Water resource system toughness evaluation method based on multiple links

Abstract

The invention relates to the field of water resource toughness evaluation, and particularly discloses a multilink-based water resource system toughness evaluation method, which adopts a PCMCI algorithm to quantify the causal connection strength of each element of a water resource complex network, and constructs a regional water resource system multilink network. Analyzing a causal relationship and intensity transfer characteristics among indexes of multiple links under different time lag; based on a causal diagnosis result, describing a causal relationship of multi-link variables of the toughness of the water resource system, performing multi-scale analysis on each link network and toughness, determining a key index and a transfer entropy value of each time-space link, quantifying the influence degree of each sub-link on the toughness of the water resource system, and determining the toughness of the water resource system. Therefore, the tough key link and important conduction ring of the water resource system are disclosed.

Description

Technical Field

[0001] The present invention belongs to the field of water resource evaluation, and specifically relates to a water resource system resilience evaluation method based on multiple links. Background Art

[0002] Under the synergistic influence of the changing environment and the rapid development of the economy and society, water shortages in river basins and the accompanying ecological and environmental problems are becoming increasingly serious, and water security and high-quality development are facing challenges. The resilience of water resource systems emphasizes coexistence with risks, which is more in line with the needs of normalized risk management of water and drought disasters. At the same time, adaptability in responding to global climate change is reflected through the process of enhancing resilience, exploring the resilience factors of adaptive management in natural-social-ecological systems, resisting uncertain risks and the sustainable development of water resource systems.

[0003] An ecosystem is a complex network composed of many biological and environmental factors. A complete water resource system involves more and more complex nodes. Therefore, complex networks, as a representation of organic systems, have a relatively distinct interdisciplinary feature and are widely used in natural sciences, social sciences, and computer science, becoming one of the current research hotspots. Therefore, water resource systems under changing environments are also characterized by complex networks.

[0004] The water resources system can be understood as a relationship network, which is composed of nodes. These nodes maintain the existence of the system as a whole according to certain rules and mutual relationships. In the water resources system, the network structure as a complex system is everywhere, such as the network between meteorology and precipitation, the network between precipitation and runoff, the social network between people, the resource sharing network, the green economy network, the water resources supply and demand network, the game network between water use departments, the dynamic equilibrium network between water demand and water supply, the circulation network between infrastructure and users, etc. The study of complex networks is to examine the properties of large-scale nodes and their connections in the network from a statistical perspective. The differences in these properties mean that different internal structures of the network will lead to different system functions. The complex network is based on nodes and edges. It is composed of many interconnected nodes and edges, and is often represented by graphs. In the real water resources system, each subject or thing (various factors in the water resources system) can be regarded as a node, and the game rules between factors are regarded as the edges connecting the nodes. Therefore, the different subjects in the water resources system constitute a network. In the water resources system, due to factors such as climate change or human activities, changes in certain nodes or edges will affect the development of the entire system. Therefore, the water resources system is consistent with complex network theory.

[0005] Traditional complex networks usually refer to single-layer single-link networks. With the development of network science, people gradually realize that real complex systems all show multi-link or hierarchical structures. Multi-link networks reflect the dual complexity of nodes and topological structures, which makes up for the shortcomings of single-layer single-link networks in describing topological complexity. Multi-layer networks emphasize that in reality, networks are by no means isolated, but rather they influence each other to form an inseparable whole.

[0006] As a research paradigm with evolutionary dynamics and nonlinearity, resilience has attracted scholars to study and explore it, but its research mainly covers various fields such as meteorology, hydrology, economy, society, and ecology. The complexity of the system has led to different focuses on resilience in different disciplines. The concept of resilience has different definitions due to different emphases in different institutions and disciplines. At present, the academic community has not reached a consensus on the definition of resilience. On the one hand, this shows the diversified development of the concept of resilience, and on the other hand, it also highlights that the current academic research on resilience is still in the stage of a hundred schools of thought. The main reason for the inability to unify the definition of resilience is related to the object of resilience, the subject of resilience, the characteristics of resilience, and the resilience process. Therefore, it is urgent to interpret the concept and connotation of water resource system resilience from the perspective of complex water resource systems, and then analyze the characteristics of water resource system resilience, scientifically understand the resilience of water resource systems, and form effective and systematic water security technology, which will provide important scientific and technological support for the high-quality development of river basins, and is also an urgent technological breakthrough in the current river basin development process.

[0007] There are many factors that affect the resilience of water resource systems, including disastrous hydrological and meteorological disturbances, socioeconomic levels, ecological factors, infrastructure, science and technology, governance capabilities, etc. These factors interact with each other and affect the resilience of water resource systems. The multi-link chain effect is obvious. If a risk occurs in a certain link or node, it may be transmitted and spread throughout the entire link, causing an imbalance in water resource supply and demand, aggravating the water crisis in the basin, and thus reducing the resilience of the water resource system. Therefore, it is an important direction for the expansion and innovation of complex water resource systems to clarify the multi-link characteristics of water resource system resilience, analyze the multi-link evolution and development process of water resource system resilience, clarify the inter-feedback chain relationship between complex networks, and reveal the key links of changes in water resource system resilience. Summary of the invention

[0008] In view of the existing defects and problems, the present invention provides a water resource system resilience evaluation method based on multi-links, comprising the following steps:

[0009] S1. Based on regional monitoring data and statistical data, collect system data on meteorology, hydrology, economy, society, ecological environment, and infrastructure related to the resilience of the water resources system in the region, determine the indicators related to the resilience of the water resources system under each system, systematically classify the indicators related to the resilience of the water resources system in each system, and build a multi-link water resources system resilience indicator system;

[0010] S2. Calculate the causal connection strength of each sub-link in the multi-link based on the PCMCI algorithm, delete the duplicate links and loops in the multi-link network, and construct a resilient multi-link network of the water resources system containing multiple sub-links;

[0011] S3. Rank the indicators in each sub-link of the multi-link network of water resource system resilience according to their importance, and select the top three indicators as the key indicators of each sub-link;

[0012] S4, reducing the dimension of the key indicators of each sub-link to obtain the time series of each sub-link after dimension reduction;

[0013] S5. Calculate the resilience of regional water resources system based on the water resources resilience logistic regression model;

[0014] S6. Calculate the multi-scale transfer entropy of each sub-link to the resilience of the water resource system to quantify the impact of each sub-link on the resilience of the water resource system.

[0015] In the above-mentioned multi-link-based water resource system resilience evaluation method, the sub-links in step S2 include a meteorological and hydrological link, a socio-economic link, and an engineering regulation link. The indicators in the meteorological and hydrological link include temperature, sunshine duration, annual precipitation, total water resources, surface water resources, groundwater resources, and drought severity; the indicators in the socio-economic link include permanent population, urbanization level, GDP, industrial added value, agricultural irrigation area, proportion of primary industry, proportion of secondary industry, proportion of tertiary industry, water consumption per 10,000 yuan of GDP, and average water consumption per mu of agricultural irrigation; the indicators in the engineering regulation link include water storage, water diversion, water lifting, unconventional water, groundwater supply, industrial and agricultural water use, domestic water use, and ecological water use.

[0016] The above-mentioned multi-link-based water resource system resilience evaluation method, in step S2, calculates the causal connection strength of each main sub-link, including the following steps:

[0017] (1) Constructing directed edges of time series: Constructing a parent node set for each variable According to the absolute test statistic, Sort the elements in the , and select the p elements with the largest statistical test as the condition set S; the condition set S is iteratively increased from the empty set, and removed China Independent Elements, forming a partial connectivity graph, for all time series nodes They are all connected with directed edges to ensure that the time lag order τ>0 to obtain a causal direction that conforms to the time sequence;

[0018] (2) Perform conditional independence tests to remove unnecessary edges, remove homologous edges based on the temporal consistency assumption, and detect and Independence of τ>0 is tested sequentially. The test condition is and To determine whether independence exists,

[0019]

[0020] Where: is the causal parent of the variable Set; suppose there are two time series MetX1 and MetX2, Then there is a causal relationship Right now in Indicates that conditional independence is not met;

[0021] If conditional independence exists, then there is no direct causal relationship between the two variables under a given set of conditions, and the edge between the variables is removed;

[0022] If conditional independence does not exist, the two variables are correlated under a given set of conditions, and the edge is retained to indicate that there may be a causal relationship between the two variables.

[0023] In the above-mentioned multi-link-based water resource system resilience evaluation method, water resource resilience is calculated based on a multivariate logistic regression model in step S5.

[0024]

[0025] 0≤COR≤1

[0026] Where: F(x1), F(x2), F(x3) are the closeness levels of the three system dimensions; α, β1, β2, β3 are the parameters of the regression model; COR is the system resilience level.

[0027] In the above multi-link-based water resource system resilience evaluation method, in step S6, the multi-scale transfer entropy of each sub-link to the water resource resilience is calculated.

[0028]

[0029] Where: Y is the sequence of sub-links, X is the sequence of water resource system resilience COR, represents the conditional entropy of Xt given the past state of X; For X t Conditional entropy given known past states of X and Y; is the transfer entropy from the sublink to the COR at scale N;

[0030] The multi-scale transfer entropy of the sub-link to the resilience COR of the water resources system can be expressed as:

[0031]

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The method of the present invention quantifies the causal connection strength of the complex water resource dynamic system network by using the PCMCI algorithm, and constructs a multi-link network of the water resource system in the basin in combination with the hydraulic connection between regions; based on the complex multi-link network theory of the water resource system, the resilience of the water resource system is comprehensively analyzed and interpreted, and based on the PCMCI causal diagnosis results, the causal relationship of the multi-link variables of the water resource system resilience is described, and each link network and resilience are analyzed at a multi-scale, showing the characteristic information of each sub-link at different spatiotemporal scales; the transfer entropy value at each spatiotemporal scale is determined, and the amount of information transmission and its influence of each sub-link change on resilience are quantified, and then the key links in the resilience of the water resource system are analyzed, so as to comprehensively characterize the resilience of the water resource system and provide theoretical support for the security of water resources in the basin.

[0034] 2. The method of the present invention can determine the sub-link with the greatest impact on water resource resilience through multiple links, find the key links that affect water resource resilience, and accurately analyze the indicators in each link that have a greater impact on the resilience of the water resource system, providing a theoretical basis for regulating water resource resilience.

[0035] 3. The method of the present invention selects the corresponding optimal adaptability relationship in each link model according to the strength of causal association and the size of significance, and quantitatively evaluates each indicator in each link, which is conducive to analyzing key links and important transmission links.

[0036] 4. The water resource system characterization based on the multi-link complex network theory and the water resource adaptive management system considering the combined influence of climate change and human activities will provide a scientific basis for my country's water resource allocation, planning, regulation and response to future water resource shortages and distribution issues. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a multi-link network diagram of the water resources system.

[0038] Figure 2 The multi-link characteristics of water resource system resilience.

[0039] Figure 3Multi-link variable relationship diagram of water resource system resilience.

[0040] Figure 4 This is the time series and process diagram of the MetLink indicators in the Fenhe River Basin.

[0041] Figure 5 This is the time series and process diagram of the SocLink indicator of the Fenhe River Basin economic and social link.

[0042] Figure 6 This is the time series and process diagram of the WatLink indicators of the Fenhe River Basin Engineering Control Link.

[0043] Figure 7 This is the time series and process diagram of the ResLink indicator of the resilience multi-link network of the Fenhe River Basin water resources system. DETAILED DESCRIPTION

[0044] Example 1: To further illustrate the method of the present invention, this example takes the Fenhe River, the second largest tributary of the Yellow River, as the research object. The Fenhe River Basin has prominent problems such as water resources, water environment, water ecology, and water disasters. It is an important water source and ecological protection area in Shanxi Province and even the whole country, and a key basin for flood control and ecological restoration in Shanxi Province. Due to the influence of climate change and human activities, the basin has formed a complex network system in which many factors such as meteorology, hydrology, ecology, society, and economy are closely linked and mutually influenced in the process of "nature-society-ecology cycle".

[0045] First, collect and organize the data of the Fenhe River Basin in the past 60 years and establish a basic data and information database. The main data types include meteorological, hydrological, water supply data, remote sensing images of landforms and underlying surfaces, basin economic and social, water network construction information, etc. Take advantage of GIS technology in spatial analysis, prediction and decision-making support to store, analyze and manage data, and use it to construct water supply resource system resilience indicators.

[0046] The multi-link network of water resource system resilience is a complex system. Based on the actual data and the principles of scientificity, comprehensiveness, systematicity and feasibility, the indicators of each link in the multi-link network of water resource system resilience are systematically classified and analyzed, and the relevant indicators of each link network system are selected. This embodiment determines the three main links that constitute the multi-link network of water resource system resilience in the Fenhe River Basin, namely: the hydrological and meteorological link MetLink, the economic and social link SocLink, and the engineering control link WatLink. The water resource system resilience indicator system is shown in Table 1 below.

[0047] Table 1 Multi-link water resources system resilience index system

[0048]

[0049]

[0050] The PCMCI algorithm is used to analyze the causal connection strength of multi-link complex networks, as follows.

[0051] First, construct the directed edges of the time series and construct the parent node set for each variable According to the absolute test statistic, Sort the elements in the , and select the p elements with the largest statistical test as the condition set S; the condition set S is iteratively increased from the empty set, and removed China Independent Elements, forming a partial connectivity graph, for all time series nodes They are all connected by directed edges. As long as the time lag order τ>0 is guaranteed, a causal direction that conforms to the time sequence can be obtained;

[0052] Secondly, we perform conditional independence tests to remove unnecessary edges, remove homologous edges based on the temporal consistency hypothesis, and detect and Independence of τ>0 is tested sequentially. The test condition is and To determine whether independence exists,

[0053]

[0054] Where: is the causal parent of the variable Set; suppose there are two time series MetX1 and MetX2, Then there is a causal relationship Right now in Indicates that conditional independence is not met;

[0055] If conditional independence exists, then there is no direct causal relationship between the two variables under a given set of conditions, and the edge between the variables is removed;

[0056] If conditional independence does not exist, the two variables are correlated under a given set of conditions, and the edge is retained to indicate that there may be a causal relationship between the two variables.

[0057] This embodiment uses the PCMCI algorithm to quantify the causal connection strength of the complex water resources power system network, deletes duplicate links and loops in the network, combines the hydraulic connections between regions, and constructs a multi-link network of meteorology, hydrology, economy, society, ecology, infrastructure, science and technology, and governance capacity of the basin water resources system, such as Figure 1 shown.

[0058] The multi-link network of water resource system resilience is a multi-dimensional interweaving, dynamic transmission feature and complex nonlinear relationship. According to the function of water resource complex system, the multi-link network SLink is divided into meteorological and hydrological link MetLink (including meteorological and hydrological elements), economic and social link SocLink (including economic, social, life, ecological, industrial, agricultural and other elements), and water network link WatLink (including infrastructure, science and technology, governance capacity and other elements). These are the driving factors and boundary conditions that cause the resilience of water resource system to change at different time and space scales. The multi-link characteristics and multi-link variable relationships of water resource system resilience are as follows: Figure 2 and Figure 3 shown.

[0059] This example explores the causal link strength of each indicator under different time lags (the maximum time lag length maxlag is set to 5). The significance level of PCMCI is set to 0.05 (ie pc_alpha = 0.05). The causal link strength results of different links in the Fenhe River Basin are as follows.

[0060] (1) Causal connection strength of the meteorological-hydrological link

[0061] The meteorological and hydrological link MetLink has the most prominent one-year lag and causal relationship. The calculation results are ranked according to the importance of indicators. The indicator significance and causal connection strength of the meteorological and hydrological link are shown in Table 2 and Figure 4 .

[0062] Table 2 Significance of indicators and causal link strength of MetLink

[0063]

[0064] As shown in Table 2, the importance indicators of the meteorological and hydrological link MetLink are ranked in order: M4 total water resources > M3 annual precipitation > M7 water inflow > M5 surface water resources > M6 groundwater resources > M2 sunshine duration > M1 temperature. Among them, M4 total water resources ranks first, indicating that the total water resources have the most significant impact on the hydrological and meteorological link, and the total water resources are the most critical indicator for measuring the stability of water resources in a river basin; M3 annual precipitation follows closely, and annual precipitation is one of the important sources of water resources. The prediction and analysis of precipitation helps to assess the supply and demand of water resources, provide a basis for the reasonable allocation and scheduling of water resources, and play a leading role in the entire link; M7 water inflow ranks third, which reflects the water supply status of rivers, lakes, reservoirs and other water bodies in a specific time period, and shows the change of water resources in the river basin from the side.

[0065] M2 sunshine duration has a significant positive impact on multiple indicators (such as M3 annual precipitation, M4 total water resources and M5 surface water resources) under a lagged state. Sunshine time directly affects evaporation, transpiration and surface water circulation. Especially in seasonal changes and climate patterns, longer sunshine duration will promote the accumulation of water vapor in the atmosphere, which will then form precipitation, affect the dynamic balance of surface and groundwater, and accelerate the circulation of water resources. Therefore, it promotes the growth of total water resources and surface water resources in a certain lagged period. M7 drought degree is a key negative indicator. It has a significant inhibitory effect on multiple indicators (such as M3 annual precipitation and M4 total water resources). A strong drought degree indicates that the less precipitation, the less total water resources. There is a strong positive relationship between the M6 ​​groundwater resources and the M5 surface water resources. Surface water and groundwater are closely connected through the hydrological cycle. Part of the precipitation forms surface runoff; the other part will seep into the ground and become the source of groundwater recharge. Therefore, the circulation of surface water and groundwater is interrelated and changes in the same direction. The M6 ​​groundwater resources are also affected by its past values, showing continuity in time. The decrease or increase of groundwater in the past directly affects the current groundwater reserves. If groundwater was over-exploited in the past, then the current groundwater resources will be relatively scarce. The M3 annual precipitation and the M4 total water resources show a trend of mutual promotion. With the increase of annual precipitation, the total water resources also increase.

[0066] Through the analysis of the causal relationship between various hydrological and meteorological indicators, it can be seen that the various elements in the water resources system are interdependent and are jointly affected by natural conditions and human activities. Natural factors such as sunshine duration, precipitation, drought degree, and the interaction between surface water and groundwater determine the dynamic changes of water resources. The complex causal relationship between these indicators constitutes the basic framework of the hydrological and meteorological system, which jointly affects the operation and changes of the link.

[0067] (2) Causal connection strength of socioeconomic links

[0068] The significance and causal relationship of the economic and social link SocLink with a lag of five years are the most prominent. The calculation results are ranked according to the importance of the indicators, as shown in Table 3 and Figure 5 shown.

[0069] Table 3 Significance of indicators and causal connection strength of SocLink

[0070]

[0071] From Table 3 and Figure 5It can be seen that the importance indicators of the economic and social link SocLink are ranked in order: S7 secondary industry share > S2 urbanization level > S1 permanent population > S4 industrial added value > S3 GDP > S8 tertiary industry share > S9 water consumption per 10,000 yuan of GDP > S5 agricultural irrigation area > S6 primary industry share > S10 agricultural irrigation per mu water consumption. Among them, S7 secondary industry share ranks first. As an important part of the national economy, the proportion of the secondary industry directly affects the speed and quality of economic growth. In the process of industrialization, the development of the secondary industry is one of the main driving forces for economic growth. S2 urbanization level ranks second. The improvement of urbanization level has become an important engine for promoting economic growth. The optimization of industrial structure has enabled the rapid development of the secondary and tertiary industries. S1 permanent population ranks third. With the development of social economy, urbanization has promoted the redistribution of urban and rural populations and increased the number of permanent residents, which is conducive to promoting economic development.

[0072] The proportion of secondary industry in S7 is significantly correlated with the proportion of primary industry in S6, urbanization level in S2, permanent population in S1, GDP in S3, and industrial added value in S4 in multiple lag periods, especially with the proportion of primary industry in S6 after 4 periods. This indicates that the decline in the proportion of primary industry in S6 will lead to an increase in the proportion of secondary industry in S7. With the rapid development of the economy and society, the limited water resources have more input into secondary industry than the water supply of primary agriculture. This change in the supply and demand structure has led to a gradual decline in the proportion of primary industry in the national economy, while the proportion of secondary industry has increased accordingly. The proportion of secondary industry in S7 has an interactive relationship with multiple indicators such as permanent population in S1, urbanization level in S2, and industrial added value in S4 without lag period, indicating that the proportion of secondary industry in S7 has control and influence on resource allocation or strategy adjustment in the complex network of economic and social links.

[0073] The urbanization level of S2 shows a negative correlation with the proportion of primary industry in S6 after lag of 4 periods, which indicates that the increase of urbanization level of S2 leads to the decrease of the proportion of primary industry in S6. With economic development, the industrial structure will gradually shift from the primary industry dominated by agriculture to the secondary and tertiary industries dominated by industry and services. This shift is an important symbol of economic modernization and an important driving force in the process of urbanization. The industrial added value of S4 shows a positive correlation with the urbanization level of S2 after lag of 2 periods. The historical changes of the urbanization level of S2 have a direct impact on the industrial added value of S4. The urbanization level of S2 is also affected by indicators such as the permanent population of S1 and the proportion of secondary industry in S7, especially the interaction without lag period, which shows that the urbanization level of S2 has a high degree of interdependence with these indicators at the current point in time. The increase of permanent population and the proportion of secondary industry promotes the improvement of urbanization level to a certain extent.

[0074] The permanent population of S1 is negatively affected by the proportion of primary industry in S6 with a lag of 4 periods, that is, the early decline in the proportion of primary industry in S6 will lead to an increase in the permanent population of S1. With the advancement of industrialization and urbanization, the proportion of primary industry has declined while the secondary and tertiary industries have developed rapidly. This phenomenon reflects the adjustment of the economic structure. Population mobility and migration have promoted the development of cities and further promoted the increase of permanent population. The strongest connection is between the permanent population of S1 and the lagged S3GDP of 2 periods, indicating that the historical value of S3GDP has a significant positive impact on the permanent population of S1. The higher the regional GDP and the more prosperous the economic development, the greater the probability of the floating population turning into permanent population.

[0075] There is a strong causal relationship between the complex network of economic and social links, and most indicators have a long-term direct or indirect impact on the operation of the economy and society. Among them, the increase in GDP, industrial added value, urbanization level and the decline in the proportion of primary industry are the main driving factors of this link. The lagged effect of economic growth (GDP) and the increase in the proportion of secondary industry reflect the typical characteristics of developing countries or regions in the process of industrialization and urbanization. The interaction between these indicators reveals the complex relationship between industry and agriculture, urbanization and population migration, and reflects the important influencing characteristics in modern economic development.

[0076] (3) Causal connection strength of engineering control links

[0077] The significance and causal relationship of the two-year lag of the engineering control link WatLink are the most prominent. The calculation results are ranked according to the importance of the indicators, as shown in Table 4 and Figure 6 shown.

[0078] Table 4 Significance of indicators and causal connection strength of WatLink engineering control link

[0079]

[0080]

[0081] From Table 4 and Figure 6It can be seen that the importance index of the engineering control link WatLink is ranked as follows: E8 domestic water use > E6 groundwater supply > E4 water extraction > E5 unconventional water > E3 water diversion > E9 ecological water use > E2 water storage > E1 water conservancy investment > E7 industrial and agricultural water use. Among them, E8 domestic water use ranks first in the link. The demand for domestic water directly affects the allocation of water resources. Through reasonable engineering control measures, such as the construction of reservoirs and pumping stations, water resources can be reasonably allocated in time and space to ensure a stable supply of domestic water. E6 groundwater supply ranks second. The stability and sustainability of groundwater directly affect the stability of the water supply system. Engineering control needs to ensure the reasonable exploitation and utilization of groundwater resources to maintain the long-term stable operation of the water supply system. E4 water extraction ranks third. Through the construction and operation of water extraction facilities, the balance of water resources in the ecosystem can be maintained, and ecological problems such as groundwater level decline and wetland shrinkage caused by over-exploitation can be avoided. Water resources can be allocated across river basins and regions, effectively alleviating the problem of uneven distribution of water resources and meeting various needs such as agricultural irrigation, urban water supply, and industrial water use.

[0082] E8 domestic water use plays a leading role in the system, especially its significant lagged impact on E4 water extraction, E5 unconventional water and E6 groundwater supply, affecting the future status of other indicators, mainly reflecting its negative regulatory effect on other indicators in the system.

[0083] The hysteresis factor of E6 groundwater supply has a significant positive impact on E4 water extraction, and the current state of E8 domestic water has a certain positive impact on E4 water extraction, and the two have a trend of change in the same direction. The future state of E4 water extraction is driven by these two indicators, indicating that they jointly affect the evolution of E4 water extraction in the system. The amount of water extraction is regulated by domestic water and groundwater supply. When the latter is insufficient, corresponding water extraction measures need to be implemented to ensure the rational allocation of water resources.

[0084] E2 water storage has a strong self-feedback mechanism for itself, which is an important means of water resource management. It ensures the stable operation of the water storage system and the safety of water supply through regulation and management. Especially in the lag 2 period, it shows a significant negative correlation, and there is a self-regulation effect. When the water storage decreases, it will be regulated accordingly through the regulation project to avoid problems such as imbalance between supply and demand. The negative correlation between E2 water storage and E3 water diversion shows that the current value of E3 water diversion has an inhibitory effect on E2 water storage. The increase in water diversion will lead to a decrease in water storage, and there is an obvious mutual restriction relationship between the two.

[0085] The self-feedback mechanism of water storage and the mutual constraints with water diversion in the engineering control link reflect the cooperation and regulation between different water sources in water resources management. Water storage measures have a significant impact on domestic water use, groundwater supply and water extraction in engineering control by optimizing the water supply structure and improving the utilization rate of water resources, ensuring the stable supply and effective management of water resources at different times. In an effective water resources management system, the dynamic balance between water storage and water diversion is the key to ensuring the sustainable use of water resources. The driving role of domestic water use emphasizes the traction effect of residents' water demand on the entire system. It has a significant impact on multiple indicators, indicating that domestic water demand is an important guiding factor for system changes. Solving this problem is the primary task of stabilizing the engineering control link.

[0086] (4) Causal connection strength of multi-link complex networks

[0087] The top three indicators (9 in total) of each link in the multi-link network of water resource system resilience were analyzed to explore the causal relationship between key indicators. The one-year lagged significance and causal relationship were the most prominent. The calculation results were ranked according to the importance of the indicators, as shown in Table 5 and Figure 4 shown.

[0088] Table 5 Significance of important indicators and causal connection strength of the multi-chain network ResLink of water resource system resilience

[0089]

[0090] From Table 5 and Figure 7 It can be seen that the importance indicators of the water resource system resilience multi-chain network ResLink are ranked in the following order: S7 secondary industry proportion > M3 annual precipitation > M4 total water resources > E4 water extraction > M7 water inflow level > S2 urbanization level > S1 permanent population > E8 domestic water use > E6 groundwater supply.

[0091] S7 The proportion of secondary industry is the variable with the strongest connection strength in the complex network of the entire water resources system resilience, indicating that it is the core node in the entire causal chain and has a causal relationship with almost all important variables. In the secondary industry, especially industrial manufacturing and mining, a large amount of water resources are required in the production process. With the increase in the proportion of secondary industry, the scale of production in the industry has expanded, which directly leads to an increase in water resource consumption. Water resources management and regulation should be rationally planned to avoid reducing the resilience of the basin water resources system.

[0092] The relationship between the proportion of secondary industry in S7 and domestic water use in E8 is the strongest in the first lag period. In general, the allocation of water resources will be affected by the water demand of different users. When the proportion of secondary industry increases, it means that the demand for water resources in these industries will also increase accordingly, resulting in a relative decrease in the portion of water resources allocated to domestic water use in the total limited amount. In addition, the relationship with the annual precipitation in M3 is very significant at the current time point and in the first lag period. When the precipitation in the current year is abundant, the industrial water supply and water resource scheduling in the current year and the next year are relatively sufficient, which promotes the growth of the secondary industry.

[0093] M3 annual precipitation has a large number of links and is closely related to variables such as M4 total water resources and E4 water withdrawal. The degree of precipitation surplus and shortage is an important factor affecting the amount of water resources in the basin, which is also the basis for deciding whether to implement water withdrawal measures and realize water resource scheduling. Among them, annual precipitation is not only affected by the natural environment, but also indirectly affected by socio-economic factors such as S7 secondary industry proportion. For example, a high proportion of secondary industry may affect the total amount and distribution of precipitation by changing the surface runoff and groundwater recharge pattern.

[0094] The total amount of water resources in M4 also has a significant causal relationship with variables such as the proportion of secondary industry in S7 and the degree of water inflow in M7. The former has a trend of change in the same direction. The abundance of water resources will promote the development speed of the secondary industry. The latter has a negative trend of change, which is manifested in promoting the growth of total water resources during flood season and inhibiting it during dry season. It also changes in the same direction as the groundwater supply in E6. Water resources replenish groundwater through surface precipitation seepage. When the total amount of water resources decreases, the amount of water extraction in E4 will increase accordingly to ensure the balance between supply and demand. In addition, it shows a negative change with the urbanization level in S2. The higher the urbanization level, the less groundwater extraction should be, reflecting the scientific, coordinated and sustainable water resources system formed with social development.

[0095] For the key indicator analysis of the multi-link network of water resource system resilience, the proportion of secondary industry, annual precipitation and total water resources are all important factors affecting the resilience of water resource systems. In order to improve the resilience of water resource systems, it is necessary to start from multiple aspects, including optimizing the industrial structure, adjusting the proportion of secondary industry and coordinating with water resource management policies, especially in areas with limited industrial development and water resources, the demand for total water resources should be comprehensively considered, and the amount of resources should be reasonably planned and dispatched to maintain and steadily improve the resilience level of water resource systems in the basin. At the same time, it is also necessary to pay close attention to climate change, such as the changing trends of external environmental factors such as annual precipitation, so as to take timely engineering measures to deal with potential water resource system problems.

[0096] Since the resilience of water resource system is a complex multi-level system that is closely connected and mutually influenced in the evolution and development of multi-link network, in order to quantitatively study the nonlinear characteristics of the impact of multi-temporal and spatial interactions of multi-links of water resource system on resilience, this paper proposes a multi-scale transfer entropy method based on the transfer entropy algorithm, which targets the key links and important transmission links of the change of resilience of water resource system, analyzes the process and effect of key links on the change of system resilience, and quantitatively characterizes the degree of influence of key links on the resilience of water resource system.

[0097] First, the resilience of the regional water resource system was calculated based on the Logistic regression model of water resource resilience. For details, see "Analysis of the Evolution of Water Resource System Resilience in River Basins and the Effect of Water Network Construction", Water Resources Protection, and the method published by Wan Fang, Wang Yu, Wang Chenghao, etc. to calculate the water resource resilience of the Fenhe River Basin;

[0098] The regression model based on multivariate logistic is:

[0099]

[0100] 0≤COR≤1

[0101] Where: F(x1), F(x2), F(x3) are the closeness levels of the three links; α, β1, β2, β3 are the parameters of the regression model; COR is the system resilience level.

[0102] Then, each link network is multi-scaled to display the information of each sub-link at different time and space scales;

[0103] Finally, the transfer entropy value of each sub-link at different time and space scales is determined, indicating the amount of information transmitted by the changes in each sub-link on resilience, that is, the degree of impact, thereby analyzing the key links of the resilience of the water resources system.

[0104] The calculation of transfer entropy requires discretization of the time series and estimation of the conditional probability density function. In practice, a larger data set is required to obtain more accurate calculation results. This embodiment uses the k-NN method to more effectively capture local data structures in high-dimensional space, does not rely on specific probability distribution assumptions, is applicable to the characteristics of various complex and nonlinear systems, and applies the nearest neighbor estimator to solve this problem and improve the accuracy of the calculation.

[0105] First, choose the embedding dimension L and the delay time L Y , reconstruct the phase space of the two time series X and Y and construct an embedding vector. For each time point t, find Z in the joint embedding space Z t The k nearest neighbors of a region are selected and the maximum distance among these neighbors is recorded as ε(t). This distance represents the scale of the local area and is used for subsequent neighbor counting.

[0106] This embodiment uses the Euclidean distance to calculate ε(t),

[0107]

[0108] Where: x i and i are the values ​​of two samples x and y on the i-th feature, and n is the total number of features.

[0109] The transfer entropy of a discrete process can be expanded into the difference of conditional entropies,

[0110]

[0111] Where: Indicates that X is known in the past state t The conditional entropy of Indicates that X is known when X and Y are known. t The conditional entropy of .

[0112] Based on the k-NN method, the conditional entropy estimation formula is:

[0113]

[0114] Where: ψ is the Digamma function (logarithmic derivative of the Γ function); N is the total number of samples; n i (t) is the number of neighbors whose distance to the i-th sample point does not exceed ε(t) in the conditional space.

[0115] Substituting the conditional entropy estimation formula into the transfer entropy definition formula will give the transfer entropy value.

[0116] Construct the multi-scale transfer entropy of each link network (MetLink, SocLink, WatLink) to the resilience COR of the water resource system (taking MetLink as an example) TE N MetLink→COR , the formula is as follows:

[0117]

[0118] Where: Y is the sequence of meteorological and hydrological links MetLink; X is the sequence of water resource system resilience COR; Represents X t Conditional entropy given past states of X; For X t Conditional entropy given the past states of X and Y; TE N MetLink→COR is the transfer entropy from MetLink to COR at scale N.

[0119] The multi-scale transfer entropy from the meteorological and hydrological link MetLink to the water resources system resilience COR can be expressed as:

[0120]

[0121] Similarly, the multi-scale transfer entropy DHTE of the economic and social link (SocLink) and the water network link (WatLink) to the water resource resilience COR is calculated N SocLink→COR , Based on the transfer entropy of each sub-link, the key links and important transmission links that affect the resilience of the water resources system are identified.

[0122] This embodiment uses SPSS to perform dimensionality reduction analysis on the main indicators of the three links of the Fenhe River Basin multi-link network from 2010 to 2022 (the first three in order of importance), synthesizes and calculates the main indicators of the links, and the results are shown in Table 6 below.

[0123] Table 6 Dimensionality reduction analysis results of main indicators of each link

[0124]

[0125] The time series of each link after dimensionality reduction is calculated, and the transfer entropy between the time series of each link and the resilience of the water resources system in the Fenhe River Basin from 2010 to 2022 is calculated respectively to quantify the transfer entropy of each sub-link change on the resilience of the water resources system and its degree of influence.

[0126] It can be calculated by cross-validation method that the optimal k value for transfer entropy calculation is 1. Substitute it into the calculation and the results are shown in Table 7.

[0127] Table 7 Transfer entropy of each link to the resilience network of water resources system

[0128]

[0129] From the calculation results in Table 7, it can be seen that the transfer entropies of the hydrometeorological link MetLink and the socioeconomic link SocLink are very close, indicating that they have similar strengths in terms of information transmission and influence on the resilience of the water resources system; the transfer entropy of the engineering regulation link WatLink is 191.831, which is significantly higher than the other two links.

[0130] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-link-based water resource system resilience evaluation method, characterized by: The following steps are involved: S1. Based on regional monitoring data and statistical data, collect system data on meteorology, hydrology, economy, society, ecological environment, and infrastructure related to the resilience of the water resources system in the region, determine the indicators related to the resilience of the water resources system under each system, systematically classify the indicators related to the resilience of the water resources system in each system, and build a multi-link water resources system resilience indicator system; S2. Calculate the causal connection strength of each sub-link in the multi-link based on the PCMCI algorithm, delete the duplicate links and loops in the multi-link network, and construct a resilient multi-link network of the water resources system containing multiple sub-links; S3. Rank the indicators in each sub-link of the multi-link network of water resource system resilience according to their importance, and select the top three indicators as the key indicators of each sub-link; S4, reducing the dimension of the key indicators of each sub-link to obtain the time series of each sub-link after dimension reduction; S5. Calculate the resilience of regional water resources system based on the water resources resilience logistic regression model; S6. Calculate the transfer entropy of each sub-link time series to the resilience of the water resource system to quantify the impact of each sub-link on the resilience of the water resource system.

2. The multi-link-based water resource system resilience evaluation method according to claim 1 is characterized by: The sub-links in step S2 include a meteorological and hydrological link, a socio-economic link, and an engineering regulation link. The indicators in the meteorological and hydrological link include temperature, sunshine duration, annual precipitation, total water resources, surface water resources, groundwater resources, and drought severity; the indicators in the socio-economic link include permanent population, urbanization level, GDP, industrial added value, agricultural irrigation area, proportion of primary industry, proportion of secondary industry, proportion of tertiary industry, water consumption per 10,000 yuan of GDP, and average water consumption per mu of agricultural irrigation; the indicators in the engineering regulation link include water storage, water diversion, water lifting, unconventional water, groundwater supply, industrial and agricultural water use, domestic water use, and ecological water use.

3. The multi-link-based water resource system resilience evaluation method according to claim 1 is characterized by: The calculation of the causal connection strength of each main sub-link in step S2 includes the following steps: (1) Constructing directed edges of time series: Constructing a parent node set for each variable According to the absolute test statistic, Sort the elements in the , and select the p elements with the largest statistical test as the condition set S; the condition set S is iteratively increased from the empty set, and removed China Independent Elements, forming a partial connectivity graph, for all time series nodes They are all connected with directed edges to ensure that the time lag order τ>0 to obtain a causal direction that conforms to the time sequence; (2) Perform conditional independence tests to remove unnecessary edges, remove homologous edges based on the temporal consistency assumption, and detect and Independence of τ>0 is tested sequentially. The test condition is and To determine whether independence exists, Where: is the causal parent of the variable Set; suppose there are two time series MetX1 and MetX2, Then there is a causal relationship Right now in Indicates that conditional independence is not met; If conditional independence exists, then there is no direct causal relationship between the two variables under a given set of conditions, and the edge between the variables is removed; If conditional independence does not exist, the two variables are correlated under a given set of conditions, and the edge is retained to indicate that there may be a causal relationship between the two variables.

4. The multi-link-based water resource system resilience evaluation method according to claim 1 is characterized by: In step S5, water resource resilience is calculated based on the multivariate logistic regression model. 0≤COR≤1 Where: F(x1), F(x2), F(x3) are the closeness levels of the three system dimensions; α, β1, β2, β3 are the parameters of the regression model; COR is the system resilience level.

5. The multi-link-based water resource system resilience evaluation method according to claim 1 is characterized in that: In step S6, the multi-scale transfer entropy of each sub-link to water resource resilience is calculated. Where: Y is the sequence of sub-links, X is the sequence of water resource system resilience COR, Represents X t Conditional entropy given past states of X; For X t Conditional entropy given the past states of X and Y; TE N Link→COR is the transfer entropy from the sublink to the COR at scale N; The multi-scale transfer entropy of the sub-link to the resilience COR of the water resources system can be expressed as:

Images