**1. Introduction**

The problem of water resources will become the most important natural resource problem facing mankind in the 21st century, and the exploitation of water resources in northern China has exceeded the carrying capacity of the resource environment, indicating that the situation facing water resources is very serious [1]. In recent years, the combined effects of climate change and human activities have led to significant changes in the river runoff of many rivers and further intensification of water scarcity, which seriously threatens social development and human life [2]. Exploring trends and turning points in runoff change and revealing the main drivers of runoff change play a key role in future water resources prediction [3].

Runoff change is a complex dynamic process as an integrated response to climate change and human activities in a watershed. The effects of climate change and human

**Citation:** Xu, J.; Gao, X.; Yang, Z.; Xu, T. Trend and Attribution Analysis of Runoff Changes in the Weihe River Basin in the Last 50 Years. *Water* **2022**, *14*, 47. https://doi.org/10.3390/ w14010047

Academic Editors: Qiting Zuo, Xiangyi Ding, Guotao Cui and Wei Zhang

Received: 28 November 2021 Accepted: 21 December 2021 Published: 25 December 2021

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**Copyright:** © 2021 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/).

activities on hydrological processes have become a hot research topic. Currently, statistical analysis methods [4], hydrological modeling methods [5], and elasticity coefficient methods based on the Budyko framework [6] are the main methods to study the impact of climate change and human activities on hydrological water resources. The elasticity coefficient method based on the Budyko framework integrates the coupled hydrothermal equilibrium of the watershed and establishes the relationship between watershed runoff and precipitation, evaporation, and underlying surface characteristics, which is easy to calculate and has been validated in many watersheds [7–9].

In recent years, significant changes in runoff and other hydrometeorological elements have occurred in the Weihe River basin, causing widespread concern. Zuo et al., used a sensitivity coefficient approach based on the Budyko framework and a hydrological modeling approach to estimate the effects of climate change and human activities on runoff in the Weihe River basin. They found that the impact of human activities on the control basins of the upper and middle reaches of the Weihe River at Linjiacun, Weijiabao, and Xianyang hydrological stations, and the control basins of the lower reaches of the Jinghe River at Zhangjiashan station, accounted for greater than 50% of the runoff changes [10]. Sun et al., found that the intensification of potential evapotranspiration due to climate warming contributed negatively to runoff changes by more than 60%, which was higher in absolute value than the positive contribution of precipitation [11]. Shi et al., found that the contribution of human activities to runoff changes in the Weihe River source area was close to 50% [12]. Zhang et al., found that intense human activities were the main cause of runoff reduction, and their contribution to the reduction in runoff was over 60% [13]. Although many previous studies have been conducted to analyze runoff changes in the Weihe River basin, the results are not entirely consistent (Table 1). The contribution of potential evapotranspiration, precipitation, and human activities to runoff changes in the Weihe River basin varies widely among the results obtained in each article due to different study periods, hydrological stations, and methods. However, generally, they indicate that the modification of the underlying surface by human activities has gradually become a major factor affecting runoff changes.

**Table 1.** Past studies in Weihe River basin.


Most of the previous studies were based on the period before the 2010s and did not explore the continuous changes of runoff in the Weihe River in the last 10 years. In order to deeply analyze the characteristics and causes of runoff changes in the Weihe River basin in recent years, this paper conducted a trend and abrupt change point test for each hydrological element in the Weihe River basin and selected the base period and change periods based on abrupt change points. This paper applies the Budyko framework to analyze the contributions of precipitation, potential evapotranspiration, and underlying surface characteristics to runoff variability and conducts an attribution analysis of runoff variability to provide a theoretical basis for the integrated management and sustainable use of water resources in the Weihe River basin and similar areas.

#### **2. Study Area**

The Weihe River is the largest tributary of the Yellow River, located in the Yellow River hinterland (103◦570–110◦170 E, 33◦420–37◦240 N), originating in the Wushu Mountain in Weiyuan County, Dingxi City, Gansu Province, and flowing through three provinces, Gansu, Ningxia, and Shaanxi, east to Tongguan County, Shaanxi Province, where it joins the Yellow River, with a main stream length of 818 km and a basin area of 134,800 km<sup>2</sup> . The Weihe

River has many tributaries, and the tributaries on both sides of the river are asymmetrically distributed. The water system on the south bank originates from the Qinling Mountains and flows through the rocky mountainous areas, which are mostly tributaries with a short course and more water and less sand. The water system on the north bank is developed on the Loess Plateau, with a large water catchment area and serious soil erosion, and is the main sand-producing area in the watershed. The largest tributary is the Jing River, with a length of 455.1 km and a basin area of 45,400 km<sup>2</sup> ; the second largest tributary is the Bei Luo River, with a length of 680 km and a basin area of 26,900 km<sup>2</sup> . The Weihe River basin is located in the transition zone between arid and humid and has a temperate monsoon climate with an average annual temperature of 7.8 ◦C~13.5 ◦C, annual precipitation of 300~800 mm, annual potential evaporation of 700~1400 mm, and annual evaporation of 400~700 mm. Combining the runoff information from the hydrological stations of Huaxian and Zhuangtou, the average multi-year runoff of the Wei River is 6.385 billion m<sup>3</sup> (Table 2).

**Table 2.** Hydrological information of the Weihe River basin.


#### **3. Data and Methodology**

*3.1. Data Collection and Preprocessing*

In this paper, annual runoff information from 1970 to 2019 at two hydrological stations in Zhuangtou and Huaxian was collected; the sum of runoff from the two hydrological stations is usually used as the annual runoff of the Weihe River basin [14]. Precipitation and daily data from ground stations including wind speed (m·s −1 ), daily maximum temperature ( ◦C), daily minimum temperature (◦C), sunshine hours, barometric pressure (kPa), elevation (m), and relative humidity (%) were taken from China Meteorological Data Service Centre (http://www.nmic.cn/ (accessed on 6 July 2021)), and meteorological data from 1970 to 2019 for 16 stations in the Weihe River basin were selected (Figure 1). The missing data of meteorological stations were interpolated with inverse distance weights using the complete data of nearby stations. The potential evapotranspiration (*ET*) was estimated using the Penman–Monteith Equation, recommended by the World Food and Agriculture Organization (FAO), and the Tyson polygon method was applied to calculate the surface rainfall and surface potential evapotranspiration of the watershed. The expression of the Penman–Monteith correction formula is as follows [15]:

$$ET = \frac{0.408\Delta (R\_{\rm nl} - G) + \gamma \frac{900}{T\_{\rm man} + 273} \mu\_2 (e\_s - e\_a)}{\Delta + \gamma (1 + 0.34 \mu\_2)} \tag{1}$$

where *ET* is the potential evapotranspiration (mm·d −1 ), *R<sup>n</sup>* is the net all-wave radiation at the canopy surface (MJ·m−<sup>1</sup> ·d −1 ), *<sup>G</sup>* is the soil heat flux density (MJ·m−<sup>2</sup> ·d −1 ), *Tmean* is the daily air temperature at 2 m above ground level (◦C), *u*<sup>2</sup> is the wind speed at 2 m above ground level (m·s −1 ), *e<sup>s</sup>* is the saturation vapor pressure (kPa), *e<sup>a</sup>* is the actual vapor pressure (kPa), ∆ is the slope of the saturated vapor pressure curve versus air temperature (kPa· ◦C −1 ), *γ* is the psychrometric constant (kPa· ◦C −1 ).

**Figure 1.** Distribution of meteorological and hydrological stations in the Weihe River basin.

#### *3.2. Methodology*

The overall research line of this paper is that the Mann–Kendall nonparametric analysis method was used to examine the trends and abrupt change points of each hydrological element in the Weihe River basin, and to select the base and change periods based on the abrupt change points. The Budyko framework is applied to explore the contribution of precipitation, potential evapotranspiration, and underlying surface parameters to runoff variability and to conduct attribution analysis of runoff variability.

#### 3.2.1. Mann–Kendall Analysis Method

The Mann–Kendall analysis was used to perform trend and mutation tests, which are easy to calculate, have a clear meaning, and are not disturbed by some outliers. They are widely used in the analysis of hydrometeorological and other series, as described in the literature [16].

## 3.2.2. Runoff Change Attribution Identification Based on the Budyko Framework
