Parameter sensitivity analysis of SWAT model for streamflow simulation with multisource precipitation datasets

Precipitation is well accepted as one of the most important input datasets for streamflow simulation using hydrological models (Liang et al. 2018). Generally, precipitation data can be obtained by ground stations, ground-based radars and remote sensing information. The precipitation data obtained by ground rainfall stations is accurate, but it is of heterogeneous spatial and temporal distributions due to the strong dependence on topography, wind direction, hill aspect and other regional factors (Price et al. 2014). Meanwhile, the precipitation data used in the soil and water assessment tool (SWAT) is typically adopted from the precipitation stations that are nearest to the centroid of the sub-basin without considering spatial heterogeneity (Neitsch et al. 2011), thus the spatial resolution of precipitation data is important for hydrological modelling. However, the sparse and heterogeneous spatial distribution of precipitation is difficult to evaluate accurately (Moine et al. 2015).

To improve the precision of precipitation data, spatial interpolation methods such as simple algorithmic averaging, Thiessen polygons, inverse distance weighting (IDW) and kriging interpolation, are proposed, and many models are established based on the spatial interpolation of meteorological observations with respect to the nonlinear relationships between precipitation and topographical factors, e.g. elevation, longitude and latitude (Teegavarapu & Chandramouli 2005). In recent years, due to the advantages of large spatial coverage, high spatial and temporal resolutions, and weak dependence on topographical conditions, meteorological data obtained from different sources, such as satellite and reanalysis, is extensively applied in the investigations on climate change, providing a new and feasible method to make up the disadvantages of observation data (Michaelides et al. 2009). The satellite and reanalysis precipitation datasets, e.g. Tropical Rainfall Measuring Mission (TRMM), Climate Forecast System Reanalysis (CFSR), Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) and Global Meteorological Forcing dataset for land surface modelling developed by Princeton University (PGF) have been extensively applied when spatially heterogeneous precipitation data is used as the input data for hydrological models such as SWAT (Hu et al. 2014; Duan et al. 2016). The multisource precipitation data obtained by satellite and reanalysis, as an important supplement for precipitation datasets in hydrological models, can improve the simulation results. For instance, it indicates that the output error induced by the error of radar precipitation data is less than the error generated during the transition from precipitation to streamflow (Wyss et al. 1990). Nevertheless, except for the serious system errors possessed by the precipitation data, the accuracy of the retrieved precipitation is relatively low due to the limitations of the physical theories and algorithms for obtaining the satellite retrieved precipitation (Wang et al. 2018), and the uncertainty of precipitation input data will lead to the transfer and accumulation of uncertainty within different modules in hydrological models. For hydrological simulation at small scales, downscaling and deviation correction processing are usually applied to homogenize the spatial resolution of precipitation inputs (Wang et al. 2015).

Moreover, parameter optimization is the most important procedure during hydrological simulation because a large number of parameters are involved as the establishment of the hydrological model (Beck 1987), and every parameter is extremely crucial for the simulation results. Generally, model parameters are the comprehensive descriptions of the historical hydrological process and underlying surface properties (Beven & Binley 1992), and these parameters are obtained directly or indirectly from the basin properties, hydrological data and parameter optimization. However, the spatial heterogeneity of parameters, the errors induced during the acquisition process of hydrological data, and the errors caused by the selections of optimization method or objective function will reduce the accuracy of hydrological simulation and introduce serious uncertainties to the parameter initial values (Beven 1993). Meanwhile, the values of model parameters are highly related with each other and the phenomenon called ‘parameters equifinality’ occurs as a few groups of parameters correspond to the same fitting functions, which will increase the uncertainty of parameter values further. Therefore, the sensitivity analysis of model parameters is necessary to understand the effect of each parameter on simulation results during hydrological simulation (Jiang et al. 2018). Parameters can be reasonably selected according to the parameter sensitivity obtained by sensitivity analysis, which will reduce the number of parameters required in the calibration process and improve the simulation efficiency. More importantly, the parameter uncertainty and the output uncertainty can be effectively decreased.

The Shiyang River basin is a typical arid area with sparse rainfall stations, so precipitation data with high quality is required to obtain satisfactory simulation results of streamflow based on the SWAT model in this basin. In this study, the geographical spatial interpolation data of observed precipitation (GSI) and multisource precipitation datasets obtained by remote sensing and reanalysis, including TRMM, China Meteorological Forcing dataset (CMDF), CFSR, CHIRPS and PGF are specially considered as the input data for SWAT. Meanwhile, the multisource precipitation datasets are downscaled based on the GSI dataset, and the downscaled datasets are then applied to streamflow simulation to discuss whether it can be provided as the feasible precipitation input data or not. The sensitivities and uncertainties of model parameters using the downscaled precipitation inputs are discussed with respect to their effects on the results of streamflow simulation, so the prediction uncertainty of streamflow is also encountered to obtain the influences of parameters on the simulation performance under multisource precipitation datasets.

As illustrated in Figure 1, the Shiyang River basin is a typical arid inland basin that is located in Gansu Province (China) and covers an area of 41,400 km². The study area consists of six sub-basins located upstream of the Shiyang River basin, including the Xida River basin, Dongda River basin, Xiying River basin, Jintai River basin, Zamu River basin and Huangyang River basin. The basic meteorological data consists of precipitation, temperature, wind speed, solar radiation, and relative humidity obtained from the meteorological station of Wushaoling. Daily precipitation data was collected from 32 rain gauge stations (Figure 1(a)) for the period of 1989–2008. Streamflow data from 1990 to 2008 was obtained from six hydrological stations, including the Xidahe reservoir station, Shagousi station, Jiutiaoling station, Nanying reservoir station, Zamusi station, and Huangyang reservoir station, as shown in Figure 1(a). The spatial distributions of the land use and soil types in 2000 are shown in Figure 1(b), which indicates that there are 18 types of land use. The main land use categories are medium-coverage grasslands, high-coverage grasslands and shrubbery. Additionally, there are 15 soil types in this area, and the three main soil types are gelic leptosols, eutric leptosols and mollic gleysols. Details about the data required by the SWAT model can be found in Table 1.

Satellite and reanalysis precipitation datasets including TRMM, CMDF, CFSR, CHIRPS and PGF were used in this study, and the detailed information of each dataset is summarized in Table 2. Specifically, TRMM 3B42, as one kind of TRMM multi-satellite precipitation analysis (TMPA) dataset (Huffman et al. 2007), can be obtained from the Goddard Earth Sciences Data and Information Services Center at http://mirador.gsfc.nasa.gov. The CMDF data, provided by the Data Assimilation and Modelling Center for Tibetan multi-spheres (DAM), is produced by merging data series, including the existing Princeton reanalysis data, Global Land Data Assimilation System (GLDAS) data, Global Energy and Water Cycle Experiment-Surface Radiation Budget (GEWEX-SRB) data, TRMM precipitation data and routine meteorological observations from the China Meteorological Administration (Li et al. 2012). The CFSR data, provided by the National Centers for Environmental Prediction, is designed and implemented as a global, high-resolution, coupled atmosphere–ocean–land surface–sea-ice system to provide the best estimations of the states of these coupled domains (Saha et al. 2010), available at https://rda.ucar.edu/pub/cfsr.html. The CHIRPS data is based on the integration of various datasets and is available at http://chg.geog.ucsb.edu/data/chirps/. Actually, the CHIRPS data includes the monthly precipitation climatology (CHPclim) data, the cold cloud duration (CCD) information, the TRMM 3B42 data (version 7), the atmospheric rainfall model (version 2) and the rain station data (Funk et al. 2015). The PGF dataset, available at http://hydrology.princeton.edu/data.pgf.php, can be constructed using four datasets, including the NCEP reanalysis data, Climatic Research Unit (CRU) monthly precipitation data, Global Precipitation Climatology Project (GPCP) daily precipitation data and TRMM 3-hour real-time data (Sheffield et al. 2006).

The parameters considered in the Bayesian statistical theory are taken as a group of fuzzy variables which are related to the joint posterior probability density (He et al. 2011). Thus, the parameter uncertainty can be quantified by the posterior probabilities of model parameters, the prior information contained by model parameters and the information contained by input data (Misirli et al. 2013). Among the method of sensitivity and uncertainty analyses of parameters, SUFI-2 (sequential uncertainty fitting procedure, version 2) is an efficient global search algorithm for calibration, parameter optimization and uncertainty analysis with a low computational cost (between 500 and 1,500 model runs) (Abbaspour 2011), and all of these can be achieved based on the SWAT-Calibration Uncertainty Programs (CUP) tool package. In SUFI-2, the parameter optimization is applied to a parameter set and the parameter uncertainties are described by the final ranges of the parameter sets (Abbaspour 2011), and generally, the optimization algorithms include the simplex method, random searching algorithm and competitive coevolutionary algorithm (Duan et al. 1992), and the global analysis methods of LH (Latin-Hypercube) is used in SUFI-2 (Abbaspour 2011).

The sensitivity and significance of each parameter are evaluated by the t-value and P-value, respectively. The t-value describes the behaviour of a sample that is composed of a certain number of observations. The P-value tests the null hypothesis. If the P-value is <0.05, the null hypothesis is rejected, while the parameter impacts on the results with a 95% probability if the P-value equals 0.05. Moreover, a parameter with a large t-value and small P-value is suggested to be sensitive to streamflow (Abbaspour 2011).

In this study, 25 parameters from five process categories, including groundwater, runoff, evaporation, channel and snow, are selected for the sensitivity and uncertainty analyses in SWAT, as listed in Table 3, where the prefix ‘v_’ indicates that the parameter value is replaced by a given value or an absolute change, and ‘r_’ indicates that the parameter value is either multiplied by 1 + a given values or denotes a relative change. The initial parameter ranges are set according to the SWAT manual, as well as previous investigations in the literature (Arnold et al. 2012).

SWAT is a hydrological model that has been proven to be able to obtain the detailed hydrological information in a basin (Silva et al. 2018). In this study, streamflow is simulated by SWAT with an ESRI QGIS interface (Dile et al. 2016). The modified Soil Conservation Service (SCS) curve number method is used to calculate the surface streamflow. Snowmelt is estimated by the energy balance equation. Potential evapotranspiration is determined by the Hargreaves method, and channel routing is simulated by a variable storage method (Neitsch et al. 2011). For monthly streamflow simulations using SWAT, three years from 1987 to 1989 are used as the warm-up period to mitigate the effects of unknown initial conditions, and the periods of 1990–2000 and 2001–2008 are selected as the calibration period and validation period, respectively.

The precipitation data used in the SWAT model includes three categories: (a) geographical spatial interpolation data of observed precipitation (GSI); (b) the original satellite and reanalysis precipitation datasets; and (c) the downscaled satellite and reanalysis precipitation datasets. The models that use different precipitation datasets as input data for SWAT modelling are labelled as M_GSI, M_TRMM, M_CMDF, M_CFSR, M_CHIRPS and M_PGF, where the subscript denotes the dataset name.

The Nash–Sutcliffe coefficient (NS), is applied to evaluate the performance of model simulation. According to the value of the NS coefficient, the model performance can be divided into different categories, including unsatisfactory performance (NS ≤ 0.50), satisfactory performance (0.50 < NS ≤ 0.65), good performance (0.65 < NS ≤ 0.75) and very good performance (0.75 < NS ≤ 1.00) (Moriasi et al. 2007). In addition to the NS, the coefficient of determination (R²) is also used to assess the fitting of the observation values and simulation results.

Streamflow simulations of six sub-basins in the Shiyang River basin based on SWAT model are performed using the GSI, original and downscaled satellite and reanalysis precipitation datasets. Figure 2 shows the monthly streamflow simulations in the calibration period with respect to the Xida River basin, Dongda River basin, Xiying River basin, Jinta River basin, Zamu River basin, and Huangyang River basin. Herein, the simulation results obtained by different precipitation datasets are compared with observation data. As can be seen from Figure 2(a), 2(c), 2(e), 2(g), 2(i) and 2(k), all five precipitation dataset models fail to reproduce the discharge records before downscaling, and based on the NS values shown in Figure 3, it also indicates that all the dataset models present unsatisfactory performance before downscaling. This can be interpreted by the fact that the spatial variability in precipitation patterns can be poorly captured because the topographic effects are not taken into consideration before downscaling.

However, as shown in Figure 2(b), 2(d), 2(f), 2(h), 2(j) and 2(l), the performances of these models can be significantly improved after downscaling, which can also be observed from the NS values of these models shown in Figure 3. It indicates that downscaling based on the GSI dataset tends to yield larger NS and R² values for different models in all sub-basins, and it is also found that most values of R² increase slightly after downscaling, while the NS values increase significantly for most models in most sub-basins.

Moreover, Figure 3 also indicates that M_GSI performs best among all the models in the Xida, Dongda and Jinta River basins, and M_CMDF performs best in the Xiying, Zamu and Huangyang River basins. The most obvious increases in NS and R² values after downscaling are obtained by M_CMDF and M_PGF, while the NS and R² values change a little for M_CFSR and M_CHIRPS before and after downscaling. Additionally, the NS and R² values are also found to decrease after downscaling such as when using M_CFSR and M_CHIRPS in some sub-basins, and this indicates that the heterogeneous patterns and intensities of precipitation are not completely eliminated from the original datasets. Therefore, the spatial accuracy of the precipitation observation data and the quality of most precipitation data from the satellite and reanalysis datasets are improved by the geographical spatial interpolation, except for the data from the CFSR and CHIRPS datasets in some sub-basins. Hence, it is also found that the geographical spatial interpolation is feasible for estimating the precipitation in areas lacking observed data in Shiyang River basin. In general, the five satellite and reanalysis precipitation datasets after downscaling are feasible for streamflow simulation in the Shiyang River basin.

Sensitivity analysis is carried out for model parameters to determine the influence of each parameter on the performance of streamflow simulation. The three most sensitive parameters and their values during the runoff simulation in the Xida River using multisource precipitation inputs, i.e. GSI, TRMM, CMDF, CFSR, CHIRPS and PGF, are listed in Table 4. It can be found that the most sensitive parameter in the Xida River is SMTMP, which indicates that the runoff simulation is very sensitive to the snow melting temperature. The value as well as varying range of this parameter change with different precipitation inputs, lying between −0.94 and 9.84. Moreover, ALPHA_BNK ranks second, third and third for GSI, CMDF and CHIRPS, respectively. GW_REVAP, GWQMN, RCHRG_DP, SMFMX and TIMP are found to be the most sensitive parameters for multisource precipitation inputs, among which the former three are groundwater parameters, and the latter two are snowmelt runoff parameters. Therefore, the most sensitive parameters in the Xida River are ice and snow melting, groundwater recharge and river base flow, and snowmelt runoff and groundwater recharge are very important for runoff production in the Xida River.

Similarly, the three most sensitive parameters in the Dongda River, Xida River, Xiying River, Jinta River, Zamu River and Huangyang River under the precipitation datasets of GSI, TRMM, CMDF, CFSR, CHIRPS and PGF are obtained, as shown in Figure 4. For the Dongda River, the most sensitive parameters are SMTMP, CN2, CN2, SMFMX, CN2, CN2 for the precipitation datasets GSI, TRMM, CMDF, CFSR, CHIRPS and PGF, respectively. Moreover, RCHRG_DP, ESCO and ALPHA_BNK belong to the top three sensitive parameters using multisource precipitation inputs. This indicates that the most sensitive parameters in the Dongda River are surface runoff, snowmelt, groundwater recharge and evaporation. For the Xiying River, the most sensitive parameters are RCHRG_DP, CN2, SMTMP, SMTMP, CH_K2 and CN2 for the six precipitation datasets, respectively. Moreover, the top three sensitive parameters include GW_DELAY, ALPHA_BNK, SMFMX, TIMP, ESCO and ALPHA_BF, which indicates that the most sensitive parameters in the Xiying River are surface runoff, snowmelt, groundwater recharge, river base flow and evaporation. For the Jinta River, the most sensitive parameters respectively are SMFMX, CN2, SMTMP, SMFMX, CN2 and CN2 for the six precipitation datasets. The top three sensitive parameters also include TIMP, CH_K2 and ESCO, and thus snowmelt, surface runoff, river base flow and evaporation are the most sensitive parameters in the Jinta River. For the Zamu River, the most sensitive parameters are SMTMP, CN2, SMTMP, SMFMX, CN2 and CN2 for the six precipitation datasets, respectively. The top three sensitive parameters also include RCHRG_DP, ALPHA_BNK, TIMP and ESCO, and this indicates that surface runoff, snowmelt, groundwater recharge, river base flow and evaporation are the most important parameters in the Zamu River. For the Huangyang River, the most sensitive parameters are CN2, CN2, SMTMP, SMFMX, CN2 and CN2 for the six precipitation datasets, and RCHRG_DP, ALPHA_BNK, GWQMN also belongs to the top three sensitive parameters, which indicates the most sensitive parameters in the Huangyang River are surface runoff, snowmelt, evaporation, groundwater recharge and river base flow.

As can be found in Figure 4, the sensitivities of most parameters vary significantly with respect to different sub-basins and precipitation datasets. Thus it is impossible to obtain a general answer of parameter sensitivity ranking for all precipitation datasets, even in the same sub-basin. However, among all the sensitivity parameters, due to the similarities in hydrological behaviour associated with similar geographic and climatic environments of different sub-basins, CN2 and SMTMP show the highest relative sensitivity for most of the sub-basins when using multisource precipitation datasets, which suggests that the surface runoff and snowmelt are of significant importance for the streamflow production in the Xida River, Dongda River, Xiying River, Jinta River, Zamu River and Huangyang River.

Furthermore, the uncertainty analysis of parameters obtained by the SUFI-2 procedure is also performed. The selected values of different parameters for different datasets and sub-basins are shown in Figure 5, where the ranges of parameter value are also provided. Parameters here include CN2, SMTMP, ALPHA_BNK, ESCO, SMFMX and RCHRG_DP. It is obvious that, even in the same sub-basin, the selected value and value range of most parameters vary significantly with respect to different dataset models. For instance, the CN2 has larger selected values in the cases of M_TRMM, M_PGF and M_CHIRPS, while in M_CMDF it is of the lowest value. The selected values of SMTMP for different datasets in the Xida River and Dongda River basins change over a small range when compared with those in other sub-basins. Moreover, the values of ALPHA_BNK are considered to be reasonable in all sub-basins. The high value of ESCO indicates that there is a high evaporation compensation in the soil, and this is consistent with the climatic, geographical and environmental conditions in the mountainous areas of sub-basins. In addition, SMFMX and RCHRG_DP show changes for different datasets and sub-basins.

However, the evaluation of the selected parameter value is associated with inherent uncertainty. Due to the model assumptions, it is typically impractical to define parameter values based on estimations according to probability distributions. Moreover, in this study, the parameter values are significantly different for the same basin when the model is calibrated using different precipitation datasets. Despite the similarities in land use, major soil types and other hydrological and meteorological conditions in all the sub-basins, the parameter values are also different for the same precipitation dataset in different sub-basins. Thus, it is impossible to apply the outcomes obtained in one sub-basin to all sub-basins. In other words, the parameter uncertainty is closely related to the properties of the basin. The results indicate that the selected value and its ranges of most parameters vary significantly with respect to different sub-basins and dataset models, which reflects the uncertainty of the model parameters and the variation of simulation performance under multisource precipitation datasets.

The performances of the precipitation datasets after downscaling for streamflow prediction with parameter optimization in the Xiying River basin are further investigated. Comparisons of the best streamflow simulations and observation data in the Xiying River basin considering different precipitation datasets are shown in Figure 6, where the black lines denote the measured streamflow and red ones denote the best streamflow simulations. Figure 6 also shows the uncertainties of streamflow prediction during the calibration period, where the green shaded area represents 95PPU. It should be noted that the TRMM dataset is limited by the time scale, thus only the data of TRMM in the period of 1999–2008 is used to simulate the streamflow.

The values of evaluation indexes of the streamflow simulation for different dataset models can also be found in Figure 6, which indicates that the six datasets have R² values greater than 0.6 and NS values greater than 0.5 during the calibration and validation period in the Xiying River basin. Considering the value of NS, the simulation performances using different precipitation datasets in the calibration period are in the rank of M_CMDF > M_TRMM > M_CHIRPS > M_CFSR > M_PGF > M_GSI, and in the validation period, the sequence is M_CFSR > M_GSI > M_CMDF > M_CHIRPS > M_PGF. Particularly, the performance of the SWAT model is better during the validation period than the calibration period in the cases of M_GSI, and other dataset models show better performance during the calibration period. One possible reason for this is that the distribution of precipitation during the calibration and validation periods is different for the six datasets. Moreover, the NS and R² in the case of parameters optimization are greater than those before parameter adjustment in the calibration period.

For streamflow simulation using M_GSI in the Xiying River basin, the timing and magnitude of flows are reasonably captured. Moreover, the M_CFSR model shows the best performance, and the values of NS are 0.78 and 0.74 in the calibration and validation periods, respectively. The streamflow simulations in the Xiying River basin using different precipitation datasets indicate that most overestimates appear in summer (i.e. June, July and August), and underestimates are more likely occur in December and January for most dataset models. In general, all the models using the six datasets are able to reproduce the observation data of streamflow in the Xiying River basin, and most of them are of consistent and satisfactory performance. The simulation results can be improved by adjusting the relevant hydrological parameters to their optimal calibrated values based on SWAT-CUP. Furthermore, the accuracy of the precipitation input impacts on the accuracy of the simulation results, and satellite and reanalysis datasets are suggested to be reasonable inputs for hydrological simulation at basin scale, especially for the basins with a lack of rainfall gauges.

Uncertainties in streamflow prediction during the calibration and validation periods using different precipitation datasets in the Xiying River basin are also shown in Figure 6, where the 95PPU contains all uncertainties from different sources. For the calibration period, the results indicate that the P-factor values of M_GSI, M_TRMM, M_CMDF, M_CFSR, M_CHIRPS, M_PGF are 0.88, 0.57, 0.87, 0.9, 0.9 and 0.86, respectively, and the R-factor values are 1.65, 0.68, 0.93, 1.56, 0.95 and 0.99, respectively. For the validation period, it also shows an acceptable performance with P-factor of M_GSI, M_CMDF, M_CFSR, M_CHIRPS, M_PGF being 0.74, 0.6, 0.82, 0.78 and 0.78, respectively, and R-factor of 1.12, 0.64, 1.27, 0.78 and 0.93, respectively. Thus most of the observation data can be covered by the 95PPU.

In the calibration period, it indicates that M_TRMM has the smallest P-factor (i.e. 0.57) among all datasets, which means that only 57% of simulated streamflow is covered by the 95% streamflow prediction uncertainty band. The values of R-factor with respect to most dataset models are less than 1, which means that the streamflow simulation distributes closely with respect to the streamflow observations as the R-factor is smaller than 1.5, except for the models using M_GSI and M_CFSR and it may be caused by the large uncertainty in simulating the streamflow peaks. Thus the prediction uncertainties using M_CMDF, M_CHIRPS and M_PGF are acceptable. While in the validation period, except for the model using CMDF where the P-factor is less than 0.7, the P-factor and R-factor values of other precipitation datasets are acceptable, indicating that the prediction uncertainties using M_GSI, M_CFSR, M_CHIRPS and M_PGF are acceptable.

Moreover, for both the calibration and validation periods, it is obvious that M_CHIRPS and M_PGF are able to achieve a good balance between the P-factor and R-factor, which shows acceptable and satisfactory uncertainties of streamflow predictions. However, in the validation period, some streamflow peak values in the 95PPU band are much lower than the observation data, except for M_CHIRPS, which indicates that the prediction uncertainty near streamflow peaks in this basin is significant, which may be caused by the uncertainties of precipitation inputs that propagate to the uncertainties of streamflow prediction (Neitsch et al. 2011).

Streamflow simulation of six sub-basins in the Shiyang River basin are investigated based on the SWAT model using the interpolation precipitation datasets of GSI, and the satellite and reanalysis precipitation datasets of TRMM, CMDF, CFSR, CHIRPS and PGF. The model performance, parameter sensitivity and uncertainty, and prediction uncertainty of streamflow simulation using the downscaled precipitation datasets, are discussed in detail. It is found that the model performance of streamflow simulation can be significantly improved by using the downscaled satellite or reanalysis precipitation datasets. For parameter optimization, the sensitivity and uncertainty of each parameter varies with precipitation datasets and sub-basins, and the parameter uncertainty with respect to different precipitation inputs can reflect the variation of simulation performance under multisource precipitation datasets. Among the model parameters, CN2 (the initial SCS runoff curve number for moisture condition II) and SMTMP (the base temperature of snow melt) are found to be of the highest relative sensitivities for most of the sub-basins, which suggests that the surface runoff and snowmelt are of significant importance for the streamflow production in Shiyang River basin. Moreover, M_CHIRPS and M_PGF are able to achieve acceptable uncertainties of streamflow predictions after parameter optimization, but the prediction uncertainty at streamflow peaks are not found to be negligible.

Financial support from the National Natural Science Foundation of China (No. 51279166 and No. 91425302) is acknowledged.