Community structure detection method and system for spatial concurrent extreme climate events

Abstract

The invention provides a community structure detection method and system for spatial concurrent extreme climate events, and the method comprises the steps: collecting lattice point temperature and rainfall data of a research region, extracting a binary time sequence of heat waves and extreme rainfall events, and carrying out the synchronous judgment calculation and significance test of the events; according to the interlayer adjacent matrix, a double-layer coupling heat wave-extreme precipitation network is constructed; based on the double-layer coupling network, a community detection method combining a Leiden algorithm and consensus clustering is adopted, and a stable community classification result is obtained; and carrying out lead-lag correlation analysis on all community pairs, identifying key community pairs with strong correlation and lag time thereof, and further discussing time-space propagation characteristics of climate events. According to the method, the advantages of double-layer coupling climate network analysis are fully utilized, the Leiden algorithm and the consensus clustering method are combined, the accuracy and stability of community detection are improved, and the spatial concurrency characteristics and the space-time propagation law of global extreme climate events can be effectively revealed.

Description

Technical Field

[0001] The present invention relates to the field of climate analysis technology, and in particular to a community structure detection method and system for spatial concurrent extreme climate events. Background Art

[0002] Affected by global warming, the frequency, intensity and impact of heat waves and extreme precipitation events have increased significantly, causing serious impacts on human life, ecological environment, economic activities, agricultural production and food security. These extreme events show spatial and temporal correlations in various regions around the world, and there may be a common circulation pattern driving mechanism behind them. However, there is currently a lack of research on the spatial concurrence of heat waves and extreme precipitation, and the impact of such concurrent events is wide-ranging and far-reaching. Taking the summer of 2022 as an example, eastern China, Western Europe, Western America, Eastern Europe and eastern Siberia experienced persistent heat waves. At the same time, Pakistan, southern China and Brazil experienced record-breaking heavy precipitation extreme events, which had a serious impact on human society. Therefore, in-depth understanding and grasp of the spatial concurrency characteristics of heat waves and extreme precipitation is of great significance for responding to the challenges brought about by global warming.

[0003] Although the complex network framework has shown wide application potential in the synchronization and propagation analysis of extreme rainfall, heat waves and droughts, by abstracting geographical locations as nodes and constructing nonlinear correlations between extreme event sequences as edges, the intrinsic connections between extreme events in different locations are revealed. However, existing research mainly focuses on single-variable climate extreme events, and there is still a gap in the comprehensive analysis of heat waves and extreme precipitation events that occur simultaneously in multiple locations. In addition, although community detection in climate network analysis can effectively cluster areas with similar climate characteristics, traditional algorithms often face the problems of disconnected communities and unstable results.

[0004] Therefore, it is urgent to develop innovative technical methods to address these challenges in the community detection problem of multivariate spatial concurrent extreme climate events. Summary of the invention

[0005] The present invention provides a community structure detection method and system for spatial concurrent extreme climate events, which are used to solve the defects in the prior art.

[0006] In a first aspect, the present invention provides a community structure detection method for spatial concurrent extreme climate events, comprising:

[0007] Collecting grid temperature and precipitation data in the study area, extracting binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, performing event synchronization determination calculation and significance test on the binary time series, and obtaining a nonlinear adjacency matrix;

[0008] A single-layer heat wave network and a single-layer extreme precipitation network are established according to the nonlinear adjacency matrix, a double-layer coupled heat wave-extreme precipitation network is constructed by calculating the interlayer connection between the heat wave layer and the precipitation layer, and a single-layer network coefficient and a double-layer network coefficient are calculated;

[0009] Based on the double-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm was used to obtain stable community classification results.

[0010] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, grid temperature and precipitation data of the study area are collected, binary time series of heat wave events and extreme precipitation events are extracted from the grid temperature and precipitation data, event synchronization determination calculation and significance test are performed on the binary time series, and a nonlinear adjacency matrix is ​​obtained, including:

[0011] Collect temperature data from the global CPC grid data set and the ERA5 reanalysis data set, collect precipitation data from the global CPC grid data set and the MSWEP data set, and use bilinear interpolation to interpolate the temperature data and the precipitation data to a preset resolution;

[0012] Extracting extreme high temperature phenomena in which the maximum temperature of the day exceeds a preset percentage quantile of the temperature series and lasts for no less than a preset number of days within a specified time period in a specific area as the heat wave event;

[0013] Extracting events where the precipitation exceeds a preset percentage quantile of the rainy day time series as the extreme precipitation event;

[0014] constructing the binary time series from the heat wave event and the extreme precipitation event;

[0015] Using a nonlinear event synchronization measurement method to calculate the event synchronization of the binary time series;

[0016] Compute a significance test for the binary time series based on the null model distribution.

[0017] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, a nonlinear event synchronization measurement method is used to calculate the event synchronization of the binary time series, including:

[0018] Extracting any two grid points on the space corresponding to the binary time series, determining a first event occurrence time point and a second event occurrence time point corresponding to the any two grid points, wherein the first event occurrence time point and the second event occurrence time point are constrained by the total number of heat wave events or the total number of extreme precipitation events at the any two grid points;

[0019] A dynamic delay is obtained by the first event occurrence time point, the previous event occurrence time point and the next event occurrence time point of the first event occurrence time point, the second event occurrence time point and the previous event occurrence time point and the next event occurrence time point of the second event occurrence time point;

[0020] Obtaining the event occurrence time difference between the arbitrary two grid points, determining the maximum delay time, and if the event occurrence time difference is less than the dynamic delay and less than the maximum delay time, determining that the events of the arbitrary two grid points are synchronous;

[0021] The cross-correlation of the total number of events between the arbitrary two grid points is determined by the time difference of the event occurrence, and the synchronization strength is obtained based on the cross-correlation of the total number of events and the total number of heat wave events or the total number of extreme precipitation events. The synchronization strength is used to evaluate the synchronicity of the events.

[0022] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, a significance test of the binary time series is calculated based on a null model distribution, comprising:

[0023] Randomly shuffle each observation value in the binary time series in the time dimension to generate a null model distribution;

[0024] A preset quantile in the null model distribution is determined as a significance threshold, and if any observed value exceeds the significance threshold, it is determined that the any observed value is significant at a preset level.

[0025] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, a single-layer heat wave network and a single-layer extreme precipitation network are respectively established according to the nonlinear adjacency matrix, a double-layer coupled heat wave-extreme precipitation network is constructed by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and the single-layer network coefficient and the double-layer network coefficient are calculated, including:

[0026] Acquire global effective grid points, perform event synchronization calculation on the global effective grid points to obtain a synchronization intensity matrix, remove weakly correlated edges in the climate network through a null model test to obtain a binary adjacency matrix, and construct the single-layer heat wave network and the single-layer extreme precipitation network based on the binary adjacency matrix;

[0027] Performing event synchronization and significance verification on any node in the single-layer heat wave network and any node in the single-layer extreme precipitation network to obtain an inter-layer interaction adjacency matrix, and constructing the double-layer coupled heat wave-extreme precipitation network based on the inter-layer interaction adjacency matrix;

[0028] Calculate the degree centrality, betweenness centrality, clustering coefficient and average synchronization distance of the single-layer network respectively;

[0029] The cross-degree centrality, cross-covariance centrality, cross-clustering coefficient, and cross-synchronization distance of the two-layer network were calculated respectively.

[0030] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, based on the double-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm is used to obtain a stable community classification result, including:

[0031] The two-layer coupled heat wave-extreme precipitation network is converted into a weighted single-layer network using a direct flattening method;

[0032] Performing community partitioning on the weighted single-layer network using the Leiden community detection algorithm to obtain an initial community partitioning result;

[0033] The consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partition result to obtain an integrated community partition result;

[0034] A lead-lag correlation analysis is performed on the integrated community partitioning result to obtain a specific community synchronization index time series, the specific community synchronization index time series is smoothed by a Butterworth low-pass filter, and a lead-lag correlation analysis is performed on the specific community synchronization index time series of any two communities to obtain the stable community classification result.

[0035] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, the weighted single-layer network is divided into communities using the Leiden community detection algorithm to obtain an initial community partition result, including:

[0036] Taking the initial node as an independent community, gradually move a single node to other communities, and determine whether to accept the movement of the current node based on the change in modularity to obtain the local movement partition result;

[0037] Modifying the local mobile division result to divide the nodes with less than a preset number of connections into two sub-community nodes;

[0038] Merge subcommunity nodes, build a new simplified network, retain the original community number, and cluster the new network again;

[0039] Repeat the above steps until the modularity stops increasing, obtain the initial community partition result, and determine the community category number to which each grid point belongs.

[0040] According to a community structure detection method for spatial concurrent extreme climate events provided by the present invention, the consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partition result to obtain an integrated community partition result, including:

[0041] Applying the Leiden community detection algorithm to a functional climate network a preset number of times to generate a preset number of partition results, the functional climate network having a number of nodes;

[0042] Sorting the preset number of partition results according to modularity, and extracting the first preset number of partitions with the highest modularity;

[0043] The consensus matrix is ​​calculated by the number of partitions in which any two nodes belong to the same community and the total number of partitions;

[0044] The items in the consensus matrix that are below the threshold are set to 0 to obtain a filtered consensus matrix;

[0045] Applying the Leiden community detection algorithm to the filtered consensus matrix again according to the preset number of times to generate a preset number of new partition results;

[0046] If the number of partitions in the preset number of new partition results is equal, and the normalized mutual information between multiple partitions is greater than a preset value, the iteration is stopped to obtain the integrated community partition result, otherwise the consensus matrix is ​​recalculated.

[0047] In a second aspect, the present invention further provides a community structure detection system for spatial concurrent extreme climate events, comprising:

[0048] A calculation and verification module is used to collect grid temperature and precipitation data in the study area, extract binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, perform event synchronization determination calculation and significance test on the binary time series, and obtain a nonlinear adjacency matrix;

[0049] A construction module is used to establish a single-layer heat wave network and a single-layer extreme precipitation network according to the nonlinear adjacency matrix, construct a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and calculate the single-layer network coefficient and the double-layer network coefficient;

[0050] The detection module is used to obtain a stable community classification result based on the double-layer coupled heat wave-extreme precipitation network by using a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm.

[0051] In a third aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the community structure detection method for spatially concurrent extreme climate events as described in any one of the above-described methods is implemented.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] Based on event synchronization and significance tests, this paper deeply analyzes the nonlinear correlation between extreme event sequences in different geographical locations, providing a solid theoretical basis for revealing the intrinsic correlation of spatial concurrent extreme climate events.

[0054] The present invention constructs a double-layer coupled climate complex network, and by analyzing the high-order characteristics of the single-layer and double-layer network topology, it improves the understanding of the nonlinear dynamics of the earth system, the teleconnection and concurrent characteristics of extreme climate events, and the energy transmission mechanism;

[0055] This paper combines the advanced Leiden community detection algorithm with consensus clustering theory for the first time, and proposes a new community clustering method for concurrent extreme climate events in multivariate space, which effectively reduces the probability of disconnection within the community and improves the stability of community division results. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0057] Figure 1 It is one of the flow charts of the community structure detection method for spatial concurrent extreme climate events provided by the present invention;

[0058] Figure 2 This is the second flow chart of the community structure detection method for spatial concurrent extreme climate events provided by the present invention;

[0059] Figure 3 It is the event synchronization calculation flow chart provided by the present invention;

[0060] Figure 4 is a network geographical distance teleconnection distribution map of different maximum delay thresholds provided by the present invention;

[0061] Figure 5 It is a flow chart of the Leiden community detection algorithm provided by the present invention;

[0062] Figure 6It is a flow chart of the consensus clustering community structure detection algorithm provided by the present invention;

[0063] Figure 7 is a community division result diagram of the double-layer coupled climate network provided by the present invention, wherein: Figure 7 (a) is the number of community grid points, Figure 7 (b) Optimization of consensus clustering parameters;

[0064] Figure 8 This is the community lead-lag correlation analysis and seasonal distribution result diagram provided by the present invention. Figure 8 (a) is the seasonal distribution, Figure 8 (b) is the lead-lag correlation coefficient, Figure 8 (c) is the number of lead-lag days;

[0065] Fig. 9 It is a structural schematic diagram of a community structure detection system for spatial concurrent extreme climate events provided by the present invention;

[0066] Fig.10 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] Aiming at the problem of community detection and analysis of multivariate spatial concurrent extreme climate events in the prior art, the present invention proposes a community structure detection method for spatial concurrent extreme climate events. Figure 1 is one of the flow charts of the community structure detection method for spatial concurrent extreme climate events provided by an embodiment of the present invention, such as Figure 1 As shown, including:

[0069] Step 100: collecting grid temperature and precipitation data in the study area, extracting binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, performing event synchronization determination calculation and significance test on the binary time series, and obtaining a nonlinear adjacency matrix;

[0070] Step 200: establishing a single-layer heat wave network and a single-layer extreme precipitation network respectively according to the nonlinear adjacency matrix, constructing a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and calculating the single-layer network coefficient and the double-layer network coefficient;

[0071] Step 300: Based on the double-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm is used to obtain a stable community classification result.

[0072] Specifically, Figure 2 As shown, the method proposed in the embodiment of the present invention includes:

[0073] Step 1: Collect grid temperature and precipitation data in the study area, extract binary time series of heat waves and extreme precipitation events, and perform event synchronization calculations and significance tests.

[0074] Step 2: Based on the nonlinear adjacency matrix calculated in step 1, a single-layer heat wave network and a single-layer extreme precipitation network are constructed. Next, the interlayer connections between the heat wave layer and the precipitation layer are calculated to further construct a double-layer coupled heat wave-extreme precipitation network. By calculating and analyzing the single-layer network coefficients and the double-layer network coefficients, we can understand the underlying topological structure of the network.

[0075] Step 3: Based on the two-layer coupled heat wave-extreme precipitation network, the community clustering method combining the Leiden community detection algorithm and consensus clustering theory is used to obtain the stable community classification results. Subsequently, all community pairs are subjected to lead-lag correlation analysis to identify key high-correlation community pairs and lag times, thereby analyzing the spatiotemporal propagation characteristics.

[0076] The present invention improves the accuracy and stability of community detection by utilizing the advantages of double-layer coupled climate network analysis and combining the scientific nature of the Leiden algorithm and consensus clustering method, and can effectively reveal the spatial concurrency characteristics and spatiotemporal propagation laws of global extreme climate events.

[0077] In one embodiment, step 1 includes:

[0078] Step 1.1: Collection of basic temperature and precipitation data. The temperature data comes from the global CPC grid dataset and the ERA5 reanalysis dataset, and the precipitation data uses the global CPC grid dataset and the MSWEP (V2.8) dataset. The bilinear interpolation technique is used to interpolate the temperature and precipitation data to the preset resolution.

[0079] Specifically, CPC grid data set (Unified Gauge-Based Analysis of Global Daily Precipitation) is generated by fusing station measured data and remote sensing inversion data, with a data resolution of 0.5°×0.5°; ERA5 data set is the fifth generation of atmospheric reanalysis products from the European Centre for Medium-Range Weather Forecasts, with a spatial resolution of 0.25°×0.25° and a temporal resolution of 1 hour. ERA5 uses a more advanced land surface assimilation system, improves the simulation of water cycle at the land-sea boundary, and optimizes the estimation of bare land evapotranspiration; the present invention uses MSWEP V2.8 (Multi-Source Weighted-Ensemble Precipitation) data set, with a spatial resolution of 0.1°×0.1° and a temporal resolution of 3 hours. This product integrates station, satellite and reanalysis data. In areas with densely populated stations and no stations, the performance of MSWEP is often better than other precipitation products. In order to ensure the consistency of the data, the present invention uses the bilinear interpolation method in the CDO (Climate Data Operators) software to uniformly interpolate the two sets of daily maximum temperature data and daily cumulative precipitation data to a resolution of 1°×1°. In the case of the present invention, the data used covers the time range of the northern hemisphere summer (June, July and August) from 1979 to 2023, and the spatial range is the global grid area from 60°S to 60°N.

[0080] Step 1.2: Extract binary time series of heat wave events and extreme precipitation events.

[0081] Heatwave events are defined as follows:

[0082] ① Identification of extreme high temperature events: Days from June to August in the Northern Hemisphere when the daily maximum temperature exceeds the 90% quantile of the temperature series are defined as extreme high temperature events;

[0083] ②Define heat wave events: select a minimum number of consecutive days of 3 to define a heat wave event;

[0084] ③ Merge consecutive heat wave events: If multiple heat wave events are consecutive in time, they are considered as a single event. The first day of the heat wave event is taken as the start time of the single event;

[0085] ④ Handling inter-year boundaries: During the inter-year period, in order to avoid the deviation of heat wave synchronization estimation between different grid points, 10 “0”s are inserted at the junction of two years;

[0086] ⑤Regional filtering: If the total number of extreme events occurring in a region is less than 3, the region will be excluded from the analysis.

[0087] Extreme precipitation events are defined as follows:

[0088] ① Identify rainy day sequences: define days with daily precipitation greater than or equal to 1 mm as rainy days;

[0089] ② Identify extreme precipitation events: Analyze the precipitation sequence of rainy days. If the precipitation on a certain day exceeds the 90% quantile of the sequence, the date is defined as an extreme precipitation day.

[0090] ③ Merge consecutive precipitation events: If multiple extreme precipitation events occur consecutively in time, they are merged into the same event, and the first day of occurrence is taken as the start date of the event;

[0091] ④ Handling cross-year boundaries: Similarly, 10 “0s” are filled at the intersection of the two years in the cross-year period to avoid deviations in the synchronous estimation of events at different grid locations;

[0092] ⑤Regional filtering: If the total number of extreme events in a region is less than 3, the region will not be included in the analysis.

[0093] Under the above definition, once a heat wave event or extreme precipitation event is detected on a certain day, the day is represented by "1", and if no extreme event occurs, it is recorded as "0". In this way, the daily temperature or daily precipitation time series of each grid point is converted into a binary time series to indicate whether a heat wave or extreme precipitation event occurs or not.

[0094] However, extreme events that occur across seasons may appear consecutively in binary time series. To distinguish events that occur in different seasons, 10 “0s” are inserted at the boundary of each year for each grid point to avoid bias in the synchronous calculation of events for different grid points.

[0095] Step 1.3: Event synchronization judgment calculation. In order to evaluate the synchronization of the time series of heat waves and extreme precipitation events between all grid point pairs around the world, the present invention adopts a nonlinear event synchronization (Event Synchronization) measurement method. This method was first proposed by Quiroga et al. in 2002 and was originally used to analyze electroencephalogram neural signals. Subsequently, Malik et al. first applied this method to the correlation between extreme precipitation in the Indian continent in 2012. The significant advantage of the event synchronization method is that it can handle the dynamic time lag of extreme events between two different spatial locations, and then measure their temporal consistency. Since this method does not need to assume that the data follows a specific probability distribution, it shows great flexibility in dealing with extreme events. In addition, the event synchronization method can accurately consider the time interval between events, which is particularly suitable for analyzing extreme events with uneven time intervals. The calculation flow chart of event synchronization is shown in the figure. Figure 3 shown.

[0096] For any two grid points i and j in space, suppose the event at grid point i occurs at time The event at grid point j occurs at time where u∈[1,l i ],v∈[1,l j ],l i and l j represents the total number of heat wave events or extreme precipitation events at land grid points i and j, respectively.

[0097] Dynamic Delay Determines the grid pairs i and j at time point and Whether a pair of events that occur are considered synchronous events is defined as follows:

[0098]

[0099] In the formula is the time point at which the event occurs at grid point i, and is the time point of the previous and next event occurrence at grid point i; is the time point at which the event occurs at grid point j, and are the time points of the previous and next events at grid point j.

[0100] To avoid a long delay between two synchronization events that is inconsistent with the real world, a maximum delay time τ is set max = 10 days. and When , the event m at the grid point i and the event n at the grid point j are considered to be synchronous. The positive and negative representation of and The order of occurrence represents the direction of spatial concurrency of extreme climate events.

[0101] In addition, we define C(i|j) to represent the total number of events that occurred in grid cell j earlier than the total number of events that occurred in grid cell i:

[0102]

[0103] Similarly, we can define C(j|i):

[0104]

[0105] in:

[0106]

[0107]

[0108] It means that the extreme climate event v occurs at grid point j earlier than the extreme event u occurs at grid point i. Opposite meaning.

[0109] Furthermore, the synchronization strength proposed by Malik et al. in 2012 is used to evaluate the degree of nonlinear correlation between two event sequences, which is defined as follows:

[0110]

[0111] Where Q i,j Normalized to Q i,j ∈[0,1]; Q i,j = 1 means that all events between grid cells i and j are completely synchronized.

[0112] Different from the static delay in linear correlation analysis, event synchronization takes into account the dynamic delay and is therefore a suitable tool for studying nonlinear time relationships. In the case of the present invention, the maximum dynamic delays of 3 days, 7 days and 10 days were used to obtain the network geographical distance teleconnection distribution maps under the three maximum dynamic delays (such as Figure 4 As shown in the figure, it can be seen from the results that the maximum dynamic delay has little effect on the calculation of the synchronization metric and the degree distribution of the network.

[0113] Step 1.4: Significance test calculation: For the synchronization strength calculated by event synchronization, a significance test is required to retain significant connections with physical significance and prune insignificant connections.

[0114] This paper adopts the method proposed by Boers et al. in 2019, using null hypothesis testing to remove weakly correlated connections from the climate network. Specifically, a null model distribution is generated by randomly shuffling each observation in the time dimension, and this distribution is used for significance testing. The 99.9 quantile of the null model is determined as the significance threshold. If the observation exceeds this threshold, the synchronization between node i and node j is considered significant at the 0.001 level, and these edges are saved in the network. Therefore, the final synchronization strength matrix is ​​converted into a binary adjacency matrix, representing the significant connections between grid points.

[0115] The specific calculation steps are as follows:

[0116] ① Randomly disrupt the sequence of heat waves or extreme precipitation events in the time dimension so that there is no significant correlation between any two time series.

[0117] ② Calculate the synchronization strength index of the event sequence based on the random field;

[0118] ③ Repeat steps ① and ② 1000 times to obtain the zero model Q of the synchronization intensity matrixnull , and obtain the reference distribution results for each grid point.

[0119] ④ Take The 99.9% quantile (significance level is p = 0.001) of ij,sig If the synchronization strength between grid points i and j exceeds this threshold, they are considered to be significantly synchronized at the 0.001 significance level, and their interconnection is retained as an edge in the complex network.

[0120]

[0121] in Indicates that the events of grid cell i are statistically significantly synchronized with the events of grid cell j.

[0122] In one embodiment, step 2 includes:

[0123] Complex network methods provide an effective tool for revealing the spatial patterns of extreme climate events and inferring the underlying physical processes. By statistically analyzing the topological structure of the network, climate data can be converted into a network model (adjacency matrix), in which nodes represent geographic grid cells and links between nodes represent the correlation of extreme events. The climate network is a spatially embedded network, and its construction process includes identifying nodes and links and detecting the correlation between nodes through similarity measures. Combined with network analysis tools, complex network methods expand traditional analytical methods and can deeply explore the nonlinear time series relationships within the climate system and draw conclusions that are difficult to reveal with traditional methods.

[0124] According to the nonlinear adjacency matrix of the event synchronization measure calculated in step 1, a single-layer heat wave network and a single-layer extreme precipitation network are established respectively. Next, the inter-layer connections between the heat wave layer and the precipitation layer are calculated to further construct a double-layer coupled heat wave-extreme precipitation network. By calculating and analyzing the coefficients of the single-layer network and the double-layer network, it can help understand the underlying topological structure of the network. The single-layer network coefficients include degree centrality, betweenness centrality, clustering coefficient, and average synchronization distance, and the double-layer network coefficients include cross-degree centrality, cross-betweenness centrality, cross-clustering coefficient, and cross-synchronization distance.

[0125] Step 2.1: Construction of a single-layer climate complex network. In the case provided by the present invention, there are 11022 valid grid points in the world. After the event synchronization calculation is completed, a synchronization intensity matrix with a dimension of 11022×11022 will be obtained. Through the null model test, the weakly correlated edges in the climate network are eliminated, and then the binary adjacency matrix with significant connections is obtained. Based on the adjacency matrices of heat waves and extreme precipitation, a single-layer heat wave or single-layer extreme precipitation complex network is constructed respectively.

[0126] Step 2.2: Construction of a two-layer coupled heat wave-extreme precipitation network. Considering the complexity of the Earth system and the interactions and feedback mechanisms between climate events, understanding the connectivity between heat waves and extreme precipitation events is crucial to revealing complex processes from local to regional and even continental scales. This paper constructs a two-layer coupled heat wave-extreme precipitation network to comprehensively describe the interactions and concurrency of these events at spatial scales.

[0127] First, the event synchronization of heat waves and extreme precipitation is calculated respectively, and a significance test is performed to construct the corresponding single-layer complex network; then, event synchronization is performed for node i in the heat wave network and node j in the extreme precipitation network, and a significance test is performed to obtain the adjacency matrix of the inter-layer interaction. Therefore, the adjacency matrix of the two-layer coupled climate network is described as follows:

[0128]

[0129] Here, Θ(·) represents the Heaviside function. represents the event synchronization measure for the i and j grid pair between the heatwave and extreme precipitation subnetworks. T is the 99.9 percentile threshold of the null model. is the Kronecker increment, which is used to avoid self-loops. The two diagonal blocks of the matrix represent the adjacency matrix of two univariate networks (heat waves or extreme precipitation), and the off-diagonal blocks represent the bivariate network blocks (the coupling relationship between heat waves and extreme precipitation).

[0130] Step 2.3: Calculation of single-layer network coefficients. By calculating the statistical topological structure of the adjacency matrix, various network metrics can be derived to deepen the understanding of the spatiotemporal concurrent characteristics of extreme events at regional and global scales. However, when dealing with climate data based on regular latitude and longitude grids, the spatial heterogeneity between adjacent grid cells must be considered, especially near the poles. To address this problem, each node is usually assigned a weight corresponding to the spatial area it represents, the so-called node split invariant (NSI) metric:

[0131] w i = cosλ i

[0132] Among them, λ i is the latitude of grid cell i, w i is the corresponding weight value.

[0133] In this paper, four single-layer network metrics of single-layer heat waves or extreme precipitation fields are calculated: degree centrality (DC), betweenness centrality (BC), clustering coefficient (CC) and mean synchronous distance (MSD). The application of these network coefficients helps to understand the "hubs" and "bottlenecks" of information propagation within the network and analyze the connectivity and propagation distance between different regions.

[0134] Degree is the number of edges connected to a node. It is used to measure the degree of connection between a grid point and the entire network. It is the most basic network metric. Degree centrality (DC) is the standardization of node degree and is defined as follows:

[0135]

[0136] Where N is the total number of grid cells in the network; Represents the synchronous adjacency matrix. The degree represents the number of grid cells that experience heat waves or extreme precipitation events synchronously with this grid cell. Grid cells with higher DC have a greater impact on the function or sensitivity of the network.

[0137] Betweenness centrality is an important indicator of information transmission, indicating the influence of a specific node on the information transmission between other nodes. The betweenness centrality (BC) of a grid point i is defined as the ratio of the sum of all shortest paths between all possible pairs of nodes passing through i to the total number of shortest paths between them. BC is defined as:

[0138]

[0139] where σ i (m,n) represents the shortest path between any two grid points m and n through grid point i; σ(m,n) represents the sum of all possible shortest paths through any two grid points m and n. Nodes with high betweenness centrality play a key role in the information transmission process in the network, acting as a "bridge" or "bottleneck" for information dissemination.

[0140] The clustering coefficient reflects the connection density between a node and its neighboring nodes. The clustering coefficient (CC) of grid point i represents the ratio of the number of edges actually connected to grid point i to the maximum number of connected edges that can exist in probability, and is defined as follows:

[0141]

[0142] where ζ i Indicates the actual number of connections between the adjacent nodes of node i; D i Represents the degree of the node; CC i The higher the value, the more tightly the nodes around grid point i are connected to each other, indicating that the synchronization of extreme events in the area is stronger.

[0143] The mean synchronization distance (MSD) represents the average spatial range of a grid point in the network that affects propagation. The definition formula is as follows:

[0144]

[0145] where d ij represents the geographical distance between grid points i and j, Q ij represents the synchronization metric, Represents the synchronized adjacency matrix. The higher the MSD value, the farther the grid points can be propagated.

[0146] Step 2.4: Calculation of two-layer network coefficients. Furthermore, the present invention also calculates four multi-layer network coefficients of the two-layer coupled heat wave-extreme precipitation event network, namely, cross-degree centrality (CDC), cross-correlation centrality (CBC), cross-clustering coefficient (CCC) and cross-synchronous distance (CSD).

[0147] The present invention constructs a double-layer network G=(V,E), where V is a grid unit and E is a connecting edge. pp Represents the subnetwork G p The internal connection of E pq Represents G p and G q In the present invention, the indexes p and q represent sub-networks, while v, w, i and j represent single grid points.

[0148] Cross-degree centrality (CDC) refers to the degree of p ) In another subnetwork G q The number of connected neighbors in is calculated as follows:

[0149]

[0150] CDC quantifies the node v on the subnetwork G p and G q The influence of coupling.

[0151] Cross-betweenness centrality (CBC) represents the interaction between two sub-networks and is defined as follows:

[0152]

[0153] Where σ(i,j) represents the total number of shortest paths from i to j. σ(i,j|v) is the number of shortest paths between i and j that also pass through v. High CBC nodes can act as communication hubs between two sub-networks.

[0154] The local cross clustering coefficient (CCC) is calculated for the node v(v∈G p ) and two randomly selected neighbors i and j (i≠j∈Gq ) becomes a neighbor. The calculation formula is as follows:

[0155]

[0156] Grid points with higher CCC indicate that the variability of different climate variables is similar in the region.

[0157] The cross-synchronous distance (CSD) represents the average geographical connection scale between a grid cell and other sub-networks. The calculation formula is as follows:

[0158]

[0159] in, is a node v(v∈G p ) and node j(j∈G q ) between them. is a significant cross-adjacency matrix. is the event synchronization strength. Regions with high CSD indicate regional to long-range connections.

[0160] In one embodiment, step 3 includes:

[0161] Based on the double-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and consensus clustering theory is used to obtain stable community classification results. Subsequently, all community pairs are subjected to lead-lag correlation analysis to identify key community pairs with strong correlation and lag time, thereby analyzing the temporal and spatial propagation characteristics of the community pairs. The Leiden community detection algorithm flow chart provided by the present invention is as follows: Figure 5 The consensus clustering community structure detection algorithm flow chart of the two-layer coupled climate network is shown in Figure 6 shown.

[0162] Step 3.1: Community clustering method combining Leiden community detection algorithm and consensus clustering theory.

[0163] Communities are clusters of nodes in a network that are tightly connected internally but loosely connected externally. In climate function networks, communities have physical meaning because they are determined by the connectivity structure of the network and represent the physical pattern of spatial covariance. Currently, there are many community detection algorithms for single-layer networks based on different optimization objectives, as well as community detection algorithms for multi-layer networks.

[0164] The present invention extends the community structure to multivariate coupled networks, but only considers pillar communities. Specifically, considering that the adjacency matrix contains all links within the heat wave layer and the extreme precipitation layer and the cross-links between the heat wave-extreme precipitation network, the present invention uses a direct flattening method to convert the multi-layer network into a weighted single-layer network, and then applies the Leiden algorithm to perform community division on it. The Leiden algorithm is an improvement on the classic community detection Louvain algorithm, which measures the quality of different community divisions based on modularity.

[0165] In network theory, modularity maximization is a technique that can discover substructures (or communities) and is defined as follows:

[0166]

[0167] Among them, Mod is the global modularity, Mod∈[0,1]; M represents the total number of connections in the undirected network, k i and k j are the degrees of node i and node j respectively; c i and c j are the communities of node i and node j respectively. If node i and node j belong to the same community, then δ(C i ,C j )=1, otherwise, δ(C i ,C j )=0. The larger the modularity value, the stronger the association between nodes within the community, and the weaker the association between nodes in different communities. It is generally believed that the network division with a modularity value between 0.3 and 0.8 has a more obvious community structure.

[0168] Since most community detection methods have uncertainty and partition volatility, in order to eliminate these randomness, the present invention adopts a consensus clustering algorithm to improve stability by integrating multiple partition results. Specifically, the consistent community structure in the climate function network is identified by iterating the Leiden algorithm 1000 times. First, a certain number of samples are extracted according to the modularity ranking, and a consensus matrix is ​​constructed. Then, threshold filtering is applied and multiple iterative calculations are performed to finally detect a stable community structure.

[0169] Step 3.1 further includes the following sub-steps:

[0170] Step 3.1.1: Leiden community detection algorithm. The Leiden algorithm was proposed by researchers at Leiden University in 2019 and is an improvement on the classic Louvain community detection algorithm. The Leiden algorithm runs faster than the Louvain algorithm and significantly reduces the probability of disconnection within the community. The Leiden community detection algorithm flowchart is as follows: Figure 5 As shown. The main steps of the Leiden algorithm are as follows:

[0171] (1) Local movement stage. In this stage, the geographical grid is regarded as a node in the network, and each node is initially regarded as an independent community. Subsequently, a single node is gradually moved from one community to another, and whether to accept the move is determined based on the change in modularity. If the movement of the node can improve the modularity, the move is accepted, thus forming a new community division.

[0172] (2) Modification of nodes within the community. Modify the division result of step (1) to further refine the node division within the community. Nodes with low connectivity within the community will be divided into two sub-communities. For example, Figure 5 In the figure, the red community is divided into two sub-communities. Although the sub-communities are treated as independent nodes when the network is condensed, they still belong to the original community. This step ensures a more refined community division and further improves the overall modularity.

[0173] (3) Network cohesion. Based on the modified community division, all nodes in each subcommunity are merged to construct a new simplified network structure. At this time, the nodes still retain their original community numbers. The new network is clustered again based on the revised community structure to further simplify and optimize the community structure.

[0174] (4) By repeating the above steps, the modularity of the network is continuously improved until the modularity no longer increases, and finally a stable community division result is obtained, the community category number of each geographic grid point is determined, and the community identification is completed.

[0175] Step 3.1.2: Consensus clustering algorithm. Consensus clustering uses the community detection results of multiple networks through multiple iterations of the community detection algorithm to obtain a stable number of communities. The process of the consensus clustering algorithm is as follows: Figure 6 shown.

[0176] Given a functional climate network G with |V| nodes and a community detection method A, the specific process of consensus clustering is as follows:

[0177] (1) Apply A to network G 1000 times, generating 1000 partition results.

[0178] (2) Sort the 1000 partition results according to modularity and select the first n partitions with the highest modularity.

[0179] (3) Calculate the consensus matrix D:

[0180]

[0181] Where n ijis the number of partitions where nodes i and j belong to the same community, and n is the total number of partitions.

[0182] (4) Set the entries in the consensus matrix D that are below the threshold θ to zero.

[0183] (5) Clustering algorithm A is applied to the filtered consensus matrix n times again to generate n partition results.

[0184] (6) If the number of partitions in (5) is equal (only consider communities larger than 1% of the total grid area), and the normalized mutual information (NMI) between multiple partitions is greater than 0.95, stop the iteration; otherwise, return to (3).

[0185] The calculation formula of NMI is as follows:

[0186]

[0187] Among them, A and B represent two groups of community structure detection results respectively; C A and C B Represent the number of community structures of A and B respectively.

[0188] In (1), the present invention selects the Leiden algorithm as the basic method of Algorithm A. In (2) and (4), n∈{25,50,100} and θ∈{0.5,0.6,0.7,0.8,0.9} are selected respectively, and the candidate with the highest modularity is selected as the input for reaching consensus clustering.

[0189] In the case provided by the present invention, community detection is performed on the global grid area from 60°S to 60°N, and the community division results are as follows: Figure 7 The spatial co-occurrence of heat waves and extreme precipitation around the world shows significant regional differences, especially in South America, Africa, Asia, and Europe. For example, southern South America shows similar community divisions to southern North America, suggesting that these regions may have similar distribution characteristics of climate extreme events. Figure 7 (a) shows the distribution of the number of grid points in each community. It can be observed that the number of grid points in community 1 is much larger than that in other communities, indicating that the concurrent characteristics of heat waves and extreme precipitation in this area are highly homogeneous in space and may represent a larger climate zone. Figure 7 (b) shows the parameter optimization results of consensus clustering. Under different clustering parameter settings, the change of modularity index shows that when n is 25 and the threshold is 0.6, the modularity is the highest, reaching 0.77, indicating that the quality of community division under this setting is the best.

[0190] Step 3.2: Conduct lead-lag correlation analysis on all community pairs, and then analyze the temporal and spatial propagation characteristics. In order to study the correlation and propagation of spatially concurrent heat waves and extreme precipitation events between community pairs, the present invention defines a synchronization index for a specific community:

[0191]

[0192] Where A is a specific community; HW k and EPE k They represent the time series of heat waves and extreme precipitation events at grid point k, respectively. This index quantifies the frequency of synchronous extreme events occurring every day in community A, and higher values ​​indicate that more regional concurrent extreme climate events occurred on date t.

[0193] Next, the SHEI time series was smoothed by a Butterworth low-pass filter (with a cutoff time of 7 days) to remove high-frequency noise. Then, the lead-lag correlation analysis of the SHEI time series of the two communities was performed, and the calculation formula is as follows:

[0194]

[0195] Among them, A and B represent two different communities; Δt represents the lag time; Ms represents the total number of summer days from 1979 to 2023. Through this analysis, on the one hand, we can identify pairs of regions with strong correlations, and on the other hand, we can get a preliminary understanding of how long it may take for spatially simultaneous extreme events to spread from one community to another.

[0196] The community lead-lag correlation analysis and seasonal distribution results provided by the present invention are shown in the figure Figure 8 shown. Figure 8 (a) shows the seasonal distribution of extreme climate events in 13 communities during the multi-year average boreal summer. In particular, extreme weather events were particularly frequent in communities 6 and 9 from mid-July to early August, while other communities showed different seasonal peaks. This indicates that the temporal characteristics of heat waves and extreme precipitation events in various regions have obvious spatial differences, which may be related to climate patterns and weather systems in different regions. Figure 8 (b) and Figure 8 (c) shows the lead-lag correlation coefficients between communities and the lead-lag days corresponding to the maximum correlation coefficient. Communities 5 and 7, which are geographically far away, show a higher positive correlation with a lag of -13 days, which means that extreme events in these regions may have a spatiotemporal propagation effect. The community information obtained from the complex network provides support for a better understanding of the interaction between extreme climate events between regions, and also provides a scientific basis for the prediction and prevention of future extreme weather events.

[0197] The community structure detection system for spatial concurrent extreme climate events provided by the present invention is described below. The community structure detection system for spatial concurrent extreme climate events described below and the community structure detection method for spatial concurrent extreme climate events described above can be referenced to each other.

[0198] Fig. 9 is a schematic diagram of the structure of a community structure detection system for spatial concurrent extreme climate events provided by an embodiment of the present invention, such as Fig. 9 As shown, it includes: a calculation and verification module 91, a construction module 92 and a detection module 93, wherein:

[0199] The calculation and verification module 91 is used to collect grid temperature and precipitation data in the study area, extract binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, perform event synchronization determination calculation and significance test on the binary time series, and obtain a nonlinear adjacency matrix; the construction module 92 is used to establish a single-layer heat wave network and a single-layer extreme precipitation network according to the nonlinear adjacency matrix, respectively, and construct a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and calculate the single-layer network coefficient and the double-layer network coefficient; the detection module 93 is used to obtain a stable community classification result based on the double-layer coupled heat wave-extreme precipitation network by using a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm.

[0200] Fig.10 An example of a physical structure diagram of an electronic device is shown in FIG. Fig.10 As shown, the electronic device may include: a processor (processor) 1010, a communication interface (Communications Interface) 1020, a memory (memory) 1030 and a communication bus 1040, wherein the processor 1010, the communication interface 1020, and the memory 1030 communicate with each other through the communication bus 1040. The processor 1010 can call the logic instructions in the memory 1030 to execute the community structure detection method of spatial concurrent extreme climate events, which includes: collecting grid temperature and precipitation data in the study area, extracting binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, performing event synchronization determination calculation and significance test on the binary time series to obtain a nonlinear adjacency matrix; establishing a single-layer heat wave network and a single-layer extreme precipitation network according to the nonlinear adjacency matrix, respectively, constructing a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and calculating the single-layer network coefficient and the double-layer network coefficient; based on the double-layer coupled heat wave-extreme precipitation network, using the community clustering method combining the Leiden community detection algorithm with the consensus clustering algorithm to obtain a stable community classification result.

[0201] In addition, the logic instructions in the above-mentioned memory 1030 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a disk or an optical disk.

[0202] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0203] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0204] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A community structure detection method for spatial concurrent extreme climate events, characterized in that: include: Collecting grid temperature and precipitation data in the study area, extracting binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, performing event synchronization determination calculation and significance test on the binary time series, and obtaining a nonlinear adjacency matrix; A single-layer heat wave network and a single-layer extreme precipitation network are established according to the nonlinear adjacency matrix, a double-layer coupled heat wave-extreme precipitation network is constructed by calculating the interlayer connection between the heat wave layer and the precipitation layer, and a single-layer network coefficient and a double-layer network coefficient are calculated; Based on the double-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm was used to obtain stable community classification results.

2. The community structure detection method for spatial concurrent extreme climate events according to claim 1 is characterized in that: Collect grid temperature and precipitation data in the study area, extract binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, perform event synchronization determination calculation and significance test on the binary time series, and obtain a nonlinear adjacency matrix, including: Collect temperature data from the global CPC grid data set and the ERA5 reanalysis data set, collect precipitation data from the global CPC grid data set and the MSWEP data set, and use bilinear interpolation to interpolate the temperature data and the precipitation data to a preset resolution; Extracting extreme high temperature phenomena in which the maximum temperature of the day exceeds a preset percentage quantile of the temperature series and lasts for no less than a preset number of days within a specified time period in a specific area as the heat wave event; Extracting events where the precipitation exceeds a preset percentage quantile of the rainy day time series as the extreme precipitation event; constructing the binary time series from the heat wave event and the extreme precipitation event; Using a nonlinear event synchronization measurement method to calculate the event synchronization of the binary time series; Compute a significance test for the binary time series based on the null model distribution.

3. The community structure detection method for spatial concurrent extreme climate events according to claim 2 is characterized in that: The event synchronization of the binary time series is calculated using a nonlinear event synchronization measurement method, including: Extracting any two grid points on the space corresponding to the binary time series, determining a first event occurrence time point and a second event occurrence time point corresponding to the any two grid points, wherein the first event occurrence time point and the second event occurrence time point are constrained by the total number of heat wave events or the total number of extreme precipitation events at the any two grid points; A dynamic delay is obtained by the first event occurrence time point, the previous event occurrence time point and the next event occurrence time point of the first event occurrence time point, the second event occurrence time point and the previous event occurrence time point and the next event occurrence time point of the second event occurrence time point; Obtaining the event occurrence time difference between the arbitrary two grid points, determining the maximum delay time, and if the event occurrence time difference is less than the dynamic delay and less than the maximum delay time, determining that the events of the arbitrary two grid points are synchronous; The cross-correlation of the total number of events between the arbitrary two grid points is determined by the time difference of the event occurrence, and the synchronization strength is obtained based on the cross-correlation of the total number of events and the total number of heat wave events or the total number of extreme precipitation events. The synchronization strength is used to evaluate the synchronicity of the events.

4. The community structure detection method for spatial concurrent extreme climate events according to claim 3 is characterized in that: Calculate the significance test of the binary time series based on the null model distribution, including: Randomly shuffle each observation value in the binary time series in the time dimension to generate a null model distribution; A preset quantile in the null model distribution is determined as a significance threshold, and if any observed value exceeds the significance threshold, it is determined that the any observed value is significant at a preset level.

5. The community structure detection method for spatial concurrent extreme climate events according to claim 1, characterized in that: A single-layer heat wave network and a single-layer extreme precipitation network are established according to the nonlinear adjacency matrix, and a double-layer coupled heat wave-extreme precipitation network is constructed by calculating the interlayer connection between the heat wave layer and the precipitation layer, and the single-layer network coefficient and the double-layer network coefficient are calculated, including: Acquire global effective grid points, perform event synchronization calculation on the global effective grid points to obtain a synchronization intensity matrix, remove weakly correlated edges in the climate network through a null model test to obtain a binary adjacency matrix, and construct the single-layer heat wave network and the single-layer extreme precipitation network based on the binary adjacency matrix; Performing event synchronization and significance verification on any node in the single-layer heat wave network and any node in the single-layer extreme precipitation network to obtain an inter-layer interaction adjacency matrix, and constructing the double-layer coupled heat wave-extreme precipitation network based on the inter-layer interaction adjacency matrix; Calculate the degree centrality, betweenness centrality, clustering coefficient and average synchronization distance of the single-layer network respectively; The cross-degree centrality, cross-covariance centrality, cross-clustering coefficient, and cross-synchronization distance of the two-layer network were calculated respectively.

6. The community structure detection method for spatial concurrent extreme climate events according to claim 1, characterized in that: Based on the two-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm was used to obtain stable community classification results, including: The two-layer coupled heat wave-extreme precipitation network is converted into a weighted single-layer network using a direct flattening method; Performing community partitioning on the weighted single-layer network using the Leiden community detection algorithm to obtain an initial community partitioning result; The consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partition result to obtain an integrated community partition result; A lead-lag correlation analysis is performed on the integrated community partitioning result to obtain a specific community synchronization index time series, the specific community synchronization index time series is smoothed by a Butterworth low-pass filter, and a lead-lag correlation analysis is performed on the specific community synchronization index time series of any two communities to obtain the stable community classification result.

7. The community structure detection method for spatial concurrent extreme climate events according to claim 6, characterized in that: The weighted single-layer network is divided into communities using the Leiden community detection algorithm to obtain an initial community partition result, including: Taking the initial node as an independent community, gradually move a single node to other communities, and determine whether to accept the movement of the current node based on the change in modularity to obtain the local movement partition result; Modifying the local mobile division result to divide the nodes with less than a preset number of connections into two sub-community nodes; Merge subcommunity nodes, build a new simplified network, retain the original community number, and cluster the new network again; Repeat the above steps until the modularity stops increasing, obtain the initial community partition result, and determine the community category number to which each grid point belongs.

8. The community structure detection method for spatial concurrent extreme climate events according to claim 7, characterized in that: The consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partition results, and an integrated community partition result is obtained, including: Applying the Leiden community detection algorithm to a functional climate network a preset number of times to generate a preset number of partition results, the functional climate network having a number of nodes; Sorting the preset number of partition results according to modularity, and extracting the first preset number of partitions with the highest modularity; The consensus matrix is ​​calculated by the number of partitions in which any two nodes belong to the same community and the total number of partitions; The items in the consensus matrix that are below the threshold are set to 0 to obtain a filtered consensus matrix; Applying the Leiden community detection algorithm to the filtered consensus matrix again according to the preset number of times to generate a preset number of new partition results; If the number of partitions in the preset number of new partition results is equal, and the normalized mutual information between multiple partitions is greater than a preset value, the iteration is stopped to obtain the integrated community partition result, otherwise the consensus matrix is ​​recalculated.

9. A community structure detection system for spatial concurrent extreme climate events, characterized in that: include: A calculation and verification module is used to collect grid temperature and precipitation data in the study area, extract binary time series of heat wave events and extreme precipitation events from the grid temperature and precipitation data, perform event synchronization determination calculation and significance test on the binary time series, and obtain a nonlinear adjacency matrix; A construction module is used to establish a single-layer heat wave network and a single-layer extreme precipitation network according to the nonlinear adjacency matrix, construct a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connection between the heat wave layer and the precipitation layer, and calculate the single-layer network coefficient and the double-layer network coefficient; The detection module is used to obtain a stable community classification result based on the double-layer coupled heat wave-extreme precipitation network by using a community clustering method combining the Leiden community detection algorithm and the consensus clustering algorithm.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the community structure detection method for spatial concurrent extreme climate events as described in any one of claims 1 to 8 is implemented.

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