**1. Introduction**

In the context of global climate change, the applicability of traditional runoff simulation and forecasting methods has gradually deteriorated, which brings challenges to hydrometeorological simulation and forecasting. The hydrological simulation of the river basin under the changing environment is mainly affected by the climatic conditions and the underlying surface conditions [1]. Climatic conditions are the driving factors of the water cycle in the basin and the prerequisite for the generation of runoff [2], which directly or indirectly affect the runoff process in the basin through changes in factors such as precipitation, evapotranspiration and temperature [3]. Global warming has become an indisputable fact [4]. The rise in temperature will cause changes in other meteorological elements. Significant changes have taken place in the type, intensity and amount of precipitation in many

**Citation:** Wu, H.; Liu, D.; Hao, M.; Li, R.; Yang, Q.; Ming, G.; Liu, H. Identification of Time-Varying Parameters of Distributed Hydrological Model in Wei River Basin on Loess Plateau in the Changing Environment. *Water* **2022**, *14*, 4021. https://doi.org/10.3390/ w14244021

Academic Editor: Fi-John Chang

Received: 18 October 2022 Accepted: 5 December 2022 Published: 9 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

regions of the world, generally showing that humid regions are becoming more humid, arid regions tend to become more arid and the interannual variability is significantly enhanced [5]. In addition, climatic conditions indirectly affect the hydrological process of the watershed by affecting the growth state of vegetation and its structure [6]. The increase and decrease in watershed runoff is inseparable from the change of the underlying surface conditions. With the promotion of large-scale afforestation and urbanization, surface vegetation coverage conditions and local water and heat flux transfer have undergone dramatic changes [7–10], as well as large-scale water intake [11], water diversion projects and reservoir construction, dispatch operation [12], and so on all leading to sudden changes in natural river runoff. It indicates that the "steady-state" basin assumption in traditional hydrological simulation is facing challenges, so the theory and method of hydrological probability distribution based on the consistency assumption obviously cannot help people accurately reveal the long-term law of water resources and flood evolution in changing environments [13,14]. In the hydrological model, it is generally assumed that the parameters representing the hydrological physical characteristics of the watershed are constant over time, which not only cannot reflect the watershed characteristics correctly, but also seriously weakens the simulation ability of the model. The identification and study of the time-varying characteristics of hydrological model parameters in "unsteady" watersheds, and the establishment of a model parameter estimation method that can reflect the climatic conditions of the watershed and the changing laws of the underlying surface, will improve the simulation and performance of hydrological models in changing environments.

The parameters of the hydrological model are usually closely related to the underlying surface conditions of the watershed, and reflect the hydrological characteristics of the watershed [15]. Since there are significant differences in climatic conditions, geographic locations, vegetation coverage, soil conditions, topography and geological conditions in different watersheds [16,17], the parameter values of the same model will also be very different in different watersheds [18]. In the beginning, the traditional watershed hydrological simulation only considers the spatial variability of the parameters of the hydrological model, but does not consider the dynamic changes of the parameters. Usually, the model parameters are considered to be static and remain unchanged over time in a given period of time. However, under the changing environment, the changes in the characteristics of watershed hydrology are not adequately reflected in the model and such assumptions may no longer be applicable. Many scholars began to question such static assumptions and carried out related researches. Kingumbi et al. [19] simulated the hydrological effect of land-use changes by the MODCOU model in the Merguellil basin in central Tunisia and evaluated the improvement in model representativeness by assigning specific parameters to the production functions in the zones of works of water and soil conservation. Vaze et al. [20] used four different conceptual hydrological models in 61 watersheds in southeastern Australia, and applied the method of segmental calibration to determine the parameter values of the model in each time period, and it was found that climate change during the study period would cause significant dynamic changes of parameters. In 273 watersheds in Austria, Merz et al. [21] identified the dynamic changes of parameters based on the HBV model and found that the changes of model parameters had a strong correlation with environmental meteorological factors such as rainfall, runoff coefficient and potential evapotranspiration. Sun [22] used the THREW model in the upper reach of the Han River, identified that all model parameters had a good correlation with the vegetation index, and proposed a dynamic parameter estimation method based on vegetation coverage, which improved the simulation effect of the model. Under the conditions of increasingly significant changes in the basin environment, the constant model parameters over time will be an important source of simulation errors [23]. Considering the dynamic changes of parameters can significantly improve the simulation effect of the hydrological model for the middle and low water sections of the runoff process [24].

The former studies qualitatively pointed out that the change of river basin environmental factors will cause dynamic changes in model parameters, but did not establish the

quantitative relationship between the factors and the parameters. They mostly focused on the influence of climate variability on the parameters, and ignored the changes in the underlying surface condition. In theory, the underlying surface conditions should have a stronger correlation with the model parameters. Therefore, it is necessary to comprehensively analyze the influence of meteorological factors in the watershed and the changes of the underlying surface conditions on the model parameters, establish a time-varying parameter estimation method based on the watershed characteristics, and further enhance the ability of the hydrological model to reflect the changes of watershed characteristics, in order to significantly improve the watershed characteristics. The study will improve the simulation and prediction effects of hydrological models in changing environments. This study takes the upper reach of the Wei River as the study area, analyzes the temporal and spatial evolution of the ecological hydrometeorological elements in the study area, reveals the temporal and spatial variation of these historical sequences and provides a basis for hydrological simulation. The SWAT model is set up in the study area and the time-varying parameter sequence of the hydrological model is obtained by segmental calibration, and the relationship between the model parameters and environmental characterization factors such as precipitation, potential evapotranspiration and the normalized difference vegetation index (NDVI) is analyzed, which provides a preliminary solution for the improvement of the distributed hydrological model. In Section 2, the study area and data are introduced. In Section 3, the methods and hydrological model are described. In Section 4, the simulation results are displayed. Finally, a conclusion is drawn in Section 5.

## **2. Study Area and Data**
