*Article* **Parameter Optimization for Uncertainty Reduction and Simulation Improvement of Hydrological Modeling**

#### **Jinyu Hui <sup>1</sup> , Yiping Wu 1,\* , Fubo Zhao <sup>1</sup> , Xiaohui Lei <sup>2</sup> , Pengcheng Sun <sup>1</sup> , Shailesh Kumar Singh <sup>3</sup> , Weihong Liao <sup>2</sup> , Linjing Qiu <sup>1</sup> and Jiguang Li <sup>4</sup>**


Received: 9 November 2020; Accepted: 6 December 2020; Published: 11 December 2020

**Abstract:** Hydrological modeling has experienced rapid development and played a significant role in water resource management in recent decades. However, modeling uncertainties, which are propagated throughout model runs, may affect the credibility of simulation results and mislead management decisions. Therefore, analyzing and reducing uncertainty is of significant importance in providing greater confidence in hydrological simulations. To reduce and quantify parameter uncertainty, in this study, we attempted to introduce additional remotely sensed data (such as evapotranspiration (ET)) into a common parameter estimation procedure that uses observed streamflow only. We undertook a case study of an application of the Soil Water Assessment Tool in the Guijiang River Basin (GRB) in China. We also compared the effects of different combinations of parameter estimation algorithms (e.g., Sequential Uncertainty Fitting version 2, particle swarm optimization) on reduction in parameter uncertainty and improvement in modeling precision improvement. The results indicated that combining Sequential Uncertainty Fitting version 2 (SUFI-2) and particle swarm optimization (PSO) can substantially reduce the modeling uncertainty (reduction in the *R*-factor from 0.9 to 0.1) in terms of the convergence of parameter ranges and the aggregation of parameters, in addition to iterative optimization. Furthermore, the combined approaches ensured the rationality of the parameters' physical meanings and reduced the complexity of the model calibration procedure. We also found the simulation accuracy of ET improved substantially after adding remotely sensed ET data. The parameter ranges and optimal parameter sets obtained by multi-objective calibration (using streamflow plus ET) were more reasonable and the Nash–Sutcliffe coefficient (NSE) improved more rapidly using multiple objectives, indicating a more efficient parameter optimization procedure. Overall, the selected combined approach with multiple objectives can help reduce modeling uncertainty and attain a reliable hydrological simulation. The presented procedure can be applied to any hydrological model.

**Keywords:** combined approach; multi-objective optimization; modeling uncertainty; model constraint; SWAT

#### **1. Introduction**

Improving the reliability of hydrological modeling simulation by reducing modeling uncertainty to support water resource planning and management is an ongoing goal for the hydrological community [1–3]. Due to the development of distributed hydrological models, hydrological research has progressed significantly. However, the equifinality resulting from different parameter sets indicates that there uncertainties remain in the modeling processes [4,5]. Such uncertainty may affect simulation accuracy and even result in misleading assessments, compromising water resource management [6,7]. Controlling the range of parameters and adding additional constraints can help reduce such modeling uncertainty [8–11]. Therefore, improving the accuracy and credibility of hydrological modeling by constraining the parameters is of high potential interest in the hydrological community [12,13].

The source of uncertainty in hydrological models can be generally classified into three categories: input and calibration data uncertainty (e.g., climate, underlying surface, and streamflow data), structural uncertainty (e.g., process descriptions and equations), and parameter uncertainty [14–17]. Of these, parameter uncertainties are common but can be easily controlled to improve model performance and credibility, which has been a major focus in the modeling uncertainty field [10,18–20]. Several approaches were also developed for parameter optimization and uncertainty analysis, of which generalized likelihood uncertainty estimation (GLUE) [21], Sequential Uncertainty Fitting version 2 (SUFI-2) [22], and particle swarm optimization (PSO) [23] are the most popular. GLUE is easy to use in model calibration but results in greater uncertainty [24,25]. The SUFI-2 method can more efficiently provide satisfactory simulations, but requires additional iterations and manual adjustment of parameter ranges after each iteration [18,26]. For example, Qiao [9] found the uncertainty indicator (i.e., *R*-factor) decreased dramatically using the four-stage SUFI-2 method to narrow the range of parameters. PSO can automatically process the parameter optimization and achieve rapid convergence of parameters [25]. These studies are valuable in the understanding of modeling uncertainties and associated analysis methods.

In most cases, it is difficult to obtain parameter values directly from field measurements and thus parameter optimization with a target hydrological variable may be needed [11,27,28]. Generally, streamflow observations are used for model calibration because they are readily available and linked to various hydrological processes [3,4]. Model calibration with streamflow only may result in acceptable streamflow simulation but incorrect representation of other processes, such as soil moisture, evapotranspiration (ET), and groundwater recharge. Previous studies found that multi-objective calibration is an effective means of improving simulations [20,29–31]. Compared to calibration with a single streamflow gaging station, using multiple streamflow gaging stations can help reduce uncertainty and improve simulation accuracy [32,33]. Zhang [34] calibrated Soil and Water Assessment Tool (SWAT) with streamflow data from three gages using four different optimization methods (PSO, GLUE, SUFI-2, and parameter solution). Chien [35] calibrated SWAT using SUFI-2 with multi-site streamflow observations and found that different regions have unique buffering capabilities in response to climate change. Additionally, for better simulation of the hydrological processes, other variables, such as ET, soil moisture, and groundwater, can be added for model calibration [4,20,29,34]. Rajib [3] found the simulation performance improved noticeably when calibrating with additional Moderate-resolution Imaging Spectroradiometer (MODIS) ET data. Qiao [9] found that the SWAT model performance can be significantly improved by introducing both groundwater storage and streamflow into the calibration procedure. Researchers also considered that the predictability of hydrological models can be significantly improved when jointly calibrating with streamflow and satellite-based ET data [3,27]. However, other reports have also indicated that calibration involving multiple variables may lead to worse model performance in streamflow simulation compared to streamflow-only calibration [20]. Clearly, many studies have verified that multi-objective (i.e., using more than one observed variable) calibration can be an efficient means to improve the performance of the model, particularly in the examination of multiple processes rather than streamflow only. However, few studies have examined

the impacts of multi-objective calibration on modeling uncertainty, which is the motivation of the current study. *Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 3 of 26 The overall goal of this study was to provide a feasible and efficient means for parameter

The overall goal of this study was to provide a feasible and efficient means for parameter optimization, and reducing and quantifying uncertainty. Thus, we applied two common optimization and uncertainty analysis approaches (SUFI-2 and PSO) and their combinations for model inversion. Each approach and combination was applied with single-objective and multi-objective calibrations to analyze the effect of different model constraints on modeling accuracy and uncertainty reduction. optimization, and reducing and quantifying uncertainty. Thus, we applied two common optimization and uncertainty analysis approaches (SUFI-2 and PSO) and their combinations for model inversion. Each approach and combination was applied with single-objective and multiobjective calibrations to analyze the effect of different model constraints on modeling accuracy and uncertainty reduction.

#### **2. Materials and Methods 2. Materials and Methods**

#### *2.1. Study Area 2.1. Study Area*

The Guijiang River is a tributary of the Xijiang River in the Pearl River Basin, located in southern China, and originates in the north of Maoer Mountain and flows southeast through Guangxi province with a length of 426 km. The drainage area of the Guijiang River Basin (GRB) (23◦–25◦ N, 110◦–111◦ E, 18,606 km<sup>2</sup> , Figure 1) is 19,288 km<sup>2</sup> . The GRB lies in the subtropical monsoon climate zone, with an uneven characteristic distribution of precipitation concentrated mostly from April to June [36,37]. The annual precipitation ranges from 1600 to 1800 mm, and the annual mean temperature (T) ranges from 18 ◦C in the upstream to 21 ◦C in the downstream [37]. Topographically, the altitude decreases from the highest in the northwest to the lowest in the southeast. Land uses mainly include forest (61%), cropland (19%), shrubland (9%), grass (7%), urban (3%), and water (1%). The main soil types are Acrisols (60%), Luvisols (14%), Anthrosols (10%), Alisols (8%), and Cambisols (6%), with other soil types accounting for less than 2% (Figure 1). The Guijiang River is a tributary of the Xijiang River in the Pearl River Basin, located in southern China, and originates in the north of Maoer Mountain and flows southeast through Guangxi province with a length of 426 km. The drainage area of the Guijiang River Basin (GRB) (23°–25° N, 110°–111° E, 18,606 km2, Figure 1) is 19,288 km2. The GRB lies in the subtropical monsoon climate zone, with an uneven characteristic distribution of precipitation concentrated mostly from April to June [36,37]. The annual precipitation ranges from 1600 to 1800 mm, and the annual mean temperature (T) ranges from 18 °C in the upstream to 21 °C in the downstream [37]. Topographically, the altitude decreases from the highest in the northwest to the lowest in the southeast. Land uses mainly include forest (61%), cropland (19%), shrubland (9%), grass (7%), urban (3%), and water (1%). The main soil types are Acrisols (60%), Luvisols (14%), Anthrosols (10%), Alisols (8%), and Cambisols (6%), with other soil types accounting for less than 2% (Figure 1).

**Figure 1.** Location, digital elevation model (DEM), land use, and soil types of the Guijiang River Basin. **Figure 1.** Location, digital elevation model (DEM), land use, and soil types of the Guijiang River Basin.
