Simulation of Spatial and Temporal Variations in the Water Yield Function in the Source Area of the Yellow River and an Analysis of Influencing Factors

Abstract

The Yellow River source area is an important eco-fragile and sensitive zone in the northeast of the Tibetan Plateau, where anthropogenic disturbances, climate change, and environmental problems have negatively affected the amount of water in the basin, which directly impacts the ecological security and high-quality sustainable development of the Yellow River Basin. Therefore, this study takes the Yellow River source area as its research area. Based on eight periods of land use from 1985 to 2020, topographic, soil, and meteorological data are combined, and a locally modified InVEST model and geological detector method are used to simulate watershed water production, evaluate the spatial differentiation characteristics of watershed water production, and analyze its spatial heterogeneity attribution. The results revealed that water production from 1985 to 2020 varied within the interval of 152.08–302.44 billion m³, with alternating decreases and increases and an overall upward trend. In the spatial distribution, the depth of water production is high in the east and low in the west, and the high-water-production area is concentrated in the counties of Maqin and Gande. In the vertical gradient, the water production capacity is strengthened with increasing altitudes. The spatial differentiation of the water production service and degree of influence is jointly determined by multiple factors. In this work, the parameter Z of the InVEST model was locally corrected to increase the applicability of the Z value to the Yellow River Basin to improve the accuracy of the simulation results, and the spatiotemporal differences in water yield from multiple perspectives were analyzed to provide a scientific basis for the ecological protection and high-quality sustainable development of the Yellow River Basin.

1. Introduction

Water resources, as an important part of an ecosystem, are essential natural resources for human survival, production, and life, as well as important resources for maintaining the stability of an ecosystem [1,2]. Globally, only 2.5% of the world’s total water resources can be utilized by human beings [3,4]. The International Conference on Water Resources (ICWR) predicts that the global demand for freshwater resources will increase by approximately 40% by the 2050s and that half of the human population will live in water-scarce areas [5]. Water scarcity has now become a major issue of global concern. China’s rapid social and economic development has caused a series of water environment problems, such as soil erosion [6] and water quality deterioration [7]. Coupled with people’s transformation of the ecosystem, water resources have become more vulnerable in response to the dual impact of climate change and human life [8], which ultimately weakens the capacity of ecosystem services. Water yield services play an important role in ecosystem services [9], and water yield service simulation, as a direct and effective method used to visualize the spatial and temporal changes in water yield in a watershed, is conducive to understanding the current situation of water resources, making this method highly important for maintaining ecological and water environment security.

There are abundant research results on water yield services, and scholars at home and abroad have analyzed the water yield services of ecosystems, forest ecological system water conservation, and the water resources of forests [10,11,12]. Additionally, researchers have investigated the water services of ecosystems and water conservation in forest ecosystems [13,14,15], and they have conducted quantitative assessments of ecosystem water yield services and water conservation in forest ecosystems, mostly adopting the material and value quantities [16,17] and the value [18,19] and value–quantity methods. However, the value and quantity assessment methods can only assess the value of each function of the ecosystem services, and there are deficiencies in the simulation and reproduction of the ecological processes of water yield services. With the development of 3S technology, and knowledge of ecosystem theory, models such as SWAT [20], WEP-L [21], SOFM neural networks [22], MIMES [23], ARIES [24], and other models [25,26,27] have begun to be applied in the field of ecosystem service water production simulation and prediction research. Currently, a variety of new models (Bayesian networks [28]) and programming techniques [29] have been used that have greatly improved application in terms of ecosystem services and sustainable development. Among the models that have been used, the InVEST model, which has a distributed algorithm of 3S technology, overcomes the limitations of traditional assessment methods and has become a new technical means for quantitative assessment, dynamic analysis, and the spatial expression of ecosystem service functions [30]. This model is the most mature, with low data requirements and few model parameters, and it has achieved extensive and reliable research results in the simulation and assessment of water yield services [31,32,33,34]. Most existing research has focused on analyzing the spatial and temporal changes in water yield services, and research on the impact mechanism of water yield is still insufficient. Among the existing methods used to assess the impact mechanism, the geographical detector method has high accuracy in regard to research on the driving mechanisms of multifactor interactions, and this method can be used to detect whether there is a link between influencing factors while also being able to comprehensively explain themultiple driving mechanisms of spatial variability. Thus, this method has been widely put to use in the characterization and attribution of spatial variability [35,36,37,38].

The source area of the Yellow River is the main water source of the Yellow River Basin [39]. The water security of the Yellow River source area plays an irreplaceable role in protecting the biodiversity of the Qinghai–Tibet Plateau, regulating the climate of the northwestern region of China and maintaining the water conservation ability of the watershed and the ecological balance of the plateau. The source area of the Yellow River is an important ecologically fragile and sensitive region in the northeastern part of the Tibetan Plateau, where anthropogenic disturbances, climate change, and environmental problems have negatively affected the water quantity of the basin, which directly affects the ecological security and quality development of the Yellow River Basin. Therefore, there is an urgent need to effectively model the water yield of the Yellow River source area and analyze its spatial heterogeneity. Research on the source area of the Yellow River has focused mostly on hydrology [40], vegetation [41], land use [42], etc., and research on the spatial distribution of water yield and its driving mechanisms is lacking. Therefore, the study optioned the source area of the Yellow River as the study area and used the InVEST model to simulate the water yield and spatial distribution characteristics in different periods on the basis of land use data from eight periods from 1985 to 2020; analyzed the different geographic subdivisions and different altitudes; and selected different influencing factors, such as topography, soil, climate, vegetation, and land use types, and combined them with the geographical detector multifactor interactive detection model to evaluate the spatial distribution of water yield and its driving mechanisms. Combined with the geographic detector multifactor interaction detection model, we assessed the spatial differentiation characteristics of water yield in the basin and analyzed the influencing factors to contribute to the ecological protection and high-quality development of the Yellow River Basin. In this work, the parameter Z of the InVEST model was modified locally to increase the applicability of the Z value to the Yellow River Basin to improve the accuracy of the simulation results, and the spatial and temporal differences in water production were analyzed from multiple perspectives. These efforts will provide a scientific basis to support the ecological protection and high-quality sustainable development of the Yellow River Basin.

2. Research Methodology and Data Sources

2.1. Overview of the Study Area

The source area of the Yellow River is located on the northeastern fringe of the Qinghai–Tibet Plateau in the hinterland of Qinghai. Its scope includes the Yellow River Basin above the Tangnaihe hydrological station, with a basin area of 122,000 km², and it is geographically located between 32°11′–36°50′ N and 95°53′–103°26′ E (Figure 1). It spans three provinces, Qinghai, Sichuan, and Gansu, from the southern slopes of Kunlun to the Buqing Mountains in the north, from the Bayan Kara Mountains in the south, and from the Yaladazhe Mountains in the west to the Animalqing Mountains in the east, with an altitude of generally above 3000 m [43]. It includes 18 counties in seven autonomous prefectures, namely Yushu, Guoluo, Hainan, Huangnan, Gannan, Ganzi, and Aba.

The source area of the Yellow River has a plateau continental climate, and the average long-term temperature is between −4 and 5 °C, of which the average daily temperature from May to September is more than 0 °C. Winters are cold, summers are cool, the warm season is short with abundant water vapor and precipitation, and the cold season is long [44]. The annual sunshine hours in the source area are high, between 2250 and 3131 h, with strong sunshine, strong radiation, and a large temperature difference between morning and evening. The long-term average precipitation in the source area is 200–800 mm and features an uneven distribution, with most precipitation being concentrated in the months of June–September. Finally, the average annual evapotranspiration is 600–1300 mm.

2.2. Research Methods

2.2.1. InVEST Water Yield Modeling

The spatial distribution of water yield in the source area of the Yellow River Basin was simulated with the help of the water yield module in the InVEST model. The module is based on the improved Budyko hydrothermal coupling equilibrium principle, and the annual-scale water yield value of each grid cell is calculated by subtracting the evapotranspiration from the precipitation, with reference to the calculation process of Daier Fu et al. [45]. The formula is as follows:

$$Y_{\mathrm{xj}}=\left(1-{\displaystyle \frac{AE{T}_{\mathrm{xj}}}{P_{\mathrm{x}}}}\right)\times P_{\mathrm{x}}$$

(1)

where Y_xj is the average annual water production of raster cell x on land cover type j; AET_xj is the annual actual evapotranspiration of land cover type j on raster x; and P_x is the annual precipitation on raster cell x. AET_xj/P_x is the ratio of the actual evapotranspiration to the precipitation, which is calculated on the basis of Zhang et al.’s [46] improved method on the basis of the Budyko curves with the following formula:

$${\displaystyle \frac{AE{T}_{\mathrm{xj}}}{P_{\mathrm{x}}}}={\displaystyle \frac{1+{\omega }_{\mathrm{x}}+R_{\mathrm{xj}}}{1+{\omega }_{\mathrm{x}}{R}_{\mathrm{xj}}+\left(1/R_{\mathrm{xj}}\right)}}$$

(2)

$${\omega }_{\mathrm{x}}=Z\times {\displaystyle \frac{PAW{C}_{\mathrm{x}}}{P_{\mathrm{x}}}}$$

(3)

$$R_{\mathrm{xj}}={\displaystyle \frac{{\mathrm{k}}_{\mathrm{ij}}\times E{T}_0}{P_{\mathrm{x}}}}$$

(4)

where R_xj is the Budyko drying index of raster cell x on land cover type j, called the ratio of potential evapotranspiration to precipitation; ω_x is the ratio of the annual available amount of modified vegetation to the expected precipitation; Z is the Zhang coefficient [46], which characterizes the seasonal factor of precipitation; k_ij is the coefficient of plant evapotranspiration, which is the ratio of the evapotranspiration of crops to the potential evapotranspiration; and ET₀ is the potential evapotranspiration. PAWC_x is the plant-available water content [47]. ET₀ and PAWC_x were calculated via Equations (5) and (6), respectively:

$$E{T}_0=0.0013\times 0.408\times RA\times \left(T_{\arg }+17\right)\times {\left(TD-0.0123P\right)}^{0.76}$$

(5)

PAWC_x = 54.509 − 0.132S_sa − 0.003(S_sa)² − 0.055S_si − 0.006(S_si)²

−0.738S_cl + 0.007(S_cl)² − 2.688S_om + 0.501(S_om)²

(6)

where RA is the solar atmospheric top radiation in MJ/(m²·d); T_arg is the mean of the average daily maximum temperature and the average daily minimum temperature in °C; TD is the difference between the average daily maximum temperature and the average daily minimum temperature in °C; P is the average monthly precipitation in mm/m; S_sa is the soil sand content in %; S_si is the soil chalk content in %; S_cl is the soil clay content (%); and S_om is the soil organic matter content (%).

The inputs to the water yield submodule of the InVEST model included root limiting layer depth data (soil depth in soil data), annual precipitation data, plant-available water content (PAWC) data, average annual potential evapotranspiration (ET₀) data, land use data, Qinghai Lake watersheds, subwatersheds, a list of biophysical parameters (

Table 1. Biophysical parameter Table.

LULC_desc	Lucode	Kc	Root_depth	LULC_veg
Cropland	1	0.542	2100	1
Forestland	2	0.81	5100	1
Grassland	3	0.563	2600	1
Shrubland	4	0.531	4000	1
Wetland	5	0.367	3000	1
Water	6	0.462	−1	0
Impervious surface	7	0.514	−1	0
Bareland	8	0.168	−1	0
Snow/Ice	9	0.344	−1	0

), and the value of the seasonal constant Z. The seasonal constant Z represents the rainfall seasonal constant of a study area, which is geographically specific. Therefore, the method is geographical, and it is not certain whether the model is applicable to our study area, so it is necessary to make localized corrections to the parameter Z. The value of Z needs to be adjusted and repeatedly calibrated in comparison with the predicted value and the observed value so that the simulation results can be more closely related to the study area and the results can be more scientific and accurate.

The biophysical parameters reflect the different attributes of the land use-type data. The lucode in the table is consistent with the land classification field in the land use raster data mentioned above, and the values of LULC_desc (name of the land use type), LULC_veg (vegetation cover code), and root depth (maximum rooting depth of the vegetation cover class) were obtained on the basis of a review of the various literature sources. The values of LULC_veg (vegetation cover code) and root_depth (maximum root depth of the vegetation cover class) were obtained from the literature, and the Kc coefficients were calculated according to the leaf area index (LAI). The leaf area index data were downloaded from the National Tibetan Plateau Science Data Center, and the evapotranspiration coefficient (KC) was calculated according to the formula in the InVEST model (version 3.2.0) [47], with values ranging from 0 to 1.5.

2.2.2. Geographical Detectors

The simulation results of the InVEST model can visualize only the results of water yield and its spatial and temporal variations, and the attribution of the obvious spatial heterogeneity of the simulation results cannot be explained. Therefore, to analyze the factors influencing water yield more comprehensively, it is necessary to analyze the factors influencing water yield with the help of a geo-detector model, which is a more mature spatial heterogeneity detection method. Geographical detectors are a statistical method used to detect spatial heterogeneity and reveal the spatial differentiation of each element, and this method was proposed by Wang Jinfeng et al. [48]. It consists of heterogeneity and factor detection, interaction detection, ecological detection, and risk detection, and studies the spatial heterogeneity phenomenon of elements from different perspectives according to different detection methods [45].

Divergence and factor detection: The spatial divergence of a given dependent variable Y and the extent to which a given independent variable factor X explains the spatial divergence of the dependent variable Y are detected. The model is then analyzed for the degree of explanation of the dependent variable Y by using the q value. The degree of explanation of the model is measured by the q value with the following formula [48]:

$$\mathrm{q}=1-{\displaystyle \frac{{\displaystyle \sum _{h=1}^L{N}_h{\sigma }_h^2}}{N{\sigma }^2}}$$

(7)

where h = 1, 2, … denotes the number of categorizations or stratifications of factor X, L denotes the total number of L layers (classes) of categorization or stratification of the factor, N_h and N denote the number of units within layer h and the whole region, respectively, and ${\sigma }_h^2$ and ${\sigma }^2$ denote the variance in water yield within layer h and the whole region, respectively. The q-value is the explanatory power (q × 100)% of the independent variable X on the spatial heterogeneity of the water yield Y, which takes the limit of [0, 1], and a greater value of q denotes a stronger explanatory ability, which indicates that Y’s spatial heterogeneity is more obvious. In the extreme case, q is 1, which means that factor X completely controls the spatial distribution of Y, and when q is 0, it means that factor X has no relationship with Y. The explanation of the spatial heterogeneity of water quantity Y is (q × 100%), which takes a value of [0, 1].

Ecological detector: A comparison is made to determine whether there is a significant difference in the degree of influence of two independent variables, factors X1 and X2, on the spatial differentiation of water yield Y. As measured by the F statistic, the formula is as follows:

$$F={\displaystyle \frac{N_{X1}\left(N_{X2}-1\right)SS{W}_{X1}}{N_{X2}\left(N_{X1}-1\right)SS{W}_{X2}}}$$

(8)

$$SS{W}_{X1}={\displaystyle \sum _{h=1}^{L1}{N}_h{\sigma }_h^2,} SS{W}_{X2}={\displaystyle \sum _{h=1}^{L2}{N}_h{\sigma }_h^2}$$

(9)

where N_X1 and N_X2 are the sample sizes of the two factors X1 and X2, respectively; SSW_X1 and SSW_X2 are the sums of the intrastratum variances of the strata formed by X1 and X2, respectively; and L1 and L2 are the numbers of strata of the variables X1 and X2, respectively.

Risk detector: The following equation is used to determine whether there is a significant difference in the mean value of an attribute between two subregions, and it is usually tested with a t statistic:

$${\mathrm{t}}_{{\overline{\mathrm{y}}}_{h=1}{-\overline{\mathrm{y}}}_{h=2}}={\displaystyle \frac{{\overline{Y}}_{h=1}-{\overline{Y}}_{h=2}}{{\left[\frac{V\mathrm{ar}\left({\overline{Y}}_{h=1}\right)}{{\mathrm{n}}_{h=1}}+\frac{V\mathrm{ar}\left({\overline{Y}}_{h=2}\right)}{{\mathrm{n}}_{h=2}}\right]}^{1/2}}}$$

(10)

where ${\overline{Y}}_h$ denotes the mean value of the attribute within stratum h, h denotes the amount of sample size within stratum h of the subregion, and Var represents variance.

Interaction detector: This detector assesses the explanatory ability of the independent variables X1 and X2 on the spatial differentiation of water yield Y when they act simultaneously or when the effects of factors X1 and X2 on Y are independent of each other. The interaction types are as follows: if q(X1 ∩ X2) < min(q(X1), q(X2)), it indicates nonlinear weakening; if min(q(X1),q(X2)) < q(X1 ∩ X2) < max(q(X1), q(X2)), it indicates one-way nonlinear weakening; if q(X1 ∩ X2) > max(q(X1), q(X2)), it indicates two-way enhancement; if q(X1 ∩ X2) = q(X1) + q(X2), it means that the two independent variables are independent; and if q(X1 ∩ X2) > q(X1) + q(X2), it indicates a nonlinear enhancement.

In this work, the water yield of the Yellow River source area was selected as the dependent variable Y, and geographical detectors were used to determine its influencing factors in different subdivisions. The influencing factors included topography, climate, soil, vegetation, land use, and other elements (

Table 2. Impact factors of water yield and service space differentiation in the Yellow River source area.

Typology	Norm	Data Type	Typology	Norm	Data Type
Situation	Average annual temperature	Progression	Land use	Land use type	(Math.) discrete
	Total annual precipitation	Progression		SHDI	Progression
	Average annual potential Evapotranspiration	Progression		CONTAG	Progression
Topography	Altitude (e.g., above street level)	Progression		MESH	Progression
	Elevation	Progression		PLAND1	Progression
Ground	Soil type	(Math.) discrete		PLAND2	Progression
Plant cover	NDVI	Progression		PLAND3	Progression
				PLAND4	Progression

Note: SHDI denotes the Shannon diversity index, CONTAG denotes the spreading degree index, MESH denotes the effective particle size, PLAND1 denotes cropland, PLAND2 denotes forested grassland, PLAND3 denotes water bodies and wetlands, and PLAND4 denotes snow and ice.

). For the land use factors, the landscape indices were selected from the SHDI, CONTAG, MESH, and PAND indicators related to the composition and structure of land use [45], and all the landscape indices were calculated via the “sliding window” function in Fragstats 4.2 software. For the construction of the interconnected fishing net, 30,570 points were generated at 2 km × 2 km intervals for multifactor spatial correlation.

2.3. Data Sources and Processing

According to the data requirements of the InVEST model and geographical detector model, the data sources used in this study included digital elevation model (DEM) data, land use data, soil data, meteorological data, administrative boundary data from the Yellow River source area, normalized difference vegetation index (NDVI) data, meteorological station data, and hydrological data. Meteorological data, including attribute data such as temperature, precipitation, humidity, sunshine, and wind speed, were obtained from the China Meteorological Science Data Sharing Service (http://data.cma.cn/, accessed on 3 July 2024). The precipitation attribute data were combined with the data from the 28 meteorological stations selected in the study area to obtain raster data with a 1000 m resolution after ArcGIS interpolation, and the meteorological data were combined with the data from the 28 meteorological stations through the improved Penman–Monteith model to simulate the annual average potential evapotranspiration [49] and then interpolated via ArcGIS to obtain the ET₀ raster data with a 1000 m resolution. The DEM, soil data, and meteorological station data were obtained from the Data Center for Resource and Environmental Sciences of the Chinese Academy of Sciences (http://www.resdc.cn, accessed on 3 July 2024). The DEM was extracted from the subwatersheds of the study area after a hydrological analysis. The soil data included the soil depth, soil texture, soil organic matter content, and soil bulk weight, which were calculated via empirical formulas [50]. The plant-available water content (PAWC) was calculated. The finished land use data were obtained from the National Tibetan Plateau Science Data Center (http://data.tpdc.ac.cn/zh-hans/, accessed on 3 July 2024), which classifies land use into nine major categories. The hydrological data were mainly used for the validation of the simulation results of the water yield submodule and were obtained from the 1997–2020 runoff data in the Qinghai Water Resources Information Network-Qinghai Water Resources Bulletin (http://slt.qinghai.gov.cn/subject/list?cid=58, accessed on 3 July 2024). The spatial parameter data of the above water yield model were set to a 1000 m resolution with the geographic coordinates of Krasovsk_1940_Albers (

Table 3. Primary data sources in the research area.

Data Type	Resolution/Scale	Specification	Data Description	Data Sources
Meteorological data	Hagrid’s point (math.)	Checkpoint	Temperature, precipitation, humidity, sunshine, wind speed	China Meteorological Science Data Sharing Service Network (http://data.cma.cn/, accessed on 3 July 2024)
DEM	30 m × 30 m	Raster	Digital elevation model (DEM)	Geospatial data cloud (https://www.gscloud.cn/search, accessed on 3 July 2024)
Land use data	30 m × 30 m	Raster	Data on finished land use types	National Tibetan Plateau Science Data Center (http://data.tpdc.ac.cn/zh-hans/, accessed on 3 July 2024)
Soil data	1000 m × 1000 m	Raster, nc	Soil texture, soil depth	Data Center for Resource and Environmental Sciences, Chinese Academy of Sciences (http://www.resdc.cn, accessed on 3 July 2024) Cold and Arid Regions Data Center
NDVI	1000 m × 1000 m	Raster	Vegetation index	National Tibetan Plateau Science Data Center (http://data.tpdc.ac.cn/zh-hans/, accessed on 3 July 2024)
LAI	30 m × 30 m	Raster	Leaf area index (LAI)	National Tibetan Plateau Science Data Center (http://data.tpdc.ac.cn/zh-hans/, accessed on 3 July 2024)
Real-time data		Pdf, xls		Qinghai Water Conservancy Information Network and other website supplements

).

2.4. Localization Correction of Model Parameters

In the InVEST water yield module, there is regionality, and the parameter Z value represents the seasonal constant while the value range is 1–30. For every set Z value, the results of the operation are inconsistent. On the basis of the data from the Yellow River source area, data integration and model operation were carried out, and the results were verified by comparison with the measured data from the Qinghai Province Water Resources Bulletin to localize the model parameters. The specific process is as follows: the simulation process of the Yellow River source area watershed took the precipitation and potential evapotranspiration data from 1994 to 2020 as the main driving data; the land use data from 2000 to 2015 were used as the auxiliary variable data; and the plant-available water content, soil depth, source area of the Yellow River watershed, source area of the Yellow River subwatershed, and biophysical parameter table were used as constant quantities. The simulation of water yield was carried out many times to calculate the average water yield. The measured precipitation data from 1994 to 2020 were downloaded from the Water Resources Bulletin of Qinghai Province for the purpose of validating the results and determining the Z parameter. By observing the actual precipitation modulus from 1994 to 2020, the years 1995, 2000, 2005, 2010, 2015, 2020, etc. were divided into two combinations, and combinations between different years were made after several repeated attempts. All the combinations of the results were entered into the model one-by-one to simulate the water yield. The result of each simulation was compared with the actual precipitation modulus for validation, and the best combination of years was selected. The years 1994–2020 were divided into two periods, 1994–2011 and 2012–2020, with the first period being used to calibrate the Z value and the second period being used to verify the accuracy of the Z value. When the calibration Z value was 14.935, the simulated water yield modulus for 1994–2011 was in relative accord with the measured water yield modulus, with a relative error of only 5.25%, and the simulated water yield modulus for 2012–2020 had an error of 5.92% with the actual water yield modulus. When multiple calibration values and validation results were compared, the water production module of the InVEST mold had the best simulation effect in the source area of the Yellow River watershed when Z = 14.935.

2.5. Validation of the Water Yield Model Results

In this work, the Z value was rate determined, and the simulation effect was best in the source area of the Yellow River when the Z value was 14.935. The adjusted Z value was substituted into the source area of the Yellow River to simulate the water yield in 8 periods, and the simulation results were compared with the runoff of Longyangxia Reservoir to verify the accuracy of the simulation results. As shown in

Table 4. Verification of the water yield simulation results.

Watershed	Year	Simulated Water Yield/Billion m3	Actual Water Yield/Billion m3	Relative Error/%
Yellow River source area	1985	270.50	-	-
	1990	152.08	-	-
	1995	198.12	181.80	8.98%
	2000	182.73	166.00	10.08%
	2005	302.44	264.94	14.15%
	2010	210.28	229.44	8.35%
	2015	162.09	177.40	8.63%
	2020	269.16	298.54	9.84%

, the InVEST model had good simulation accuracy and could better reflect the temporal and spatial changes in water yield in the source area of the Yellow River.

3. Analysis of Results

3.1. Spatial and Temporal Distributions of Water Yield Services in the Yellow River Source Area

3.1.1. Characteristics of Temporal Changes in Water Yield

The time changes shown in Figure 2 and

Table 5. Statistical table of relevant water yield data in the study area.

Shore	Year	Water Yield/Billion m3	Average Depth of Water Yield/mm	Annual Precipitation/mm	Average Potential Evapotranspiration/mm
Yellow River source area	1985	270.50	226.04	589.84	618.33
	1990	152.08	127.09	484.15	651.22
	1995	198.12	165.56	529.14	640.42
	2000	182.73	152.70	516.62	642.02
	2005	302.44	252.73	627.52	629.65
	2010	210.28	175.72	567.55	683.64
	2015	162.09	135.45	510.15	666.95
	2020	269.16	224.92	598.98	648.19

indicate that the depth of the water yield in the source area of the Yellow River Basin changed in the interval of 0–903.10 mm, the average water yield depth changed in the range of 127.09–252.73 mm, and, in 2020, the high-value area increased by 78.40mm compared to 1985, an increase of 9.28%. Moreover, the average water yield depths in 1985, 1990, 1995, 2000, 2005, 2010, 2015, and 2020 were 226.04 mm, 127.09 mm, 165.560 mm, 152.70 mm, 252.73 mm, 175.72 mm, 135.45 mm, and 224.92 mm, respectively, and the water yield depth revealed that the depth of produced water first showed a “W”-type trend of decreasing, then increasing, then decreasing, then increasing, and then basically flattening overall. From 1985 to 2000, the depth of the produced water decreased by 80.4 mm, with a rate of decrease of 5.03 mm/a, which was relatively low. From 2000 to 2020, the depth increased by 158.80 mm, the rate of increase was 7.94 mm/a, and the growth rate was relatively low. As shown in Table 5, the total amount of water yield varied from 15.208 to 30.244 billion m³. The trend in water yield fluctuated greatly, with a “W + V” pattern of alternating downward and upward trends, but the amount of water yield was basically the same throughout the study period. The water yield volume decreased to the lowest level in 1990 and then continued to increase until it reached the highest level in 2005, began to decline from 2005 to 2015, and then rapidly increased to the same level as that in 1985 from 2015 to 2020, reaching 26.916 billion m³. Overall, the water yield volume basically remained unchanged, the water yield volume was relatively high in 2005, and the water yield depth was relatively high. The water yield depth was 842.20 mm and the water yields in 1990 and 1995 were low. The water yield depth was between 100 and 200 mm.

3.1.2. Spatial Distribution of Water Yield

To better understand the change in the space distribution of the water yield services in the source area of the Yellow River, a spatial distribution map of the change in water yield in the source area of the Yellow River from 1985 to 2020 was drawn via ArcGIS 10.2 software.

The spatial distribution pattern of the water yield depth in the Yellow River source area during the period of 1985–2020 was not very obvious, and it was high in the east and low in the west (Figure 3). During the study period, the high-value areas of water yield depth were concentrated in the Maqin, Gande and Jiuzhi counties in the south central region of the Yellow River source area basin in Guoluo Prefecture and Maqu County in Gannan Prefecture in the east; in contrast, the counties of Qumalai and Chenduo in Yushu Prefecture and Shiqu County in Ganzi Prefecture were the low-value areas, and the remaining counties were the second-highest value areas of water yield depth. The interannual changes in water-producing depth showed an overall increasing trend, with increasing trends in water-producing depth from 1990 to 1995, 2000 to 2005, and 2015 to 2020 and decreasing trends in water-producing depth from 1985 to 1990, 1995 to 2000, and 2005 to 2015. The highest interannual water yield depth peaked in 2020, with 903.10 mm of precipitation, the lowest value occurred in 2015, with 681.80 mm of precipitation, and the other years fluctuated between these values.

3.1.3. Vertical Gradient Changes in Water Yield

To analyze the differentiation law of the water yield function in the vertical gradient of the study area, this paper analyzed the area share of different reported heights, and the average water yield depth of different elevations, in the source area of the Yellow River with the help of the ArcGIS software partitioning statistical tool.

Using an elevation interval of 100 m for the average value of the 1985–2020 water yield depth statistics, the water yield capacity was analyzed in terms of the vertical gradient changes. The results revealed that the overall variation in the vertical gradient of land use and water yield (i.e., altitude) from 1985 to 2020 was positively correlated with water yield capacity; that is, with increasing altitudes, the average water yield depth increased (Figure 4). The relationships between the average water yield depth and land use type were as follows: the water yield depth in the region below 3500 m above sea level remained at a relatively low level, the distribution of grassland area in this region was the lowest among regions, cultivated land was concentrated in this region, and there was a small distribution of bare land and water bodies. The land use type in this region was more diverse, the vegetation cover increased, and the surface evapotranspiration increased significantly, resulting in the water yield depth maintaining a low level. At altitudes of 3500–5000 m, cultivated land area disappeared, there was a reduction in water bodies, the woodland distribution was small, and some unutilized bare land and a small number of glaciers began to appear. Grassland was dominant in this region, making a significant contribution to water yield, and the water yield in this region gradually increased. Above 5000 m above sea level, as the proportion of bare land and snow/ice area gradually expanded, the area of grassland gradually decreased until it disappeared, and the average water yield depth also tended to increase but then decreased. The source area of the Yellow River was more strongly affected by human activities and climate change below 3500 m, and there should be a stronger intensity of carrying and storing water as the intensity of human activities decreases above 3500 m, while the effect of climate warming may promote warming and humidification, which would increase the water yield. Above 5000 m, glaciers were dominant, and, with increasing temperatures, warming, and humidification, the accelerated melting of glaciers should result in an increased water yield.

3.2. Analysis of the Drivers of Water Yield Services

3.2.1. One-Way Attribution of Spatial Differences in Water Yield Services

The degree of influence of each factor on the spatial distribution of water yield services at the basin scale in the Yellow River source area from 1985 to 2020 (Figure 5) revealed that the explanatory ability of precipitation on the spatial heterogeneity of water yield services was the highest, with a q value that fluctuated between 66% and 80%, which was much greater than the explanatory power of any other factor. Precipitation was followed by the soil type, with a q value between 40% and 45%. The explanatory power of the NDVI in the source area of the Yellow River was obvious, and its explanatory power was ranked third, with an explanatory power of 20–35%. The factors with an explanatory power between 10% and 20% were next, and their effects on the spatial heterogeneity of the water yield service were reduced in the metrics, actual annual evapotranspiration, mean annual temperature, and elevation. Among the factors with explanatory power < 10%, the q-value of land use type and slope is the highest. The difference between the two methods was not obvious. The explanatory power of the landscape pattern factor was extremely weak, and its influence on the spatial differentiation of water yield services was extremely low. As shown by the values of the explanatory power of the indicator factors (

Table 6. Single factor explanatory power q values in the source area of the Yellow River.

Shore	Indicator Factors	1985	1990	1995	2000	2005	2010	2015	2020
Yellow River source area	Average annual temperature	0.117	0.173	0.102	0.101	0.1	0.121	0.152	0.182
	Total annual precipitation	0.71	0.748	0.737	0.661	0.666	0.64	0.503	0.805
	Average annual potential Evapotranspiration	0.134	0.195	0.125	0.127	0.13	0.168	0.169	0.197
	Altitude (e.g., above street level)	0.116	0.16	0.108	0.098	0.122	0.163	0.145	0.192
	Elevation	0.059	0.018	0.041	0.043	0.058	0.038	0.06	0.035
	Soil type	0.441	0.403	0.416	0.407	0.448	0.404	0.442	0.424
	NDVI	0.247	0.27	0.256	0.176	0.204	0.205	0.108	0.353
	Land use type	0.052	0.055	0.04	0.061	0.061	0.078	0.116	0.031
	SHDI	0.042	0.05	0.034	0.038	0.025	0.05	0.07	0.012
	CONTAG	0.032	0.021	0.015	0.017	0.031	0.012	0.06	0.02
	MESH	0.009	0.009	0.01	0.016	0.003	0.002	0.003	0.009
	PLAND1 (cropland)	0.01	0.012	0.015	0.015	0.023	0.01	0.023	0.093
	PLAND2 (Forest Lawn)	0.035	0.043	0.056	0.056	0.056	0.07	0.056	0.004
	PLAND3 (water bodies)	0.008	0.004	0.009	0.004	0.008	0.008	0.008	0.007
	PLAND4 (Ice and Snow Land)	0.006	0.002	0.008	0.008	0.008	0.009	0.008	0.005

), the explanatory power of the climate factor was the strongest, and there is a significant difference in the influence between its factors, with annual total precipitation > annual actual evapotranspiration > annual mean temperature. The soil type factor, which has an important influence on the amount of water yield, was ranked second in the order of the total factors, with a strong explanatory power. The NDVI, which ranked third in the order of the total factors, had a strong explanatory power, indicating that vegetation was the most important factor affecting the spatial variability of water yield services. The stronger explanatory ability indicated that vegetation cover had different effects on water yield services in different regions; in contrast, the land use type and landscape pattern index factors had less influence on the spatial variability in water yield.

The explanatory power of the factors influencing the spatial differentiation of water yield in the counties within the source area of the Yellow River Basin also revealed high variability in terms of the categories and degree of influence (Figure 6). For example, in counties with relatively low terrains, such as Tongde, Zeku, Guinan, Henan, Luqu, Ruoergai, and Aba, the most important explanatory ability of factors is annual actual evapotranspiration, with an explanatory power as high as 87%, whereas the explanatory power of the annual actual evapotranspiration in the higher-altitude county of Chengduo was as low as less than 10%. In the higher-elevation counties of Qumalai, Chengduo, Maduo, and Dari, the highest explanatory power was obtained for annual total precipitation, but the maximum explanatory power was only 63%. The explanatory power of the elevation factor was most prominent in the Hongyuan and Xinghai counties, where the topography is more undulating, with an explanatory power of 70%. The soil type had the strongest explanatory power in Jiuzhi County, where the Ba Yan Ka La Mountains run through the whole territory, with an explanatory power of 37%. In regard to comprehensive analysis, the explanatory ability of the subcounty-scale factors was similar to that of the Yellow River source area basin scale, and the explanatory power of the climate type factors was also dominant, with precipitation and actual evapotranspiration contributing the most, while the q value of the air temperature was smaller. Compared with the Yellow River source area watershed scale, the explanatory power of temperature improved, becoming the main control factor in Shiqu County and the second control factor in the counties of Aba, Gande, Guinan, and Luqu. The explanatory power of the soil type factor significantly decreased, becoming the main control factor in Jiuzhi County, but it was lower among the control factors in other counties. Among the land use factors, the explanatory power of land use type was the highest, but the explanatory power of all the landscape pattern indices was limited, with values of less than 5%. Thus, it can be concluded that the annual actual evapotranspiration was the main controlling factor affecting the spatial differentiation of water yield in the counties with gentler topography in the northeast direction of the source area, and the gap between the explanatory power and its remaining factors was large. With the increase in topographic relief and the complexity of topography and landscape, the annual total precipitation had the strongest explanatory power, the explanatory power of precipitation was slightly greater than that of soil type, and the influence of temperature on water yield services was slightly greater. As the complexity of topography and geomorphology increased, in the high mountainous areas (Maqin and Jiuzhi counties), soil type and elevation surpassed other factors to become the most influential factors affecting the spatial variability of water yield, the explanatory power of actual annual evapotranspiration slightly decreased, while temperature and precipitation also jointly controlled the water yield service.

The main controlling factor of the spatial differentiation of water yield in the source area of the Yellow River also differed at different altitudes with less variability. Precipitation was still the main controlling factor, followed by soil type, which was consistent with the performance of the influencing factors in the whole basin (Figure 7). At the low altitudes of 2600–3000 m, the annual mean temperature, annual actual evapotranspiration, and elevation were ranked as the first, second, and third controlling factors affecting the spatial variability of water yield, respectively. The lower altitudes and higher temperatures in this region increased the evapotranspiration of water and dense vegetation, and the vegetation type and root depth directly affected the evapotranspiration coefficient of the vegetation, indirectly affecting the spatial variability of water yield; as a result, the temperature and actual evapotranspiration became the controlling factors in this area. The four altitudes of 3000–3400 m, 3400–3800 m, 3800–4200 m, and 4200–4600 m had the same influencing factors, and the first, second, and third controlling factors were the total annual precipitation, soil type, and NDVI. The vegetation gradually decreased, the evapotranspiration coefficient of the vegetation decreased, and these decreases were accompanied by an increase in precipitation at these altitudes. The complex topography of these regions, such as the alpine faults and sedimentary landforms, and the abundance of soil types, resulted in an obvious increase in the explanatory ability of soil types. The explanatory power of the land use type factor increased significantly in the high-altitude region from 4600 to 6100 m. In the high-altitude region from 4600 to 5000 m, the total annual precipitation, soil type, and land use type affected the spatial differentiation of water yield services. The higher altitude, lack of vegetation, and increased snow and ice cover in this region increased the evapotranspiration of water vapor, increasing the effect of actual evapotranspiration on the spatial differentiation of water yield. In the high-altitude region of 5000–6100 m, the annual total precipitation, annual average temperature, and land use type were influential factors affecting the spatial differentiation of water yield services. The land use type in this region was mainly snow and ice, and, in addition to precipitation as the main source of water yield, glacial meltwater mainly controlled the amount of water yield, making land use type the most influential factor. Throughout the different altitudes, the influence of the factors of the landscape pattern index on the spatial distribution of water yield services was extremely limited and negligible.

3.2.2. Interaction of Factors Influencing the Spatial Differentiation of Water Yield Services

Factor differentiation and interaction detection also confirmed that in the source area of the Yellow River Basin, and in subdivisions with different scales, the effect of factor interaction on the spatial distribution pattern of water yield was much greater than that of a single factor independent effect, and the interaction performance included both two-factor enhancement and nonlinear enhancement (

Table 7. Interaction detection results of water yield service influencing factors in different regions of the source area of the Yellow River.

Zoning	Main Interactions
Source area of the Yellow River Basin	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Aba County	Precipitation ∩ potential evapotranspiration	Potential evapotranspiration ∩ temperature	Precipitation ∩ Elevation
Chengduo County	Precipitation ∩ Temperature	Precipitation ∩ potential evapotranspiration	Precipitation ∩ Elevation
Dari County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Gande County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Guinan County	Precipitation ∩ potential evapotranspiration	Temperature ∩ potential evapotranspiration	Potential evapotranspiration ∩ soil type
Henan County	Precipitation ∩ potential evapotranspiration	Precipitation ∩ Elevation	Temperature ∩ precipitation
Hongyuan County	Elevation ∩ land use type	Potential evapotranspiration ∩ land use type	Temperature ∩ land use type
Jiuzhi County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Lvqu County	Potential evapotranspiration ∩ elevation	Temperature ∩ potential evapotranspiration	Potential evapotranspiration ∩ land use type
Maduo County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ land use type
Maqin County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Maqu County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Qumalai County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Potential evapotranspiration ∩ land use type
Ruoergai County	Potential evapotranspiration ∩ land use type	Temperature ∩ land use type	Elevation ∩ land use type
Shiquan County	Precipitation ∩ potential evapotranspiration	Precipitation ∩ Elevation	Temperature ∩ precipitation
Tongde County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
Xinghai County,	Elevation ∩ land use type	Potential evapotranspiration ∩ land use type	Temperature ∩ land use type
Zeku County	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
2600–3000	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ Elevation
3000–3400	Precipitation ∩ potential evapotranspiration	Precipitation ∩ Soil type	Precipitation ∩ land use type
3400–3800	Precipitation ∩ potential evapotranspiration	Precipitation ∩ Soil type	Precipitation ∩ land use type
3800–4200	Precipitation ∩ potential evapotranspiration	Precipitation ∩ land use type	Temperature ∩ precipitation
4200–4600	Precipitation ∩ potential evapotranspiration	Temperature ∩ precipitation	Precipitation ∩ land use type
4600–5000	Precipitation ∩ potential evapotranspiration	Precipitation ∩ land use type	Temperature ∩ precipitation
5000–6100	Precipitation ∩ land use type	Precipitation ∩ Soil type	Temperature ∩ precipitation

). Among the types of factor interactions, the interaction between climate factors had the most significant effect, and the interaction between precipitation and actual evapotranspiration had the largest explanatory power of 96% in the whole watershed and each subregion, playing the most dominant role in the spatial differentiation of water yield services. This result indicates that, at the same zonal scale, even if precipitation (actual evapotranspiration) is similar, differences in actual evapotranspiration (precipitation) significantly enhance the spatial differentiation of water yield. Second, regarding the interaction of climate factors with soil type and land use type, in different subzones, the combination of interacting factors varied according to the regional characteristics of each subzone. For example, in Ruoergai County, which is rich in topography and geomorphology, the interactions of elevation, actual evapotranspiration, and temperature with land use type were significant and differed from those in other regions. Climate factors superimposed on land use type and soil type played the second and third most dominant roles in the spatial differentiation of water yield services, respectively. In the whole source area of the Yellow River Basin, the interaction between precipitation and elevation had a high impact, with an explanatory power of between 80% and 90%. In different county subdivisions, the explanatory power of the interaction between the factors exhibited different variabilities, and the interaction between actual evapotranspiration and land use type was significantly greater in the Hongyuan and Xinghai counties than in the Luqu and Qumalai counties. At different altitudes, the interaction types of the spatial differentiation of water yield services were complex, with temperature, precipitation, actual evapotranspiration, soil type, land use type, etc. influencing each other, and the interaction between temperature and precipitation was the most significant, with an explanatory power of between 78% and 93%. Climate-type factors, importantly, influenced the spatial differentiation of water yield services in the watershed of the Yellow River source area.

4. Conclusions and Discussion

4.1. Discussion

The high-altitude, more complex and variable topography and richer soil types in the source area of the Yellow River increased the difficulty of attributing spatial heterogeneity in water yield to some extent. In this work, when the spatial distribution of water yield in the source area of the Yellow River Basin was simulated via the water yield module of the InVEST model, the value of the constant Z was calibrated and verified locally several times. Finally, the best value was obtained for the simulation, and the result was in line with the actual situation. In this work, we used the geoprobe method to identify the factors influencing the spatial differentiation of water production functions, and the results showed that both single factor analysis and multifactor interaction analysis indicated that climate-like factors were the main drivers affecting the spatial heterogeneity of water production, which was consistent with the results of existing studies [51,52]. However, the explanatory power of the landscape indices on the spatial variation in the water yield function was extremely limited in this paper, which was consistent with existing studies [53,54], showing that landscape patterns have some facilitating or inhibiting effects on the expression of ecosystem services. The results further provide a theoretical basis for the hypothesis that “this inconsistency may be related to the study scale” [45]. Future research should focus on the effect of land use landscape structures on the spatial heterogeneity of water production services to reveal the link between the spatial differentiation of water production services and landscape index factors.

Checking the relevant data of the Yellow River source area, in 1980, the source area of the Yellow River experienced consecutive dry years, and the precipitation was approximately 20% less than that of normal years [55]. The dry years in the source area and the decrease in precipitation led to a decrease in water yield but not an increase. Since the 1990s, warm temperatures have increased evaporation loss and the difference in the intra-annual precipitation distribution, which has led to an intermittent dry phenomena and intermittent increases and decreases in water yield, verifying that the simulation results of the 1990–2000 water yield results were correct. Afterward, anthropogenic management of the Yellow River source area increased, the ecological environment improved, and the dry water phenomenon began to improve in 2000. In 2003, the runoff at each hydrological station in the source area rapidly increased [56], so the water yield rapidly increased to its peak value in 2005. Owing to the 2004–2010 construction of Zhaling Lake, Eling Lake, and other small- and medium-sized lakes, the lake surface rapidly expanded [57]. From 2010 to 2015, the areas of Zhaling Lake, Eling Lake, and other small- and medium-sized lakes tended to be stable, and the decline in water yield tended to be flat [57], which was consistent with the simulation results from 2005 to 2015. After 2015, the drying phenomena disappeared, the area of the lakes was basically stable, the precipitation increased compared to that of a normal year, and the water yield began to rebound. The above information shows that the simulation results were related to climate change in the source area of the Yellow River, which confirms the credibility of the simulation results.

4.2. Conclusions

(1) From a temporal perspective, the variation range of water production depth in the Yellow River source area from 1985 to 2020 was 0–903.10 mm, with the high-value area rising by 78.40 mm, an increase of 9.28%, and the average water yield depth varying from 127.09 to 252.73 mm, with a tendency to decrease, increase, decrease, and then increase, while the overall water yield depth was basically flat. The average water yield depth varied from 127.09 to 252.73 mm. The total amount of water produced varied from 152.08 to 302.44 billion m³, and the trend in water yield was more obvious, with alternating downward and upward trends.

(2) In terms of spatial distribution, the spatial distribution pattern of water production depth in the Yellow River source area during the research period mainly shows that it is higher in the east and lower in the west. The areas with high water-producing depths are concentrated in the counties of Maqin, Gande, and Jiuzhi in the central southern Yellow River source area in Guoluo Prefecture and in Maqu County in Gannan Prefecture, east of the Yellow River source area. Maduo County in Guoluo Prefecture, the Qumalai and Chengduo counties in Yushu Prefecture, and Shiqu County in Ganzi Prefecture are areas with low water-producing depths, whereas the remaining counties are areas with the second-highest water-producing depths, and the overall interannual variation in water-producing depth shows an increasing trend.

(3) The overall change in water yield in the source area of the Yellow River watershed along the vertical gradient from 1985 to 2020 revealed that elevation was positively correlated with water yield capacity; that is, with increasing elevation, the average water yield depth gradually increased. The relationship between the average water yield depth and land use type was maintained at a low level in the low elevation area. With increasing elevation, decreasing vegetation, and the appearance of glaciers, the average depth of water yield tended to increase and then decrease.

(4) In terms of single-factor effects, the Yellow River source area has the strongest explanatory ability for climate-like factors at the basin scale, and there are significant differences, especially for precipitation, which is the most significant; additionally, the explanatory power of the landscape indicator factors is extremely weak, both overall and within the subregion. The main controlling factors of the spatial differences in water production in the source area of the Yellow River also differed at different altitudes, with less variability. At low elevations, the mean annual temperature, actual annual evapotranspiration, and elevation were the first, second, and third controlling factors influencing the spatial divergence of water yield, respectively; the 3000–4600 m altitude had the same influencing factors; and the first, second, and third controlling factors were total annual precipitation, soil type, and the NDVI. At altitudes above 4600 m, total annual precipitation and land use type became influential factors affecting the spatial differentiation of water production services. Throughout the different elevations, the explanatory power of the landscape pattern index factors for the spatial distribution of water production services was more limited.

(5) The results of multifactor interaction detection revealed that the degree of influence of the spatial differentiation of water yield services was determined by the joint effects of multiple factors. In both the Yellow River source area and each subarea, the explanatory power of the interaction between precipitation and actual evapotranspiration was dominant, followed by the interaction between climate-type factors, soil type, and land use type. In different subregions, the combination of interacting factors varied according to the regional characteristics of each subregion, but the climate-like factors superimposed on other factors were ranked second and third in terms of their dominant roles in the spatial differentiation of water yield services in the source area. Climate factors also played an important role in the spatial differentiation of water yield services in the Yellow River source area basin.

(6) To improve the water yield of the Yellow River Basin, according to the results of the study, the water yield is high in the east and low in the west, the upstream areas of the source area of the Yellow River should be protected, excessive agricultural irrigation should be controlled as much as possible, the interference of human beings in the amount of water consumption should be reduced, the pollution of the water source caused by the use of agricultural fertilizers should be controlled, and the relevant parts of the country should formulate a relevant strategy for the protection of water resources in the Yellow River Basin.