Method for identifying multi-factor relation and driving factors of toughness of water resource system

Abstract

The invention discloses a water resource system toughness multi-factor relation and driving factor identification method comprising the following steps: collecting multi-dimensional basic data of a river research area, and constructing a water resource system toughness comprehensive database; based on the system dynamics model, constructing a causal feedback network of a meteorological-hydrological-social economy-ecology-engineering five-dimensional subsystem, and simulating an internal causal feedback relationship of a water resource system; constructing a coupling degree model, and quantifying the intensity level of interaction among the plurality of subsystems by calculating the coupling degree; performing water resource system toughness influence factor importance evaluation based on a random forest algorithm; a geographic detector is introduced, and main driving factors and action mechanisms of the main driving factors influencing the toughness of the water resource system are analyzed from a spatial perspective. By adopting the identification method, a more scientific and reasonable water resource management strategy can be formulated, the toughness of a water resource system is effectively improved, and the safety and sustainable utilization of water resources are guaranteed.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of water resource management, engineering and ecology, and in particular to a method for identifying the multi-factor relationships and driving factors of water resource system resilience. Background Technology

[0002] Under the influence of global climate change, floods and droughts in provinces and regions along the Yellow River are exhibiting new characteristics such as extreme frequency, increased intensity, and intensified alternation between drought and flood. Large-scale human activities have further increased the risk of floods and droughts, and coupled with rapid economic and social development and urbanization, disaster losses have been significantly amplified. The resilience of the water resources system in provinces and regions along the Yellow River is a core element supporting high-quality development of the basin and the region. Revealing the intrinsic mechanism driven by the complex interaction of multiple factors has important theoretical value and practical significance for improving the resilience of the water resources system, ensuring water security in the basin and the region, and promoting ecological sustainable development.

[0003] Current research on the resilience of water resource systems is mainly limited to the quantitative analysis and assessment of the resilience itself, with relatively little research on the driving factors and evolution mechanisms of water resource system resilience. Existing studies mostly analyze from ecological, social, and economic perspectives; however, when multiple influencing factors are combined, it not only obscures the characteristics of the individual elements but also makes it difficult to accurately reveal the complex interaction mechanisms between the elements.

[0004] Current research on driving mechanisms mainly focuses on resource utilization constraints, watershed, urban, water resource, agricultural system resilience, regional coordination and development, and the environment. Most studies currently fail to fully reflect the dynamic relationships and intrinsic mechanisms of interdependence and mutual constraints among the various elements within the system. Therefore, it is necessary to study the driving factors of water resource system resilience, deeply analyze the influencing factors of changes in water resource system resilience, explore the driving mechanisms of water resource system resilience evolution, and provide theoretical support for improving water resource system resilience.

[0005] In conclusion, a comprehensive assessment of the resilience of water resource systems in provinces and regions along the Yellow River and an analysis of the resilience-driving mechanisms are essential. This will help to formulate more scientific and reasonable water resource management strategies, effectively enhance the resilience of water resource systems, and ensure the safe and sustainable use of water resources in order to cope with future uncertainties and challenges. Summary of the Invention

[0006] The purpose of this invention is to provide a method for identifying the multi-factor relationships and driving factors of water resource system resilience. This method combines a system dynamics model to draw a causal relationship diagram, clarifies the intrinsic connections between water resource system indicators, uses a coupling degree model to analyze the intensity of the multi-factor effects on water resource system resilience, and employs a random forest algorithm to screen key driving factors. Based on these driving factors, the invention further focuses on their spatial differentiation characteristics, introduces a geographic detector, and analyzes the main driving factors and their mechanisms of action that affect water resource system resilience from a spatial perspective.

[0007] To achieve the above objectives, this invention provides a method for identifying the multi-factor relationships and driving factors of water resource system resilience, comprising the following steps:

[0008] Step S1: Collect multidimensional basic data of the river study area and construct a comprehensive database of water resource system resilience;

[0009] Step S2: Based on the system dynamics model, construct a causal feedback network of the five-dimensional subsystem of meteorology, hydrology, socio-economic, ecology, and engineering to simulate the internal causal feedback relationship of the water resources system.

[0010] Step S3: Construct a coupling degree model and quantify the strength level of interaction between multiple subsystems by calculating the coupling degree.

[0011] Step S4: Based on the random forest algorithm and using the Bagging ensemble strategy, assess the importance of factors affecting the resilience of the water resources system.

[0012] Step S5: Introduce a geographic detector to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective.

[0013] Preferably, in step S1, multidimensional basic data of the river study area are collected to construct a comprehensive database of water resource system resilience, specifically including:

[0014] Based on monitoring and statistical data, data cleaning, desensitization, splitting, and interpolation extension techniques are used to integrate basic data of the river research area;

[0015] The integrated basic data includes meteorological and hydrological observation data, regional water supply and use statistics, economic and social development indicators, ecological and environmental indicators, water conservancy infrastructure data, and topographic and underlying surface feature data extracted based on remote sensing technology.

[0016] The above data were categorized and organized according to time and spatial scales to construct a comprehensive database of water resource system resilience.

[0017] Preferably, in step S2, based on the system dynamics model, a causal feedback network of a five-dimensional subsystem of meteorology, hydrology, socio-economic, ecology, and engineering is constructed to simulate the internal causal feedback relationship of the water resources system, specifically including:

[0018] First, establish a causal relationship network among various influencing factors, and clarify the interrelationships and feedback mechanisms among the variables of each factor.

[0019] Then, a causal feedback flow graph of the system is constructed to present the nonlinear relationships between various influencing factors and predict the dynamic evolution trend of the system's behavior.

[0020] Preferably, in step S3, a coupling degree model is constructed, and the strength level of the interaction between multiple subsystems is quantified by calculating the coupling degree. The specific process is as follows:

[0021] First, construct an evaluation function U that reflects the effects of each factor. ij As shown below:

[0022]

[0023] Among them, U ij This represents the degree to which each influencing factor achieves the target, with a value range of [0,1]; A ij and B ij These represent the upper and lower limits of the influencing factor when the water resource system reaches a steady state; x ij This represents the comprehensive evaluation value of the j-th subsystem in the i-th region;

[0024] Then, establish the coupling function C. z This is used to characterize the degree of interrelationship between factors, as shown below:

[0025]

[0026] Where z is the number of systems involved in the coupling; U1, U2, ..., U z These represent the degree to which the system has achieved its objective; C z This represents the coupling degree between regional subsystems, with a value range of [0,1].

[0027] Preferably, in step S4, the importance of factors affecting the resilience of the water resource system is assessed using a Bagging ensemble strategy based on the random forest algorithm. The specific process is as follows:

[0028] First, use Bootstrap sampling to extract k samples from the original training set, with each sample having the same size as the original training set.

[0029] Then, k decision tree models are built for each of the k samples to obtain k classification results;

[0030] Finally, a vote is taken on each record based on the k classification results to determine its final classification.

[0031] Preferably, a Bagging ensemble strategy is used based on the random forest algorithm to calculate the contribution value of each influencing factor in the river study area in a single decision tree of the model, and then the average value of the results of all trees is taken, as shown below:

[0032]

[0033] Where I(x) represents the contribution value of the influencing factors; J represents the number of decision trees; C full is the average value of the entire dataset in a single tree; n is the number of influencing factors; I l (x,l) represents the contribution of x to l trees.

[0034] Preferably, in step S5, a geographic detector is introduced to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective.

[0035] The geographic detector includes a factor detection module and an interaction detection module; the factor detection module is used to assess the explanatory power of a single factor on resilience; the interaction detection module is used to analyze the interaction between different factors and determine whether the factors jointly affect the resilience level.

[0036] Preferably, the factor detection module detects the spatial heterogeneity of the dependent variable, water resource system resilience Y, and the degree to which influencing factor X explains the spatial heterogeneity of water resource system resilience Y. The explanatory power of the factor on the spatial distribution is measured by calculating the factor explanatory power q, as shown below:

[0037]

[0038] Where q represents the explanatory power of the discretized influencing factors on the resilience of the dependent variable, water resources system, and its value ranges from 0 to 1, with a larger q value indicating stronger explanatory power; t represents the classification or stratification of the influencing factors, t = 1, 2, 3, ..., K; N t The number of samples in layer t; σ is the sample variance of layer t; N is the total sample size; 2 This represents the total sample variance.

[0039] Therefore, the above-mentioned method for identifying the multi-factor relationships and driving factors of water resource system resilience can help formulate more scientific and reasonable water resource management strategies, effectively improve the resilience of water resource systems, and ensure the safe and sustainable use of water resources to cope with future uncertainties and challenges.

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method for identifying the multi-factor relationships and driving factors of water resource system resilience;

[0042] Figure 2 This is a flowchart illustrating the construction process of the comprehensive database for water resource system resilience according to the present invention.

[0043] Figure 3 This is a system dynamics causal relationship diagram of the water resources system performance in provinces and regions along the Yellow River in this embodiment of the invention;

[0044] Figure 4 This is a schematic diagram of the random forest classification method of this invention;

[0045] Figure 5 This is the result of the random forest algorithm analysis of the importance of influencing factors in the embodiments of this invention;

[0046] Figure 6 This is a radar image of the resilience driving force detection of the water resources system in provinces and regions along the Yellow River in an embodiment of the present invention;

[0047] Figure 7 This is the explanatory power of the water resources system resilience factors in the provinces and regions along the Yellow River in this embodiment of the invention;

[0048] Figure 8 These are the detection results of water resource system resilience interactions in provinces along the Yellow River in this embodiment of the invention; wherein, (a) is the detection result of water resource system resilience interactions in 2009; (b) is the detection result of water resource system resilience interactions in 2012; (c) is the detection result of water resource system resilience interactions in 2015; (d) is the detection result of water resource system resilience interactions in 2018; and (e) is the detection result of water resource system resilience interactions in 2022. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0050] like Figure 1 As shown, a method for identifying the multi-factor relationships and driving factors of water resource system resilience includes the following steps:

[0051] Step S1: Collect multidimensional basic data of the river study area and construct a comprehensive database of water resource system resilience;

[0052] Step S2: Based on the system dynamics model, construct a causal feedback network of the five-dimensional subsystem of meteorology, hydrology, socio-economic, ecology, and engineering to simulate the internal causal feedback relationship of the water resources system.

[0053] Step S3: Construct a coupling degree model and quantify the strength level of interaction between multiple subsystems by calculating the coupling degree.

[0054] Step S4: Based on the random forest algorithm and using the Bagging ensemble strategy, assess the importance of factors affecting the resilience of the water resources system.

[0055] Step S5: Introduce a geographic detector to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective.

[0056] Example

[0057] This embodiment covers nine provinces and autonomous regions along the Yellow River: Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi, Shaanxi, Henan, and Shandong. The Yellow River is the primary water source for these provinces and autonomous regions. Overexploitation of water resources has led to problems such as the drying up of some tributaries, increased pollution, severe over-extraction of groundwater, and deterioration of the estuary's ecological environment. Therefore, this invention uses the proposed method to deeply analyze the spatial distribution and driving mechanisms of the resilience of the water resource system in the provinces and autonomous regions along the Yellow River.

[0058] Step S1: Collect multidimensional basic data of the river study area and construct a comprehensive database of water resource system resilience.

[0059] Based on monitoring and statistical data, and employing techniques such as data cleaning, desensitization, data splitting, and interpolation extension, this study integrates fundamental data from the river research area. The integration scope encompasses meteorological and hydrological observation data, regional water supply and consumption statistics, economic and social development indicators, ecological and environmental indicators, water conservancy infrastructure data, and topographic and underlying surface features extracted using remote sensing technology. All data are categorized and organized according to temporal and spatial scales. The database construction process is as follows: Figure 2 As shown in Table 1, the main data collected in this embodiment regarding the nine provinces and regions through which the Yellow River flows and their sources are also shown in Table 1.

[0060] Table 1 Data Types and Sources

[0061]

[0062] Step S2: Based on the system dynamics model, construct a causal feedback network of the five-dimensional subsystems of meteorology, hydrology, socio-economic, ecology, and engineering to simulate the internal causal feedback relationship of the water resources system.

[0063] System dynamics (SD) is a modeling method used to study the interaction and feedback mechanisms between various factors within a system by establishing causal relationship models. It is used to study the dynamic evolution of complex systems.

[0064] Water resource system resilience is a complex problem involving many factors such as fuzziness, randomness, and nonlinearity. Based on system dynamics, a causal feedback network of a five-dimensional subsystem of "meteorology-hydrology-socio-economy-ecology-engineering" is constructed to effectively simulate the internal causal feedback relationship of the water resource system, fully reflect the intrinsic connection of the five-dimensional subsystem of "meteorology-hydrology-socio-economy-ecology-engineering", and reveal the evolution law of system resilience from a mechanistic perspective.

[0065] First, establish a causal relationship network among various influencing factors to clarify the interrelationships and feedback mechanisms among the variables. Then, construct a causal feedback flow diagram of the system to intuitively present the nonlinear relationships among various influencing factors, helping decision-makers understand the synergistic mechanisms of various subsystems in the water resources system and predict the dynamic evolution trend of system behavior.

[0066] This embodiment, based on the actual conditions of the provinces and regions along the Yellow River, draws a system dynamics causal relationship diagram for the provinces and regions along the Yellow River, such as... Figure 3 As shown, the application of system dynamics models in the resilience assessment of water resource systems not only helps to understand the complex dynamic behavior of water resource systems, but also provides a scientific basis for formulating effective management strategies.

[0067] Step S3: Construct a coupling degree model and quantify the strength level of interaction between multiple subsystems by calculating the coupling degree.

[0068] Coupling refers to the interconnectedness of two or more systems (or forms of motion) resulting from their interactions. A high degree of coupling is indicated when there is an effective synergistic mechanism between system elements or systems themselves. Coupling degree, as a key indicator for quantifying the intensity of interactions between systems, reveals the dynamic characteristics of synergistic effects and effectively measures the strength of interactions between systems or elements.

[0069] To explore the internal synergistic mechanism of water resource system resilience formation in river study areas, this study introduces coupling degree to quantify the intensity of interactions between systems, based on the interrelationships and feedback mechanisms among various factors and variables in the river study area. This provides theoretical support for improving the resilience of water resource systems in river study areas.

[0070] Based on this, a coupling degree model is constructed to quantitatively characterize the interaction strength among the factors affecting the resilience of the water resources system. The coupling degree among the five-dimensional systems of "meteorology-hydrology-socio-economic-ecology-engineering" in the river study area is calculated to accurately assess the level of interaction among multiple subsystems and reveal the degree of orderly development of the water resources subsystems. The higher the coupling degree, the stronger the orderly coordination among the subsystems and the more profound the mutual influence.

[0071] First, construct an evaluation function U that reflects the effects of each factor. ij As shown below:

[0072]

[0073] Among them, U ij This represents the degree to which each influencing factor achieves the target, with a value range of [0,1]; A ij and B ij These represent the upper and lower limits of the influencing factor when the water resource system reaches a steady state; x ij This represents the comprehensive evaluation value of the j-th subsystem in the i-th region;

[0074] Then, establish the coupling function C. z This is used to characterize the degree of interrelationship between factors, as shown below:

[0075]

[0076] Where z is the number of systems involved in the coupling; U1, U2, ..., U z These represent the degree to which the system has achieved its objective; C z This represents the coupling degree between regional subsystems, with a value range of [0,1]. The coupling strength of each influencing factor is expressed in C. z It is weakest when =0, in C z It is strongest when =1.

[0077] This embodiment is based on the index data of each subsystem of "meteorology-hydrology-socio-economy-ecology-engineering" in the provinces and regions along the Yellow River. Using the coupling degree model, the coupling degree between the two systems, three systems, four systems and five systems is calculated respectively. The coupling degree between the five subsystems in the provinces and regions along the Yellow River from 2009 to 2022 is shown in Table 3.

[0078] Table 3 Calculation results of the water resource system's resilience and system coupling degree

[0079]

[0080] As shown in Table 3, there are high-strength coupling relationships among the resilient subsystems of the water resources system in the provinces and regions along the Yellow River, all exceeding 0.6, indicating a significant degree of interaction among the various subsystems. Furthermore, with the increase in the number of coupled systems, the system coupling degree gradually decreases, indicating a weakening of the interaction between subsystems and a gradual stabilization of the system.

[0081] In the coupling of the two subsystems, the meteorological and hydrological systems exhibit the highest coupling degree (0.965) within the water resources system of the provinces along the Yellow River, indicating a close relationship and highly interactive nature between them. The increasingly severe global climate change in the provinces along the Yellow River has strengthened the interaction and feedback mechanisms between the meteorological and hydrological systems. Changes in precipitation, its spatial and temporal distribution, and rising temperatures will affect surface runoff; simultaneously, the warming and precipitation pattern changes caused by climate change will profoundly impact evapotranspiration. This results in the strongest mutual influence between the hydrological and meteorological systems in the coupling of the two systems. The socio-economic-ecological system is the second strongest, with a coupling degree of 0.948. The socio-economic system and the ecosystem are complex, interdependent, and mutually influential systems. In the initial stages of socio-economic development, the ecological environment is often neglected, causing certain impacts on the natural environment. However, ecosystem degradation, in turn, constrains socio-economic development. Therefore, it is necessary to improve the ecological environment through economic development to achieve sustainable development. This feedback mechanism achieves a dynamic equilibrium, making the interaction between the two systems even closer.

[0082] In the three subsystems, the coupling degree of socio-economic, ecological, and engineering components in the water resources system of provinces along the Yellow River is the highest, reaching 0.801. This is mainly due to the close relationship between resource utilization and pressure, ecological protection and economic development, and the complex relationships between water conservancy projects in supporting the socio-economic system and impacting the ecological environment. With population growth and economic development, the demand for water resources is constantly increasing, putting enormous pressure on the ecological environment. On the other hand, economic development also provides financial and technological support for ecological protection. These relationships are intertwined and mutually influential, jointly constituting the complexity and dynamism of the water resources system in provinces along the Yellow River. The coupling degree between meteorology, socio-economic, and engineering is the second highest (0.792). Meteorology, through hydrology, constrains the sustainability of socio-economic development; socio-economic development, through water resource allocation (such as artificial rainfall), has a reciprocal effect on meteorology and water conservancy projects. Due to differences in natural and economic development, water scarcity under extreme drought in provinces along the Yellow River strengthens the dependence of meteorology and socio-economic systems on the water system, making water conservancy projects crucial for balancing supply and demand. This multi-directional coupling relationship makes the interaction among the three components complex.

[0083] The four systems of meteorology, hydrology, socio-economics, and engineering also exhibit a high degree of coupling in the water resources system of provinces and regions along the Yellow River (0.722). Meteorological conditions affect hydrological processes, which in turn feed back into the meteorological system. Socio-economic activities further influence the operation of hydrology and water conservancy projects by demanding and utilizing water resources. Water conservancy projects, in turn, meet the needs of socio-economic development by regulating water supply and indirectly affect the ecological environment.

[0084] In the overall water resources system of provinces and regions along the Yellow River, the coupling strength of the five subsystems is also relatively high, reaching 0.704, indicating that the subsystems of "meteorology-hydrology-socio-economy-ecology-engineering" in the water resources system are closely connected.

[0085] Step S4: Based on the random forest algorithm and using the Bagging ensemble strategy, assess the importance of factors affecting the resilience of the water resources system.

[0086] The Random Forest Algorithm (RF) improves model accuracy by integrating the prediction results of multiple decision trees. When evaluating the importance of time-series features, the RF model uses out-of-bag (OOB) data for testing. By perturbing the OOB sample values ​​of specific feature parameters, the magnitude of change in the prediction error of the decision trees is observed. If perturbing a feature parameter leads to a significant increase in prediction error, then that feature is considered highly important. This method of evaluating indicator importance based on error changes provides an objective basis for indicator selection.

[0087] The Random Forest algorithm employs a Bagging ensemble strategy (i.e., bootstrapping and random feature selection). It generates diverse training subsets through sampling with replacement and randomly selects feature subspaces during node splitting. This dual randomization mechanism not only effectively reduces the risk of model overfitting and significantly improves generalization performance, but also makes it suitable for analysis tasks in high-dimensional feature spaces. It enables a quantitative assessment of the importance of each feature, helping to understand the relationships between variables in the dataset. Therefore, it is suitable for assessing the importance of factors influencing the resilience of water resource systems.

[0088] Random forest classification is a combined classification model composed of many decision tree classification models, each with a vote to select the optimal classification result. First, bootstrap sampling is used to sample k samples from the original training set, each with the same sample size as the original training set. Then, k decision tree models are built for each of the k samples, resulting in k classification results. Finally, based on the k classification results, each record is voted on to determine its final classification, as follows: Figure 4 As shown.

[0089] Therefore, based on the random forest classification model, the contribution value of each influencing factor in the river study area is calculated in a single decision tree of the model, and then the average value of the results of all trees is taken, as shown below:

[0090]

[0091] Where I(x) represents the contribution value of the influencing factors; J represents the number of decision trees; C full is the average value of the entire dataset in a single tree; n is the number of influencing factors; I l(x,l) represents the contribution of x to l trees.

[0092] The resilience of water resource systems is a continuous and complex dynamic process, and its development level is influenced by many factors. To explore the impact of natural and human activities on the resilience of water resource systems, this embodiment selects 34 indicators to investigate the main driving factors, where A1-A4 are "meteorological" factors; B1-B6 are "hydrological" factors; C1-C 12 The elements are categorized as follows: D1-D7 represent "socio-economic" factors; D1-D7 represent "ecological" factors; and E1-E5 represent "engineering" factors. The random forest algorithm is applied to calculate the importance of indicators for factors influencing the resilience of the water resource system, such as... Figure 5 As shown.

[0093] Step S5: Introduce a geographic detector to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective.

[0094] Geo detectors are used to explore the spatial differentiation characteristics and formation mechanisms of geographic features. By quantitatively analyzing spatial stratification heterogeneity—that is, the distribution differences of the same geographic phenomenon across different sub-regions—they effectively identify the key driving factors behind geographic phenomena. Geo detectors can handle the influence of multiple factors in complex systems, effectively identify the main driving factors, and perform dimensionality reduction to avoid potential multicollinearity problems.

[0095] Changes in single and multiple factors in the complex network of water resources systems will cause changes in the resilience of water resources systems. Therefore, in the analysis of the mechanism of water resources system resilience, geographic detectors are used to analyze the main driving factors that cause changes in the resilience of water resources systems and the superposition effect between different factors, and to examine the interaction relationship between different driving factors of water resources system resilience.

[0096] The geographic detector includes a factor detection module and an interactive detection module. The factor detection module is used to assess the explanatory power of a single factor on resilience, specifically detecting the spatial heterogeneity of the dependent variable Y (water resource system resilience) and the degree to which influencing factor X explains the spatial heterogeneity of water resource system resilience Y. The explanatory power q-value is calculated to measure the factor's ability to explain spatial distribution, as shown below:

[0097]

[0098] Where q represents the explanatory power of the discretized influencing factors on the resilience of the dependent variable, water resources system, and its value ranges from 0 to 1, with a larger q value indicating stronger explanatory power; t represents the classification or stratification of the influencing factors, t = 1, 2, 3, ..., K; N t The number of samples in layer t; σ is the sample variance of layer t; N is the total sample size;2 This represents the total sample variance.

[0099] The interaction detection module is used to analyze the interactions between different factors. By comparing the explanatory power of single-factor and two-factor analyses of resilience, it determines whether these factors jointly enhance or weaken the resilience level. The interaction results can be categorized into five types, as shown in Table 2.

[0100] Table 2. Types and Judgment Criteria of Interactions of Detection Factors

[0101] Interaction types Judgment criteria Nonlinear attenuation <![CDATA[q(X1∩X2)<Min[q(X1),q(X2)]]]> Single-factor nonlinear attenuation <![CDATA[Min[q(X1),q(X2)]<q(X1∩X2)<Max[q(X1),q(X2)]]]> Two-factor enhancement <![CDATA[q(X1∩X2)>Max[q(X1),q(X2)]]]> Nonlinear enhancement <![CDATA[q(X1∩X2)>q(X1)+q(X2)]]> independent <![CDATA[q(X1∩X2)=q(X1)+q(X2)]]>

[0102] Where X represents the influencing factor.

[0103] This embodiment is from Figure 5 Two of the most important indicators from each of the five subsystem indicator systems were selected as the main influencing factors for geographic exploration, as shown in Table 4.

[0104] Table 4. Selection of influencing factors of geographic detectors

[0105]

[0106] Note: "+" indicates that the indicator has a positive effect on the resilience of the water resources system, and "-" indicates a negative effect.

[0107] To meet the data type requirements of the geographic detector model for independent variables, the natural breakpoint classification method in ArcGIS software was used to divide all detection factors into five levels. This classification method can determine the optimal classification boundary based on the distribution characteristics of the data itself, ensuring the highest homogeneity within each category and the greatest heterogeneity between categories, which meets the model's requirements for analyzing discrete independent variables.

[0108] (1) Results and analysis of single-factor detection.

[0109] The impact of various influencing factors on the resilience of the water resources system in 2009, 2013, 2016, 2019, and 2022 was calculated based on geographic detectors. The single-factor detection results are shown in Table 5 and... Figure 6 As shown.

[0110] Table 5 Single-factor detection results of the geographic detector

[0111]

[0112] based on Figure 6The results of water resource system resilience surveys in provinces and regions along the Yellow River show that the degree of explanation (q-value) of influencing factors varies across different historical periods. This indicates that water resource system resilience is an evolving process, influenced by climate change and human activities at different stages, with its main driving factors also differing. To clarify the driving mechanisms affecting water resource system resilience and understand the degree of influence of different factors, the mean values ​​of single-factor survey results are analyzed, such as... Figure 7 As shown.

[0113] Depend on Figure 7 It can be seen that the main driving factors of the resilience of the water resources system in the provinces and regions along the Yellow River are B2 (per capita water resources) > B3 (surface water resources) > A1 (annual precipitation) > D4 (ecological water use) > E1 (reservoir storage) > C9 (water use per 10,000 yuan of GDP) > C6 (water resources development and utilization rate) > D7 (forest coverage rate) > A2 (temperature) > E2 (unconventional water). Among them, the 5-year average q value of B2 (per capita water resources) is 0.585, ranking first. Per capita water resources are an important factor affecting the resilience of the water resources system. It is the most direct indicator reflecting the characteristics of water resources endowment in the region and is directly related to the regional water resources supply and demand balance and sustainable utilization capacity.

[0114] The average value of B3 (surface water resources) q is 0.573, ranking second. Surface water is the main water source for provinces and regions along the Yellow River. Especially in arid or semi-arid areas, the development and utilization of surface water is crucial for maintaining ecological balance and ensuring socio-economic development.

[0115] A1 (annual precipitation) ranks third. Rainfall in the provinces and regions along the Yellow River is highly seasonal and unevenly distributed throughout the year. The runoff during the flood season accounts for more than 60% of the annual runoff. Changes in annual precipitation directly affect the total amount and distribution of water resources. Abundant precipitation means plentiful water resources and sufficient natural water replenishment, which helps maintain the balance and stability of the water resource system.

[0116] D4 (ecological water consumption) ranks fourth (0.479). Ecological water consumption includes not only the water required to maintain the basic ecological functions of rivers, but also the water demand of ecosystems such as wetlands, forests, and grasslands. Ensuring ecological water consumption is crucial for maintaining the stability and resilience of ecosystems.

[0117] The average value of E1 (reservoir storage) q is 0.468, ranking 5th. Reservoir storage is an important means of regulating water resources and can effectively alleviate the contradiction between water supply and demand caused by seasonal changes in precipitation. In the context of climate change, the scientific management of reservoirs can mitigate the impact of drought on agriculture, industry, and people's lives, cope with extreme drought events, and enhance the resilience of water resource systems.

[0118] (2) Interaction detection results and analysis.

[0119] The results of factor detection analysis show the individual influence of each driving factor on the resilience level of the water resource system. Since the resilience of the water resource system is affected by multiple factors, the geographic detector model can not only quantitatively analyze the degree of influence of each driving factor, but also explore the intensity of the interaction between driving factors.

[0120] Therefore, this study utilizes the interaction detection module in a geographic detector to explore the combined influence of two factors on the resilience of the water resources system. This aims to determine whether the explanatory power of the indicator factors on the resilience of the water resources system is enhanced or weakened, and whether there are independent influences between them. The results of the factor detection are then subjected to interaction detection analysis, and the results show the following: Figure 8 As shown.

[0121] Depend on Figure 8 It is evident that the combined influence of different driving factors is greater than that of a single factor acting alone, and the effects exhibit both dual-factor enhancement and nonlinear increase, indicating the absence of mutually independent factors. The pairwise interactions of different factors have a greater impact on the resilience of the water resources system than any single factor, suggesting that changes in the resilience level of the water resources system in the study area are the result of the interaction of multiple factors. The number of nonlinearly enhanced interaction groups increased from 12 in 2009 to 14 in 2022, while the number of dual-factor enhanced groups decreased by 2. This trend reflects that the interaction mechanisms among the driving factors are becoming more complex, highlighting the trend of multiple factors acting together. This nonlinear enhancement indicates that the interaction of multiple factors needs to be comprehensively considered in the process of water resource utilization to achieve sustainable water resource utilization and balanced regional development.

[0122] Taking the 2022 interaction detection results as an example, the interaction between B2 (per capita water resources) and C6 (water resource development and utilization rate) and E2 (unconventional water sources) in provinces along the Yellow River showed a nonlinear enhancement, reflecting the synergistic effect of these factors under different conditions and their complex dynamic nonlinear relationship. The nonlinear enhancement relationship between B2 (per capita water resources) and C6 (water resource development and utilization rate) stems from the complex relationship between the two in water resource management in provinces along the Yellow River. Increasing the water resource development and utilization rate can increase the available water volume and per capita water resources in the short term, but over-exploitation will lead to resource depletion, reduce sustainability and resilience, and manifest as nonlinear enhancement. E2 (unconventional water sources) Unconventional water resources, as an important supplement to traditional water sources, play a key role in coping with extreme drought and water scarcity. By developing and utilizing alternative water sources such as reclaimed water, rainwater harvesting, and mine water, the total regional water supply can be increased, dependence on traditional freshwater resources can be reduced, and the water shortage problem can be effectively alleviated.

[0123] In 2022, C6 (water resources development and utilization rate) and other factors in the water resources system of provinces and regions along the Yellow River showed a nonlinear enhancement. The main reason is that C6 (water resources development and utilization rate) is one of the important factors affecting the resilience of the water resources system in provinces and regions along the Yellow River. It directly determines the amount of available water in the region. Its interaction with other factors (such as meteorology-hydrology-socio-economic-ecology-engineering) involves a complex feedback regulation mechanism. In the water resources system of provinces and regions along the Yellow River, when water resources development and utilization rate works together with other factors, its comprehensive effect is significantly greater than the individual effects of each factor, and it has a stronger impact on the resilience of the water resources system.

[0124] The combined effect of E2 (unconventional water sources), C9 (water consumption per 10,000 yuan of GDP), and D4 (ecological water consumption) in provinces and regions along the Yellow River exhibits a non-linear enhancement. In recent years, water consumption per 10,000 yuan of GDP in provinces and regions along the Yellow River has continued to decline, and regional water use efficiency has significantly improved. This downward trend reflects the significant effect of water-saving measures and technological progress on reducing water consumption per unit of economic output. With the increase in the utilization of unconventional water sources, the water supply also increases accordingly. By replacing some conventional water resources, overall water use efficiency is improved, and the decline in water consumption per 10,000 yuan of GDP will further increase. The role of unconventional water sources in the water resource system is becoming increasingly prominent. With the advancement of the ecological protection and high-quality development strategy in the Yellow River Basin, the demand for ecological water is increasing year by year, and the proportion of ecological water use is rising. To meet the ecological water demand, the utilization of unconventional water sources is particularly important.

[0125] Therefore, the above-mentioned method for identifying the multi-factor relationships and driving factors of water resource system resilience can help formulate more scientific and reasonable water resource management strategies, effectively improve the resilience of water resource systems, and ensure the safe and sustainable use of water resources to cope with future uncertainties and challenges.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for identifying the multi-factor relationships and driving factors of water resource system resilience, characterized in that, Includes the following steps: Step S1: Collect multidimensional basic data of the river study area and construct a comprehensive database of water resource system resilience; Step S2: Based on the system dynamics model, construct a causal feedback network of the five-dimensional subsystem of meteorology, hydrology, socio-economic, ecology, and engineering to simulate the internal causal feedback relationship of the water resources system. Step S3: Construct a coupling degree model and quantify the strength level of interaction between multiple subsystems by calculating the coupling degree. Step S4: Based on the random forest algorithm and using the Bagging ensemble strategy, assess the importance of factors affecting the resilience of the water resources system. Step S5: Introduce a geographic detector to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective.

2. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, In step S1, multidimensional basic data of the river study area are collected to construct a comprehensive database of water resource system resilience, specifically including: Based on monitoring and statistical data, data cleaning, desensitization, splitting, and interpolation extension techniques are used to integrate basic data of the river research area; The integrated basic data includes meteorological and hydrological observation data, regional water supply and use statistics, economic and social development indicators, ecological and environmental indicators, water conservancy infrastructure data, and topographic and underlying surface feature data extracted based on remote sensing technology. The above data were categorized and organized according to time and spatial scales to construct a comprehensive database of water resource system resilience.

3. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, In step S2, based on the system dynamics model, a causal feedback network of a five-dimensional subsystem (meteorology, hydrology, socio-economic, ecology, engineering) is constructed to simulate the internal causal feedback relationships of the water resources system, specifically including: First, establish a causal relationship network among various influencing factors, and clarify the interrelationships and feedback mechanisms among the variables of each factor. Then, a causal feedback flow graph of the system is constructed to present the nonlinear relationships between various influencing factors and predict the dynamic evolution trend of the system's behavior.

4. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, In step S3, a coupling degree model is constructed, and the strength level of the interaction between multiple subsystems is quantified by calculating the coupling degree. The specific process is as follows: First, construct an evaluation function U that reflects the effects of each factor. ij As shown below: Among them, U ij This represents the degree to which each influencing factor achieves the target, with a value range of [0,1]; A ij and B ij These represent the upper and lower limits of the influencing factor when the water resource system reaches a steady state; x ij This represents the comprehensive evaluation value of the j-th subsystem in the i-th region; Then, establish the coupling function C. z This is used to characterize the degree of interrelationship between factors, as shown below: Where z is the number of systems involved in the coupling; U1, U2, ..., U z These represent the degree to which the system has achieved its objective; C z This represents the coupling degree between regional subsystems, with a value range of [0,1].

5. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, In step S4, the importance of factors affecting the resilience of the water resources system is assessed using the Bagging ensemble strategy based on the random forest algorithm. The specific process is as follows: First, use Bootstrap sampling to extract k samples from the original training set, with each sample having the same size as the original training set. Then, k decision tree models are built for each of the k samples to obtain k classification results; Finally, a vote is taken on each record based on the k classification results to determine its final classification.

6. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 5, characterized in that, Using the random forest algorithm and employing a Bagging ensemble strategy, the contribution of each influencing factor in the river study area is calculated in a single decision tree of the model. The results from all trees are then averaged, as shown below: Where I(x) represents the contribution value of the influencing factors; J represents the number of decision trees; C full is the average value of the entire dataset in a single tree; n is the number of influencing factors; I l (x,l) represents the contribution of x to l trees.

7. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, In step S5, a geographic detector is introduced to analyze the main driving factors and their mechanisms of action that affect the resilience of the water resource system from a spatial perspective. The geographic detector includes a factor detection module and an interactive detection module; The factor detection module is used to assess the explanatory power of a single factor on resilience; The interaction detection module is used to analyze the interactions between different factors and determine whether the factors jointly affect the resilience level.

8. The method for identifying the multi-factor relationships and driving factors of water resource system resilience according to claim 1, characterized in that, The factor detection module detects the spatial heterogeneity of the dependent variable, water resource system resilience Y, and the extent to which influencing factor X explains the spatial heterogeneity of water resource system resilience Y. The explanatory power (q) of a factor is measured by calculating its explanatory power to the spatial distribution, as shown below: Where q represents the explanatory power of the discretized influencing factors on the resilience of the dependent variable, water resources system, and its value ranges from 0 to 1, with a larger q value indicating stronger explanatory power; t represents the classification or stratification of the influencing factors, t = 1, 2, 3, ..., K; N t The number of samples in layer t; σ is the sample variance of layer t; N is the total sample size; 2 This represents the total sample variance.

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