods have been proposed for estimating streamflow in ungauged basins, and most of them involve the use of hydrological models (McIntyre et al. 2005; Castiglioni et al. 2010; Ahiablame et al. 2012; Booker & Snelder 2012; El-Hames 2012). Parameter estimation is a key step of hydrological modeling, which largely determines the accuracy of streamflow simulation and prediction (Xu 2003; Lee et al. 2005; McIntyre et al. 2005). Due to high heterogeneity in landscape properties, hydrological model parameters cannot be measured directly at the catchment scale, which usually are inferred by a calibration process (Xu 1999; Vaché & McDonnell 2006; Jin et al. 2009). However, parameter calibration in ungauged basins cannot be directly performed because of the lack of observations. An alternative strategy is to transfer model parameters from gauged basins to ungauged basins, i.e., parameter regionalization (Blöschl 2006; Zhang & Chiew 2009; Pechlivanidis et al. 2010; Kizza et al. 2013). An overview of the parameter regionalization methods has been presented by He et al. (2011) and Parajka et al. (2013).

Model complexity is also an important criterion of model selection in addition to the goodness-of-fit. The complexity of hydrological models, which is commonly quantified by the number of model parameters, has significant impacts on parameter regionalization in ungauged basins (Chiew et al. 1993; Perrin et al. 2001). The calibration and parameter regionalization of the hydrological model is not straightforward as the number of model parameters increases (McCabe et al. 2005). It is generally expected that a model with a high degree of freedom (complex model) will perform better in the calibration period in comparison to a simple model (due to higher degrees of freedom). However, this is not always the case in the ‘untrained’ validation period (Wheater et al. 1993; Wagener et al. 2001b; Hailegeorgis & Alfredsen 2015). Some studies have suggested the model users avoid using complex models to estimate streamflow in ungauged basins (Jakeman & Hornberger 1993; Lee et al. 2005; Bárdossy 2007; Skaugen et al. 2015). A complex model may result in model over-parameterization, which can bring a large degree of uncertainty in streamflow prediction (Jakeman & Hornberger 1993; Bárdossy 2007; Skaugen et al. 2015). Nevertheless, conclusions from other studies were in favor of complex models (Vaché & McDonnell 2006; Li et al. 2015).

The Xinanjiang (XAJ) model, as the most widely used hydrological model in China, has two different versions, as follows: (1) the simple version with seven parameters (XAJ7) and (2) the complex version with 14 parameters (XAJ14). The main objective of this study is to evaluate which of these two models, XAJ7 and XAJ14, is more suitable for streamflow prediction in ungauged basins. In this study, model efficiency is not the only criterion of model evaluation, and parameter identifiability and independence are also considered. This paper is structured as follows: the section below describes the two XAJ model versions, study area and data sources; then the next section introduces methods used for model evaluation; followed by a section focusing on the results and discussion; and, finally the summary and conclusions are presented.

XAJ MODEL DESCRIPTION AND STUDY AREA

XAJ model description

The XAJ14 model has more extensive applications than the XAJ7 model in China, and it has been employed in the China National Flood Forecasting System (WMO 2011; Yao et al. 2014). The XAJ14 model contains the following four modules: runoff generation, three-layer evapotranspiration (ET), separation of runoff components, and runoff routing (Table 1). Generally, ET occurs in the top three soil layers; the actual evapotranspiration (AET) is estimated as a function of potential evapotranspiration (PET) and available soil moisture. AET first occurs in the upper layer at potential rate until the water storage is exhausted. Then, the water storage in the lower layer begins to supply for AET. AET occurs in the deepest layer of soil only when the lower storage layer is reduced to a proportion of storage capacity. A similar mechanism is also used to describe the soil moisture repletion process among the three soil layers. The XAJ14 model uses a single parabolic curve to describe the spatial heterogeneity of the soil moisture storage capacity and assumes that the runoff is not produced until the soil moisture storage reaches field capacity (Zhao 1992; Cheng et al. 2006). The generated runoff is separated into the following three components: surface runoff, interflow, and groundwater according to different free water storage structures. The surface runoff directly flows into the river, and the interflow and groundwater is released slowly to river channels through a single linear reservoir. Finally, the Muskingum routing equation is adopted to calculate the discharge at the watershed outlet.

Table 1

Descriptions of model parameters in the XAJ14 and XAJ7 models

Module Pars. Parameter descriptions Range and units 
Runoff generation Bb Exponential of the distribution to tension water capacity 0–1 
IMP Percentage of impervious and saturated areas in the catchment 0–0.1 (%) 
Evapotranspiration UMb,c Average soil moisture storage capacity of the upper layer 5–100 (mm) 
LM Average soil moisture storage capacity of the middle layer 50–300 (mm) 
DMb,c Average soil moisture storage capacity of the deepest layer 5–100 (mm) 
ET coefficient of the deepest layer 0.1–0.2 
Runoff separation SM Areal mean free water capacity of the surface soil layer 10–60 (mm) 
EX Exponential of the spatial distribution curve of free water storage capacity 1.0–1.5 
KI Outflow coefficient of free water storage to the interflow 0.3–0.7 
KG Outflow coefficient of free water storage to the groundwater 0.1–0.2 
FCa Steady recharge constant to groundwater 0.5–15 (mm/d) 
Routing CI Recession constant of the lower interflow storage 0.1–0.9 
CGb Recession constant of the lower groundwater storage 0.95–0.99 
XEb Muskingum coefficient of geometry factor 0–0.5 
KEb Muskingum coefficient of residence time of water 1–3 (d) 
Module Pars. Parameter descriptions Range and units 
Runoff generation Bb Exponential of the distribution to tension water capacity 0–1 
IMP Percentage of impervious and saturated areas in the catchment 0–0.1 (%) 
Evapotranspiration UMb,c Average soil moisture storage capacity of the upper layer 5–100 (mm) 
LM Average soil moisture storage capacity of the middle layer 50–300 (mm) 
DMb,c Average soil moisture storage capacity of the deepest layer 5–100 (mm) 
ET coefficient of the deepest layer 0.1–0.2 
Runoff separation SM Areal mean free water capacity of the surface soil layer 10–60 (mm) 
EX Exponential of the spatial distribution curve of free water storage capacity 1.0–1.5 
KI Outflow coefficient of free water storage to the interflow 0.3–0.7 
KG Outflow coefficient of free water storage to the groundwater 0.1–0.2 
FCa Steady recharge constant to groundwater 0.5–15 (mm/d) 
Routing CI Recession constant of the lower interflow storage 0.1–0.9 
CGb Recession constant of the lower groundwater storage 0.95–0.99 
XEb Muskingum coefficient of geometry factor 0–0.5 
KEb Muskingum coefficient of residence time of water 1–3 (d) 

aThe parameter that only belongs to XAJ7 model.

bThe parameters that are shared by XAJ7 and XAJ14 models.

cThe parameter range of UM and DM in the XAJ7 are 10–150 and 50–350, respectively.

Note that the range of parameters comes from the published studies of Li et al. (2009) and Zhao et al. (1980).

The XAJ7 model has a similar model structure to XAJ14 (Figure 1), and it can be regarded as the simplified version of the XAJ14 model (Zhao et al. 1980). There are three differences between the XAJ7 and XAJ14 models: (1) the XAJ7 model does not consider the impact of impervious surface on runoff generation; (2) the XAJ7 model calculates AET using a two-layer rather than three-layer ET sub-model; and (3) corresponding to the two-layer water storage, the generated runoff is separated into two components (surface runoff and subsurface runoff) using the Horton's concept of steady infiltration rate. In the saturated areas of the watershed, the portion of the generated runoff that exceeds the steady infiltration rate forms surface runoff, and the rest forms subsurface runoff. Detailed descriptions of model structures, parameters, and state variables in the XAJ7 and XAJ14 can be found in Figure 1 and Table 1.
Figure 1

Model structures for seven-parameter (a) and fourteen-parameter (b) XAJ models.

Figure 1

Model structures for seven-parameter (a) and fourteen-parameter (b) XAJ models.

Study area and data used

Twenty-six mountainous catchments with limited anthropogenic influences were selected as test catchments (Figure 2). These test catchments are located in the Poyang Lake basin of Jiangxi Province (113 °42′–118 °15′ E, 24 °30′–29 °48′ N), which is the largest freshwater lake in China. The elevations in the study area decrease from south to north, ranging from 1,700 m to 50 m above mean sea level (a.m.s.l). The study area has a subtropical wet climate governed by the East Asian monsoon. Approximately 60–70% of the annual precipitation occurs in the wet season from May to October. The land use type is predominantly forest and grassland, and soil types are dominated by red soil and paddy soil. Table 2 summarizes the physical and climatic characteristics of the catchments.
Table 2

Summary of the catchment physical and climatic characteristics

Catchment characteristics Min Median Max 
Catchment area (km2435 1,081 3,548 
Mean annual rainfall (mm) 1,341 1,544 1,940 
Aridity index 0.58 0.80 0.92 
Runoff coefficient 0.48 0.58 0.72 
Percent forest cover (%) 48 75 92 
Stream length (km) 36 57 99 
Mean elevation (m) 76 178 348 
Catchment slope (‰) 1.5 5.2 16.7 
Catchment characteristics Min Median Max 
Catchment area (km2435 1,081 3,548 
Mean annual rainfall (mm) 1,341 1,544 1,940 
Aridity index 0.58 0.80 0.92 
Runoff coefficient 0.48 0.58 0.72 
Percent forest cover (%) 48 75 92 
Stream length (km) 36 57 99 
Mean elevation (m) 76 178 348 
Catchment slope (‰) 1.5 5.2 16.7 
Figure 2

Location of the study area and spatial distribution of the hydrological stations.

Figure 2

Location of the study area and spatial distribution of the hydrological stations.

Daily meteorological data from 42 stations were obtained from the Meteorological Bureau of Jiangxi Province. PET was estimated by the Hargreaves and Samani equation (Hargreaves & Samani 1985). Basin average rainfall and PET were calculated by the Thiessen polygons method based on the available meteorological stations in and around each catchment. Observed streamflow data were provided by China's Hydrological Year Book, published by the Hydrological Bureau of the Ministry of Water Resources, China. All test catchments have 17 years of continuous streamflow data from 1970 to 1986. The period 1971–1978 was used for model calibration (1970 was used for model warm up), and the period 1979–1986 was used for model validation.

METHODOLOGY

Parameter regionalization methodology

For basins without streamflow records, model parameters must be estimated from other sources, such as neighboring basins or physically similar basins where streamflow data are available. The methods allowing the transfer of hydrological model parameters from gauged to ungauged basins can be called parameter regionalization approaches (Oudin et al. 2010). Parameter regionalization approaches typically include the following steps: (1) identifying the gauged basins (donor basins), which have similar hydrological characteristics as the ungauged basins (target basins); (2) calibrating model parameters in donor basins (calibration mode); (3) validating model performance on an independent period (validation mode); and (4) transferring the model parameters from donor basins into target basins for streamflow simulations and predictions (regionalization mode) if the validation results are satisfactory. In this study, only one donor basin was used as a target basin. Two commonly used parameter regionalization methods were employed, spatial proximity and physical similarity. The difference between the two methods lies in how the donor basin is chosen. The spatial proximity method chooses a donor basin based on spatial distances between the centroids of two neighboring catchments, while the physical similarity method chooses a donor basin based on the similarity of the catchment characteristics between two catchments (Parajka et al. 2013). In the regionalization mode, each of the 26 catchments was first considered as a donor basin for calibration and validation, and then each one in turn was considered as a target basin to receive optimized parameter values from the donor basin. The catchment characteristics in Table 2 were considered in the physical similarity method. The Kay approach (Kay et al. 2007) was used to combine the seven catchment characteristics into a single similarity index (θ): 
formula
1
where j represents the number of catchment characteristics. XiD and XiT are the values of the catchment characteristic for the donor basin and target basin, respectively. σXi is the standard deviation of the characteristics over all catchments, and wj is the weight attributed to the jth catchment characteristic. The weight values of each catchment characteristic have a significant impact on donor basin selection (Burn & Boorman 1993; Oudin et al. 2008; Zhang & Chiew 2009; Arsenault et al. 2015). In this study, the entropy method was used to determine the weight coefficient of each catchment characteristic, enabling the measurement of useful catchment characteristic information and avoiding the subjective influence of decision-makers (Yu & Lai 2011). More detailed descriptions about entropy-based weight measures can be found in Wang & Lee (2009) and Zou et al. (2006).

Model performance assessment criteria

The Kling–Gupta efficiency (KGE) (Gupta et al. 2009) was used as an objective function to calibrate model parameters. The KGE incorporates three basic assessment criteria, can provide a reliable measurement of the overall agreement between simulated and observed values (Pechlivanidis et al. 2014), and is defined as: 
formula
2
where γ is the correlation coefficient between simulated and observed values; α is the relative variability in simulated and observed values, and β is the ratio of the mean values of simulated and observed values. A value of KGE= 1 indicates a perfect fit between observed and simulated values.
In addition to the KGE, a complementary evaluation was carried out based on the following three criteria: percent bias (PBIAS), Nash–Sutcliffe efficiency (NSE) (Nash & Sutcliffe 1970), and NSE of log-transformed flows. PBIAS is used to measure the difference between the observed and simulated total runoff. NSE is a valuable means to evaluate high flow simulations (Pushpalatha et al. 2011). NSE calculated on log transformed flows (NSElog) has been proven to be an efficient evaluation criterion for low flow simulations (Oudin et al. 2006; Pushpalatha et al. 2012). PBIAS= 0, NSE= 1, and NSElog= 1 indicate a perfect fit between the observed and simulated values. The three criteria can be expressed as follows: 
formula
3
 
formula
4
 
formula
5
where and are the simulated and observed streamflow, respectively; is the mean observed streamflow; N is the total number of days in the calibration period; and ɛ is a small constant to avoid having zero in the denominator of Equation (5). Model parameters are automatically optimized using the particle swarm optimization algorithm to maximize the objective function. This optimization algorithm proposed by Eberhart & Kennedy (1995) has been widely applied to optimize the parameters of hydrological models (Gill et al. 2006; Zhang & Chiew 2009; Luo et al. 2012).

Parameter sensitivity and identifiability analysis

Parameter sensitivity analysis is an important way to identify dominant hydrological processes that exhibit major influence on the simulation results (Wagener et al. 2003; Abebe et al. 2010). Here, a modified version of the regional sensitive analysis method was employed to analyze parameter sensitivity (Freer et al. 1996; Wagener & Kollat 2007). Monte Carlo random sampling was performed considering a uniform probability distribution for all parameters in the XAJ7 and XAJ14 models (Table 1). A total of 10,000 simulations were run for each model. The parameter sets were then split into ten groups of equal size based on the evaluation criterion of KGE (Figure 3). In general, the sensitivities of the parameters were determined by comparing the differences in cumulative distribution functions (CDFs) of parameter groups (Freer et al. 1996; Wagener & Kollat 2007). A larger difference between the two CDFs indicates a higher sensitivity of parameter to model performance. The parameter sensitivity can be quantitatively described by calculating the area between the CDFs of the best and the worst groups of parameter populations. Figure 3 presents the scheme map of parameter sensitivity calculation. For the j-th parameter ϕ, the normalized common area (Aj) under the two CDFs can be calculated as follows: 
formula
6
and the sensitivity coefficient (SC) of the parameter ϕ is calculated as: 
formula
7
where pb is the cumulative frequency of the best group parameter populations; pw is the cumulative frequency of the worst group parameter populations; N is the number of bins of the parameter range being split (N= 500 used in this study), and M is the number of parameters.
Figure 3

Scheme map of parameter sensitivity measures.

Figure 3

Scheme map of parameter sensitivity measures.

Parameter identifiability is also an important concern of model evaluation (Wagener et al. 2001a, 2003). Generally, only a few parameters in a hydrological model are identifiable based on automatic parameter calibration. The poorly identifiable parameters result from an insensitivity of model outputs to these parameters, parameter interaction, or both (Doherty & Hunt 2009), which produces a similar model performance within a full range (i.e., parameter equifinality) and negatively affects hydrological predictions (Schoups et al. 2008). Parameter identifiability can be measured by calculating the gradient of the cumulative distribution of the top 10% best performing parameter sets (Wagener et al. 2001b). Figure 4 shows the schematic diagram for measuring a well and a poorly identifiable parameter. The scatter plots in Figure 4(a) and 4(b) show the two parameter populations against corresponding objective function (KGE) values. In this study, the top 10% best performing parameter sets were used to derive a CDF. One can then split the parameter range into ten groups of equal size and calculate the gradient of cumulative distribution for each group (Figure 4(c) and 4(d)). A steeper gradient in the cumulative distribution indicates a more identifiable parameter in the top 10% best performing parameter sets. As suggested by Wagener & Kollat (2007), the largest gradient value (max_id) is used as an indicator for measuring parameter identifiability. More detailed descriptions of parameter identifiability measurement can be found in Wagener & Kollat (2007).
Figure 4

Sketch map of parameter identifiability measures based on parameter populations conditioned on KGE.

Figure 4

Sketch map of parameter identifiability measures based on parameter populations conditioned on KGE.

RESULTS AND DISCUSSION

Model evaluation in calibration, validation, and regionalization modes

Figure 5 shows the comparisons of model performance for the XAJ7 and XAJ14 in calibration, validation, and regionalization modes. None of the comparisons show statistically significant differences in model performance. In calibration mode, the XAJ14 model performs better than the XAJ7 model and yields higher KGE and lower PBIAS values than XAJ7. The difference in model performance decreases significantly when moving from calibration mode to validation mode where the two models achieve similar model performance, indicating the potential inconsistency of complex models to perform similarly under ‘trained’ and ‘untrained’ (spatial and/or temporal) conditions. Similar findings also have been reported by Michaud & Sorooshian (1994), Yew Gan et al. (1997), Perrin et al. (2001), and Bai et al. (2015) using different hydrological models.
Figure 5

Model performance for the XAJ14 and XAJ7 models in calibration mode (a) and (b) and validation mode (c) and (d). In each boxplot, the bottom, middle, and top of the box are the 25th, 50th, and 75th percentiles, and the bottom and top whiskers are the 10th and 90th percentiles. Data points inside the boxes are the average values, and data points beyond the whiskers are the maximum and minimum values.

Figure 5

Model performance for the XAJ14 and XAJ7 models in calibration mode (a) and (b) and validation mode (c) and (d). In each boxplot, the bottom, middle, and top of the box are the 25th, 50th, and 75th percentiles, and the bottom and top whiskers are the 10th and 90th percentiles. Data points inside the boxes are the average values, and data points beyond the whiskers are the maximum and minimum values.

Figure 5 shows model regionalization results based on physical similar and spatial proximity methods. The physical similar method performs slightly better than the spatial proximity method in the regionalization mode. Model regionalization results are poorer than the model calibration and validation results, with median KGE values from the regionalization results being approximately 0.10 to 0.15 lower than the calibration and validation results. The XAJ14 and XAJ7 models achieve similar regionalization results whether for the physical similar method or the spatial proximity method, indicating that more complex process representations in the XAJ14 model do not improve streamflow prediction ability in ungauged basins compared with the simple XAJ7 model.

Regionalization under high flow and low flow simulations

The NSE and NSElog are used to evaluate high flow and low flow simulations, respectively. The physical similarity method is used for model parameterization due to its better performance than the spatial proximity method. Figure 6 shows the regionalization results under high flow and low flow simulations. The XAJ7 model is slightly better than the XAJ14 model in high flow simulations, and the median NSE values from XAJ14 and XAJ7 are 0.62 and 0.60, respectively. However, for low flow simulations, the XAJ7 model performs better than the XAJ14 model, and the median NSElog obtained from XAJ14 and XAJ7 are 0.25 and 0.36, respectively. The two models perform better in high flow simulations than in low flow simulations. Similar conclusions were also drawn by Pushpalatha et al. (2011) and Zhang et al. (2014), who also reported that rainfall–runoff models have minimal ability to predict low flows. This result could be partly caused by the objective function used in the hydrological model calibration, which is more sensitive to medium and high flows than to low flows. Use of a low flow sensitive objective function may have resulted in different conclusions.
Figure 6

Model regionalization results for high flow (a) and low flow (b) simulations.

Figure 6

Model regionalization results for high flow (a) and low flow (b) simulations.

Parameter identifiability and independence

As mentioned in the section ‘Parameter sensitivity and identifiability analysis’, the max_id was used as an indicator of parameter identifiability. Figure 7 shows the median max_id in XAJ7 and XAJ14 models for over 26 test basins. The median max_id values in XAJ7 range from 0.39 to 0.49, with an average of 0.44, while the values in XAJ14 range from 0.28 to 0.40, with an average of 0.33. This indicates that model parameters in XAJ7 are easier to identify than those in XAJ14. For the parameters shared by the two models, the XAJ7 model has higher max_id values than the XAJ14 model, which indicates that model simplification can enhance parameter identifiability.
Figure 7

Comparison of the parameter identifiability between XAJ7 and XAJ14 models based on median max_id over 26 test basins. The pars1 indicates the parameters that are shared by XAJ7 and XAJ14 models; the pars2 indicates the parameter that only belongs to XAJ7; the pars3 indicates the parameters that only belong to XAJ14.

Figure 7

Comparison of the parameter identifiability between XAJ7 and XAJ14 models based on median max_id over 26 test basins. The pars1 indicates the parameters that are shared by XAJ7 and XAJ14 models; the pars2 indicates the parameter that only belongs to XAJ7; the pars3 indicates the parameters that only belong to XAJ14.

We also analyzed the independence of model parameters for the two hydrological models. Table 3 shows the correlation coefficients of calibrated model parameters in XAJ14 and XAJ7 models. The interdependence of the calibrated parameters is weak for XAJ7, and the correlation coefficients between model parameters range from −0.25 and 0.26. The weak correlations between the parameters of XAJ7 probably stem from the parsimony of the model. Compared to XAJ7, the parameter interdependence in XAJ14 is more pronounced, and the correlation coefficients between some parameters are greater than 0.50 or less than −0.50, indicating that some of the parameters in XAJ14 model are covariant with each other and have a similar effect on the streamflow simulations.

Table 3

Correlation coefficients between model parameters

 Parameters
 
Model UM DM CG XE KE LM/FC IMP SM EX KG KI CI 
XAJ14 
 B 1.00              
 UM 0.15 1.00             
 DM -0.02 0.21 1.00            
 CG 0.02 −0.30 0.18 1.00           
 XE 0.07 −0.01 −0.19 0.00 1.00          
 KE −0.13 0.01 −0.31 −0.31 −0.17 1.00         
 LM 0.16 0.50 0.63 −0.13 −0.07 0.24 1.00        
 IMP 0.21 0.05 0.14 0.17 0.70 0.24 0.06 1.00       
 C −0.04 −0.41 0.10 0.28 0.07 −0.10 −0.16 −0.17 1.00      
 SM 0.09 0.13 −0.42 −0.26 0.31 0.53 0.07 −0.47 −0.07 1.00     
 EX 0.21 −0.03 −0.37 0.01 0.04 −0.38 0.07 0.03 −0.17 0.24 1.00    
 KG 0.13 0.36 −0.27 0.54 0.22 −0.14 0.20 −0.46 −0.37 0.16 −0.05 1.00   
 KI 0.04 0.42 −0.03 −0.44 −0.32 −0.04 −0.07 0.24 0.56 0.03 0.17 0.25 1.00  
 CI −0.15 −0.14 0.36 0.26 0.75 0.03 0.03 0.61 0.03 -0.54 −0.23 0.58 0.19 1.00 
XAJ7 
 B 1.00              
 UM 0.07 1.00             
 DM −0.01 −0.15 1.00            
 CG −0.11 −0.19 0.07 1.00           
 XE 0.20 −0.09 −0.01 0.10 1.00          
 KE −0.24 0.05 −0.20 −0.21 −0.25 1.00         
 FC 0.23 0.17 0.26 −0.19 0.10 0.10 1.00        
 Parameters
 
Model UM DM CG XE KE LM/FC IMP SM EX KG KI CI 
XAJ14 
 B 1.00              
 UM 0.15 1.00             
 DM -0.02 0.21 1.00            
 CG 0.02 −0.30 0.18 1.00           
 XE 0.07 −0.01 −0.19 0.00 1.00          
 KE −0.13 0.01 −0.31 −0.31 −0.17 1.00         
 LM 0.16 0.50 0.63 −0.13 −0.07 0.24 1.00        
 IMP 0.21 0.05 0.14 0.17 0.70 0.24 0.06 1.00       
 C −0.04 −0.41 0.10 0.28 0.07 −0.10 −0.16 −0.17 1.00      
 SM 0.09 0.13 −0.42 −0.26 0.31 0.53 0.07 −0.47 −0.07 1.00     
 EX 0.21 −0.03 −0.37 0.01 0.04 −0.38 0.07 0.03 −0.17 0.24 1.00    
 KG 0.13 0.36 −0.27 0.54 0.22 −0.14 0.20 −0.46 −0.37 0.16 −0.05 1.00   
 KI 0.04 0.42 −0.03 −0.44 −0.32 −0.04 −0.07 0.24 0.56 0.03 0.17 0.25 1.00  
 CI −0.15 −0.14 0.36 0.26 0.75 0.03 0.03 0.61 0.03 -0.54 −0.23 0.58 0.19 1.00 
XAJ7 
 B 1.00              
 UM 0.07 1.00             
 DM −0.01 −0.15 1.00            
 CG −0.11 −0.19 0.07 1.00           
 XE 0.20 −0.09 −0.01 0.10 1.00          
 KE −0.24 0.05 −0.20 −0.21 −0.25 1.00         
 FC 0.23 0.17 0.26 −0.19 0.10 0.10 1.00        

Note that the values greater (less) than or equal to 0.50 (−0.50) are shown in bold.

Overall, parameter identifiability and independence analysis indicate that model parameters in XAJ7 are easier to identify and have less correlation behavior than those in the XAJ14 model. Lack of parameter identifiability and parameter interaction could lead to large uncertainties in streamflow prediction (Beven 1993; Wheater et al. 1993). This is likely the reason why the complex XAJ14 model cannot consistently outperform the XAJ7 model in validation and regionalization modes.

Model complexity for prediction in ungauged basins

Streamflow PUB require the development of a model that is able to capture the dominant hydrological processes and avoid parameter interaction and lack of identifiability (Wagener et al. 2004b; Young 2006; Reusser et al. 2011). Under the premise of similar prediction ability, the simplistic models are more attractive than sophisticated models for regionalization because they are easier to parameterize. Model comparison results suggest that the increased model complexity of the XAJ14 model results in, as expected, a better performance of streamflow simulation than the XAJ7 model in calibration mode. This is mainly due to higher degree of freedom of XAJ14, which allows parameters to compensate for model structure uncertainty and lack of process understanding. However, model selection should additionally focus on the model performance in the validation and regionalization modes, which represent the model's ‘untrained’ conditions and reflect the actual streamflow prediction capability where the XAJ7 performs comparably or even better (in low flow simulations) than the XAJ14 model (Figure 5). Additionally, parameter sensitivity analysis suggests that not all hydrological modeling processes are active or at the same level of importance (Figure 8). For the XAJ14 model, only four parameters (SM, KI, XE, and KE) related to runoff separation and routing processes are sensitive to simulation results. With respect to the XAJ7 model, it retains the routing process from XAJ14 and simplifies the runoff generation, evapotranspiration, and runoff separation processes. These simplifications enhance parameter identifiability and reduce the parameter interdependence. Generally, the simple XAJ7 is a better choice than XAJ14 for regionalization in ungauged basins.
Figure 8

Sensitivity of model parameters for XAJ14 model and XAJ7 model.

Figure 8

Sensitivity of model parameters for XAJ14 model and XAJ7 model.

SUMMARY AND CONCLUSION

The main objective of this study was to determine whether the XAJ7 or XAJ14 model is more suitable for streamflow prediction in ungauged basins. Model evaluation was performed not only based on model performance, but also on the dependence on parameter identifiability. The results showed that the XAJ14 model benefits from the increased complexity and yields better model performance than the simple XAJ7 model in calibration mode. However, the superior performance cannot be sustained in validation and regionalization modes where the simple XAJ7 model performed similarly or even better (in low flow simulations) than the complex XAJ14 model. Parameter identifiability and independence analysis suggested that model parameters in the simple XAJ7 model are more identifiable and have less correlation behavior than those in the complex XAJ14 model, which probably causes the inconsistency of model performance between XAJ14 and XAJ7 models in different modes. Considering model efficiency, parameter identifiability, and independence, the XAJ7 model is a better choice than the XAJ14 model for streamflow prediction in ungauged basins.

In addition, current hydrological research highlights the development of an integrated model of water-related processes and the development of land surface process models (Foley et al. 1996; Arnold et al. 1998; Liu et al. 2008), in which the hydrological model only serves as a sub-model to simulate water balance. These models without exception have a large number of parameters, which makes reliable parameter estimation a challenging task. Compared with the XAJ14 model, the simple XAJ7 model seems more suitable to be coupled with other water-related models, or to be embedded into a land surface model.

ACKNOWLEDGEMENTS

This research was supported by the Natural Science Foundation of China (41201034, 41330529), the program for ‘Bingwei’ Excellent Talents in Institute of Geographic Sciences and Natural Resources Research, CAS (Project No. 2013RC202), Chinese Academy of Sciences Visiting Professorship for Senior International Sciences (Grant No. 2013T2Z0014) and Natural Sciences Foundation of Jiangsu Province (BK20141059).

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