Abstract

The spatial variability of precipitation is often considered to be a major source of uncertainty for hydrological models. The widely used Soil and Water Assessment Tool (SWAT) is insufficient to calculate a sub-basin's mean areal precipitation (MAP) since it only uses data from the rainfall station nearest to the centroid of each sub-basin. Therefore, Inverse Distance Weighting (IDW), Thiessen Polygons (TP) and Ordinary Kriging (OK) were applied as alternative interpolation methods in this study to calculate sub-basin MAP. The MAP results from the four methods used for the Xixian Basin were quite different in terms of amount and spatial distribution. The SWAT model performance was then assessed at monthly and daily timescales, based on Nash–Sutcliffe efficiency (NSE), the Coefficient of Determination (R2) as well as Percentage Bias (PBIAS) at the basin outlet. The results under different network densities and spatial distributions of gauge stations indicated that the modified MAP models did not have an advantage over the default Nearest Neighbour (NN) method in simulating monthly streamflow. However, the modified areal precipitation obtained through IDW and TP showed relatively high accuracy in simulating daily flows as the applied rainfall stations changed. The difference in terms of estimated rainfall and streamflow in this study confirmed that evaluation of interpolation methods is necessary before building a SWAT model.

Introduction

The ability of hydrological models to accurately predict streamflow depends to a great extent on how well spatial data describe the relevant characteristics. Compared with other spatial data, the spatial variability of precipitation greatly affects the accuracy of hydrological modelling (Lopes, 1996; Manguerra & Engel, 1998). The Soil and Water Assessment Tool (SWAT) has been widely used for river basins around the world. It was developed to predict the impact of land management practices on water, sediment and agricultural chemical yields in large complex watersheds over long periods of time (Neitsch et al., 2011). As a physically based distributed model, SWAT requires specific information about spatial variables such as hydro-meteorological data, a Digitised Elevation Model (DEM), land use and soil map (Arnold et al., 1998). However, in many practical cases, data to characterize spatially varying inputs are simply not available and the understanding of spatial variable processes is far from complete. The current method of SWAT representing precipitation in each sub-basin is simplistic since it only uses data from a single gauge station. To address this problem, a comparison of other interpolation methods used to estimate mean areal precipitation (MAP) for each sub-basin in a SWAT model was made in this study.

To date, there has been much research into how to capture rainfall variability scientifically. The effects of different precipitation inputs on streamflow simulation have been tested using numerous MAP models (e.g., proximate gauge, weighted average, surface fitting and remote sensed methods). Szcześniak & Piniewski (2015) chose Nearest Neighbour (NN), Inverse Distance Weighting (IDW), Thiessen Polygon (TP) and Ordinary Kriging (OK) methods to calculate sub-basin areal precipitation. The results indicated that OK, IDW and TP were more accurate than the default NN method. Wagner et al. (2012) assessed several interpolation methods and found that regression-based methods showed the best performance. Tuo et al. (2016) tested the influence of NN, IDW and two satellite-based data sets (TRMM and CHIRPS) on simulating streamflow using a SWAT model. The results showed that the IDW method was the most accurate method and the CHIRPS data set produced satisfactory performance. Zeiger & Hubbart (2017) used multiple methods (n = 19) to estimate MAP with precipitation data from 11 distributed monitoring sites, and four remotely sensed data sets. The inverse distance weighted, linear local polynomial interpolation, and multi-quadric function surface-fitting methods were the most accurate methods for daily and monthly SWAT model estimates of streamflow in this study. Currently, satellite-based precipitation products increasingly provide an alternative method to ground-based rainfall estimates and are applied to distributed hydrological models such as SWAT for watersheds with few rain gauges in much research (Strauch et al., 2012; Yang et al., 2014; Tuo et al., 2016; Zeiger & Hubbart 2017). However, remotely sensed data should be assessed before implementation and the performance of it is not always satisfactory (Li et al., 2012; Yang et al., 2014). In summary, the results from the current literature consistently show that introducing other interpolation methods improves model accuracy in most cases.

Notably, the accuracy of MAP methods was strongly influenced by network density as well as by the spatial distribution of the rain gauge stations that applied (Lopes 1996; Chaplot et al., 2005). However, most of the above-mentioned studies only paid attention to either interpolation methods or to the network density of the MAP model. Further, few studies compared daily simulation performance based on a SWAT model but were instead limited to monthly and annual timescales. In this study, the network density is defined as the number of gauge stations per square kilometre within the study region and the reliability of interpolation methods under different network densities at both monthly and daily time steps were also assessed.

The main objective of this paper is to construct an assessment system of interpolation methods that describe the spatial variability of precipitation in hydrological models. The specific objectives are: (1) to compare sub-basins' areal rainfall calculated by different interpolation methods; (2) to evaluate the simulation accuracy of alternative MAP methods using calibrated monthly and daily SWAT models; and (3) to examine the reliability of MAP methods in the Xixian region under different network densities and spatial distributions of gauge stations.

Materials and methods

Description of the study site and input data

The study was conducted in Xixian Basin (113°15′–114°46′E, 31°31′–32°43′N), which is located in the upstream of the Huai River, East China (see Figure 1). According to a previous study (Zhang et al., 2011), the correlation coefficient of precipitation and runoff in the Xixian Basin is relatively high and the region is less affected by human activities. The total drainage area of the basin is 10,190 km² and the main channel of the basin lasts about 250 km. Most of the area is plains and gentle hills with an average elevation of 142 m, showing a trend of decreasing elevation from west to east. The study area is located in the transition zone between a subtropical zone and warm temperate zone, with mean annual temperature ranging from 14 to 16 °C and mean annual precipitation ranging from 800 to 1,400 mm, half of which falls between June and September. Peak flow usually occurs during the rainy season and is often accompanied by severe floods. Soil in the Xixian Basin is dominated by paddy soil, yellow cinnamon soil and yellow brown loam. The basin is mainly covered by semi-natural vegetation, with coniferous forest and broad-leaved forest on the higher elevations in the west, whereas rice and wheat occupy lower elevations.

Fig. 1.

Location of Xixian Basin showing hydrological and meteorological stations.

Fig. 1.

Location of Xixian Basin showing hydrological and meteorological stations.

The main inputs for a SWAT model are a DEM, land use, soil, rainfall and meteorological data. The DEM map was created using a 90*90 m Shuttle Radar Topography Mission (SRTM) that came from the International Scientific and Technical Data Mirror Site (http://www.gscloud.cn). The land use data (Figure 2(a)) for 1995 (with a spatial resolution of 1 km) were provided by the Institute of Geographic Sciences and Natural Resources Research and reclassified according to SWAT land use type. The soil map (Figure 2(b)) (with a spatial resolution of 1 km) was extracted from the China soil map from the Harmonized World Soil Database (HWSD). The projection of all the spatial data in this research was transformed into a Universal Transverse Mercator (UTM) coordinate system with a central meridian of 111°E. Daily rainfall data for a normal climate period from 1982 to 2000 (Ma et al., 2014) were collected from 61 rainfall stations in Xixian Basin. Daily maximum and minimum temperatures, solar radiation, wind speed and relative humidity from 1982 to 2000 were provided by two weather stations. The daily discharge measurements at the basin outlet were collected from 1982 to 2000. For model calibration and validation, daily discharge data were converted to monthly data and divided into two periods.

Fig. 2.

Xixian Basin distribution maps for: (a) soil type; and (b) land use.

Fig. 2.

Xixian Basin distribution maps for: (a) soil type; and (b) land use.

MAP method description

Of all the MAP models, weighted average methods are the most widely used. Replacing the default NN method, different weighted average methods (IDW, TP and OK) were adopted to estimate MAP for each sub-basin in this study. These three methods represent distance weighting, area weighting and optimal unbiased estimation, respectively. The general equation for weighted average methods is: 
formula
(1)
where is the MAP for n rain gauges termed ; is the observed precipitation at each gauge; and is the weight estimated for each gauge.

Inverse distance weighting

The IDW method is based on the assumption that points close to each other are more correlated than points further apart (Galván et al., 2014). The weight for each gauge is calculated according to Equation (2): 
formula
(2)
where is the distance between gauge and the centroid of the sub-basin; parameter is the power value and was set to 2 in this study. In order to eliminate the influence of distant stations, only the precipitation of the five stations nearest to the centroid were considered in this research.

Thiessen Polygons

The Thiessen method is performed by dividing a region into sub-regions centered on each precipitation gauge. The fraction of each Thiessen sub-region contributing to each sub-basin can be computed and the weighted averages can be used to estimate the MAP for each sub-basin. The weight for each gauge is calculated according to Equation (3): 
formula
(3)
where is the area of the sub-basin; is the area of each sub-region; and is the number of Thiessen Polygons (TP).

Ordinary Kriging

The key point of the Kriging method is to determine the weight coefficient. The weights of Ordinary Kriging (OK) are estimated with the following two requirements: (1) the estimation is unbiased; and (2) the estimation is optimal. Through a series of mathematical deductions (Ly et al., 2011), the formula of OK weights is: 
formula
(4)
 
formula
(5)
where is the position to be interpolated; is the position of gauge i(j); μ is the Lagrange constant; is the value of the variogram between and . The variogram is a function that relates the semi-variance γ to lag h. With sample data, an ordered set of semi-variances can be calculated, which constitute the experimental variogram. The usual formula for this is: 
formula
(6)
where is the number of pairs of observations separated by the lag ; is the value of a property z at position , which here represents precipitation. In order to obtain a continuous function of semi-variance, it is necessary to fit a mathematical model to the discrete sample of semi-variance. The Spherical model, Exponential model and Gaussian model are some common variance models used. Once the mathematical model is fitted, the semi-variance for each can easily be estimated so that the Kriging weights can be calculated according to the above equation.

SWAT model description

SWAT (Soil and Water Assessment Tool) is a physically based, spatially distributed and continuous hydrological model developed by the Agricultural Research Service (ARS) of the United States Department of Agriculture (USDA). It was designed to predict the impact of land management practices on water, sediment and chemical yields in large complex watersheds with varying soils, land use and management, over long periods of time (Neitsch et al., 2011).

SWAT executes the process of watershed delineation and stream definition based on information from a DEM. The catchment size threshold value which is defined by the user determines the sub-basin size. Climatic data from the station nearest to the sub-basin's centroid are used in the model simulations as per SWAT's standard setup. Sub-basins are further subdivided into multiple hydrologic response units (HRUs) that are comprised of unique land use, slope and soil characteristics. Runoff is simulated separately at the HRU level and routed to obtain the discharge process of the basin outlet. In this case, Soil Conservation Service (SCS) Curve Numbers (CNs) were applied to estimate surface runoff, the Penman-Monteith method was adopted for potential evapotranspiration, and the Muskingum method was employed to simulate channel flood routing.

Model evaluation indicators

The SWAT model performance under different MAP methods was evaluated using Nash–Sutcliffe efficiency (NSE), the Coefficient of Determination (R2), as well as Percentage Bias (PBIAS) to avoid the specific limitations of a single evaluation indicator (Willmott et al., 2015). NSE and R2 indicate the fitness between the simulated streamflow process and observed streamflow process, and PBIAS demonstrates the bias of the simulated water amount. NSE, R2 and PBIAS are calculated as follows: 
formula
(7)
 
formula
(8)
 
formula
(9)
where  and are measured and simulated streamflow at each time step i; and are the mean measured and simulated streamflow; and n is the number of time steps. NSE ranges from to 1, and R2 from 0 to 1. The closer NSE and R2 are to 1, the better the SWAT model performs. The optimum value of PBIAS is zero, with positive values indicating model underestimation and negative values indicating overestimation. Streamflow estimation results with NSE and R2 greater than 0.6, and PBIAS between −20 and 20% were considered to be relatively satisfactory results in this study.

Results and discussion

SWAT model construction

In this study, ArcSWAT 2012, a SWAT model (version 2012) interface in the ArcGIS 10.2 system, was applied to develop a SWAT model for Xixian Basin. In order to better characterize the spatial variability of rainfall, a relatively low threshold value was chosen for this research. A threshold value of 7,000 ha resulted in a river system closest to the actual situation, and the sub-basins were then automatically divided according to the river system. The study area was further divided into 414 HRUs by making overlay analysis of a soil map and land use map. The period from 1982 to 1984 served as a warm-up period for the SWAT model, allowing state variables to assume certain initial values for model calibration. According to the available data, daily (monthly) runoff data from 1985 to 1995 were used for calibration and the remaining data from 1996 to 2000 were used for validation.

A global sensitivity analysis was run using the default NN method and the top seven most sensitive parameters were selected for the calibration of all MAP models. The seven relatively sensitive parameters are: moisture condition II curve number (CN2); base flow recession constant (ALPHA_BF); delay time for aquifer recharge (GW_DELAY); threshold water level in shallow aquifer for base flow (GWQMN); soil available water capacity (SOL_AWC); threshold water level in shallow aquifer for revaporation (REVAPMN); effective hydraulic conductivity in main channel alluvium (CH_K2). The process of parameter calibration was based on SWAT-CUP (SWAT Calibration and Uncertainty Program) version 5.1.6, and the SUFI-2 algorithm (Abbaspour et al., 2004, 2007) was used to calibrate and validate the model parameters automatically. The calibration was ended after four iterations of 500 simulations each (i.e., a total of 2000 simulations) for all the MAP methods at monthly and daily timescales. The parameter range of the last iteration was regarded as the optimum parameter range and the parameter set within the optimum range that produced the maximum value of object function NSE was the best parameter set.

Comparison of mean areal precipitation (MAP) results

In order to study the impact of MAP input on streamflow simulation based on SWAT, virtual gauge stations were set up at the centroid of all the sub-basins and the MAP of each sub-basin was taken to be equal to the precipitation input of the virtual station. The precipitation data from different MAP methods from 1982 to 2000 were then imported into the virtual stations as the sub-basin's areal rainfall. The marked differences in the number of gauges concerned in the NN method (n = 1 gauge per sub-basin), IDW method (n = 5 gauges per sub-basin), TP method (n = 2–8 gauges per sub-basin) and OK method (n = 60 gauges per sub-basin) were notable. The distribution of 87 virtual stations and the Thiessen Polygons of 61 rain gauge stations are shown in Figure 3.

Fig. 3.

Distribution of virtual rain gauge stations and Thiessen Polygons.

Fig. 3.

Distribution of virtual rain gauge stations and Thiessen Polygons.

Figure 4 presents the mean annual precipitation under four MAP methods. There are great differences in the amount and spatial distribution of the annual precipitation estimated by the four methods. The annual totals range from 664.3 to 1,245.5 millimetres per year (mm/a) for NN, from 752.9 to 1,243.1 mm/a for IDW, from 664.3 to 1,243.9 mm/a for TP and from 802.9 to 1,139.4 mm/a for the OK method. Generally, the sub-basins located in the northern parts of the study area displayed relatively lower precipitation, whereas the sub-basins in the southwestern and southern parts of the Xixian Basin have the highest precipitation. The extreme points of precipitation in this region are comparatively scattered under the NN method according to Figure 4(a). However, the annual totals began to show obvious spatial variability as the gauge density increased and the spatial distribution of annual precipitation under the OK method is in good agreement with the available precipitation maps of the region (Du, 2014).

Fig. 4.

Mean annual precipitation in the Xixian Basin under the (a) NN, (b) TP, (c) IDW and (d) OK methods.

Fig. 4.

Mean annual precipitation in the Xixian Basin under the (a) NN, (b) TP, (c) IDW and (d) OK methods.

The difference of overall precipitation between the SWAT default NN method and other weighted average methods is illustrated by a comparison of daily precipitation for two selected sub-basins (ID = 48, 81) in Figure 5, representing low and high precipitation in the region, respectively (as shown in Figure 4). The daily values under other MAP methods could be higher, lower, or similar, compared to the NN method. For a sub-basin of low precipitation (sub-basin ID: 48), the lower precipitation events can be totally missed (zero value for x-axis as indicated by some of the data points falling on the y-axis line) and the high precipitation extremes are relatively smaller in the NN method compared to the IDW and TP. For a sub-basin of high precipitation (sub-basin ID: 81), the daily values were similar in most cases as compared to the NN method, whereas the daily precipitation estimated by the OK method are generally lower than those estimated by a single gauge, which is probably due to taking gauges that are far from the centroid into account.

Fig. 5.

Comparison of daily precipitation from the SWAT default method and other weighted average methods, illustrated by two selected sub-basins.

Fig. 5.

Comparison of daily precipitation from the SWAT default method and other weighted average methods, illustrated by two selected sub-basins.

Generally speaking, there are great differences in both quantity and spatial distribution of the estimated areal precipitation in the study region under the four MAP methods. Comparing and assessing the SWAT model driven by different MAP methods is very instructive. Given that there are no observed values for the sub-basins' areal precipitation, it is still hard to say which MAP model is suitable for this region. An alternative approach to evaluate the different MAP methods is to validate them in hydrological models (Ly et al., 2011). Thus, the simulated streamflow under NN, IDW, TP and OK was evaluated at monthly and daily time steps at sub-basin level in the next section.

Comparison of streamflow simulations

Model performance under the existing rainfall stations

The SWAT models for different MAP scenarios were independently calibrated using the SUFI-2 algorithm after running a sensitivity analysis. The initial parameter ranges and iteration times for model calibration under all the MAP methods were exactly the same, so as to eliminate the influence of parameter uncertainty. Calibration and validation were performed for monthly and daily data, using the data given by the Xixian gauge station at the watershed outlet. The calibrated parameter values for each MAP method of monthly and daily models are presented in Table 1.

Table 1.

Calibrated values of the selected parameters used in setting up monthly and daily SWAT models.

Parameter sensitivity ranka Parameterb Suggested ranges in SWAT Final value or ranges used for NN Final value or ranges used for IDW Final value or ranges used for TP Final value or ranges used for OK 
Monthly 
r_CN2 35–98 59–93 62–96 60–94 62–96 
v_ALPHA_BF 0–1 0.88 0.81 0.79 0.87 
v_GW_DELAY 0–500 85.65 66.33 50.02 288.84 
v_GWQMN 0–5,000 1.44 1.26 1.33 0.96 
r_SOL_AWC 0–1 0.06–1 0.06–1 0.06–1 0.06–1 
v_REVAPMN 0–500 3.01 3.00 3.15 2.05 
v_CH_K2 –0.01–500 115.06 102.31 144.60 189.48 
Daily 
r_CN2 35–98 47–73 49–76 51–80 60–93 
v_ALPHA_BF 0–1 0.49 0.74 0.74 0.73 
v_GW_DELAY 0–500 88.80 64.55 64.55 261.50 
v_GWQMN 0–5,000 2.84 2.65 2.65 1.73 
r_SOL_AWC 0–1 0.05–1 0.06–1 0.06–1 0.07–1 
v_REVAPMN 0–500 13.73 6.92 6.92 13.60 
v_CH_K2 –0.01–500 77.21 106.39 106.39 151.79 
Parameter sensitivity ranka Parameterb Suggested ranges in SWAT Final value or ranges used for NN Final value or ranges used for IDW Final value or ranges used for TP Final value or ranges used for OK 
Monthly 
r_CN2 35–98 59–93 62–96 60–94 62–96 
v_ALPHA_BF 0–1 0.88 0.81 0.79 0.87 
v_GW_DELAY 0–500 85.65 66.33 50.02 288.84 
v_GWQMN 0–5,000 1.44 1.26 1.33 0.96 
r_SOL_AWC 0–1 0.06–1 0.06–1 0.06–1 0.06–1 
v_REVAPMN 0–500 3.01 3.00 3.15 2.05 
v_CH_K2 –0.01–500 115.06 102.31 144.60 189.48 
Daily 
r_CN2 35–98 47–73 49–76 51–80 60–93 
v_ALPHA_BF 0–1 0.49 0.74 0.74 0.73 
v_GW_DELAY 0–500 88.80 64.55 64.55 261.50 
v_GWQMN 0–5,000 2.84 2.65 2.65 1.73 
r_SOL_AWC 0–1 0.05–1 0.06–1 0.06–1 0.07–1 
v_REVAPMN 0–500 13.73 6.92 6.92 13.60 
v_CH_K2 –0.01–500 77.21 106.39 106.39 151.79 

Note:aA t-test was used to identify the relative significance of each parameter; bv refers to the absolute change in the parameter made by replacing a parameter by a given value; r refers to the relative change in the parameter made by multiplying the parameter by 1 plus the factor in the given range.

Table 2 presents a statistical evaluation of simulated streamflow on a monthly scale. For the monthly model, NSE, R2 and absolute values of PBIAS were in the range of 0.86–0.93, 0.87–0.94 and 1.1–10.7, respectively. The NSE and R2 values for the NN method were slightly closer to 1 compared to other MAP models during the calibration and validation periods, whereas the absolute PBIAS value for NN was much greater than for the others in the calibration period. Visual comparisons of observed and simulated streamflow data on the monthly scale are shown in Figure 6. Monthly hydrographs from the Xixian hydrological station during the calibration period indicated no striking differences in performance under all the methods, whereas the NN method resulted in slightly better simulations and the OK method tended to cause overestimation in low flow periods.

Table 2.

Mean areal precipitation (MAP) input effects on calibrated SWAT model results on the monthly scale.

MAP method Calibration period (1985–1995)
 
Validation period (1996–2000)
 
NSE R2 PBIAS NSE R2 PBIAS 
NN 0.93 0.94 −10.7 0.91 0.91 −1.6 
IDW 0.92 0.93 −1.1 0.90 0.90 5.6 
TP 0.92 0.92 −2.4 0.90 0.90 5.6 
OK 0.91 0.91 3.4 0.86 0.87 4.5 
MAP method Calibration period (1985–1995)
 
Validation period (1996–2000)
 
NSE R2 PBIAS NSE R2 PBIAS 
NN 0.93 0.94 −10.7 0.91 0.91 −1.6 
IDW 0.92 0.93 −1.1 0.90 0.90 5.6 
TP 0.92 0.92 −2.4 0.90 0.90 5.6 
OK 0.91 0.91 3.4 0.86 0.87 4.5 

Note: NSE: Nash–Sutcliffe efficiency; R2: Coefficient of Determination; PBIAS: Percentage Bias.

Fig. 6.

Calibration results (for the period 1985–1995) under the (a) NN, (b) TP, (c) IDW and (d) OK methods at the Xixian gauge stations. The results represent mean monthly discharge of the best simulation, i.e., highest NSE values obtained in a set of 2000 simulations (broken lines) and observed discharge data (solid lines).

Fig. 6.

Calibration results (for the period 1985–1995) under the (a) NN, (b) TP, (c) IDW and (d) OK methods at the Xixian gauge stations. The results represent mean monthly discharge of the best simulation, i.e., highest NSE values obtained in a set of 2000 simulations (broken lines) and observed discharge data (solid lines).

Table 3 presents a statistical evaluation of simulated streamflow on a daily scale. For the daily model, NSE, R2 and absolute values of PBIAS were in the range of 0.64–0.70, 0.64–0.71 and 8.6–19.6, respectively. The IDW method resulted in the greatest NSE and R2 on a daily scale, followed by the TP and OK methods. Notably, the NN method resulted in PBIAS values greater than 15% in both the calibration and validation periods, suggesting that simulated values were much lower than observed values. Daily hydrographs under the four MAP methods at the Xixian hydrological station in two selected periods are shown in Figure 7. In the daily model, the simulated flow under the NN method appeared to be the closest to observed values among all the MAP models in high flow periods. However, it showed a large underestimation in low flow periods, which is probably due to the NN method having missed lower precipitation events (Figure 5). By contrast, the OK method performed the best in the low flow period but performed worst at peak flow. According to Formulas (8) and (9), NSE and R2 are calculated by the square of discharge data, which enhances the effect of high-flow discharge. This probably resulted in relatively low NSE and R2 under the OK method. In general, the IDW as well as the TP method can obtain relatively satisfactory results in both the high flow and low flow periods.

Table 3.

Mean areal precipitation (MAP) input effects on the calibrated SWAT model results on the daily scale.

MAP method Calibration period (1985–1995)
 
Validation period (1996–2000)
 
NSE R2 PBIAS NSE R2 PBIAS 
NN 0.64 0.66 19.6 0.69 0.71 18.1 
IDW 0.68 0.69 8.6 0.70 0.71 12.3 
TP 0.66 0.67 9.7 0.69 0.70 12.3 
OK 0.67 0.64 9.6 0.69 0.68 14.9 
MAP method Calibration period (1985–1995)
 
Validation period (1996–2000)
 
NSE R2 PBIAS NSE R2 PBIAS 
NN 0.64 0.66 19.6 0.69 0.71 18.1 
IDW 0.68 0.69 8.6 0.70 0.71 12.3 
TP 0.66 0.67 9.7 0.69 0.70 12.3 
OK 0.67 0.64 9.6 0.69 0.68 14.9 

Note: NSE: Nash–Sutcliffe efficiency; R2: Coefficient of Determination; PBIAS: Percentage Bias.

Fig. 7.

Calibration results (during the years 1985–1995) under the NN, TP, IDW and OK methods at the Xixian gauge station in two selected periods: (a) 25 May 1987–22 September 1987; and (b) 10 May 1989–23 September 1989. The results represent mean daily discharge of the best simulation and observed discharge data.

Fig. 7.

Calibration results (during the years 1985–1995) under the NN, TP, IDW and OK methods at the Xixian gauge station in two selected periods: (a) 25 May 1987–22 September 1987; and (b) 10 May 1989–23 September 1989. The results represent mean daily discharge of the best simulation and observed discharge data.

Considering the entirety of our evaluation results, the model simulations at monthly and daily time steps are accurate enough under all the MAP methods to confirm that the SWAT model can be applied to the Xixian Basin. Daily streamflow, as expected, were poorer than monthly simulations. This was likely caused by the complexity of daily hydrological processes. Overall, the NN method performed the best in monthly simulations, and the IDW method came second. The IDW method performed the best in daily simulations, and the TP method came second. Different MAP methods were applicable in different periods, reflected by the satisfactory results that were obtained under the NN method in high flow periods and under the OK method in low flow periods at a daily time step.

Model performance under different gauge network densities

The density of rain gauges has a significant effect on the accuracy of hydrological model outputs (Anctil et al., 2006; Xu et al., 2013). In order to take network density into account, the rainfall stations in the study region were artificially reduced to 25%, 50% and 75% by the principles of uniform distribution and random distribution in space (see Figures 8 and 9). Different MAP methods were applied to calculate daily rainfall data based on the selected stations, which were then input into the SWAT model to estimate the streamflow at the Xixian hydrological station from 1985 to 1995. The model was no longer calibrated and the parameter values for each MAP method were set according to Table 1.

Fig. 8.

Distribution of rain gauge stations (a) 25%, (b) 50%, (c) 75% and Thiessen Polygons in the Xixian Basin (gauge stations uniformly distributed).

Fig. 8.

Distribution of rain gauge stations (a) 25%, (b) 50%, (c) 75% and Thiessen Polygons in the Xixian Basin (gauge stations uniformly distributed).

Fig. 9.

Distribution of rain gauge stations (a) 25%, (b) 50%, (c) 75% and Thiessen Polygons in the Xixian Basin (gauge stations randomly distributed).

Fig. 9.

Distribution of rain gauge stations (a) 25%, (b) 50%, (c) 75% and Thiessen Polygons in the Xixian Basin (gauge stations randomly distributed).

Table 4 presents the evaluation indicators of the monthly and daily SWAT models obtained by using different MAP inputs. Generally speaking, the MAP models applied in this study resulted in relatively satisfactory hydrological simulation results at the basin outlet. The monthly NSE and R2 values were greater than 0.8 and the absolute values of PBIAS were less than 20%, whereas the daily NSE and R2 values were greater than 0.6 and the absolute values of PBIAS were less than 25%. In most cases, NSE and R2 for the Xixian monthly and daily estimations increased with the increase of network density, which is in agreement with present conclusions that a high gauge concentration is necessary (Chaplot et al., 2005). Further, there is no evident relationship between the absolute value of PBIAS and network density. Assuming that the object function NSE is used as the main evaluation criteria, it can be seen that uniform station selection resulted in better results than random selection at both monthly and daily time steps.

Table 4.

Comparison of the monthly and daily model simulations under four MAP method.

ID Gauge Name NN
 
IDW
 
TP
 
OK
 
NSE R2 PBIAS (%) NSE R2 PBIAS (%) NSE R2 PBIAS (%) NSE R2 PBIAS (%) 
Monthly 
Xixian 0.91 0.91 −1.6 0.90 0.90 5.6 0.90 0.90 5.6 0.86 0.87 4.5 
Xixian25%, Ua 0.89 0.90 9.5 0.88 0.89 2.8 0.87 0.88 4.2 0.83 0.84 14.8 
Xixian50%, U 0.90 0.90 −2.2 0.89 0.91 4.6 0.89 0.90 7.0 0.85 0.86 14.5 
Xixian75%, U 0.90 0.91 −4.8 0.91 0.91 2.3 0.91 0.91 2.4 0.86 0.86 8.2 
Xixian25%, R 0.86 0.89 12.5 0.85 0.86 9.4 0.85 0.86 11.3 0.84 0.85 8.8 
Xixian50%, R 0.87 0.88 9.7 0.85 0.87 1.9 0.84 0.87 6.7 0.82 0.82 15.3 
Xixian75%, R 0.89 0.90 −1.4 0.88 0.89 0.3 0.88 0.89 1.5 0.87 0.89 12.1 
Daily 
Xixian 0.69 0.71 18.1 0.70 0.71 12.3 0.69 0.70 12.3 0.69 0.68 14.9 
Xixian25%, U 0.63 0.64 9.9 0.66 0.66 9.8 0.65 0.66 10.3 0.63 0.63 6.5 
Xixian50%, U 0.65 0.65 24.1 0.69 0.69 −7.8 0.69 0.69 −6.5 0.65 0.65 19.4 
Xixian75%, U 0.67 0.69 15.7 0.71 0.72 14.2 0.71 0.72 15.3 0.67 0.68 8.8 
Xixian25%, R 0.64 0.66 10.7 0.65 0.66 10.1 0.65 0.66 18.5 0.63 0.65 11.6 
Xixian50%, R 0.65 0.65 22.6 0.67 0.69 8.7 0.66 0.67 11.2 0.64 0.68 10.2 
Xixian75%, R 0.68 0.68 16.9 0.70 0.71 −5.3 0.70 0.71 9.8 0.69 0.70 11.8 
ID Gauge Name NN
 
IDW
 
TP
 
OK
 
NSE R2 PBIAS (%) NSE R2 PBIAS (%) NSE R2 PBIAS (%) NSE R2 PBIAS (%) 
Monthly 
Xixian 0.91 0.91 −1.6 0.90 0.90 5.6 0.90 0.90 5.6 0.86 0.87 4.5 
Xixian25%, Ua 0.89 0.90 9.5 0.88 0.89 2.8 0.87 0.88 4.2 0.83 0.84 14.8 
Xixian50%, U 0.90 0.90 −2.2 0.89 0.91 4.6 0.89 0.90 7.0 0.85 0.86 14.5 
Xixian75%, U 0.90 0.91 −4.8 0.91 0.91 2.3 0.91 0.91 2.4 0.86 0.86 8.2 
Xixian25%, R 0.86 0.89 12.5 0.85 0.86 9.4 0.85 0.86 11.3 0.84 0.85 8.8 
Xixian50%, R 0.87 0.88 9.7 0.85 0.87 1.9 0.84 0.87 6.7 0.82 0.82 15.3 
Xixian75%, R 0.89 0.90 −1.4 0.88 0.89 0.3 0.88 0.89 1.5 0.87 0.89 12.1 
Daily 
Xixian 0.69 0.71 18.1 0.70 0.71 12.3 0.69 0.70 12.3 0.69 0.68 14.9 
Xixian25%, U 0.63 0.64 9.9 0.66 0.66 9.8 0.65 0.66 10.3 0.63 0.63 6.5 
Xixian50%, U 0.65 0.65 24.1 0.69 0.69 −7.8 0.69 0.69 −6.5 0.65 0.65 19.4 
Xixian75%, U 0.67 0.69 15.7 0.71 0.72 14.2 0.71 0.72 15.3 0.67 0.68 8.8 
Xixian25%, R 0.64 0.66 10.7 0.65 0.66 10.1 0.65 0.66 18.5 0.63 0.65 11.6 
Xixian50%, R 0.65 0.65 22.6 0.67 0.69 8.7 0.66 0.67 11.2 0.64 0.68 10.2 
Xixian75%, R 0.68 0.68 16.9 0.70 0.71 −5.3 0.70 0.71 9.8 0.69 0.70 11.8 

Note:aThe subscript 25%, 50% and 75% indicates that the number of gauge stations was decreased to 25%, 50% and 75%, respectively; U or R indicates that the gauge stations were selected either uniformly or randomly.

Scatter plots of NSE, R2 and PBIAS are presented in Figure 10, providing a quick overview of the comparison between the NN and other interpolation methods. For NSE and R2 at a monthly time step, the differences between NN and IDW, and NN and TP were not significant. The NN method resulted in obviously better performance than IDW and TP in a few cases. However, the monthly simulation accuracy under the OK method was much poorer than for NN. Based on NSE and R2 at a daily time step, the SWAT model under the IDW and TP methods performed better than the default NN method, whereas OK had no clear superiority over NN in daily streamflow simulation. In the first and fourth quadrants of the three PBIAS scatter plots, the absolute values of monthly and daily PBIAS under the NN method were always greater than those under the other interpolation methods, especially for the IDW and TP methods. Most of the monthly PBIAS dots were located in the second quadrant, indicating that the other interpolation methods resulted in underestimation of monthly streamflow whereas the NN method overestimated total the water amount in the monthly model. Notably, OK tended to cause severe underestimation in simulating monthly water yield compared to IDW and TP and led to greater bias than the NN method.

Fig. 10.

Scatter plots of NSE, R2 and PBIAS, comparing the monthly and daily SWAT model performance under different MAP models.

Fig. 10.

Scatter plots of NSE, R2 and PBIAS, comparing the monthly and daily SWAT model performance under different MAP models.

To conclude, the other MAP models did not show a great advantage over the default NN method in simulating monthly streamflow using SWAT in the Xixian Basin. As the network density changed, the model performance under the IDW, TP and OK methods was sometimes even poorer than the NN method. However, the alternative MAP methods can improve the accuracy of the SWAT model in simulating daily flows. For example, the IDW and TP interpolation methods resulted in better performance under different network densities and spatial distribution of gauge stations.

Conclusions

This study aimed to evaluate interpolation methods that describe the spatial variability of precipitation using a SWAT model. Firstly, we calculated the MAP input using NN, IDW, TP and OK interpolation methods for each sub-basin. The amount and spatial distribution of the areal precipitation estimated by four MAP methods were compared. Secondly, we compared the NSE, R2 and PBIAS of the SWAT model driven by different MAP inputs at monthly and daily time steps in order to assess the accuracy of four interpolation methods. Finally, we changed the gauge stations that applied in the calculations in order to verify the reliability of the MAP models under different network densities and spatial distributions of rainfall stations. From the above analysis, the general conclusions are as follows:

  1. The estimated MAP indicated that the sub-basins' precipitation under four interpolation methods were quite different in terms of amount and spatial distribution. Within the MAP models, the NN method totally missed lower precipitation and OK method underestimated the higher precipitation in the Xixian Basin.

  2. The SWAT model performance indicated that the monthly and daily streamflow simulations under different interpolation methods had high enough accuracy in the Xixian Basin. Slightly worse simulation results were observed under the NN method in low flow periods and under the OK method in high flow periods, which was in agreement with the precipitation estimation results. The SWAT default NN method is ineffective at capturing the sub-basin's rainfall variability. Therefore, it is recommended that different interpolation methods be applied to calculate MAP during dry and rainy seasons in future studies.

  3. The SWAT model performance was influenced by the station density and spatial distribution of the rain gauge stations used in interpolation. The NSE and R2 values for the Xixian monthly and daily streamflow estimations increased with the increase of network density. A relatively uniform spatial distribution of gauge stations is also highly recommended to improve the accuracy of the SWAT model.

  4. In general, in terms of NSE, R2 and PBIAS under all the interpolation methods, the model performance was almost the same on a monthly timescale. However, a notable improvement was observed in all evaluation indicators on a daily timescale under alternative interpolation methods in the study region. In this study, the IDW and TP methods were better able (compared to NN and OK) to maintain relatively high accuracy in simulating daily streamflow as the applied rainfall stations changed. These two methods could be introduced into the areal precipitation calculations in the SWAT model in the future, given their simulation accuracy and computational efficiency.

Results from the Xixian Basin confirm that spatial variability of precipitation has a great effect on streamflow simulation. Thus, the interpolation method adopted in a certain basin must be evaluated before simulating streamflow. Our study, taking the Xixian Basin as an example, performed a comprehensive assessment of aspects of areal precipitation distribution, monthly and daily streamflow simulation accuracy and model accuracy under different network densities. The procedures and results of this research are instructive for the follow-up application of hydrological modelling.

Acknowledgments

The first author acknowledges the following financial support: the National Key R&D Program of China (2017YFC0405601); the National Natural Science Foundation of China (51479062/41371048); the Fundamental Research Funds for the Central Universities (2015B14314); the UK–China Critical Zone Observatory (CZO) Program (41571130071).

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