Assessment and Enhancement of Ecosystem Service Supply Efficiency Based on Production Possibility Frontier: A Case Study of the Loess Plateau in Northern Shaanxi

Abstract

Enhancing the supply efficiency of ecosystem services plays a central role in improving both natural ecosystems and human well-being. Taking the Loess Plateau of Northern Shaanxi as an example, this study utilizes InVEST to assess the ecosystem services of water yield and habitat quality. The optimal solutions for the combination of these two services are calculated on the basis of the Pareto principle. The production possibility frontier curves for the two services are fitted, and the services’ supply efficiency is measured. Furthermore, this study employs ordinary least squares and geographically weighted regression to analyze the dominant factors affecting supply efficiency. The results comprise the following findings: (1) There are eighteen solutions representing the optimal combinations between the two services. (2) The supply efficiency of the two services increases from northwest to southeast in spatial distribution. (3) The dominant factors vary among different zones of supply efficiency. Population, hydrology, and gross domestic product (GDP) are the dominant factors in the general-efficiency, sub-low-efficiency, and low-efficiency supply zones, respectively. Hydrology, NDVI, and GDP are the dominant factors in the sub-high-efficiency supply zone, while GDP, terrain, and population are the dominant factors in the high-efficiency supply zone. In conclusion, this paper proposes recommendations for reducing trade-offs and enhancing supply efficiency between ecosystem services. These include dynamic supervising for the high-efficiency supply zone, moderate greening in the sub-high-efficiency supply zone, stabilizing the population in the general-efficiency supply zone, and reducing development intensity in low- and sub-low-efficiency zones. The study reveals the potential and approaches for improving the supply of ecosystem services and offers guidance for formulating ecological protection plans.

1. Introduction

The ecosystem is not only the Earth’s support system but also the foundation on which humans depend for survival [1]. Ecosystem services (ESs) refer to the components of nature directly enjoyed, consumed, or otherwise used to yield human well-being [2,3]. Since the implementation of the Millennium Ecosystem Assessment [4], the assessment of ESs has become a significant research topic in various fields such as ecology, geography, and land science. This interest has helped establish a “bridge” between natural ecosystems and human societal systems [5]. The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES), officially established by the United Nations Environment Programme (UNEP) in 2012, further promotes advanced research on ESs at the global and regional levels [6]. Given the continuous competition for scarce natural resources and the ever-rising growth of human material demands [7], research focusing on trade-offs and synergy relationships between various ESs to maximize their benefits has gained recent interest [8].

Different ESs exhibit highly complex mutual trade-off relationships [9]; that is, different types of ESs conflict with each other. Currently, there is a wealth of research on the trade-offs of ESs [10,11,12,13], covering the classification of ESs trade-offs [14], analysis methods for ESs trade-offs [15,16], approaches to mitigating trade-offs [17], etc. ESs trade-offs can be categorized into spatial, temporal, reversible, and trade-offs between services [9]. Existing research mostly focuses on trade-offs between services. ES trade-off analysis methods encompass statistical methods [18], comparative analysis [19,20], scenario analysis [21], and mapping methods [22]. Among them, the scenario analysis method can guide the future development of ecological environmental policies. Liang et al. (2021) conducted research on the trade-off analyses and optimization of water-related ESs based on this method, providing a basis for water conservation management [23]. Additionally, Zhu et al. (2022) combined a scenario simulation to study identifying priority areas for water ecosystem services, ensuring the sustainable development of aquatic and terrestrial ecosystems [24]. Methods for mitigating trade-offs include primarily ecosystem-based methods [25], landscape-scale methods [26,27], multiobjective optimization methods [28], and policy intervention methods [29], most of which focus on regulating the ESs supply of trade-offs [30]. The aforementioned research has laid a solid foundation for optimizing regional ecosystem regulations based on ESs trade-offs.

However, because of insufficient research on the optimal trade-off and reasonable regulatory intensity among ESs, most research results and measures cannot be effectively implemented. The production possibility frontier (PPF), based on production theory and Pareto efficiency theory, offers the possibility to address these shortcomings [31]. This method is a multiobjective optimization method that explores all Pareto optimal combinations between ESs. From the optimal combination, the PPF curve was obtained using the function fitting. The points on the curve can be considered the ideal trade-off state between two ESs, with the shortest distance from any point to the curve being an indicator of the regulatory optimization level [32,33]. Therefore, combining the PPF method with the shortest distance allows for quantitative measurement of the supply efficiency between different ESs, providing robust data support for subsequent optimization recommendations. Exploring the issue of ESs trade-off with this method offers more possibilities for the practical optimization of the regional ecosystem.

A deeper understanding of trade-offs is the prerequisite for achieving sustainable management of multiple ESs [5]. Understanding ESs trade-offs from various perspectives can broaden the horizons of managers at all levels. In particular, exploring the factors of ESs trade-offs accurately and thoroughly can help managers consider ecological, social, political, and other aspects of the decision-making process [34]. The factors of ESs trade-offs are natural and social [35]; natural factors mainly include climate, terrain, vegetation, etc. [36], while social factors encompass population, technology, GDP, policy, degree of land use intensification, etc. [37]. Developing ecosystem protection plans based on the ESs trade-off factors and trade-off zone is an effective way to strengthen ESs protection and management [38], and it is also a necessary means to mitigate trade-offs [1]. Before the plan is formulated, interdisciplinary research methods should be employed to conduct studies in appropriate regions [39]. The Northern Shaanxi Loess Plateau, situated in the center of the Loess Plateau, constitutes the critical component of China’s ecological security framework and plays a pivotal role in maintaining the ecological balance of the country [40,41]. As one of the typical geomorphic regions in China, the Northern Shaanxi Loess Plateau’s unique topography, characterized by extensive loess deposits, makes it highly susceptible to soil erosion and degradation. The delicate balance between economic development and environmental preservation in this region has made it a microcosm of the challenges faced by many ecologically sensitive areas globally [42]. Due to the specific environmental and socio-economic conditions in this region, water resources and biodiversity conservation are often key priorities for sustainable development and environmental protection [43]. Therefore, the services of WY become crucial ESs in this region, as it directly affects water resources for both ecosystems and human use [44]. The ecological health is critical for preserving biodiversity and ensuring the long-term sustainability of this region. Habitat quality (HQ) is a key ESs that reflects the ability of ecosystems to support various species and maintain their populations [45]. These two ESs are essential components of the region’s ecological health. Combining these two ESs can provide a holistic view of ecosystem performance and allow for the exploration of trade-offs. For example, land management decisions that optimize water yield (WY) may inadvertently harm HQ [46]. Understanding these relationships is essential for balanced and sustainable land use planning. By considering both ESs, the study offers a comprehensive assessment of the ecological state.

Over the past two decades, this region has undergone significant land-use changes due to the Western Development Strategy and the Grain for Green Program, which resulted in major alterations to ESs in the area [47]. The findings of ESs trade-off assessment in this region have been quite fruitful [48]. Ye et al. (2022) analyzed the trade-off relationship between WY and HQ in the Loess Plateau of Northern Shaanxi based on vegetation restoration [47], laying the foundation for further quantitative analysis of the supply efficiency as well as the influencing factors between these two ESs. Therefore, conducting research on ES trade-offs in the Loess Plateau of Northern Shaanxi, a region characterized by a fragile ecological environment and prominent man-land contradictions, can provide scientific insights and guidance for altering land use type, ensuring the sustainable management of ESs, and promoting high-quality, sustainable development [49]. Additionally, the findings from this study benefit similar regions facing ecological conservation challenges and provide critical guidance for formulating local ecological protection plans.

In summary, this paper focuses on the Loess Plateau of Northern Shaanxi and, using InVEST to calculate WY and HQ, analyzes the trade-off between these two services. The Pareto principle and multiobjective optimization are applied to fit the PPF curve of the trade-off between the two services. The optimization potential of each zone is measured, and the main factors affecting the optimization potential are analyzed using geographically weighted regression (GWR). Finally, optimization and regulation suggestions are proposed. This study is innovative in its research perspectives; on the one hand, the existing ESs trade-off rarely uses the PPF method to quantitatively measure optimization potential, and on the other, conducting ESs trade-off research from the perspective of optimization potential and its influencing factors is more conducive to the implementation of relevant plans and measures.

The specific contributions of this research have three aspects. (1) It quantifies the trade-off relationship between WY and HQ in the Loess Plateau of Northern Shaanxi, seeking the optimal fitting curve between these two services and laying theoretical foundations and data support for regional ESs zoning and regulation. (2) It delineates the spatial management of areas based on the optimization potential of each unit within the region, which can provide a basis for formulating ESs optimization policies. (3) It measures the dominant factors responsible for optimizing ESs trade-offs in each managed area, aiming to propose more concrete ecological protection strategies.

2. Materials and Methods

2.1. Study Area

The Loess Plateau of Northern Shaanxi makes up the center of the Loess Plateau, in the north of Shaanxi province and faces the Loess Plateau of western Shanxi across the Yellow River in the east and the Loess Plateau of eastern Gansu across the Ziwuling Mountains in the west [50]. It also connects with the Guanzhong Basin in the south and the Ordos in the north, covering an area of approximately 80,003 km² (Figure 1) [50]. The northern part of the region is covered with sandy grassland, while the southern part is mainly composed of loess hilly gullies and a beam-shaped low hilly mountain [51]. The terrain is higher in the northwest and lower in the southeast [52]. The region is characterized by a warm temperate semi-arid monsoon climate, with an annual average precipitation of 350–600 mm, with the southeast experiencing higher rainfall compared with the northwest [53]. The annual average evaporation is in the range of 900–1200 mm, with higher evaporation intensity in the northern part [49]. The average annual temperature ranges from 8 to 12 degrees Celsius [51].

Since the implementation of the Grain for Green Program in 1999, there have been significant changes in the land-use patterns in the Loess Plateau of Northern Shaanxi. The areas under cultivated land have decreased, while the areas under forests and grasslands have significantly increased, leading to an improvement in vegetation coverage and the overall ecological environment [49,54]. As a result of these alterations in the ecological environment, the HQ and WY have undergone significant changes. A recent study by Ye et al. (2022) verified the changes in these two services over the past two decades and demonstrated significant spatial trade-offs in the Loess Plateau of Northern Shaanxi [47]. Therefore, researching the trade-off relationship between HQ and WY in the Loess Plateau of Northern Shaanxi is of great significance for enhancing ESs and optimizing ecological environment management policies.

2.2. Methods

2.2.1. InVEST Model

The Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) model is an ESs assessment tool primarily designed to balance the relationship between development and conservation, seeking the optimal model for natural resource management and economic development [48,55,56]. The Annual Water Yield and Habitat Quality modules in InVEST are applied to calculate the WY and HQ in the Loess Plateau of Northern Shaanxi, respectively. The purpose of WY services is to maintain various water demands in the region and the water cycle of the ecosystem itself. The value of WY can be used to express the ability of WY services in the research region. The WY module in InVEST calculates the WY of each grid based on the Budyko water–energy balance formula and water balance equation, as well as other factors such as terrain, soil, vegetation, climate, etc. This study uses a 3 km × 3 km grid as the basic unit to calculate the WY of each unit, thereby quantitatively assessing the WY capacity of different land uses. The total number of basic units is 9291. The basic formula for calculating WY in InVEST is:

$$Y_x=\left(1-\frac{{AET}_x}{P_x}\right)\times P_x$$

(1)

In Equation (1), $Y_x$ is the annual WY of the grid unit $x$, ${AET}_x$ is the actual evapotranspiration (mm) of the grid unit $x$, and $P_x$ is the annual average precipitation (mm) of the grid unit $x$.

HQ serves as the foundation for various ESs and constitutes the ecological environment upon which the survival of organisms depends. It is crucial for the habitat of organisms and is assessed and calculated using the habitat quality index. The InVEST habitat quality module combines landscape-type sensitivity and external threat factors. It takes into account the influence distance and spatial weighting of threat factors to calculate HQ. This module also fully considers the impact of land-use patterns and their changes on HQ. The calculation formula is:

$$Q_{xj}=H_j\left[1-\left(\frac{D_{xj}^z}{D_{xj}^z+k^2}\right)\right]$$

(2)

In Equation (2), $Q_{xj}$ represents the habitat quality index of the grid $x$ in the land use type $j$. $H_j$ is the habitat suitability of land use type $j$, with values ranging from 0 to 1. The larger the value of $H_j$, the better the habitat suitability. $D_{xj}$ represents the degree of HQ degradation, $k$ is a semi-saturated parameter, usually taking half of the maximum value of habitat degradation, and $z$ is usually a constant, with a value of 2.5.

Following the InVEST user manual and relevant studies on Northern Shaanxi’s Loess Plateau HQ, cultivated land, desert, bare rock, and urban, rural, and other construction land are selected as HQ threat factors. Their degradation type, maximum threat distance, weight, and suitability and sensitivity to different habitats are all referred to in Zhou and Cao (2022) [57].

2.2.2. Production Possibility Frontier

In recent years, the PPF method based on production and Pareto efficiency theories was introduced into the research exploring the trade-off relationship among ESs [58,59,60]. This method uses a specific ecosystem service as the x-axis and another as the y-axis. The points on the coordinate system represent combinations of the two ESs under specific environmental conditions. The envelope constraints or the outer boundaries of all these points are defined as the PPF. In this study, multiobjective optimization was adopted as a specific PPF implementation method; in other words, we used the multiobjective optimization method to identify all Pareto optimal combinations of WY and HQ. Thus, PPF was further defined as the optimal combination of the two ESs, and the PPF curve was obtained through function fitting.

In this paper, HQ is represented on the x-axis and WY on the y-axis. Each point in the coordinate system represents a combination of the two ESs in the corresponding grid cell. The PPF boundary was mainly determined by factors that contribute to the formation of ecosystems, such as the type of land use, finance, technology, etc. Using the WY and HQ calculated by InVEST, a scatter plot was created to allow for the calculation of Pareto optimum points. The mathematical characteristics of the Pareto optimum point are:

$$\left\{\begin{array}{c}\forall i\in \left\{\mathrm{1,2}\right\},{ES}_i\left(p\right)\ge {ES}_i\left(p^{\prime }\right)\\ \exists j\in \left\{\mathrm{1,2}\right\},{ES}_j\left(p\right)\ge {ES}_j\left(p^{\prime }\right)\end{array}\right.$$

(3)

In Equation (3), ${ES}_1$ and ${ES}_2$ represent HQ and WY, respectively. $p$ is a specific raster unit, and $p^{\prime }$ is any other raster unit inside the region of interest.

If the HQ of the grid unit $p$ is not less than that of $p^{\prime }$, and the WY of the grid unit $p$ is absolutely greater than that of $p^{\prime }$, then the ecosystem service combination represented by the grid unit $p$ is superior to any other grid unit $p^{\prime }$. The point corresponding to the grid unit $p$ is then defined as the Pareto optimum point. Not only one Pareto optimum point is searched by multiobjective optimization, but rather a set of effective combinations. Combining the distribution characteristics of the Pareto optimum points, their curve-fitting is performed, and the fitting effect is evaluated by $R^2$ and the significance of each coefficient. In this study, a power function was selected to fit the identified Pareto optimum points, resulting in a PPF curve for WY and HQ.

The points on the PPF curve represent the optimal combination of the two ESs under certain resource conditions. The grid units corresponding to the points on the curve is the unit with the high efficiency in resource allocation under the constraints of a certain resource and environmental capacity. The points within the PPF curve indicate that their ecosystem service supply efficiency has not reached optimal. The closer the points are to the PPF curve, the higher the supply efficiency, and vice versa. Therefore, we quantitatively measured the supply efficiency of each point by defining the shortest distance between the point and the PPF curve. The formula for calculating the shortest distance is:

$$D_i=min\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2},\left(j=\mathrm{1,2},\cdots ,n\right)$$

(4)

In Equation (4), $D_i$ is the shortest distance between a non-optimum point and the PPF curve, $(x_i,y_i)$ and $(x_j,y_j)$ are non-optimum points and any point on the curve, respectively, and $n$ represents the number of points on the PPF curve.

2.2.3. Analytical Methods for Environmental Factors

(1)

Selection of Environmental Factors

Factors that change ESs include natural and social factors [61]. Natural factors encompass terrain, climate, hydrology, and vegetation, while social factors include population, GDP, urbanization, and transportation accessibility [36,37]. Research has revealed that WYs are significantly influenced by factors such as humidity and precipitation [62]. HQ is closely associated with vegetation type, temperature, and slope orientation [63]. Previous finding has indicated that the dynamic relationships among different ESs are notably influenced by factors such as population, GDP, and urbanization [64,65]. Taking into account the various reasons mentioned above and ensuring that the variance inflation factor (VIF) for each factor is below 5, this study has selected the eight aforementioned environmental factors.

The calculation for the corresponding factors is as follows. The terrain factor is calculated through the moving window method based on DEM [66]. Based on the data on temperature, humidity, and wind speed, climate factors are expressed by constructing climate indexes [67]. Hydrological factors are expressed by constructing the hydrological index based on annual precipitation and distance from water sources [68]. The transportation index is calculated based on cost distance to assess the accessibility of the road network [69]. The remaining factors are obtained based on

Table 1. Data sources.

Data Type	Data Sources
Land use, watershed, population density	Resource and Environment Science and Data Center of the Chinese Academy of Sciences (https://www.resdc.cn)
Precipitation, evapotranspiration	National Tibetan Plateau Data Center (https://data.tpdc.ac.cn/home)
Plant-available water content, root-restricting layer depth	Harmonized World Soil Database (http://webarchive.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/index.html?sb=1)
NDVI	National Aeronautics and Space Administration (https://www.nasa.gov)
DEM	Geospatial Data Cloud (https://www.gscloud.cn/home)
Temperature, relative humidity, wind speed, sunshine	National Meteorological Scientific Data Center (https://data.cma.cn)
Road network	National Catalogue Service for Geographic Information (https://www.webmap.cn/main.do?method=index)
Urbanization, GDP	National Bureau of Statistics (http://www.stats.gov.cn)

.

(2)

Ordinary Least Squares and Geographically Weighted Regression

Ordinary least squares (OLS) is a statistical method commonly used to explain the relationship between a single dependent variable and multiple independent variables. In this study, OLS was employed to calculate the regression relationship between supply efficiency and various influencing factors (hydrology, population density, climate, transportation, terrain fluctuation, urbanization, GDP, and NDVI) to determine the extent of the effect of these factors on supply efficiency.

$$y_i={\beta }_0+\sum _{j=1}^n{\beta }_j{x}_{ij}+{\epsilon }_i$$

(5)

In Equation (5), $y_i$ is the observed value of the grid unit $i$ in the study region, $x_{ij}$ is the value of the $j^{th}$ independent variable in the grid unit $i$, ${\epsilon }_i$ represents the independently distributed random error term, ${\beta }_0$ represents the intercept of the least squares regression, and ${\beta }_j$ represents the regression coefficient of the $j^{th}$ independent variable (driving factor).

Since the OLS is a linear non-spatial regression model, it can only explore the regression relationship between independent variables and the dependent variable overall. In other words, OLS can only estimate parameters in the “global” or “average” sense and cannot effectively capture the spatial variation of parameters that vary with location [70,71,72,73]. Geographically weighted regression (GWR) is an improvement over the traditional linear regression model. GWR can reflect the changes in the relationships between variables that occur with spatial position and subsequently capture the spatial heterogeneity of parameters. The specific calculation formula is:

$$y_i={\beta }_0\left(u_i,v_i\right)+\sum _{k=1}^p{\beta }_k(u_i,v_i)x_{ik}+{\epsilon }_i$$

(6)

In Equation (6), $y_i$ is the value of the dependent variable of the sampling point, ${\beta }_0$ is the intercept, and $(u_i,v_i)$ is the coordinates of the sampling point. ${\beta }_0(u_i,v_i)$ and ${\beta }_k(u_i,v_i)$ represent the constant term of the sampling point and the coefficient of the $i^{th}$ variable of the sampling point, respectively. $x_{ik}$ represents the $i^{th}$ independent variable of the sampling point, and ${\epsilon }_i$ represents the random error term.

2.3. Data Sources

The data required for this study includes land use, annual precipitation, evapotranspiration, plant-available water content, root-restricting layer depth, watershed boundary data, NDVI, GDP, population density, temperature, relative humidity, wind speed, sunshine, road network, DEM, and urbanization. Data sources are shown in Table 1. The specific year for the data used is 2020. To ensure the consistency of the base map and boundaries, all data were uniformly projected onto the CGCS2000 coordinate system.

3. Results

3.1. Spatial Trade-Off among Ecosystem Services

The spatial distribution of HQ and WY in the Loess Plateau of Northern Shaanxi in 2020 is shown in Figure 2. The range of HQ values is from 0 to 1, where low values are close to 0, medium values are around 0.5, and high values are close to 1. The range of WY values is from 0 to 409.28, where low values are close to 0, medium values are around 204.64, and high values are close to 409.28.

The spatial distribution of HQ has a strong regularity, showing an increasing trend from northwest to southeast. Specifically, the northwest shows a more uniform distribution of low values with a small number of medium values, while medium values dominate the northeast. There is a clear regularity in the south, where high values characterize the vast majority of the area, and the southeast and southwest show a symmetrical distribution of high values. Medium values are predominant in the east, with only a few sporadically distributed low values. The west and the east exhibit similar distribution characteristics. The west has more areas of low values, and they are relatively concentrated compared with the east.

For the spatial distribution of WY, most regions are dominated by low to medium values. The vast majority of the northern region is characterized by low values, with a few scattered areas of medium to high values. The southeast and southwest show a more symmetrical feature of low values with a symmetry axis of high values in the middle. Additionally, there is a band-like distribution of medium values in these regions. Low and medium values are distributed alternately in the eastern region, with a few scattered areas of high values along the eastern edge. The characteristics of the western region are clear, showing a uniform distribution of low values.

The above observations and the comparison in Figure 2 indicate that the WY service has generally low-to-medium value, while the HQ is predominantly characterized by medium to high values. Therefore, there is an overall trade-off between WY and HQ. Specifically, there is a strong spatial trade-off between WY and HQ in the southern, western, and northeastern regions. However, the spatial trade-off between WY and HQ in the eastern and northwestern regions is relatively weak.

3.2. Optimal Fitting of Ecosystem Services

The spatial relationship between WY and HQ was further analyzed using the PPF calculation method described above, as shown in Figure 3. Each point in Figure 3 represents the combination of WY and HQ in the corresponding grid. The blue points with red pentagons are Pareto optimum points representing optimal combinations of the two ESs where one service cannot be improved without compromising the other. The blue points without red pentagons represent non-Pareto optimum points. The power function derived from the Pareto optimum point marked in red was used for fitting. The fitted function of the PPF curve is $y=108.5x^{-0.3747}$, with a goodness of fit ($R^2=0.743$). The fitted curve has a concave downward characteristic and eventually levels off. The curve indicates that the WY gradually decreases and tends to stabilize with the increase in HQ, suggesting that when the HQ reaches a certain value, the WY reaches the balance state. In other words, even if the HQ further increases, it will not lead to a change in WY. Furthermore, additional analysis shows that when the HQ ranges from 0.5 to 0.7, the density of scattered WY points in the range of 0 to 100 is the highest, showing that under certain resource and environmental constraints, WY is the main ESs of the Loess Plateau in Northern Shaanxi.

3.3. Analysis of Ecological Spatial Zoning and Environmental Factors

3.3.1. Analysis of Spatial Zoning

Using the shortest distance calculation method described above, the shortest distance between each non-Pareto optimum point and the PPF curve was calculated, ranging from 0.0017 to 108.5037. The shortest distance was used as a measure of ecosystem service supply efficiency. The smaller the value of the shortest distance, the greater the supply efficiency. On the basis of the shortest distance, the study region is divided into five zones using the natural break method (Figure 4). As indicated in Figure 4, the values of the shortest distances generally show a decreasing trend from the northwest to the southeast. Therefore, the overall distribution pattern of ecosystem service supply efficiency demonstrates an increasing trend from the northwest to the southeast.

The first zone covered by the study represents areas with a high-efficiency supply, with shortest distances ranging between 0.0017 and 23.4858. This zone is primarily concentrated in the southern central part of the study region, forming a circular distribution, with additional scattered occurrences in the eastern and northeastern regions. Surrounding the first is the second zone with sub-high-efficiency supply and the shortest distance between 23.4859 and 45.1555. This zone extends into the central part of the study area, simultaneously scattering through the northern region. The third zone has the shortest distances, ranging between 45.1556 and 64.7010, representing areas of general-efficiency supply. The gradient of this zone is in a southwest-to-northeast direction in the upper-middle part of the study region, with scattered occurrences in the southern region. The fourth zone is adjacent to the third and exhibits a similar distribution pattern. However, it is more concentrated compared with the third zone. The range of shortest distances in the fourth zone is between 64.7011 and 84.7823, representing areas with sub-low-efficiency supply. The fifth zone has a low-efficiency supply, and the shortest distance in this zone is 84.7824–108.5037. This zone is concentrated in the northwestern part of the study region.

3.3.2. Comparison of Models

This study primarily investigated the impact of various factors on the supply efficiency of WY and HQ in the Loess Plateau of Northern Shaanxi. Taking into account the actual conditions in the study region, NDVI, GDP, hydrology, population density, climate, transportation, terrain fluctuation, and urbanization were selected as relevant factors and used to calculate their individual impact on each zone and subsequently determine each zone’s dominant factor. For each zone, OLS and GWR calculations were performed separately. The goodness of fit ($R^2$) for all zones is presented in

Table 2. R² of ordinary least squares and geographically weighted regression.

	Methodology Type
Hierarchical Zoning		OLS	GWR
first zone		0.069	0.295
second zone		0.093	0.279
third zone		0.198	0.452
fourth zone		0.270	0.537
fifth zone		0.252	0.601

. In calculations performed using OLS, the VIF for each factor in each zone was found to be less than 5.

As indicated in Table 2, GWR exhibits better goodness of fit compared with OLS. Therefore, the results obtained by GWR provide a better explanation for the dependent variable. Hence, we further explored the dominant factors affecting the supply efficiency in each zone using the GWR.

3.3.3. Identification of Dominant Factors

GWR 4.09 software was employed to calculate the regression coefficients for all factors in each zone. Additionally, ArcGIS was utilized to visually represent the regression coefficients.

Let the supply efficiency for the first to the fifth zone be represented as $y_1{,y}_2,y_3{,y}_4,$ and $y_5$, respectively. Let the hydrological factor be denoted as $x_1$, the NDVI factor as $x_2$, the GDP factor as $x_3$, the urbanization factor as $x_4$, the terrain fluctuation factor as $x_5$, the transportation factor as $x_6$, the climate factor as $x_7$, and the population density factor as $x_8$.

For every zone with a high-efficiency supply $y_1$, sub-high-efficiency supply $y_2$, general-efficiency supply $y_3$, sub-low-efficiency supply $y_4$, and low-efficiency supply $y_5$, the coefficients of environmental factors are shown in

Table 3. The coefficients of environmental factors in each zone.

	Environmental Factors	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{x}}_6$	${\mathit{x}}_7$	${\mathit{x}}_8$
Supply Efficiency
$y_1$		7.4	11.239	−20.48	6.232	22.611	1.305	1.662	−80.412
$y_2$		−34.366	13.175	−18.519	−0.817	−0.87	3.169	5.733	12.174
$y_3$		−37.627	16.099	−38.596	8.665	6.592	2.844	5.477	50.677
$y_4$		−43.955	1.183	−45.129	8.921	2.794	−0.047	15.202	−19.823
$y_5$		−21.777	−14.393	−60.318	−9.249	−1.377	−0.179	15.191	−82.696

. Therefore, the fitted formula for the relationship between supply efficiency and all factors can be provided by the coefficients.

In the high-efficiency supply zone, the coefficients of $x_3$ and $x_8$ are negative. Therefore, GDP and population are negatively correlated with the supply efficiency of this zone, while the coefficients of the other factors are positive. The factors, ranked in descending order according to the absolute values of their regression coefficients, are $x_8,x_5,x_3,x_2,x_1,x_4,x_7$, and $x_6$. Therefore, the dominant factors influencing the supply efficiency of this zone are population, terrain, and GDP. In the zone with sub-high-efficiency supply, $x_2,x_6$, and $x_8$ are factors with positive coefficients. Therefore, NDVI, transportation, and population promote the improvement of supply efficiency in this zone, while the other factors have inhibitory effects. The order of the absolute values of the regression coefficients of each factor in this zone from large to small is $x_1,x_3,x_2,x_8,x_7,x_6,x_5$, and $x_4$. Thus, hydrology, NDVI, and GDP are the dominant factors in the zone with sub-high-efficiency supply.

In the general-efficiency supply zone, the coefficient of $x_1,x_3$ is negative, while the coefficients of the other factors are positive. The factors, ranked in descending order based on the absolute values of their regression coefficients, are $x_8,x_3,x_1,x_2,x_4,x_5,x_7$, and $x_6$. Therefore, the dominant factors in this zone are population, GDP, and hydrology. In the zone with sub-low-efficiency supply, there is an equal presence of positively and negatively correlated factors. Among them, $x_1,x_3,x_6$ and $x_8$ exhibit a negative correlation. The factors, ranked in descending order based on the absolute values of their regression coefficients, are $x_3,x_1,x_8,x_7,x_4,x_5,x_2$, and $x_6$. Therefore, the dominant factors in this zone are GDP, hydrology, and population. The coefficient of $x_7$ exhibits a positive correlation in the zone with the low-efficiency supply, while the other factors show a negative correlation. The factors, ranked in descending order based on the absolute values of their regression coefficients, are $x_8, x_3,x_1,x_7,x_2,x_4,x_5$, and $x_6$. Therefore, the dominant factors in this zone are population, GDP, and hydrology.

Among the factors governing the five zones, $x_3$ is the dominant factor in all zones. $x_1$ and $x_8$ are the dominant factors in four of the five zones, and $x_2$ and $x_5$ are the dominant factors in one zone. Hence, $x_3,x_8$, and $x_1$ are the major contributing factors among the dominant factors across all zones, indicating that hydrology, GDP, and population are the primary factors affecting the ecosystem service supply efficiency. These are the results of the analysis of the importance of each factor under the zonal framework. Similarly, it is possible to explore the impact of each factor on ESs within a nonzonal framework. Applying the OLS and GWR to the entire study region, the goodness of fit for the fitted coefficients obtained by OLS was $R^2=0.634$, while the goodness of fit for the fitted coefficients obtained by GWR is $R^2=0.744$. Therefore, even in the nonzonal situation, the effectiveness of the GWR remains superior to the OLS.

Let the supply efficiency under the nonzonal condition be represented as $y$ and the representation of each factor remains as described above. Further calculations were made to obtain the fitting formula for each factor on supply efficiency, as shown in Equation (7). Among all the factors, the coefficients of $x_1, x_3, x_5$, and $x_8$ is negative, and the rest of the factors are positively correlated. The factors, ranked in descending order based on the absolute values of their regression coefficients, are $x_8, x_3,x_1,x_2,x_4,x_6,x_7$, and $x_5$. Therefore, the dominant influencing factors in the nonzonal framework are population, GDP, and hydrology. This is consistent with the result of the zonal analysis, further validating the correctness of the dominant factors and the rationality of the zonal analysis.

$$y=-85.601x_1+24.2x_2-110.067x_3+16.13x_4-0.293x_5+11.461x_6+ 2.218x_7+217.201x_8$$

(7)

3.3.4. Spatial Characteristics of Environmental Factors

From the perspective of zonal analysis, the dominant factors for each zone were analyzed based on the absolute values of the regression coefficients of the factors. Alternatively, the analysis can also be approached from the perspective of the spatial distribution of each factor, examining their distribution characteristics. The spatial distribution of each factor is depicted in Figure 5.

From the zonal analysis, overall analysis, and the magnitude of regression coefficients, the dominant factors include population, GDP, hydrology, and transportation. The population factor mainly affects the supply efficiency of ESs in the third, fourth, and fifth zones of the study region, with a lower impact in other regions. The factor of GDP has a significant impact on the central part of the study region. The impact of hydrology is mainly concentrated in the third and fourth zones, while transportation’s impact covers a wide range, primarily focusing on the eastern and central regions. Factors that have a low impact on supply efficiency include terrain fluctuation, urbanization, NDVI, and climate. The significant impact of terrain fluctuation on the supply efficiency in the study area is mainly distributed in the central and northern regions, with a notable influence in a few other regions. The impacts of urbanization are relatively concentrated, clustered mainly in the northwest and northern regions. The significant impact of NDVI is mainly concentrated in the fifth zone with the low-efficiency supply. The impact of climate on the study region is primarily focused on the central region and exhibits a strip-like distribution.

4. Discussion

4.1. Response of Supply Efficiency to Environmental Factors

Different factors variously affect the ecosystem service supply efficiency [74]. In this study, the population factor emerges as the most pronounced impact on supply efficiency. Research conducted by other scholars has also underscored that population constitutes one of the most critical factors influencing supply efficiency [31,75]. Changes in population can directly alter ESs. For instance, as the population increases, the demand for vital ESs like food, water, and others also rises, consequently disrupting the balance and supply efficiency of ESs [76,77,78]. In the context of the Loess Plateau of Northern Shaanxi, population primarily influences the fourth zone characterized by sub-low-efficiency supply. This is primarily due to the fact that this zone houses a comparatively larger population than the other zones. The magnitude of this impact becomes more pronounced with higher population counts, as evidenced by the larger absolute values of the regression coefficients.

GDP represents another significant factor affecting supply efficiency [79,80]. With economic development and increased GDP, people’s material needs are satisfied. Particularly after reaching the well-off status, there is a gradual increase in people’s demand for eco-recreation, aligning with Maslow’s demand level [81]. Thus, changes in GDP also lead to variations in the demand for eco-recreation, subsequently affecting the ecosystem service supply efficiency [82,83]. For example, the northern part of the Loess Plateau in Northern Shaanxi has a relatively high GDP, significantly dampening the effect on supply efficiency. The GDP in the southeastern part is low, and this part of the regional GDP significantly contributes to supply efficiency.

NDVI is an important indicator for detecting vegetation growth status and cover [84]. It also serves as a significant factor influencing the efficiency of the service [85,86]. Implementing the Grain to Green Program has led to increasing the area of forest and grassland, thus restoring vegetation cover. In the early stages of the Grain to Green Program, the vegetation was relatively undeveloped, resulting in lower water consumption. However, the well-developed root network leads to increased soil porosity, thereby absorbing more water. As a result, WY tends to increase during the initial phase [87]. With time, the vegetation gradually grows larger, the water consumption increases significantly, and the evaporation intensity also increases. These factors lead to the decline in regional WY [88]. The inhibitory effect of NDVI on supply efficiency is evident in the northwest of the Loess Plateau. This is partly due to the substantial proliferation of vegetation cover and partly due to intensifying water consumption by mature vegetation in this region during the past two decades.

Supply efficiency can also be affected by other factors such as hydrology, transportation, terrain fluctuation, climate, and urbanization. For instance, intensifying rainfall, as a type of hydrology, could lead to an augmentation of water conservation due to the increase in retained surface water and water erosion capacity. This alters the balance among different ESs, thereby influencing supply efficiency [89,90]. Our investigation showed that the significant impact of hydrology on supply efficiency in the Loess Plateau of Northern Shaanxi was mainly concentrated in the third and fourth zones and parts of the second zone. Transportation accessibility plays a crucial role in shaping regional economic development. Alternations in accessibility directly impact land-use types, consequently affecting the supply efficiency of ecosystem service [91,92]. The substantial influence of transportation on the supply efficiency of the Northern Shaanxi Loess Plateau is predominantly centered in the central region. Terrain fluctuation acts as a controlling factor that affects both the supply and demand for ESs. In general, terrain fluctuation shapes the capacity of ESs by controlling the human activities and spatial distribution patterns of landscapes, thereby affecting supply efficiency [93,94]. The effect of terrain fluctuation on supply efficiency in the Loess Plateau of Northern Shaanxi is scattered, with a more pronounced effect observed in the northern and central regions.

Climate can directly influence ESs. For example, when the temperature is high, the evapotranspiration of surface water accelerates, which results in a change in WY. Climate change has a significant influence on vegetation growth, leading to shifts in vegetation distribution and subsequently impacting ESs indirectly [95,96]. In the Loess Plateau of Northern Shaanxi, the effects of climate on supply efficiency are primarily noticeable in the central and eastern regions, with a small impact observed in the northern region. The intensification of urbanization increases the demand for land, reducing the ecological land and also changing the type of land use, consequently affecting ecosystem service [97]. The impacts of urbanization on the Loess Plateau of Northern Shaanxi are relatively concentrated, mainly in the western peripheral regions and the northwest.

4.2. Corresponding Measures for Improving the Supply Efficiency

This study is based on supply efficiency to zones and assesses the dominant factors affecting each zone. On the basis of the above results, this paper proposes optimization recommendations aimed at mitigating the trade-off between WY and HQ and enhancing supply efficiency in the Loess Plateau of Northern Shaanxi. The specific suggestions are as follows

In the high-efficiency supply zone, the combination of WY and HQ has temporarily reached the optimal state. Thus, the primary objective for this zone is to sustain its current efficiency status. The combination of these two ESs in the sub-high-efficiency supply zone has reached a relatively optimal level, but the supply efficiency can still be improved. The dominant factors in this zone include hydrology, NDVI, and GDP. NDVI demonstrates a positive correlation with improving supply efficiency, while hydrology and GDP show a negative correlation. Therefore, it is advisable for this zone to establish protected areas, reduce human interference, and engage in moderate afforestation and reforestation efforts to enhance supply efficiency. The dominant factors in areas with general-efficiency supply are hydrology, GDP, and population.

Among these factors, the population exhibits a positive correlation, while hydrology and GDP show a negative correlation. Consequently, in the development process of this zone, it is essential to prevent population outmigration and maintain a certain population level. In zones with sub-low-efficiency supply, GDP, hydrology, and population continue to be dominant factors, but these dominant factors are all negatively correlated with improving supply efficiency. Due to the significant impact of GDP, it is imperative to establish suitable development policies for this zone to mitigate further adverse impacts on the ecological environment resulting from extensive development. For the zone characterized by the low-efficiency supply, the dominant factors are population, GDP, and hydrology, all negatively correlated. Population emerges as the most significant adverse factor. Therefore, the primary objective for this zone is to establish ecological boundaries, curtail human activities, and simultaneously guide surplus labor outmigration as appropriate.

In summary, ESs with trade-off relationships can still be improved when they do not meet the physical constraints. Using the supply efficiency calculations between WY and HQ and considering the specific situation in Northern Shaanxi, this paper offers the following recommendations for each zone. For the high-efficiency supply zone, the emphasis should be on efficiency supervision. In the sub-high-efficiency supply zone, the Grain to Green Program should be carried out appropriately. Measures should be taken to prevent population outmigration in the general-efficiency supply zone. In the sub-low-efficiency zone, large-scale development should be avoided. Efforts should be made to guide the outmigration of surplus labor in the low-efficiency supply zone.

5. Conclusions

In this study, we initially used InVEST to calculate WY and HQ in the Loess Plateau of Northern Shaanxi. Then, the trade-offs between the two ESs were analyzed. By utilizing the shortest distance to represent the supply efficiency of grid units, we have revealed the potential for enhancing the supply of ESs. We analyzed the impact of each factor on each zone, identifying potential approaches to enhance the ecosystem service supply efficiency. The main conclusions of this study are as follows:

(1)

There is a spatial variation in the trade-off relationship between WY and HQ in the Loess Plateau of Northern Shaanxi. Strong spatial trade-offs existed between WY and HQ in the south, west, and northeast regions. The spatial trade-off relationship between WY and HQ was weaker in the eastern and northwestern regions.

(2)

There is an optimal combination of WY and HQ in the Loess Plateau of Northern Shaanxi, and the spatial characteristics of the supply efficiency of the two services are significant. There are eighteen optimal combination solutions for WY and HQ, and the fitted PPF curve based on the optimal combination solutions is $y=108.5x^{-0.3747}$. The supply efficiency of the two services exhibits an increasing distribution from northwest to southeast. Using the magnitude of supply efficiency, the study area is categorized into the zones of high-efficiency supply, sub-high-efficiency supply, general-efficiency supply, sub-low-efficiency supply, and low-efficiency supply.

(3)

The dominant factors influencing supply efficiency vary across each zone. Population, hydrology, and GDP are the dominant factors affecting supply efficiency across the entire region, as well as in the zone of general-efficiency supply, sub-low-efficiency supply, and low-efficiency supply. The dominant factors of high-efficiency supply are hydrology, NDVI, and GDP, while the dominant factors are GDP, topography, and population in the zone of high-efficiency supply.

In conclusion, this paper proposes recommendations for reducing trade-offs and enhancing supply efficiency between ESs. These include dynamic supervising for high-efficiency supply zones, moderate greening in sub-high-efficiency supply zones, stabilizing population in general-efficiency supply zones, and reducing development intensity in sub-low-efficiency zones and low-efficiency supply zones.