Decomposition of contribution to runoff changes and spatial differences of major tributaries in the middle reaches of the Yellow River based on the Budyko framework

Climate change directly affects the abundance and depletion of runoff, while human activities change the underlying surface conditions through land-use/land-cover changes and the construction of water conservancy facilities, thereby affecting the process of yielding and runoff. In recent years, the evolution and vulnerability of water resources under changing environments have been a research focus in academia. Climate change and human activities are two important factors in changing environments, and their impact on the hydrological cycle has received extensive attention (Barnett et al. 2005; Piao et al. 2010), with a range of methods deployed including statistical methods (Hou et al. 2018; Luan et al. 2021), meteorological–hydrological methods (Wang et al. 2018a, 2018b), hydrological models (Zhai & Tao 2017), and elastic coefficient methods based on the Budyko framework (Tang & Wang 2021). The statistical method requires less data, and the calculation process is simple but lacks a physical basis. The meteorological–hydrological method mainly includes the climatic elasticity method and the hydrological sensitivity method, which are mainly used for analysis on long-time scales and do not reflect changes in the flow process (Wang et al. 2018a, 2018b). The hydrological model has a clear physical mechanism and can undertake multi-time scale analysis and calculation but requires high quality and quantity of input data and has large uncertainties (Leavesley 1994). The elastic coefficient method based on the Budyko framework has been widely used because of its reliable physical basis and simple calculation process (Wang et al. 2020).

Since the 1950s, the availability of water and sand in the Yellow River basin has decreased sharply due to the influence of climate and human activities, with the most obvious decline in the middle reaches (Zhao et al. 2013; Li et al. 2014). In recent years, many studies have evaluated the contribution of climate and human activities to runoff by considering the middle reaches as a whole or selecting a particular tributary (Li et al. 2018, 2019; Liu et al. 2021; Yu et al. 2021; Ni et al. 2022). The Budyko framework is an important method for decomposing the contribution of runoff changes and has been widely used in studying the contribution of vegetation (Wang et al. 2021; Ji et al. 2022), soil and water conservation measures (Liang et al. 2015; Yu et al. 2021), constructions of reservoirs/dams (Tian et al. 2019), and climate change (Zheng et al. 2021; Ni et al. 2022) to runoff in the middle reaches of the Yellow River (MRYR) and its sub-basins.. Liu et al. (2021) found that human activities contributed 62% (1987–2003) and 59% (2004–2016) to the reduction of runoff in the MRYR compared to the base period (1965–1986) by comparing the measured runoff with the ‘natural runoff’. But in the Wuding (WD) River Basin, Yu et al. (2021) found that precipitation was the main factor in runoff reduction in the 1970s–1990s compared to the base period of 1957–1971, and the influence of vegetation measures gradually increased and became dominant after 2000. Therefore, it is necessary to use consistent methods and data from the same period to clarify the causes of runoff changes in each tributary of the MRYR. It also provides the essential basis for subsequent site-specific water resource management.

In this study, we first analyzed the trends of hydrometeorological elements by Mann–Kendall (M-K) trend analysis, then divided the study period into two periods: the base period and the abrupt change period by M–K abrupt change analysis, and calculated the coefficients of substratum in the two periods by Budyko's water-heat balance equation. Finally, the effects of precipitation, potential evapotranspiration, and underlying surface parameter on runoff were calculated by using the elasticity coefficient method to quantify the contribution of climate change and human activities to runoff changes in nine sub-basins in the MRYR. Comparing and analyzing hydrometeorological elements and changes in the sub-basins can provide a theoretical basis for future water resources management and protection in the middle reaches.

The terrain of the MRYR is high in the northwest and low in the southeast with the terrain dominated by plateaus. The main landforms in the study area include loess hilly and gully area, residual plateau area, northwest aeolian sand area, loess terrace area, alluvial plain, and rocky mountainous area. Vegetation transitioned from the warm temperate deciduous broad-leaved forest belt to the temperate grassland belt from south to north. Except for a few rocky mountainous areas, most areas of the study area are covered by loess with deep soil layers. The main soils are loess soil, cinnamon soil, and black loam soil.

There are eight main tributaries in the MRYR, including Huangfuchuan (HF) River, Kuye (KY) River, Wuding (WD) River, Yan River (YR), Wei River, and Yiluo (YL) River on the right bank, and Fen River (FR) and Qin River (QR) on the left bank. Among them, the Weihe River is the largest tributary of the Yellow River, with a drainage area of 134,800 km². The larger tributaries of the Weihe River are mostly concentrated on the north bank. Among them, the major tributaries larger than 10,000 km² are the Hulu River, the Jing River (JR), and the Beiluo (BL) River. The FR is the second-largest tributary of the Yellow River and the largest river in Shanxi Province. Many important industrial cities are concentrated in the basins of the FR. The QR and the YL River are one of the main sources of floods in the Yellow River. Because of their proximity to the lower reaches of the Yellow River, the occurrence of floods poses a great threat to the lower reaches. The typical middle reaches selected in this study are HF River, KY River, WD River, YR, FR, JR, BL River, QR, and YL River (Figure 1 and Table 1), which basically cover the entire MRYR.

This study uses the meteorological data of 54 meteorological stations in and around the MRYR from 1960 to 2020 (Figure 1), including average, maximum/minimum temperature, precipitation, average wind speed, sunshine hours, relative humidity, etc. Data are obtained from the China Meteorological Scientific Data Sharing Service Network (https://www.nmic.cn/). The potential evapotranspiration (E₀) is calculated using the Penman–Monteith formula recommended by the Food and Agriculture Organization of the United Nations (FAO). The mean areal precipitation and E₀ in each river basin are calculated using the Thiessen polygon method calculation. The annual runoff data of each hydrological station were obtained from the Hydrological Bureau of the Yellow River Water Conservancy Commission. Human water withdrawal data are from the Yellow River Water Resources Bulletin for 1990–2020. Digital Elevation Model (DEM) data come from Geodata Spatial Cloud (http://www.gscloud.cn/). The land-use data come from the global land cover (GLC) data set (Global Land Surface Satellite-GLC (GLASS-GLC)) published by Liu et al. (2020) with a spatial resolution of 5 km × 5 km, including annual data from 1982 to 2015. The normalized vegetation index (NDVI) data come from the National Earth System Science Data Center, National Science & Technology Infrastructure of China (http://www.geodata.cn), with a spatial resolution of 5 km.

Usually, ⁠, is the drought index, and is assumed to be a universal function that satisfies all watersheds.

Considering the differences in regional climate and geography, scholars have successively proposed various empirical formulas based on Budyko's theory. Previous studies have shown that the hydrothermal coupling balance equation considering the characteristic parameters of the underlying surface can simulate the annual runoff in various catchments in China (Xing et al. 2018) (Table 2). In this study, the Fu Baopu formula (Table 2) was used for analysis and calculation (Fu 1981).

Table 2

Hydrothermal coupled equilibrium equation based on Budyko hypothesis

Method .	Formula .
Choudhury-Yang
Fu
Zhang
Wang-Tang

Method .	Formula .
Choudhury-Yang
Fu
Zhang
Wang-Tang

Note: The underlying surface parameter (n) reflects the watershed characteristics and is a function of vegetation type, soil properties, and topographical characteristics.

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The positive and negative values of the elastic coefficient represent the positive and negative correlation between the influence factor and the runoff, and the absolute value represents the degree of influence of the influence factor on the runoff.

⁠, ⁠, and are the changes of precipitation, potential evapotranspiration, and underlying surface coefficients in the change period relative to the base period, respectively.

Compared with Period I, the precipitation in WD and BL slightly increased in Period II. However, the precipitation in other sub-basins showed decreasing trends, especially in QR, FR, and YL (Figure 4(a)). Meanwhile, the potential evapotranspiration in these three sub-basins decreased in Period II (with a larger relative decrease in the QR), while the other basins increased (Figure 4(b)).

Except for precipitation (P, Figure 4(a)) and potential evapotranspiration (E₀, Figure 4(b)), other variables changed consistently in all sub-basins. Runoff (Figure 4(d)) and runoff coefficients (Figure 4(e)) decreased in nine sub-basins, while the ratio of potential evapotranspiration to precipitation (E₀/P, Figure 4(c)) and underlying surface parameter (n) (Figure 4(f)) increased. The runoff was more sensitive to changes in precipitation, potential evapotranspiration, and underlying surface parameter (n) (Figure 4(g)–4(i)). Among the basins with large changes are mainly HF, FR, and QR.

From 1960 to 2020, the MRYR showed a non-significant decreasing trend in precipitation and potential evapotranspiration, but a significant decrease in runoff (Table 3), indicating the importance of human activities on runoff generation in the region. This is also responsible for the spatial variation in human and climate change contributions across the nine sub-basins in this study.

Human water withdrawal is also an important reason for the significant decrease in runoff in the MRYR. The Yellow River Water Resources Bulletin shows that human water withdrawal in the MRYR increased from 67 × 10⁸ m³ in the 1990s to 94 × 10⁸ m³ in the 2010s (Table 8). Using 1990–1999 as the base period, we calculated the growth rates of human water withdrawals for 2000–2009 and 2010–2020. In both periods, the Toudaoguai-Longmen (Figure 1, including HF, KY, WD, and YR) section experienced significantly higher water withdrawal growth than the other two river sections, according to Table 8.

Spatial differences in human activities lead to significantly higher human activity contributions in HF and KY (with higher NDVI and human water withdrawal growth rates) than in other sub-basins. Therefore, there is a need to develop water resources planning and management plans for sub-basins according to the socio-economic development, land use, and other factors in different sub-basins to cope with future climate change and the impact of human activities on water resources.

The present study on the contribution of climate and human activities to runoff in nine sub-basins of the MRYR is consistent with the results of previous studies. For sensitivity analysis, the sensitivity of runoff to the underlying surface parameter was shown to be highly dependent on the drought index (E₀/P). The higher the drought index, the greater the sensitivity of runoff to underlying surface change (Berghuijs et al. 2017; Li & Quiring 2021). This variation is also evident in our study. Runoff is more sensitive to the underlying surface parameter in the more arid northern sub-basins (Table 5). In addition, both our and previous results show that the sensitivity of runoff to the underlying surface parameter is higher in MRYR than in precipitation and potential evapotranspiration (i.e., > > ⁠) (Wang et al. 2021; Ni et al. 2022). Such a pattern has been verified in other arid basins around the world (Berghuijs et al. 2017; Li & Quiring 2021). Li & Quiring (2021) attributed this mainly to the asymmetry of E₀/P = 1 in the Budyko equation.

Studies have found that human activities are the main cause of runoff decline in MRYR and its sub-basins, with a contribution rate exceeding 50% (Zhang et al. 2008; Hu et al. 2020). For the nine sub-basins covered in this study, the contribution of human activities to runoff ranged from 55.1 to 95.8% (Table 6). These findings are generally consistent with the results of previous studies.

Some uncertainties and limitations in runoff attribution must be acknowledged. First, there is a strong interaction between vegetation and climate (Liu et al. 2006; Strengers et al. 2010), making it difficult to fully distinguish between their contributions to runoff. In addition, this study did not quantitatively disentangle the contributions of soil and water conservation measures, human water withdrawal, and watershed scale to runoff. This study provides a basis for establishing their quantitative relationships with substrate coefficients and quantitatively calculating the runoff contributions of these human activities.

This study used the linear propensity estimation method, the M–K test method, and the Budyko hydrothermal coupling balance equation to analyze the variation trends of precipitation, runoff, and potential evapotranspiration in the MRYR and nine typical river basins from 1960 to 2020. The contribution rate of climate change and human activities to the runoff change in the study area is quantitatively decomposed. The main research conclusions are as follows:

• (1)

  MRYR has tended to be drier during the past decades, with decreasing precipitation and increasing potential evapotranspiration. Spatially, the precipitation in the five northern sub-basins (HF, KY, WD, YR, FR) was less than that in the southern region, and the potential evapotranspiration was greater during the 1960–2020 period, indicating a drier condition in the northern sub-basins. A significant decrease in precipitation (p < 0.01) could only be detected in QR, while changes in other watersheds were not significant. In addition, the changes of potential evapotranspiration were more different, and the trend of HF, YL, and QH decreased significantly (p < 0.05). All other sub-basins increased, with significant trends in WD, FR, and BL (p < 0.01). The runoff in MRYR and all sub-basins showed a significant decreasing trend (p < 0.01).

• (2)

  We divided the study period into the base period (before the abrupt change point, period I) and change period (after the abrupt change point, period II). Compared with period I, runoff and runoff coefficients decreased in all nine sub-basins during Period II. 2161;. The drought index, underlying surface parameter, runoff sensitivity to rainfall, potential evapotranspiration, and underlying surface parameter increased. Spatially, the sensitivity of runoff to the underlying surface parameter was proportional to the drought index, and the drier the location, the more sensitive runoff was to underlying surface changes. In addition, the sensitivity of runoff to the underlying surface parameter was higher than that of precipitation and potential evapotranspiration. This may be caused by the asymmetry of E₀/P = 1 in the Budyko equation.

• (3)

  Using the Budyko hydrothermal coupling balance equation, it was found that compared with the base period, both meteorological changes and human activities in the change period resulted in the reduction of runoff, and human activities were the main reason for the reduction. Human activities in the HF River and KY River basins contributed more than 90% to the reduction of runoff, and the contribution rate of human activities in other basins was more than 55%. Since the NDVI growth rate and human water withdrawal growth rate are significantly higher in the HF and KY sub-basins, their human activity contributes significantly more than the other sub-basins.

This study was jointly supported by the National Natural Science Foundation of China (51679252, U2240201) and the National Key Research and Development Program (2017YFC0404401). Acknowledgment for the data support from ‘National Earth System Science Data Center, National Science & Technology Infrastructure of China. (http://www.geodata.cn)’. Yanyu Dai acknowledges the China Scholarship Council (CSC) for the scholarship support (No. 202108110149).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.