Study on the Annual Runoff Change and Its Relationship with Fractional Vegetation Cover and Climate Change in the Chinese Yellow River Basin

: In the context of global climate change and ecological restoration projects, significant changes have been observed in the fractional vegetation cover (FVC) in the Yellow River basin. The increased vegetation growth accelerates water consumption, exacerbating drought and water scarcity issues, thereby heightening regional water resource shortage risks. This study targets the Yellow River basin in China, employing a pixel-based model to convert NDVI into FVC datasets. We establish a pixel-wise mathematical model for annual runoff and environmental factors based on residual analysis and methods like multiple linear regression. Using climate model data from CMIP6 as independent variables, in conjunction with the statistical model, we elucidate the spatiotemporal characteristics of annual runoff in the Yellow River basin under future climate scenarios. Our results indicate that, under four different climate scenarios, the average annual runoff in the Yellow River basin is projected to increase. The increases are quantified as 0.008 mm/a, 0.065 mm/a, 0.25 mm/a, and 0.24 mm/a for SSP126, SSP245, SSP370, and SSP585 scenarios, respectively. From 2022 to 2040, the spatial distribution of the runoff change rates under the SSP245 and SSP370 scenarios show an increasing trend in upstream areas such as the Qinhe and Longmen regions, with rates ranging from 6.00 to 8.61 mm/a. During the period from 2041 to 2060, all four climate scenarios indicate minimal changes in the runoff depth in the northern part of the Yellow River basin. From 2061 to 2080, under the SSP126 and SSP245 scenarios, the spatial distribution of the runoff shows significant increases in the river source area and a decreasing trend in the middle reaches, with rates ranging from 4.52 to 11.39 mm/a. For the period from 2081 to 2100, the runoff change rates vary significantly under the four climate scenarios. These findings provide a detailed understanding of how future climate scenarios could impact water resource distribution in the Yellow River basin, offering critical insights for regional water management and policy making to mitigate potential water scarcity challenges.


Introduction
Runoff is a fundamental component of the hydrological cycle and a key element in the water balance (Hu et al., 2022).Its patterns of variation closely reflect the natural geographical features of a region and hold significant importance for the sustainable development of flood control, irrigation, navigation, power generation, and other industries (Chen et al., 2022;Zhuang et al., 2023).Various factors influence the spatial and temporal distribution of runoff, such as climate change, human activities, vegetation cover, and underlying surface conditions.Climate change and human activities are typically considered the primary factors affecting regional runoff.With the intensification of global warming, rising temperatures promote glacier melt and permafrost degradation, which can facilitate runoff formation on one hand but increase evapotranspiration on the other, hindering runoff aggregation (Wang et al., 2016).
Additionally, changes in vegetation cover in recent years have had a more significant impact on runoff.As a crucial component of the basin's underlying surface, changes in vegetation cover affect both runoff generation and aggregation, thereby influencing the basin's runoff (Cong et al., 2020).Lush vegetation can improve the basin's climate conditions by altering precipitation patterns to promote runoff.However, as vegetation growth increases evapotranspiration and soil moisture consumption, it can also lead to reduced runoff (Jiao et al., 2017;An et al., 2019).Against the backdrop of economic and social development and a growing population, the pressing need to understand the impact of factors like vegetation changes on runoff in the basin, as well as to explore and forecast future runoff patterns, has become a vital area of research.This is of strategic significance for regional sustainable development and the equitable allocation of water resources.
The mechanisms driving runoff through vegetation and the response of vegetation changes to runoff have become focal points of research in recent years.Studies, such as that by Guang et al. (2014), have shown that a decrease in vegetation cover in the Yellow River Basin leads to reduced rainfall interception and water storage capacity.
Moreover, different regions experience varying degrees of influence from changes in vegetation cover.A decrease in vegetation cover reduces evapotranspiration, thereby increasing river runoff.Jing et al. (2017) found a strong positive correlation between runoff changes in the Yellow River Basin and NDVI and precipitation.However, the relationship between NDVI and runoff, and the runoff coefficient, is relatively complex when viewed on an interannual basis and lacks clear correlations.Liu et al. (2018) discussed the impact of vegetation on runoff in terms of vegetation structure and vegetation cover, highlighting the varying importance of vegetation cover on runoff at different scales.Vegetation cover also controls runoff and soil erosion in different slopes and regions.According to Cai et al. (2019), former Soviet scholars suggested that for every 1% increase in forest vegetation cover, the annual runoff increased by 1.1 mm.Forested areas, characterized by high vegetation cover, decrease annual runoff because wetter forests have a stronger runoff evapotranspiration capacity.In 1909, the results of the American-led Wagon Wheel Gap experiment indicated that deforestation of 81 ha of scrub willow and coniferous forests would increase annual water yield by approximately 30 mm (Muhury et al., 2022).Stednick (1996) summarized experiments in 95 American watersheds and found that, after clear-cutting rates reach 100%, annual runoff could increase by as much as 750 mm or as little as 117 mm.
From the research mentioned above, innovative studies have examined the runoff response mechanism induced by vegetation changes.However, research that quantitatively analyzes the relationship between vegetation and runoff or explicitly establishes mathematical models or relationships between vegetation and runoff is still relatively scarce (Jean-Paul et al., 2001;Wolfgang et al., 2001).Due to the complexity and spatial heterogeneity resulting from changes in underlying surfaces caused by vegetation changes, accurately reflecting the mechanisms by which vegetation cover affects basin runoff (Fu et al., 2006;Bao et al., 2013) is challenging.Therefore, it is crucial to establish a response mechanism model that considers multiple influencing factors, such as vegetation cover, and their impacts on runoff.Faced with issues like water scarcity, decreasing river runoff, and increasing conflicts in water resource supply and demand, changes in vegetation in the Yellow River Basin are bound to exacerbate issues like changes in underlying surfaces and increased water consumption.
Consequently, this may alter the hydrological cycle patterns in the Yellow River Basin and, in turn, affect the spatiotemporal distribution of runoff, significantly impacting the sustainable utilization of water resources in the basin.
This study establishes a statistical model for future runoff predictions in the Yellow River Basin under future climate scenarios.Using statistical and remote sensing methods, including PCA-MLR combined multiple regression models, vegetation cover data, and a range of runoff influencing factor data such as meteorological and hydrological data, soil moisture, and soil temperature as independent variables, this model is based on validated remote sensing data of contemporary Yellow River Basin runoff depth.The study also uses CMIP6 climate model data as input to forecast future runoff depth in the Yellow River Basin.

Study area
The Yellow River Basin, located between 96°E to 119°E and 32°N to 42°N , spans a total length of 5464 kilometers, making it the fifth-longest river in the world and the second-longest in China.The Yellow River Basin traverses four distinct topographical units from west to east, including the Tibet Plateau, Inner Mongolia Plateau, Loess Plateau, and the North China Plain, covering a vast area of 75.2443×10 4 km 2 .The region enjoys abundant sunshine, with annual sunshine hours ranging from 2000 to 3300 min, and most areas experience annual precipitation between 200 and 650 mm.
Temperature exhibits significant variations throughout the year, with temperatures in the northern regions (above 37°N) ranging from 31 to 37°C, and in the southern areas, temperatures typically fall between 21 and 31°C.The Upper Yellow River, stretching from the river's source to the Tangnaihai hydrological station, is considered the river's source region.The upper section extends from the river's source to Huankou Town in Togto County, Inner Mongolia Autonomous Region, with a total river length of 3471.6 kilometers and a basin area of 42.8×10 4 km2, representing 53.8% of the total Yellow River Basin.This section has fewer tributaries and some siltation in the riverbed.The Middle Yellow River, known as the Taohuayu section, extends from Huankou Town to Zhengzhou City in Henan Province, covering a river length of 1206.4 km and a basin area of 34.4×10 4 km 2 , accounting for 43.3% of the total Yellow River Basin.This section features a drop in elevation of 890 m and an average gradient of 7.4‱.The Lower Yellow River, extending from Taohuayu to the river's mouth where it enters the sea, encompasses a basin area of 2.3×10 4 km 2 , representing only 3% of the total basin area.For the purposes of this study, 14 sub-basins were selected from the Upper, Middle, and Lower regions of the Yellow River Basin, and some of these sub-basins were named after their upstream and downstream hydrological control stations (Figure 1).

Data Sources and Processing (1) Meteorological and Hydrological Data
The meteorological and hydrological data used in this study include:Measured data from 93 meteorological stations within the Yellow River Basin for the period of 1951 to 2012.These data were obtained from the China Meteorological Science Data Sharing Service website (http://data.cma.cn/) and encompass daily precipitation and daily average temperature datasets.Missing data were interpolated using linear interpolation, adjacent year data, and hydrological analog methods.Nation-wide 38year cumulative precipitation and mean temperature datasets for the years 1982 to 2012, with a spatial resolution of 1 kilometer.These datasets were sourced from the National Earth System Science Data Center of the National Science and Technology Infrastructure Platform (http://www.geodata.cn/).A monthly runoff dataset with a spatial resolution of 0.08333° for China from 1960 to 2012.This dataset was also obtained from the National Earth System Science Data Center (http://www.geodata.cn/).
(2) Soil Data A monthly soil volumetric water content dataset with a spatial resolution of 0.08333° for China from 1960 to 2012.The dataset is provided in NetCDF format and is derived from the National Earth System Science Data Center (http://www.geodata.cn/).This dataset is driven by land surface basic information data and historical meteorological data and was simulated using the TRIPLEX-GHG model.
The land surface basic information data and historical meteorological data used to drive the model are publicly available and have been verified for accuracy.The model simulation results have been validated in related academic or thesis publications.A monthly soil temperature dataset with a spatial resolution of 0.08333° for China from 1960 to 2012.This dataset is provided in NetCDF format and was sourced from the National Earth System Science Data Center (http://www.geodata.cn/). (

(4) CMIP6 Climate Model Data
The future climate model simulation data used in this study for precipitation, temperature, vegetation cover, soil temperature, and soil moisture are derived from the research outcomes of our team (Jian et al., 2023a;Jian et al., 2023b)

Methodology (1) PCA-MLR Multiple Linear Regression Model
Principal Component Analysis (PCA) is a multivariate statistical method that, through dimensionality reduction techniques, transforms multiple variables into a few principal components.Assuming that a data matrix with n variables, X1, X2, ..., Xn, and k samples can be represented as: where,
The mathematical expression of the Multiple Linear Regression (MLR) model after dimensionality reduction using PCA is as follows:

Data analysis
To provide a more detailed description of the specific calculation process, this study selects an example pixel for PCA-MLR model computation.The basic data information for this pixel is presented in Table S1 1).
Based on initial eigenvalues greater than 1, after extracting 3 factors, the cumulative contribution of the factors reaches 85.469%.This indicates that a relatively small amount of original information is lost, and the performance of the top three factors in the factor analysis is quite satisfactory, making them valuable for research.
Therefore, for this pixel, three principal components are selected as the subjects of study.The component score coefficient matrix for each influencing factor is obtained.
When the data for the five influencing factors are input, the following formulas are derived for the calculation of the three principal components: By utilizing equations ( 5) -( 7), the calculation of the three principal components is performed, and the results are presented in Table 2.
For the pixel during the years 1982 to 1999, a multiple linear regression was conducted to fit the runoff coefficient as the dependent variable against F1, F2, and F3 as the independent variables.The resulting regression equation relating the dependent variable runoff coefficient to the principal components is as follows: By substituting equations ( 5)-( 7) into equation ( 8), the final linear regression model equation for the pixel with the five major influencing factors is obtained as follows: 1 2 3 4 5 0.0409 0.0006 0.0081 0.0158 0.0102 0.361 X X X X X Using this model, the runoff coefficients for this pixel in the years 2000 to 2012 were calculated, and then compared with the actual measured values to compute the relative error (Figure 3).The relative errors for all years are less than 30%, indicating that the model has a high level of accuracy and provides effective predictions for the runoff coefficients of this pixel.
Using Python 3.8.2iterative code, the steps two and three from Figure 2 were repeated, ultimately computing the spatial distribution and frequency of the regression parameters (including the regression constant μ0 and the regression coefficients μ1, μ2, μ3, μ4, μ5) for the runoff coefficient influencing factors for all pixels in the Yellow River basin, based on the PCA-MLR model.

Runoff coefficient model
The regression coefficient μ1 for FVC tends to be close to 0 in the upper reaches of the Yellow River, including Datonghe and Shizuishan to Tou Daoguai basins, while it exhibits a more complex distribution in the Hekou region, Yiluo River, Weihe, and other basins, ranging between -9.11 and 14.88 (Figure 4a and Figure 5a).The precipitation coefficient μ2 ranges from 0.2×10 -3 to 1.5×10 -3 in most parts of the Yellow River basin (Figure 4b and Figure 5c).In the Shizuishan to Tou Daoguai and Yiluohe, Weihe basins, the coefficient is positive, indicating a positive influence of precipitation in these regions on runoff.
The Yellow River basin experiences significant diurnal and interannual temperature variations.The temperature coefficient μ3 falls between -0.43 and 0.53 (Figure 4c and Figure 5d).In most areas, μ3 is positive, primarily distributed in the upper and middle reaches of the Yellow River basin.However, it is negative in the southeastern part of the Weihe, Yiluohe basin, and downstream Yellow River basin.
The soil water content coefficient μ4 ranges from -0.237 to 0.339, with most areas being negative.The exceptions are the Yellow River source area and downstream Daicunba area, which are mostly positive.The soil temperature coefficient μ5 is predominantly negative, exceeding 50% (Figure 3e and Figure 4f).Occasional positive values are observed in the Yellow River source area, Yiluohe, and downstream regions, indicating that soil temperature in these areas has a positive promoting effect on runoff, while negative values act as inhibitors.The constant term is negative in the Hekou region and downstream areas but mostly positive in other regions.The constant term might encompass factors like evapotranspiration and human activities (Figure 4f).
Regional analysis and zone-based statistical calculations were conducted on the runoff-related factor regression coefficients for the 14 sub-basins of the Yellow River, resulting in the average regression coefficients for these factors (Table 3).The Rsquared values, which are all greater than 0.70, indicate that the computed equations have statistical significance and can be utilized for predicting the runoff coefficients of the basins.
In the midstream of the Yellow River, the predicted runoff values are generally higher than the observed values.In contrast, the predictions for the source area and downstream of the Yellow River closely align with the observed values, and they are at the basin's highest level.The predicted runoff depths in the northern Hetao Plain region closely resemble the observed values.Under observed conditions, there is a noticeable variation in runoff depth in the midstream of the basin, with a gradual decline since 2008, indicating a drying trend.Under the predicted conditions, the runoff in the midstream of the Yellow River also shows a decreasing trend starting in 2008, but the reduction is slightly less compared to the observed runoff values (Figure 6 and Figure S2).
The majority of pixels have coefficients exceeding 0.7.In particular, the southern part of the basin exhibits more favorable prediction results, whereas regions in the north, such as the Hetao area, as well as certain upstream areas, demonstrate relatively poorer predictive performance (Figure 7).The relative errors for most years fall within the range of -30% to 30%.Among these, the year 2006 exhibits the smallest maximum error among all years at 16.85%.In contrast, 2010 shows the largest relative error at -28.57%.Moreover, most pixels have negative relative errors, indicating that in most cases, the predicted runoff coefficient values are higher than the observed values (Figure 8).

Future Spatiotemporal Runoff Predictions under Climate Models
Based on the established runoff coefficient model, using CMIP6 climate model data as input, the runoff depth in the Yellow River basin shows an upward trend under all four climate scenarios, namely SSP126, SSP245, SSP370, and SSP585.The fitted slopes for these scenarios are all greater than 0, measuring 0.008 mm/a, 0.065 mm/a, 0.25 mm/a, and 0.24 mm/a, respectively.Among these scenarios, SSP370 and SSP585 exhibit the fastest growth rate of runoff under the climate models.With the exception of the SSP126 scenario, where the growth is less pronounced, the other three emission scenarios all show a significant upward trend in runoff depth.However, the magnitude of runoff changes remains considerable across all emission scenarios.The lowest value is observed in 2022 under the SSP370 climate scenario, at 42.5 mm, while the peak appears in 2091 under the same scenario, at 87.61 mm (Figure 9).In the SSP126 and SSP245 climate scenarios, the Yellow River source area has a higher runoff level, with areas exceeding 600 mm more extensive than in the SSP370 and SSP585 scenarios.However, in the SSP370 and SSP585 scenarios, the peak runoff depth is larger, and the distribution is more uniform.The Weihe downstream and the Yiluohe exhibit slightly higher runoff depths compared to other regions.Overall, the runoff prediction model is generally consistent with the historical runoff distribution in the Yellow River basin.
From 2022 to 2040, in the SSP126 and SSP245 climate scenarios, the runoff depth in the midstream of the Yellow River is higher than in the SSP370 and SSP585 scenarios, with the maximum value occurring in the SSP126 scenario at 800.04 mm (Figure 10a, e, i, m).This gap gradually narrows from 2041 to 2060 and 2061 to 2080.
However, in the SSP370 and SSP585 scenarios, the runoff depth in the Yellow River source area remains lower than in the SSP126 and SSP245 scenarios.This may be attributed to the more intensive human activities and higher concentrations of carbon dioxide emissions in the SSP370 and SSP585 scenarios, resulting in significant changes in upstream vegetation cover and underlying surfaces, subsequently affecting runoff depth (Figure 10b, f, j, n).From 2081 to 2100, the differences among the four climate scenarios are most pronounced in the Yellow River source area, with the lowest runoff depth in the SSP370 scenario.

Spatial Distribution of Runoff Change Rates under Future Climate Models
From 2022 to 2040, the spatial distribution of runoff change rates for SSP245 and SSP370 is similar.In the Qinhe and Longmen areas, annual runoff shows an upward trend with rates ranging from 6.00 to 8.61 mm/a (Figure 11e, i).From 2041 to 2060, in all four climate scenarios, there is almost no change in runoff depth in the northern part of the Yellow River basin.This is due to water scarcity in the region, resulting in extreme arid conditions.Only under the SSP585 climate scenario, the annual runoff in the source area exhibits a significant upward trend (Figure 11b, f, j, n).From 2061 to 2080, the annual runoff change rates in the source area show a significant increase in the SSP126 and SSP245 climate scenarios, while the midstream runoff decreases, with rates ranging from 4.52 to 11.39 mm/a.In contrast, under the SSP370 and SSP585 climate scenarios, runoff depth decreases in the source area with a slope of -5.67 to -2.39 mm/a, while there is an increasing trend in the midstream with a slope of 16.04 to 21.43 mm/a (Figure 11c, g, k, o).From 2081 to 2100, the runoff change rates vary significantly among the four climate scenarios.Under the SSP126 climate scenario, rivers like the Jinghe and Fenhe show an increasing trend in runoff, while in most parts of the Yellow River basin under the SSP245 climate scenario, there is little to no significant change in runoff depth, ranging from 0 to 0.26 mm/year.However, in the lower Yellow River area, runoff depth decreases, with a maximum rate of -9.65 mm/a.
Under the SSP370 and SSP585 climate scenarios, annual runoff continues to increase in the source area, with rates greater than 0. There is a substantial difference in the midstream of the Yellow River basin.In the SSP370 climate scenario, runoff depth decreases with a rate of -18.10 mm/a, while under the SSP585 climate scenario, runoff depth in the midstream increases with a rate of 9.84 mm/a.

Vegetation Coverage and Runoff
This study, based on the PCA-MLR model, reveals significant spatial heterogeneity in the regression coefficients of runoff influencing factors at the pixel level in the Yellow River basin.Different regions in the Yellow River basin exhibit varying mechanisms by which runoff is influenced by changes in vegetation coverage.
These findings align with those of Yang et al. (2022), who argue that the response of runoff to vegetation changes and the magnitude of vegetation coverage's impact on basin water yield vary significantly across different hydroecological zones.Even within the same hydrological region, there are pronounced differences among different experimental basins.For instance, in the upper reaches and source areas of the Yellow River, vegetation coverage coefficients can be both positive and negative.This variation is attributed to the rich diversity of vegetation types in the source area, including coniferous forests, broad-leaved forests, shrublands, and herbaceous plants, all of which have distinct effects on basin runoff.For example, a 10% change in coniferous forest vegetation coverage can lead to an approximately 40 mm change in annual basin runoff.In contrast, broad-leaved forests and shrublands or herbaceous plants under the same conditions only result in changes of 25 mm and 10 mm, respectively (Guo et al., 2022).These differences are a major reason for the substantial variability in vegetation coverage regression coefficients in the source area.In regions where vegetation coverage coefficients approach 0, these areas are typically more arid due to insufficient precipitation and higher temperatures.Vegetation water requirements are not met, limiting plant growth and resulting in even scarcer regional runoff.This aligns with the findings of Sun et al. (2011), which emphasize the complexity of runoff generation and the varying impact factors affecting runoff depth in different regions of the Yellow River basin, characterized by substantial spatial heterogeneity.The Yellow River basin has shown a consistent trend of declining runoff over the years.Indiscriminate afforestation may exacerbate the tension in regional water resources.Therefore, this study suggests that afforestation projects like those carried out in the Yellow River basin should be tailored to specific regional conditions.
For instance, in arid regions in the northwest, drought-resistant vegetation like grasslands and windbreak shrubs should be prioritized (Fu and Burgher et al., 2015;Zhao et al., 2019).In areas with relatively abundant water resources in the south, converting high-altitude, steep-sloped farmlands into forests can enhance regional water retention and soil conservation capabilities, thereby positively influencing basin runoff levels (Yang et al., 2023).

Runoff Prediction under Future Climate Models
Previous studies have predominantly relied on basic data models for simulations.Yalcin (2023) utilized GCMs data in conjunction with the distributed hydrological model SWAT (Soil and Water Analysis Tool) and reported that, under the Delta downscaling scenario, future runoff is expected to decrease, with a 12.79% increase by 2080.In contrast, this study suggests that from 2020 to 2040, except for SSP245, the Yellow River source area runoff exhibits a decreasing trend in SSP126, SSP370, and SSP585.While this is broadly consistent with the former study, the extent of reduction differs.This variation may be attributed to the use of different models, as the previous study employed a distributed hydrological model, whereas this study used regression models.Furthermore, the application of different climate scenarios could also introduce variations.Zhou et al. (2023)  runoff changes, and its findings are in line with those of distributed hydrological models (Li et al., 2008;Li et al., 2012;Ji et al., 2021).The factors affecting runoff considered in this study are quite extensive, encompassing climate, vegetation, soil elements, and more.The developed regression model for the Yellow River basin's runoff demonstrates good simulation performance, allowing for pixel-level simulations of runoff's temporal and spatial changes using future climate models, combining precision with broad applicability.
. CMIP6 future precipitation data are based on down-scaled results from three climate models: ACCESS-ESM1-5, CESM2-WACCM, and IPSL-CM6A-LR.The subsequent research utilizes a multi-model ensemble (MME) dataset based on these three models.CMIP6 future temperature data are based on down-scaled results from three climate models: ACCESS-CM2, CESM2-WACCM, and NorESM2-LM.The subsequent research utilizes a multi-model ensemble average (MME) dataset based on these three models.CMIP6 future vegetation cover data are based on down-scaled results from the GFDL-ESM4 model and are used for subsequent research.CMIP6 future soil temperature data are based on down-scaled results from CESM2-FV2, CESM2-WACCM, and CESM2-WACCM-FV2 models.CMIP6 future soil moisture data are based on down-scaled results from CESM2-FV2, CESM2-WACCM-FV2, and MIROC6 models.
The predicted runoff depth patterns for the four climate scenarios exhibit a roughly similar distribution.The maximum runoff depth fluctuates between 661.46 and 837.84 mm (Figure10e, l).The upper Hetao Plain and regions such as Xiaheyuan to Shizuishan and Shizuishan to Toudaoguai are comparatively arid, with almost zero runoff depth.
adopted the VIC(Variable Infiltration Capacity Model)     to partition the Yellow River basin into grids and simulate large-scale hydrological processes.Their results closely matched the spatial distribution of actual runoff, with a mean relative error of -7.9% between calculated runoff and observed values, consistent with the conclusions of this study.Future runoff in the Yellow River basin displays an increasing trend from the northwest to the southeast.Nevertheless, the VIC model did not account for the influence of human activities on basin hydrology.In contrast, this study considered the spatial and temporal changes in runoff under various future climate scenarios and incorporated human activities into the analysis, making it more comprehensive and innovative in comparison.Based on the above research, traditional hydrological models have their limitations in forecasting runoff changes over a large area in the Yellow River basin.This study holds an advantage in simulating future

Figure 4
Figure 4 Surface pixel correlation coefficient based on PCA~MLR model.(a) The partial regression coefficient μ1 of the independent variable FVC obtained through PCA-MLR model calculation.(b) The partial regression coefficient μ2 of the independent variable precipitation.(c) The partial regression coefficient μ3 of the independent variable temperature.(d) The partial regression coefficient μ4 of the independent variable soil volumetric moisture content.(e) The partial regression coefficient μ5 of the independent variable soil temperature.(f) The constant term μ0.

Figure 5
Figure 5 Frequency distribution of each partial regression coefficient.(a) Constant term μ0; (b) FVC coefficient μ1; (c) Precipitation coefficient μ2; (d) Temperature coefficient μ3; (e) Soil water content coefficient μ4; (f) Soil temperature coefficient μ5, with interval distribution and the ratio of the number of pixels occupied.

Figure 6
Figure 6 Illustrates the predicted runoff depth distribution pattern in the Yellow River basin from 2000 to 2012 based on the PCA-MLR combined model.The panels labeled a through m correspond to the predicted runoff depth distribution patterns for the years2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, and 2012,   respectively.

Figure 9
Figure 9 Temporal variation trend of runoff depth under four future climate emission scenarios in the Yellow River Basin.

Figure 10
Figure 10 Spatial pattern of runoff depth at different time periods under four discharge scenarios in the Yellow River Basin.

Figure 11
Figure 11 Spatial pattern of runoff depth change rate at different time periods in the Yellow River Basin under four discharge scenarios.
Using the PCA principal component analysis method, it is possible to select the most significant variables from multiple variables, thus improving the accuracy of the linear regression simulation.Therefore, this study employs a combined PCA-MLR multivariate linear regression model and uses Python 3.8.2iterativecodefor pixel-wise computation on the Yellow River basin surface.Subsequently, the principal components obtained through PCA, namely F1, F2, ..., Fm, are used in linear regression with runoff data to estimate the coefficients β1, β2, β3, β4, β5.Ultimately, linear correlation coefficients μ1, μ2, ..., μn are derived to establish a predictive regression model for runoff, with the specific calculation process outlined in Figure2.Data from the 1982-1999 period are used for model prediction, while data from the 2000-2012 period are employed for validation.
3)where, α1 represents the predicted runoff coefficient in the PCA-MLR model; β0 is the intercept term; β1, ..., βm are the partial regression coefficients in MLR; μ0 is the intercept term, and μ1, ..., μm are the final regression coefficients for α1 with variables X1, X2, ..., Xm; F1, F2, ..., Fm are the independent variables, i.e., the first, second, ..., m th principal components.where,R,runoffdepth (mm), P, precipitation (mm), Xi, each of the influencing factors, including FVC, precipitation (mm), air temperature (℃), soil water content (%), soil temperature (℃), while μ0 and μi are coefficients.Due to the strong intercorrelations among the influencing factors of the runoff coefficient, establishing a direct relationship using a multivariate linear regression equation may result in data loss, leading to multicollinearity issues, creating spurious regressions, which are not conducive to the prediction of the runoff coefficient in the Yellow River basin.Therefore, this study adopts a combined PCA-MLR multivariate linear regression model to enhance prediction accuracy for the runoff coefficient in the Yellow River basin.The specific approach is as follows: firstly, principal component analysis (PCA) is used to reduce the dimensionality of the selected variables, transforming originally correlated variables into a few independent variables that capture the essential information.

Table 1
The variance of the common factors

Table 2
Results of the calculation of the three principal components for the years 1982 to 1999