A water resource change attribution method and system fusing physical constraint structural equation

Abstract

The application belongs to the technical field of water resource attribution and climate change impact assessment, and particularly discloses a water resource change attribution method and system fusing a physical constraint structural equation, which comprises the following steps: a sample matrix about climate factors, human factors and water resource indexes is established; a structural equation model fusing a physical constraint is constructed, including: a measurement module, which maps observation data of the climate factors, the human factors and the water resource indexes into latent variables with clear physical meanings; a structure module, which realizes causal relationship modeling between the latent variables; and a water balance physical constraint is introduced; parameter estimation is performed on the structural equation model based on the sample matrix, path coefficients are obtained, and attribution contribution rates of the climate factors and the human factors to water resource change are determined. The application can ensure that the attribution result is in line with statistical significance and meets hydrological mechanism, and can avoid unreasonable explanation in physics, thereby providing a scientific basis for basin water resource management and climate change adaptation.

Description

Technical Field

[0001] This invention belongs to the technical field of water resource attribution and climate change impact assessment, and more specifically, relates to a water resource change attribution method and system that integrates physical constraint structural equations. Background Technology

[0002] Water resources are a fundamental element for sustainable socio-economic development, and their changes are influenced by both climate factors (such as precipitation and evapotranspiration) and human activity factors (such as water intake, land use change, and reservoir regulation). How to quantitatively distinguish the relative contributions of climate change and human activities to water resource evolution is a core scientific issue in hydrological and water resources research and water conservancy engineering planning.

[0003] Existing attribution studies mostly employ empirical statistical models or trend decomposition methods, such as the double cumulative curve method, elasticity coefficient method, and distributed hydrological model simulation comparison method. These methods can explain water resource changes to a certain extent, but they have the following shortcomings: (1) Most methods rely on empirical formulas or scenario comparisons, lack a unified mathematical framework, and are difficult to systematically reveal the interaction mechanism of multiple factors; (2) Some methods rely on the calibration of complex hydrological model parameters. When the input data is insufficient or the parameter uncertainty is large, the stability and credibility of the attribution results are affected; (3) Structural equation modeling (SEM), as a causal inference method, has been introduced into some hydrological and ecological studies to characterize the relationship between latent variables and observed indicators. However, existing SEM applications usually only focus on statistical fitting effects and fail to effectively introduce physical constraints of the water cycle, such as water balance relationships, which may lead to inconsistencies between model inference results and actual hydrological processes.

[0004] For example, existing SEM applications in water resource attribution often ignore the closed-loop constraint relationship of "precipitation-evapotranspiration-runoff-water storage change", which may result in path coefficients that contradict physical laws. On the other hand, the estimation results of path coefficients lack physical prior constraints on the sign and amplitude, which may lead to unreasonable results such as precipitation being negative for runoff and water use being positive for water resources, thus reducing the scientific validity and interpretability of the attribution conclusions.

[0005] In summary, existing methods for attribution analysis of water resource changes have at least the following defects or need for improvement: (1) There is a lack of a unified method that combines statistical modeling with physical constraints. The physical laws of the water cycle are not effectively introduced in the model inference process, resulting in the results lacking rationality in hydrology; (2) Existing methods are not capable enough in explaining the synergistic and interactive effects of multiple factors. Summary of the Invention

[0006] In view of the above-mentioned deficiencies or improvement needs of the existing technology, the present invention provides a water resource change attribution method and system that integrates physical constraint structural equations, the purpose of which is to improve the accuracy and rationality of identifying the contribution rate of different influencing factors to water resource changes.

[0007] To achieve the above objectives, according to one aspect of the present invention, a water resource change attribution method integrating physical constraint structural equations is proposed, comprising the following steps: Establish a sample matrix for climate factors, human factors, and water resource indicators; A structural equation model incorporating physical constraints is constructed, including: a measurement module mapping observed data of climate factors, human factors, and water resource indicators into latent variables with explicit physical meaning; a structural module modeling causal relationships between latent variables through path coefficients; and water balance physical constraints expressed as follows: Where P represents precipitation, ET represents evapotranspiration, Q represents runoff, and ΔS represents the change in terrestrial water storage; Based on the sample matrix, the structural equation model with integrated physical constraints is used to estimate the parameters and obtain the path coefficients. The contribution coefficients of climate factors and human factors to water resources are determined according to the path coefficients, and then the attribution contribution rates of climate factors and human factors to water resource changes are obtained.

[0008] As a further preferred embodiment, the measurement module is represented as follows:

[0009] in, x For the vector of exogenous observed variables, y A vector of endogenous observed variables; x These are exogenous latent variables, including climate factors. x C With human factors x H ; or Endogenous latent variables, including water cycle processes or R With water resources or W Λ x With Λ y For the factor loading matrix, d and This is the measurement error term; The structural module is represented as follows:

[0010] in, B The path coefficient matrix between endogenous latent variables. C This is the path coefficient matrix from exogenous latent variables to endogenous latent variables. gThis is the structural disturbance term.

[0011] As a further preferred method, parameter estimation is performed on the structural equation model with fused physical constraints based on the sample matrix, including: Based on the structural equation model with sample matrix and fused physical constraints, an iterative optimization algorithm is used to minimize the objective function and iteratively calculate the path coefficient matrix. B and C ; The objective function Represented as:

[0012] Where, Σ( i ) represents the model's latent covariance matrix; i The parameters to be estimated include the path coefficient matrix. B and C S is the sample covariance matrix, which is calculated from the sample matrix; tr() represents the trace of the matrix. p This represents the number of observed variables.

[0013] As a further preferred method, when using an iterative optimization algorithm to minimize the objective function, the objective function value is calculated as follows: based on the current path coefficient matrix... B and C By combining the structural equation model with physical constraints, the implicit covariance matrix Σ( i Then, the corresponding objective function value is calculated.

[0014] As a further preferred option, when performing parameter estimation, the water balance physical constraint is directly involved in the parameter estimation as a hard constraint; or, the water balance physical constraint is added to the objective function as a soft constraint in the form of a penalty term.

[0015] As a further preferred method, the contribution coefficients of climate factors and human factors to water resources are determined based on path coefficients, including: Based on path coefficient matrix B and C The path coefficients of each exogenous latent variable on water resources were obtained. T ηW , j This leads to the contribution coefficient of individual climate factors or human factors to water resources. C j :

[0016] in, C j Single factorj Contribution coefficient to water resources n This represents the total number of exogenous latent variables. T ηW , j , T ηW , m Exogenous latent variables j , m Path coefficients for water resources.

[0017] As a further preferred option, based on the contribution coefficients of climate factors and human factors to water resource quantity, the attribution contribution rates of climate factors and human factors to water resource changes are obtained, including: Based on the contribution coefficients of various climate factors to water resources, the total contribution coefficient of climate factors to water resources is obtained. C climate Based on the contribution coefficients of each human factor to water resources, the total contribution coefficient of human factors to water resources is obtained. C human ; Then, the attribution contribution rates of climate factors and human factors to water resource changes are determined based on the following formula:

[0018]

[0019] G climate + G human = 1 in, G climate The attribution contribution rate of climate factors to water resource changes. G human The attribution contribution rate of human factors to water resource changes.

[0020] As a further optimization, a sample matrix of climate factors, human factors, and water resource indicators is established, including: Acquire data on climate factors, human factors, and water resource indicators, and perform data standardization to obtain a sample matrix of climate factors, human factors, and water resource indicators. The climate factor data includes precipitation P, temperature T, and potential evapotranspiration PET; the human factor data includes water consumption WU, land use / urbanization rate LU, and reservoir capacity regulation coefficient RES; and the water resource index data includes runoff Q, evapotranspiration ET, change in terrestrial water storage ΔS, and available water resources WR.

[0021] As a further preferred approach, data consistency processing is performed, including: Spatial unit alignment: unifying data from different sources to the scale of watershed, province, or city / county, and unifying the time series of all data to the same time series; Data preprocessing: Missing values ​​in the data are filled using multiple imputation methods, skewed data are logarithmically transformed, and finally, all climate factors, human factors, and water resource indicators are Z-score standardized to form a sample matrix.

[0022] According to another aspect of the present invention, a water resource change attribution system integrating physical constraint structural equations is provided, including a processor for executing the above-described water resource change attribution method integrating physical constraint structural equations.

[0023] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. This invention proposes a structural equation modeling framework that integrates physical constraints. It introduces water balance physical constraints into the statistical inference of the structural equation model, enabling joint attribution analysis of climate factors and human activity factors. By effectively incorporating the physical laws of the water cycle, it improves the accuracy and rationality of identifying the contribution rates of different influencing factors to water resource changes. This invention ensures that the attribution results are both statistically significant and conform to hydrological mechanisms, avoiding physically unreasonable explanations and providing a scientific basis for watershed water resource management and climate change adaptation.

[0024] 2. This invention characterizes the synergistic and feedback mechanisms among climate change, human activities, and surface processes by adding latent variables and interaction paths to a structural equation model. The model utilizes multi-source observational data to construct a multi-factor network structure and achieves quantitative identification and significance testing of direct, indirect, and interaction effects through the joint solution of multiple sets of equations. Specifically, direct effects are reflected through the direct path from exogenous latent variables to water resource latent variables; indirect effects are reflected through the path chain where exogenous latent variables influence water resource latent variables via water cycle process latent variables; and interaction effects are reflected through a multi-factor network structure formed by climate factors and human activity factors as common driving factors of multiple endogenous latent variables, and are quantitatively identified through path coefficient estimation and significance testing. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the water resource change attribution method integrating physical constraint structural equations according to an embodiment of the present invention; Figure 2 This is a diagram showing the direct and indirect relationships between different factors and water resources in embodiments of the present invention; Figure 3 This is a diagram showing the model iteration results of an embodiment of the present invention; Figure 4 This is a graph showing the change in total water resources data according to an embodiment of the present invention; Figure 5 This is a graph showing the variation of annual average precipitation data in an embodiment of the present invention; Figure 6 This is a graph showing the variation of annual average temperature data in an embodiment of the present invention; Figure 7 This is a graph showing the annual total runoff data variation according to an embodiment of the present invention; Figure 8 This is a graph showing the annual water supply data variation according to an embodiment of the present invention; Figure 9 This is a graph showing the annual water storage data variation according to an embodiment of the present invention; Figure 10 This is a graph showing the annual water quality data changes according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] This invention provides a water resource change attribution method that integrates physical constraint structural equations, such as... Figure 1 As shown, it includes the following steps: (1) Obtain data on climate factors, human factors and water resources indicators, and perform consistency processing on these data to obtain a sample matrix of climate factors, human factors and water resources indicators.

[0028] Specifically, climate factor data includes precipitation (P), temperature (T), and potential evapotranspiration (PET); human factor data includes water consumption (WU), land use / urbanization rate (LU), and reservoir capacity regulation coefficient (RES); and water resource index data includes runoff (Q), evapotranspiration (ET), change in terrestrial water storage (ΔS), and available water resources (WR).

[0029] Furthermore, data consistency processing is performed, including: Spatial unit alignment. Unify data from different sources to the watershed, provincial, or municipal / county scale, and unify the time series of all data to the same time series. Data preprocessing. Missing values ​​were imputed using multiple imputation. Skewed data underwent logarithmic transformation. Finally, all data on climate factors, human factors, and water resource indicators were Z-score standardized to form an N×p sample matrix, where N is the number of samples and p is the number of indicators.

[0030] (2) Construct a structural equation model that incorporates physical constraints.

[0031] The structural equation model incorporating physical constraints includes a measurement module and a structural module, and incorporates water balance physical constraints, as detailed below: Measurement Module: Maps observational data of multi-source climate factors, human factors, and water resource indicators into latent variables with explicit physical meaning, and explicitly models observation errors; the measurement module defines the relationship between latent variables and observed indicators using the following formula:

[0032] In the formula, x For the vector of exogenous observed variables, y For the vector of endogenous observed variables, x For exogenous latent variables (including climate factors) x C With human factors x H ), or Endogenous latent variables (including water cycle processes) or R With water resources or W ), Λ x With Λ y These are the factor loading matrices, d and This represents the measurement error term. By fixing one factor loading for each latent variable to 1, or equivalently fixing the variance of the latent variables to 1, the unique identifiability of the model parameters is achieved, giving the estimation results of the latent variables clear statistical significance and a physical interpretation basis.

[0033] The structural module, building upon the measurement module, models and estimates the causal relationships between latent variables; it requires defining the relationship between endogenous and exogenous latent variables to obtain equations that satisfy their characteristics.

[0034] In the formula, B The path coefficient matrix between endogenous latent variables. C This is the path coefficient matrix from exogenous latent variables to endogenous latent variables. or As an endogenous latent variable, x As an exogenous latent variable, g For the structural perturbation term, E[ζ] = 0, Var(ζ) < ∞. The path structure includes: or R ← x C , x H ,as well as or W ← or R , x C , x H ;where the matrix B It must be acyclic, and ( I B It is reversible to ensure that the causal chain is clear and the model is identifiable.

[0035] Physical constraints of water balance:

[0036] In the formula, P represents precipitation, ET represents evapotranspiration, Q represents runoff, and ΔS represents the change in terrestrial water storage.

[0037] Prior settings for path coefficients: When estimating path coefficients, physical signs and magnitude priors are set. First, the path coefficients of precipitation P on runoff Q are set. β PQ >0; then use the path coefficient of water quantity WU to water resource quantity WR. β WU,WR <0; and the path coefficient of reservoir capacity regulation coefficient RES to runoff or water resources. β RES It can be positive or negative depending on the season, but is limited to [ Within 1,1] or other reasonable physical ranges.

[0038] (3) Use the sample matrix to estimate the parameters of the structural equation model with integrated physical constraints to obtain the path coefficients.

[0039] (3.1) Establish the objective function, where the objective function under the maximum likelihood method is... for:

[0040] In the formula, Σ( i ) represents the model's latent covariance matrix; i The parameters to be estimated include the path coefficient matrix. B and C And used to construct the model's implicit covariance matrix Σ( i Other free parameters (factor loading matrix Λ) x With Λ y S is the sample covariance matrix; p The number of observed variables; tr() represents the trace of a matrix, which is the sum of the elements on the main diagonal of the matrix. It is a standard operator in linear algebra used to measure the weighted difference between two covariance matrices on a global scale. This represents the statistical fitting loss of a structural equation model, calculated based on the sample covariance matrix. S With the model's implicit covariance matrix Σ( i The difference between ).

[0041] (3.2) Based on the structural equation model with sample matrix and fused physical constraints, the objective function is minimized iteratively using an iterative optimization algorithm to obtain the path coefficient matrix. B and C .

[0042] Specifically, initial parameter values ​​are set at the beginning, including factor loadings of latent variables, path coefficients between latent variables, residual variances, and historical sample correlation coefficients. The sample covariance matrix S is pre-calculated based on the sample matrix. During iterative calculations, the current path coefficient matrix is ​​used... B and C By combining the structural equation model with physical constraints, the implicit covariance matrix Σ of the model is updated. i ), and Σ( i ) and sample covariance matrix S Substitute the values ​​into the objective function and calculate the objective function value.

[0043] Furthermore, the physical constraints of water balance can be directly substituted into the parameter estimation of the structural equation model as hard constraints, or they can be added to the objective function as soft constraints in the form of penalty terms.

[0044] In the formula, F The adjusted objective function is... l A value greater than 0 represents a penalty coefficient used to balance statistical fitting error with physical consistency. During parameter estimation, the objective function is evaluated using the least squares method. F Minimize the model to ensure statistical fitting accuracy while meeting the physical consistency requirements of water balance as much as possible.

[0045] (4) Based on the path coefficient, the contribution coefficients of climate factors and human factors are obtained, and then the attribution contribution rates of climate factors and human factors to water resource changes are obtained.

[0046] (4.1) Based on the path coefficient matrix B and C This yields the contribution coefficients of individual climate and human factors to water resources. Specifically, these include: Based on path coefficient matrix B and C The total path coefficient matrix is ​​obtained as follows:

[0047] In the formula, TRepresenting exogenous latent variables x j Endogenous latent variables or i The path coefficients can be used to calculate the relationship between exogenous latent variables and endogenous latent variables (water resources). or W Path coefficients T ηW , j .

[0048] This leads to the contribution coefficients of each individual climate factor or human factor to water resources. C j :

[0049] in, C j Single factor j Contribution coefficient to water resources n This represents the total number of exogenous latent variables. T ηW , j , T ηW , m Exogenous latent variables j , m Path coefficients for water resources.

[0050] (4.2) Based on the contribution coefficients of each climate factor to water resources, the total contribution coefficient of climate factors to water resources is obtained. C climate Based on the contribution coefficients of each human factor to water resources, the total contribution coefficient of human factors to water resources is obtained. C human .

[0051] (4.3) Determine the attribution contribution rates of climate factors and human factors to water resource changes: Assuming that changes in water resources are influenced only by climatic and human factors, i.e.: G climate + G human = 1 The attribution contribution rates of climate factors and human factors to water resource changes are calculated based on the total contribution coefficients of climate factors and human factors:

[0052]

[0053] In the formula, G climate Represents the total contribution rate of climate factors. G human Represents the total contribution rate of human factors.

[0054] Furthermore, the contribution coefficient and significance level of each climate factor or human factor are calculated. The significance level is used to assess the statistical significance of path coefficients among latent variables in the structural equation model. When path coefficients are insignificant or the overall model goodness of fit does not meet a preset threshold, the model can be reset, including adjusting the path structure, parameter constraints, or physical penalty weights, and the parameter estimation steps can be re-executed to obtain a final model that meets both statistical and physical consistency requirements.

[0055] The following are specific examples: Taking a province in China as an example, this study quantifies the impact of climate change and human activities on regional water resources. A comprehensive dataset of annual water resource indicators for the province (1998-2023) is used. Figure 4 A graph representing the changes in the province's total water resources (WR) from 1998 to 2023. Figure 5 A graph representing the change in annual precipitation (P) in the province from 1998 to 2023. Figure 6 A graph representing the changes in annual temperature (T) in the province from 1998 to 2023. Figure 7 The graph represents the changes in the province's annual runoff (Q) from 1998 to 2023. Figure 8 A graph representing the changes in the province's annual water supply (WU) from 1998 to 2023. Figure 9 A graph representing the changes in the province's annual water storage from 1998 to 2023. Figure 10 The graph represents the annual water quality changes in the province from 1998 to 2023, and SEM analysis was used to analyze the causal relationships. The impact of human activities and climate on water resources was analyzed.

[0056] First, a structural equation model is constructed. Then, water resource change data and its driving data are input for model calibration and evaluation. The model's performance is assessed based on pre-set evaluation indicators. If a model shows poor fit, it is revised, and the calibration and evaluation process is repeated until a satisfactory fit is achieved, forming a final well-fitting SEM model. This model is used to determine the contributions of human activities and climate change to water resource change. Maximum likelihood estimation is employed for SEM modeling. Several goodness-of-fit indices are used to evaluate model fit, including CFI (Comparative Fit Index), RMSEA (Approximate Root Mean Square Error), and SRMR (Root Mean Square Residual). If the original model fits poorly, it is modified several times by removing or changing insignificant (p>0.05) paths. An SRMR below 0.05, an RMSEA below 0.08, and a CFI close to 1 indicate a good model fit. When multiple models pass these criteria, the best model is determined by comparing the goodness-of-fit indices. The Python third-party library semopy is used to complete SEM modeling, calibration, evaluation, and fitting.

[0057] The final simulation results of the structural equation model are shown in Table 1. HAC, CC, and WRC represent human activity factors, climate change factors, and water resource changes, respectively. From this, we can see that: HAC→CC: The positive path coefficient from HAC to CC is 0.942 (standardized), indicating a strong correlation between potential human activity factors and potential climate factors. As the level of human activity increases, climate variables also rise. The high coefficient reflects the global warming trend, emphasizing that human activities causing climate change is an important reality during the research period.

[0058] CC→WRC: The direct path from climate potential to water resources has a positive value of 0.791, confirming the strong impact of climate change on annual water resource variability. Years with high precipitation show an increase in total water resources. This climate path has the greatest direct impact on WRC, is statistically significant, reflects the critical role of climate, and underscores the indispensable contribution of nature.

[0059] HAC→WRC (Direct): HAC has a direct positive impact of 0.214 on WRC. The increase in water consumption in Hubei is consistent with the increase in water resources, but this direct impact is small and statistically unsound. This indicates that after considering the impact of climate, the net direct impact of human activities on the total annual water resources is slight. This may be due to regulatory balance, and it also reflects the limitations of the annual summary data. The direct impact of human activities on the total annual water volume is secondary.

[0060] Indirect HAC → WRC via CC: Multiplying HAC→CC and CC→WRC, the indirect effect is approximately 0.745, representing the pathway by which human activities affect water resources by altering the climate. Human impact on water is mostly mediated by climate factors.

[0061] Total effect: The total effect of human activities on water resources is 0.959 (direct 0.214 + indirect 0.745), while the total impact of climate change on water resources is 0.791. Overall, human impact slightly exceeds the direct impact of climate on water. Of the differences in water resource changes explained, approximately 55% is related to human factors and 45% is related to climate factors.

[0062] Table 1 Simulation Results

[0063] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A water resource change attribution method integrating physical constraint structural equation modeling, characterized in that, Includes the following steps: Establish a sample matrix for climate factors, human factors, and water resource indicators; A structural equation model incorporating physical constraints is constructed, including: a measurement module mapping observed data of climate factors, human factors, and water resource indicators into latent variables with explicit physical meaning; a structural module modeling causal relationships between latent variables through path coefficients; and water balance physical constraints expressed as follows: Where P represents precipitation, ET represents evapotranspiration, Q represents runoff, and ΔS represents the change in terrestrial water storage. Based on the sample matrix, the structural equation model with physical constraints is used to estimate the parameters and obtain the path coefficients. The contribution coefficients of climate factors and human factors to water resources are determined according to the path coefficients, and then the attribution contribution rates of climate factors and human factors to water resource changes are obtained. The measurement module is represented as follows: in, x For the vector of exogenous observed variables, y A vector of endogenous observed variables; ξ These are exogenous latent variables, including climate factors. ξ C With human factors ξ H ; η Endogenous latent variables, including water cycle processes η R With water resources η W Λ x With Λ y For the factor loading matrix, δ and This is the measurement error term; The structural module is represented as follows: in, B The path coefficient matrix between endogenous latent variables. Γ This is the path coefficient matrix from exogenous latent variables to endogenous latent variables. ζ For structural disturbance terms; Parameter estimation is performed on the structural equation model with fused physical constraints based on the sample matrix, including: Based on the structural equation model with sample matrix and fused physical constraints, an iterative optimization algorithm is used to minimize the objective function and calculate the path coefficient matrix. B and Γ ; The objective function Represented as: Where, Σ( θ ) represents the model's latent covariance matrix; θ The parameters to be estimated include the path coefficient matrix. B and Γ S is the sample covariance matrix, which is calculated from the sample matrix; tr() represents the trace of the matrix. p The number of observed variables; Water balance physical constraints can be directly substituted as hard constraints into the parameter estimation of the structural equation model, or added as soft constraints in the form of penalty terms to the objective function. In the formula, F The adjusted objective function is... λ >0 is the penalty coefficient, used to balance statistical fitting error with physical consistency.

2. The water resource change attribution method integrating physical constraint structural equations as described in claim 1, characterized in that, When using an iterative optimization algorithm to minimize the objective function, the objective function value is calculated as follows: based on the current path coefficient matrix... B and Γ By combining the structural equation model with physical constraints, the implicit covariance matrix Σ( θ Then, the corresponding objective function value is calculated.

3. The water resource change attribution method integrating physical constraint structural equations as described in claim 1, characterized in that, When performing parameter estimation, the physical constraints of water balance are directly involved in the parameter estimation as hard constraints; or, the physical constraints of water balance are added to the objective function as soft constraints in the form of penalty terms.

4. The water resource change attribution method integrating physical constraint structural equations as described in claim 1, characterized in that, The contribution coefficients of climate and human factors to water resources are determined based on path coefficients, including: Based on path coefficient matrix B and Γ The path coefficients of each exogenous latent variable on water resources were obtained. T ηW , j This leads to the contribution coefficient of individual climate factors or human factors to water resources. C j : in, C j Single factor j Contribution coefficient to water resources n This represents the total number of exogenous latent variables. T ηW , j , T ηW , m Exogenous latent variables j , m Path coefficients for water resources.

5. The water resource change attribution method integrating physical constraint structural equations as described in claim 4, characterized in that, Based on the contribution coefficients of climate factors and human factors to water resource quantity, the attribution contribution rates of climate factors and human factors to water resource changes are obtained, including: Based on the contribution coefficients of various climate factors to water resources, the total contribution coefficient of climate factors to water resources is obtained. C climate Based on the contribution coefficients of each human factor to water resources, the total contribution coefficient of human factors to water resources is obtained. C human ; Then, the attribution contribution rates of climate factors and human factors to water resource changes are determined based on the following formula: G climate + G human = 1 in, G climate The attribution contribution rate of climate factors to water resource changes. G human The attribution contribution rate of human factors to water resource changes.

6. The water resource change attribution method that integrates physical constraint structural equations as described in any one of claims 1-5, characterized in that, Establish a sample matrix for climate factors, human factors, and water resource indicators, including: Acquire data on climate factors, human factors, and water resource indicators, and perform data standardization to obtain a sample matrix of climate factors, human factors, and water resource indicators. The climate factor data includes precipitation P, temperature T, and potential evapotranspiration PET; the human factor data includes water consumption WU, land use / urbanization rate LU, and reservoir capacity regulation coefficient RES; and the water resource index data includes runoff Q, evapotranspiration ET, change in terrestrial water storage ΔS, and available water resources WR.

7. The water resource change attribution method integrating physical constraint structural equations as described in claim 6, characterized in that, Data consistency processing includes: Spatial unit alignment: unifying data from different sources to the scale of watershed, province, or city / county, and unifying the time series of all data to the same time series; Data preprocessing: Missing values ​​in the data are filled using multiple imputation methods, skewed data are logarithmically transformed, and finally, all climate factors, human factors, and water resource indicators are Z-score standardized to form a sample matrix.

8. A water resource change attribution system integrating physical constraint structural equations, characterized in that, Includes a processor for executing the water resource change attribution method according to any one of claims 1-7, which incorporates physical constraint structural equations.

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