Water resource dynamic toughness evaluation method based on absorption and recovery dual drive

Abstract

The invention discloses a water resource dynamic toughness evaluation method based on absorption and recovery dual-drive, which comprises the following steps: collecting multi-source data of a target drainage basin, and constructing a water resource evaluation basic database; selecting a multi-dimensional drought index, and extracting a drought impact strength factor after dimensionality reduction by a principal component analysis method; calculating the marginal expected loss of each index under the extreme drought condition based on the factor and each drought index; simulating a dynamic response path of a comprehensive factor of the water resource system in each period in the future through an impulse response function by relying on a time-varying parameter vector autoregression model; toughness parameters such as absorption intensity and recovery time are calculated according to the response path, a dual-drive toughness measurement function is constructed, the dynamic toughness value of the target drainage basin is measured and calculated, and evaluation is completed. According to the method, the response characteristics and the recovery capability of the water resource system under drought impact can be systematically evaluated, and a theoretical basis is provided for regional water resource risk prevention and control and adaptive management.

Description

Technical Field

[0001] This invention relates to the field of water resource system analysis and management technology, and in particular to a method for assessing the dynamic resilience of water resources based on a dual-drive approach of absorption and recovery. Background Technology

[0002] In recent years, the combined impacts of global climate change and human activities have intensified, posing multiple severe challenges to watershed water resource systems, including water scarcity, frequent droughts, and ecological degradation. These challenges not only directly threaten the sustainable socio-economic development of the watershed but also pose significant hidden dangers to regional ecological security. Against this backdrop, "resilience," as a key indicator for accurately characterizing a system's ability to resist external disturbances, adapt to environmental changes, and recover core functions from disturbances, has become a core dimension in the field of water resource system research. Quantitatively assessing the resilience of watershed water resource systems is not only a core prerequisite for revealing the dynamic response mechanism of the system under external disturbances but also an important foundation for formulating scientific and effective water resource regulation strategies and improving the system's resilience and adaptability.

[0003] Internationally, some scholars pioneered the theory of ecosystem resilience and applied it to ecosystem management practices, laying a solid theoretical foundation for resilience research. Subsequent scholars further expanded the framework of resilience research, delving into the intrinsic connections between a system's resilience to disturbances, adaptation, and change, thus deepening the connotation of the resilience concept. Subsequently, resilience theory gradually extended across disciplines, finding widespread application in environmental science, socio-ecological systems, and other resource- and environment-related research fields. With the increasing prominence of water resource issues, resilience thinking has been introduced into the field of water resources and gained widespread attention from the academic community. The concept of "enhancing the resilience of water resource systems by improving their ability to cope with risks and recover" has been widely recognized by researchers, and scholars both domestically and internationally have conducted extensive exploratory research on the resilience of water resource systems.

[0004] Currently, research on the resilience assessment of water resource systems is mainly advancing along two major technical directions: First, a comprehensive evaluation framework is constructed based on an indicator system. For example, some scholars have proposed a watershed “3Rs” resilience assessment framework and a flood or water resource resilience assessment system is constructed based on the pressure-state-response (PSR) framework to achieve a preliminary identification of the spatiotemporal pattern of resilience. Second, measurement analysis is carried out using model tools. For example, system dynamics (SD) simulation is combined with a functional resilience framework to assess the response mechanism of the water resource-agriculture-community coupled system in semi-arid regions, or artificial neural networks are used to couple system dynamics modeling to assess the resilience level of water resource systems under disaster events.

[0005] However, existing evaluation methods generally suffer from limitations of static assessment, making it difficult to accurately characterize the dynamic recovery process of a system after an impact, and failing to effectively capture the time-varying characteristics of system resilience. Significant research gaps remain in key areas such as revealing the internal risk transmission mechanism of the system, achieving dynamic quantitative expression of resilience levels, and reconstructing the dynamic recovery path of the system under real disturbances. Particularly for semi-arid watersheds in northern China, drought is the dominant type of disturbance, but current technologies have not yet formed a complete technical system encompassing "drought impact factor extraction - risk transmission simulation - dynamic resilience measurement," making it difficult to accurately quantify the intensity and recovery time of the system's absorption of disturbances, and thus failing to meet the actual needs of precise prevention and adaptive management of water resource risks in watersheds.

[0006] Therefore, developing a water resource system resilience measurement technology that combines physical mechanisms and dynamic adaptability has become a core challenge that urgently needs to be addressed in the field of water resources. Summary of the Invention

[0007] The purpose of this invention is to provide a dynamic resilience assessment method for water resources based on absorption and recovery dual-drive, so as to achieve dynamic and accurate quantification of water resource resilience, clearly present the differences in disturbance resistance and recovery capabilities at different times, and provide scientific decision support for watershed drought prevention and control and optimal allocation of water resources.

[0008] To achieve the above objectives, this invention provides a method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery, comprising the following steps: S1. Collect multi-source data from the target watershed and construct a basic data and information database for water resource assessment; S2. Select multi-dimensional drought indicators, and use principal component analysis to reduce the dimensionality of the multi-dimensional drought indicators before extracting the drought impact intensity factor. S3. Based on the drought impact intensity factor and various drought indicators, calculate the marginal expected loss of each drought indicator under extreme drought conditions. S4. Based on the time-varying parameter vector autoregression model, the dynamic response path of the comprehensive factors of the water resources system in future periods is simulated using the impulse response function. S5. Based on the dynamic response path obtained in S4, calculate the resilience parameters of the water resource system, including absorption intensity and recovery time. S6. Construct a water resource system resilience measurement function driven by absorption and recovery, calculate the dynamic resilience value of the target watershed water resource system, and evaluate the resilience of the water resource system.

[0009] Preferably, in S1, the multi-source data collected includes meteorological data, potential evapotranspiration data, annual precipitation data, socio-economic data, target watershed water conservancy project data, water supply and use data, land use type, soil data, DEM data, and boundary vector data.

[0010] Preferably, the meteorological data includes precipitation, daily average temperature, daily maximum temperature, daily minimum temperature, wind speed, humidity, and sunshine duration; Water supply and use data include industrial and agricultural water use, residential water use, ecological water use, surface water supply, groundwater supply, and wastewater reuse; Land use types include cultivated land, forest land, grassland, water area, construction land, and unused land; Soil data includes soil depth, sand, silt, clay, and soil organic matter content.

[0011] Preferably, in S2, the selected multidimensional drought indicators include the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), the Palmer Drought Severity Index (PDSI), the Vegetation Status Index (VCI), and the Standardized Runoff Index (SRI).

[0012] Preferably, in S2, the original drought index matrix is ​​set as follows: In the formula, The length of the time series. Principal component analysis was used to reduce the dimensionality of the standardized multi-dimensional drought index matrix, and the drought impact intensity factor reflecting the characteristics of complex drought was extracted. : ; In the formula, The standardized index matrix; This is the eigenvector corresponding to the largest eigenvalue.

[0013] Preferably, S3 includes the following steps: S31. The drought impact intensity factor is expressed in the form of logarithmic rate of change. Time series of various drought indicators Convert them into rate of change sequences respectively and : ; ; In the formula, Drought impact intensity factor The rate of change sequence, This is a series of rates of change for drought indicators. Represents drought indicators; It refers to time; S32, Based on drought impact intensity factor With the series of changes of each indicator Establish bivariate GARCH(1,1) models to estimate conditional volatility: ; In the formula, This represents the conditional variance, reflecting the intensity of its fluctuations. It is a constant term. Used to measure new information Impact on current fluctuations It represents unpredictable random shocks or unexpected information; β Characterizing the persistence of fluctuations, satisfying α + β Stationarity condition <1; conditional volatility calculated based on parameter estimation results. and standardized residuals ; S33. Based on standardized residuals, the dynamic conditional correlation coefficient (DCC) model is used to estimate the drought impact intensity factor. Compared with the series of changes in various drought indicators The dynamic correlation between them; Dynamic conditional covariance matrix of the DCC model with dynamic conditional correlation coefficient The formula is as follows: ; In the formula, It is the unconditional covariance matrix of the standardized residuals. and These are DCC parameters, representing the impact and duration of the external shock, respectively. Standardized residuals including all variables at time t-1; This represents the transpose of the standardized residual; Based on the estimated DCC parameters, the dynamic correlation coefficient is calculated. : ; In the formula, It is a matrix The Middle Line number The elements in the column, the dynamic correlation coefficient, reflect the time-varying characteristics of the correlation between drought impact factors and drought indicators; S34. Using the Value at Risk (VaR) of the drought impact intensity factor as the threshold for extreme events. c Define the critical point for extreme drought events: when the drought shock factor is below [a certain threshold]. c At that time, it was believed that an extreme drought had occurred, based on the following: ; In the formula, The drought shock factor change rate sequence at a confidence level quantiles below, It is the conditional volatility of the drought intensity shock factor; ; In the formula, The marginal expected loss due to drought consists of two parts: where, This reflects the direct transmission through correlation; This reflects the inherent heterogeneity risk of drought indicators; Let represent the sequence of changes in the i-th drought index.

[0014] Preferably, S4 is as follows: A system of indicators characterizing the water resources system was constructed, and the comprehensive factors of the water resources system were calculated using principal component analysis (PCA). This is used to characterize the performance of the water resource system; The expected loss of drought indicators Comprehensive factors of water resources system Substituting these parameters into the time-varying parameter vector autoregressive model TVP-VAR, it is used to describe the linkage between drought impact intensity and water resource system performance, and all parameters... Both are time-varying: ; In the formula, This is the time-varying intercept vector, representing the time when all lagged variables are zero. and The baseline level; The lag order of the model is determined by the information criterion AIC, which indicates how many periods of the past have influenced the current state. This represents the time-varying coefficient matrix, which quantifies the strength of the influence of past variables on current variables; This is a vector of random error terms, representing external disturbances to the system. exist At any given time, a unit positive systemic drought shock is simulated, that is, an unexpected risk increase of standard deviation is applied to the time-varying parameter vector autoregressive model, and the impact of this drought shock on the future is tracked. Comprehensive factors of water resources system The impact, ; For each time point Each yielded an impulse response curve. Each point on the curve represents a point on the curve. After being subjected to drought for a long time, the water resource system in the first The degree to which the system deviates from its steady state.

[0015] Preferably, S5 is as follows: Constructing absorption strength that reflects the resilience of water resource systems Indicators used to characterize the system's stability through structural buffering and functional stability: ; In the formula, Indicates absorption intensity. The area of ​​the shaded region represents the system loss. This represents the system state before any risk shock occurs. Assume at time... Water resource system variables Systemic risks The impact of the first The response period is The formula is expressed as: ; In the formula, The number of impulse response periods. It represents the maximum absolute value of the impulse response; The recovery time of a water resource system is the average time it takes for the system to absorb disturbances. The recovery time is characterized by a weighted average of the impulse response function values ​​over a period of time, as shown in the following formula: .

[0016] Preferably, in S6, the process of constructing the water resource system resilience measurement function is as follows: Combining the water resource system's resistance to shocks (absorption strength) and its recovery capacity after the shock (recovery time), the following formula is used to comprehensively measure the robustness and resilience of the water resource system in response to disturbances, i.e., the dynamic resilience value: ; In the formula, , This measure indicates the water resource system's tolerance to disturbances; it represents the disturbances caused by shocks that the water resource system fails to absorb, i.e., the unstable portion. ; The disturbance term that causes instability due to the impact; The efficiency factor represents the system's recovery from a shock and is used to describe the decay process of the disturbance.

[0017] Therefore, the present invention employs the above-mentioned dynamic resilience assessment method for water resources based on absorption and recovery dual drivers, and the beneficial effects are as follows: (1) This invention captures time-varying features through the TVP-VAR model and combines the impulse response function to characterize the dynamic recovery trajectory under drought impact. It solves the problem that traditional methods are difficult to reflect the time-series evolution of system resilience, accurately presents the differences in system anti-disturbance and recovery capabilities at different times, and the evaluation results are more in line with actual working conditions.

[0018] (2) This invention integrates DCC-GARCH-MES and TVP-VAR models, which not only accurately captures the clustering and dynamic transmission mechanism of drought risk fluctuations, but also ensures the temporal adaptability of system response simulation. At the same time, through the dual-drive measurement function of "absorption-recovery", the resilience assessment has both physical meaning and quantitative support, which significantly improves the technical reliability.

[0019] (3) This invention can be implemented based on conventional observation data, with clear steps and adjustable parameters, and can be adapted to the characteristics of water resources systems in different watersheds. The evaluation results can accurately identify low-resilience areas and key risk periods, providing a scientific basis for watershed drought disaster prevention and control, water resource optimization and the formulation of adaptive regulation strategies, and helping to improve the risk resistance of water resources systems.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual-drive of the present invention; Figure 2 This is a schematic diagram of the response path of a water resource system to shocks according to an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual-drive of the present invention. Figure 3 This is a schematic diagram of the nonlinear characteristics of system absorption intensity based on impulse response, according to an embodiment of the dynamic resilience assessment method for water resources based on dual absorption and recovery of the present invention. Figure 4 This is a schematic diagram of system resilience analysis based on impulse response function (IRF) in an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual drive of the present invention. (a) shows the system resilience analysis based on impulse response function (IRF), and (b) shows the difference in the centroid of different absorption structures in the water resource system. Figure 5 This is a schematic diagram illustrating the changing trends of the expected marginal loss of a river system in different regions during drought, based on an embodiment of the water resource dynamic resilience assessment method based on absorption and recovery dual-drive of the present invention. (a) is... City, (b) is City, (c) is city; Figure 6 This is a schematic diagram illustrating the changing trends of the expected marginal loss of a river system in different regions during drought, based on an embodiment of the water resource dynamic resilience assessment method based on absorption and recovery dual-drive of the present invention. (a) is... City, (b) is City, (c) is city; Figure 7 This is a schematic diagram of the three-dimensional impact comparison of impulse response in different regions of a river basin, based on an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual-drive of the present invention. (a) is... City, (b) is City, (c) is city; Figure 8 This is a schematic diagram of the three-dimensional impact comparison of impulse response in different regions of a river basin, based on an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual-drive of the present invention. (a) is... City, (b) is City, (c) is city; Figure 9 This is a schematic diagram illustrating the changing trends of absorption intensity in various cities within a river basin, based on an embodiment of the dynamic resilience assessment method for water resources driven by both absorption and recovery according to the present invention. Figure 10 This is a schematic diagram illustrating the trend of recovery time changes in various cities in a river basin, based on an embodiment of the dynamic resilience assessment method for water resources driven by both absorption and recovery according to the present invention. Figure 11 This is a schematic diagram comparing the resilience index and overall resilience of a river basin's water resources system according to an embodiment of the dynamic resilience assessment method for water resources based on absorption and recovery dual-drive of the present invention. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0024] This invention proposes a macro-financial resilience analysis framework. By combining the Time-Varying Parameter-Vector Autoregression (TVP-VAR) model with the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity-Marginal Expected Shortfall (DCC-GARCH-MES) model, it is applied to the field of water resource systems. This constructs a model that integrates shock factor extraction, risk transmission simulation, and a dynamic resilience measurement function with a physical mechanism. Based on the two key characteristics of water resource systems—the intensity of disturbance absorption and the resilience captured by recovery time—this invention constructs a measure function for the resilience of water resource systems with a physical mechanism.

[0025] Absorption intensity quantifies the ability of a water resource system to absorb external shocks from a "scale" perspective, i.e., resistance. Recovery time measures the time required for the water resource system to recover to its pre-shock level from a "speed" perspective, i.e., recoverability. This invention applies a time-varying parameter vector autoregression (TVP-VAR) model and an impulse response function (IRF) to characterize the dynamic response process of a watershed water resource system to drought shocks; based on the impulse response function, a water resource system resilience measurement function model with a physical mechanism of "absorption intensity-recovery time" is constructed. Taking a river basin in a typical semi-arid region of northern China as the research object, based on observational data from 2003 to 2022 and extrapolated data from 2023 to 2032, a complete time series covering 30 years is formed. The system systematically evaluates the response characteristics and recovery capacity of its water resource system under drought shocks, providing theoretical support for regional water resource disaster prevention and adaptive regulation.

[0026] like Figure 1 As shown, the present invention provides a method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery, comprising the following steps: S1. Collect multi-source data from the target watershed to construct a basic data and information database for water resource assessment.

[0027] This invention combines monitoring and statistical data, employing techniques such as data mining, scale integration, data analysis, and multi-source heterogeneous data assimilation. It collects and organizes precipitation data and daily runoff data from 36 hydrological stations in a river basin, totaling nearly 60 years of data, and establishes a basic data and information database. The main data types include meteorological, hydrological, and water supply data, remote sensing images of landforms and underlying surfaces, as well as information on the basin's economic and social development and water network construction. The data are sourced from the Yellow River Conservancy Commission and the "Yellow River Basin Hydrological Yearbook," among others.

[0028] Leveraging the advantages of GIS technology in spatial analysis, forecasting, and decision support, this study stores, analyzes, and manages data, and utilizes it for constructing resilience indicators for water supply systems. Data types and sources are shown in Table 1. Using observational data from 2009–2022 as the basic training set, the Prophet time series forecasting model is employed to predict meteorological, hydrological, and socio-economic indicators for 2023–2032.

[0029] Table 1. Data Types and Sources

[0030] As shown in Table 1, the multi-source data collected in this invention includes meteorological data, potential evapotranspiration data, annual precipitation data, socioeconomic data, target watershed water conservancy project data, water supply and use data, land use types, soil data, DEM data, and boundary vector data. Meteorological data includes precipitation, daily average temperature, daily maximum temperature, daily minimum temperature, wind speed, humidity, and sunshine duration. Water supply and use data includes industrial and agricultural water use, residential water use, ecological water use, surface water supply, groundwater supply, and wastewater reuse. Land use types include cultivated land, forest land, grassland, water bodies, construction land, and unused land. Soil data includes soil depth, sand grains, silt grains, clay grains, and soil organic matter content.

[0031] S2. Multi-dimensional drought indicators are selected, and principal component analysis is used to reduce the dimensionality of these indicators before extracting the drought impact intensity factor. For a watershed, a single drought indicator cannot systematically and comprehensively reflect the intensity of drought impact. Therefore, this invention integrates multiple drought indicators into a single drought impact intensity, aiming to construct a composite indicator that can comprehensively reflect the multi-dimensional drought characteristics of the watershed. The multi-dimensional drought indicators selected in this invention include the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), the Palmer Drought Severity Index (PDSI), the Vegetation State Index (VCI), and the Standardized Runoff Index (SRI). These indicators characterize drought from different perspectives (meteorology, agriculture, hydrology) and different physical processes, each with its own emphasis, complementing each other and jointly constituting a comprehensive drought monitoring impact intensity system. However, the coexistence of multiple indicators also brings information redundancy and interpretation complexity. This invention uses principal component analysis to reduce the dimensionality of the above indicators and extract the watershed drought impact intensity factor.

[0032] Let the original drought index matrix be... In the formula, The length of the time series. Principal component analysis was used to reduce the dimensionality of the standardized multi-dimensional drought index matrix, and the drought impact intensity factor reflecting the characteristics of complex drought was extracted. : ; In the formula, The standardized index matrix; The eigenvector corresponding to the largest eigenvalue retains most of the variance information of the original index and can effectively characterize the intensity of compound drought impact.

[0033] S3. Based on the drought impact intensity factor and various drought indicators, calculate the marginal expected loss of each drought indicator under extreme drought conditions.

[0034] This step integrates the DCC-GARCH-MES model with TVP-VAR and impulse response functions to construct a complete dynamic response framework for water resources systems under drought impact. The GARCH(1,1) model is applied to estimate volatility and residuals, DCC captures dynamic correlations, and MES is calculated based on VaR thresholds to quantify the multivariate transmission mechanism of drought risk. A time-varying parameter system is constructed using the TVP-VAR model and impulse response function (IRF) to simulate the dynamic trajectory of the system state after the impact, providing a theoretical basis for subsequent calculations of the "absorption intensity" and "recovery time" of the water resources system.

[0035] The Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity-Marginal Expected Loss Model (DCC-GARCH-MES) can be used to quantify the risk transmission mechanism within a financial market system under extreme risk events and characterize the marginal contribution of financial institutions to the overall financial system's losses. Given its ability to capture dynamic correlations among multiple variables and the transmission of extreme risks, this model is introduced into water resource system research to characterize the dynamic nonlinear interactions and impact transmission processes among multiple variables during disturbances such as drought. This invention is used to capture the volatility and clustering of drought impacts, characterize and delineate the overall intensity of drought impacts, and effectively measure the marginal expected loss under drought disturbances.

[0036] First, a bivariate GARCH(1,1) model is established to analyze the time-varying correlation between various drought indicators and shock factors. The conditional volatility and standardized residuals of each series are estimated to eliminate their heteroscedasticity. Then, the dynamic correlation between drought shock factors and drought indicators is captured. Finally, a marginal expected loss (MES) model is introduced to assess the expected marginal contribution of each indicator to the overall system loss under extreme drought scenarios, measuring the degree to which drought indicators are expected to deviate from their normal state when extreme drought events occur. The specific steps are as follows: S31. The drought impact intensity factor is expressed in the form of logarithmic rate of change. Time series of various drought indicators Convert them into rate of change sequences respectively and This is done to eliminate trend components in time series data, making the data smoother and highlighting the characteristics of change. ; ; In the formula, Drought impact intensity factor The rate of change sequence, This is a series of rates of change for drought indicators; the specific forms of change for both are shown in the formula above. Represents drought indicators; It refers to time.

[0037] S32, Based on drought impact intensity factor With the series of changes of each indicator We established bivariate GARCH(1,1) models to estimate conditional volatility: ; In the formula, This represents the conditional variance, reflecting the intensity of its fluctuations. It is a constant term. Used to measure new information Impact on current fluctuations It represents unpredictable random shocks or unexpected information; β Characterizing the persistence of fluctuations, satisfying α + β Stationarity condition <1; conditional volatility calculated based on parameter estimation results. and standardized residuals .

[0038] S33. Based on standardized residuals, the dynamic conditional correlation coefficient (DCC) model is used to estimate the drought impact intensity factor. Compared with the series of changes in various drought indicators The dynamic correlation between them. The dynamic conditional correlation coefficient and the dynamic conditional covariance matrix of the DCC model. The formula is as follows: ; In the formula, It is the unconditional covariance matrix of the standardized residuals. and These are DCC parameters, representing the impact and duration of the external shock, respectively. Standardized residuals including all variables at time t-1; This represents the transpose of the standardized residuals; the DCC model allows the correlation coefficient to change over time, thus reflecting the time-varying nature of drought risk transmission mechanisms.

[0039] Based on the estimated DCC parameters, the dynamic correlation coefficient can be calculated. : ; In the formula, It is a matrix The Middle Line number The elements in the column, the dynamic correlation coefficient, reflect the time-varying characteristics of the correlation between drought impact factors and drought indicators.

[0040] S34. To assess the overall systemic loss transmission under extreme drought events, the Value at Risk (VaR) of the drought impact intensity factor is used as the threshold for extreme events. c Define the critical point for extreme drought events: when the drought shock factor falls below a certain threshold. c At that time, it was believed that an extreme drought had occurred, based on the following: ; In the formula, The drought shock factor change rate sequence at a confidence level quantiles below, It is the conditional volatility of the drought intensity shock factor, with a confidence level. Usually 5% is taken: ; In the formula, The marginal expected loss due to drought consists of two parts: where, This reflects the direct transmission through correlation; This reflects the inherent heterogeneity risk of drought indicators; Indicates the first i A sequence of drought index change rates.

[0041] The impulse response function (IRF) is used to reveal the dynamic transmission mechanisms within a multivariate economic system. In a vector autoregressive (VAR) model, the impulse response function represents the dynamic impact path of a one-standard-deviation unexpected shock (the "impulse" IRF) from an endogenous variable on the current and future values ​​of all endogenous variables in the system. However, traditional VAR models assume that the relationships between variables are fixed, and their impulse response functions are also static, making it difficult to capture the time-varying structural characteristics prevalent in real-world economic systems.

[0042] The Time-Varying Parameter Vector Autoregression (TVP-VAR) model transforms the model parameters from "static" to "dynamic," thereby capturing the time-varying nature of the system's intrinsic structure. It represents the changes in the system structure over time under the influence of shocks, allowing the dynamic correlation structure between variables to change over time. This model can more realistically reflect the nonlinear response characteristics of the water resource system under changes in the external environment.

[0043] S4. Based on the time-varying parameter vector autoregression model, using the impulse response function, the dynamic response path of the comprehensive factors of the water resources system in future periods is simulated, specifically as follows: The multi-link network of water resources systems is a complex system. Based on actual data and adhering to the principles of scientific rigor, comprehensiveness, systematicity, and feasibility, an index system characterizing the water resources system is constructed. Principal component analysis (PCA) is then used to calculate the comprehensive factors of the water resources system. This is used to characterize the performance of the water resource system; The expected loss of drought indicators Comprehensive factors of water resources system Substituting these parameters into the time-varying parameter vector autoregressive model TVP-VAR, it is used to describe the linkage between drought impact intensity and water resource system performance, and all parameters... Both are time-varying: ; In the formula, This is the time-varying intercept vector, representing the time when all lagged variables are zero. and The baseline level; The lag order of the model is determined by the information criterion AIC, which indicates how many periods of the past have influenced the current state. This represents the time-varying coefficient matrix, which quantifies the strength of the influence of past variables on current variables; is a vector of random error terms, representing external disturbances to the system.

[0044] like Figure 2 As shown, in At any given time, a unit positive systemic drought shock is simulated, that is, an unexpected risk increase of standard deviation is applied to the time-varying parameter vector autoregressive model, and the impact of this drought shock on the future is tracked. Comprehensive factors of water resources system The impact, .

[0045] For each time point Each yielded an impulse response curve. Each point on this curve represents in After being subjected to drought for a long time, the water resource system in the first The degree of deviation from the system's steady state is measured. The impulse response function is used to characterize the dynamic deviation path of a water resource system after being impacted by drought. The absorption intensity is calculated based on the ratio of the loss area enclosed by the impulse response curve to the system's steady state; the recovery time is determined by the centroid position of the time-weighted absolute value of the impulse response.

[0046] Figure 2 The simulation depicted the path changes of a water resource system after being subjected to a shock. It illustrated the initial state of the water resource system when it remained undisturbed, using... It indicates. In At a certain moment, the system is impacted, causing its trajectory to deviate, and this deviation persists until... After a certain time, the system returns to a steady state. Based on the theory of system shock research, the system's response function to a shock is defined as... In this case, (Shaded area) indicates from arrive The total impact of the shock on the water resource system reflects the breadth of the shock's influence on the water resource system. The total amount of water resources in the system represents the portion that was not affected by the impact. express. The fluctuation range of the region Defined as the number of observations within the sample period. The maximum response value is the core factor affecting absorption intensity (resistance), represented by the maximum absolute value of the impulse response function, reflecting the depth of the impact of the shock on the water resource system. Therefore, and The larger the value, the greater the impact of the shock. The magnitude of the drag is determined by the ratio of these two factors.

[0047] S5. Based on the dynamic response path obtained in S4, calculate the resilience parameters of the water resource system, including absorption intensity and recovery time, specifically: (1) Based on resilience theory, a water resource system is capable of resisting disturbances, absorbing influences, recovering quickly, and adapting to changes when facing external shocks and pressures, thereby maintaining its core structure and functions. When a water resource system is subjected to external shocks, it will temporarily deviate from its original operating trajectory. To quantify the inherent ability of a water resource system to withstand performance degradation when resisting shocks, this invention constructs an absorption strength that reflects the resilience of the water resource system. Indicators used to characterize the system's stability through structural buffering and functional stability: ; In the formula, Indicates absorption intensity. The area of ​​the shaded region represents the system loss. This represents the system state before any risk shock occurs.

[0048] contrast Figure 3 In scenarios A and B, the duration of the effects is both... arrive When there are significant differences in the degree of influence between them, such as or The absorption intensity in scenario A is not necessarily greater than that in scenario B because the relationship between absorption intensity and impact amplitude is non-linear. A larger impact amplitude does not necessarily mean a smaller absorption intensity, which is related to... The absorption intensity is related to the area. Therefore, as a ratio indicator, the absorption intensity can reflect the shock resistance of the water resource system, indicating that the greater the absorption intensity, the greater the shock resistance.

[0049] Assessing the resilience of a water resource system requires the response function of the system variables to external shocks, and the impulse response function provides just such a model. Assume that at time t... Water resource system variables Systemic risks The impact of the first The response period is The formula can be expressed as: ; In the formula, The number of impulse response periods. It represents the maximum absolute value of the impulse response.

[0050] (2) The recovery time of the water resources system is the average time for the water resources system to absorb the disturbance. The longer the duration, the longer it takes for the system to recover to its original level, the more delayed the "center of gravity" of the impact, the greater the uncertainty faced by the water resources system, and the more profound the impact on the system.

[0051] exist Figure 4 In (a), the area of ​​ABCD is expressed as from The impact occurred to Up to a certain point in time, the total amount and area of ​​the accumulated "unrecovery effect" of the shock. Then by and The overall effect determines the recovery performance. The larger the area of ​​ABCD, the longer the system can resist unrecovered shocks, and the worse the overall recovery performance.

[0052] ① Forward center of gravity: This means that in the early stages of the impact, The curve is very steep and drops rapidly, indicating that the system quickly absorbs most of the impact (i.e., (Rapidly decreasing). In this case, even time It is increasing, but due to... It decreased very rapidly, in the early stages of the rectangular area formation. The smaller the impact, the faster it is absorbed, indicating that the system has strong resilience.

[0053] ② The center of gravity is at the back: This means The curve is relatively flat in the initial stage, and the system absorbs the impact very slowly; most of the absorption is completed in the later stage. The center of gravity is closer to the front and Approaching When in position, in the initial stage, The relatively smaller values ​​indicate that the shock is absorbed more quickly. Using a weighted averaging method, longer durations are given greater weight as the absorption center shifts backward, resulting in longer recovery times and indicating relatively weaker recoverability.

[0054] Figure 4 (b) shows a comparison between scenario C and scenario D. It is assumed that both scenarios have the same impact intensity and duration, i.e., the same... Area of ​​influence However, their absorption structures are significantly different. In scenario C, the absorption "center of gravity" is forward, indicating that most of the impact is absorbed in the earlier stages. In scenario D, the absorption "center of gravity" is backward. To capture the differences in absorption structure, this invention uses a time-period weighted average of the impulse response function values ​​to characterize the recovery time, as shown in the following equation: .

[0055] S6. Construct a water resource system resilience measurement function driven by absorption and recovery, calculate the dynamic resilience value of the target watershed water resource system, and evaluate the resilience of the water resource system.

[0056] Toughness is positively correlated with absorption strength; the higher the absorption strength, the higher the resistance to impact and the higher the toughness. Recovery time is used to represent recoverability; toughness is negatively correlated with recovery time; the longer the recovery time, the lower the toughness.

[0057] The specific process of constructing the water resource system resilience measurement function in this invention is as follows: Combining the water resource system's resistance to shocks (absorption strength) and its recovery capacity after the shock (recovery time), the following formula is used to comprehensively measure the robustness and resilience of the water resource system in response to disturbances, i.e., the dynamic resilience value: ; In the formula, , This measure indicates the water resource system's tolerance to disturbances; it represents the disturbances caused by shocks that the water resource system fails to absorb, i.e., the unstable portion. ; The disturbance term that causes instability due to the impact; The efficiency factor represents the system's recovery from a shock and is used to describe the decay process of the disturbance.

[0058] The closer this exponential decay factor is to 1, the higher the recovery efficiency and the faster the disturbance is eliminated; the longer the recovery time, the closer the factor is to 0, indicating a slow and inefficient recovery process. Ideally, a highly resilient water resource system should simultaneously possess high absorption capacity to minimize instability disturbances and short recovery time to maximize recovery efficiency, thus exhibiting excellent robustness and recoverability in the face of disturbances.

[0059] Example 1: Measurement of marginal expected loss under drought shock: Marginal expected loss due to drought As a key indicator for quantifying the impact of different drought intensities on the overall stability of a water resources system, its positive and negative changes reveal the system's vulnerability and resilience to drought shocks. A positive value indicates that the drought shock exacerbates the deviation of the water resources system from its normal state, increasing system vulnerability. A larger positive value indicates greater pressure from the drought shock on the system, leading to decreased system stability. A negative value reflects an enhanced ability of the system to withstand drought shocks, with the impact of the drought shocks gradually being absorbed, and the system returning to a stable equilibrium state. The marginal expected losses of various cities in a river basin under drought shocks are shown below. Figure 5 , Figure 6 As shown.

[0060] according to Figure 4 It can be seen that the risk trajectories in different regions show significant differences and have clear phased characteristics. For example... Figure 5 As shown in (a), The marginal expected loss value of the market has consistently remained low, approaching zero in most years, and tending towards negative values, especially in the forecast period (after 2023), indicating the strongest system stability; such as Figure 5 As shown in (c), The market's marginal expected loss rose most significantly during the historical period (2018-2023), while the amplitude narrowed rapidly during the forecast period; for example... Figure 6 As shown in (b) in the figure, The marginal expected loss in the market fluctuates wildly, and although it has declined during the forecast period, it remains within the medium-risk range; Figure 6 As shown in (c), The market's marginal expected loss had been running at a high level previously, but is showing a clear downward trend in the forecast period; for example... Figure 6 As shown in (a) in the figure, The marginal expected loss of the market is generally at a moderate level. For example... Figure 5 As shown in (b) in the figure, The marginal expected loss showed an increasing trend in the early stage, while it showed a decreasing trend in the forecast period. After the marginal expected loss of the whole basin reached its peak between 2018 and 2023, it generally showed a moderate trend in the forecast period. However, the differences in the level and volatility of marginal expected loss between regions are still significant, revealing the heterogeneity of water resource endowment and system structure in different regional water resource systems.

[0061] Dynamic Response of Water Resource Systems to Drought Shocks: Drought shocks typically trigger negative impulse responses in water resource variables, such as reduced surface runoff and declining groundwater levels, while positive impulse responses activate the system's own regulatory capabilities, such as management measures optimizing resource allocation. The fluctuation range of the impulse response values ​​reflects the system's sensitivity to shocks, and the time-varying parameter structure of the TVP-VAR model can capture the dynamic evolution of this sensitivity. The response process further reveals the duration and impact pattern of the shock, thereby identifying the magnitude of the system's deviation from the drought shock and the speed and characteristics of its recovery to steady state.

[0062] The dynamic response process of a river basin's water resources system to drought shocks is characterized by applying a time-varying parameter vector autoregression (TVP-VAR) model and impulse response function (IRF). Figure 7 , Figure 8 As shown, the three axes of the three-dimensional impulse response plot are defined as follows: the X-axis represents the year time series; the Y-axis represents the period after the impact (0–3 years), used to depict the transmission and attenuation process of the drought impact in the system; and the Z-axis represents the impulse response value, reflecting the fluctuation amplitude of the system state variables affected by the drought risk impact. The blue-green surface in the figure presents the actual response trajectory of the system to the drought impact during the historical observation period (2008–2022), while the blue-red surface shows the evolution path of the system response during the future prediction period (2023–2032).

[0063] The city's water resources system exhibits robust characteristics. Its impulse response surface shows gentle fluctuations throughout the analysis period, with response values ​​controlled between -0.05 and 0.15. This limited fluctuation range indicates that the system has low sensitivity to external drought shocks. Regardless of the historical or forecast period, the system state typically returns to its equilibrium position quickly within 1-2 periods after an impact, demonstrating strong resilience.

[0064] The city's water resources system exhibits highly sensitive transition characteristics. Historical response surface fluctuations are large, ranging from -0.2 to 0.2, reflecting the extreme instability of the early system's response to drought shocks. However, the predicted period's impulse response process is similar to the historical period, but with reduced amplitude, its response amplitude significantly converging to a narrower range of -0.1 to 0.075, and the surface smoothness significantly improved. This transition from violent oscillations to relative stability indicates that the system is evolving from a highly sensitive state towards greater resilience.

[0065] The city's impulse response exhibits strong early-stage buffering capacity followed by gradual stabilization. Historically, the system displays an alternating positive and negative response pattern with a wide amplitude fluctuation range, reflecting its high sensitivity to drought disturbances. During the forecast period, the response amplitude significantly converges, and the surface geometry changes from a high-pitched to a low-lying state, indicating a decrease in the system's sensitivity to external disturbances and a gradual increase in stability.

[0066] The city's water resources system exhibits low sensitivity characteristics. Throughout the analysis period, the response surface remained within a narrow range of -0.20 to 0.16, showing a flat shape and minimal variation. After the first shock event, the system experienced a significant disturbance, and the response values ​​at each period did not converge to the zero axis, indicating poor system resilience to shock disturbances. A high degree of continuity was observed between the historical and forecast periods, with no significant model transitions or structural changes, suggesting that the water resources system will gradually stabilize in the future.

[0067] The city's impulse response process exhibits characteristics of high sensitivity and easy recovery. During the historical period (2016-2020), the system showed concentrated deep negative responses, while the forecast period showed a gradual stabilization trend. The sustained negative response for 1-2 periods after a drought shock indicates that drought shocks will lead to short-term damage to the water resource system's function, and the system lacks an effective buffering mechanism. Furthermore, the system's impulse response process to most drought shocks converges within three periods. As an important industrial and agricultural base in the region, the city has a relatively simple water resource system structure, which makes the system sensitive to disturbances but has a short recovery cycle, thus resulting in strong overall resilience.

[0068] The city's water resources system consistently exhibits volatility. Although the response amplitude is relatively small, the impulse response values ​​are predominantly negative throughout the analysis period. When faced with drought impacts, the system shows significant fluctuations in the later stages of the impact, indicating that while the system initially possesses some resilience, its vulnerability accumulates over time due to the lack of sustained stress resistance and recovery mechanisms. The high similarity between the forecast period and historical periods suggests that without external intervention, this chronic vulnerability may persist, putting the system under pressure from consecutive drought impacts.

[0069] The basin as a whole exhibits sensitive characteristics of large oscillations, with a wide range of comprehensive response amplitudes, alternating positive and negative responses, and a steep and complex surface. This macroscopic instability reflects the incoordination between the various subsystems within the basin, and the conflicting responses between upstream and downstream areas and different regions, resulting in low resilience at the overall level.

[0070] The resilience measurement of a river basin's water resources system: the dynamic changes in absorption intensity and recovery time reflect the complex interaction between natural hydrological processes and human activities, further revealing the response mechanism and evolutionary patterns of the water resources system to drought shocks within the basin. Based on the analysis of the changing trends of absorption intensity in various regions of a river basin from 2003 to 2032, each region exhibits a common characteristic of "fluctuating increase" in both historical and forecast periods, with a clear hierarchical differentiation, such as... Figure 9 As shown. The city's absorption intensity has remained at the highest level, demonstrating a sustained and stable ability to withstand shocks; City and The city is in the second tier, and its changing trends are relatively synchronized; while city, City and The city's water resources have remained at a low level for a long time, indicating a relatively limited system buffering capacity. All regions reached their peak around 2022, after which the predicted values ​​all turned to decline. The main reason is that the predicted drought impact is expected to intensify in the future, which may weaken the overall absorption capacity of the watershed's water resources system to absorb future drought impacts.

[0071] The changes in recovery time exhibit a more complex spatiotemporal pattern, such as Figure 10 As shown, during the historical period (2008-2022), the recovery time in most regions showed a trend of decreasing fluctuations, indicating that the overall speed of system recovery from drought shocks accelerated and resilience improved. Among these, The city consistently had the shortest recovery time, demonstrating its stable recovery capacity; while city, City and The recovery time for cities is relatively long. Entering the forecast period (after 2023), the recovery time for each region shows a further shortening trend, indicating future improvements in the structure of the water resource system and the enhancement of water resource management capabilities.

[0072] The absorption intensity and recovery time indices for each region were calculated as annual averages based on interannual data from 2008 to 2032, thus reflecting their long-term resilience characteristics. Based on this, the absorption intensity (AS) and recovery time (RT) for each region were substituted into the resilience measurement function constructed by formula (12) to calculate the water resource system resilience value for each region. The overall resilience of the watershed was characterized by the arithmetic mean of the resilience values ​​for each region, thereby comprehensively reflecting the system resilience pattern of a river basin under drought impact. The calculation results are as follows: Figure 11 As shown in Table 2.

[0073] Table 2 Comparison of the resilience level of a river basin's water resources system

[0074] An empirical analysis of the resilience of a river basin's water resources system reveals significant spatial differentiation in how different regions cope with drought impacts. Regarding recovery time, the analysis shows that the performance of each city is not simply correlated with its absorption intensity, but rather is closely related to its own water resource endowment and system structure. The city exhibited the highest average absorption intensity (0.621) and a shorter recovery time (1.65 years), demonstrating comprehensive high resilience. As a regional economic development center, its systemic buffering and immediate response capabilities to disaster disturbances were the most outstanding. City (0.530) and The absorption intensity of the city (0.497) is at a moderate level, and its basic functions are easily impaired during droughts. City (0.477) City (0.473) and The absorption intensity of the city (0.430) is relatively weak, indicating that the structure of these systems is more fragile. The system's industrial structure is relatively simple, and its recovery time is the shortest (1.40 years). The city's absorption intensity was low (0.430), and the recovery time was long (1.72 years). The reason is that... The city is a typical resource-based water-scarce region with extremely uneven spatial and temporal distribution, resulting in a complex situation of "nine droughts in ten years, drought every summer, and alternating droughts and floods." This vulnerability makes its water resource system lag behind and persist when facing drought impacts, leading to a prolonged system recovery cycle. The city exhibited the longest average recovery time (1.84 years), indicating that the region's water resource system required a long recovery time from drought shocks. This is related to its geographical location in the middle reaches of a river, where the area faces pressure from reduced upstream water flow while simultaneously needing to ensure downstream water supply, thus doubly constraining the system's recovery capacity. This spatial pattern aligns well with the geographical characteristics of a river basin: the upstream region ( , The water resources system has a stable structure and strong absorption capacity; the middle reaches ( , The recovery period for downstream areas is relatively long; while the recovery period for downstream areas is relatively long. Benefiting from a simple industrial structure and relatively abundant groundwater resources and water conservancy infrastructure, the system has a slightly stronger recovery capacity; As the end of the basin, it is more dependent on unstable upstream water and external water transfer, thus the recovery period is longer.

[0075] Table 2 shows the resilience of the regional water resources system: > > > > > Overall, the resilience of the water resources system in a certain river basin exhibits a gradient characteristic, with the upstream being stronger, the downstream being weaker, and the midstream being relatively weaker. The city serves as a model of high resilience. The city-owned enterprises are rapidly recovering, while , , and They exhibit vulnerability to varying degrees, among which The market performance is characterized by "difficult recovery". , Both cities are classified as "vulnerable and slow to recover." The recovery capacity of the water resources system in a certain river basin has achieved an overall leap in historical period, shifting from a fragile state dependent on slow natural changes to a resilient state dominated by major water conservancy projects and comprehensive management measures. The speed at which the entire system recovers from the impact of drought has significantly accelerated.

[0076] Therefore, this invention adopts the above-mentioned dynamic resilience assessment method for water resources based on absorption and recovery dual-drive, and quantitatively assesses the impulse response characteristics and resilience level of the water resource system under drought impact by extracting drought intensity impact factors, calculating the marginal expected loss of drought, and analyzing the impulse response process of the TVP-VAR model.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery, characterized in that, Includes the following steps: S1. Collect multi-source data from the target watershed and construct a basic data and information database for water resource assessment; S2. Select multi-dimensional drought indicators, and use principal component analysis to reduce the dimensionality of the multi-dimensional drought indicators before extracting the drought impact intensity factor. S3. Based on the drought impact intensity factor and various drought indicators, calculate the marginal expected loss of each drought indicator under extreme drought conditions. S4. Based on the time-varying parameter vector autoregression model, the dynamic response path of the comprehensive factors of the water resources system in future periods is simulated using the impulse response function. S5. Based on the dynamic response path obtained in S4, calculate the resilience parameters of the water resource system, including absorption intensity and recovery time. S6. Construct a water resource system resilience measurement function driven by absorption and recovery, calculate the dynamic resilience value of the target watershed water resource system, and evaluate the resilience of the water resource system.

2. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 1, characterized in that, In S1, the collected multi-source data includes meteorological data, potential evapotranspiration data, annual precipitation data, socio-economic data, target watershed water conservancy project data, water supply and use data, land use type, soil data, DEM data, and boundary vector data.

3. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 2, characterized in that, Meteorological data include precipitation, daily average temperature, daily maximum temperature, daily minimum temperature, wind speed, humidity, and sunshine duration; Water supply and use data include industrial and agricultural water use, residential water use, ecological water use, surface water supply, groundwater supply, and wastewater reuse; Land use types include arable land, forest land, grassland, water area, construction land, and unused land; Soil data includes soil depth, sand, silt, clay, and soil organic matter content.

4. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 1, characterized in that, In S2, the selected multidimensional drought indicators include the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), the Palmer Drought Severity Index (PDSI), the Vegetation Status Index (VCI), and the Standardized Runoff Index (SRI).

5. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 4, characterized in that, In S2, let the original drought index matrix be... In the formula, The length of the time series. Principal component analysis was used to reduce the dimensionality of the standardized multi-dimensional drought index matrix, and the drought impact intensity factor reflecting the characteristics of complex drought was extracted. : ； In the formula, The standardized index matrix; This is the eigenvector corresponding to the largest eigenvalue.

6. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 5, characterized in that, S3 includes the following steps: S31. The drought impact intensity factor is expressed in the form of logarithmic rate of change. Time series of various drought indicators Convert them into rate of change sequences respectively and : ； ； In the formula, Drought impact intensity factor The rate of change sequence, This is a series of rates of change for drought indicators. Represents drought indicators; It refers to time; S32, Based on drought impact intensity factor With the series of changes of each indicator Establish bivariate GARCH(1,1) models to estimate conditional volatility: ； In the formula, This represents the conditional variance, reflecting the intensity of its fluctuations. It is a constant term. Used to measure new information Impact on current fluctuations It represents unpredictable random shocks or unexpected information; β Characterizing the persistence of fluctuations, satisfying α + β Stationarity condition <1; conditional volatility calculated based on parameter estimation results. and standardized residuals ; S33. Based on standardized residuals, the dynamic conditional correlation coefficient (DCC) model is used to estimate the drought impact intensity factor. Compared with the series of changes in various drought indicators The dynamic correlation between them; Dynamic conditional covariance matrix of the DCC model with dynamic conditional correlation coefficient The formula is as follows: ； In the formula, It is the unconditional covariance matrix of the standardized residuals. and These are DCC parameters, representing the impact and duration of the external shock, respectively. Standardized residuals including all variables at time t-1; This represents the transpose of the standardized residual; Based on the estimated DCC parameters, the dynamic correlation coefficient is calculated. : ; In the formula, It is a matrix The Middle Line number The elements in the column, the dynamic correlation coefficient, reflect the time-varying characteristics of the correlation between drought impact factors and drought indicators; S34. Using the Value at Risk (VaR) of the drought impact intensity factor as the threshold for extreme events. c Define the critical point for extreme drought events: when the drought shock factor is below [a certain threshold]. c At that time, it was believed that an extreme drought had occurred, based on the following: ； In the formula, The drought shock factor change rate sequence at a confidence level quantiles below, It is the conditional volatility of the drought intensity shock factor; ； In the formula, The marginal expected loss due to drought consists of two parts: where, This reflects the direct transmission through correlation; This reflects the inherent heterogeneity risk of drought indicators; Let represent the sequence of changes in the i-th drought index.

7. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 6, characterized in that, S4 specifically refers to: A system of indicators characterizing the water resources system was constructed, and the comprehensive factors of the water resources system were calculated using principal component analysis (PCA). This is used to characterize the performance of the water resource system; The expected loss of drought indicators Comprehensive factors of water resources system Substituting these parameters into the time-varying parameter vector autoregressive model TVP-VAR, it is used to describe the linkage between drought impact intensity and water resource system performance, and all parameters... Both are time-varying: ； In the formula, This is the time-varying intercept vector, representing the time when all lagged variables are zero. and The baseline level; The lag order of the model is determined by the information criterion AIC, which indicates how many periods of the past have influenced the current state. This represents the time-varying coefficient matrix, which quantifies the strength of the influence of past variables on current variables; This is a vector of random error terms, representing external disturbances to the system. exist At any given time, a unit positive systemic drought shock is simulated, that is, an unexpected risk increase of standard deviation is applied to the time-varying parameter vector autoregressive model, and the impact of this drought shock on the future is tracked. Comprehensive factors of water resources system The impact, ; For each time point Each yielded an impulse response curve. Each point on the curve represents a point on the curve. After being subjected to drought for a long time, the water resource system in the first The degree to which the system deviates from its steady state.

8. The method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery as described in claim 7, characterized in that, S5 specifically refers to: Constructing absorption strength that reflects the resilience of water resource systems Indicators used to characterize the system's stability through structural buffering and functional stability: ； In the formula, Indicates absorption intensity. The area of ​​the shaded region represents the system loss. This represents the system state before any risk shock occurs. Assume at time... Water resource system variables Systemic risks The impact of the first The response period is The formula is expressed as: ； In the formula, The number of impulse response periods. It represents the maximum absolute value of the impulse response; The recovery time of a water resource system is the average time it takes for the system to absorb disturbances. The recovery time is characterized by a weighted average of the impulse response function values ​​over a period of time, as shown in the following formula: 。 9. A method for assessing the dynamic resilience of water resources based on a dual-driven approach of absorption and recovery, as described in claim 8, is characterized in that... In S6, the specific process of constructing the water resource system resilience measurement function is as follows: Combining the water resource system's resistance to shocks (absorption strength) and its recovery capacity after the shock (recovery time), the following formula is used to comprehensively measure the robustness and resilience of the water resource system in response to disturbances, i.e., the dynamic resilience value: ； In the formula, , This measure indicates the water resource system's tolerance to disturbances; it represents the disturbances caused by shocks that the water resource system fails to absorb, i.e., the unstable portion. ; The disturbance term that causes instability due to the impact; The efficiency factor represents the system's recovery from a shock and is used to describe the decay process of the disturbance.

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