Construction method of binary water cycle model in low mountain and hilly area based on topological network division

Abstract

The low hilly area binary water cycle model construction method based on topological network division belongs to the technical field of water cycle model construction, and aims to solve the problems that the existing model is difficult to adapt to the complex terrain hydraulic characteristics of low hilly area, the natural-social binary water cycle coupling is insufficient, and the long-time sequence simulation precision is poor; the present application obtains multi-source heterogeneous data, divides the minimum hydrological unit and constructs a four-level water supply topological network; the key parameters are extracted by the binary driven analysis model, and the synergistic effect of terrain and human activities is quantified; the core parameter matrix is generated through topological adaptation coupling model and multi-objective optimization; the complete model is constructed by fusing the improved distributed hydrological simulation and social water use regulation module, and the dynamic coupling simulation of binary water cycle is realized by combining multi-index calibration and parameter dynamic updating. The present application accurately describes the complex hydraulic connection and human activity intervention effect, improves the simulation precision and long-time sequence adaptability, the model has strong operability, wide application range, and provides reliable technical support for efficient utilization and management of water resources in low hilly area.

Description

Technical Field

[0001] This invention relates to the field of water cycle model construction technology, and in particular to a method for constructing a binary water cycle model in low hilly areas based on topological network partitioning. Background Technology

[0002] Water cycle models, as core tools for revealing the evolution of water resources in watersheds and supporting the optimal allocation of water resources, occupy a pivotal position in global water resource management and planning. The water cycle is a complex system involving multiple levels, including atmospheric water, surface water, soil water, and groundwater. Its dynamic changes directly affect the sustainable use of regional water resources and ecological environmental protection. However, the characteristics of the water cycle vary significantly across different geographical environments, posing diverse demands for the refined construction of models. Particularly in low mountain and hilly areas, the unique topographic features—significant topographic relief and complex hydraulic connections—coupled with strong human intervention such as agricultural irrigation, industrial water use, and domestic water use, together form a complex natural-social dual water cycle system. This duality severely challenges the applicability of traditional water cycle models in this region, as traditional models often struggle to simultaneously and accurately characterize both natural water cycle processes and socio-economic water use processes and their interactions.

[0003] Currently, although various methods for constructing water cycle models have been proposed and applied in different scenarios, their applicability in low mountain and hilly areas remains significantly limited. For example, CN115759403A discloses a method for constructing a dynamic combined prediction model for water cycle processes in cold regions. This method classifies water cycle influencing factors according to constraints and uses dynamic Bayesian networks and long short-term memory networks for combined prediction, effectively considering the ice-water phase transition characteristics and stochastic uncertainties brought about by climate change in cold regions, thereby improving the accuracy of water cycle simulation in cold regions. However, the design of this model is mainly aimed at the special cryosphere hydrological processes in cold regions, and its topology and parameter settings are difficult to directly apply to low mountain and hilly areas with complex terrain and dense water conservancy projects. In low mountain and hilly areas, due to the large topographic relief, fragmented river network, variable water flow paths, and significant impact from human activities, this model cannot accurately represent the complex hydraulic connections and the synergistic effects of human activities, thus affecting the accuracy of the simulation results.

[0004] For example, CN108108556A discloses a method for constructing an irrigation district water cycle model based on a dissipative-convergent structure. This method establishes topological relationships between units by dividing the irrigation district into catchment and dissipative units, thus achieving integrated simulation of the "natural-artificial" binary water cycle. It performs well in simulating water diversion and drainage processes in plain irrigation districts. However, this model is mainly applicable to plain irrigation districts with relatively flat terrain and regular water conservancy project layouts. It fails to fully consider the characteristics of low-mountain and hilly areas, such as steep slopes, fragmented river networks, and the difficulty in dividing the smallest hydrological units. In low-mountain and hilly areas, water flows through multiple paths, control nodes are dispersed, and the slope confluence process is significantly affected by terrain and vegetation. The dissipative-convergent structure of this model is difficult to adapt to these complex hydraulic characteristics, resulting in insufficient detail in depicting the nonlinear laws of slope confluence and the dynamic regulation of social water use, thus failing to meet the accurate simulation requirements of the binary water cycle in low-mountain and hilly areas.

[0005] Furthermore, existing models have shortcomings in quantifying the synergistic effects of topographic factors, underlying surface changes, and human activities. The water cycle in low-mountain and hilly areas is influenced not only by natural factors such as rainfall, evaporation, and infiltration, but also by human activities such as land-use change and water conservancy project regulation. However, existing models often fail to simultaneously consider the combined effects of these natural and socio-economic factors, leading to discrepancies between simulation results and reality. Particularly in long-term simulations, the accuracy and adaptability of existing models often decline significantly due to the failure to fully consider the dynamic changes in human activities and their long-term impact on the water cycle, making it difficult to meet the urgent needs for efficient water resource utilization and sustainable management in low-mountain and hilly areas.

[0006] In summary, developing a method for constructing a binary water cycle model that can adapt to the topographic and hydraulic characteristics of low-mountain and hilly areas, deeply couple natural hydrological processes with socio-economic water use processes, and accurately quantify the synergistic effects of topographic factors, underlying surface changes, and human activities has become a key issue urgently needing to be addressed in the field of water resource management. The successful development of this method will help improve the accuracy of water cycle simulation in low-mountain and hilly areas, providing a scientific basis and technical support for the optimal allocation and sustainable management of regional water resources. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a method for constructing a binary water cycle model in low mountain and hilly areas based on topological network partitioning. This method addresses the shortcomings of existing water cycle models, which are difficult to adapt to the natural characteristics of areas with significant topographic relief, fragmented river networks, and complex hydraulic connections. These models are unable to accurately depict the synergistic effects of human activities and natural hydrological processes, and suffer from insufficient coupling depth of the natural-social binary water cycle process, poor adaptability to long-term simulations due to parameter staticization, and high difficulty in partitioning the smallest hydrological unit. This method fills the technical gap in the accurate simulation of the binary water cycle in this region and provides core technical support for the study of water resource evolution patterns, optimal allocation of water resources, and sustainable management in low mountain and hilly areas.

[0008] To achieve the above technical objectives, the present invention adopts the following technical solution: This invention provides a method for constructing a binary water cycle model in low hilly areas based on topological network partitioning. Through a complete process design including multi-source heterogeneous data acquisition and preprocessing, hydrological unit partitioning and topological network construction, parameter extraction and quantification, coupled model building and parameter matrix generation, complete model construction and calibration verification, and dynamic parameter updating, it achieves deep dynamic coupling simulation of natural water cycle and socio-economic water use processes in low hilly areas. The specific steps are as follows: Step 1: Acquisition and Preprocessing of Multi-Source Heterogeneous Data: Comprehensive collection of core natural hydrological data and socio-economic driving data related to the dual water cycle in low mountain and hilly areas. The core natural hydrological data includes watershed DEM data, soil texture data, rainfall-runoff time series data, and vegetation cover spatiotemporal data. The socio-economic driving data includes land use change maps, water use structure time series data, and water conservancy project topology data. The collected raw data undergoes preprocessing such as missing value imputation, outlier correction, coordinate system unification, spatial resolution matching, and topology verification to ensure the integrity, accuracy, and consistency of the data, providing a high-quality data foundation for subsequent model construction.

[0009] Step 2: Minimum Hydrological Unit Division and Water Supply System Topology Network Construction: A hierarchical partitioning algorithm is adopted. Based on the watershed DEM data, the river network skeleton is extracted. The connectivity between the main stream and tributaries of the river network is determined by the Strahler classification method. The minimum hydrological units are divided with the ends of the tributaries as boundaries, combined with the topographic slope threshold and soil texture type boundaries, to ensure that the topography and soil characteristics within the units are relatively uniform. Through GIS spatial overlay analysis, the spatial coordinates of water conservancy projects such as reservoirs, pumping stations, and irrigation canals are associated with the minimum hydrological units to construct a four-level water supply system topology network including water sources, canals, users, and control nodes. The water flow transmission paths and key control nodes between units are clarified, and the edge weights of the topology network are defined as water flow transmission capacity coefficients to accurately characterize the complex hydraulic connections and water flow transmission characteristics of the region.

[0010] Step 3: Extraction and Quantification of Key Water Cycle Parameters: A binary driving analysis model is constructed, consisting of a natural hydrological analysis submodule and a socio-economic driving analysis submodule. The natural hydrological analysis submodule extracts key natural hydrological parameters such as precipitation interception, soil infiltration, and slope runoff based on runoff generation and confluence mechanisms. The socio-economic driving analysis submodule extracts key socio-economic parameters such as land use conversion coefficient, water use efficiency coefficient, and engineering regulation coefficient based on human activity feedback patterns. A correlation matrix between natural hydrological parameters and socio-economic parameters is established through Pearson correlation analysis and grey relational model. The synergistic coefficients of topographic factors, underlying surface changes, and human activities are quantified. A set of key water cycle parameters containing subsets of natural hydrological parameters and socio-economic parameters is obtained. The parameter set is then standardized to eliminate dimensional differences and improve parameter applicability.

[0011] Step 4: Construction of Topology Adaptive Coupling Model and Generation of Core Parameter Matrix: A topology adaptive coupling model based on the nonlinear theory of slope runoff and the principle of social water supply and demand balance is constructed. This model includes a nonlinear slope runoff module and a social water supply and demand balance module, which accurately characterize the nonlinear laws of slope runoff in low hilly areas and the supply and demand balance characteristics of social water use, respectively. The two modules are integrated through a weighted coupling algorithm, and the coupling weight is dynamically adjusted based on the human activity intensity index of the smallest hydrological unit. The standardized water cycle key parameter set is input into the topology adaptive coupling model. Combining the runoff generation and runoff characteristics of the smallest hydrological unit and the hydraulic constraints of the topological network, a multi-objective optimization model is constructed with the objectives of minimizing historical runoff simulation error and minimizing water supply and demand balance deviation. The non-dominated sorting genetic algorithm NSGA-Ⅲ is used to solve the model, generating a binary water cycle model core parameter matrix with row dimensions corresponding to the smallest hydrological unit and column dimensions corresponding to the water cycle key parameter types.

[0012] Step 5: Construction and Multi-Indicator Calibration and Verification of the Complete Binary Water Cycle Model: Based on the core parameter matrix, a complete binary water cycle model for the low-mountain and hilly area is constructed by integrating the distributed hydrological simulation module and the social water use regulation module. The distributed hydrological simulation module adopts an improved SWAT model framework, optimizing the runoff generation, confluence, and evaporation calculation logic for the characteristics of the low-mountain and hilly area. It introduces a terrain slope correction coefficient to correct the number of SCS curves, uses a two-dimensional confluence model to replace the traditional one-dimensional confluence, and combines remote sensing data to use a dual-source evaporation model to calculate the actual evaporation. The social water use regulation module includes a water use structure simulation submodule and an engineering regulation simulation submodule, respectively based on… The Logistic growth model simulates various dynamic changes in water use and simulates the scheduling process of water conservancy projects such as reservoirs and pumping stations based on topological network hydraulic constraints. A multi-index comprehensive verification system is adopted, selecting the Nash efficiency coefficient (NSE), determinism coefficient (R²), and relative error (RE) as verification indicators for runoff simulation, and the supply-demand balance coefficient (θ) as verification indicator for water use simulation. The system divides the period into a calibration period and a verification period. The model parameters are automatically calibrated using the SCE-UA optimization algorithm. The applicability of the model is tested using independent data. If the verification indicators do not meet the standards, the system returns to the topology-adaptive coupling model to re-optimize the core parameter matrix. The calibration is iterated until the indicators meet the standards.

[0013] Step 6: Dynamic Update of Core Parameter Matrix: A dynamic update mechanism is introduced. Based on the cycle of changes in watershed hydrology and human activities, the sliding time window length is set, and a rolling optimization algorithm is used to dynamically adjust the core parameter matrix. The parameter sensitivity coefficient within each time window is calculated, a sensitivity coefficient threshold is set, key parameters with absolute values ​​greater than or equal to the threshold are retained and re-optimized, while parameters with absolute values ​​less than the threshold remain unchanged. The updated core parameter matrix is ​​smoothed using the Kalman filtering algorithm to ensure that the parameter updates conform to the actual hydrological and human activity trends, thereby improving the model's adaptability to long-term simulations.

[0014] The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning provided by this invention has the following beneficial effects: 1. This invention is specifically adapted to the terrain and hydraulic characteristics of low mountain and hilly areas. It achieves accurate division of the smallest hydrological units through a hierarchical partitioning algorithm, constructs a four-level water supply system topology network, accurately represents complex hydraulic connection relationships, and effectively solves the problems of high difficulty in unit division and inaccurate hydraulic feature characterization in traditional models.

[0015] 2. This invention deeply integrates heterogeneous natural and social data through a binary-driven analytical model, quantifies the synergistic effect coefficient of terrain and human activities, and breaks through the limitations of traditional models in terms of single data utilization and weak parameter correlation, providing solid parameter support for model simulation.

[0016] 3. This invention constructs a topology-adaptive coupling model and introduces a multi-objective optimization algorithm to deeply couple natural hydrology and social water use processes, and integrates and optimizes distributed hydrology and social water use regulation modules, which greatly improves the model simulation accuracy.

[0017] 4. This invention introduces a sliding time window and Kalman filtering dynamic update mechanism to adjust the core parameter matrix in real time, effectively capturing the long-term changes in hydrology and human activities, and significantly improving the model's long-term adaptability.

[0018] 5. The model construction process of this invention does not rely on special data or equipment. The core algorithm logic is clear and highly operable. It adopts a multi-index calibration and verification and iterative optimization process to ensure the stability of simulation at different time scales. It can be directly applied to the optimal allocation and collaborative management of water resources in low mountain and hilly areas. It can also be adapted to other similar landform areas through parameter adjustment, and has broad engineering promotion and practical application prospects.

[0019] 6. This invention divides the smallest hydrological units into hierarchical partitions and constructs a four-level topological network by combining the spatial location of water conservancy projects. It clarifies the water flow transmission path and control nodes, and constructs a coupled model based on the nonlinear theory of slope confluence and the principle of social water supply and demand balance. It deeply couples natural hydrology and socio-economic water use processes, solving the problem that traditional models are difficult to accurately represent the synergistic effect of complex hydraulic connections and human intervention.

[0020] 7. This invention designs a dedicated analytical submodule for two types of heterogeneous data, quantifies the synergistic effect coefficient through the generation and confluence mechanism and the feedback law of human activities, and forms a complete set of key parameters of the water cycle, breaking through the limitations of traditional models and providing solid data support for accurate simulation.

[0021] 8. This invention integrates and improves the distributed hydrology and social water use regulation module, optimizes the calculation logic of runoff generation and evaporation in low mountain and hilly areas, introduces a multi-objective optimization algorithm to generate the core parameter matrix, and ensures the accuracy of the initial simulation and captures long-term change characteristics through a dynamic update mechanism, thereby improving the applicability of long-term series.

[0022] 9. This invention adopts a comprehensive verification system with multiple indicators such as Nash efficiency coefficient and supply-demand balance coefficient. It combines automatic calibration algorithm and iterative optimization process to ensure simulation stability. The core algorithm is highly operable and is not only applicable to water resource optimization in low mountain and hilly areas, but can also be adapted to similar landform areas through parameter adjustment. It has broad prospects for promotion and application.

[0023] 10. This invention effectively solves the technical problem that existing models are unable to accurately simulate the natural-social dual water cycle process under the complex terrain and strong human activity influence in low mountain and hilly areas. It overcomes the limitations of traditional models such as insufficient terrain adaptability, insufficient coupling of human activities, and limited accuracy and adaptability, and achieves dynamic coupling and accurate simulation.

[0024] 11. This invention significantly improves the accuracy and adaptability of binary water cycle simulation in low mountain and hilly areas. Through multiple sets of comparative experiments and practical application cases, it has been verified that this invention is advanced and practical in the field of water cycle model construction.

[0025] 12. This invention, by dynamically coupling the natural water cycle with socio-economic water use processes, enables the model to more accurately reflect the actual evolution of regional water resources, providing a scientific basis for the optimal allocation of water resources.

[0026] 13. This invention introduces a topographic factor quantification and human activity intervention module to accurately quantify the impact of topographic features and human activities on the water cycle process, thereby improving the reliability and practicality of simulation results.

[0027] 14. This invention applies high-precision numerical algorithms and parallel computing technology to improve the model's long-term simulation capability and computational efficiency, meeting the needs of efficient utilization and sustainable management of water resources in low mountain and hilly areas.

[0028] 15. This invention constructs a binary water cycle model framework that includes natural and social subsystems. The natural subsystem covers atmospheric water, surface water, soil water and groundwater, while the social subsystem includes processes such as agricultural irrigation, industrial water use and domestic water use, thus achieving comprehensive simulation.

[0029] 16. This invention constructs a human activity intervention module, incorporating factors such as land use change and water conservancy project regulation into the model, to achieve deep coupling between the natural water cycle and socio-economic water use processes, reflecting the full picture of the actual water cycle.

[0030] 17. This invention employs high-precision numerical algorithms and parallel computing technology to improve long-term simulation capabilities and computational efficiency, solve the computational bottleneck problem in long-term simulation, and ensure stable and reliable simulation results.

[0031] 18. The model construction process of this invention is simple and easy to implement, does not rely on special data and equipment, the core algorithm is highly portable, and can be quickly adapted to different terrains and human activity characteristics by adjusting parameters, thus expanding the application scope of the model. Attached Figure Description

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is an overall flowchart of the construction method in Embodiment 1 of the present invention; Figure 2 This is an architecture diagram of the binary-driven analytical model of Embodiment 1 of the present invention; Figure 3 This is an architecture diagram of the topology adaptation coupling model of Embodiment 1 of the present invention; Figure 4This is a diagram illustrating the architecture of the complete binary water cycle model in a low-mountain and hilly area according to Embodiment 1 of the present invention. Figure 5 This is a time-series comparison chart of measured daily runoff and simulated daily runoff at the Meijiangqiao Hydrological Station in Embodiment 2 of the present invention; Figure 6 This is a histogram showing the distribution of runoff simulation error in the binary water cycle model for low mountain and hilly areas according to Embodiment 2 of the present invention. Figure 7 This is a convergence curve of parameter iteration for the binary water cycle model in the low mountain and hilly area in Embodiment 2 of the present invention; Figure 8 This is a sensitivity spectrum for the dynamic updating of core parameters of the binary water cycle model in the low mountain and hilly area in Embodiment 2 of the present invention. Detailed Implementation

[0033] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 This embodiment provides a method for constructing a binary water cycle model in a low-mountain and hilly area based on topological network partitioning, such as... Figure 1 As shown, this specifically includes: acquiring multi-source heterogeneous data on the dual water cycle in low mountain and hilly areas, wherein the multi-source heterogeneous data includes core natural hydrological data and socio-economic driving data; The core natural hydrological data includes watershed DEM (Digital Elevation Model) data, soil texture data, rainfall-runoff time series data, and vegetation cover spatiotemporal data; the socioeconomic driving data includes land use change maps, water use structure time series data, and water conservancy project topology data. Based on the digital elevation model and the smallest hydrological unit of the river network, and combined with the spatial location of water conservancy projects, a topological network of the water supply system is constructed to clarify the water flow transmission path and control nodes between units. The multi-source heterogeneous data is subjected to feature extraction and correlation mapping through a binary driving analytical model to obtain a set of key parameters of the water cycle. The binary driving analytical model is constructed based on the mechanism of natural hydrological processes and the feedback law of socio-economic driving, and quantifies the synergistic effect coefficient of topographic factors, underlying surface changes and human activities. The key parameters of the water cycle are input into the topology-adaptive coupling model. The core parameter matrix of the binary water cycle model is generated by combining the runoff generation and confluence characteristics of the smallest hydrological unit with the hydraulic constraints of the topology network. The topology-adaptive coupling model is constructed based on the nonlinear theory of slope runoff and the principle of social water supply and demand balance. Based on the core parameter matrix, a complete binary water cycle model for low mountain and hilly areas is constructed by integrating a distributed hydrological simulation module and a social water use regulation module. The model is calibrated and verified using historical runoff data and water use statistics to achieve dynamic coupling simulation of natural water cycle processes and socio-economic water use processes.

[0034] Furthermore, the acquisition and preprocessing of multi-source heterogeneous data covered two major dimensions: natural hydrology and socio-economic factors, as detailed below: Core natural hydrological data: watershed DEM data (spatial resolution 30m), soil texture type map (1:100,000), rainfall-runoff time series data (daily-scale observation data from 3 meteorological stations and 2 hydrological stations within the watershed), and vegetation cover spatiotemporal data (MODIS NDVI (Moderate-resolution Imaging Spectroradiometer Normalized Difference Vegetation Index) product, temporal resolution 16 days, spatial resolution 250m). Socioeconomic driving data: land use change maps (based on Landsat satellite imagery, every 5 years), water use structure time series data (agricultural, industrial, domestic, and ecological water consumption, sourced from watershed statistical yearbooks), and water conservancy project topology data (spatial coordinates and scale parameters of irrigation canals). Data preprocessing steps include: imputing missing values ​​in rainfall-runoff data using linear interpolation, and processing outliers using... Criteria were identified and corrected; vegetation cover data and land use data were unified into a single projection coordinate system, WGS84 (World Geodetic System 1984), and spatial resolution was made consistent through resampling; topological verification was performed on water conservancy project data to ensure the accuracy of the connectivity between water supply nodes and channels.

[0035] Furthermore, a hierarchical partitioning algorithm is used to divide the smallest hydrological units and construct a topological network, as detailed below: Based on DEM data, the hydrological analysis tools of ArcGIS (Arc Geographic Information System) were used to extract the river network framework. The Strahler classification method was used to divide the river network into 5 levels to determine the connectivity between the main stream and tributaries. Using the end of the fifth-level tributary as the boundary, and combining the topographic slope threshold (set based on the actual topography of the watershed) and the soil texture type boundary, the hydrological response unit division algorithm is used to divide the Meijiang watershed into 236 smallest hydrological units with a unit area of ​​2~4km², ensuring that the topography and soil characteristics within each unit are relatively uniform. By using GIS (Geographic Information System) spatial overlay analysis, the spatial coordinates of water conservancy projects such as reservoirs, pumping stations, and irrigation canals are associated with the smallest hydrological units to construct a four-level topology structure of water source, canal, user, and control node. The edge weights of the topology network are defined as the water flow transmission capacity coefficients, and calculated using the formula: (1); Among them, calibration coefficient The index parameter was set to 1.2 based on historical water supply data of the basin. , , (Based on the topography, soil and hydrological characteristics of the watershed) For unit to unit The length of the channel to the power of 0.8 (km). For unit The catchment area to the power of 0.5 ( ), The saturated hydraulic conductivity of the soil (cm / h) For unit To unit The average slope to the power of 0.6 (dimensionless).

[0036] Furthermore, a set of key parameters for the water cycle is extracted using a binary-driven analytical model, such as... Figure 2 As shown, the specific implementation is as follows: The natural hydrological analysis submodule extracts key parameters such as precipitation interception, soil infiltration, and slope runoff based on runoff generation and confluence mechanisms. The actual infiltration rate is calculated using a formula. (2); Among them, stable infiltration rate The initial infiltration rate is determined based on soil texture type (0.8 cm / h for sandy loam, 0.5 cm / h for loam, and 0.3 cm / h for clay loam). for 3~5 times; attenuation coefficient Calibration was performed using measured infiltration data (value range 0.1~0.3). Cumulative rainfall (cm) It is a natural constant.

[0037] Socioeconomic Driver Analysis Submodule: Extracts relevant parameters based on feedback patterns of human activities. Total regional water consumption is calculated using the following formula: (3); in, This represents the total water consumption of the region. These correspond to water use for agriculture, industry, domestic use, and ecological purposes, respectively. Initial water consumption figures for all types of water use in 1990 (in ten thousand kilowatt-hours) ); The growth rates for various water use categories are as follows: agriculture 0.02, industry 0.05, domestic use 0.03, and ecological use 0.01. For time span (years); Water use efficiency correction coefficients (0.92 for agriculture, 0.85 for industry, 0.95 for domestic use, and 1.0 for ecology) are determined based on the effectiveness of water conservation policies. This represents the total number of water usage types. Parameter Correlation and Co-quantification: Using Pearson correlation analysis and grey relational model, a correlation matrix is ​​established between natural hydrological parameters (such as infiltration rate and runoff velocity) and socioeconomic parameters (such as land use conversion rate and water use efficiency). Quantifying the synergistic effect coefficient : (4); The results showed that the synergistic effect coefficient between the rate of conversion of cultivated land to urban land and the slope runoff velocity was the highest (0.87), providing a basis for subsequent model coupling; among them, To quantify the synergistic effect coefficient, For indexing natural hydrological parameters, For socioeconomic parameter indexing, For the correlation matrix The maximum value in.

[0038] Parameter set standardization: The extracted subsets of natural hydrological parameters (six items including rainfall attenuation coefficient and soil saturated hydraulic conductivity) and socioeconomic parameters (six items including land use conversion rate and agricultural water quota) are standardized according to a formula to unify the parameter values ​​to [0.1, 1.0]: (5); in, For the standardized first One parameter, These are the original parameter values. , These are the minimum and maximum values ​​of the original parameters. , This represents the boundary of the standardized parameter interval.

[0039] Furthermore, the topology-adaptive coupling model includes a slope runoff nonlinear module and a social water supply and demand balance module, such as... Figure 3 As shown, the specific implementation is as follows: Nonlinear module for slope runoff: Calculates slope runoff velocity based on the improved kinematic wave equation, the formula is as follows: (6); In the formula, The velocity of the runoff on the slope; The confluence velocity on a flat surface is taken as 0.5 m / s; Slope (dimensionless); Vegetation coverage (dimensionless, value range 0~1); , , The coefficients are based on topographic and vegetation characteristics and are set to 0.3, 0.7, and 0.5 respectively. It is a natural exponential function; The social water supply and demand balance module calculates the supply and demand difference based on the water resource supply and demand balance equation. The formula is as follows: (7); in, for The difference between supply and demand at any given moment; For the first Water supply from each water source (in ten thousand) ); Water supply guarantee rate (reservoir 0.95, river 0.85, groundwater 0.8); For the first Water consumption per user (in ten thousands) ); Water use priority coefficients (domestic 1.0, industrial 0.9, agricultural 0.8, ecological 0.7); The total number of water sources, with a value of 3 (corresponding to 3 main water sources); This represents the total number of water user types, with a value of 4 (corresponding to 4 types of water users).

[0040] Module fusion and parameter matrix generation: Two modules are fused using a weighted coupling algorithm, with coupling weights... The human activity intensity index is dynamically adjusted based on the smallest hydrological unit, and the formula is as follows: (8); In the formula, The basic coupling weight is set to 0.4. The maximum possible water consumption in the region (calculated based on water resource carrying capacity) is 520 million cubic meters. ).

[0041] By inputting the key parameters of the water cycle into the topology-adaptive coupling model, and using the minimization of historical runoff simulation error and the minimization of water supply and demand balance deviation as objective functions, a multi-objective optimization model is constructed: (9); (10); in, To account for the relative error in runoff simulation, To address the supply and demand imbalance, For parameter weights, For unit Hydraulic constraint parameters , To constrain the upper and lower limits of the indicator, , The boundary of the parameter value range, To optimize the objective function for multiple objectives, Numbering the smallest hydrological unit, Index of key parameters for the water cycle; The non-dominated sorting genetic algorithm NSGA-III was used to solve the problem. The population size was set to 200 and the number of iterations was set to 100, resulting in a core parameter matrix of 236×12 dimensions. (236 smallest hydrological units × 12 key parameters).

[0042] Furthermore, it integrates a distributed hydrological simulation module with a social water use regulation module, such as... Figure 4 As shown, construct the complete model and perform calibration and verification; Distributed hydrological simulation module: Employs an improved SWAT (Soil and Water Assessment Tool) model framework, optimized for the characteristics of low mountain and hilly areas, including a runoff calculation module: Introducing a terrain slope correction factor and revising the SCS (Soil Conservation Service) curve number formula. (11); in, The corrected curve number. For the standard curve number, For slope, This is the slope correction factor, with a value of 0.02; The confluence calculation module uses a two-dimensional confluence model instead of the traditional one-dimensional confluence model, considering the coupled confluence process of the slope and the river channel. The formula is as follows: (12); in, For traffic, For time, , For spatial coordinates, , They are respectively , Convergence velocity in direction, It represents the lateral inflow, and is a partial differential symbol, characterizing the local rate of change of the variable; Evaporation calculation module: Combining remote sensing inversion of vegetation cover spatiotemporal data, a dual-source evaporation model is used to calculate the actual evaporation, distinguishing between vegetation transpiration and soil evaporation.

[0043] The social water use regulation module includes sub-modules for water use structure simulation and engineering regulation simulation. The water use structure simulation sub-module simulates the dynamic changes in various water use patterns based on the Logistic growth model, with the following formula: (13); in, For the first Water use Water consumption at any given time For the first The maximum carrying capacity of water-type water, The growth rate coefficient, The time of the growth inflection point; in, For the maximum carrying capacity of various water uses, For the growth rate system, The inflection point time of growth (calibrated based on historical water use data); Engineering regulation simulation submodule: Based on the hydraulic constraints of the topology network, simulate the reservoir scheduling process, and calculate the discharge flow according to the scheduling rule formula (14): (14); in, for Real-time reservoir discharge flow; for Real-time inbound traffic; The threshold for the outflow rate corresponding to the reservoir's beneficial storage capacity; This is the standard scheduling coefficient, with a value of 0.8. This is the excess flood control factor, with a value of 0.5.

[0044] Model calibration and validation: The calibration period was from 1990 to 2010, and the validation period was from 2011 to 2020. The SCE-UA (Shuffled Complex Evolution - University of Arizona) optimization algorithm was used to automatically calibrate the model parameters. The validation metrics included NSE (Nash-Sutcliffe Efficiency Coefficient). (Coefficient of Determination), RE (Relative Error), and water simulation accuracy index (θ). Periodic verification results: NSE = 0.82. |RE|=12%, =0.95; Validation results during the validation period: NSE=0.78, |RE|=14%, =0.93, all indicators meet the qualified standard, indicating that the model has good applicability.

[0045] Furthermore, the core parameter matrix is ​​dynamically adjusted based on a sliding time window, as specifically implemented below: The sliding time window length is set to 5 years (based on the hydrological and human activity change cycle of the Meijiang River Basin), with 2010 as the first window end point, and it is updated sequentially. Calculate the parameter sensitivity coefficient within each time window: (15); in, The parameter sensitivity coefficient within each time window, The model simulation error is represented by the complementary value of NSE. These are the elements of the core parameter matrix.

[0046] The sensitivity coefficient threshold was set to 0.1. Key parameters with absolute values ​​≥ 0.1 (such as land use conversion rate and soil saturated hydraulic conductivity) were retained and solved again through a multi-objective optimization model. Parameters with absolute values ​​< 0.1 remained unchanged. The updated core parameter matrix is ​​smoothed using the Kalman filter algorithm, employing formula (16), to ensure that the parameter updates are smooth and conform to the actual trend of change. (16); in, The filter gain is calculated using the model prediction error covariance and the observation error covariance. for Timing simulation error; The observation matrix; For the first Within the first time window The first smallest hydrological unit corresponding to the first Specific values ​​for key parameters of water cycle.

[0047] Through the above implementation process, this implementation constructs a binary water cycle model for low mountain and hilly areas based on topological network division. This model can accurately depict the dynamic coupling relationship between the natural water cycle and socio-economic water use processes in the Meijiang River Basin, providing technical support for the optimal allocation and collaborative management of regional water resources.

[0048] Example 2 In another preferred embodiment, based on Embodiment 1, this embodiment provides a method for constructing a binary water cycle model in a low mountain and hilly area based on topological network partitioning. Based on Embodiment 1, this embodiment verifies the Meijiang River Basin (115°22′~116°38′E, 25°18′~26°25′N) as the study area. The total area of ​​the basin is 2908 km², which is a typical low mountain and hilly landform with large topographic relief. The elevation ranges from 120m to 1050m. The soil types in the basin are mainly red soil and yellow soil, accounting for 68.3% and 21.5% respectively, and the average vegetation coverage over many years is 72%. The area is 8% affected by the subtropical monsoon climate, with an average annual rainfall of 1560 mm. Rainfall from June to September accounts for 62.4% of the annual total. The study period is from 1990 to 2024, a total of 35 years. The period from 1990 to 2010 is the calibration period (21 years), and the period from 2011 to 2024 is the validation period (14 years). By collecting complete natural hydrological and socio-economic data of the watershed, the proposed method for constructing a binary water cycle model in low hilly areas based on topological network partitioning is comprehensively validated. The performance of the model in terms of runoff simulation, water supply and demand balance simulation, and parameter dynamic adaptability is evaluated.

[0049] During the data preparation phase, the core natural hydrological data included the following: watershed DEM data, which used the ASTERGDEM (Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model) product with a spatial resolution of 30m; soil texture data, which came from the results of the Second National Soil Survey (1:100,000); and rainfall-runoff time-series data, which were obtained from measured data from three national meteorological stations (Ningdu, Shicheng, and Ruijin) and two hydrological control stations (Meijiangqiao and Qilizhen) within the watershed. Rainfall data were obtained from daily-scale observations, and runoff data were obtained from daily-scale measured flow data. Vegetation cover spatiotemporal data were obtained using MODISNDVI (MODerate-resolution Imaging Spectroradiometer Normalized Difference Vegetation) technology. The Medium Resolution Imaging Spectroradiometer (MTIS) Normalized Difference Vegetation Index (MOD13Q1) product has a temporal resolution of 16 days and a spatial resolution of 250m. Monthly vegetation cover data was obtained using the maximum value synthesis method. In the socio-economic driving data, the land use change map is based on seven periods of Landsat satellite imagery from 1990, 1995, 2000, 2005, 2010, 2015, and 2020, interpreted by Landsat 5TM (Thematic Mapper) and Landsat 8OLI (Operational Land Imager). The interpretation accuracy was verified to be 92.6% in field studies. Water use structure time-series data are sourced from publications such as the *Jiangxi Provincial Water Resources Bulletin* and the *Ningdu County Statistical Yearbook*, including agricultural water (AW), industrial water (IW), domestic water (DW), and ecological water (EW). The water conservancy project topology data was obtained through field surveys and compilation of planning data from water conservancy departments. There are 3 medium-sized reservoirs, 42 small reservoirs, and 56 pumping stations in the basin. The total length of irrigation canals is 1,860 km. The policy control text data includes the implementation details and coverage of the 1998 policy of returning farmland to forest, the 2005 water-saving irrigation demonstration project, and the strictest water resources management system in 2013.

[0050] After the model is built, the runoff simulation results of the rate-setting and validation periods are first validated, and the Nash efficiency coefficient (NSE) and the coefficient of determination (COP) are selected. The relative error (RE) is used as the core evaluation indicator, and the supply-demand balance coefficient (θ) is introduced to assess the accuracy of water use simulation. θ is calculated as the ratio of simulated water supply to actual water supply, with an ideal value of 1.0. During the calibration period, the simulated daily runoff NSE at Meijiangqiao hydrological station was 0.83, R² was 0.87, and RE was -3.2%; the simulated daily runoff NSE at Qilizhen hydrological station was 0.81, R² was 0.85, and RE was 2.8%. During the validation period, the simulated daily runoff NSE at Meijiangqiao hydrological station was 0.79, R² was 0.83, and RE was -4.5%; the simulated daily runoff NSE at Qilizhen hydrological station was 0.77, R² was 0.82, and RE was 3.6%. Regarding supply-demand balance simulation, during the calibration period... The average value is 0.96, during the verification period. The average value is 0.94, which is within the acceptable range of 0.9-1.1, indicating that the model has high accuracy in the coupled simulation of natural water cycle and social water use processes.

[0051] To further quantify the optimization effect of each module of the model, a comparison table of core performance indicators was constructed (Table 1). The indicators involved in the table include runoff simulation accuracy and NSE (Nash-Sutcliffe Efficiency Coefficient). (Coefficient of Determination), RE (Relative Error), water simulation accuracy index (θ), parameter calibration efficiency index, average iteration number (AIN), average convergence time (ACT), and model dynamic adaptability index, parameter update sensitivity (PUS), simulation error fluctuation coefficient (SEFC). The coefficients are as follows: AIN is the average number of iterations during the automatic calibration of model parameters; ACT is the average time required for parameters to reach the convergence criterion; PUS is the percentage of parameters with a sensitivity coefficient ≥ 0.1 during the dynamic update of the core parameter matrix; and SEFC is the ratio of the standard deviation to the mean of the simulation error during the validation period. The data in the table show that the model in this application has NSE higher than 0.77, R² higher than 0.82, absolute RE less than 5.0%, and θ between 0.93 and 0.96 during both the calibration and validation periods, demonstrating excellent simulation accuracy. Regarding parameter calibration, AIN takes only 86 iterations, and ACT takes 28.5 minutes, significantly lower than traditional models, indicating higher efficiency in parameter calibration. In terms of dynamic adaptability, PUS reaches 83.6%, and SEFC is only 0.12, indicating that the model can accurately capture the changing characteristics of key parameters and exhibits good stability in simulation error.

[0052] Table 1 Comparison of Core Performance Indicators of the Model

[0053] Regarding the effectiveness of runoff time-series simulation, by analyzing the dynamic changes in measured and simulated daily runoff at the Meijiangqiao hydrological station during the validation period, a runoff simulation time-series comparison chart was drawn, such as... Figure 5 As shown, the graph contains two curves: observed daily runoff and simulated daily runoff. The time axis covers 3652 days, from January 1, 2011 to December 31, 2020. The graph clearly shows a high degree of consistency between the simulated and observed daily runoff trends. Particularly during major floods in June 2013, July 2016, and August 2019, the simulated values ​​accurately captured the timing and magnitude of the flood peaks. For example, on June 18, 2013, the observed peak flow was 1860 m³ / s, while the simulated peak flow was 1805 m³ / s, with a relative error of only 2.96%. On July 9, 2016, the observed peak flow was 2120 m³ / s. The simulated peak flow rate is 2058. The relative error was 2.92%. The simulation error curve fluctuated around zero as a whole, with no obvious systematic deviation. The number of days with an absolute error exceeding 10% accounted for only 7.3% of the total number of days, and was mainly concentrated in the dry season (December to February). This is consistent with the actual situation in the low mountain and hilly areas where runoff replenishment is complex and observation errors are relatively large during the dry season.

[0054] To analyze the model's simulation performance at different time scales, histograms of runoff simulation error distributions at monthly, seasonal, and annual scales were plotted, such as... Figure 6 As shown in the figure, the error range is plotted on the x-axis, and the number of samples in the corresponding range is plotted on the y-axis. Each time scale includes the error distribution characteristics of measured and simulated values. On the monthly scale, the simulation error is mainly concentrated between -5% and 5%, accounting for 78.3% of the samples, while the sample proportion with an error range between -10% and 10% reaches 92.5%. On the quarterly scale, the average simulation error for spring (March to May), summer (June to September), autumn (October to November), and winter (December to February) is 1.8%, -2%, and -2%, respectively. The absolute values ​​of the errors were 0.3%, 0.9%, and -3.1%, all less than 5%, with the summer sample showing the most concentrated error distribution. This is related to the abundant rainfall and relatively stable runoff formation mechanism in summer. On an annual scale, the annual runoff simulation errors during the 10-year validation period ranged from -4.8% to 3.6%, with the smallest simulation error in 2015 at only 0.3% and the largest in 2018 at -4.8%. The stability of the annual-scale simulation was significantly higher than that of the monthly and seasonal scales, fully demonstrating the reliability of this model in long-term water cycle simulation.

[0055] The effectiveness of the parameter iterative optimization process is crucial for ensuring model performance. By recording the changes in the objective function values ​​during the optimization of the core parameter matrix within a certain period, a parameter iterative convergence curve was plotted, as shown below. Figure 7 As shown, the figure contains curves in two dimensions, namely the runoff simulation error (…). ) and water supply and demand imbalance ( The trend of the number of iterations is as follows: the number of iterations gradually increases from 1 to 150. As can be seen from the curve, in the early stage of iteration (1 to 30 times). and All showed a rapid downward trend, among which It dropped from an initial 28.6% to 8.3%. The percentage dropped from the initial 19.8% to 6.5%, indicating that the model parameters rapidly approached the optimal value in the initial iterations; during the middle of the iterations (31st to 80th iterations). and The rate of decline gradually slowed down. It decreased from 8.3% to 3.2%. The percentage dropped from 6.5% to 2.1%, and parameter optimization entered the fine-tuning stage, in the later stages of iteration (81st to 150th iterations). and The function value generally stabilizes, with fluctuations all less than 0.3%. When the number of iterations reaches 86, the objective function value satisfies the convergence condition. and (The iteration stops, and compared to the traditional model with an average of more than 150 iterations, the parameter convergence efficiency of this model is improved by 42.7%, which greatly shortens the model construction cycle.)

[0056] To verify the dynamic adaptability of the model parameters, sensitivity plots of the dynamic update of core parameters were plotted, such as... Figure 8 As shown, this graph uses a time window (5 years per window, 5 windows in total: 2000-2004, 2005-2009, 2010-2014, 2015-2019, 2020-2024) as the horizontal axis and the parameter sensitivity coefficient ( Using y as the ordinate, six core parameters were selected for analysis, namely: , The graph shows that the sensitivity of different parameters varies significantly across different time windows, including AWD (Agricultural Water Quota), LUT (Land Use Transformation Rate), RSC (Reservoir Scheduling Coefficient), and PSC (Policy Implementation Strength Coefficient). and As natural hydrological parameters, the sensitivity coefficients are relatively stable, with average values ​​of 0.18 and 0.15 for each window, and fluctuations all less than 0.03. AWD, LUT, RSC, and PSC, as socio-economic parameters, show more significant changes in sensitivity coefficients over time. LUT reached a peak of 0.27 during the 2010-2014 window, which is related to the accelerated conversion rate of cultivated land to urban land within the basin during this period (an average annual conversion area of ​​12.8...). Closely related to the water cycle, the PSC was 0.23 in the 2015-2019 window, corresponding to the full implementation of the water-saving irrigation policy in 2015. The sensitivity coefficient of AWD showed an overall downward trend, from 0.21 in 1990-1994 to 0.13 in 2020-2024, reflecting the continuous improvement of agricultural water use efficiency. In the five time windows, the proportion of parameters with sensitivity coefficients ≥0.1 was 78.5%, 81.2%, 85.7%, 83.3%, and 80.6%, respectively, with an average proportion of 81.9%. This indicates that the model can accurately identify key parameters that significantly affect the water cycle process and adjust parameter values ​​in a timely manner through a dynamic update mechanism to ensure the model's adaptability and simulation accuracy in long-term series.

[0057] Based on the above verification results, the proposed method for constructing a binary water cycle model in low hilly areas based on topological network partitioning has shown significant effectiveness in the Meijiang River Basin. The runoff simulation NSE during both the calibration and validation periods is higher than 0.77, and the R² is higher than 0.82. The water supply and demand balance coefficient is also high. All values ​​are between 0.93 and 0.96. The parameter iteration convergence efficiency is 42.7% higher than that of traditional models, and the average sensitivity of dynamic update of core parameters reaches 81.9%. All performance indicators are excellent. It can accurately depict the dynamic coupling relationship between natural water cycle and socio-economic water use in low mountain and hilly areas, and provide reliable technical support for regional water resource optimization and collaborative management.

[0058] In the preferred embodiment, the core natural hydrological data mentioned in step 1 includes watershed DEM data, soil texture data, rainfall-runoff time series data, and vegetation cover spatiotemporal data. The socio-economic driving data includes land use change maps, water use structure time series data, and hydraulic engineering topology data. This configuration comprehensively covers all dimensions of information on the evolution of natural hydrology and socio-economic water use in low mountain and hilly areas. DEM and soil data support the characterization of topography and underlying surface, rainfall-runoff and vegetation data reflect the dynamic characteristics of the natural water cycle, and land use, water use structure, and hydraulic engineering data fully present the ways and intensity of human intervention in the water cycle. The multi-source data complement and verify each other, greatly improving the completeness and reliability of the model input data. This lays a solid data foundation for subsequent hydrological unit division, parameter extraction, and coupled simulation, avoiding the distortion of simulation results due to single or missing data, and making the model closer to the real water cycle state of the region.

[0059] In the preferred embodiment, the minimum hydrological unit described in step 2 is divided using a hierarchical partitioning algorithm, and then a water supply system topology network is constructed. Specifically, the river network skeleton is extracted based on the watershed DEM data, and the Strahler classification method is used to classify the river network into levels, determining the connectivity between the main stream and tributaries; using the ends of the river network tributaries as boundaries, combined with topographic slope thresholds and soil texture type boundaries, a hydrological response unit partitioning algorithm is used to divide the watershed into minimum hydrological units; through GIS spatial overlay analysis, the spatial coordinates of reservoirs, pumping stations, and irrigation canals are associated with the minimum hydrological units to construct a system including water sources. The model employs a four-level topology structure comprising channels, users, and control nodes; the edge weights of the topology network are defined as water flow transmission capacity coefficients. This configuration enables refined and homogeneous division of hydrological units, ensuring relative consistency in topography, soil, and underlying surface conditions within each unit. The four-level topology clearly reconstructs the complete chain of water source transmission and distribution, engineering control, and water consumption. The edge weights accurately quantify water flow transmission capacity, comprehensively depicting the hydraulic connectivity relationships under the fragmented river network and complex water conservancy engineering layout in low-mountain and hilly areas. This allows the model to realistically reflect the physical processes of water flow transmission, distribution, and control, improving the accuracy and rationality of the hydraulic relationship representation.

[0060] In the preferred embodiment, the binary-driven analytical model described in step 3 is constructed based on the mechanism of natural hydrological processes and the feedback law of socio-economic driving forces, quantifying the synergistic effect coefficients of topographic factors, underlying surface changes, and human activities. This setting breaks down the separation between natural hydrological and socio-economic data, incorporating natural elements such as topographic relief, soil characteristics, and vegetation changes, as well as human elements such as land use transformation, water use structure adjustment, and engineering scheduling into a unified analytical framework. Through mechanism modeling and law fitting, the model achieves a quantitative expression of the synergistic effect of multiple elements, enabling the model to no longer simply simulate natural hydrological processes, but to truly reflect the evolution law of the water cycle driven by both natural conditions and human activities. This significantly improves the model's explanatory power and simulation rationality for the binary water cycle system, and is more in line with the actual hydrological characteristics under high-intensity human activity interference in low mountain and hilly areas.

[0061] In the preferred embodiment, the binary driven analytical model in step 3 includes a natural hydrological analysis submodule and a socio-economic driven analysis submodule. The natural hydrological analysis submodule extracts key parameters of precipitation interception, soil infiltration, and slope runoff based on runoff generation and confluence mechanisms. The above settings strictly follow the hydrological and physical mechanisms, extracting core parameters from the complete path from precipitation landing, vegetation interception, soil infiltration to slope runoff, accurately capturing the key characteristics of slope runoff formation, transformation, and convergence in low mountain and hilly areas. It can objectively reflect the impact of topographic slope, soil type, and vegetation cover on key links of the natural water cycle, giving the natural water cycle simulation a solid physical foundation, avoiding systematic biases caused by empirical parameters, improving the simulation accuracy of key hydrological processes such as runoff, infiltration, and evaporation, and making the model output results more consistent with actual field observation patterns.

[0062] In the preferred embodiment, the socio-economic driving analysis submodule described in step 3 extracts land use conversion coefficient, water use efficiency coefficient, and engineering regulation coefficient parameters based on the feedback patterns of human activities. The above settings focus on major water use scenarios such as agricultural irrigation, industrial production, urban and rural life, and ecological water replenishment in low mountain and hilly areas. It accurately extracts core parameters that reflect human water use behavior and the intensity of engineering regulation, and can dynamically track the impact of land use changes, water-saving policy implementation, and water conservancy project operation on the water cycle system. It transforms the water demand, supply capacity, and regulation rules of the socio-economic system into calculable model parameters, realizes the quantitative simulation of social water use processes, and allows the model to fully cover the entire chain of "natural water production - social water use - engineering water regulation", thereby improving the integrity of the dual system coupling.

[0063] In the preferred embodiment, step 3 establishes a correlation matrix between natural hydrological parameters and socioeconomic parameters using Pearson correlation analysis and a grey relational model. And the synergistic effect coefficient is quantified by formula (4); the above settings can objectively identify the correlation strength and direction of action between natural elements and human activity elements, clarify the influence weight of factors such as topographic change, land use transformation, and water use structure adjustment on the water cycle process, transform the originally scattered and independent parameters into an internally related whole, effectively improve the logic and consistency of the parameter system, avoid mutual contradiction or ambiguous action between parameters, provide a reliable basis for subsequent coupled model calculation and parameter matrix optimization, and make the model more accurately reflect the water cycle response law under the joint action of multiple factors.

[0064] In the preferred embodiment, the key water cycle parameter set mentioned in step 3 includes a subset of natural hydrological parameters and a subset of socioeconomic parameters. The natural hydrological parameter subset includes rainfall attenuation coefficient, soil saturated hydraulic conductivity, vegetation interception, slope runoff roughness, groundwater recharge coefficient, and evaporation capacity coefficient. The socioeconomic parameter subset includes land use conversion rate, agricultural water quota, industrial water reuse rate, per capita domestic water user index, water conservancy project regulation threshold, and policy implementation intensity coefficient. The parameter set is then standardized. The above settings construct a complete parameter system covering both natural and social dimensions, fully supporting the simulation of the entire process of runoff generation, evaporation, water use, and scheduling. Standardization can eliminate differences in the dimensions and orders of magnitude of different parameters, improve the comparability and compatibility between parameters, make parameter input more stable and calculation more efficient, and at the same time ensure that the parameter system has good portability and adjustability, adapting to the characteristics of different low mountain and hilly watersheds, and improving the overall applicability of the model.

[0065] In the preferred embodiment, the topology-adaptive coupling model in step 4 includes a slope confluence nonlinear module and a social water supply and demand balance module. The slope confluence nonlinear module calculates the slope confluence velocity based on the improved kinematic wave equation. The above settings fully consider the characteristics of large topographic relief and strong nonlinearity of slope confluence in low mountain and hilly areas. The improved kinematic wave equation can more accurately reflect the influence of slope and vegetation on the confluence velocity, breaking through the simulation deviation caused by the constant confluence velocity in traditional models. It can realistically depict the characteristics of fast water flow convergence velocity and significant spatiotemporal changes on hilly slopes, improve the simulation accuracy of slope confluence process, and make the output of the natural hydrology module more consistent with the hydrological laws driven by regional topography, providing a high-quality natural hydrology simulation foundation for subsequent binary coupling.

[0066] In the preferred embodiment, the social water supply and demand balance module in step 4 calculates the supply and demand difference based on the water resource supply and demand balance equation and the hydraulic constraints of the topological network. It incorporates elements such as water supply capacity, water demand, engineering scheduling, and water transmission loss into a unified calculation. Combined with the water flow transmission constraints of the topological network, it truly reflects the supply and demand relationship between different water sources, different users, and different nodes. It can dynamically identify water-scarce nodes, surplus water sources, and areas with supply and demand contradictions, accurately quantify the regional water resource supply and demand balance status, provide quantitative basis for water resource regulation and engineering scheduling, and transform social water use simulation from static quota accounting to dynamic balance calculation, thereby improving the model's ability to characterize the social water cycle system.

[0067] In the preferred embodiment, step 4 uses a weighted coupling algorithm to fuse the two modules, with the coupling weights... The intensity index of human activity is dynamically adjusted based on the smallest hydrological unit. The above settings realize the flexible coupling of natural hydrological processes and social water use processes. The coupling weight is automatically adjusted according to the intensity of human activity in different units. The role of social water use module is strengthened in areas with dense human activity, and the contribution of natural hydrological module is highlighted in areas with strong natural attributes. This avoids the simulation bias caused by fixed weights, and makes the model more spatially consistent with the "natural-social" binary intensity distribution characteristics of the watershed, thereby improving the spatial rationality and overall accuracy of the coupled simulation.

[0068] In the preferred embodiment, step 4 employs a multi-objective optimization algorithm to determine the elements of the core parameter matrix, and the core parameter matrix is ​​as follows: , row dimension Corresponding to the smallest hydrological unit number, column dimension The model corresponds to the key parameter types of the water cycle; a multi-objective optimization model is constructed with the objective functions of minimizing historical runoff simulation errors and minimizing water supply and demand balance deviations; the non-dominated sorting genetic algorithm NSGA-Ⅲ is used to solve the optimization model, obtaining the core parameter matrix in the Pareto optimal solution set; the above settings transform parameter optimization into a multi-objective balance problem, taking into account both runoff simulation accuracy and supply and demand balance simulation accuracy. The NSGA-Ⅲ algorithm has efficient convergence and global optimization capabilities, which can quickly obtain the optimal parameter combination, avoid local optima or overfitting of parameters, and generate a parameter matrix with strong stability and high applicability, greatly improving the efficiency of model parameter calibration and simulation reliability, allowing the model to maintain stable output in long-term simulations.

[0069] In the preferred embodiment, the distributed hydrological simulation module in step 5 adopts an improved SWAT model framework, and introduces a terrain slope correction coefficient to correct the formula for the number of SCS curves in the runoff calculation module. The above settings are designed to address the characteristics of large slope variations and runoff patterns that are significantly affected by terrain in low mountain and hilly areas. By correcting the slope, the number of SCS curves is made to better reflect the actual runoff capacity of the region. This overcomes the limitations of the traditional SWAT model, which is highly applicable in flat areas but has large runoff errors in hilly areas. It accurately reflects the surface runoff of different slope units, improves the simulation accuracy of total watershed runoff and spatial distribution, and makes the improved model more suitable for the terrain-driven runoff mechanism in low mountain and hilly areas.

[0070] In the preferred scheme, in step 5, the two-dimensional confluence model formula (12) is used in the confluence calculation module to replace the traditional one-dimensional confluence, considering the coupled confluence process of the slope and the river channel. The above settings upgrade the one-dimensional linear confluence to two-dimensional planar confluence, which can simulate the lateral diffusion of water flow on the slope and the longitudinal convergence of the river channel, restore the complete process of slope confluence, slope foot confluence and river channel confluence in low mountain and hilly areas, and more realistically reflect the spatiotemporal characteristics of flood evolution and runoff convergence. In particular, it enhances the simulation ability of rainstorm floods and rapid confluence in small watersheds, and makes the model more reliable in the simulation of extreme hydrological events.

[0071] In the preferred scheme, in step 5, the evaporation calculation module uses a dual-source evaporation model to calculate the actual evaporation by combining the spatiotemporal data of vegetation cover retrieved from remote sensing, distinguishing between vegetation transpiration and soil evaporation. This setting decomposes the evaporation process into two independent components: vegetation transpiration and soil evaporation. It dynamically reflects the evaporation capacity of different seasons and underlying surfaces by combining remote sensing vegetation data, accurately quantifying the evaporation of different types of units such as forest land, cultivated land, and bare land. This overcomes the shortcomings of traditional models that calculate evaporation as a single total amount, improves the accuracy of water balance calculation, and allows the model to more accurately reflect the regional water consumption patterns.

[0072] In the preferred embodiment, the social water use regulation module in step 5 includes a water use structure simulation submodule and an engineering regulation simulation submodule. The water use structure simulation submodule simulates the dynamic changes of various water uses based on the Logistic growth model. The above settings adopt the Logistic model that conforms to the laws of socio-economic development to simulate the growth, saturation and transformation process of agricultural, industrial, domestic and ecological water use. It can reflect the changes in water use structure brought about by urbanization, industrial upgrading and water conservation policies, upgrade static water use quotas to dynamic water use trends, improve the rationality of long-term water use prediction and simulation, and make social water use simulation more in line with the actual regional development.

[0073] In the preferred scheme, the engineering regulation simulation submodule in step 5 simulates the scheduling process of reservoirs and pumping stations based on the hydraulic constraints of the topological network. The reservoir scheduling rule adopts formula (14). The above settings incorporate the reservoir's beneficial scheduling, flood scheduling, and pumping station water lifting scheduling into the topological hydraulic constraint framework. According to the actual engineering operation rules, the discharge flow, water storage changes, and water transfer distribution are simulated, which truly reflects the role of water conservancy projects in the temporal and spatial redistribution of runoff. It can dynamically simulate engineering scheduling schemes under different water inflow conditions, improve the authenticity and operability of water resource regulation simulation, and provide simulation support for the optimized operation of the project.

[0074] In the preferred embodiment, when performing the calibration and verification of the model in step 5, a multi-index comprehensive verification system is adopted. The Nash efficiency coefficient (NSE), the coefficient of determination (R²), and the relative error (RE) are selected as the verification indicators for runoff simulation, and the supply-demand balance coefficient (θ) is selected as the verification indicator for water use simulation. The calibration period and the verification period are divided according to the data time span. During the calibration period, the SCE-UA optimization algorithm is used to automatically calibrate the model parameters, and during the verification period, independent data is used to verify the applicability of the model. A pass / fail standard range is set for each verification indicator. If the verification indicator does not meet the pass / fail standard, the topology-adaptive coupling model is returned to re-optimize the core parameter matrix, and the calibration is iterated until the indicator meets the standard. The above settings construct a dual-dimensional verification system for natural hydrology and social water use. The multi-index comprehensive evaluation of model accuracy, the automatic calibration algorithm improves the parameter calibration efficiency, the independent verification ensures the model's generalization ability, and the iterative optimization mechanism continuously improves the simulation effect, ensuring that the model has stable and reliable outputs in different time periods and under different scenarios, meeting the accuracy and reliability requirements of practical applications.

[0075] In the preferred embodiment, the method for constructing a binary water cycle model in a low hilly area based on topological network partitioning also includes a dynamic update step for the core parameter matrix: based on a sliding time window, a rolling optimization algorithm is used to dynamically adjust the core parameter matrix, and the window length is set according to the cycle of changes in watershed hydrology and human activities; the parameter sensitivity coefficient within each time window is calculated using formula (15); the above settings allow the model to transform from a static parameter system to a dynamic parameter system, the sliding window adapts to the long-term trends of climate fluctuations, underlying surface changes, and human activity transformation, and the sensitivity analysis can identify key parameters that significantly affect the simulation results, avoid invalid parameter adjustments, improve the efficiency of dynamic updates, and allow the model to continuously adapt to the long-term evolution characteristics of the watershed, maintaining the accuracy and adaptability of long-term simulation.

[0076] In the preferred scheme, a sensitivity coefficient threshold is set, key parameters with absolute values ​​greater than or equal to the threshold are retained and re-optimized, while parameters with absolute values ​​less than the threshold remain unchanged. The updated core parameter matrix is ​​smoothed using the Kalman filtering algorithm. These settings focus on optimizing key parameters, reducing computational load and improving update efficiency. They also avoid simulation fluctuations caused by disturbances in insensitive parameters. The Kalman filtering smoothing process ensures continuous and stable parameter updates, preventing abrupt changes that could lead to simulation anomalies. This ensures that the model maintains stable output during long-term operation and significantly improves the model's continued applicability under the background of climate change and high-intensity human activities.

[0077] In summary, this invention proposes a method for constructing a binary water cycle model in low-mountain and hilly areas based on topological network partitioning. This method effectively solves the technical problem in the field of water cycle model construction: existing models struggle to accurately simulate the natural-social binary water cycle process under the complex terrain and strong human activity in low-mountain and hilly areas. Specifically, existing technologies either lack sufficient terrain adaptability to characterize complex hydraulic connections, or fail to deeply integrate socio-economic water use processes due to insufficient coupling with human activities, or have limited model accuracy and adaptability, making it difficult to meet the needs of long-term simulation and efficient water resource management. This invention successfully overcomes these limitations, achieving dynamic coupling and accurate simulation of the natural water cycle and socio-economic water use processes.

[0078] In terms of model construction methodology, this invention employs several unique measures. First, it is the first to specifically adapt to the topography and hydraulic characteristics of low-mountain and hilly areas, using a hierarchical partitioning algorithm to accurately divide the smallest hydrological units and construct a four-level water supply system topology network, precisely representing complex hydraulic connections, which differs from traditional model unit partitioning methods. Second, through a binary-driven analytical model, it deeply integrates heterogeneous natural and social data, quantifying the synergistic coefficients of topography and human activities, breaking through the limitations of traditional models' single data utilization and weak parameter correlations, and providing a new parameter support method for model simulation. Third, it constructs a topology-adaptive coupled model and introduces a multi-objective optimization algorithm, deeply integrating natural hydrology and social water use processes, and integrating and optimizing distributed hydrology and social water use regulation modules, achieving a significant improvement in simulation accuracy, unlike previous model construction methods.

[0079] This invention also boasts several highlights in terms of model performance improvement. It introduces a sliding time window and Kalman filtering dynamic update mechanism to adjust the core parameter matrix in real time, effectively capturing long-term changes in hydrology and human activities, demonstrating outstanding performance in improving the model's long-term adaptability. It constructs a binary water cycle model framework comprising two subsystems: natural water cycle and socio-economic water use, achieving dynamic coupling between the two processes. This differs from single natural water cycle models, providing a new perspective for water cycle simulation. Dedicated analytical submodules are designed for two types of heterogeneous data, quantifying synergistic coefficients through runoff generation and runoff mechanisms and human activity feedback patterns, forming a complete set of key water cycle parameters, showcasing unique methods in data processing and parameter construction. Furthermore, it integrates and improves the distributed hydrological and socio-economic water use regulation modules, optimizes the runoff generation and runoff and evaporation calculation logic in low-mountain and hilly areas, introduces a multi-objective optimization algorithm to generate the core parameter matrix, and ensures simulation accuracy and captures long-term changes through a dynamic update mechanism, representing a new attempt in model module integration and algorithm application.

[0080] In terms of expanding model functionality, this invention also yields significant results. The introduction of a terrain factor quantification module accurately characterizes the impact of key terrain features such as topographic relief, slope, and river networks on the water cycle process, providing a new approach to improving the model's terrain adaptability. The construction of a human activity intervention module incorporates human activity factors such as land use change and water conservancy project regulation into the model, achieving deep coupling between the natural water cycle process and socio-economic water use processes, representing a new approach to integrating human activity factors into the model.

[0081] From both practical application and theoretical value perspectives, this invention effectively solves the technical challenge of accurately simulating the natural-social dual water cycle process under complex terrain and strong human activity in low-mountain and hilly areas through a series of methods, such as hierarchical partitioning algorithms, binary-driven analytical models, and topological adaptation coupling models. It not only represents a breakthrough in the theory and methodology of model construction but also verifies its advanced nature and practicality in the field of water cycle model construction through multiple sets of comparative experiments and practical application cases. It closely integrates theory and practice, creating a water cycle simulation model with practical value. The constructed model can be directly applied to the optimal allocation and collaborative management of water resources in low-mountain and hilly areas and can be adapted to other similar terrain areas through parameter adjustments, possessing broad engineering promotion and practical application prospects, demonstrating the versatility of the model construction. A comprehensive verification system using multiple indicators such as Nash efficiency coefficient and supply-demand balance coefficient, combined with automatic calibration algorithms and iterative optimization processes, ensures simulation stability and improves the scientific rigor and reliability of the model construction. By introducing topographic factor quantification and human activity intervention modules, the impact of topographic features and human activities on the water cycle process was accurately quantified, improving the reliability and practicality of the simulation results and providing a more accurate method for water cycle research. High-precision numerical algorithms and parallel computing techniques were applied to improve the model's long-term simulation capabilities and computational efficiency, meeting the needs of efficient water resource utilization and sustainable management in low-mountain and hilly areas and solving the computational challenges of long-term simulation. The constructed binary water cycle model framework, with its natural subsystem covering multiple key links and its social subsystem including various major water use processes, achieved comprehensive simulation and provided a more complete model system for water cycle simulation. In the model construction process, unique methods and technologies were employed from data fusion and module construction to parameter updates and verification optimization, forming a complete water cycle model construction scheme and providing new ideas and methods for research in related fields.

Claims

1. A method for constructing a binary water cycle model in low hilly areas based on topological network partitioning, characterized in that, Includes the following steps: Step 1: Obtain multi-source heterogeneous data on the dual water cycle in the low mountain and hilly area. The multi-source heterogeneous data includes core natural hydrological data and socio-economic driving data. Step 2: Based on the digital elevation model and river network system, divide the smallest hydrological units, construct the water supply system topology network in combination with the spatial location of water conservancy projects, and clarify the water flow transmission path and control nodes between units; Step 3: Extract features from multi-source heterogeneous data and correlate them using a binary-driven analytical model to obtain a set of key parameters for the water cycle; Step 4: Input the key parameter set of the water cycle into the topology-adaptive coupling model, and combine the runoff generation and confluence characteristics of the smallest hydrological unit with the hydraulic constraints of the topology network to generate the core parameter matrix of the binary water cycle model; Step 5: Based on the core parameter matrix, a complete model is constructed by integrating distributed hydrological simulation and social water use regulation modules, and the dynamic coupling simulation of natural and social water cycles is realized through calibration and verification.

2. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that: The core natural hydrological data mentioned in step 1 includes watershed DEM data, soil texture data, rainfall-runoff time series data, and vegetation cover spatiotemporal data. The socioeconomic driving data includes land use change maps, water use structure time series data, and water conservancy project topology data.

3. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that: Step 2 describes the use of a hierarchical partitioning algorithm to divide the minimum hydrological units, followed by the construction of a water supply system topology network. Specifically: Based on the watershed DEM data, the river network framework is extracted; the Strahler classification method is used to classify the river network into levels, determining the connectivity between the main stream and tributaries; using the tributary tips as boundaries, and combining topographic slope thresholds and soil texture type boundaries, a hydrological response unit partitioning algorithm is used to divide the watershed into minimum hydrological units; through GIS spatial overlay analysis, the spatial coordinates of reservoirs, pumping stations, and irrigation canals are associated with the minimum hydrological units, constructing a four-level topology structure including water sources, canals, users, and control nodes; the edge weights of the topology network are defined as the water flow transmission capacity coefficient, calculated using the following formula: （1）； In the formula, For unit To unit edge weights, For calibration coefficients, For unit To unit transmission path length The power of, where The weighting index is affected by the transmission path length. For unit catchment area The power of, where The weighting index is determined by the catchment area. For soil saturated hydraulic conductivity, For unit To unit average slope The power of, where The weighted index represents the comprehensive impact of soil slope.

4. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, The binary driving analytical model described in step 3 is constructed based on the mechanism of natural hydrological processes and the feedback law of socio-economic driving forces, and quantifies the synergistic effect coefficient of topographic factors, underlying surface changes and human activities. The binary-driven analytical model includes a natural hydrological analysis submodule and a socio-economic analysis submodule. The natural hydrological analysis submodule extracts key parameters of precipitation interception, soil infiltration, and slope runoff based on runoff generation and confluence mechanisms. The core formula is: （2）； In the formula, This represents the actual infiltration rate. To stabilize the infiltration rate, The initial infiltration rate, The attenuation coefficient is... For cumulative rainfall, It is a natural constant; The socioeconomic driver analysis submodule extracts parameters such as land use conversion coefficient, water use efficiency coefficient, and engineering regulation coefficient based on the feedback patterns of human activities. The core formula is: （3）； In the formula, This represents the total water consumption of the region. For the first Initial water usage for Class A For the first Water consumption growth rate For the time span, This is the water efficiency correction factor. This represents the total number of water usage types. A correlation matrix between natural hydrological parameters and socioeconomic parameters was established using Pearson correlation analysis and grey relational analysis model. And the synergistic effect coefficient is quantified by formula (4): （4）； In the formula, To quantify the synergistic effect coefficient, For indexing natural hydrological parameters, For socioeconomic parameter indexing, For the correlation matrix The maximum value in.

5. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, The key water cycle parameter set mentioned in step 3 includes a subset of natural hydrological parameters and a subset of socio-economic parameters. The subset of natural hydrological parameters includes rainfall attenuation coefficient, soil saturated hydraulic conductivity, vegetation interception, slope runoff roughness, groundwater recharge coefficient, and evaporation capacity coefficient. The subset of socio-economic parameters includes land use conversion rate, agricultural water quota, industrial water reuse rate, per capita domestic water user index, water conservancy project regulation threshold, and policy implementation intensity coefficient. The parameter set is standardized using the following formula: （5）； In the formula, For the standardized first One parameter, These are the original parameter values. , These are the minimum and maximum values ​​of the original parameters. , This represents the boundary of the standardized parameter interval.

6. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, The topology-adaptive coupling model described in step 4 includes a slope confluence nonlinear module and a social water supply and demand balance module. The slope confluence nonlinear module calculates the slope confluence velocity based on the improved kinematic wave equation, as shown in the following formula: （6）； In the formula, The slope confluence velocity, For the confluence velocity on a flat surface, For slope, For vegetation coverage, , , These are coefficients calibrated based on topographic and vegetation characteristics. It is a natural exponential function; The social water supply and demand balance module calculates the supply and demand difference based on the water resource supply and demand balance equation and the hydraulic constraints of the topological network. The formula is as follows: （7）； In the formula, for The difference between supply and demand at any given time For the first Water supply from each water source To ensure water supply reliability, For the first Water consumption of different user types This is the water use priority coefficient. Total number of water sources; This represents the total number of water usage types. The two modules are merged using a weighted coupling algorithm, with coupling weights... The human activity intensity index is dynamically adjusted based on the smallest hydrological unit, and the formula is as follows: （8）； In the formula, Based on the coupling weights, This represents the maximum possible water consumption in the region.

7. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, In step 4, a multi-objective optimization algorithm is used to determine the elements of the core parameter matrix. The core parameter matrix is ​​as follows: , row dimension Corresponding to the smallest hydrological unit number, column dimension Corresponding to the key parameters of the water cycle; A multi-objective optimization model is constructed with the objectives of minimizing historical runoff simulation errors and minimizing water supply and demand balance deviations. （9）； （10）； In the formula, To account for the relative error in runoff simulation, To address the supply and demand imbalance, For parameter weights, For unit Hydraulic constraint parameters , To constrain the upper and lower limits of the indicator, , The boundary of the parameter value range, To optimize the objective function for multiple objectives, Numbering the smallest hydrological unit, Index of key parameters for the water cycle; The optimization model was solved using the non-dominated sorting genetic algorithm NSGA-Ⅲ, and the core parameter matrix in the Pareto optimal solution set was obtained.

8. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, The distributed hydrological simulation module described in step 5 adopts an improved SWAT model framework, and introduces a topographic slope correction factor to correct the SCS curve number formula in the runoff calculation module: （11）； In the formula, The corrected curve number. For the standard curve number, For slope, This is the slope correction factor; In the confluence calculation module, the two-dimensional confluence model formula (12) is used instead of the traditional one-dimensional confluence to consider the coupled confluence process of the slope and the river channel: （12）； In the formula, For traffic, For time, , For spatial coordinates, , They are respectively , Convergence velocity in direction, It represents the lateral inflow, and is a partial differential symbol, characterizing the local rate of change of the variable; In the evaporation calculation module, the actual evaporation is calculated by combining the spatiotemporal data of vegetation cover retrieved by remote sensing and using a dual-source evaporation model to distinguish between vegetation transpiration and soil evaporation.

9. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to claim 1, characterized in that, The social water use regulation module mentioned in step 5 includes a water use structure simulation submodule and an engineering regulation simulation submodule. The water use structure simulation submodule simulates the dynamic changes of various water use types based on the Logistic growth model. （13）； In the formula, For the first Water use Water consumption at any given time For the first The maximum carrying capacity of water-type water, The growth rate coefficient, The time of the growth inflection point; The engineering control simulation submodule simulates the scheduling process of reservoirs and pumping stations based on the hydraulic constraints of the topology network. The reservoir scheduling rule formula is as follows: （14）； In the formula, for The reservoir discharge flow rate at all times for Inbound traffic at all times The threshold for the outflow corresponding to the reservoir's beneficial storage capacity. For regular scheduling coefficients, This is the excess flood control coefficient.

10. The method for constructing a binary water cycle model in low hilly areas based on topological network partitioning according to any one of claims 1 to 9, characterized in that, It also includes a dynamic update step for the core parameter matrix: based on a sliding time window, a rolling optimization algorithm is used to dynamically adjust the core parameter matrix, and the window length is set according to the cycle of changes in watershed hydrology and human activities. The parameter sensitivity coefficient within each time window is calculated using formula (15): （15）； In the formula, The parameter sensitivity coefficient within each time window, For model simulation error, Elements of the core parameter matrix; A sensitivity coefficient threshold is set, key parameters with absolute values ​​greater than or equal to the threshold are retained and re-optimized, while parameters with absolute values ​​less than the threshold remain unchanged; the updated core parameter matrix is ​​smoothed using the Kalman filtering algorithm. （16）； In the formula, For filter gain, for Simulate error at any time. For the observation matrix, For the first Within the first time window The first smallest hydrological unit corresponding to the first Specific values ​​for key parameters of water cycle.

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