Parameter Sensitivity Analysis of SWAT Modeling in the Upper Heihe River Basin Using Four Typical Approaches

Abstract

Parameter sensitivity analysis is a significant part of quantifying model uncertainty, effectively identifying key parameters, and improving the efficiency of parameter optimization. The Soil and Water Assessment Tool (SWAT) model was applied to the upper Heihe River basin (UHRB) in China to simulate the monthly runoff for 11 years (1990–2000). Four typical sensitivity analyses, namely, the Morris screening, Sobol analysis, Fourier amplitude sensitivity test (FAST), and extended Fourier amplitude sensitivity test (EFAST), were used to determine the critical parameters affecting hydrological processes. The results show that the sensitivity parameters defined by the four methods were significantly different, resulting in a specific difference in the simulation effect of the SWAT model. The reason may be the different sampling process, sensitivity index, and calculation principle of each method. The snow-melt base temperature (SMTMP) and snowfall temperature (SFTMP) related to the snow-melt process, the available water capacity of the soil layer (SOL_AWC), saturated hydraulic conductivity (SOL_K), depth from the soil surface to the bottom of the layer (SOL_Z), moist bulk density (SOL_BD), deep aquifer percolation fraction (RCHRG_DP), and threshold depth of water in the shallow aquifer required for return flow to occur (GWQMN) related to the soil water and groundwater movement, baseflow alpha factor for bank storage (ALPHA_BNK) related to the base flow regression, and average slope steepness (HRU_SLP) are all very sensitive parameters. The 10 key parameters were optimized 100 times with the sequential uncertainty fitting procedure version 2 (SUFI-2). The Nash–Sutcliffe efficiency coefficient (NSE), Kling–Gupta efficiency coefficient (KGE), mean square error (MSE), and percentage bias (PBIAS) were 0.89, 200, 8.60, and 0.90, respectively. The simulation results are better than optimizing the sensitive parameters defined by the single method and all the selected parameters. The differences illustrate the rationality and importance of parameter sensitivity analysis for hydrological models and the synthesis of multiple approaches to define sensitive parameters. These conclusions have reference significance in the parameter optimization of the SWAT model when studying alpine rivers by constructing the SWAT model.

1. Introduction

As an essential tool for simulating runoff, the hydrological model can quantitatively reflect the evolution and physical mechanisms of hydrological phenomena [1,2]. Hydrological models can be classified into lumped, semidistributed, and distributed according to the degree of the description of spatial characteristics. With the development of hydrological theory and computer technology, the research and application of distributed hydrological models are increasingly extensive [3,4]. Developing hydrological models is significant to water resource management and planning, hydrological forecasting, and optimal reservoir operation [5].

Compared with the traditional lumped model, the distributed hydrological model based on the physical mechanism demands more input parameters [6]. Moreover, the spatial difference of parameters in the hydrological land surface process, errors in the acquisition process, and the difficulties in parameter evaluation give the input of the initial parameter values of the model significant uncertainties [7,8,9,10] that reduce the operational efficiency and simulation accuracy of the distributed hydrological model. In addition, the insufficient understanding of the sensitivity of model parameters is an essential factor affecting the application of distributed hydrological models [11,12]. Therefore, it is necessary to understand the influence of each parameter in the model on the simulation results. Parameter sensitivity analysis can improve the efficiency of model calibration and increase the reliability of model application [13,14,15,16].

Sensitivity analysis usually includes local and global sensitivity analyses. Many studies showed that the global sensitivity analysis method is more suitable for multiparameter hydrological model research [17,18,19,20]. Common global analysis methods include Morris screening [21,22], Sobol analysis [23], the Fourier amplitude sensitivity test (FAST) [24,25,26], and the extended Fourier amplitude sensitivity test (EFAST) [27]. These sensitivity analysis methods have been widely used in hydrological models. The most critical parameters of physical distributed model SHETRAN were identified using the Morris screening method [6]. Houle et al. used Sobol sensitivity analysis to identify parameter sensitivities of the variable infiltration capacity (VIC) snow model, a physical model [28]. Linhoss et al. used the variance-based FAST method to quantitatively identify the Pitman semidistributed hydrologic model’s parametric uncertainty and sensitivity [29]. The EFAST method was used to conduct global sensitivity analyses for three modules in the hydrological soil–water–atmosphere–plant–world–food study (SWAP-WOFOST) model to identify the parameters that significantly influenced the objective variables [30]. However, it is not clear which method performs better, as these studies lack a comparison of the sensitivity analyses above.

The Soil and Water Assessment Tool (SWAT) is a widely used hydrological model that has had successful application in many fields [31,32,33,34]. The SWAT model has many parameters, rendering calibrating the parameters time-consuming and laborious. Therefore, some studies were carried out on SWAT model parameters to define the most sensitive parameters, and reduce parameter calibration, and computational and temporal costs [13,16,35,36,37,38,39]. Due to the different methods that researchers adopt, the selected sensitivity parameters are different and lack representation to some extent, not allowing for a comparison to determine the best approach.

The upper reach of Heihe River is located in the semiarid alpine area of the Qilian Mountains in Northwest China. As a typical alpine river basin, the upper reaches of Heihe River, with complex underlying surface properties, diversiform climate conditions, and various runoff sources [40,41,42] can be used as a representative example to analyze the parameter sensitivity of the SWAT model. This study used the SWAT model on the upper reaches of the Heihe River basin with parameters screened using four typical parameter sensitivity analysis methods: Morris screening, Sobol analysis, the Fourier amplitude sensitivity test (FAST), and the extended Fourier amplitude sensitivity test (EFAST) to conduct sensitivity analysis on the parameters related to runoff simulation in SWAT model. The objectives of this work are to: (1) compare the sensitivity analysis results of the four methods, (2) define a series of sensitive parameters that most affected the monthly runoff simulation of the SWAT model, and (3) verify whether the calibration results of the four methods were better than that of the single method. The results of this study have reference significance for the parameter optimization of the SWAT model when studying alpine rivers by constructing the SWAT model.

2. Data and Methods

2.1. Study Area

Heihe River originates from the Qilian Mountains, passes through the Hexi Corridor, and ends at Ejin Banner in northern Inner Mongolia [43,44,45]; its length of which is about 800 km. The Heihe River basin (HRB) is between 98°–101°30′ E and 38°–42° N with an area of approximately 1,432,000 km², rendering it the second-largest inland river region of Northwest China. Bounded by Yingluoxia and Zhengyixia stations, the basin is divided into upper, middle, and lower reaches with unique and complex geographical characteristics. The upper Heihe River basin (UHRB) is between 37°30′–39°41′ N and 97°28′–101°16′ E (Figure 1), the main runoff-producing area of the HRB, and the study area of this paper, including some regions of Qilian and Sunan counties. Runoff consists of surface runoff, glacier meltwater, and a small amount of groundwater regression [46]. The UHRB is located in a typical continental alpine and semiarid climate area with an elevation of about 2000–5500 m, annual precipitation of 300–700 mm, and a multiyear average temperature of −5 to 4 °C. The vegetation of the UHRB is mountain forest steppe, and the distribution of the vegetation belt plays a crucial role in runoff regulation and storage. In addition, there are permanent glaciers and snowfields in the study area.

2.2. SWAT Model

The SWAT model is a distributed watershed scale hydrological model developed by the Agricultural Research Service of the United States Department of Agriculture (ARS-USDA) [47,48,49] that mainly includes the hydrological-process, soil-erosion, and pollution-load submodels. The key modules involved in the hydrological process submodel of the SWAT model are the surface-runoff, evapotranspiration, soil-water-movement, underground-runoff, and river-confluence modules. The SCS curve number method is generally used to simulate the surface runoff. The simulation of evapotranspiration is to calculate the actual evapotranspiration on the basis of potential evapotranspiration, including the evaporation of vegetation canopy retention, vegetation, and soil. Soil water movement is simulated by vertical stratified water balance, and infiltration and interflow are considered. The simulation of groundwater runoff is divided into shallow and deep groundwater runoff, which involves phreatic re-evaporation and irrigation, and is realized on the basis of the water balance equation. The confluence calculation of the runoff flowing into a river channel is based on the variable-storage or Muskingum method [50,51].

The following input data are required for building the SWAT model. The digital elevation model (DEM) of the Shuttle Radar Topography Mission (SRTM) with a 30 m resolution was derived from the Geospatial Data Cloud (http://www.gscloud.cn/, accessed on 25 April 2022). The soil dataset with a 1 km resolution used in this study is Harmonized World Soil Database version 1.2 (HWSD v1.2) [52], which was obtained from the Food and Agriculture Organization (FAO). Using the QGIS tools, the soil dataset was further reclassified into 16 types (Figure 2). Land-use and land-cover (LULC) data with a resolution of 1 km were downloaded from the Resource and Environment Science and Data Center (https://www.resdc.cn/, accessed on 10 April 2022). According to the database provided by the SWAT model, the LULC was reclassified into nine types (Figure 2). The daily meteorological data were obtained from the National Meteorological Science Data Center (http://data.cma.cn/, accessed on 20 March 2022), including the maximal and minimal temperature, precipitation, relative humidity, and wind speed of 10 meteorological stations from 1988 to 2000. The daily streamflow data of the Yingluoxia hydrometric station from 1990 to 2000 were obtained from the Environmental and Ecological Science Data Center for West China, National Natural Science Foundation of China.

The UHRB was divided into 17 sub-basins in this study on the basis of DEM data for runoff simulation. We set 1988–1989 as the warm-up period, and 1990–2000 as the simulation period. Following swat model documentation and SWAT-sensitivity analysis (SA) platform [53,54] recommendations, 30 parameters related to runoff, simulated in the SWAT model, were selected (

Table 1. Description and hydrological process of 30 selected parameters.

Parameters	Description	Hydrologic Process
CN2	Initial SCS runoff curve number for moisture condition II	Surface runoff processes
SURLAG	Surface runoff lag coefficient
ESCO	Surface runoff lag coefficient	Potential and actual evapotranspiration processes
EPCO	Plant uptake compensation factor
CANMX	Maximal canopy storage (mm H2O)
SOL_ALB	Moist soil albedo
SOL_Z	Depth from the soil surface to the bottom of the layer (mm)	Soil water processes
SOL_BD	Moist bulk density (Mg/m3 or g/cm3)
SOL_AWC	Available water capacity of the soil layer (mm H2O/mm soil)
SOL_K	Saturated hydraulic conductivity (mm/h)
GW_REVAP	Groundwater evapotranspiration coefficient	Groundwater processes
GW_DELAY	The delay time
REVAPMN	Threshold depth of water in the shallow aquifer for evapotranspiration or percolation to the deep aquifer to occur (mm H2O)
GWQMN	Threshold depth of water in the shallow aquifer required for return flow to occur (mm H2O)
ALPHA_BF	Baseflow alpha factor (1/day)
RCHRG_DP	Deep aquifer percolation fraction
CH_K2	Effective hydraulic conductivity in main channel alluvium (mm/h)	Channel water routing processes
CH_N2	Manning’s “n” value for the main channel
ALPHA_BNK	Baseflow alpha factor for bank storage (days)
SMFMX	Melt factor for snow on 21 June (mm H2O/°C/day)	Snow processes
SMFMN	Melt factor for snow on 21 December (mm H2O/°C/day)
SFTMP	Snowfall temperature (°C)
SMTMP	Snow melt base temperature (°C)
TIMP	Snowpack temperature lag factor.
SLSUBBSN	Surface runoff lag coefficient	Time of concentration processes
OV_N	Manning’s “n” value for overland flow
CH_N1	Manning’s “n” value for the tributary channels
CH_K1	Effective hydraulic conductivity in tributary channel alluvium (mm/h)	Transmission losses from surface runoff Processes
HRU_SLP	Average slope steepness (m/m)	Lateral flow processes
TLAPS	Temperature lapse rate (°C/km)	Elevation bands

). The Nash–Sutcliffe efficiency coefficient was used to estimate the degree of fitting between the measured and simulated monthly average flow. The sensitivity analysis of the 30 parameters was carried out by using various analytical methods to determine the most sensitive parameters in the SWAT runoff model.

2.3. Sensitivity Analysis Methods

The sensitivity analysis methods (Morris, Sobol, FAST, and EFAST) used in this study were included in the SWAT-AS platform. A brief introduction to these sensitivity analysis methods is provided in this section.

2.3.1. Morris Screening Method

Morris screening is a qualitative global sensitivity analysis method first proposed by Max D. Morris in 1991 that calculates the relative sensitivity of model parameters with low computational cost, and sorts the sensitivity of model parameters [21,22]. In the process of Morris sample generation, a base sample point $X^1$ is first generated on which the disturbance factor variable $\mathsf{\Delta }=s/\left(1-p\right)$ is added to generate other sample points $X^i$. After generating different sample points, $M+1$ sample points are obtained, and the specific process is obtained with the following equation:

$$B^{*}=\left\{J_{M+1,1}{X}^{\left(1\right)}+\left(\mathsf{\Delta }/2\right)\left[\left(2\times B-J_{M+1,1}\right)D+J_{M+1,1}\right]\right\}\mathrm{P}$$

(1)

where $B^{*}$ is the $\left(M+1\right)\times M$ parameter sample matrix, each row represents a parameter sample, and M is the number of model parameters. $J$ is the identity matrix. D is an $M\times M$ diagonal matrix, and each diagonal element had the same probability as that of ±1. P is $M\times M$ random confusion matrix. $X^{\left(1\right)}$ is the primary sample of a row vector. At the same time,

$$B=\left[\begin{array}{c}0 0 0 \cdots 0\\ 1 0 0 \cdots 0\\ 1 1 0 \cdots 0\\ 1 1 1 \cdots 0\\ ⋮ ⋮ ⋮ ⋮ ⋮\\ 1 1 1 1 1\end{array}\right]$$

(2)

The generated parameter sample matrix $B^{*}$ has the following characteristics. There was only one different parameter value in the model parameter samples of two adjacent rows, and the parameter values of the other M-1 models wer identical. The calculation formula for the elementary effect (EE) of the model parameters is shown in Equation (1).

$$E{E}_i=\frac{f\left(x_1,\cdots ,x_{i-1},x_i+\mathsf{\Delta },x_{i+1},\cdots ,x_M\right)-f\left(x_1,\cdots ,x_M\right)}{\mathsf{\Delta }}$$

(3)

where $E{E}_i$ is the elementary effect value of the $i$th model parameter. $x_1,\cdots ,x_M$ is the model parameter value. Generally, the Morris screening method adopts two calculation indices, the mean and standard deviation of the elementary effect, to judge the importance or sensitivity of parameters. To avoid the negation of the positive and negative when $E{E}_i<0$, Campolongo et al. [55] suggested replacing the mean µ with the modified mean μ*. The calculation formula is as follows:

$${\mu }_i^{*}=\frac{1}{n}{{\displaystyle \sum }}_{j=1}^n\left|E{E}_i\left(j\right)\right|$$

(4)

$${\sigma }_i=\sqrt{\frac{1}{n-1}{{\displaystyle \sum }}_{j=1}^n{\left[E{E}_i\left(j\right)-\frac{1}{n}{{\displaystyle \sum }}_{j=1}^{n}E{E}_i\left(j\right)\right]}^2}$$

(5)

where $E{E}_i\left(j\right)$ is the elementary effect value calculated from the $i$th model parameter and the $j$th sample. n is the number of model parameter samples. ${\mu }_i^{*}$ is the modified mean elementary effect value of the $i$th model parameter. ${\sigma }_i$ is the standard deviation of the elementary effect value of the $i$th parameter. The larger the modified mean elementary effect value of a parameter in the SWAT model is, the higher the sensitivity of the parameter. The larger the standard deviation of the elementary effect value is, the greater the interaction between this parameter and other SWAT model parameters is.

2.3.2. Sobol Analysis Method

Sobol’s analysis method, first proposed by Sobol in 1993 [23], is a widely used quantitative global sensitivity analysis method. Compared with the qualitative sensitivity analysis method, this method can directly calculate the sensitivity index of model parameters. Sobol’s method is based on the idea of variance decomposition, and the total variance is decomposed into variance in terms of the interaction of one or several model parameters.

If $y=f\left(X\right)=f\left(x_1,x_2,\cdots ,x_M\right)$ represents the model structure, $x_1,x_2,\cdots ,x_M$ represent the model parameters, and M is the number of model parameters. Then, the variance decomposition formula can be expressed as follows.

$$V\left(y\right)={{\displaystyle \sum }}_{i=1}^M{V}_i+{{\displaystyle \sum }}_{i<j}^M{V}_{ij}+\cdots +V_{1,2,\cdots ,M}$$

(6)

where $V\left(y\right)$ represents the total variance of model output y. $V_i$ is the variance term of the $i$th parameter. $V_{ij}$ represents the variance term of the joint action of the $i$th and $j$th parameters. $V_{1,2,\cdots ,M}$ represents the variance term of the interaction of all parameters. The indicees of first-order sensitivity $S_i$, second-order sensitivity $S_{ij}$, and total sensitivity $S_{Ti}$ are defined as follows.

$$S_i=\frac{V_i}{V\left(y\right)}$$

(7)

$$S_{ij}=\frac{V_{ij}}{V\left(y\right)}$$

(8)

$$S_{Ti}=1-\frac{V_{-i}}{V\left(y\right)}$$

(9)

where $V_{-i}$ represents the variance without the effect of the $i$th parameter. First-order sensitivity $S_i$ and the second-order sensitivity $S_{ij}$ represent the influence of a single SWAT model parameter and the combination of two SWAT model parameters on the SWAT model output, respectively. Total sensitivity $S_{Ti}$ describes the influence on the combination with the SWAT model parameters, including the $i$th parameter on the SWAT model output. Moreover, the difference between total sensitivity $S_{Ti}$ and first-order sensitivity $S_i$ can be used to analyze the mutual effect between the $i$th SWAT model parameter and other model parameters, which is described by the interaction effect.

$$I{E}_i=S_{Ti}-S_i$$

(10)

where $I{E}_i$ stands for the interaction effect of the $i$th model parameter.

2.3.3. FAST Analysis Method

The Fourier amplitude sensitivity test (FAST) is a method introduced in the 1970s for analyzing the parameter sensitivity of models [24,25,26]. Its theory is derived from the analysis of variance and Fourier transformation. The core of this method is to use the appropriate search curve to search in the multidimensional space of parameters to transform the multidimensional integral into the one-dimensional integral. Then, the model becomes a periodic function with independent parameters. Fourier analysis is performed on the output of the model to generate the Fourier amplitude for each frequency. The magnitude of the Fourier amplitude is used to indicate the sensitivity of each parameter. The larger the amplitude is, the more sensitive the model is to this parameter and vice versa. This amplitude is also known as the importance measure [56,57].

For the hydrological model $y=f\left(X\right)=f\left(x_1,x_2,\cdots ,x_M\right)$, $M$ is the number of model parameters. Depending on the appropriate search function, model $y=f\left(X\right)$ can be converted into $y=f\left(s\right)$. According to the characteristics of the sine function, for any positive integer frequency, the $s$ value at $\left[-\pi , \pi \right]$ or $\left[0, 2\pi \right]$ can show complete periodicity, so that the model output can be expanded into the form of the Fourier series.

$$f\left(s+2\pi \right)=f\left(s\right)$$

(11)

$$f\left(s\right)={{\displaystyle \sum }}_{i=1}^M{A}_{i}sin\left({\omega }_{i}s\right)$$

(12)

$$A_i={{\displaystyle \int }}_{-\pi }^{\pi }f\left(s\right)sin\left({\omega }_{i}s\right)ds$$

(13)

where $A_i$ represents the amplitude of the $i$th parameter, ${\omega }_i$ is the frequency, $s$ is sampled at equal intervals within the interval $\left[-\pi , \pi \right]$, and each parameter obtained by sampling is input into the model. $A_i$ can be obtained with the approximate calculation of the following formula.

$$A_i=\frac{a_i}{n}{{\displaystyle \sum }}_{j=1}^{n}f\left(s_j\right)sin\left({\omega }_i{s}_j\right)$$

(14)

where $n$ is the number of samples, and $a_i$ is an integer. We want to ensure ${{\displaystyle \sum }}_{i=1}^M{a}_i{\omega }_i\ne 0$. In this paper, the larger the $A_i$ of a parameter in the SWAT model is, the greater the sensitivity of this parameter.

2.3.4. EFAST Analysis Method

On the basis of FAST, S et al. [27] proposed an improved extended Fourier amplitude sensitivity test (EFAST) combined with the variance decomposition theory of Sobol’s method. In this method, the spectrum of the Fourier series is obtained with the Fourier transform, and the variance of the model results caused by each parameter and their interaction is obtained with the spectrum curve.

According to the appropriate search function, model $y=f\left(X\right)$ can be converted into $y=f\left(s\right)$ and obtained with Fourier transform [58,59].

$$f\left(s\right)={{\displaystyle \sum }}_{-\infty }^{\infty }\left(A_{j}cosjs+B_{j}sinjs\right)$$

(15)

where $j\in Z^0=\left\{-\infty ,\cdots ,-1,1,\cdots ,\infty \right\}$, $A_j$ and $B_j$ can be calculated with the following formula.

$$A_j=\frac{1}{2\pi }{{\displaystyle \int }}_{-\pi }^{\pi }f\left(s\right)cosjsds B_j=\frac{1}{2\pi }{{\displaystyle \int }}_{-\pi }^{\pi }f\left(s\right)sinjsds$$

(16)

The spectral curve of the Fourier series is defined as ${\mathsf{\Lambda }}_j=A_j^2+B_j^2$, $A_j=A_{-j}$, $B_j=B_{-j}$. The output variance caused by parameter $x_i$ is

$$V_i={{\displaystyle \sum }}_{p\in Z^0}\mathsf{\Lambda }p{\omega }_i=2{{\displaystyle \sum }}_{p=1}^{+\infty }\mathsf{\Lambda }p{\omega }_i$$

(17)

where $p$ is the spectrum of the Fourier transform; the model’s total variance can be obtained by summing the ranges of all frequencies.

$$V={{\displaystyle \sum }}_{j\in Z^0}{\mathsf{\Lambda }}_j=2{{\displaystyle \sum }}_{j=1}^{+\infty }{\mathsf{\Lambda }}_j$$

(18)

Sampling $s$ at equal intervals within the interval $\left[-\pi , \pi \right]$ and running the model many times can estimate the values of $A_j$ and $B_j$.

$$A_j=\frac{1}{n}{{\displaystyle \sum }}_{m=1}^{n}f\left(s_m\right)cos\left(j{s}_m\right) B_j=\frac{1}{n}{{\displaystyle \sum }}_{m=1}^{n}f\left(s_m\right)sin\left(j{s}_m\right)$$

(19)

where $n$ is the number of samples. According to $A_j$, $B_j$, and the corresponding frequency ${\omega }_i$ of parameter $x_i$, variance $V_i$ and total variance $V$ caused by each parameter can be calculated, that is, the first-order sensitivity ($S$) of each parameter can be obtained. To calculate the total sensitivity parameter $x_i$, frequency ${\omega }_i$ needs to be set for $x_i$, and a different frequency ${\omega }_i^{\prime }$ needs to be set for other parameters. By calculating the spectral values of ${\omega }_i^{\prime }$ on $p{\omega }_i^{\prime }$, partial variance $V_{-i}$ can be obtained that influences all parameters except parameter $x_i$ and their interactions. The total sensitivity ($S_T$) of parameter $x_i$ is calculated as follows.

$$S_{Ti}=\frac{V-V_{-i}}{V}$$

(20)

Similar to Sobol’s analytical method, first-order sensitivity $S_i$ and total sensitivity $S_{Ti}$ describe a single SWAT model parameter and the combination with model parameters on the SWAT model output, respectively.

3. Results

3.1. Morris Results

The Morris-at-a-time (MOAT) sampling method is used to generate model parameter samples and analyze model parameter sensitivity. The previous literature [60] showed that the MOAT method is relatively stable, which means that the influence of model calculation times on the results is not prominent. In this study, it was assumed that model parameters obeyed uniform distribution. Horizontal number $p$ = 4 was used to generate 3100 samples of 100 groups of parameters (CN2 parameter sampling results are shown in Figure 3). Figure 4 and Figure 5 depict the modified mean (${\mu }^{*}$) and the standard deviation distributions ($\sigma$) of each parameter, respectively, under the condition that NSE is taken as the objective function.

Figure 4 shows that the modified means (${\mu }^{*}$) of SMTMP and SOL_Z parameters were 21.5627 and 16.3527, respectively, larger than those of others, indicating that they were the two most sensitive parameters and had a significant influence on the output results of the SWAT model. After them, SFTMP, HRU_SLP, ALPHA_BNK, SOL_AWC, SOL_BD, ALPHA_BF, GWQMN, SOL_K, RCHRG_DP, and CANMX were relatively essential parameters that had a specific influence on the model output. The modified means (${\mu }^{*}$) of EPCO, OV_N, CH_N1, CH_N2, REVAPMN, SURLAG, and TLAPS were less than 0.1, indicating that they had a negligible effect on SWAT model results, i.e., insensitive parameters.

Figure 5 shows that the standard deviations ($\sigma$) of parameters SOL_Z and SMTMP were 31.6447 and 28.8774, respectively, indicating that these two parameters interacted with other parameters except themselves. After them, the standard deviations ($\sigma$) of parameters ALPHA_BNK, ALPHA_BF, SFTMP, HRU_SLP, and SOL_AWC were relatively large, which proves that the interactions between the above and other parameters were relatively significant. The standard deviations ($\sigma$) of parameters REVAPMN, SURLAG, and TLAPS were 0, suggesting that there was almost no interaction between these and other parameters.

3.2. Sobol Results

A total of 6200 samples of 100 groups of parameters were generated by Sobol’s sequence sampling method (CN2 parameter sampling results are shown in Figure 6) [61]. Figure 7 and Figure 8 depict the indices of first-order sensitivity ($S$) and total sensitivity ($S_T$), respectively. Figure 7 shows that the first-order sensitivity ($S$) of parameter SMTMP was significantly greater than that of other parameters, up to 0.3539, indicating that variation in this parameter significantly impacted the output results of the SWAT model. The first-order sensitivity ($S$) levels of CANMX, SLSUBBSN, EPCO, OV_N, CN2, and ESCO were relatively tiny, only 0.0093, 0.0032, 0, 0, −0.0003, and −0.0041, respectively, which proved that these parameters were insensitive. The first-order sensitivity ($S$) of parameters CN2 and ESCO was negative, which was mainly due to the simplified calculation formula adopted in the calculation of first-order sensitivity ($S$), which was different from the real variance [61]. Except for the above parameters, the first-order sensitivity ($S$) of the other parameters showed a slight difference, meaning that they may have been relatively sensitive parameters.

Figure 8 shows that the total sensitivity ($S_T$) of parameter SMTMP was as high as 0.7117, indicating that the combination of SMTMP and other parameters noticeably impacted the SWAT model results. In addition to parameter SMTMP, the total sensitivity ($S_T$) levels of parameters SFTMP, SOL_Z, SOL_AWC, SOL_BD, and SOL_K were large, 0.3327, 0.2913, 0.2865, 0.2731 and 0.2679, respectively. The results show that the combination of these and other parameters influenced the results of the SWAT model. However, the total sensitivity ($S_T$) levels of parameters HRU_SLP, CANMX, ESCO, SLSUBBSN, CN2, EPCO, and OV_N were very low, all less than 0.1, suggesting that the combination of these and other parameters hardly affected the results of the SWAT model.

According to the total sensitivity ($S_T$) and first-order sensitivity ($S$), the interaction effect ($IE$) was calculated as shown in

Table 2. Calculation results of the interaction effect.

Parameter	IE	Parameter	IE	Parameter	IE
SMTMP	0.3578	REVAPMN	0.1753	GW_REVAP	0.1674
SFTMP	0.2814	ALPHA_BF	0.1753	RCHRG_DP	0.1661
SOL_BD	0.2226	CH_N2	0.1753	GWQMN	0.1636
SOL_Z	0.2095	SURLAG	0.1753	HRU_SLP	0.0138
TIMP	0.1977	TLAPS	0.1753	ESCO	0.0125
SOL_AWC	0.189	CH_N1	0.1753	CANMX	0.001
SMFMX	0.1768	GW_DELAY	0.1752	CN2	0.0004
SOL_K	0.1764	ALPHA_BNK	0.1739	EPCO	0
CH_K1	0.1754	CH_K2	0.1735	OV_N	0
SOL_ALB	0.1753	SMFMN	0.1704	SLSUBBSN	−0.0019

. Among all the parameters, SMTMP and SFTMP had apparent interaction effects, suggesting that the interaction between these two and other parameters except themselves noticeably impacted the model results. The interaction effect ($IE$) of parameters CANMX, CN2, EPCO, OV_N, and SLSUBBSN was minimal, almost close to 0, which suggests that the combination of these and other non-self-parameters had negligible influence on the SWAT model results.

3.3. FAST Results

The FAST sampling method generated a total of 3100 samples of 100 groups of parameters (CN2 parameter sampling results are shown in Figure 9). Figure 10 depicts the amplitude ($A$) of all the parameters related to the runoff of the SWAT model; the amplitude ($A$) of parameter SMTMP was up to 0.3694, much higher than that of the other parameters, indicating that this parameter was vital and sensitive. Some parameters, such as SFTMP, SOL_Z, and HRU_SLP, had high amplitudes ($A$) of 0.0867, 0.0856, and 0.0391, respectively, which indicates that these parameters also significantly impacted the output results of the SWAT model. The amplitude ($A$) of parameters GW_DELAY, EPCO, TIMP, CH_N1, GW_REVAP, and SURLAG, on the other hand, was less than 0.005, and they could be considered to be insensitive parameters. As a result, the influence of the above parameter variations on the result of the SWAT model was minimal.

3.4. EFAST Results

Considering that the EFAST analysis method improved and was developed from FAST, the sampling method and sample number of the EFAST were the same as those of FAST. After calculation with the EFSAT analysis method, the first-order sensitivity ($S$) and total sensitivity ($S_T$) of the SWAT model parameters are shown in Figure 10 and Figure 11. Among all the selected parameters, the first-order sensitivity ($S$) of parameter SMTMP was 0.5333, which was much greater than that of other parameters, indicating that SMTMP was a significantly sensitive parameter. In addition to SMTMP, the first-order sensitivity ($S$) levels of parameters SFTMP, SOL_BD, RCHRG_DP, SOL_K, HRU_SLP, SOL_Z and SOL_AWC were also high, at 0.0713, 0.0361, 0.0326, 0.0265, 0.0241, 0.0237, and 0.0224, respectively. Calculations show that they were also sensitive parameters that played a non-negligible role and influenced the model results.

Figure 12 shows that the total sensitivity ($S_T$) of parameter SMTMP was as high as 0.3577, indicating that the interaction between SMTMP and other SWAT model parameters significantly impacted the model output. The total sensitivity of other parameters RCHRG_DP, SOL_AWC, SFTMP, and SOL_BD was 0.1372, 0.1359, 0.1196, and 0.1140, respectively, which also indicates that the interaction of parameters influenced the model results.

3.5. Result Comparison of Different Methods

The parameters were sorted according to the parameter sensitivity index calculated with each method, and the top 10 parameters were then selected from each method, as shown in

Table 3. Comparison of sensitive parameters calculated with different methods.

Ranking	Morris	Sobol’	FAST	EFAST
1	SOL_Z	SMTMP	SMTMP	SMTMP
2	SMTMP	SOL_AWC	SFTMP	RCHRG_DP
3	ALPHA_BNK	SOL_Z	SOL_Z	SFTMP
4	SFTMP	SOL_K	HRU_SLP	SOL_BD
5	HRU_SLP	GWQMN	SOL_K	SOL_AWC
6	ALPHA_BF	RCHRG_DP	ESCO	SOL_K
7	SOL_AWC	GW_REVAP	ALPHA_BNK	HRU_SLP
8	SOL_BD	SMFMX	RCHRG_DP	GWQMN
9	GWQMN	SMFMN	SOL_AWC	ESCO
10	RCHRG_DP	CH_K2	GWQMN	GW_REVAP

. The sensitivity parameters calculated with each analytical method show significant differences. This also indicates that the sensitivity analysis of hydrological model parameters using a single sensitivity method has certain limitations. However, some parameters were highly sensitive in different methods, such as SMTMP, SOL_AWC, GWQMN, and RCHRG_DP, which also indicates that they may be very sensitive parameters and greatly influence the results of the SWAT model.

3.6. Identification of Sensitive Parameters

To integrate the results of four analytical methods, the 30 parameters were first ranked according to the index calculated with each sensitivity analysis method, so that each parameter had four ranking numbers. Then, four sort numbers for each parameter were added to obtain the total sort number and order it from smallest to largest. The smaller the sort number is, the more sensitive the parameter is. Lastly, the top ten parameters were taken as sensitive parameters: SMTMP, SOL_AWC, SFTMP, RCHRG_DP, SOL_K, SOL_Z, GWQMN, SOL_BD, ALPHA_BNK, and HRU_SLP. The calculated parameters were highly sensitive and representative of various methods.

The ten parameters above were optimized 100 times in the constructed SWAT model with the sequential uncertainty fitting procedure version 2 (SUFI-2).

Table 4. Initial ranges and final optimal values of critical parameters.

Ranking	Parameter	Value Range	Optimal Value	Ranking	Parameter	Value Range	Optimal Value
1	SMTMP	(−5, 5)	−4.65	6	SOL_Z	(0, 1000)	625
2	SOL_AWC	(0, 1)	0.075	7	GWQMN	(0, 1000)	535
3	SFTMP	(−5, 5)	2.05	8	SOL_BD	(0.9, 2.5)	1.116
4	RCHRG_DP	(0, 1)	0.945	9	ALPHA_BNK	(0, 1)	0.695
5	SOL_K	(0, 100)	5.5	10	HRU_SLP	(0, 1)	0.845

describes the upper and lower boundary ranges of crucial parameter values and the optimal parameter values obtained with calibration. To demonstrate the necessity of parameter sensitivity analysis, 30 parameters (Table 1) related to runoff simulated by the SWAT model without sensitivity analysis were optimized under the condition that other things were equal. Moreover, to compare the sensitive parameters calculated with a single analytical method with those calculated by integrating the results of four analytical methods, the parameters in Table 3 were also optimized.

Figure 13 compares the observed streamflow and the simulation results for the Yingluoxia hydrological station at a monthly scale under six optimization parameter conditions. The simulation effect of the SWAT model under the C10 scenario was better than that under other scenarios, especially in low-flow simulation. Figure 14 describes the statistical comparison between simulated and measured flow values under six parameter optimization scenarios. The closer the values of NSE and Kling–Gupta efficiency coefficient (KGE) were to 1, the better the simulation effect was. The closer the mean square error (MSE) and percentage bias (PBIAS) were to 0, the better the simulation effect was. The values of NSE, MSE, PBIAS, and KGE of the C10 scenario were 0.89, 200, 8.60, and 0.90, respectively, indicating that the C10 scenario achieved the best performance among all scenarios. By comparing the statistical indices of the C10 and C30 scenarios, defining sensitive parameters was proven necessary to improve the simulation effect of the SWAT model. Comparing the statistical indices of the C10-Morris, C10-Sobol, C10-FAST, and C10-EFAST scenarios shows that the performance of optimizing sensitive parameters defined by a single analysis method was not stable. For example, the c10-EFAST scenario achieved good performance in PBIAS and KGE with 10.80 and 0.84, respectively, while poor performance in NSE and MSE with 0.85 and 200, respectively. Further comparison of the statistical indices of these scenarios and the C30 scenario shows that only using a single analytical method to analyze the sensitivity of SWAT model parameters had no noticeable improvement on the simulation effect, and even had adverse effects. For example, the PBIAS of the C10-Sobol and C10-FAST scenarios was even higher than that of the C30 scenario. Comparing the statistical indices of these scenarios and the C10 scenario proves that combining the results of the four analytical methods to define the SWAT model’s sensitive parameters could significantly improve the model’s simulation effect.

4. Discussion

Previous studies indicated that, when parameter sensitivity analysis methods are different, the calculated parameter sensitivity also has differences; the simulation effect of the SWAT model is also different [13,16]. In this study, four parameter sensitivity analysis methods were adopted for calculation. Under the circumstance that other conditions of the SWAT model were consistent, although some of the sensitivity parameters obtained were the same, there were still differences in most of the parameters. The different sampling processes, sensitivity indices, and calculation principles of each method may contribute to the above phenomenon.

The sampling method of Morris is the MOAT sampling method, that of Sobol is the Sobol sequence sampling method, and that of EFAST and FAST is the FAST sampling method. The comparison of Figure 3, Figure 6 and Figure 9 shows that the three sampling methods had apparent differences. From the perspective of the sensitivity index, the Morris method calculated the mean value and variance of the elementary effect. In contrast, the three other methods decomposed the variance of the model output and then calculated the ratio. This shows that the Morris method differs from the other three methods. The calculation principles of the four methods were also significantly different. The Morris method mainly calculates the elementary effect. The Sobol method primarily regards breaking down the variance of the model output. The FAST and EFAST methods specifically decompose the variance in terms of the Fourier transform. These differences among the four methods lead to significant differences in the analyzed sensitivity parameters.

The simulation results of the SWAT model prove that the sensitive parameters determined by combining the results of multiple analytical methods are more reasonable than those specified by a single method. Therefore, when discussing the sensitivity of model parameters, a combination of various approaches can be used to reduce the uncertainty brought by the approach.

Among the 10 selected sensitive parameters, SMTMP and SFTMP belong to the snow-melt process parameters, and are sensitive because the UHRB is at a high altitude and covered with snowpacks, resulting in the snow-melt water being an important supply source for the Heihe River [17,37,62]. SOL_AWC, RCHRG_DP, SOL_K, SOL_Z, GWQMN, and SOL_BD control groundwater recharge and discharge processes. The UHRB is located in an arid inland area of Northwest China, with little precipitation but massive evaporation. As a result, the runoff generation and confluence processes of the HRB are affected by groundwater [17,37,62]. ALPHA_BNK belongs to the baseflow decline process. In the months with less precipitation in the HRB, the amount of river flow is entirely dependent on the baseflow, and its decline speed distinctly impacts the Heihe River flow [17,37,62]. Combined with the high altitude and complex terrain of the UHRB, the channel confluence velocity of the upper reaches of the Heihe River is affected by topography. HRU_SLP is a terrain parameter that significantly impacts the channel confluence of the upper reaches of Heihe River [17,37,62]. The 10 parameters above are sensitive because of the unique climatic and topographical conditions in the HRB from a physical point of view. This also indicates that, in analyzing the sensitivity of model parameters, sensitivity index should be considered from a mathematical aspect, and comprehensive analysis should be performed from the underlying surface of the basin, climatic conditions, and other aspects [63,64,65].

5. Conclusions

In this study, four analytical approaches, Morris, Sobol, FAST, and EFAST, available in SWAT-SA, were used to screen the critical parameters of the SWAT model for monthly runoff simulation for the study of the UHRB in China. The following are the main findings of this study.

(1)

Combined with the results calculated with the four parameter sensitivity analysis methods, 10 sensitive SWAT model parameters were defined: SMTMP, SOL_AWC, SFTMP, RCHRG_DP, SOL_K, SOL_Z, GWQMN, SOL_BD, ALPHA_BNK, and HRU_SLP.

(2)

The parameter sensitivity calculated with each analytical method was different, resulting in an apparent difference between the statistical indicators of the flow simulation value obtained by optimizing these sensitive parameters. The different sampling processes, sensitivity indices, and calculation principles of each method may be the main reasons.

(3)

By optimizing the most sensitive parameters combined with the results of the four methods, the NSE, MSE, PBIAS, and KGE of the flow simulation value and the measured value were 0.89, 200, 8.60, and 0.90, respectively, which were better than optimizing the sensitive parameters defined by a single method and all selected parameters. The differences in performance indicate the rationality and importance of parameter sensitivity analysis for hydrological models, and the synthesis of multiple approaches to define sensitive parameters.