Research on Spatial Spillover Effects of Comprehensive Carrying Capacity of Water and Soil Resources: Evidence from the Yellow River Basin, China

Abstract

Water and soil resources (WSRs) determine the healthy development of the socio-economic systems. This research seeks to clarify the spatiotemporal evolution characteristics, spatial spillover effects, and key constraint factors influencing the comprehensive carrying capacity (CCC) of WSR in the Yellow River (YR) Basin from 2012 to 2023, thereby supporting the healthy development of the river basin. Based on the structural relationships among the internal elements of this system, the entropy method and an extensible cloud model are employed in this study to evaluate the WSR-CCC. Based on the estimation theory and spatial econometrics methods, the temporal and spatial evolution process of WSR-CCC was explored, and the obstructive factors were analyzed. We made the following discoveries: (1) The WSR-CCC demonstrates a fluctuating upward tendency, gradually moving from critical overload level IV to sustainable level II, but inter-provincial disparities expand. (2) The spatial pattern exhibits a gradient of higher levels in the western region, lower levels in the eastern region, stronger intensity in the northern region, and weaker intensity in the southern region, with weak spatial correlation. However, the spatial spillover effect is significant, with club convergence and the Matthew effect coexisting. (3) The obstacle factors exhibit a drive–influence–state three-stage dominant characteristic. The findings provide actionable insights for coordinating WSR optimization and ecological conservation.

1. Introduction

The WSR determines the upper limit of development, and they are of irreplaceable importance for maintaining balanced ecosystems, protecting agricultural production, supporting industrial development, and meeting the needs of human daily life [1,2]. Therefore, the preservation and rational utilization of WSR have always been regarded as core issues in studying global environmental change [3,4]. In recent years, the continuous expansion of the scope and depth of human activities has accelerated the depletion of WSR, triggering a series of environmental issues. The FAO pointed out in “The state of WSR in the world food and agriculture: systems at breaking point”, indicated that the state of the WSR is continually deteriorating and is “on the verge of limits.” By 2050, it will be arduous to satisfy the food demands of an anticipated global population of nearly 10 billion, which underscores the critical impact of the weakening of WSR-CCC on human development [5,6].

Resource carrying capacity reflects the limit that the resource system of a certain region can withstand the healthy development of population, economy, and society within a specific period. Regarding the research on resource carrying capacity, Li et al. [7] selected China’s water-scarce northwest region as a case study and gauged the WRCC across five provinces in this region from 2000 to 2022. Zhang and Chen [8] evaluated the WRCC of the YR Basin from 2000 to 2022 based on the natural output and usage dimensions of water resources, and pointed out that natural rainfall and social activities were the main driving factors. Fan et al. [9] also assessed the WRCC of the YR Basin from 2011 to 2020 based on the TOPSIS model, and the temporal and spatial distribution of WRCC within the spatial boundaries as well as the obstructive factors were also discussed. Zhu and Cao [10] evaluated China’s WRCC from the perspectives of resource endowment, social activities, economic development and ecological environment. The above achievements provide references for this study, but they ignore the spatial spillover effect caused by resource flow. At the same time, they are all evaluations of a single factor and do not consider the natural connection between water and soil resources.

As a typical open dissipative system, WRCCs form a multi-level nonlinear interaction network through material cycles, energy flow, and information feedback mechanisms [11]. Information feedback is the process via which the water–soil resource system adjusts its internal structure and functional output based on the interaction information among water resources, among land resources, and between water and soil resources. WSR-CCC exhibit a naturally tight coupling relationship. According to the dissipative structure theory, the two resource types maintain dynamic balance through entropy exchange with the outside world. For example, the system continuously interacts with the outside world through the precipitation–runoff–evaporation of water resources and the organic matter input–erosion output of soil resources, and the negative entropy flow offsets the increase in internal entropy [12]. This internal connection leads to water flow acting as a carrier of pollutants, driven by surface runoff erosion and groundwater seepage to transport pollutants across regions [13]. From a spatial point of view, this characteristic endows WSR pollution with significant spatial spillover and spatial correlation; that is, water and soil resources pollution in a specific area will transcend the region’s boundary and affect the soil and water resources in adjacent areas [14,15]. Therefore, water and soil resources present significant vertical stratification and horizontal heterogeneity characteristics in the spatial dimension, and the two factors realize functional synergy through substance exchange at the surface–underground interface to jointly form a complex ecological conservation system for the basin, as illustrated in Figure 1.

The study of the WSR-CCC, as a core issue of regional sustainable development [16], has shifted from the analysis of single elements to the evaluation of multi-system coupling. Early scholars focused on the independent evaluation of water or soil resources [17,18]. Although this type of research reveals the threshold of a single factor, it ignores the interaction mechanism of WSR as an open system [19]. Under the guidance of the concept of systems science, scholars have gradually shifted toward the collaborative evaluation of water and soil resources [20,21,22]. Many scholars’ research has effectively improved the scientificity and systematic nature of the evaluation system. Compared with early single-factor evaluation methods, the new evaluation system integrates natural, economic, and social factors that affect water resources and land resources. Based on frameworks such as DPSIR, it fully takes into account the dynamic evolution relationship between WSR and the external environment, rather than simply summing up the evaluation results of a single factor. Thus, it more truly reflects the CCC of the system and provides a methodological basis for research [23,24,25]. The existing studies were carried out from an all-inclusive perspective and mainly focus on establishing index systems, evaluating regional carrying capacity, and exploring the utilization efficiency of WSR [26,27,28]. In spatiotemporal evolution characteristics research, academic community has adopted the Spatial optimization model [29], the non-parametric estimation theory [30], and spatial autocorrelation [31] to continuously innovate and enrich this field to promote cognitive deepening. As an important representation of regional resource interaction, the spatial spillover effect has expanded from the economic domain to the resource and environment domain. Some spatial econometric models have also been employed to describe the spatial characteristics of the research subjects [32,33]. As the scope of research continues to expand, such methods have gradually expanded into the environment field, being applied to the study of WSR. Scholars began to quantify the ecological spillover of the WSR use change among basins using spatial measurement methods [34,35], adding the WSR-CCC to regional association networks. This breaks through the “localization” limitation in traditional research and providing a new analysis dimension for the coordinated management of resources across administrative regions [36,37].

Existing studies have laid theoretical foundations for investigating the WSR-CCC via multidimensional evaluation and spatiotemporal analysis and made progress in collaborative evaluation. However, they lack in-depth exploration of the water and soil coupling system’s spatial spillover effect in the YR Basin [31]. First, existing research overlooks the heterogeneity of spillover intensity, failing to distinguish differences in spillover effects across regions with different carrying capacity levels. Second, they present insufficient analysis of spillover pathways, without clarifying how the carrying capacities of adjacent provinces affect the local region. Therefore, the aim of this study is to establish a scientifically complete methodological framework for assessing the WSR-CCC in the YR Basin, with the expectation of providing a basis for the formulation of resource utilization policies. This research innovatively proposed an indicator system to examine the WSR-CCC. On this basis, the extensible cloud model was applied to quantify and grade the CCC, and kernel density analysis as well as spatial autocorrelation analysis are used to reveal its spatiotemporal evolution features. The spatial statistical model was employed to measure the spatial spillover effect of the WSR-CCC among various regions of the YR Basin. Finally, the obstructive factors that affect the WSR-CCC were analyzed.

2. Materials and Methods

2.1. Study Area

The YR Basin meanders eastward across nine provinces and regions in China. It spans roughly 5464 km in total length, and its study area is shown in Figure 2. This basin was selected as the research object due to its typicality and strategic significance: as a key energy and agricultural base in China, it is crucial for water resources allocation and ecological security, yet it bears prominent resource–environment contradictions, making it representative for water–soil carrying capacity research. It also faces complex and severe water–soil challenges. For instance, the per capita water resource volume is far lower than the national average level; additionally, the ecological environment conditions in most areas within the basin are rather fragile, with prominent issues including soil erosion, intermittent tributaries, and degraded wetland functions, reflecting the interplay of natural constraints and human activities typical of large river basins [38].

2.2. Indicator System

As the foundation for regional sustainable development, water and soil resources are intricately linked to ecological environment, economic development, and social demands. Therefore, taking WSR-CCC as the theme and comprehensively assessing its utilization status and potential at different development stages is greatly significant for achieving ecological security and sustainable development. Taking into account the availability of data and in combination with relevant literature [39,40], this study employs the five-dimensional DPSIR framework specifically designed for the WSR-CCC in the YR Basin. Widely adopted in environment research, this framework illuminates dynamic interactions between human activities and environmental systems. For example, Carr et al. [41] further validating its effectiveness in integrating multi-dimensional factors for sustainable development assessment, providing methodological support for its adaptation in this study. Among them, driving factors act as the initial power and generate pressure through direct or indirect resource allocation and behavior incentives. Pressure factors act on the core of the system, causing changes in functional output and altering the state of WSR. State factors, as a real-time representation of the system, not only reflect the comprehensive results of pressure and response but also trigger a series of impacts through changes in dynamic thresholds, prompting people to respond, relieve pressure, restore the state, balance the impacts, and suppress the unfavorable development trends caused by driving factors, preventing impacts from deteriorating further. This forms a dynamic feedback–adjustment relationship among the dimensions, maintaining the internal stability of the WSR. The logical relationship is shown in Figure 3 [42].

Driving factors represent the core forces behind socioeconomic development related to WSR-CCC. The positive impact of basin development on the WSR can be measured using indicators such as per capita gross domestic product (D1), population growth rate (D2), urbanization level (D3), and per capita disposable income (D4). Indicators such as D4, its growth can not only enhance the willingness of residents and enterprises to invest in water-saving and soil conservation technologies, but also raise public awareness of ecological protection, which will help reduce the pressure on the water and soil resource system [42]. Pressure factors reflect the environmental stress effects generated by human activities. Key constraints during resource utilization are revealed through indicators including the utilization rates of resources (water resource P1, soil resource P2), water consumption per unit of GDP (P3), and the proportion of rocky desertification area (P4) [43]. The state factor reflects the background characteristics of the WSR system by describing the current status of water and soil resources. Indicators such as per capita water resources (S1), per capita soil resources (S2), water and soil matching coefficients (S3), and per land water resources are included to reflect the health levels of ecosystems [44]. Influencing factors assess the eco-economic effects of resource use. The two-way effect of resource utilization on system sustainability is analyzed through indicators like industrial wastewater discharge (I1), chemical fertilizer and pesticide load (I2), industrial sulfur dioxide emissions (I3), and domestic sewage discharge (I4) [34]. Response factors quantify the effectiveness of policy regulation. Indicators such as the water and soil conservation investment ratio (R1), green land coverage (R2), the sewage centralized treatment rate (R3), and environmental infrastructure investment (R4) are used to evaluate management measures’ improvement of system resilience [45]. Therefore, establishing a comprehensive evaluation index system for WSR-CCC can not only fully reflect the status and potential of resource utilization but also provide a scientific basis for formulating and implementing relevant policies, thereby promoting sustainable management and protection of WSR in the YR Basin (

Table 1. An evaluation index system for the WSR-CCC.

Dimensionality	Indicator Name	Unit	Benefit
Driving factor	Per capita gross domestic product (D1)	yuan/person	+
	Population growth rate (D2)	%	−
	Urbanization level (D3)	%	+
	Per capita disposable income(D4)	yuan/person	+
Pressure factor	Water resources utilization ratio (P1)	%	−
	Land resources utilization ratio (P2)	%	−
	Water consumption per unit of GDP (P3)	m3/million	−
	Rocky desertification area ratio (P3)	%	−
State factor	Water resources per capita (S1)	m3/person	+
	Land resources per capita (S2)	ha/person	+
	Water–soil matching coefficient (S3)	-	+
	Water resources per land (S4)	m3/ha	+
Influence factor	Industrial wastewater discharge (I1)	tons	−
	Chemical fertilizer pesticide load (I2)	kg/ha	−
	Industrial sulfur dioxide discharge (I3)	tons	−
	Domestic sewage discharge (I4)	million m3	−
Response factor	Water and soil conservation investment ratio (R1)	%	+
	Green land coverage (R2)	%	+
	Sewage centralized treatment rate (R3)	%	+
	Environmental infrastructure investment (R4)	yuan	+

).

Due to the fact that the data for 2024 has not yet been finalized, this study used panel data from 2012 to 2023 for nine provinces in the YR Basin. The original data mainly came from the Statistical Yearbook of relevant regions, the China Environmental Statistics Yearbook, the Ecological Environment Status Bulletin, and relevant data of the provincial environmental protection department.

2.3. Research Methodology

2.3.1. Kernel Density Estimation

Kernel density estimation derives density function estimates via local weighted averaging over data point neighborhoods, eliminating the need for a priori assumptions about data distributions and enabling the direct inference of probability density characteristics from sample data. Compared with other kernel functions, the Gaussian kernel function has three key advantages: First, it adapts well to the continuous carrying capacity index in this study (which shows a normal distribution tendency), effectively reducing estimation deviation and accurately capturing distribution changes among different geographical units. Second, it generates a smoother density curve, facilitating the analysis of the gradual characteristics of the WSR-CCC evolution across stages. Third, this method is consistent with most previous studies on the resource carrying capacity that used the Gaussian kernel function, ensuring methodological consistency when comparing results. Taking into account the advantages of this method, this study employs it to describe the dynamic evolution of the WSR-CCC, the following equations were used in this study [46]:

$$f\left(x\right)={\displaystyle \frac{1}{mk}}{\displaystyle {\sum }_{i=1}^{m}R\left(\frac{x-x_i}{k}\right)}$$

(1)

$$R\left(x\right)={\displaystyle \frac{1}{\sqrt{2\pi }}}\exp \left(-{\displaystyle \frac{x^2}{2}}\right)$$

(2)

In Equations (1) and (2), $m$ represents the amount of data, $x$ represents the average value, $R\left(x\right)$ is the Gaussian function, and $k$ is the bandwidth. Kernel functions are typically symmetric probability density functions. In the Gaussian kernel function, $k$ determines the smoothness of the kernel. A smaller bandwidth leads to more fluctuation in the estimation results, while a larger bandwidth results in smoother estimates.

2.3.2. Spatial Autocorrelation

To measure the correlation of a certain variable across adjacent geographical spaces, this study introduced the spatial autocorrelation model. It can be measured in different ways, often using the global Moran index ($\mathrm{M}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{n}’\mathrm{s} \mathrm{I}$), which has the range $\left[-1, 1\right]$, the left and right ends within this range respectively represent negative correlation and positive correlation. The following equations were used in this study [47]:

$$I={\displaystyle \frac{m}{{\displaystyle {\sum }_{a=1}^m{\displaystyle {\sum }_{b=1}^m{l}_{ab}}}}}\times {\displaystyle \frac{{\displaystyle {\sum }_{a=1}^m{\displaystyle {\sum }_{b=1}^m{l}_{ab}\left(c_a-\overline{c}\right)\left(c_b-\overline{c}\right)}}}{{\displaystyle {\sum }_{a=1}^m{\left(c_a-\overline{c}\right)}^2}}}$$

(3)

In Equation (3), $C_a$ and $C_b$ are the WSR-CCC of province $a$ and $b$, respectively; $\overline{C}$ represents the average value of the WSR-CCC; and $l_{ab}$ is a spatial adjacency matrix.

2.3.3. Space Markov Chains

A Markov chain belongs to a category of stochastic processes, characterized by the probability distribution of its future states relying solely on the current state, with no dependence on any past states. Compared with traditional models, the Space Markov chains not only focuses on state transitions over time but also considers state transitions across different spatial locations and the impacts of spatial interactions on these transitions. It reveals the evolution of spatial patterns and the impacts of spatial interactions on regional development.

The basic method used was as follows: Based on the continuous numerical values of the regional phenomenon after quantification, the phenomenon was discretized into $\mathrm{k}$ types of states. Subsequently, the changes and their probabilities for each type were calculated, thereby approximating the evolution process of the regional phenomenon as a Markov process. Firstly, the matrix $F_{\mathrm{t}}$ was constructed to represent the state probabilities of WSR-CCC during a specific period. The spatial transfer of WSR-CCC in different periods was represented by another matrix $E$. It is the Markov transition probability matrix, where the elements $P_{ab}$ represent the probability that a region in type $a$ at time $t$ and transitioning to type $b$ at time $t+1$. The formula used for $P_{ab}$ was as follows [48]:

$$P_{ab}=Z_{ab}/Z_a$$

(4)

In Equation (4), $Z_{ab}$ represents the total number of regions where the transfer has occurred, while $Z_a$ represents the total number of regions that belong to type $a$.

Integrating the “space” element into the above method, the matrix $E$ is decomposed to form $M$ transition condition probability matrices ($m\times m$), where each element in the matrix represents the regional transition probability for the space lag type of m. The lag value calculation formula is [49]:

$$La{\mathrm{g }}_i={\displaystyle \sum _{j=1}^n{Y}_j}{W}_{ij}$$

(5)

In Equation (5), $Y_j$ represents the WSR-CCC of Province $j$ within the basin, $W_{ij}$ indicates the adjacency status between Province $i$ and Province $j$. 1 indicates adjacency, while 0 indicates non-adjacency.

2.3.4. Obstacle Model

This model serves as an effective approach for analyzing the degree of obstruction provided by influencing factors to specific goals, and in this study, this model was introduced to determine the key factors that affect the WSR-CCC in the YR Basin. The specific calculation formula used was as follows [50]:

$$H_{ij}=P_{ij}{F}_j/{\displaystyle \sum _{i=1}^m}{P}_{ij}{F}_j$$

(6)

In Equation (6), $H_{ij}$ is the degree of the obstacle; $P_{ij}$ is the deviation of the indicator, and $F_j$ is the weight of the evaluation index.

2.3.5. Software for Data Analysis and Visualization

To ensure methodological reproducibility, all software used in this study and their specific applications are summarized as follows: Microsoft Excel (2021) was used for preliminary data organization from yearbooks and bulletins, and for calculating the barrier degree model. Origin (2023b) was critical for visualization, generating box plots to display inter-provincial differences and plotting barrier degree charts to track dynamic trends. ArcGIS (10.8) supported spatial analysis, spatial correlation analysis and mapping the spatial distribution of the WSR-CCC. MATLAB (R2023a) handled advanced modeling and time-series analysis, including the extensible cloud model for quantifying fuzziness and randomness, kernel density estimation for temporal evolution (2012–2023), and Markov chain analysis to construct transition matrices and verify spatial proximity effects.

3. Results

3.1. Spatiotemporal Evolution Characteristics of the WSR-CCC

3.1.1. Temporal Evolution Characteristics

Under the framework of the extensible cloud model, this study achieves the accurate grading of the WSR-CCC in the YR Basin through systematic methods, including weighting model, forward and reverse cloud parameter generation, and membership degree calculation. The grading results of the WSR-CCC of the basin continuously increased from 0.2009 in 2012 to 0.7128 in 2023, promoting level from critical overload level IV to sustainable level II. Among them, 2020 was a key turning point (Ex = 0.6012), as the entire basin entered the threshold of weak carrying capacity level III for the first time, and 66.7% of the provinces entered the level II range in 2023, indicating that pressure borne by the WSR system had been fundamentally relieved (Figure 4).

The obtained results are displayed in the form of a box plot (Figure 5). It shows the overall characteristics of the WSR-CCC from 2012 to 2023, reflecting the gradual emergence of the effectiveness of WSR management policies. To verify the significance of the difference of values in different time periods, we used Duncan multiple interval test. The test results indicated that the carrying capacity index during 2012–2016 was significantly lower than that during 2017–2023, and the interquartile range of the box in 2012–2016 remained at 0.10–0.15, before expanding to more than 0.20 in 2017 (reaching a maximum of 0.23 in 2021). The gap between the upper and lower quartiles increased from 0.23 to 0.58, indicating that the gap in carrying capacity between provinces widened with the development process (p < 0.05). There were differences in the WSR-CCC among provinces, showing an obvious skewed distribution. The boxes generally presented a pattern of spatial compression in the lower quartile and spatial expansion in the upper quartile, i.e., the characteristic of “low-value agglomeration and high-value dispersion.”

To further reveal the evolutionary characteristics of the WSR-CCC in the YR Basin, the kernel density function was employed to estimate level of WSR-CCC from 2012 to 2023, and a kernel density estimation map was drawn (Figure 6). The core density curve of the WSR-CCC shows a rightward shifting trend, and the shifting range presents a three-stage characteristic of “gentle-decelerated-accelerated”, indicating that the WSR-CCC generally showed an upward trend, though the growth rate from 2016 to 2018 was slower than those in other research periods. Regarding the distribution pattern, a flictuation in peak height showed “decreasing–increasing–decreasing again”, and the peak width experienced fluctuations of “expanding–narrowing–expanding again”, indicating that regional differences first expanded, then contracted, and ultimately re-emerged as new imbalances in the later period. To quantify the growth rate difference during the slow-growth stage, segmented linear regression was conducted with 2016 and 2018 as breakpoints. The analysis identified that the regression coefficient (growth rate) of the 2016–2018 segment was 0.021 (R² = 0.76, p < 0.05), significantly lower than those of the 2012–2016 segment (0.046, R² = 0.88, p < 0.01) and the 2019–2023 segment (0.053, R² = 0.91, p < 0.01). This confirms that the growth rate from 2016 to 2018 was slower than those in other research periods, consistent with the ‘decelerated’ characteristic of the kernel density curve’s rightward shift. In general, although the early peak was skewed to the left, reflecting the generally low carrying capacity state, the main peak was stably located in the medium-to-high value area after 2020, and the basin-wide average value climbed above 0.7, indicating that the Basin gradually transitioned from critical overload to a sustainable carrying state.

3.1.2. Spatial Evolution Characteristics

For the purpose of analyzing its spatial evolution characteristics of the WSR-CCC in the YR Basin, its distribution was mapped using ArcGIS 10.8 (Figure 7). From a spatial perspective, despite the provincial average increased significantly carrying capacity across the nine basin provinces during the study period, its spatial evolution revealed an uneven pattern characterized by proceeding more rapidly in the west and more vigorously in the north compared to the east and south. From 2012 to 2016, the carrying capacities of Qinghai and Gansu fluctuated sharply, and Inner Mongolia achieved a steady growth rate of 34.4%; the carrying capacities of Shanxi and Shaanxi, in the middle reaches, increased steadily, while that of Shandong Province, in the lower reaches, was constrained by water resources, with a growth rate of 15.4%, ranking lowest in the basin in terms of absolute value. From 2017 to 2020, Gansu, in the upper reaches, achieved three-stage leapfrog growth with a growth rate of 63.1%; Inner Mongolia broke through the 0.50 threshold in 2020; and Ningxia experienced the only negative growth in the entire region. From 2021 to 2023, a spatial structure of “dual-core driven and low-value trapped” was formed, with Shanxi and Shaanxi as the primary core and the Gansu–Qinghai Plateau as the secondary core, while Ningxia continued to face sustained pressure. The WSR-CCC in the entire Basin presents a gradient pattern of “high in the west, low in the east, and prominent core”.

In addition, to assess the spatial autocorrelation of the WSR-CCC across the Basin, the global Moran’s I index was utilized (

Table 2. Moran’s I value of the WSR-CCC.

Year	$\mathbf{M}\mathbf{o}\mathbf{r}\mathbf{a}\mathbf{n}’\mathbf{s} \mathbf{I}$	$\mathbf{Z}$
2012	0.1456	1.0474
2013	−0.0493	0.3198
2014	−0.1755	−0.1841
2015	−0.2887	−0.7886
2016	−0.3087	−0.7013
2017	−0.3111	−0.7928
2018	−0.1777	−0.1977
2019	0.2621	1.4817
2020	−0.2126	−0.3121
2021	0.0687	0.6767
2022	−0.3186	−0.7755
2023	−0.2467	−0.4401

). From 2012 to 2023, Moran’s I showed a “W”-shaped evolution trend: the positive value in 2012 was 0.1456, but the index turned negative from 2013, and the absolute value generally worsened during 2013–2017, reaching −0.3111 in 2017, indicating that the spatial distribution gradually changed from agglomeration to dispersion, and inter-regional differences continued to increase. From 2018 to 2023, Moran’s I was only positive (0.2621 and 0.0687) in 2019 and 2021, and it was continuously negative in other years, fluctuating between −0.3186 and −0.1777. It should be noted that although Moran’s I shows a “W”-shaped trend in magnitude, all p-values are greater than 0.05, which means that this trend is not statistically significant. This contradiction can be explained by the small number of study units (9 provinces): the global Moran I test has low statistical power when the number of spatial units is less than 30, leading to it failing to detect significant spatial correlation even if there is a numerical trend. Therefore, the “W”-shaped trend of Moran’s I only reflects the directional change in spatial correlation, not a statistically confirmed stable pattern.

To compensate for the limited statistical power of the global Moran’s I index resulting from the small number of areal units, this study turned to local autocorrelation analysis to examine spatial clustering and uncover underlying associations. The LISA agglomeration map for the WSR-CCC (2012–2023), the spatial agglomeration characteristics were summarized as follows (Figure 8): In 2012, Gansu displayed a “Low–High Outlier” characteristic (local carrying capacity was low, while neighboring areas maintained high capacity), and Ningxia and western Inner Mongolia formed a “Low–Low Cluster”. In 2013, Shandong’s carrying capacity decreased, while neighboring province Henan retained localized high capacity, creating a regional “Low–High” pattern. In 2016, Shaanxi’s capacity decreased, contrasting with the sustained high capacity in northern Sichuan and southern Gansu, further reinforcing the “Low–High” pattern. Moreover, 2018 saw a sharp decrease in carrying capacity in Shaanxi and Shanxi, whereas the carrying capacities of Henan and northern Sichuan remained at high levels, forming an externally driven “Low–High” distribution. A key turning point emerged in 2021, when Ningxia persisted as a “Low–High Outlier”, the capacities of Inner Mongolia and Gansu improved, and Shanxi and Henan established the basin’s first “High–High Cluster”. During 2022–2023, Ningxia and western Inner Mongolia maintained long-term “Low–High Outlier” status, while Shanxi, Henan, and Shandong consolidated the “High–High Cluster” pattern. Collectively, these dynamics indicated that the basin’s overall spatial correlation for comprehensive carrying capacity was dominated by heterogeneity, with no stable large-scale agglomeration pattern being formed; instead, localized collaborative or dependent agglomeration gradually emerged, reflecting the uneven impact of regional resource endowments, policy implementation, and inter-provincial interactions on carrying capacity evolution. These LISA-derived agglomeration patterns hold critical policy implications for advancing inter-provincial cooperation in the Basin: For provinces with long-term “Low–High Outlier” characteristics (e.g., Ningxia, western Inner Mongolia), the pattern underscores their low intrinsic water–soil resource carrying capacities and heavy reliance on ecological support from high-capacity neighboring provinces (e.g., Gansu, Shaanxi), necessitating the establishment of a targeted ecological compensation mechanism, where beneficiary provinces (Ningxia, Inner Mongolia) provide economic subsidies or technical assistance to ecological donor provinces (Gansu, Shaanxi) to safeguard the sustainability of cross-border ecological support; for the emerging and consolidated “High–High Cluster” (Shaanxi, Henan, Shandong), the pattern signals the formation of a synergistic carrying capacity improvement mechanism, which should be further scaled up through a dedicated cross-provincial coordination platform, formulating unified water pollution discharge standards, building inter-provincial sewage treatment networks, and promoting cross-regional technology transfer, thereby drive coordinated improvement in the basin’s WSR-CCC.

3.2. Spatial Spillover Effects of the WSR-CCC

State transition probabilities of carrying capacity levels for adjacent periods across evaluation units (2012–2023) were calculated via a traditional Markov chain-based transition probability matrix (

Table 3. Markov transition probability matrix types for the WSR-CCC.

t/t + 1	n	1	2	3	4
1	23	0.7826	0.1739	0.0435	0.0000
2	25	0.1600	0.4800	0.3200	0.0400
3	24	0.0000	0.2083	0.4583	0.3333
4	18	0.0000	0.1111	0.0000	0.8889

). A notable characteristic of this matrix is that markedly higher probabilities on the diagonal than elsewhere, revealing that the type transition of the WSR-CCC has a certain stability, and there is a phenomenon similar to “club convergence”. This means that provinces with similar carrying capacity levels tend to stay in their current level clusters (clubs) and struggle to jump to other clusters in the short term. The diagonal values indicate that high-level types (88.89%) possess greater stability than low-level (78.26%) and medium-low-level types (48.00%). Furthermore, a comparison of probabilities at the diagonal two ends shows that the upward transition probability is higher than the downward transition probability, signaling an overall improvement in the WSR-CCC within the YR Basin. In addition, the cross-type transfer probability of WSR-CCC in each region of the YR basin is generally low, which reflects that the improvement of WSR-CCC can only follow a gradual path, and although it is very challenging to achieve “leapfrog” development in the future, it is not impossible.

According to Formulas (4) and (5), this study quantified the geographical proximity effect by constructing a neighborhood spatial weight matrix and decomposed the traditional state transition probabilities into conditional transition probabilities under four spatial lag scenarios (

Table 4. The spatial Markov transition probability matrix types of the WSR-CCC.

Domain Type	t/t + 1	n	1	2	3	4
1	1	0.0000	0.0000	0.0000	0.0000	0.0000
	2	11.0000	0.0000	0.4545	0.5455	0.0000
	3	7.0000	0.0000	0.1429	0.4286	0.4286
	4	4.0000	0.0000	0.5000	0.0000	0.5000
2	1	12.0000	0.5833	0.3333	0.0833	0.0000
	2	13.0000	0.3077	0.5385	0.0769	0.0769
	3	13.0000	0.0000	0.2308	0.6154	0.1538
	4	1.0000	0.0000	0.0000	0.0000	1.0000
3	1	7.0000	1.0000	0.0000	0.0000	0.0000
	2	1.0000	0.0000	0.0000	1.0000	0.0000
	3	4.0000	0.0000	0.2500	0.0000	0.7500
	4	9.0000	0.0000	0.0000	0.0000	1.0000
4	1	4.0000	1.0000	0.0000	0.0000	0.0000
	2	0.0000	0.0000	0.0000	0.0000	0.0000
	3	0.0000	0.0000	0.0000	0.0000	0.0000
	4	4.0000	0.0000	0.0000	0.0000	1.0000

). Under the low spatial lag scenario, the WSR-CCC in medium-low-level areas remaining stable was 45.45%, and the upward transition probability was 54.55%; the probability of medium-high-level areas remaining stable was 42.86%, and the upward and downward transition probabilities were 28.57% and 28.57%, respectively. High-level areas remained stable. Under the medium-low spatial lag scenario, the stability probabilities for medium-high-level, medium-low-level, and low-level regions were 61.54%, 53.85%, and 58.33%, respectively, and the upward transition probabilities were 33.33%, 7.69%, and 15.38%, notably, high-capacity regions under this scenario showed a 100% downward transition probability. When the spatial lag was medium-high, medium-high-level regions had a 75% stability probability and a 25% upward transition probability; both low-level and medium-low-level regions had a tendency to transition to high-level states. Under the spatial lag was high, the probability of low-level areas had upward transition was 50%, medium-low-level and medium-high-level regions showed 0% upward transition probabilities, and high-level regions remained largely stable. In general, the probability transfer matrices under the four types of spatial lags are different, and there was a Matthew effect of “strong always strong, weak always weak” in the WSR-CCC among regions to some extent, inconsistent with the results of the traditional Markov chain, indicating that geographical factors exert a notable influence on the dynamic evolution of high-quality energy development. The specific differences were reflected in two aspects: (1) For low-carrying-capacity provinces (type 1), the traditional Markov chain showed an upward transition probability of 0.2174, while under the high-spatial-lag condition (neighboring provinces were type 4), the upward transition probability of type 1 provinces increased to 0.50, 2.3 times the traditional result. (2) For high-carrying-capacity provinces (type 4), the traditional Markov chain showed a stability probability of 0.8889, while under the medium-low-spatial-lag condition (neighboring provinces were type 2), the stability probability of type 4 provinces decreased to 0, and the downward transition probability reached 1.0. This contradiction indicates that the traditional Markov chain overestimated the stability of low-carrying-capacity provinces and underestimated the impact of neighboring provinces on high-carrying-capacity provinces, while the incorporation of spatial lag factors in the spatial Markov chain corrects this deviation.

3.3. Obstacle Factors of the WSR-CCC

According to Formula (6), this study identified the obstacle degrees of the criterion-layer indicators associated with the WSR-CCC in the YR Basin during the 2012–2023 period, and their spatiotemporal characteristics were summarized, as shown in Figure 9. Regarding the overall obstacle degree range for each indicator, driving factors showed an obstacle degree that first rising and then falling, reaching a peak of 0.3204 in 2017 and a decreasing trend from 2017 to 2022, and they were the primary obstacle factors eight times during 2012–2023. Pressure factors maintained a low obstacle degree with slight fluctuations, ranging from 0.0340 to 0.0762 in most years. State factors exhibited significant fluctuations in obstacle degree, assuming first place in 2023, which indicates a gradual increase in their constraint on carrying capacity. Impact factors maintained a high obstacle degree for a long time, fluctuating from 0.2264 (2012) to 0.2914 (2023), and they were a key obstacle factor in most periods. Response factors had an obstacle degree ranging from 0.1792 to 0.2774, ranking second or third among obstacle factors and accounting for a stable proportion of constraints. In terms of the three-stage dominant characteristics of obstacle factors, Stage 1 (2012–2019) saw driving factors as the dominant obstacle, with their obstacle degree consistently higher than those of other indicators, playing a long-term core constraint role. Stage 2 (2020–2021) witnessed a decrease in the obstacle degree of driving factors, while impact factors became the primary obstacle, forming a transitional stage of “driving-impact competition”. Finally, Stage 3 (2022–2023) featured state factors and impact factors jointly serving as the core obstacles, with state factors having the top-ranked obstacle degree and the two indicators presenting a “dual constraint” pattern.

4. Discussion

4.1. Interpretation of Spatiotemporal Evolution Characteristics

The evolution process of the WSR-CCC in the YR Basin (2012–2023) shows a leap from “critical overloading” to “sustainable”. The observed trend of gradual improvement in carrying capacity over time is basically aligns with the findings of Sun et al. [51] and Chen et al. [24]. This transformation is closely associated with national and regional management policies centered on the “Ecological Conservation and Sustainable, High-Quality Growth of the YB Basin”: these policies curb excessive resource consumption and ecological pressure by optimizing resource allocation, advancing pollution governance, and controlling high-energy-consuming industries, thereby creating space for the recovery of carrying capacity. However, box plot and kernel density estimation reveal “low-value agglomeration and high-value dispersion,” indicating unresolved inter-provincial imbalance—driven by natural endowment differences and uneven policy response. Spatially, the “high in the west, low in the east, strong in the north, weak in the south” gradient reflects the interaction of natural and human factors: the upper reaches (Qinghai, Gansu) maintain high carrying capacity due to low economic development and resource pressure, while the lower reaches (Shandong) see slow growth due to high-intensity industrial–agricultural water consumption. Qiao et al. [52] also highlighted the unbalanced spatial pattern of the WRCC in the Yellow River Basin, with the west being stronger and the east weaker. Weak spatial correlation (mostly negative and insignificant global Moran’s I) indicates limited spatial spillover, restricted by geographical barriers and administrative divisions, calling for improved cross-regional coordination. Local autocorrelation confirms “high-high” agglomeration in Shanxi–Shaanxi and “low-low” agglomeration in Ningxia–Inner Mongolia, emphasizing differentiated governance [53,54]. For “Low-Low Cluster” regions, governance should focus on alleviating resource pressure and improving ecological foundations, such as implementing agricultural water-saving irrigation to reduce water resource strain, establishing a “coal-water linkage” mechanism to limit the scale of high-water-consumption coal chemical projects, and participating in the Basin’s cross-provincial ecological compensation mechanism, using the obtained compensation funds to construct soil and water conservation projects. For “High–High Cluster” regions, the priority should be to consolidate and expand synergistic advantages while avoiding resource degradation, such as setting up a cross-provincial joint mechanism to unify industrial wastewater standards, promoting the sharing of water-saving technologies, and moderately developing ecological agriculture to reduce fertilizer and pesticide loads, thus preventing the degradation of the water and soil resource system caused by excessive agricultural activities.

4.2. Mechanism of Spatial Spillover Effects

Traditional Markov chain analysis verifies the “club convergence” of carrying capacity—regions with similar levels tend to maintain status, and short-term cross-level leapfrog development is difficult. This stems from the need for long-term resource–technology–policy investment and the path dependence of development models, making it difficult for low-level regions to catch up. Spatial Markov chain results highlight the role of geographical proximity role: high-level neighbors (e.g., Qinghai) promote local upward transition via technology–policy spillover, while low-level neighbors (e.g., Ningxia) inhibit improvement. The “Matthew effect” arises from high-level regions’ siphoning of talent/funds/policies and low-level regions’ pollution spread, widening regional gaps. The result obtained in this study is consistent with the findings of Wang et al. [55] and Diao et al. [56]: there are significant resource and technology spillover effects among geographically adjacent regions, and high-level regions can, therefore, drive the development of surrounding regions.

4.3. Analysis of Obstacle Factor Stages

The “drive–influence–state” three-stage evolution of obstacle factors reflects the water–soil resource system’s dynamic adjustment: In 2012–2019, high-intensity economic growth and population expansion caused excessive resource development, becoming the core constraint. In 2020–2021, tightened environmental policies eased driving pressure, but accumulated industrial–agricultural pollution became the main obstacle (reflecting environmental governance lag). In 2022–2023, the joint constraints of state and impact factors emerged—long-term human activities degraded the resource background, and an extreme climate exacerbated constraints. The Basin’s WRCC has long been constrained by two primary factors: the over-exploitation of water resources and ecological degradation, a finding that aligns with the studies by Ding et al. [57] and Pang et al. [58]. These stages guide governance: upper reaches should protect ecological advantages to avoid over-development; middle-lower reaches focus on reducing pollution and improving resource efficiency; low-level regions need cross-regional ecological compensation to break the “low-level trap”.

4.4. Limitations and Future Research Directions

Two main limitations are acknowledged: First, the evaluation index system and analytical depth have room for improvement—extreme climate events are not included in the index system, which may limit the interpretation of results. Second, the spatial weight matrix only considers geographical adjacency, ignoring economic and social connections, which may underestimate the actual spatial spillover effect and affect the comprehensiveness of spatial mechanism analysis.

Future research should focus on two directions: First, it should integrate multi-source data to supplement extreme climate-related indicators and optimize the evaluation system, while combining quantitative methods (e.g., panel regression) to analyze the driving mechanism of carrying capacity evolution. Second, it should construct a comprehensive spatial weight matrix incorporating geographical, economic, and social factors to more accurately measure spatial spillover effects. Third, it should apply the Spatial Durbin Model can be employed to simulate the evolution of carrying capacity under various scenarios and comprehensively analyze the spatial spillover mechanisms. This method not only has advantages in quantifying both direct and indirect effects of explanatory variables but can also incorporate other control variables simultaneously, effectively avoiding omitted variable bias. This characteristic enables the SDM to more accurately identify the scale and action path of spatial spillover effects, thereby providing more targeted policy support for the high-quality watershed development [59].

5. Conclusions

This study employs the cloud model to measure the WSR-CCC in the YR Basin from 2012 to 2023. It analyzes their spatiotemporal distribution characteristics through kernel density estimation and spatial autocorrelation, further examines spillover effects using spatial Markov chains, and identifies key factors influencing the barrier degree model. The results are as follows:

(1)

The basin’s carrying capacity demonstrates a significant upward trajectory, transitioning from critical overload level IV to sustainable level II and the pressure has been fundamentally alleviated, but inter-provincial disparities increased. The box plot revealed a prominent pattern of low-value clustering and high-value dispersion. The kernel density curves show a three-stage growth trend, namely gradual growth, decelerated growth, and accelerated growth, as well as peak evolution that changed from bimodal to trimodal and then to unimodal forms. This reflects a shift toward regional equilibrium, though low-value convergence remained slow and high-value dispersion increased.

(2)

A “west-high east-low, north-strong south-stagnant” gradient emerged: upper-reach provinces (Qinghai, Gansu, Shanxi, Shaanxi, Henan, Shandong) formed high-value zones, while Ningxia and Sichuan stayed below average. Global Moran’s I (all > 0.05) indicated no stable spatial self-organization, with weak inter-provincial agglomeration; local LISA clustering showed dynamic high-value synergy and low-value dependency, highlighting the need for zonal regulation.

(3)

The traditional Markov chain analysis shows that the transition of carrying capacity types exhibits club convergence characteristics. The stability levels of low and relatively low levels are lower than that of high levels, and the upward transition probability exceeds the downward one, indicating a positive development trend. The spatial Markov chain reveals a significant geographical proximity effect: transition probabilities vary substantially under different spatial lag contexts, demonstrating a Matthew effect where strong regions continue to strengthen and weak regions further deteriorate.

(4)

The criterion layer obstacle degree shows a three-stage dominant feature of “driving-influencing-state”: from 2012 to 2019, driving factors were the core constraint, with development pressure driven by economic growth and population expansion prevailing. During 2020–2021, impact factors became the primary obstacle, as constraints from industrial pollution and agricultural non-point source pollution intensified. In 2022–2023, state and impact factors showed joint dominance, where extreme climate and cumulative long-term development degraded the water–soil resource base, overlapping with pollution constraints to form a composite bottleneck.

In the future, we should focus on addressing obstacle factors, implement targeted regulation, dynamically monitor spatial correlation patterns, and strengthen multi-factor collaborative responses to achieve the sustainable improvement of the WSR-CCC in the Basin.