A comparison of single- and multi-site calibration and validation: a case study of SWAT in the Miyun Reservoir watershed, China

Abstract

An essential task in evaluating global water resource and pollution problems is to obtain the optimum set of parameters in hydrological models through calibration and validation. For a large-scale watershed, single-site calibration and validation may ignore spatial heterogeneity and may not meet the needs of the entire watershed. The goal of this study is to apply a multi-site calibration and validation of the Soil and Water Assessment Tool (SWAT), using the observed flow data at three monitoring sites within the Baihe watershed of the Miyun Reservoir watershed, China. Our results indicate that the multi-site calibration parameter values are more reasonable than those obtained from single-site calibrations. These results are mainly due to significant differences in the topographic factors over the large-scale area, human activities and climate variability. The multi-site method involves the division of the large watershed into smaller watersheds, and applying the calibrated parameters of the multi-site calibration to the entire watershed. It was anticipated that this case study could provide experience of multi-site calibration in a large-scale basin, and provide a good foundation for the simulation of other pollutants in follow-up work in the Miyun Reservoir watershed and other similar large areas.

Keywords

calibration / soil and water assessment tool / Miyun Reservoir / multi-site

Introduction

Hydrological models are often used to evaluate water resource and pollution problems, including the impact of climate change on water resources, water resources planning and watershed management (Parajuli et al., 2008; Wang et al., 2009; Liu et al., 2013). A physically-based distributed hydrologic model is complex and requires multiple parameters. Under ideal conditions, the parameter values of a given model are determined either through measurements or are directly determined based on the watershed’s characteristics. However, due to the spatial variability of non-point source model parameters, measurement of the parameters is a complex, time-consuming and expensive process. As a result, many parameter values of the agricultural non-point source model are still obtained by estimates (Yang et al., 2008; Gong et al., 2011). A model’s parameter values are valid only on a certain spatial and temporal scale, and the spatial scale and temporal scale differences caused by the hydrological characteristics are the main causes of parameter uncertainty (Shen et al., 2012, 2013).

The processes of hydrological model parameter setting, calibration and validation are time consuming. Usually, the calibration requirements for the study of a medium-sized catchment can take as long as several months (Zhang et al., 2013). To tackle this problem, many different automatic calibration methods have been developed, such as the Parameter Estimation (PEST) method (Méndez et al., 2013), the shuffled complex evolution (SCE-UA) global optimization algorithm (Duan et al., 1992), Genetic Algorithms (GA) (Zhang et al., 2009) and the Soil and Water Assessment Tool (SWAT) Calibration and Uncertainty Programs (SWAT-CUP) (Abbaspour, 2011). In addition to the methods mentioned above, Particle Swarm Optimization (PSO), the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Artificial Immune Systems (AIS), and Differential Evaluation (DE) have also been successfully applied to parameter estimation in hydrologic models.

The single-site calibration has been found to be limited in its effectiveness (Anderton et al., 2002) because of the numerous parameters within the hydrological models, and a single-site calibration cannot express the spatial variability of a large watershed. Increases in the watershed area, due to the increased consumption of water (including agricultural irrigation and industrial and domestic water) have led to a rapid depletion of water flow. More attention needs to be paid to the influence of human activity on water flow, where currently multi-site calibration is used to address this problem. For example, Gong et al. (2012) used a multi-gauge calibration in the Daning River of China’s Three Gorges Reservoir Region. The multi-objective (SPEA2) optimization method was applied in the Reynolds Creek Experimental Watershed by Zhang et al. (2008). The multi-site calibration method was proposed for use in the Chaohe watershed in northern China (Wang et al., 2012), and the multi-variable and multi-site method was implemented in the Motueka catchment (Cao et al., 2006). Overall, this multi-site calibration method can make full use of the available data, and it has been suggested as an effective methodology for reducing uncertainties in the hydrological model, particularly in a large watershed with high heterogeneity and spatial variability. Many researchers have noted that the use of multi-site data during the calibration and validation process has resulted in a better simulation (Bekele and Nicklow, 2007; Rasolomanana et al., 2012).

In this study, a distributed model, the Soil and Water Assessment Tool (SWAT), was applied to the Baihe watershed of the Miyun Reservoir watershed. In past decades, water flow to the Miyun Reservoir has decreased greatly because of climate variability, human activity and increased population (Ma et al., 2010; Wang et al., 2012). As a result, human activity and climate variability have seriously affected the Miyun Reservoir watershed. In this case, the calibration and validation that is performed based on a single-site may introduce errors. In this research project, a multi-site calibration and validation process was used, and our results were compared to single-site calibration and validation results within a large, complex watershed. The watershed was divided into a number of smaller watersheds, each of which was calibrated to ensure the optimal results. The multi-site parameters were applied to the entire watershed to enable not only full use of the data, but also to bring about a reduction in the uncertainty and the effects of spatial heterogeneity. Thus, the goal of this research is to apply a multi-site calibration and validation of the Miyun Reservoir watershed and provide a reference basis for the large-scale basin calibration and validation process. The multi-site calibration and validation procedure can determine parameter values that are more reasonable to local conditions, not only improve the calibration efficiency.

Material and methods

The SWAT and SWAT-CUP model

The watershed model used in this study is the Soil and Water Assessment Tool (SWAT, Arnold et al., 1998), which is one of the most widely used watershed models throughout the world. The SWAT is a semi-distributed and physically-based model that operates on a daily time-step, and has been widely used to study water, sediment, nutrient and pesticide transport (Parajuli et al., 2009; Cho et al., 2012; Frey et al., 2013). The sensitive parameters were calibrated by the SWAT Calibration and Uncertainty Programs Version (SWAT-CUP) (Abbaspour, 2011). The Sequential Uncertainty Fitting version-2 (SUFI-2) algorithm is a key program in the SWAT-CUP package that interfaces with SWAT. In this study, considering the uncertainty in the input data, the SUFI2 method was used because of its high calibration efficiency (Shen et al., 2013; Bai et al., 2016).

The description of the multi-site calibration approach

Step 1 The watershed division process

In this step, the SWAT model database was established, which included a digital elevation model, land use data, soil data, meteorological data, and rainfall data. As a physically based semi-distributed hydrological model, the SWAT model must discretize the watershed. In this SWAT model, the watershed is divided into sub-watersheds by setting up the catchment area threshold, which is further discretized into HRUs (Hydrologic Response Units). The entire watershed was divided into smaller watersheds based on the characteristics of the watershed and sub-watersheds, as well as the setting of monitoring sites.

Step 2 The multi-site formation process

In this step, the SWAT model was used to simulate the smaller watersheds, and the SWAT-CUP model was applied to calibrate and validate them in order to find the most reasonable parameters. The calibrated parameters in these small watersheds were used throughout the entire watershed in order to form a multi-site environment. Then, the results of the multi-site environment were simulated by the SWAT model, which was used to compare with the measured values.

Case study

Watershed and data

The Baihe watershed, which is located in the northeast part of the Municipality of Beijing, lies within the Miyun Reservoir watershed (Fig. 1). The Miyun Reservoir lies within the rural counties area of the Municipality of Beijing. There are two main rivers, the Baihe River and the Chaohe River, flowing into the Miyun Reservoir, which is the most important drinking water source for the city of Beijing. The drainage areas of the Baihe River have an area of approximately 9000 km², which covers 60% of the area of the Miyun Reservoir watershed. The average annual air temperature within the study area ranges from 9°C to 10°C, and the annual rainfall has varied between 300 and 700 mm over the past 50 years (Xu et al., 2009). The dominant land types in the Baihe River area are forest (47.67%), grassland (28.02%), and agricultural (22.37%), with the remainder categorised as water bodies and other land uses. The Heihe River, the Honghe River, the Tanghe River and other tributaries flow into the Baihe River.

The database used by the SWAT model is shown in Table 1. Data from forty-one rainfall sites (2006–2010) and five weather stations (1978–2010) were used in this study. The flow data from three gauges, Zhangjiafen (ZJF), Sandaoying (SDY), Xiabao (XB), were collected for this study from 2006 to 2010 (Fig. 1). The management practices, such as planting, harvest and tillage operations, were obtained from field investigations.

Evaluation criteria

Two statistical criteria were used to evaluate the performance of the SWAT model predictions: the coefficient of determination (R²) and the Nash–Sutcliffe efficiency (E_NS) (Nash and Sutcliffe, 1970R² and E_NS are calculated, respectively, as follows:

(1)R^{\mathrm{2}}={\displaystyle \frac{{\left[{\displaystyle \sum _{i=\mathrm{1}}^n\left(O_i-\overline{O}\right)\left(P_i-\overline{P}\right)}\right]}^{\mathrm{2}}}{{\displaystyle \sum _{i=\mathrm{1}}^n{\left(O_i-\overline{O}\right)}^{\mathrm{2}}}{\displaystyle \sum _{i=\mathrm{1}}^n{\left(P_i-\overline{P}\right)}^{\mathrm{2}}}}},

(2)E_{NS}=\mathrm{1}-{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^n{(O_i-P_i)}^{\mathrm{2}}}}{{\displaystyle \sum _{i=\mathrm{1}}^n{\left(O_i-\bar{O}\right)}^{\mathrm{2}}}}},

where P_iand O_iare the simulated and observed values, respectively, for the i^th pair, and n is the total number of paired values. \bar{P}is the mean value of the simulated data, \bar{O}is the mean value of the observed data. R²ranges from 0 to 1; larger values indicate an improved accuracy of the simulation. The value of E_NS is in the range of ‒∞ to 1; the simulation result is poor when E_NS is below 0. E_NS = 0.5 is recommended as a lower limit (Moriasi et al., 2007); however, according to a SWAT research summary, many of the E_NS values did not reach this lower limit.

Results

Watershed division

In this study, the Baihe watershed was divided into 59 sub-watersheds. ZJF was used as the control site for the entire watershed. Because of the multi-site calibration in the Baihe River, SDY and XB were selected as the other sites in the Heihe River and Baihe River (a tributary of the whole Baihe River), respectively, which are two tributaries in the upstream part of the Baihe River. The sub-watersheds of the two watersheds are the same as for the entire river, as described in detail in Table 2. As shown in Fig. 1, the Baihe watershed is divided into three parts: the SDY watershed, the XB watershed and the remaining basin (RB) (Table 2). The RB label was used in order to distinguish it from the entire ZJF. Thus, the entire watershed is divided into three parts: the ZJF label is used for the single-site calibration, while the SDY, XB, and the RB are used for the multi-site calibration. The SDY and XB can be regarded as small watersheds, which are individually calibrated and validated.

Because there are many parameters in the SWAT model, identifying the most sensitive input parameters is an essential component of the calibration procedure. In this study, the analysis function of SWAT was used, and the sensitive parameters of the three watersheds were carried out in the ZJF, SDY and XB, respectively. The most sensitive parameters were basically the same for the three sites, and there was only a slight difference in the order.

As presented in Table 3, the most sensitive parameters were selected. The XB and SDY parameters were used in their respective watersheds, and the RB part was controlled by the parameters of ZJF. The parameters in the basin input file (.bsn) have single values across the whole watershed. The E_NS and R² values were used to evaluate the performance of the multi-site calibration.

Calibration and validation results

Using the flow data from 2006 to 2010 of ZJF, XB, and SDY, the SWAT model was calibrated and validated. As shown in Table 4, the calibration was done by using the data from 2006 to 2007 and the validation performed with the data from 2008 to 2010. The results of the single-site and multi-site processes are presented in Table 4 and Figs. 2–5 for the calibration and validation period. The results of the three sites indicate that the SWAT model performed well in reflecting the characteristics of Miyun Reservoir watershed.

Discussion

Comparative analysis of the single-site results

From the calibration and validation results, SDY has the best E_NS and R² values. Current research results indicate that climate variability and human activity have been identified as the two main reasons for the decrease in flows (Wang et al., 2009; Ma et al., 2010). According to research on the Miyun Reservoir, both human activity and climate change have seriously influenced the flow of the Miyun Reservoir (Wang et al., 2006; Wang et al., 2009; Zhao et al., 2012). There are no large hydraulic projects in the SDY watershed, which is located upstream of the Heihe River, a large tributary of the Baihe River, so the simulation result is good.

When using the ZJF gauge as the main outlet of the entire basin, the values E_NS and R² are lower than those of the SDY, and they are also low when compared with results of other researchers in the Miyun Reservoir watershed. The main reason for this discrepancy is that data used by other researchers is from the 1970s to 1990s (Wang et al., 2008; Xu et al., 2009). Because the watershed area is large, it is significantly influenced by human activities and climate change; e.g., studies have shown that the flow had reduced by 0.36×10⁸ m³/yr (2.28 mm/yr) over the past 50 years (Ma et al., 2010). All of the above factors influenced our results.

Multi-site versus single-site analysis

When performing the multi-site analysis, differences were observed between the single-site and multi-site calibration and validation. There are several reasons for this. First, the entire watershed covers an area of approximately 9000 km² and includes two large reservoirs, the Yunzhou Reservoir and the Baihebao Reservoir, which were built in 1970 and 1983, respectively (Wang et al., 2009, Fig. 1; Bao et al., 2012). The Baihebao Reservoir supplies quantities of water to the city of Beijing. Water resource management activities, such as those associated with agricultural irrigation and supplying water for city use, not only increase the complexity of the management process but also introduce great uncertainties into the hydrological simulation. Damming has the most significant impact on the ecological environment (Li and Li, 2008), and the impact of climate variability also cannot be ignored. The application of multi-site calibration and validation can take full account of the characteristics of different watersheds and human activities within the large basin, while making full use of multi-site data (Bekele and Nicklow, 2007).

Second, when considering the conditions of the watershed, Wang et al. (2012) indicated that the middle and downstream areas of the Miyun Reservoir watershed were usually characterized by mountain and natural weathering; however, the Inner Mongolia Plateau is located in the northern part of the watershed, with a high soil water storage capacity. Cao et al. (2006) concluded that soil properties are responsible for the differences between the simulated and measured values. The geographic location and soil type were obviously different in SDY and XB, so the single parameters cannot accurately meet the requirement of the entire watershed. Researchers also believe that in a large watershed, using a single parameter over the entire watershed may lead to a high degree of uncertainty; thus, the multi-site approach is expected to achieve better simulation results (Gong et al., 2012).

Third, the parameter values with the greatest differences across the three sites are shown in Table 5. Among these parameters are CN2, CH_K2, and SOL_K. These differences among the optimized parameter values reveal that the relationships between flow and topography, land use, and precipitation are different for each sub-watershed. SDY, which is located in the upper region of the entire watershed and has the smallest area of the sub-watersheds considered here, exhibits parameters with the greatest differences among the three sites. CN2 (denoted as Curve number II), depends on the soil and land use type. It was seen that surface runoff increased when CN2 increased, but the basic flow was reduced. The CN2 value of the SDY sub-watershed was significantly larger than that of the other two sub-watersheds, which indicates that the surface runoff of SDY was higher. This higher surface runoff was apparently related not only to the soil and land use type, but also the direct abstraction of water from the other sites. Because of the lack of human activities, the environment of the SDY sub-watershed is close to its natural state. The value of CH_K2 in SDY was larger than those at the other sites due to the composition of thehe bed. The EPCO in XB was larger than that in SDY and RB; i.e., more moisture can be absorbed from the lower layers of the soil (Abbaspour, 2011). The differences in SOL_K and SOL_BD were mainly due to the soil type. Apart from the differences of land use, soil and area mentioned above, humidity and temperature also exhibited differences. As previously mentioned, the Mongolian plateau is in the northern part of the watershed, while the city of Beijing is in the south, so there are significant differences between them, which is one of the reasons for the differences in the parameter values of the different sites. The simulation results of those parameters were in agreement with the results of other researchers. Rasolomanana et al. (2012) indicate that an excellent water quality modelling performance in predicting may mask a loss of performance and unbalanced internal model components; this masking might be the reason for the differences in the parameter values between the single- and multi-site approaches. Bekele and Nicklow (2007) proposed that the distribution of the optimal parameters also obtained better results. Different sites using the different optimal parameter values may reflect the characteristics of the different watersheds, thereby enabling optimization of the modelling of the entire watershed. The analysis results above demonstrate that parameter values are significantly different between the multi-site approach and the single-site approach. This is closely related to the climate, topography, land use and soil type of the study area. For these reasons, the parameter values of the multi-site approach are more reasonable. Therefore, when performing calibration and validation in a large watershed, more desirable results will be achieved if the large watershed is divided into a plurality of small catchments.

Gong et al. (2012) applied a multi-gauge calibration to the modelling of the Daning River of China’s Three Gorges Reservoir Region. Their results indicated that the multi-gauge and single-gauge schemes have no apparent differences in their performances. This lack of difference is probably attributed to the characteristics of the watershed. The Daning River is located in southern China, which has abundant rainfall, and the area of its watershed is less than one quarter of the area of the Baihe watershed. Because of the small size of the catchment, the lack of human activity and the abundance of rainfall, the flow of the Daning River has exhibited no significant change in recent years. Due to the small study area, the parameter values of single-sites are interchangeable within the watershed, while this change is impossible in the large watershed considered in this paper. The parameter values of SDY cannot be used in XB. Thus, the multi-sites calibration and validation is more useful in a large watershed.

Currently, there are two types of calibration methods that are usually employed when using SWAT. One method aggregates the different objective function values calculated at each site into one value and then estimates the parameter value by using the single objective optimization algorithm, while the other optimizes the different objective functions calculated at multiple sites simultaneously by using multi-objective evolutionary algorithms (Zhang et al., 2008). The two methods require a complex mathematical operation, thus increasing the time and difficulty of the calibration. In addition, using the optimization algorithm may also cause homogenisation of parameters, which does not achieve the goal that a large watershed should use multiple parameters. The result of the multi-site approach has been improved compared to the single-site approach, but not significantly. The multi-site calibration parameter values are more reasonable with respect to the local condition, and provide a good foundation for the simulation of other pollutants in follow-up works (e.g., sediment, nutrients).

Currently, studies of the calibration and validation at large watersheds which are significantly disturbed by human activities are relatively lacking; this multi-site method may play an important role in such watersheds, by achieving the best calibration and validation results, thereby enabling more reasonable modelling results. Compared with the same type of studies, this case study can provide the experience of multi-site calibration in a large-scale basin.

Conclusions

With the increased use of semi-physically based distributed hydrologic models, calibration and validation of such hydrologic models is becoming an increasingly important issue, especially for use in large watersheds. In this study, a semi-distributed hydrological model, SWAT, was applied in the Baihe watershed of the Miyun watershed to determine the optimal hydrological model parameters using the observed flow data at three monitoring sites. The large watershed was divided into smaller watersheds by the locations of the monitoring sites, and the optimal parameters of the smaller watersheds were used for the model of the entire watershed. Our results demonstrate that the multi-site calibration parameter values are more reasonable. While the multi-site approach does not greatly improving the simulation results, its advantages lay in determining the parameter values that are more reasonable to the local condition. The multi-site calibration and validation make use of the capability of the SWAT model with multi-site data and reduce the spatial heterogeneity. In this study, a multi-site calibration and validation was applied to the Miyun Reservoir watershed. This case study provides readers with the experience of multi-site calibration in a large-scale basin compared with the same type of research. Much work needs to be performed on model validation. Future studies will focus on determining the important model parameters and regularly monitoring the nutrient and sediment data from different tributaries to calibrate and validate the SWAT model.

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