Evaluation and prediction of carrying capacity of soil and water resources in Lanzhou City based on the CA–Markov model Open Access

Water is the source of life, and soil is the basis for survival; together, they represent some of the most valuable resources on Earth (Chen et al. 2018). As basic natural and strategic economic resources, water and soil are central to regional spatial planning and essential for maintaining ecological balance, supporting biological survival, and promoting socio-economic development (Wei 2012). Scientific evaluation of the carrying capacity of soil and water resources is crucial for assessing the degree of coordinated development between regional resources, population, and economy (Chadenas et al. 2008). The concept of ‘carrying capacity’, which refers to the maximum load an object can bear without causing irreversible damage, is widely used as an indicator for evaluating the sustainability of a region. On this scale, social systems and ecological functions are closely related (Graymore et al. 2010). With rapid economic development and a continuous increase in population, soil and water resources face increasingly severe challenges (Zimeng et al. 2023). Therefore, studying the water–land resource-carrying capacity and formulating reasonable water–land resource protection policies are essential to adapting to rapid economic and social development.

Lanzhou is situated in the inland regions of northwestern China, covering a vast area; however, most of this area falls under arid and semi-arid regions, leading to prominent issues such as water resource shortages, soil erosion, and fragile ecological environments. Furthermore, the country has entered a new phase of development characterized by rapid economic growth and population increase, which necessitates a stable and high-quality supply of water and land. However, this growth also results in large amounts of polluting discharges, posing significant challenges to water and land resources (He & Wang 2022). With the proposal for ecological protection and high-quality development of the Yellow River Basin, it is crucial to ensure the protection and rational use of soil and water resources in Lanzhou.

In recent years, both domestic and international scholars have increasingly shifted their focus from singular indicative evaluation methods to studying the efficiency and matching coefficients of soil and water resources to studying the efficiency and matching coefficients of their utilization. Raup and the group were pioneers in simultaneously evaluating water and land resources, highlighting that expanding land use can increase uncertainties in water availability (Zhang et al. 2018). Zhuangyan et al. applied the particle swarm optimization method, projection pursuit method, and the Gini coefficient method to assess the carrying capacity of soil and water resources in Yan'an City and propose measures for sustainable development and resource use. Similarly Yan (2015) and Chen Hongmei utilized the driving force–pressure–state–impact–response (DPSIR) model to evaluate soil and water resource-carrying capacity in Heilongjiang Province, analyzing regional evolution patterns (Hongmei 2016). Meanwhile, Guo Jiawei used the Gini coefficient method to study soil and water resource matching in Huining County (Jiawei 2018), and Li Wenjing et al. employed the Gini coefficient and matching coefficients to comprehensively analyze changes in arable land and soil–water matching in the Amu Darya River Basin (Wenjing et al. 2021).

Previous studies predominantly focused on evaluating regional soil and water resource-carrying capacities without identifying influencing factors or predicting future trends. Building upon this foundation, our study adopts the DPSIR framework to construct an evaluation system for soil and water resource-carrying capacity. We objectively determine the weights of each evaluation index using the entropy weighting method and utilize the cloud model as an evaluation tool. This approach comprehensively addresses the complexity and uncertainty inherent in soil and water resource management in Lanzhou City.

The city's rivers belong to the Yellow River system, including its mainstream and first-class tributaries such as Huangshui, Wanchuan River, and Zhuanglang River. According to the Gansu Province Water Resources Bulletin for 2022, Lanzhou's average temperature ranges from 7.2 to 12.0 °C, with annual precipitation ranging between 195.3 and 461.5 mm. The national land survey data reveal a total area of 19,787,700 acres, with 3,906,300 acres designated for cultivation. Forest land covers 146,537.64 ha, boasting a forest coverage rate of 8.35%, while grasslands span 683,131.55 ha, with a vegetation cover of 54.94%.

By the end of 2022, Lanzhou's resident population will reach 4,415,300 people, with urban residents constituting 84.07% of the total population. The city's gross domestic product (GDP) for 2022 totals 334.35 billion yuan, with the secondary sector contributing 34.4% and the tertiary sector 63.64%. The city's total water resources amount to 315 million m³, yet surface water mineralization increases gradually from south to north, highlighting the geographical feature of brackish water and coexistence with drought conditions.

The scientific construction of an indicator evaluation system is essential for assessing the carrying capacity of soil and water resources. The DPSIR model, an improvement on the pressure-state-response (PSR) model, serves as a conceptual framework that systematically captures the interactions and mutual influences between human activities and the natural environment. It encompasses social, economic, ecological, and other dimensions, offering comprehensive and scientific insights. This model is widely used in developing indicator systems for carrying capacity evaluation. The DPSIR model comprises five subsystems: driving force–pressure–state–impact–response (Fan et al. 2023). The driving force denotes factors directly affecting soil and water resource-carrying capacity, categorized into natural (e.g., climate, topography) and anthropogenic (stemming from human activities). Pressure represents the impact of these driving forces on soil and water resources, encompassing aspects such as population growth, resource development, and environmental pollution. The state reflects the resultant condition of resource use and industrial structure influenced by driving forces and pressures. Impact pertains to how the state of land and water resources affects socio-economic development, including economic losses due to resource scarcity. Response entails measures and actions undertaken by humans to foster sustainable development of soil and water resources, including policy formulation, technological innovation, and more. Applying the DPSIR framework, we selected 23 indicators to evaluate the carrying capacity of soil and water resources in Lanzhou City. These indicators were chosen based on criteria of scientific rigor, representativeness, and accessibility. The evaluation indicator system is detailed in Table 1.

The evaluation standards for the carrying capacity of water and soil resources should accurately and objectively reflect the level of coordinated development among the regional population, economy, ecological environment, and water resources. Tailored to the unique conditions of Lanzhou City's water and soil resources, these standards are structured into five grades. The specific grading criteria for each index are detailed in Table 2.

Carrying capacity refers to the ability of a resource to meet current demands while maintaining sustainability. Weak carrying capacity suggests that a resource is nearing its limits. Criticality and overload indicate that resource utilization has surpassed sustainable thresholds, leading to the gradual degradation of ecosystems. In cases of severe overload, resource depletion and ecological degradation become particularly severe, potentially resulting in irreversible ecological damage.

The Cronbach's alpha reliability coefficient method serves as a tool for assessing the stability or reliability of an indicator system through a reliability coefficient (Li et al. 2012). A higher reliability coefficient indicates a greater degree of confidence in the measurement's consistency and dependability.

Calculated by MATLAB programming, the confidence analysis of the indicators of the carrying capacity of soil and water resources in Lanzhou City from 2010 to 2022 was carried out, and the results are shown in Table 3. The deviation standardization method was used to normalize the indicators to reduce the influence of positive and negative indicators on the evaluation process (Fu & Zhao 2006).

As can be seen from Table 4, the Cronbach's alpha reliability coefficients of the selected years are all between 0.7 and 0.8, indicating that the indicator system has a high degree of credibility and the evaluation indicator system is reasonably constructed.

The figures in this paper are divided into statistical data and land-use data. Statistical data from the ‘Gansu Provincial Statistical Yearbook’ and the ‘Gansu Provincial Water Resources Bulletin’(2010–2022); Land-use data were obtained from the Geospatial Data Cloud Platform, with a spatial resolution of 30 m for Landsat 8 remote sensing image data related to the study area. The land-use data were classified into nine types, including cropland, forest, shrubland, grassland, water bodies, snowy mountains/glaciers, Barren, Impervious, and wetlands using a combination of supervised classification by ENVI 5.3 software and manual visual interpretation; ArcGIS 10.8 software was used to process the distance and elevation (DEM) data through projection transformation and resampling. Euclidean distances were used to calculate the distances from different land classes to town centers, motorways, main roads, and railways.

Current data forecasting methods include exponential smoothing, moving averages, linear regression, support vector machines, neural networks, Markov chain models, random forests, and particle swarm optimization, among others. These methods exhibit strong predictive capabilities in their respective fields. Given the irregularity of the data sample distribution and the extended forecasting period in this study, a gray forecasting model was selected for socio-economic data prediction. This model effectively captures trends in data variation and combines quantitative and qualitative analysis, resulting in highly accurate predictions. The CA–Markov model, which integrates spatial and temporal information, considers the dynamic processes of land use change, providing detailed spatial predictions and handling complex land-use patterns. Additionally, it can efficiently integrate data from various sources, further enhancing prediction accuracy.

In summary, this study develops an evaluation index system for soil and water resource-carrying capacity utilizing the DPSIR model. The entropy weight method is employed to objectively ascertain the weights of various evaluation indicators, while a cloud model functions as the evaluative tool, thoroughly addressing the complexity and uncertainty inherent in water and soil resource management in Lanzhou. The CA–Markov model is implemented to elucidate the characteristics of land-use conversion rules, competition dynamics, restriction protocols, and policy regulations in forecasting soil and water resource-carrying capacity (Figure 2). Additionally, a gray prediction model is integrated to project the evaluation indicators, with the objective of anticipating future carrying capacity. The evaluation system encompasses multiple dimensions, including natural conditions, socio-economic factors, the efficiency of soil and water resource utilization, environmental impacts, and management responses, thus providing a comprehensive overview of the current status and trends in the sustainable utilization of soil and water resources.

Then generate cloud droplets with normal random number x_i and affiliation degree μ_i, which are represented by (x_i, μ_i) as vertical and horizontal coordinates, by repeating the above operations until a certain number of cloud droplets are generated to draw the cloud map. Finally, according to the distribution of cloud drops in the cloud diagram, the evaluation level is determined.

The cellular automata (CA) model is a lattice dynamics model that is discrete in time, space, and state, with localized spatial interactions and temporal causality and has the ability to simulate the spatiotemporal evolutionary processes of complex systems (Xiaodong et al. 2012). Coupling the CA model with the Markov model can accurately simulate the complexity and uncertainty of each land use transformation in the study area under the interaction of human–land relationships (Xu et al. 2020). In this study, the FLUS software is used to achieve the coupling of the above models, which integrates the spatial computational ability of the adaptive inertia mechanism with the ability of the Markov model to predict trends in land-use type changes and the number of land-use types, so that the model can more accurately reflect the spatiotemporal trend of land-use changes in the simulation. In the model run, the Markov and CA models are closely related through the coupling of the number of land types on the time series. When the spatial simulation reaches the requirements of one stage, the simulation results of that stage will be used as inputs for the next stage, and it will participate in the next stage along with the drivers and demands of the next stage. This coupling ensures that the two different models feedback to each other in the simulation, achieving sufficient integration to help reduce the possibility of error transmission in the results (Rimal et al. 2018).

Determine the weights of the indicators using the entropy weight method, and then combine them with the cloud model to carry out a comprehensive evaluation (Xu et al. 2022). Specific steps are as follows:

• (1) Calculate the cloud numerical characteristics (E_x, E_n, H_e) for each evaluation metric, where H_e is an empirical constant and E_x can be obtained by the following equation:

  

  (3)

C_max − C_min is the maximum and minimum values of the rank thresholds, respectively.

The final affiliation is then obtained by averaging the different levels of affiliation

• (3) According to the data of the selected indicators, use the entropy weighting method to find the corresponding weight w_i of each indicator.

• (4) Calculate the integrated affiliation degree and determine the evaluation grade according to the principle of maximum affiliation degree in the cloud model.

  

  (7)

The FLUS model was used to predict the land-related data, which was then combined with the gray prediction model to predict the carrying capacity of soil and water resources in the study area for 2027. The specific steps are as follows:

• (1) Driving factor selection and processing

Considering the natural and human conditions of the study area, appropriate driving factors were selected based on the accessibility, consistency, quantifiability, spatial variability, and relevance to the study objectives of the driving factor data, as well as the principle of comprehensiveness in factor selection. Using ArcGIS 10.8 software, the DEM was projected and resampled, and then the slope and slope direction tools provided by geographic information system (GIS) were used to produce the raster data of slope and slope direction in the study area; the POI (points of interest) crawler tool was used to obtain the distribution of the settlements in the study area, which was converted into comma-separated values (CSV) format data for importing into ArcGIS; and the Euclidean distances were used to draw raster data of different land classes relative to rivers, highways, settlements, railways, and other factors.

• (2) Land-use data prediction

Land-use remote sensing images from 2 years were selected, and operations, such as resampling, were carried out to ensure that the type assignment numbers and spatial resolution of the land-use data were consistent. One-year land-use data and driving factor data were imported into FLUS software, and the artificial neural network (ANN)-based probability-of-occurrence estimation self module was used to create a suitability atlas. Then, the Markov module provided by FLUS was used to determine the evolution endpoints, and finally, the adaptive inertia and competition mechanism CA module was used to predict the land-use data. Since FLUS software exports raster data with a spatial resolution of 30 m, the raster number can be used to calculate the area of land classes for evaluation.

• (3) Statistical data prediction

Data outliers are monitored and processed by deleting outliers, replacing outliers, or using interpolation to ensure the accuracy of the prediction. After completing the outlier processing, the gray prediction model is used to predict the statistical data.

As can be seen from the cloud diagram, each level of the indicator has a cross-section in the cloud diagram, for example, when the proportion of agricultural GDP is 2.44%, the degree of affiliation of the indicator belonging to levels Ⅰ to Ⅴ obtained by the cloud model calculation is 0.030, 0, 0, 0.013, 0.834, respectively, which can be interpreted as follows: the probability that the agricultural GDP is at level V is 0.834, and the probability of it being level Ⅳ is 0.013, which is unlikely to be Class III and Class II, and the possibility of being Class I is 0.030. This means that the possibility of being Class V is the greatest. It reflects that the cloud model retains the uncertainty and ambiguity of qualitative concepts when quantifying them.

As can be seen from the figure, the weights of the indicators calculated by the entropy weighting method are more evenly distributed, and the weight values are all concentrated between 2 and 8%. Among them, the urbanization rate, the number of water-producing systems, the per capita water resources, and the population density contribute the most to the carrying capacity. Indicators such as the reduction rate of arable land area and the proportion of agricultural GDP have less influence on the carrying capacity of soil and water resources.

In determining the land-use transition parameters of the FLUS model, we established a relatively low transfer coefficient for arable land in accordance with the ‘Gansu Province Territorial Spatial Planning (2021–2035)’ to ensure the stability of arable land resources. Additionally, based on the ‘Ecological Protection and High-Quality Development Planning for the Yellow River Basin in Gansu Province,’ we set an extremely low transfer coefficient for wetlands and water bodies to safeguard ecological functions from degradation. Furthermore, considering the rate of urbanization, we defined the transformation coefficient for urban construction land to reflect the impact of urban land expansion on surrounding land types. Finally, guided by expectations for economic development and population growth, we determined the transition parameters for agricultural land, forests, grasslands, and other land types to achieve a rational land-use layout that supports sustainable development goals.

Figure 7 shows that from 2010 to 2027, the area of arable land in each category in Lanzhou City increased from 1712.4 to 1841.9 km², and the area of construction land and wasteland also increased to varying degrees; the area of grassland decreased from 1.07 × 104 to 1.03 × 104 km². Among them, the increase in the area of arable land can be attributed to policies such as the red line policy, high-standard farmland, agricultural production subsidies, and other policies (Zhou 2021); economic and social development will lead to an increase in construction land, but due to urban and rural construction planning and other factors of the limitations of the increase is relatively slow (Shang et al. 2021); the increase in the area of wasteland as well as the decrease in the area of grassland may be due to the combined effect of various factors, including climate change, inappropriate use of land resources, mismanagement of water resources, and desertification of the land, and so on (Chuanxiong et al. 2011).

The basic data of the study area from 2010 to 2022 were selected to predict the data for 2027, and then the evaluation index data were calculated from these data. The prediction results are shown in Table 5. The simulation accuracy of the prediction model is generally derived from the ratio of the variance of the true error to the variance of the original data, i.e. the a posteriori difference ratio. The a posteriori difference ratio of C < 0.35 (high accuracy), C < 0.5 (qualified accuracy), and C < 0.65 (basically qualified accuracy).

To reduce prediction error, the abnormal data for the total sown area in 2010 and 2011 were removed. Initially, the C-value was 0.71, which did not meet the prediction accuracy requirements. After removing the abnormal data, the C-value decreased to 0.39, meeting the accuracy requirements. Due to significant fluctuations in the affected area and disaster-affected area data, attempts to use methods, such as index smoothing, were ineffective. Consequently, this study utilized the average value instead of the predicted value for evaluation.

Furthermore, by observing the predicted C-value of each index, it is evident that the gray prediction model does not achieve high prediction accuracy for the water production modulus, irrigation water consumption (μ), rainfall, and other data significantly influenced by policy and geography. This may be attributed to the prediction principle of the gray prediction model, which identifies the degree of dissimilarity between the development trends of the system factors to conduct correlation analysis and subsequently establishes the corresponding differential equation model. Future studies will explore new prediction methods to forecast such data more accurately.

Based on the principle of maximum affiliation of the cloud model and considering the weights, the grades of the carrying capacity of soil and water resources in Lanzhou City from 2010 to 2027 were determined. The specific results are presented in Table 6.

As shown in Table 6, the current status of water and soil resources in Lanzhou City is relatively unsatisfactory, with Ⅳ (overloading) in 2010, 2011, 2014–2016, and Ⅴ (serious overloading) in the next 5 years predicted. According to the weight of each evaluation index combined with the ‘Gansu Provincial Statistical Yearbook’, ‘Gansu Provincial Water Resources Bulletin’ data analyzed: (1) The urbanization rate and population density, as negative indicators, have a high weighting in the evaluation system of the carrying capacity of soil and water resources. However, with the economic and social development, the urbanization rate and population density will still show an increasing trend, and the carrying capacity will further deteriorate. Therefore, while guiding the rapid economic development, we should do a good job of coordinating between socio-economic development and environmental protection and further increase the proportion of investment in environmental management. (2) Per capita water resources are also an important indicator affecting the carrying capacity of regional soil and water resources. Lanzhou, as a typical soil and water erosion area and ecologically fragile area in the northwestern interior, has an arid climate with little rain and scarce water resources. The per capita water resources are only 7.137 billion m³, which seriously affects the sustainable development of local soil and water resources. Therefore, the management and deployment of water resources have been strengthened, and a sound water resource dispatch system has been established to rationally allocate water resources and ensure the security of the water supply. Regulating the distribution and utilization of water resources through the construction of reservoirs, storage projects, and other facilities is indispensable for the sustainable utilization of local soil and water resources. (3) The number of water-producing systems is an important indicator for evaluating the use efficiency of water resources. The higher the value, the greater the proportion of total water resources per unit that comes from rainfall, and vice versa, the proportion from rainfall is relatively small 2021, the number of water-producing systems in Lanzhou was only 0.09, much lower than that of Tianshui (0.2), Linxia (0.2), and Gannan (0.43), indicating that the proportion of total water resources per unit that comes from rainfall is low, and the efficiency of water resources is low. This indicates that the proportion of total water resources per unit from rainfall in Lanzhou City is low, and the efficiency of water resource utilization is not high. Reasonable use of local rainfall resources can effectively alleviate the shortage of water resources. (4) As an indispensable part of modern agriculture, chemical fertilizers and pesticides play an important role in increasing crop yields and ensuring food security. However, in using chemical fertilizers and pesticides, it is important to be fully aware of the environmental and ecological problems they may cause. Excessive use of chemical fertilizers may change the structure of the soil, making it soft and increasing its permeability, thus reducing its ability to retain water and fertilizers and increasing the risk of soil erosion and water loss. Reasonable reductions in the amount of pesticides and chemical fertilizers applied per unit of arable land and the promotion of sustainable agricultural techniques will reduce the consumption and pollution of soil and water resources by agriculture.

In conclusion, the confidence coefficient of the evaluation index system of the carrying capacity of land and water resources in Lanzhou City constructed by the DPSIR model in this study is between 0.7 and 0.8, with a high degree of credibility; the weights of the indexes are determined by the entropy weighting method, and the cloud model is used as the evaluation tool of the evaluation system, which comprehensively takes into consideration the complexity and uncertainty of the management of soil and water resources in Lanzhou City; the FLUS model is used to predict the Kappa coefficient of the future land use situation using FLUS model reaches more than 0.7, and the results are more accurate; most of the a posteriori difference ratios of the socio-economic data predicted using the gray prediction model are less than 0.35, which is in line with the requirements of accuracy, but the prediction accuracy of the data of the affected area, the disaster area data with large fluctuations, and the data of the water production modulus, the average acre of irrigation water use, and rainfall that are greatly affected by the policy and the geographical area are not high, and the follow-up efforts needs to try new methods to improve the accuracy of this kind of data. Follow-up efforts need to try new methods to improve the prediction accuracy of such data. Generally speaking, the prediction system for evaluating the carrying capacity of soil and water resources in Lanzhou constructed in this study has a high degree of credibility. According to the prediction results, from 2010 to 2027, the carrying capacity of water and soil resources in Lanzhou City is poor, overloaded, or even seriously overloaded, and the sustainable use of water and soil resources faces serious challenges. The key indicators in the evaluation system include urbanization rate, population density, per capita water resources, number of water-producing systems, and the use of fertilizers and pesticides. These indicators play an important role in evaluating the development status and resource use efficiency of the region. Increasing urbanization rates and population density will exacerbate resource consumption and environmental pressure, while insufficient water resources per capita will threaten the sustainable development of the region. Low water yield coefficients reflect a lack of water use efficiency, while excessive use of chemical fertilizers and pesticides may lead to changes in soil structure and an increased risk of soil erosion. Therefore, in order to achieve sustainable economic and social development and protect the ecological environment, it is necessary to strike a balance between economic growth and environmental protection in the context of social development and take effective measures to optimize the structure of resource use, improve the efficiency of water resource use, and reduce the use of chemical fertilizers and pesticides in order to ensure sustainable use of soil and water resources and to promote long-term economic and social prosperity and stability.

This study focuses on Lanzhou City in Gansu Province, situated against the backdrop of water scarcity, soil erosion, and fragile ecological environments in the northwestern inland region. The primary objective is to investigate the spatiotemporal evolution of soil and water resource-carrying capacity. By employing the DPSIR model, entropy weight method, and cloud model, we systematically analyze the intricate and dynamic challenges associated with Lanzhou's soil and water resource-carrying capacity, considering critical factors such as the upper limits of water resource utilization and ecological protection thresholds. Utilizing extensive socio-economic data and spatial remote sensing analysis, we examine the spatiotemporal differentiation characteristics and evolutionary patterns of the driving factors influencing Lanzhou's soil and water resource-carrying system. Furthermore, we leverage the CA–Markov model and gray prediction model as theoretical frameworks to project the status of soil and water resource-carrying capacity from 2023 to 2027. The primary conclusions drawn from this research are as follows:

• (1) Through the DPSIR model, we construct the evaluation system of the carrying capacity of soil and water resources, using the Cronbach's alpha reliability coefficient method to carry out the reliability analysis. The selected years of the Cronbach's alpha reliability coefficient are in the range of 0.7–0.8; the index system has a high degree of credibility, and the construction of the evaluation index system is reasonable.

• (2) Through the entropy weighting method– cloud model evaluation method, it can be determined that the carrying capacity of soil and water resources from 2011 to 2022 is at levels Ⅳ (overloaded) and Ⅴ (seriously overloaded), and the overall efficiency of soil and water resources utilization is on the low side, and the sustainable utilization of soil and water resources is facing a serious challenge. Among them, the urbanization rate, the number of water-producing systems, and the per capita water resources have the greatest influence on the carrying capacity of soil and water resources.

• (3) The prediction method of the FLUS-gray prediction model can be obtained that compared with the current situation, the carrying capacity of soil and water resources in Lanzhou City will further deteriorate from 2023 to 2027, which will affect the sustainable development of soil and water resources.

Based on this, the following development recommendations are proposed:

• (1) Develop a comprehensive assessment system for soil and water resources to provide a solid scientific foundation for the rational planning and allocation of water resources.

• (2) Actively promote the regional reuse of reclaimed water and implement a multifaceted system of water-saving strategies to comprehensively optimize water resource allocation, thereby achieving the conservation and intensive utilization of water resources to support sustainable economic and social development.

• (3) Future agricultural development should focus on enhancing support for organic and ecological agriculture through policies such as financial subsidies, tax incentives, and technical training. Moreover, it is crucial to intensify efforts in agricultural technological innovation by developing efficient, low-toxicity biopesticides and environmentally friendly fertilizers while promoting water-saving irrigation and soil enhancement techniques. These initiatives will facilitate the transition of agriculture toward a greener, healthier, and more sustainable future.

• (4) Adjust the industrial structure, establish development goals for industries, optimize urban functional positioning, and create a distinctive industrial system while encouraging the development of water-saving and water resource recycling technologies.

• (5) Reform the water pricing mechanism to promote the efficient use of water resources. Tailored to the specific water resource endowments and utilization conditions of different regions, explore and implement diverse water resource allocation schemes and water-saving strategies for various sectors. Additionally, expedites the enhancement of water conservation infrastructure.

The dynamics of soil and water resource-carrying capacity represent a complex phenomenon characterized by the interplay of multiple factors, multi-tiered drivers, and interconnected processes. This research aligns with the framework of typical high-order, multi-feedback integrated system challenges. This study simulates the evolutionary processes and future trajectories of soil and water resource-carrying capacity in Lanzhou City through the integration of multi-source data fusion, the establishment of a coupling evaluation system, and the application of the CA–Markov model. This approach partially mitigates the shortcomings inherent in traditional assessments, which often exhibit a singular and linear perspective in their simulations. Nevertheless, certain limitations persist. The carrying capacity of soil and water resources is inherently constrained by a multitude of factors. Although this study employs both the CA–Markov model and the gray prediction model to forecast future carrying capacity, the accuracy of predictions related to data significantly influenced by policies and regional variances – such as water production coefficients, average irrigation water usage per acre, and rainfall – remains relatively low. This limitation primarily stems from the gray prediction model's dependance on identifying discrepancies in development trends among system variables, conducting correlation analyses, and subsequently establishing corresponding differential equation models for predictions. Moreover, the parameter settings of the CA–Markov model are intricate, and the predictive outcomes are constrained by the assumptions inherent in the model parameters.

Consequently, future research will persist in refining predictive models and methodologies. Building upon the CA–Markov model, we will enhance parameter settings and undertake sensitivity analyses to evaluate the impact of variations in model parameters on the results. Furthermore, we will investigate the incorporation of advanced algorithms, such as machine learning and deep learning, to improve the predictive accuracy of critical data, including water production coefficients, average irrigation water usage per acre, rainfall, and cultivated land area. Additionally, we will conduct multi-scenario simulation analyses. By developing various policy scenarios, we aim to simulate the evolutionary trends of soil and water resource-carrying capacity under diverse policy interventions, thereby validating the rationale and effectiveness of policy recommendations.

This study was supported by the Strategic Research and Consultation Project of the Chinese Academy of Engineering (Grant No. GS2022ZDI02), the Gansu Province Youth Science and Technology Fund (Grant No.24JRRA262) and the Major Cultivation Project of the Scientific Research Innovation Platform in Universities by the Department of Education of Gansu Province (Grant No. 2024CXPT-14).

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

The authors declare there is no conflict.