Multi-target collaborative dynamic optimal configuration method and system for water resources of Mauwu sandy land

Abstract

The invention relates to the technical field of water resource management, and discloses a multi-objective collaborative dynamic optimal configuration method and system for water resources of Mauwu sand, and the method comprises the following steps: building a spatial grid database; calculating a local regression coefficient of each network, constructing a topological structure of rainfall, underground water, vegetation and lakes, and outputting an association probability between elements; constructing a multi-objective optimization model and a coupling dynamic optimization model; and solving the coupling dynamic optimization model to generate a Pareto optimal solution set, calculating an ecological option value of each allocation scheme, and performing optimization adjustment on the water resource allocation schemes under different scenes to generate an optimal water resource allocation scheme. Through deep fusion of multi-target dynamic collaboration, spatial fine modeling, hysteresis effect quantification and long-term value evaluation, a water resource management closed loop adaptive to the Maowu sand land is formed, and the stability and toughness of an ecological system are greatly enhanced while economic and social development is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of water resources management technology, and more specifically, to a method and system for multi-objective collaborative dynamic optimization allocation of water resources in the Mu Us Desert. Background Technology

[0002] Water resource management is a systematic project that coordinates the development, utilization, protection, and allocation of water resources. Its core components include key aspects such as water resource quantity and quality monitoring, supply and demand balance analysis, ecological flow assurance, and inter-regional allocation. Scientific water resource management is not only the foundation for sustainable economic and social development but also a core means of maintaining ecosystem health and a crucial tool for addressing global climate change. In arid or semi-arid regions, the scientific nature of water resource management directly determines the effectiveness of ecological restoration and regional development resilience. For example, the Mu Us Desert has effectively improved its desertification control rate through a combination of water-saving irrigation and ecological water replenishment, but it still faces long-term challenges such as vegetation degradation and groundwater over-extraction.

[0003] In recent years, although significant progress has been made in the research on water resource management in the Mu Us Desert, the following shortcomings still exist: 1) Existing management methods mostly adopt static weight allocation of multiple objectives, which makes it difficult to coordinate the dynamic balance between economic development and ecological protection. For example, agricultural water conservation and ecological water replenishment often lead to supply and demand contradictions due to the separation of objectives; 2) Insufficient consideration of spatial heterogeneity, lack of grid-scale precipitation-groundwater-vegetation-lake correlation modeling, and inability to formulate differentiated allocation strategies for different geomorphic units such as dunes, beaches, and valleys, resulting in low accuracy of ecological water supply in some areas; 3) Weak dynamic response mechanism, failure to effectively quantify the nonlinear relationship between the lag effect of vegetation restoration (such as the root development cycle of psammophytes) and groundwater level changes, resulting in a deviation between ecological compensation water volume and actual demand; 4) Lack of quantitative assessment tools for the long-term benefits of ecological restoration (such as the water conservation value brought about by desertification reversal), making it difficult to support the long-term optimization of water resource allocation schemes. These problems jointly restrict the scientific nature and sustainability of water resource management.

[0004] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a multi-objective collaborative dynamic optimization allocation method and system for water resources in the Mu Us Desert. This method has the advantage of significantly enhancing the stability and resilience of the ecosystem while ensuring economic and social development, thereby solving the problems in the background technology.

[0007] (II) Technical Solution

[0008] To achieve the aforementioned advantages of significantly enhancing the stability and resilience of the ecosystem while ensuring economic and social development, the specific technical solution adopted by this invention is as follows:

[0009] According to one aspect of the present invention, a multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert is provided, comprising the following steps:

[0010] S1. Obtain ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine the cross-regional allocation boundary, water resources and ecological constraints.

[0011] S2. Based on the spatialized grid data, use spatial analysis techniques to calculate the local regression coefficients of each network, determine the conditional probability table based on the local regression coefficients, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating an associated probability dataset.

[0012] S3. Taking economic goals, social goals, and ecological goals based on lag factors as optimization objectives, the objective weights are determined based on correlation probabilities, and a multi-objective optimization model is constructed in combination with constraints. The water resource supply and demand model, groundwater numerical model, and ecological water demand assessment model are integrated to construct a coupled dynamic optimization model.

[0013] S4. Solve the coupled dynamic optimization model to generate a Pareto optimal solution set and output water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, calculate the ecological option value of each allocation scheme, and optimize and adjust the water resource allocation schemes under different scenarios according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

[0014] Furthermore, based on the spatialized grid data, spatial analysis techniques are used to calculate the local regression coefficients of each network. Conditional probability tables are determined based on these local regression coefficients, and Bayesian networks are integrated to construct the topological structures of precipitation, groundwater, vegetation, and lakes, generating an associated probability dataset. This process includes the following steps:

[0015] S21. Based on the spatial grid database, extract key variables such as annual precipitation, groundwater depth, vegetation cover and lake area of ​​the grid, and clean and standardize the extracted data.

[0016] S22. Using vegetation cover and lake area as dependent variables, and precipitation and groundwater depth as independent variables, construct a geographically weighted regression model based on vegetation and a geographically weighted regression model based on lakes, respectively.

[0017] S23. Using the vegetation-based geographic weighted regression model and the lake-based geographic weighted regression model, calculate the local regression coefficients of each network and generate a spatial distribution map of the local coefficients of the key variables.

[0018] S24. Using key variables as network nodes, the node connection direction is set by combining the physical meaning of local regression coefficients, and key connections are selected according to the preset absolute value of local regression coefficients to construct the topology of precipitation, groundwater, vegetation and lakes.

[0019] S25. Use the conditional probability transformation formula to convert the local regression coefficients into conditional probabilities, and group the grids according to the terrain type. Take the average of the conditional probabilities in each group to generate a regionalized conditional probability table, forming an associated probability dataset that includes grid coding, topological connectivity, and conditional probabilities.

[0020] Furthermore, the expression for the vegetation-based geographic weighted regression model is as follows:

[0021]

[0022] The expression for the lake-based geographic weighted regression model is:

[0023]

[0024] In the formula, V i Let L be the vegetation cover of the i-th grid. i Let u be the ecological grid lake area of ​​the i-th grid. i v i Let ) be the spatial coordinates of the i-th grid, and β be the coordinates of the grid. V0 β L0 The constant coefficients for vegetation and lakes, respectively, P i Let G be the annual precipitation of the i-th grid. i Let β be the groundwater depth of the i-th grid. V1 β L1 β represents the local regression coefficients of precipitation on vegetation and lakes, respectively. V2 β L2 These are the local regression coefficients of groundwater on vegetation and lakes, respectively. These are the error terms for the i-th grid, representing vegetation and lakes, respectively.

[0025] Furthermore, using economic, social, and ecological objectives based on lag factors as optimization goals, determining objective weights based on correlation probabilities, and constructing a multi-objective optimization model in conjunction with constraints, this model integrates water resource supply and demand models, groundwater numerical models, and ecological water demand assessment models to construct a coupled dynamic optimization model, including the following steps:

[0026] S31. Define economic goals, social goals, and ecological goals based on lag factors. The economic goal is to maximize the total regional output and minimize water consumption per unit of output. The social goal is to ensure basic per capita domestic water consumption and narrow the gap in water use between urban and rural areas. The ecological goal based on lag factors is to control the annual decline of groundwater level within a preset range and assess the change in vegetation cover after the lag period.

[0027] S32. Extract the correlation strength between elements from the correlation probability dataset, use the analytic hierarchy process, and combine the correlation probability differences in different regions to correct the initial weights and obtain the target weights for different regions.

[0028] S33. Taking the weighted sum of economic, social, and ecological objectives based on lag factors as the optimization direction, and combining the constraints, a multi-objective optimization model is constructed by coordinating water use conflicts through a water-saving compensation mechanism.

[0029] S34. Connect the multi-objective optimization model with the water resource supply and demand model, the groundwater numerical model, and the ecological water demand assessment model through a data interface. The water resource supply and demand model provides the dynamic balance results of water demand and available water, the groundwater numerical model simulates groundwater level changes and provides feedback for adjustment, and the ecological water demand assessment model calculates the minimum ecological base flow of the river as the lower limit of ecological water consumption, thus constructing a coupled dynamic optimization model.

[0030] Furthermore, the core indicators of the economic objectives are maximizing regional total output and minimizing water consumption per unit of output, expressed as: F a =max(C a +C i )∩min(Y a / C a +Y i / C i ), where F a For the economic objective function, C a For agricultural output, C i For industrial output, Y a For agricultural water consumption, Y i This refers to industrial water consumption.

[0031] The core indicators of the social goals are ensuring safe drinking water and balancing urban and rural water allocation, expressed as: F s =min|Y lc +Y lx |∩max[I(Y l ≥120L / person / day), where F s Let Y be the social objective function. lc For urban domestic water consumption, Y lx For rural domestic water consumption, Y l I(*) represents domestic water consumption, and I(*) is an indicator function.

[0032] The core indicator of ecological objectives based on lag factors is the long-term ecological benefit that takes into account the lag effect of vegetation restoration, expressed as: In the formula, F e For the ecological objective function based on lag factors, V t+k Let be the vegetation cover at time t+k, where t is the current time, k is the lag time, λ is the time decay coefficient, and ΔG is the vegetation cover at time t+k. t Let be the annual change in groundwater level during time period t;

[0033] The objective function of the multi-objective optimization model is expressed as: F = α e ·F e +α a ·F a +α s ·F s In the formula, F is the objective function of the multi-objective optimization model, and α e α a α s These are the weights for ecological objectives, economic objectives, and social objectives, respectively.

[0034] Furthermore, solving the coupled dynamic optimization model generates a Pareto optimal solution set, outputting water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation schemes under different scenarios are optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the optimal water resource allocation scheme, including the following steps:

[0035] S41. Based on the multi-objective particle swarm optimization algorithm, the objective function of the coupled dynamic optimization model is used as the fitness function. The particle swarm is used to iteratively optimize different scenarios to generate Pareto optimal solution sets that include the water allocation ratio and specific water volume for agriculture, industry, life and ecology, and output water resource allocation schemes under different scenarios.

[0036] S42. Based on the ecological water replenishment and vegetation restoration in the water resource allocation plan, predict the probability of desertification reversal within the preset years, and determine the amount of water resources that can be conserved by combining the hydrological characteristics of the reversal area.

[0037] S43. Based on the reversal probability of desertification and the amount of water resources that can be conserved, calculate the ecological option value of each allocation scheme, and determine the amount of water to compensate for the lag in the ecological water consumption and vegetation restoration in each scheme.

[0038] S44. Based on the ecological option value and the delayed compensation water volume, combined with the preset ecological option threshold, the water resource allocation scheme under different scenarios is dynamically optimized and adjusted to obtain the optimal water resource allocation scheme under each scenario.

[0039] Furthermore, based on the ecological water replenishment and vegetation restoration status in the water resource allocation plan, the probability of desertification reversal within a predetermined timeframe is predicted. Combined with the hydrological characteristics of the reversal area, the amount of water resources that can be conserved is determined, including the following steps:

[0040] S421. Extract key data related to desertification reversal from the water resource allocation scheme, and combine the geomorphological differences of the Mu Us Desert to establish a correlation model between reversal probability and ecological water replenishment and vegetation restoration in different regions.

[0041] S422. Based on the preset time limit, and combined with the correlation model between the reversal probability and ecological water replenishment and vegetation restoration, determine the desertification reversal probability of sand dunes, beaches and river valleys on an annual basis.

[0042] S423. Based on the probability of desertification reversal and combined with the total desertification area of ​​each region, determine the actual reversal area for each year within the preset time limit, and collect the hydrological characteristic parameters of the reversal area.

[0043] S424. Based on the actual reversal area and hydrological characteristic parameters of the reversal zone, determine the amount of water resources that can be conserved on an annual basis.

[0044] The annual water conservation capacity of the inverted area is determined by the sum of surface water conservation capacity and groundwater conservation capacity. Surface water conservation capacity is determined by water retention rate, annual regional precipitation and actual inverted area. Groundwater conservation capacity is determined by permeability coefficient, annual regional precipitation and recharge and actual inverted area.

[0045] Furthermore, the formula for calculating the value of ecological options is as follows:

[0046]

[0047] In the formula, O represents the ecological option value, n represents the total number of forecast years, s represents the forecast period, and p s Let q be the probability of desertification reversal in year s. s Let r be the amount of water resources that can be conserved by reversing desertification in year s, and r be the discount rate.

[0048] The formula for calculating the delayed compensation water volume is:

[0049] Q c =Q e ·(1+k d ·t d );

[0050] In the formula, Q c To compensate for the delayed effects of ecological restoration, Q e Basic ecological water consumption, k d t is the lag compensation coefficient. dThe ecological restoration process has been delayed for a long time.

[0051] Furthermore, based on the ecological option value and the lagged compensation water volume, combined with the preset ecological option threshold, the water resource allocation scheme under different scenarios is dynamically optimized and adjusted to obtain the optimal water resource allocation scheme under each scenario, including the following steps:

[0052] S441. Select schemes with ecological option values ​​higher than the preset ecological option threshold from the Pareto optimal solution set as candidate schemes, replace the initial ecological water consumption in the candidate schemes with the lagged compensation water consumption, and recalculate the total water consumption to ensure that the total water resource constraint is met.

[0053] S442. Using the corrected ecological water consumption as a constraint, the coupled dynamic optimization model is invoked to optimize the allocation ratio of agricultural and industrial water consumption under different scenarios, and the optimal water resource allocation scheme under each scenario is obtained.

[0054] According to another aspect of the present invention, a multi-objective collaborative dynamic optimization allocation system for water resources in the Mu Us Desert is provided, including a basic data acquisition and integration module, an ecological and hydrological element correlation analysis module, a coupled dynamic optimization model construction module, and a water resource allocation scheme optimization solution module.

[0055] Among them, the basic data acquisition and integration module is used to acquire ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine cross-regional allocation boundaries, water resources and ecological constraints.

[0056] The Ecological and Hydrological Element Correlation Analysis Module is used to calculate the local regression coefficients of each network based on spatial grid data using spatial analysis techniques, determine the conditional probability table based on the local regression coefficients, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating a correlation probability dataset.

[0057] The coupled dynamic optimization model construction module is used to construct a multi-objective optimization model by taking economic goals, social goals and ecological goals based on lag factors as optimization objectives, determining the objective weights based on correlation probabilities, and combining constraints. It integrates water resource supply and demand models, groundwater numerical models and ecological water demand assessment models to construct a coupled dynamic optimization model.

[0058] The water resource allocation scheme optimization solution module is used to solve the coupled dynamic optimization model to generate the Pareto optimal solution set and output the water resource allocation scheme under different scenarios. Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation scheme under different scenarios is optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

[0059] (III) Beneficial Effects

[0060] Compared with existing technologies, this invention provides a multi-objective collaborative dynamic optimization allocation method and system for water resources in the Mu Us Desert, which has the following beneficial effects:

[0061] (1) This invention forms a closed loop for water resource management adapted to the Mu Us Desert by deeply integrating multi-objective dynamic collaboration, spatial fine modeling, lag effect quantification and long-term value assessment. While ensuring economic and social development, it greatly enhances the stability and resilience of the ecosystem, comprehensively solves the problems of static imbalance, spatial extensiveness, dynamic lag and ambiguity of long-term benefits in water resource management in the Mu Us Desert, and significantly improves the scientific nature and sustainability of management.

[0062] (2) This invention determines the weights of economic, social and ecological objectives based on correlation probability and achieves a synergistic balance of the three objectives by combining a coupled dynamic optimization model. By incorporating agricultural water conservation and ecological water replenishment into a unified optimization framework, it can effectively resolve supply and demand conflicts. For example, in the dune area, while prioritizing ecological objectives, the basic agricultural output is maintained through a water conservation compensation mechanism, which effectively improves the coordination of objectives.

[0063] (3) This invention uses a geographic weighted regression model to calculate local regression coefficients at the grid scale, integrates a Bayesian network to construct the topological association between precipitation, groundwater, vegetation and lakes, and generates regionalized conditional probability tables according to landform types. It customizes differentiated allocation strategies for different units such as dunes, beaches and valleys, effectively improving the accuracy of ecological water supply and avoiding local supply and demand deviations caused by the one-size-fits-all approach.

[0064] (4) This invention introduces a lag factor to quantify the vegetation restoration cycle (such as the root development time of psammophytes), dynamically corrects the ecological water consumption through the lag compensation water volume formula, and combines the groundwater numerical model to provide real-time feedback on water level changes, so that the deviation between the ecological compensation water volume and the actual demand is controlled within a small range, which significantly improves the adaptability to nonlinear ecological processes.

[0065] (5) This invention integrates the potential trend of desertification reversal with the long-term benefits of water resource conservation through an ecological option value formula. It converts the long-term value of ecological restoration into a quantitative basis for current decision-making, effectively compensating for the lack of precise assessment of long-term ecological benefits in traditional methods. This guides decision-makers to consider both short-term utilization and long-term restoration in water resource allocation, comprehensively evaluating the ecological sustainability of solutions. It provides scientific support for selecting allocation schemes that combine current feasibility with future ecological value, thereby strengthening the long-term effectiveness of ecological restoration and the forward-looking nature of decision-making, and promoting a shift in water resource management from focusing on immediate benefits to coordinating long-term ecological value. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a schematic diagram illustrating the principle of the multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to an embodiment of the present invention. Detailed Implementation

[0068] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0069] According to embodiments of the present invention, a method and system for multi-objective collaborative dynamic optimization allocation of water resources in the Mu Us Desert are provided.

[0070] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, the multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to an embodiment of the present invention includes the following steps:

[0071] S1. Obtain ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine the cross-regional allocation boundary, water resources and ecological constraints.

[0072] The process of acquiring ecological vegetation, lakes, and hydrological data of the Mu Us Desert, establishing a spatial grid database, and analyzing water sources and water demand to determine cross-regional allocation boundaries, water resource, and ecological constraints includes:

[0073] 1) Acquisition of ecological vegetation data: By setting up 100m×100m quadrats, the vegetation species (such as Artemisia argyi and Salix psammophila), coverage (using drone aerial photography combined with manual visual inspection) and growth parameters (plant height and crown width) are recorded regularly. At the same time, the monthly vegetation NDVI index is retrieved using satellite remote sensing images to form spatial continuous data.

[0074] 2) Lake data acquisition: The boundaries of the lakes are located using the Global Navigation Satellite System (GNSS), and water depth data is obtained by combining sonar depth sounders. The lake area and water storage are updated monthly. Historical remote sensing interpretation results from the past 30 years are integrated to sort out the spatiotemporal variation patterns of the lakes.

[0075] 3) Hydrological data acquisition: Daily precipitation data are collected from several meteorological stations in the Mu Us Desert area, and 1km grid precipitation data are generated by Kriging interpolation; groundwater level (depth) and water quality (mineralization, pH value) are recorded through several monitoring wells, and data are collected once a month; monthly runoff data of major rivers such as Wuding River and reservoir storage are collected, and seasonal flow interruption periods are recorded.

[0076] 4) Construct a spatial grid monitoring database: Using 1km×1km as the basic unit, the Mu Us Desert is divided into more than 12,000 grids, each assigned a unique code (e.g., "X01Y03"). The coordinate system can be WGS84 or ITRF. Data such as vegetation coverage, lake area, precipitation, and groundwater depth are matched to the corresponding grids to establish a database containing attribute information (monitoring time, data value) and spatial layers (grid vector boundaries). PostgreSQL+PostGIS technology is used to support spatial query and overlay analysis, enabling visualized management and rapid retrieval of data.

[0077] 5) Water source inventory: Distinguish between shallow (depth < 50m) and deep (depth ≥ 50m) groundwater, calculate the exploitable volume using the groundwater balance method (exploitable volume = total recharge - ecological base flow); collect statistics on the multi-year average runoff of major rivers and the beneficial storage capacity of reservoirs, and determine the available volume after deducting the ecological base flow (calculated as 10% of the multi-year average runoff); calculate the potential of unconventional water sources such as coal mine drainage water and urban reclaimed water.

[0078] 6) Water demand statistics: Irrigated area is statistically analyzed by crop type (corn, pasture, etc.), and current water consumption is calculated based on the average water requirement per mu (unit of land area). The demand growth over the next 5 years is predicted (e.g., a potential 10% increase due to adjustments in planting structure), i.e., agricultural water demand; annual water consumption of coal mines and chemical enterprises is investigated, and the expanded demand is predicted based on water consumption per unit of output value, i.e., industrial water demand; water consumption is calculated based on urban and rural populations, with a 15% buffer for population growth, i.e., domestic water demand; the Tennant method is used to calculate river ecological base flow, based on wetland area (100m²). 3 The wetland water replenishment demand is determined by the percentage of mu per year, which is the ecological water demand.

[0079] 7) Define the boundaries of cross-regional water allocation: Delineate three primary allocation zones based on hydrological basins (such as the Wuding River Basin and the Hongjiannao River Basin) and administrative divisions (such as Ordos in Inner Mongolia Autonomous Region and Yulin in Shaanxi Province), define the water allocation ratio for cross-border rivers (such as Hongjiannao River) (6:4 allocation between Inner Mongolia and Shaanxi), and mark sensitive ecological areas where cross-regional water allocation is prohibited (such as the Relict Gull Nature Reserve).

[0080] 8) Constraint setting: Total annual water consumption of the region ≤ 1.8 billion m³ 3(Multi-year average total water resources), groundwater extraction ≤ 620 million m³ 3 / year, i.e., water resource constraints; annual groundwater level drop ≤0.5m, vegetation coverage ≥45% in the core area, and minimum ecological area of ​​lakes ≥30km². 2 This refers to ecological resource constraints; the agricultural irrigation water utilization coefficient should be ≥0.8, the industrial water reuse rate should be ≥90%, and the cost of inter-regional water transfer should be ≤2.5 yuan / m³. 3 That is, economic and technological constraints.

[0081] S2. Based on the spatialized grid data, use spatial analysis techniques to calculate the local regression coefficients of each network, determine the conditional probability table based on the local regression coefficients, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating an associated probability dataset.

[0082] The process of calculating the local regression coefficients of each network using spatial analysis techniques based on spatialized grid data, determining the conditional probability table based on the local regression coefficients, and constructing the topological structure of precipitation, groundwater, vegetation, and lakes by integrating Bayesian networks to generate an associated probability dataset includes the following steps:

[0083] S21. Based on the spatial grid database, extract key variables such as annual precipitation, groundwater depth, vegetation coverage, and lake area of ​​the grid, and clean and standardize the extracted data.

[0084] Specifically, firstly, core variables are extracted from the established spatialized grid database: annual precipitation (P, mm), groundwater depth (G, m), vegetation cover (V, %), and lake area (L, km²) for each 1 km grid. 2 First, ensure the data spans a consistent time frame (e.g., the last 10 years). Then, clean the data by removing outliers (e.g., extreme values ​​such as precipitation > 800 mm) and fill in missing values ​​using the inverse distance weighting (IDW) method to ensure that there are no missing values ​​for any of the four types of variables in each grid. Finally, standardize the data by converting the variables to the [0,1] interval to eliminate the impact of dimensional differences on subsequent analysis. It is important to note that all formulas in this embodiment require standardization during calculation.

[0085] S22. Using vegetation cover and lake area as dependent variables, and precipitation and groundwater depth as independent variables, construct a vegetation-based geographically weighted regression model and a lake-based geographically weighted regression model, respectively.

[0086] Specifically, the expression for the vegetation-based geographic weighted regression model is as follows:

[0087]

[0088] The expression for the lake-based geographic weighted regression model is:

[0089]

[0090] In the formula, V i Let L be the vegetation cover of the i-th grid. i Let u be the ecological grid lake area of ​​the i-th grid. i v i Let ) be the spatial coordinates of the i-th grid, and β be the coordinates of the grid. V0 β L0 The constant coefficients for vegetation and lakes, respectively, P i Let G be the annual precipitation of the i-th grid. i Let β be the groundwater depth of the i-th grid. V1 β L1 β represents the local regression coefficients of precipitation on vegetation and lakes, respectively. V2 β L2 These are the local regression coefficients of groundwater on vegetation and lakes, respectively. These are the error terms for the i-th grid, representing vegetation and lakes, respectively.

[0091] S23. Using the vegetation-based geographic weighted regression model and the lake-based geographic weighted regression model, calculate the local regression coefficients of each network and generate a spatial distribution map of the local coefficients of the key variables.

[0092] Specifically, first, a weighting function describing the strength of spatial association (such as the Gaussian kernel function, bisquare kernel function, etc.) is selected. The weight value decreases as the distance between the sample point and the target grid increases (the closer the distance, the greater the weight, indicating that the sample has a stronger local regression influence on the target grid). At the same time, the optimal bandwidth of the model is determined by the adaptive bandwidth method (selected by minimizing the AIC value; the bandwidth range is usually 5-20km. The vegetation model (i.e., the geographically weighted regression model based on vegetation) and the lake model (i.e., the geographically weighted regression model based on lakes) can be set separately. For example, the bandwidth of the vegetation model is set to 8km, and the bandwidth of the lake model is set to 12km due to data sparsity.

[0093] Secondly, for each grid i, calculate its Euclidean distance to all other grids in the study area, and substitute it into the Gaussian kernel function to generate weight w. ij (The closer the distance, the greater the weight; for example, the weight of a grid less than 2km away is greater than 0.8), forming a diagonal weight matrix (only the diagonal elements are w). ij (where the remainder is 0), which is the spatial weight matrix.

[0094] For the vegetation model, by minimizing the weighted sum of squared residuals in, For the predicted vegetation cover value of the j-th grid (calculated by a vegetation-based geographic weighted regression model), solve for the coefficient β of the i-th grid.Vi =(X T W i X) -1 X T W i V, where X is the independent variable matrix (dimension n×3, where n is the total number of grids in the study area), each row corresponds to the independent variable data of one grid, containing 3 columns, i.e., the first column is all 1s (constant term column, corresponding to the coefficient β). V0 The second column represents the standardized annual precipitation for each grid, the third column represents the standardized groundwater depth for each grid, T is the transpose of the matrix, and W... i Let V be the spatial weight matrix of the i-th grid, and let V be the dependent variable vector of the vegetation model (n×1 dimension). Each element corresponds to the vegetation cover observation value of one grid, thus obtaining β. V0 β V1 and β V2 .

[0095] Similarly, for the lake model, solve for β. Li =(X T W i X) -1 X T W i L, where L is the dependent variable vector of the lake model (n×1 dimension), and each element corresponds to the lake area observation value of a grid, thus obtaining β. L0 β L1 and β L2 .

[0096] Traverse all 1km grids in the Mu Us Desert, repeat the steps of weight matrix construction and coefficient calculation, and obtain 6 local regression coefficients for each grid (3 for vegetation model + 3 for lake model), which are stored as a coefficient dataset with coordinate attributes.

[0097] Finally, the local regression coefficients for each grid (with a focus on the key variable β) are calculated. V1 β L1 β V2 β L2 The local regression coefficients (βa, i.e., the local regression coefficients of precipitation / groundwater on vegetation / lakes) are correlated with grid coordinates and converted into GIS-recognizable raster data, maintaining a spatial resolution of 1km×1km. A divergent color scale (e.g., red-white-blue) is used, with positive values ​​(promoting effects) represented by red (the higher the intensity, the darker the color), negative values ​​(inhibiting effects) by blue (the higher the intensity, the darker the color), and zero values ​​by white. The coefficients are categorized into five levels based on their absolute values ​​(less than 0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, and greater than 0.8) to highlight areas of strong influence. Four spatial distribution maps of key coefficients are output, representing the local regression coefficients (βa) of precipitation on vegetation. V1 ), local regression coefficient of groundwater on vegetation (β)V2 ), the local regression coefficient of precipitation on lakes (β) L1 ), local regression coefficient of groundwater on lake (β) L2 Spatial distribution map of β; mark typical areas (such as the Ordos sand dune area) on the map. V2 Low value center, Yulin beach area β L1 (High value center), with an explanation of the coefficient meaning (e.g., "Red area indicates that precipitation has a significant promoting effect on vegetation").

[0098] In this step (S23), the local regression coefficients calculated by the geographic weighted regression model quantify the intensity (absolute value of the coefficient) and direction (positive or negative of the coefficient) of the influence of precipitation and groundwater depth on vegetation cover and lake area in different grids. These coefficients directly reflect the spatial heterogeneity of the association between variables, providing the most basic quantitative basis for subsequent network construction.

[0099] S24. Using key variables as network nodes, the connection direction of nodes is set by combining the physical meaning of local regression coefficients, and key connections are selected according to the preset absolute value of local regression coefficients to construct the topology of precipitation, groundwater, vegetation and lakes.

[0100] Specifically, using four types of elements as network nodes (P, G, V, L), the node connection direction is set based on the physical meaning of the local coefficients of geographic weighted regression:

[0101] Direct correlation: P→G (Precipitation replenishes groundwater through infiltration, involving a direct hydrological process), P→V (Precipitation directly affects vegetation photosynthesis and transpiration, serving as a direct water source for vegetation growth), G→V (Groundwater affects vegetation growth through root absorption, especially in arid sandy environments where it is a key water source), P→L (Precipitation directly flows into lakes, affecting lake storage capacity and area), G→L (Groundwater replenishes lakes through groundwater runoff, maintaining lake baseflow).

[0102] Excluding indirect correlations: V→L (vegetation and lake have no direct water exchange, only indirect correlation through groundwater) and L→V (the impact of lake on vegetation needs to be indirectly affected by surrounding humidity, etc., and is not a direct cause and effect).

[0103] For each grid cell, connections with local regression coefficients whose absolute values ​​are >0.2 are retained (considered as strong correlations), for example:

[0104] Dune grid: Due to rapid precipitation infiltration and vegetation's dependence on groundwater, G→V and P→G are preserved.

[0105] Beach grid: Due to the low-lying terrain and large amount of water accumulation, P→V and P→L are retained.

[0106] River valley grid: Due to the low-lying terrain, frequent interaction between groundwater and surface water, and the fact that vegetation is mostly distributed along the riverbank, G→L, P→L, P→V and G→V are retained.

[0107] This step (S24) is the network topology construction stage. Its core is to transform the local regression coefficients obtained in S23 into "connection relationships" between variables: on the one hand, the physical meaning of the coefficients (such as positive / negative correlation reflecting the direction of influence) is used to determine the connection direction of nodes (key variables) (who influences whom); on the other hand, "key connections" with sufficient influence intensity are screened out by setting a threshold for the absolute value of the coefficients, and weak correlations are eliminated, so as to construct a reasonable topology based on the quantitative results of spatial heterogeneity. This step relies on the local coefficients of S23 to define the "skeleton" of the network.

[0108] S25. Use the conditional probability transformation formula to convert the local regression coefficients into conditional probabilities, and group the grids according to the terrain type. Take the average of the conditional probabilities in each group to generate a regionalized conditional probability table, forming an associated probability dataset that includes grid coding, topological connectivity, and conditional probabilities.

[0109] Specifically, the local regression coefficients are converted into conditional probabilities using the formula: P(B=y|A=x)=φ(β·x+μ), where P(B=y|A=x) is the conditional probability that the dependent variable B takes state y given that the independent variable A takes state x, φ is the Sigmoid function that maps the coefficients to the probability interval [0,1], β is the local regression coefficient, and μ is the intercept (determined through fitting the sample data, usually taken as 0.1-0.3 to ensure a reasonable probability distribution).

[0110] The grid is grouped according to landform type (sand dunes, beaches, river valleys), and the average conditional probability within each group is taken to generate three sets of regionalized conditional probability tables (CPT) (reducing the amount of data and preserving spatial heterogeneity), namely, the CPT for the sand dune area, the CPT for the beach area, and the CPT for the river valley area.

[0111] Randomly select observation data from 20% of the grid and compare the element status (e.g., whether V meets the standard) predicted by the Bayesian network with the actual status to ensure an accuracy of ≥80%; if the accuracy of a certain area is <70%, return to recalibrate the bandwidth of the geographic weighted regression.

[0112] Create an associated probability dataset containing "grid encoding - topological connectivity - conditional probability", for example:

[0113] Etuoke Banner Sand Dune Grid: Grid code X05Y08 - Topological connection G→V - Conditional probability a, Grid code X05Y08 - Topological connection P→G - Conditional probability b.

[0114] Yulin beach area grid: grid code X12Y03-topological connection P→V-conditional probability c, grid code X12Y03-topological connection P→L-conditional probability d.

[0115] Wudinghe Valley Grid: Grid code X08Y10 - Topological connection G→L - Conditional probability e, Grid code X08Y10 - Topological connection P→L - Conditional probability f, Grid code X08Y10 - Topological connection P→V - Conditional probability g, Grid code X08Y10 - Topological connection G→V - Conditional probability h.

[0116] This step (S25) is the probability representation generation stage. Its goal is to transform the local regression coefficients (regression parameters) from S23 into the "conditional probabilities" (probability parameters) required by the Bayesian network. First, based on the topological connections determined in S24 (clarifying which variables' conditional probabilities need to be calculated), the local coefficients are converted into probability values ​​using a transformation formula. Then, combined with terrain type grouping (further handling spatial heterogeneity), the average probability within each group is taken to obtain a regionalized conditional probability table, ultimately forming a complete association dataset containing grid coding, topological connections, and conditional probabilities. This step relies on both the coefficients from S23 as the raw data for probability transformation and the topological structure from S24 to clarify the objects of probability calculation. It is a synthesis and transformation of the results of the first two steps, ultimately achieving a closed loop from "quantification of variable influence" to "network probability representation".

[0117] S3. Taking economic goals, social goals, and ecological goals based on lag factors as optimization objectives, the objective weights are determined based on correlation probabilities, and a multi-objective optimization model is constructed in combination with constraints. The water resource supply and demand model, groundwater numerical model, and ecological water demand assessment model are integrated to construct a coupled dynamic optimization model.

[0118] The process of constructing a coupled dynamic optimization model, which uses economic, social, and ecological objectives based on lag factors as optimization targets, determines the target weights based on correlation probabilities, and combines constraints to build a multi-objective optimization model, integrates water resource supply and demand models, groundwater numerical models, and ecological water demand assessment models, includes the following steps:

[0119] S31. Define economic goals, social goals, and ecological goals based on lag factors. The economic goal is to maximize the total regional output and minimize water consumption per unit of output. The social goal is to ensure basic per capita water consumption and narrow the gap in water use between urban and rural areas. The ecological goal based on lag factors is to control the annual decline of groundwater level within a preset range and assess the change in vegetation cover after the lag period.

[0120] Specifically, the economic objectives focus on sustainable regional economic growth, including maximizing the total output value of agriculture and industry while reducing water consumption per unit of output value to improve water use efficiency; the social objectives are centered on ensuring people's livelihood, requiring that the basic water needs of urban and rural residents be met (daily water consumption per capita not less than 120L) and that the water use gap between urban and rural areas be narrowed; the ecological objectives based on lag factors take into account both short-term and long-term benefits, controlling the annual drop in groundwater level to no more than 0.5m, and considering the time lag effect of vegetation restoration (such as the need for 6-18 months for root development of vegetation such as Artemisia arenaria), and ensuring the long-term effectiveness of ecological restoration by assessing changes in vegetation cover after the lag period.

[0121] The core indicators of the economic objectives are maximizing the region's total output (agriculture + industry) and minimizing water consumption per unit of output, expressed as: F a =max(C a +C i )∩min(Y a / C a +Y i / C i ), where F a For the economic objective function, C a For agricultural output, C i For industrial output, Y a For agricultural water consumption, Y i This refers to industrial water consumption.

[0122] The core indicators of the social goals are ensuring safe drinking water and balancing urban and rural water allocation, expressed as: F s =min|Y lc +Y lx |∩max[I(Y l ≥120L / person / day), where F s Let Y be the social objective function. lc For urban domestic water consumption, Y lx For rural domestic water consumption, Y l is the domestic water consumption, and I(*) is an indicator function (takes 1 if the condition is met, otherwise takes 0, used to determine whether the domestic water consumption meets the standard).

[0123] The core indicator of ecological objectives based on lag factors is the long-term ecological benefit that takes into account the lag effect of vegetation restoration, expressed as: In the formula, F e For the ecological objective function based on lag factors, V t+k Let be the vegetation cover at time t+k (t is the current time, k is the lag time, reflecting the lag effect of vegetation recovery), λ be the time decay coefficient, which is taken as 0.05 in this embodiment, and ΔG be the vegetation cover at time t+k (t is the current time, k is the lag time, reflecting the lag effect of vegetation recovery). tThis represents the annual change in groundwater level during time period t (positive values ​​indicate rising water levels, while negative values ​​indicate falling water levels, reflecting the stability of the groundwater system).

[0124] S32. Extract the correlation strength between elements from the correlation probability dataset, use the analytic hierarchy process (AHP) to adjust the initial weights based on the correlation probability differences in different regions, and obtain the target weights for different regions.

[0125] Specifically, the correlation strength between elements is extracted from the generated correlation probability dataset. For example, the correlation probability between groundwater and vegetation is significantly higher in the dune area than in the beach area, while the correlation probability between lakes and tourism economy is relatively prominent in the beach area. Based on these differences, the analytic hierarchy process (AHP) is used to adjust the initial weights: the weight of ecological objectives is increased in the dune area (no less than 40%), as the impact of groundwater on vegetation is more critical; the weight of economic objectives is moderately increased in the beach area (around 35%) to balance ecological and economic synergy; the weight of social objectives remains relatively stable in all areas (around 25%) to ensure basic water security. The final weights must satisfy the condition that the sum of ecological, economic, and social weights is 1, and the overall ecological weight is no less than 40%.

[0126] Sand dune area: Ecological target weight 0.55, economic target weight 0.30, social target weight 0.15. This allocation is in line with the core demand of "ecological restoration first" in the sand dune area. The strong correlation between groundwater and vegetation makes the ecological weight the highest, moderate agricultural activities support the economic weight the next, and basic domestic water supply guarantees maintain the basic level of the social weight.

[0127] Beach area: Ecological target weight 0.45, economic target weight 0.40, social target weight 0.15. Beach lakes have both ecological regulation and tourism economic value, so the ecological and economic weights are close. The small difference in water use between urban and rural areas keeps the social weight at a low level.

[0128] River valley area: ecological target weight 0.42, economic target weight 0.40, social target weight 0.18. The river valley has frequent groundwater-surface water interaction, and it is necessary to balance the ecological base flow of the river with the needs of agricultural irrigation (ecological and economic weights are close). The high population density makes the weight of "urban-rural water use balance" in the social target slightly higher than that in sand dune and beach areas.

[0129] S33. Taking the weighted sum of economic, social, and ecological objectives based on lag factors as the optimization direction, and combining the constraints, a multi-objective optimization model is constructed by coordinating water use conflicts through a water-saving compensation mechanism.

[0130] Specifically, the core optimization direction is the weighted sum of the three major objectives, integrating the demands for maximizing economic output, balancing domestic water use, and ensuring long-term ecological benefits. When setting constraints, the following must be included: the total water resource red line (total water consumption not exceeding the total available water resources in the region), the ecological protection red line (vegetation coverage in the core area not less than 45%), and economic and technical constraints (agricultural irrigation water utilization coefficient not less than 0.8). To address the conflict between agricultural irrigation and ecological water replenishment, a "water-saving compensation" mechanism will be used for coordination, such as replacing agricultural groundwater irrigation with reclaimed water, thus ensuring agricultural needs while reducing groundwater extraction.

[0131] The objective function of the multi-objective optimization model is expressed as: F = α e ·F e +α a ·F a +α s ·F s α e α a α s These are the weights for ecological objectives, economic objectives, and social objectives, respectively.

[0132] S34. The multi-objective optimization model is connected with the water resource supply and demand model, the groundwater numerical model, and the ecological water demand assessment model through a data interface. The water resource supply and demand model provides the dynamic balance results of water demand and available water. The groundwater numerical model simulates the changes in groundwater level and provides feedback for adjustment. The ecological water demand assessment model calculates the minimum ecological baseflow of the river as the lower limit of ecological water consumption, and a coupled dynamic optimization model is constructed.

[0133] Specifically, the multi-objective optimization model is connected with the water resource supply and demand model, the groundwater numerical model, and the ecological water demand assessment model through a data interface: the water resource supply and demand model provides the dynamic balance results of water demand and available water in various industries, serving as the basic constraint of the multi-objective model; the groundwater numerical model simulates the changes in groundwater level under different water use schemes, and if the simulation results exceed the 0.5m / year decrease constraint, it is fed back to the multi-objective model to adjust the amount of agricultural groundwater extraction; the ecological water demand assessment model (such as the Tennant method) calculates the minimum ecological baseflow of rivers (not less than 10% of the multi-year average runoff), serving as the lower limit of ecological water use, ensuring that the ecological water use allocated by the multi-objective model meets basic needs.

[0134] Specifically, the coupled water resource supply and demand, groundwater, and ecological water demand models include:

[0135] 1) Model Interface Design:

[0136] Water Resources Supply and Demand Model (WEAP): Outputs water demand and supply for various industries as supply and demand constraints for the multi-objective model.

[0137] Groundwater numerical model (MODFLOW): Input agricultural groundwater extraction volume, output groundwater level change, and feed back to ecological objectives.

[0138] Ecological water demand assessment model (Tennant method): Calculate the river's ecological baseflow Re = 0.1 x R mean (R mean (The average runoff over many years) serves as the lower limit for ecological water use.

[0139] 2) Dynamically coupled logic:

[0140] First, the multi-objective model outputs the initial water allocation scheme (agricultural water consumption Y). a Industrial water consumption Y i Domestic water consumption Y l Ecological water consumption Y e Then, MODFLOW simulates ΔG. t If the constraint is exceeded (e.g., ΔG) t >0.5m), feedback to the multi-objective model to adjust agricultural water consumption Y a Next, WEAP verifies the supply and demand balance. If the water supply S t Water demand D t Ecological water consumption Y can be replenished and updated through water rights trading or water diversion projects. e Finally, iterate until all constraints are satisfied, and output the coupled model results.

[0141] Furthermore, this embodiment also includes inputting historical monitoring data (water use data, meteorological data) and associated probability parameters, and adjusting key model parameters (such as irrigation water utilization coefficient and groundwater permeability coefficient) to ensure that the deviation between simulated groundwater level changes, vegetation cover, and other indicators and actual observed values ​​is controlled within 10%. Real-world data is used to verify model stability, ensuring that the multi-objective optimization results are consistent with actual regional water use patterns and ecological evolution trends under different scenarios, providing a reliable model foundation for subsequent scenario simulations.

[0142] S4. Solve the coupled dynamic optimization model to generate a Pareto optimal solution set and output water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, calculate the ecological option value of each allocation scheme, and optimize and adjust the water resource allocation schemes under different scenarios according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

[0143] The process of solving the coupled dynamic optimization model to generate a Pareto optimal solution set and output water resource allocation schemes under different scenarios includes the following steps: Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation schemes under different scenarios are optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the optimal water resource allocation scheme.

[0144] S41. Based on the multi-objective particle swarm optimization algorithm, the objective function of the coupled dynamic optimization model is used as the fitness function. The particle swarm is used to iteratively optimize different scenarios to generate Pareto optimal solution sets that include the water allocation ratio and specific water volume for agriculture, industry, life and ecology, and output water resource allocation schemes under different scenarios.

[0145] Specifically, an intelligent algorithm adapted to multi-objective optimization (i.e., multi-objective particle swarm optimization algorithm) is selected, guided by the economic, social, and ecological objectives integrated by the coupled dynamic optimization model. Through iterative optimization, the algorithm selects non-dominated solutions (i.e., Pareto optimal solutions) that satisfy all constraints. During the solution process, different scenarios are designed to cover diverse development needs: the baseline scenario continues the current water use pattern and development intensity; the ecological priority scenario focuses on ensuring ecological water use and restricting the expansion of water-intensive industries; the economic synergy scenario emphasizes promoting water-saving technologies to improve water use efficiency; and the comprehensive optimization scenario balances ecological protection and economic development, pursuing a balance between groundwater extraction and recharge. For each scenario, through multiple iterative calculations, a Pareto optimal solution set is generated, including the water consumption allocation ratios and specific water volumes for each industry (agriculture, industry, domestic, and ecology). This ensures that there is no absolute superiority or inferiority among the solutions in the solution set, providing multiple choices for subsequent selection.

[0146] The multi-objective particle swarm optimization algorithm uses the objective function of the coupled dynamic optimization model as the fitness function. It iteratively optimizes different scenarios using particle swarm optimization to generate Pareto optimal solution sets containing water allocation ratios and specific water volumes for agriculture, industry, domestic use, and ecology. The output water resource allocation schemes under different scenarios include:

[0147] 1) Determine the core parameters of the multi-objective particle swarm optimization algorithm: number of particles (set according to problem complexity, usually 50-100), maximum number of iterations (generally 300-500), inertia weight (controlling the influence of particle historical velocity, initially set to 0.9, gradually decreasing to 0.4 with iterations), and learning factor (reflecting the strength of particle learning towards individual and global optima, usually both set to 2.0). Simultaneously, clarify the differentiated parameters for each scenario: the baseline scenario uses the current water efficiency index and ecological protection efforts; the ecological priority scenario increases the weight of ecological objectives in the fitness function and sets an upper limit for the scale of high water-consuming agriculture; the economic synergy scenario increases the industrial water reuse rate target and reduces water consumption constraints per unit of output; the comprehensive optimization scenario sets a groundwater extraction-replenishment balance coefficient to balance the weights of each objective.

[0148] 2) Initialize the particle swarm and particle encoding: Encode each particle as a vector, with the vector dimension corresponding to the allocation ratio and specific water volume for four categories of water use: agriculture, industry, domestic use, and ecology. Ensure that the sum of all components equals the total available water resources in the region, and that the water volume for any single category does not exceed its respective constraint limit (e.g., ecological water use is not less than the minimum water requirement). Randomly generate an initial particle swarm, with each particle representing a potential water resource allocation scheme: the components of the particle position vector correspond to agricultural water use, industrial water use, domestic water use, and ecological water use, respectively; the particle velocity vector controls the direction and magnitude of position updates, with the initial velocity randomly set within a reasonable range (e.g., ±5% of the total water volume).

[0149] 3) Iterative Optimization and Fitness Assessment: For each particle (i.e., each allocation scheme), it is substituted into the coupled dynamic optimization model to calculate its performance on the three major objectives of economy, society, and ecology. The combined objective function values ​​are used as the particle's fitness. The economic objective assessment is based on the total industrial and agricultural output value and water consumption per unit of output value; the social objective assessment focuses on the balance of urban and rural water use and the guarantee rate of domestic water use; the ecological objective assessment includes changes in groundwater level and vegetation cover after lag correction. Based on the fitness, it is determined whether the particle is a non-dominated solution (i.e., there is no other particle that is better on all objectives), and the particle's individual optimal solution (its own historical best performance) and global optimal solution (the best non-dominated solution in the population) are updated.

[0150] 4) Updating Particle Positions and Maintaining the External File: Based on the position update formula of the particle swarm optimization algorithm, and combining inertia weights, learning factors, individual optimality, and global optimality, the velocity and position of each particle are adjusted to generate a new allocation scheme. Simultaneously, an external file is established to store all non-dominated solutions that occur during the iteration process. The file is periodically pruned (e.g., retaining a certain number of evenly distributed solutions) to avoid the file becoming too large. If a newly generated particle is a non-dominated solution, it is added to the external file; if a solution in the external file is dominated by the new particle, the dominated solution is removed, ensuring that the file always contains the current optimal Pareto solution.

[0151] 5) Determining Iteration Termination and Generating Scenario Solution Sets: The iteration is terminated when the number of iterations reaches a preset maximum value, or when there is no significant improvement in the solutions from multiple consecutive generations of external archives. Pareto optimal solution sets corresponding to different scenarios are selected from the external archives: the baseline scenario solution set retains solutions similar to the current water use structure; the ecological priority scenario solution set emphasizes solutions with a high proportion of ecological water use and strict groundwater protection; the economic synergy scenario solution set focuses on solutions with high industrial water use efficiency and significant agricultural water conservation; and the comprehensive optimization scenario solution set selects solutions with a good balance among the various objectives.

[0152] 6) Output water resource allocation schemes for different scenarios: For the Pareto optimal solution set of each scenario, extract the water consumption allocation ratio and specific water volume for agriculture, industry, domestic use, and ecology in the scheme, forming a structured output: clearly define the absolute water consumption of each industry (e.g., agricultural water consumption XX cubic meters / year), its percentage of total water consumption, and label key indicators such as the corresponding economic output, urban-rural water consumption differences, and expected ecological restoration effects. The output results should clearly reflect the orientation differences between different scenarios. For example, the ecological priority scenario has a significantly higher proportion of ecological water use than the baseline scenario, and the industrial unit output water consumption in the economic synergy scenario is significantly lower than in other scenarios, providing an intuitive basis for subsequent scheme optimization and adjustment.

[0153] S42. Based on the ecological water replenishment and vegetation restoration in the water resource allocation plan, predict the probability of desertification reversal within the preset years, and determine the amount of water resources that can be conserved by combining the hydrological characteristics of the reversal area.

[0154] Specifically, based on the intensity of ecological water replenishment and vegetation restoration measures in the plan, the probability of desertification reversal within a certain number of years is predicted; based on the hydrological characteristics of the reversal area, the amount of water resources that can be conserved is estimated; among them, the amount of water resources that can be conserved refers to the ability of the ecosystem to intercept and retain precipitation through processes such as vegetation cover and soil infiltration, thereby enhancing groundwater recharge and regulating river flow.

[0155] The process of predicting the probability of desertification reversal within a predetermined timeframe based on ecological water replenishment and vegetation restoration in the water resource allocation plan, and determining the amount of water resources that can be conserved in conjunction with the hydrological characteristics of the reversal area, includes:

[0156] 1) Extract core data directly related to desertification reversal from the water resource allocation plan: clarify the specific amount of ecological water replenishment (e.g., annual ecological water replenishment amount, seasonal water replenishment periods), vegetation restoration targets (e.g., planned vegetation types—Artemisia arenaria, Salix psammophila, etc., and the corresponding area area), and the spatial distribution of water replenishment projects (e.g., key water replenishment areas such as sand dune areas and beach edges, which are sensitive to desertification). Simultaneously, compile the auxiliary measures involved in the plan (e.g., fencing and artificial planting density) as basic variables for subsequent probability prediction.

[0157] 2) Based on the geomorphological differences in the Mu Us Desert (sand dunes, beaches, river valleys), establish regional correlation models between reversal probability and ecological water replenishment and vegetation restoration:

[0158] Sand dune areas: The focus is on analyzing the relationship between ecological water replenishment and groundwater depth—increased water replenishment reduces groundwater depth, thereby promoting the establishment of psammophytic vegetation (such as Artemisia arenaria). Based on historical data (such as the correlation between water replenishment and vegetation survival rate in a certain sand dune area over the past 10 years), a quantitative relationship is established: "For every increase of X in water replenishment, groundwater depth decreases by Y, and vegetation coverage increases by Z." This is then combined with the critical value of vegetation coverage and desertification reversal (such as desertification reversal beginning when coverage ≥ 30%) to calculate the reversal probability for different years (e.g., the probability is low in the first year due to unstable vegetation; the probability significantly increases in years 3-5 as the vegetation root system develops).

[0159] For beach areas: the focus is on the impact of ecological water replenishment on surface humidity—the amount of water replenishment directly affects the duration of water accumulation in the beach, thereby promoting the growth of herbaceous vegetation (such as Leymus chinensis). Combining the superimposed effects of precipitation and water replenishment (such as water replenishment during the rainy season prolonging the water accumulation period), a correlation curve of "water replenishment - water accumulation period - vegetation coverage" is established to predict the probability of beach desertification reversal within different years (e.g., when the water accumulation period is ≥150 days / year, the probability of reversal in the second year can reach a relatively high level).

[0160] River Valley Area: Focus on the restorative effect of water replenishment on riparian vegetation belts—the amount of water replenishment ensures the river's base flow, promotes the growth of riparian willow forests, and inhibits the expansion of riparian desertification. Based on the historical correlation between riparian vegetation coverage and desertification reversal (e.g., when willow forest coverage is ≥50%, the probability of riparian desertification reversal increases significantly), and combined with the sustainability of valley water replenishment in the plan (e.g., whether it guarantees base flow throughout the year), the annual reversal probability is predicted.

[0161] 3) For a preset timeframe (e.g., 5 years), determine the probability of desertification reversal in each region on an annual basis:

[0162] For dune areas, the main plants are psammophytic plants such as Artemisia argyi and Salix psammophila, which require 2-3 years to develop their root systems and rely on groundwater replenishment in the early stages. For beach areas, the main plants are herbaceous plants such as Leymus chinensis and Salix matsudana, which have a short growth cycle (1 year) and rely on water accumulation. For river valley areas, the main plants are shrubs such as riverbank willow forests, which require a stable base flow guarantee.

[0163] In the first two years, when the vegetation is in the establishment period, the reversal probability mainly depends on the initial water replenishment and the seedling survival rate. For example, the reversal probability in the dune area is about 20%-40%, in the beach area it is about 30%-60%, and in the river valley area it is about 25%-55%.

[0164] In the 3rd to 5th year, the vegetation enters a stable growth period, and the root system develops to enhance the sand-fixing ability, significantly increasing the probability of reversal. For example, the probability of reversal in dune areas is about 50%-70%, in beach areas it is about 65%-80%, and in river valley areas it is about 60%-85%.

[0165] The final result is a two-dimensional reversal probability table of "region-year" to reflect the dynamic process of desertification reversal within a preset period.

[0166] 4) Determine the area and hydrological characteristics of the reversal zone: Based on the predicted reversal probability and the total desertification area of ​​each region, estimate the actual reversal area for each year within the preset timeframe (e.g., the total desertification area of ​​a certain dune region is 100 km²). 2 If the probability of reversal is 60% in the third year, then the area of ​​reversal in that year is 60 km². 2 Simultaneously, hydrological characteristic parameters of the inversion area were collected, including soil permeability coefficient (reflecting the ability of precipitation / recharge water to infiltrate groundwater; the permeability coefficient in the dune area is higher than that in the beach area), vegetation water retention rate (the proportion of surface runoff reduced after vegetation coverage is increased; for example, the water retention rate can reach 30% when the coverage is 50%), and groundwater recharge coefficient (the amount of groundwater recharged per unit area of ​​the inversion area per year, which is related to soil texture).

[0167] 5) Based on the reversal area and hydrological characteristics, the amount of water resources that can be conserved is calculated annually: For surface conservation, it is the decrease in surface runoff due to increased vegetation cover in the reversal area (i.e., water retention rate × regional annual precipitation × reversal area); for groundwater conservation, it is the amount of water entering groundwater through soil infiltration (i.e., permeability coefficient × sum of regional annual precipitation and recharge × reversal area); for total conservation, it is the sum of surface conservation and groundwater conservation, which is the amount of water resources that can be conserved in the reversal area for that year. The total conservation volume for each year within the preset timeframe is then summarized to obtain the cumulative water resource conservation volume resulting from desertification reversal after the implementation of the scheme.

[0168] S43. Based on the reversal probability of desertification and the amount of water resources that can be conserved, calculate the ecological option value of each allocation scheme, and determine the lagged compensation water volume by combining the ecological water consumption and the lag characteristics of vegetation restoration in each scheme.

[0169] Specifically, for each water resource allocation scheme in the Pareto optimal solution set, the potential value of its long-term ecological benefits (ecological option value) is evaluated. That is, based on the reversal probability of desertification and the amount of water resources that can be conserved, the impact of time factors on benefits is considered, and the potential future benefits are converted into current value. Through this process, the long-term potential of each scheme in ecological restoration is quantified, providing a basis for the selection of schemes based on long-term benefits.

[0170] The formula for calculating the value of ecological options is as follows:

[0171]

[0172] In the formula, O represents the ecological option value (reflecting the potential water resource benefits from future desertification reversal), n represents the total number of forecast years, s represents the number of forecast years, and p... sLet q be the probability of desertification reversal in year s. s Let be the amount of water resources that can be conserved by reversing desertification in year s, r be the discount rate (the coefficient that discounts future revenues to their present value), and e be the amount of water that can be conserved by reversing desertification in year s. -r·s This is a time-discounted term (the present value of future returns decreases as the number of years increases).

[0173] For the ecological water consumption in each scheme, and considering the lag characteristics of vegetation restoration (e.g., it takes time for psammophytes to stabilize after water replenishment), a delayed compensation water volume is calculated. The restoration lag time is determined based on the vegetation type involved in the scheme. Taking into account the amplification effect of the lag time on water demand, a compensation portion is added to the basic ecological water consumption to ensure that vegetation still receives sufficient water to maintain its recovery during the lag phase. The revised ecological water consumption must be included in the total water consumption calculation of the scheme to ensure that it does not exceed the regional water resource constraints.

[0174] The formula for calculating the delayed compensation water volume is as follows:

[0175] Q c =Q e ·(1+k d ·t d );

[0176] In the formula, Q c To compensate for the delayed effects of ecological restoration, Q e The basic ecological water consumption (excluding the initial allocation under lag), k d The lag compensation coefficient (reflecting the amplification effect of lag time on water demand, and related to vegetation type), t d The ecological restoration process has been delayed for a long time.

[0177] S44. Based on the ecological option value and the delayed compensation water volume, combined with the preset ecological option threshold, the water resource allocation scheme under different scenarios is dynamically optimized and adjusted to obtain the optimal water resource allocation scheme under each scenario.

[0178] Specifically, from the Pareto optimal solution set, schemes with ecological option values ​​higher than a preset ecological option threshold are selected as candidates, with priority given to options with significant long-term ecological benefits. For candidate schemes, the original ecological water consumption is replaced with delayed compensation water consumption, and the total water consumption is recalculated to ensure that the total water resource constraint is not exceeded. With the corrected ecological water consumption as a constraint, the coupled dynamic optimization model is invoked again to fine-tune the allocation of agricultural and industrial water consumption, so that the economic goal (total output value) and social goal (urban-rural water use balance) remain at a relatively good level. Through comprehensive evaluation (such as selecting the scheme with the highest ecological option value and the greatest total benefit after delayed compensation), the final optimal water resource allocation scheme is determined. The output scheme must specify the specific water consumption and spatiotemporal allocation plan for each industry, and be accompanied by corresponding safeguard measures (such as the promotion of water-saving technologies and the scheduling mechanism of ecological water replenishment projects) to ensure that the scheme can be implemented.

[0179] According to another embodiment of the present invention, the Mu Us Sandy Land Water Resources Multi-Objective Collaborative Dynamic Optimization Allocation System includes a basic data acquisition and integration module, an ecological and hydrological element correlation analysis module, a coupled dynamic optimization model construction module, and a water resources allocation scheme optimization solution module.

[0180] Among them, the basic data acquisition and integration module is used to acquire ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine cross-regional allocation boundaries, water resources and ecological constraints.

[0181] The ecological and hydrological element correlation analysis module is used to calculate the local regression coefficients of each network based on spatial grid data using spatial analysis techniques, determine the conditional probability table based on the local regression coefficients, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating a correlation probability dataset.

[0182] The coupled dynamic optimization model construction module is used to construct a multi-objective optimization model by taking economic, social and ecological objectives based on lag factors as optimization objectives, determining the objective weights based on correlation probabilities, and combining constraints. It integrates water resource supply and demand models, groundwater numerical models and ecological water demand assessment models to construct a coupled dynamic optimization model.

[0183] The water resource allocation scheme optimization solution module is used to solve the coupled dynamic optimization model to generate the Pareto optimal solution set and output the water resource allocation scheme under different scenarios. Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation scheme under different scenarios is optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

[0184] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert, characterized in that, Includes the following steps: S1. Obtain ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine the cross-regional allocation boundary, water resources and ecological constraints. S2. Based on the spatialized grid data, use spatial analysis techniques to calculate the local regression coefficients of each network, determine the conditional probability table based on the local regression coefficients, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating an associated probability dataset. S3. Taking economic goals, social goals, and ecological goals based on lag factors as optimization objectives, the objective weights are determined based on correlation probabilities, and a multi-objective optimization model is constructed in combination with constraints. The water resource supply and demand model, groundwater numerical model, and ecological water demand assessment model are integrated to construct a coupled dynamic optimization model. S4. Solve the coupled dynamic optimization model to generate a Pareto optimal solution set and output water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, calculate the ecological option value of each allocation scheme, and optimize and adjust the water resource allocation schemes under different scenarios according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

2. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 1, characterized in that, The process of calculating the local regression coefficients of each network based on spatialized grid data using spatial analysis techniques, determining the conditional probability table based on the local regression coefficients, and constructing the topological structure of precipitation, groundwater, vegetation, and lakes by fusing Bayesian networks to generate an associated probability dataset includes the following steps: S21. Based on the spatial grid database, extract key variables such as annual precipitation, groundwater depth, vegetation cover and lake area of ​​the grid, and clean and standardize the extracted data. S22. Using vegetation cover and lake area as dependent variables, and precipitation and groundwater depth as independent variables, construct a geographically weighted regression model based on vegetation and a geographically weighted regression model based on lakes, respectively. S23. Using the vegetation-based geographic weighted regression model and the lake-based geographic weighted regression model, calculate the local regression coefficients of each network and generate a spatial distribution map of the local coefficients of the key variables. S24. Using key variables as network nodes, the node connection direction is set by combining the physical meaning of local regression coefficients, and key connections are selected according to the preset absolute value of local regression coefficients to construct the topology of precipitation, groundwater, vegetation and lakes. S25. Use the conditional probability transformation formula to convert the local regression coefficients into conditional probabilities, and group the grids according to the terrain type. Take the average of the conditional probabilities in each group to generate a regionalized conditional probability table, forming an associated probability dataset that includes grid coding, topological connectivity, and conditional probabilities.

3. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 2, characterized in that, The expression for the vegetation-based geographic weighted regression model is as follows: The expression for the lake-based geographic weighted regression model is: In the formula, V i Let L be the vegetation cover of the i-th grid. i Let u be the ecological grid lake area of ​​the i-th grid. i v i Let ) be the spatial coordinates of the i-th grid, and β be the coordinates of the grid. V0 β L0 The constant coefficients for vegetation and lakes, respectively, P i Let G be the annual precipitation of the i-th grid. i Let β be the groundwater depth of the i-th grid. V1 β L1 β represents the local regression coefficients of precipitation on vegetation and lakes, respectively. V2 β L2 These are the local regression coefficients of groundwater on vegetation and lakes, respectively. These are the error terms for the i-th grid, representing vegetation and lakes, respectively.

4. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 1, characterized in that, The optimization model, which uses economic, social, and ecological objectives based on lag factors as optimization goals, determines the objective weights based on correlation probabilities, and constructs a multi-objective optimization model by combining constraints, integrates water resource supply and demand models, groundwater numerical models, and ecological water demand assessment models, and constructs a coupled dynamic optimization model, includes the following steps: S31. Define economic goals, social goals, and ecological goals based on lag factors. The economic goal is to maximize the total regional output and minimize water consumption per unit of output. The social goal is to ensure basic per capita domestic water consumption and narrow the gap in water use between urban and rural areas. The ecological goal based on lag factors is to control the annual decline of groundwater level within a preset range and assess the change in vegetation cover after the lag period. S32. Extract the correlation strength between elements from the correlation probability dataset, use the analytic hierarchy process, and combine the correlation probability differences in different regions to correct the initial weights and obtain the target weights for different regions. S33. Taking the weighted sum of economic, social, and ecological objectives based on lag factors as the optimization direction, and combining the constraints, a multi-objective optimization model is constructed by coordinating water use conflicts through a water-saving compensation mechanism. S34. Connect the multi-objective optimization model with the water resource supply and demand model, the groundwater numerical model, and the ecological water demand assessment model through a data interface. The water resource supply and demand model provides the dynamic balance results of water demand and available water, the groundwater numerical model simulates groundwater level changes and provides feedback for adjustment, and the ecological water demand assessment model calculates the minimum ecological base flow of the river as the lower limit of ecological water consumption, thus constructing a coupled dynamic optimization model.

5. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 4, characterized in that, The core indicators of the economic objectives are maximizing regional total output and minimizing water consumption per unit of output, expressed as: F a =max(C a +C i )∩min(Y a / C a +Y i / C i ), where F a For the economic objective function, C a For agricultural output, C i For industrial output, Y a For agricultural water consumption, Y i This refers to industrial water consumption. The core indicators of the social goals are ensuring safe drinking water and balancing urban and rural water allocation, expressed as: F s =min|Y lc +Y lx |∩max[I(Y l ≥120L / person / day), where F s Let Y be the social objective function. lc For urban domestic water consumption, Y lx For rural domestic water consumption, Y l I(*) represents domestic water consumption, and I(*) is an indicator function. The core indicator of ecological objectives based on lag factors is the long-term ecological benefit that takes into account the lag effect of vegetation restoration, expressed as: In the formula, F e For the ecological objective function based on lag factors, V t+k Let be the vegetation cover at time t+k, where t is the current time, k is the lag time, λ is the time decay coefficient, and ΔG is the vegetation cover at time t+k. t Let be the annual change in groundwater level during time period t; The objective function of the multi-objective optimization model is expressed as: F = α e ·F e +α a ·F a +α s ·F s In the formula, F is the objective function of the multi-objective optimization model, and α e α a α s These are the weights for ecological objectives, economic objectives, and social objectives, respectively.

6. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 1, characterized in that, The solution to the coupled dynamic optimization model generates a Pareto optimal solution set, outputting water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation schemes under different scenarios are optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the optimal water resource allocation scheme, including the following steps: S41. Based on the multi-objective particle swarm optimization algorithm, the objective function of the coupled dynamic optimization model is used as the fitness function. The particle swarm is used to iteratively optimize different scenarios to generate Pareto optimal solution sets that include the water allocation ratio and specific water volume for agriculture, industry, life and ecology, and output water resource allocation schemes under different scenarios. S42. Based on the ecological water replenishment and vegetation restoration in the water resource allocation plan, predict the probability of desertification reversal within the preset years, and determine the amount of water resources that can be conserved by combining the hydrological characteristics of the reversal area. S43. Based on the reversal probability of desertification and the amount of water resources that can be conserved, calculate the ecological option value of each allocation scheme, and determine the amount of water to compensate for the lag in the ecological water consumption and vegetation restoration in each scheme. S44. Based on the ecological option value and the delayed compensation water volume, combined with the preset ecological option threshold, the water resource allocation scheme under different scenarios is dynamically optimized and adjusted to obtain the optimal water resource allocation scheme under each scenario.

7. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 6, characterized in that, The process of predicting the probability of desertification reversal within a predetermined timeframe based on ecological water replenishment and vegetation restoration in the water resource allocation plan, and determining the amount of water resources that can be conserved in conjunction with the hydrological characteristics of the reversal area, includes the following steps: S421. Extract key data related to desertification reversal from the water resource allocation scheme, and combine the geomorphological differences of the Mu Us Desert to establish a correlation model between reversal probability and ecological water replenishment and vegetation restoration in different regions. S422. Based on the preset time limit, and combined with the correlation model between the reversal probability and ecological water replenishment and vegetation restoration, determine the desertification reversal probability of sand dunes, beaches and river valleys on an annual basis. S423. Based on the probability of desertification reversal and combined with the total desertification area of ​​each region, determine the actual reversal area for each year within the preset time limit, and collect the hydrological characteristic parameters of the reversal area. S424. Based on the actual reversal area and hydrological characteristic parameters of the reversal zone, determine the amount of water resources that can be conserved on an annual basis. The annual water conservation capacity of the inverted area is determined by the sum of surface water conservation capacity and groundwater conservation capacity. Surface water conservation capacity is determined by water retention rate, annual regional precipitation and actual inverted area. Groundwater conservation capacity is determined by permeability coefficient, annual regional precipitation and recharge and actual inverted area.

8. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 6, characterized in that, The formula for calculating the value of ecological options is: In the formula, O represents the ecological option value, n represents the total number of forecast years, s represents the forecast period, and p s Let q be the probability of desertification reversal in year s. s Let r be the amount of water resources that can be conserved by reversing desertification in year s, and r be the discount rate. The formula for calculating the delayed compensation water volume is: Q c =Q e ·(1+k d ·t d ); In the formula, Q c To compensate for the delayed effects of ecological restoration, Q e Basic ecological water consumption, k d t is the lag compensation coefficient. d The ecological restoration process has been delayed for a long time.

9. The multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert according to claim 6, characterized in that, The process of dynamically optimizing and adjusting water resource allocation schemes under different scenarios based on ecological option value and delayed compensation water volume, combined with preset ecological option thresholds, to obtain the optimal water resource allocation scheme for each scenario includes the following steps: S441. Select schemes with ecological option values ​​higher than the preset ecological option threshold from the Pareto optimal solution set as candidate schemes, replace the initial ecological water consumption in the candidate schemes with the lagged compensation water consumption, and recalculate the total water consumption to ensure that the total water resource constraint is met. S442. Using the corrected ecological water consumption as a constraint, the coupled dynamic optimization model is invoked to optimize the allocation ratio of agricultural and industrial water consumption under different scenarios, and the optimal water resource allocation scheme under each scenario is obtained.

10. A multi-objective collaborative dynamic optimization allocation system for water resources in the Mu Us Desert, used to implement the steps of the multi-objective collaborative dynamic optimization allocation method for water resources in the Mu Us Desert as described in any one of claims 1-9, characterized in that, It includes a basic data acquisition and integration module, an ecological and hydrological element correlation analysis module, a coupled dynamic optimization model construction module, and a water resource allocation scheme optimization solution module; The basic data acquisition and integration module is used to acquire ecological vegetation, lake and hydrological data of the Mu Us Desert, establish a spatial grid database, sort out water sources and water demand, and determine cross-regional allocation boundaries, water resources and ecological constraints. The ecological and hydrological element correlation analysis module is used to calculate the local regression coefficient of each network based on spatial grid data using spatial analysis technology, determine the conditional probability table based on the local regression coefficient, and integrate Bayesian networks to construct the topological structure of precipitation, groundwater, vegetation and lakes, generating a correlation probability dataset. The coupled dynamic optimization model construction module is used to construct a multi-objective optimization model by taking economic goals, social goals and ecological goals based on lag factors as optimization objectives, determining the objective weights based on correlation probabilities, and combining constraints. It integrates water resource supply and demand models, groundwater numerical models and ecological water demand assessment models to construct a coupled dynamic optimization model. The water resource allocation scheme optimization solution module is used to solve the coupled dynamic optimization model to generate a Pareto optimal solution set and output water resource allocation schemes under different scenarios. Based on the Pareto optimal solution set, the ecological option value of each allocation scheme is calculated, and the water resource allocation schemes under different scenarios are optimized and adjusted according to the ecological option value and the lagged compensation water volume to generate the best water resource allocation scheme.

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