A method and system for detecting community structure in the event of concurrent extreme weather events in space.

Abstract

This invention provides a method and system for detecting community structure in spatially concurrent extreme climate events, comprising: collecting gridded temperature and precipitation data of the study area, extracting binary time series of heat waves and extreme precipitation events, and performing event synchronization determination calculations and significance tests; constructing a two-layer coupled heat wave-extreme precipitation network based on the inter-layer adjacency matrix; obtaining stable community classification results based on the two-layer coupled network using a community detection method combining the Leiden algorithm and consensus clustering; performing lead-lag correlation analysis on all community pairs to identify key community pairs with strong correlations and their lag times, and further exploring the spatiotemporal propagation characteristics of climate events. This invention fully utilizes the advantages of two-layer coupled climate network analysis, combining the Leiden algorithm and consensus clustering method to improve the accuracy and stability of community detection, and can effectively reveal the spatial concurrency characteristics and spatiotemporal propagation patterns of global extreme climate events.

Description

Technical Field

[0001] This invention relates to the field of climate analysis technology, and in particular to a method and system for detecting community structure during concurrent extreme climate events in space. Background Technology

[0002] Due to global warming, the frequency, intensity, and impact of heat waves and extreme precipitation events have increased significantly, severely affecting human life, the ecological environment, economic activities, agricultural production, and food security. These extreme events exhibit spatial and temporal correlations across different regions of the world, potentially driven by shared circulation patterns. However, research on the spatial co-occurrence of heat waves and extreme precipitation is currently lacking, despite the wide-ranging and profound impacts of such events. For example, in the summer of 2022, eastern China, Western Europe, western America, Eastern Europe, and eastern Siberia experienced a persistent heat wave, while Pakistan, southern China, and Brazil experienced record-breaking heavy precipitation events, causing severe impacts on human societies. Therefore, a deep understanding and grasp of the spatial co-occurrence characteristics of heat waves and extreme precipitation is crucial for addressing the challenges posed by global warming.

[0003] While complex network frameworks have demonstrated broad application potential in the synchronization and propagation analysis of extreme rainfall, heat waves, and droughts—by abstracting geographical locations as nodes and constructing edges based on the nonlinear correlations between extreme event sequences to reveal the intrinsic connections between extreme events in different locations—existing research primarily focuses on univariate climate extreme events. Comprehensive analysis of simultaneous heat waves and extreme precipitation events occurring in multiple locations remains lacking. Furthermore, although community detection in climate network analysis can effectively cluster regions with similar climate characteristics, traditional algorithms often face problems such as disconnected communities and unstable results.

[0004] Therefore, there is an urgent need to develop innovative technical methods to address the challenges of community detection of multivariable spatially concurrent extreme climate events. Summary of the Invention

[0005] This invention provides a method and system for detecting community structure during concurrent extreme weather events in space, in order to address the deficiencies in existing technologies.

[0006] In a first aspect, the present invention provides a method for detecting community structure during concurrent extreme weather events in space, comprising:

[0007] Gridded temperature and precipitation data of the study area are collected, and binary time series of heat wave events and extreme precipitation events are extracted from the gridded temperature and precipitation data. Event synchronization determination calculation and significance test are performed on the binary time series to obtain a nonlinear adjacency matrix.

[0008] Based on the nonlinear adjacency matrix, a single-layer heat wave network and a single-layer extreme precipitation network are established respectively. By calculating the interlayer connection between the heat wave layer and the precipitation layer, a double-layer coupled heat wave-extreme precipitation network is constructed, and the single-layer network coefficient and the double-layer network coefficient are calculated.

[0009] Based on the aforementioned dual-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 stable community classification results.

[0010] According to a method for detecting community structure in spatially concurrent extreme climate events provided by the present invention, gridded temperature and precipitation data of a study area are collected. Binary time series of heat wave events and extreme precipitation events are extracted from the gridded temperature and precipitation data. Event synchronization determination calculations and significance tests are performed on the binary time series to obtain a nonlinear adjacency matrix, including:

[0011] Temperature data from the global CPC grid dataset and the ERA5 reanalysis dataset are collected, and precipitation data from the global CPC grid dataset and the MSWEP dataset are collected. Bilinear interpolation is used to interpolate the temperature data and the precipitation data to a preset resolution.

[0012] The extreme high-temperature phenomenon in a specific region and within a specified time period, where the daily maximum temperature exceeds a preset percentage quantile of the temperature sequence and the duration is not less than a preset number of days, is extracted as the heat wave event;

[0013] Events with precipitation exceeding a preset percentage quantile in the time series of rainy days are extracted as the extreme precipitation events;

[0014] The binary time series is constructed from the heat wave event and the extreme precipitation event;

[0015] The event synchronicity of the binary time series is calculated using a nonlinear event synchronization metric method.

[0016] The significance test of the binary time series is calculated based on the null model distribution.

[0017] According to a method for detecting community structure in spatially concurrent extreme climate events provided by the present invention, the event synchronicity of the binary time series is calculated using a nonlinear event synchronization metric method, including:

[0018] Extract any two grid points in the space corresponding to the binary time series, and determine the first event occurrence time and the second event occurrence time corresponding to the two grid points. The first event occurrence time and the second event occurrence time are constrained by the total number of heat wave events or the total number of extreme precipitation events of the two grid points.

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

[0020] Obtain the event occurrence time difference between any two grid points, determine the maximum delay time, and if the event occurrence time difference is less than the dynamic delay and less than the maximum delay time, then determine that the events of any two grid points are synchronous.

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

[0022] According to the present invention, a method for detecting community structure in spatially concurrent extreme climate events, the significance test of the binary time series is calculated based on the null model distribution, including:

[0023] Each observation in the binary time series is randomly shuffled along the time dimension to generate a null model distribution;

[0024] A preset quantile in the null model distribution is determined as a significance threshold. If any observation exceeds the significance threshold, then the observation is determined to be significant at a preset level.

[0025] According to the community structure detection method for concurrent extreme climate events in space provided by the present invention, a single-layer heat wave network and a single-layer extreme precipitation network are established based on the nonlinear adjacency matrix, and a double-layer coupled heat wave-extreme precipitation network is constructed by calculating the interlayer connectivity between the heat wave layer and the precipitation layer. The single-layer network coefficient and the double-layer network coefficient are calculated, including:

[0026] Obtain global effective grid points, perform event synchronization calculations on the global effective grid points to obtain the synchronization intensity matrix, remove weakly correlated edges in the climate network through zero 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 respectively.

[0027] Event synchronization and saliency verification are performed on any node in the single-layer heat wave network and any node in the single-layer extreme precipitation network to obtain the inter-layer interaction adjacency matrix. The double-layer coupled heat wave-extreme precipitation network is constructed from the inter-layer interaction adjacency matrix.

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

[0029] Calculate the cross-degree centrality, cross-sigma centrality, cross-clustering coefficient, and cross-synchronization distance of the two-layer network.

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

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

[0032] The weighted single-layer network is divided into communities using the Leiden community detection algorithm to obtain initial community partitioning results.

[0033] The consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partitioning results, resulting in an integrated community partitioning result.

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

[0035] According to a method for detecting community structure in spatially 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 initial community partitioning results, including:

[0036] Using the initial node as an independent community, individual nodes are gradually moved to other communities. The decision on whether to accept the move of the current node is based on the change in modularity, thus obtaining the local move partitioning result.

[0037] Modify the local movement partitioning result to divide nodes with fewer than the preset number of connections into two sub-community nodes;

[0038] Merge sub-community nodes to build a new simplified network, retain the original community IDs, and then re-cluster the new network;

[0039] Repeat the aforementioned steps until the modularity no longer increases, to obtain the initial community partitioning result, and determine the community category number to which each grid point belongs.

[0040] According to the present invention, a method for detecting the community structure of concurrent extreme climate events in space utilizes the consensus clustering algorithm to eliminate the uncertainty and variability in the initial community partitioning results, obtaining integrated community partitioning results, including:

[0041] The Leiden community detection algorithm is applied to the functional climate network a preset number of times to generate a preset number of partition results. The functional climate network has several nodes.

[0042] The partition results of the preset number of partitions are sorted according to the modularity, and the top preset number of partitions with the highest modularity are extracted.

[0043] Calculate the consensus matrix using the number of partitions belonging to the same community for any two nodes and the total number of partitions;

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

[0045] The Leiden community detection algorithm is applied again to the filtered consensus matrix a 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 are all equal, and the normalized mutual information between multiple partitions is greater than a preset value, then the iteration stops and the integrated community partition result is obtained; otherwise, the consensus matrix is ​​recalculated.

[0047] Secondly, the present invention also provides a community structure detection system for concurrent extreme weather events in space, comprising:

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

[0049] The 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, respectively. By calculating the interlayer connection between the heat wave layer and the precipitation layer, a double-layer coupled heat wave-extreme precipitation network is constructed, and the single-layer network coefficient and the double-layer network coefficient are calculated.

[0050] The detection module is used to obtain stable community classification results based on the dual-layer coupled heat wave-extreme precipitation network by employing a community clustering method that combines the Leiden community detection algorithm and the consensus clustering algorithm.

[0051] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the community structure detection method for concurrent extreme climate events in space as described above.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] Based on event synchronization and significance testing, this invention provides an in-depth analysis of the nonlinear correlation between extreme event sequences in different geographical locations, offering a solid theoretical foundation for revealing the intrinsic correlation between concurrent extreme climate events in space.

[0054] This invention constructs a two-layer coupled climate complexity network. By analyzing the high-order topological characteristics of single-layer and two-layer networks, it improves the understanding of the nonlinear dynamics of the Earth system, the teleconnection and concurrent characteristics of extreme climate events, and the energy transfer mechanism.

[0055] This invention is the first to combine the advanced Leiden community detection algorithm with consensus clustering theory, proposing a new community clustering method for multivariate spatial concurrent extreme weather events. This method effectively reduces the probability of disconnection within communities and improves the stability of community partitioning results. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0057] Figure 1 This is one of the flowcharts illustrating the community structure detection method for concurrent extreme climate events in space provided by this invention;

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

[0059] Figure 3 This is a flowchart of the event synchronization calculation provided by the present invention;

[0060] Figure 4 This invention provides a network geographic distance teleconnection distribution map with different maximum delay thresholds;

[0061] Figure 5 This is a flowchart of the Leiden community detection algorithm provided by the present invention;

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

[0063] Figure 7 This is a community partitioning result diagram of the two-layer coupled climate network provided by the present invention, wherein, Figure 7 (a) represents the number of community grid points. Figure 7 (b) Optimize consensus clustering parameters;

[0064] Figure 8 This is a diagram showing the community lead-lag correlation analysis and seasonal distribution results provided by this invention. Figure 8 (a) shows the seasonal distribution. Figure 8 (b) is the lead-lag correlation coefficient. Figure 8 (c) represents the number of days ahead of or behind the deadline;

[0065] Figure 9 This is a schematic diagram of the community structure detection system for concurrent extreme climate events in space provided by the present invention;

[0066] Figure 10 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0068] To address the problem of community detection and analysis of multivariate spatially concurrent extreme weather events in existing technologies, this invention proposes a method for detecting community structure in spatially concurrent extreme weather events. Figure 1 This is one of the flowcharts illustrating the community structure detection method for concurrent extreme weather events in space provided by an embodiment of the present invention, such as... Figure 1 As shown, including:

[0069] Step 100: Collect gridded temperature and precipitation data of the study area, extract binary time series of heat wave events and extreme precipitation events from the gridded temperature and precipitation data, perform event synchronization determination calculation and significance test on the binary time series, and obtain a nonlinear adjacency matrix;

[0070] Step 200: Establish a single-layer heat wave network and a single-layer extreme precipitation network based on the nonlinear adjacency matrix. Construct a double-layer coupled heat wave-extreme precipitation network by calculating the interlayer connection between the heat wave layer and the precipitation layer. Calculate the single-layer network coefficient and the double-layer network coefficient.

[0071] Step 300: Based on the aforementioned dual-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 stable community classification results.

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

[0073] Step 1: Collect gridded temperature and precipitation data for the study area, extract binary time series of heat waves and extreme precipitation events, and perform event synchronization determination calculation and significance test.

[0074] Step 2: Based on the nonlinear adjacency matrix calculated in Step 1, construct a single-layer heat wave network and a single-layer extreme precipitation network, respectively. Next, calculate the interlayer connectivity between the heat wave layer and the precipitation layer to further construct a two-layer coupled heat wave-extreme precipitation network. By calculating and analyzing the coefficients of the single-layer and two-layer networks, we can better understand the underlying topology of the network.

[0075] Step 3: Based on the aforementioned dual-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, lead-lag correlation analysis is performed on all community pairs to identify key highly correlated community pairs and their lag times, thereby analyzing the spatiotemporal propagation characteristics.

[0076] This invention leverages the advantages of dual-layer coupled climate network analysis, combined with the scientific rigor of the Leiden algorithm and consensus clustering methods, to improve the accuracy and stability of community detection. It can effectively reveal the spatial concurrency characteristics and spatiotemporal propagation patterns of global extreme climate events.

[0077] In one embodiment, step 1 includes:

[0078] Step 1.1: Collection of basic temperature and precipitation data. Temperature data was obtained from the global CPC grid dataset and the ERA5 reanalysis dataset, while precipitation data used the global CPC grid dataset and the MSWEP (V2.8) dataset. Bilinear interpolation was employed to interpolate the temperature and precipitation data to a preset resolution.

[0079] Specifically, the CPC gridded dataset (Unified Gauge-Based Analysis of Global Daily Precipitation) is generated by fusing station-measured data and remote sensing inversion data, with a resolution of 0.5°×0.5°; the ERA5 dataset is the fifth-generation atmospheric reanalysis product from the European Centre for Medium-Range Weather Forecasts (ECMWF), with a spatial resolution of 0.25°×0.25° and a temporal resolution of 1 hour. ERA5 employs a more advanced land surface assimilation system, improves the simulation of the land-sea boundary water cycle, and optimizes the estimation of bare land evapotranspiration; this invention uses the MSWEP V2.8 (Multi-Source Weighted-Ensemble Precipitation) dataset, with a spatial resolution of 0.1°×0.1° and a temporal resolution of 3 hours. This product fuses station, satellite, and reanalysis data, and in densely populated and stationless areas, MSWEP often outperforms other precipitation products. To ensure data consistency, this invention uses bilinear interpolation in 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 this invention, the data used covers the time range of Northern Hemisphere summer (June, July, and August) from 1979 to 2023, and the spatial range is a gridded area from 60°S to 60°N globally.

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

[0081] The definition of a heat wave event is as follows:

[0082] ① Identify extreme heat events: Days in the Northern Hemisphere from June to August whose daily maximum temperature exceeds the 90th percentile of the temperature series are defined as extreme heat events;

[0083] ② Define a heatwave event: Select the minimum number of consecutive 3 days to define a heatwave event;

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

[0085] ④ Handling the year-end boundary: During the year-end period, in order to avoid the deviation of the synchronous estimation of heat waves between different grid points, 10 "0"s are inserted at the boundary between two years;

[0086] ⑤ Region 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] The definition of extreme precipitation events is 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 90th percentile of the sequence, then that date is defined as an extreme precipitation day.

[0090] ③ Merging consecutive precipitation events: If multiple extreme precipitation events occur consecutively in time, they are merged into a single event, with the first day of occurrence taken as the starting date of the event;

[0091] ④ Handling year-end boundaries: Similarly, fill the two-year boundary at the year-end period with 10 "0"s to avoid bias in the synchronous estimation of events at different grid points;

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

[0093] Under the above definition, a day is represented by "1" if a heat wave or extreme precipitation event is detected, and by "0" if no extreme event occurs. 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 has occurred.

[0094] However, extreme events that occur across seasons may appear consecutively in a binary time series. To distinguish events occurring in different seasons, 10 zeros are inserted at the boundary between years for each grid point to avoid bias in the synchronous calculation of events at different grid points.

[0095] Step 1.3: Event Synchronization Judgment Calculation. To assess the synchronicity of heatwave and extreme precipitation event time series among all grid pairs globally, this invention employs a nonlinear event synchronization metric. This method was first proposed by Quiroga et al. in 2002, initially used to analyze electroencephalogram (EEG) neural signals. Subsequently, Malik et al. first applied this method to the correlation between extreme precipitation events in the Indian subcontinent in 2012. A significant advantage of the event synchronization method is its ability to handle the dynamic time lags between extreme events at two different spatial locations, thus measuring their temporal consistency. Because this method does not assume that the data follows a specific probability distribution, it exhibits great flexibility in handling extreme events. Furthermore, the event synchronization method can accurately consider the time intervals between events, making it particularly suitable for analyzing extreme events with non-uniform time intervals. The event synchronization calculation flowchart is shown below. Figure 3 As shown.

[0096] For any two grid points i and j in space, assume that the event at grid point i occurs at time point j. The event at lattice point j occurs at time point. 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 The grid pairs i and j at time points are determined. and Whether a pair of events is considered a synchronous event is defined as follows:

[0098]

[0099] In the formula Let i be the time point at which the event occurs. and Let i be the time points when the previous and next events occurred; Let j be the time point of the event occurrence. and Let J be the time points when the previous and next events occurred at grid point J.

[0100] To avoid excessively long delays between two synchronized events that contradict real-world conditions, a maximum delay time τ is set. max =10 days. When and At that time, it is assumed that event m at grid point i and event n at grid point j are synchronous. Positive and negative representation and The order in which they occur represents the direction of the concurrent propagation of extreme weather events in space.

[0101] Furthermore, C(i|j) is defined as representing the total number of events occurring in grid cell j that precedes the total number of events occurring in grid cell i:

[0102]

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

[0104]

[0105] in:

[0106]

[0107]

[0108] This indicates that extreme weather event v occurred at grid point j before extreme weather event u occurred at grid point i. The meanings are opposite.

[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, and its definition is as follows:

[0110]

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

[0112] Unlike the static delay in linear correlation analysis, event synchronization considers dynamic delay, making it a suitable tool for studying nonlinear temporal relationships. In this invention, maximum dynamic delays of 3 days, 7 days, and 10 days were used to obtain network geographic distance telecorrelation distribution maps under these three maximum dynamic delays (e.g., ...). Figure 4 As shown in the figure, the results indicate that the maximum dynamic delay has little impact 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 through event synchronization, a significance test is required to retain physically meaningful significant connections and remove insignificant connections.

[0114] This invention employs the method proposed by Boers et al. in 2019, utilizing null hypothesis testing to eliminate weakly correlated connections from the climate network. Specifically, a null model distribution is generated by randomly shuffling each observation along 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 an observation exceeds this threshold, the synchronization between node i and node j is considered significant at the 0.001 level, and these edges are preserved in the network. Therefore, the final synchronization strength matrix is ​​transformed into a binary adjacency matrix, representing significant connections between grid points.

[0115] The specific calculation steps are as follows:

[0116] ① Randomly shuffle the sequences 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 event sequences based on random fields;

[0118] ③ Repeat steps ① and ② 1000 times to obtain the null model Q of the synchronization intensity matrix.null This yields the reference distribution results for each grid point.

[0119] ④ Take The 99.9th percentile (significance level p = 0.001) was used as the threshold θ for a significant connection between two grid points. ij,sig If the synchronization strength between grid points i and j exceeds the threshold, they are considered to be synchronously significant at the 0.001 significance level, and their interconnection is preserved as an edge in the complex network.

[0120]

[0121] in This indicates that the events in grid cell i and the events in grid cell j are statistically significantly synchronized.

[0122] In one embodiment, step 2 includes:

[0123] Complex network methods offer an effective tool for revealing spatial patterns of extreme climate events and inferring underlying physical processes. By statistically analyzing the network topology, climate data can be transformed into a network model (adjacency matrix), where nodes represent geographic grid cells and links between nodes represent the correlations between extreme events. Climate networks are spatially embedded networks; their construction involves identifying nodes and links and detecting correlations between nodes using similarity metrics. Combined with network analysis tools, complex network methods extend traditional analytical approaches, enabling in-depth exploration of nonlinear time-series relationships within the climate system and yielding conclusions that are difficult to reveal using traditional methods.

[0124] Based on the nonlinear adjacency matrix of the event synchronization metric obtained in step 1, a single-layer heat wave network and a single-layer extreme precipitation network are established. Next, the inter-layer connectivity between the heat wave layer and the precipitation layer is calculated to further construct a two-layer coupled heat wave-extreme precipitation network. Calculating and analyzing the coefficients of the single-layer and two-layer networks helps to understand the underlying topology of the networks. The coefficients of the single-layer network include degree centrality, betweenness centrality, clustering coefficient, and average synchronization distance; the coefficients of the two-layer network include cross degree centrality, cross betweenness centrality, cross clustering coefficient, and cross synchronization distance.

[0125] Step 2.1: Construction of a Single-Layer Complex Climate Network. In the case provided by this invention, there are 11,022 valid grid points globally. After the event synchronization calculation is completed, a synchronization intensity matrix with dimensions of 11,022 × 11,022 will be obtained. Through null model verification, weakly correlated edges in the climate network are removed, thus obtaining a significantly connected binary adjacency matrix. Based on the adjacency matrices of heat waves and extreme precipitation, single-layer complex networks for heat waves or extreme precipitation are 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 for revealing complex processes from local to regional and even continental scales. This invention 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 separately and its significance is tested to construct the corresponding single-layer complex network. Then, event synchronization is performed on node i in the heat wave network and node j in the extreme precipitation network, and its significance is tested to obtain the adjacency matrix of inter-layer interactions. Therefore, the adjacency matrix of the two-layer coupled climate network is described as follows:

[0128]

[0129] Where Θ(·) represents the Heaviside function. This represents the event synchronization metric for grid pairs i and j between the heat wave and extreme precipitation subnetworks. T is the 99.9 percentile threshold of the null model. These are Kronecker increments used to avoid self-loops. The two diagonal blocks of the matrix represent the adjacency matrices of two univariate networks (heat waves or extreme precipitation), while the off-diagonal blocks represent bivariate network blocks (the coupling relationship between heat waves and extreme precipitation).

[0130] Step 2.3: Single-layer network coefficient calculation. By calculating the statistical topology of the adjacency matrix, various network metrics can be derived, thereby deepening the understanding of the spatiotemporal concurrency characteristics of extreme events at the regional and global scales. However, when processing 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 issue, each node is typically assigned a weight corresponding to the spatial region it represents, known as the node split invariant (NSI) metric.

[0131] w i =cosλ i

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

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

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

[0135]

[0136] Where N is the total number of grid cells in the network; This represents the synchronous adjacency matrix. The degree indicates the number of grid cells that experience a heat wave or extreme precipitation event synchronously with this grid cell. Grid cells with higher DC have a greater impact on the network's functionality or sensitivity.

[0137] Betweenness centrality is an important indicator of information transmission, representing the influence of a specific node on information transmission between other nodes. The betweenness centrality (BC) of lattice node 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 from 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 crucial role in the information transmission process in the network, acting as "bridges" or "bottlenecks" for information propagation.

[0140] Clustering coefficients reflect the connection density between a node and its neighboring nodes. The clustering coefficient (CC) of grid node i represents the ratio of the actual number of edges connected to grid node i to the probabilistically maximum number of possible edges, defined as follows:

[0141]

[0142] Where ζ i D represents the actual number of connections between the adjacent nodes of node i; i Represents the degree of a node; CC i The higher the value, the more tightly the nodes around grid point i are connected to each other, indicating that the extreme events in this region are more synchronized.

[0143] The average synchronization distance (MSD) represents the average spatial range of a grid point's influence on propagation within a network, defined by the following formula:

[0144]

[0145] Where d ij Q represents the geographical distance between grid points i and j. ij Indicates synchronization measurement. This represents the synchronous adjacency matrix. A higher MSD value indicates that grid points can propagate to a more distant region.

[0146] Step 2.4: Calculation of two-layer network coefficients. Furthermore, this invention also calculates four multi-layer network coefficients for the two-layer coupled heatwave-extreme precipitation event network: Cross-degree centrality (CDC), Cross-symmetry centrality (CBC), Cross-clustering coefficient (CCC), and Cross-synchronization distance (CSD).

[0147] This invention constructs a two-layer network G = (V, E), where V is a grid cell and E is a connecting edge. pp Represents subnetwork G p The internal connections of E, and E pq G represents p and G q Interactive connections between them. In this invention, indices p and q represent sub-networks, while v, w, i, and j represent individual grid points.

[0148] Cross-degree centrality (CDC) refers to the degree of cross-degree centrality of a node v (v∈G). p In another subnetwork G q The number of connected neighbors in the network is calculated using the following formula:

[0149]

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

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

[0152]

[0153] Here, 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. A high CBC node can act as a communication hub between two sub-networks.

[0154] Local cross-clustering coefficient (CCC) is calculated for node v (v∈G). p ) and two randomly selected neighbors i and j (i ≠ j ∈ G)q The probability of becoming neighbors. The calculation formula is as follows:

[0155]

[0156] A higher number of grid points in the CCC indicates that the variability of different climate variables in the region is similar.

[0157] Cross-synchronization distance (CSD) represents the average geographic connectivity scale between a grid cell and other subnetworks. The calculation formula is as follows:

[0158]

[0159] in, It is node v (v∈G) p ) and node j (j∈G) q The geographical distance between them. It is a significant cross-adjacency matrix. It represents the event synchronization strength. A high CSD indicates a region's connection to a long-range network.

[0160] In one embodiment, step 3 includes:

[0161] Based on the aforementioned dual-layer coupled heat wave-extreme precipitation network, a community clustering method combining the Leiden community detection algorithm and consensus clustering theory is employed to obtain stable community classification results. Subsequently, lead-lag correlation analysis is performed on all community pairs to identify key community pairs with strong correlations and their lag times, thereby analyzing the temporal and spatial propagation characteristics of these community pairs. The flowchart of the Leiden community detection algorithm provided by this invention is shown below. Figure 5 As shown, the flowchart of the consensus clustering community structure detection algorithm for a two-layer coupled climate network is as follows: Figure 6 As shown.

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

[0163] A community is a cluster of nodes in a network that is tightly interconnected internally but loosely connected externally. In climate function networks, communities have physical significance because they are determined by the network's connectivity structure and represent physical patterns 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] This invention extends the community structure to multivariate coupled networks, but only considers pillar communities. Specifically, considering that the adjacency matrix includes all links within the heatwave and extreme precipitation layers, as well as cross-links between the heatwave-extreme precipitation networks, this invention employs a direct flattening method to convert the multilayer network into a weighted single-layer network, and then applies the Leiden algorithm for community partitioning. The Leiden algorithm is an improvement on the classic Louvain algorithm for community detection, and it measures the quality of different community partitions based on modularity.

[0165] In network theory, maximizing modularity is a technique for discovering substructures (or communities), defined as follows:

[0166]

[0167] Where Mod is the global modularity, Mod∈[0,1]; M represents the total number of connections in the undirected network. k i and k j c represents the degree of node i and node j, respectively; i and c j Let be the communities of nodes i and j, respectively. If nodes i and j belong to the same community, then δ(C i C j ) = 1, otherwise, δ(C) = 1. i C j The modularity value is 0. A higher modularity value indicates stronger connections between nodes within a community and weaker connections between nodes in different communities. Generally, network partitions with modularity values ​​between 0.3 and 0.8 are considered to have a more pronounced community structure.

[0168] Since most community detection methods suffer from uncertainty and partitioning volatility, this invention employs a consensus clustering algorithm to improve stability by integrating multiple partitioning results. Specifically, the Leiden algorithm is iterated 1000 times to identify consistent community structures in the climate function network. First, a certain number of samples are extracted based on the modularity ranking, and a consensus matrix is ​​constructed. Then, threshold filtering is applied and iterative calculations are performed multiple times to finally detect stable community structures.

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

[0170] Step 3.1.1: Leiden Community Detection Algorithm. The Leiden algorithm, proposed by researchers at Leiden University in 2019, 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 disconnected communities. The flowchart of the Leiden community detection algorithm is shown below. Figure 5 As shown. The main steps of Leiden's algorithm are as follows:

[0171] (1) Local Movement Phase. In this phase, geographical grid points are treated as nodes in the network, with each node initially forming an independent community. Subsequently, individual nodes are gradually moved from one community to another, and the decision to accept the move is based on the change in modularity. If the movement of a node increases the modularity, the movement is accepted, thus forming a new community division.

[0172] (2) Modification of nodes within the community. The partitioning result from step (1) is modified to further refine the node partitioning within the community. Nodes with lower connectivity within the community will be divided into two sub-communities. For example, Figure 5 In the process, the red community was revised and divided into two sub-communities. Although the sub-communities are treated as independent nodes during network cohesion, they still belong to the original community. This step ensures a more refined community division while further improving the overall modularity.

[0173] (3) Network Cohesion. Based on the revised community division, all nodes in each sub-community are merged to construct a new simplified network structure. At this point, the nodes retain their original community numbers. The new network is then 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 obtains a stable number of communities by iterating the community detection algorithm multiple times and utilizing the community detection results from multiple networks. The process of the consensus clustering algorithm is as follows: Figure 6 As 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 to generate 1000 partition results.

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

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

[0180]

[0181] In the formula n ijis the number of partitions in which nodes i and j belong to the same community, and n is the total number of partitions.

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

[0183] (5) Apply clustering algorithm A to the filtered consensus matrix n times to generate n partition results.

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

[0185] The formula for calculating NMI is as follows:

[0186]

[0187] Where A and B represent two sets of community structure detection results, respectively; C A and C B These represent the number of community structures in A and B, respectively.

[0188] In (1), the Leiden algorithm is selected as the basic method of algorithm A in this invention. 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 consensus clustering.

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

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

[0191]

[0192] Where A represents a specific community; HW k and EPE k Let represent the time series of heatwave and extreme precipitation events at grid point k, respectively. This index quantifies the frequency of synchronous extreme events occurring daily in community A; a higher value indicates that more regionally concurrent extreme climate events occurred on date t.

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

[0194]

[0195] Here, A and B represent two different communities; Δt represents the lag time; and Ms represents the total number of summer days from 1979 to 2023. This analysis allows us to identify strongly correlated regional pairs and to gain a preliminary understanding of how long it might take for spatially simultaneous extreme events to propagate from one community to another.

[0196] The community lead-lag correlation analysis and seasonal distribution results provided by this invention are shown in the figure below. Figure 8 As shown. Figure 8 (a) shows the seasonal distribution of extreme weather events in the multi-year average Northern Hemisphere summer across 13 communities. Communities 6 and 9 show particularly frequent extreme weather events from mid-July to early August, while other communities exhibit different seasonal peaks. This suggests significant spatial differences in the temporal characteristics of heat waves and extreme precipitation events across regions, potentially related to different regional climate patterns and weather systems. Figure 8 (b) and Figure 8 (c) The lead-lag correlation coefficients and the lead-lag days corresponding to the maximum correlation coefficients are shown for each community. Communities 5 and 7, which are geographically distant, show a high positive correlation with a lag of -13 days, suggesting that extreme events in these areas may have spatiotemporal propagation effects. Community information obtained from complex networks supports a better understanding of the interactions between extreme climate events in different regions and provides a scientific basis for the prediction and prevention of future extreme weather events.

[0197] The community structure detection system for concurrent extreme weather events in space provided by this invention is described below. The community structure detection system for concurrent extreme weather events in space described below can be referred to in correspondence with the community structure detection method for concurrent extreme weather events in space described above.

[0198] Figure 9 This is a schematic diagram of the community structure detection system for concurrent extreme weather events in space provided in an embodiment of the present invention, as shown below. Figure 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 gridded temperature and precipitation data of the study area, extract binary time series of heat wave events and extreme precipitation events from the gridded 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 build 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 interlayer 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 stable community classification results 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] Figure 10 An example of a physical structure diagram of an electronic device is shown below. Figure 10 As shown, the electronic device may include: a processor 1010, a communications interface 1020, a memory 1030, and a communications bus 1040, wherein the processor 1010, the communications interface 1020, and the memory 1030 communicate with each other through the communications bus 1040. The processor 1010 can call logic instructions in the memory 1030 to execute a community structure detection method for spatially concurrent extreme climate events. This method includes: collecting gridded temperature and precipitation data of the study area; extracting binary time series of heat wave events and extreme precipitation events from the gridded temperature and precipitation data; performing event synchronization determination calculation and significance testing 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 based on the nonlinear adjacency matrix; constructing a double-layer coupled heat wave-extreme precipitation network by calculating the inter-layer connections of the heat wave layer and the precipitation layer; calculating the single-layer network coefficients and the double-layer network coefficients; and obtaining stable community classification results based on the double-layer coupled heat wave-extreme precipitation network using a community clustering method combining the Leiden community detection algorithm and a consensus clustering algorithm.

[0201] Furthermore, the logical instructions in the aforementioned memory 1030 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0202] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0203] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments 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, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for detecting community structure during concurrent spatial extreme weather events, characterized in that, include: Gridded temperature and precipitation data of the study area are collected, and binary time series of heat wave events and extreme precipitation events are extracted from the gridded temperature and precipitation data. Event synchronization determination calculation and significance test are performed on the binary time series to obtain a nonlinear adjacency matrix. Based on the nonlinear adjacency matrix, a single-layer heat wave network and a single-layer extreme precipitation network are established respectively. By calculating the interlayer connection between the heat wave layer and the precipitation layer, a double-layer coupled heat wave-extreme precipitation network is constructed, and the single-layer network coefficient and the double-layer network coefficient are calculated. Based on the aforementioned dual-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 stable community classification results.

2. The community structure detection method for concurrent extreme climate events in space according to claim 1, characterized in that, Gridded 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 gridded temperature and precipitation data. Event synchronization determination and significance testing are performed on the binary time series to obtain a nonlinear adjacency matrix, including: Temperature data from the global CPC grid dataset and the ERA5 reanalysis dataset are collected, and precipitation data from the global CPC grid dataset and the MSWEP dataset are collected. Bilinear interpolation is used to interpolate the temperature data and the precipitation data to a preset resolution. The extreme high-temperature phenomenon in a specific region and within a specified time period, where the daily maximum temperature exceeds a preset percentage quantile of the temperature sequence and the duration is not less than a preset number of days, is extracted as the heat wave event; Events with precipitation exceeding a preset percentage quantile in the time series of rainy days are extracted as the extreme precipitation events; The binary time series is constructed from the heat wave event and the extreme precipitation event; The event synchronicity of the binary time series is calculated using a nonlinear event synchronization metric method. The significance test of the binary time series is calculated based on the null model distribution.

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

4. The method for detecting community structure in concurrent extreme climate events in space according to claim 3, characterized in that, The significance test of the binary time series is calculated based on the null model distribution, including: Each observation in the binary time series is randomly shuffled along the time dimension to generate a null model distribution; A preset quantile in the null model distribution is determined as a significance threshold. If any observation exceeds the significance threshold, then the observation is determined to be significant at a preset level.

5. The method for detecting community structure in concurrent extreme climate events in space according to claim 1, characterized in that, Based on the aforementioned nonlinear adjacency matrix, a single-layer heat wave network and a single-layer extreme precipitation network are established respectively. By calculating the interlayer connectivity between the heat wave layer and the precipitation layer, a two-layer coupled heat wave-extreme precipitation network is constructed. The single-layer network coefficients and the two-layer network coefficients are calculated, including: Obtain global effective grid points, perform event synchronization calculations on the global effective grid points to obtain the synchronization intensity matrix, remove weakly correlated edges in the climate network through zero 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 respectively. Event synchronization and saliency verification are performed on any node in the single-layer heat wave network and any node in the single-layer extreme precipitation network to obtain the inter-layer interaction adjacency matrix. The double-layer coupled heat wave-extreme precipitation network is constructed from the inter-layer interaction adjacency matrix. Calculate the degree centrality, betweenness centrality, clustering coefficient, and average synchronization distance of a single-layer network; Calculate the cross-degree centrality, cross-sigma centrality, cross-clustering coefficient, and cross-synchronization distance of the two-layer network.

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

7. The method for detecting community structure in concurrent extreme climate events in space according to claim 6, characterized in that, The weighted single-layer network is divided into communities using the Leiden community detection algorithm to obtain initial community partitioning results, including: Using the initial node as an independent community, individual nodes are gradually moved to other communities. The decision on whether to accept the move of the current node is based on the change in modularity, thus obtaining the local move partitioning result. Modify the local movement partitioning result to divide nodes with fewer than the preset number of connections into two sub-community nodes; Merge sub-community nodes to build a new simplified network, retain the original community IDs, and then re-cluster the new network; Repeat the aforementioned steps until the modularity no longer increases, to obtain the initial community partitioning result, and determine the community category number to which each grid point belongs.

8. The method for detecting community structure in concurrent extreme climate events in space according to claim 7, characterized in that, The consensus clustering algorithm is used to eliminate the uncertainty and partition volatility in the initial community partitioning results, resulting in integrated community partitioning results, including: The Leiden community detection algorithm is applied to the functional climate network a preset number of times to generate a preset number of partition results. The functional climate network has several nodes. The partition results of the preset number of partitions are sorted according to the modularity, and the top preset number of partitions with the highest modularity are extracted. Calculate the consensus matrix using the number of partitions belonging to the same community for any two nodes and the total number of partitions; Set the items in the consensus matrix that are below the threshold to 0 to obtain the filtered consensus matrix; The Leiden community detection algorithm is applied again to the filtered consensus matrix a 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 are all equal, and the normalized mutual information between multiple partitions is greater than a preset value, then the iteration stops and the integrated community partition result is obtained; otherwise, the consensus matrix is ​​recalculated.

9. A community structure detection system for concurrent extreme weather events in space, characterized in that, include: The calculation and verification module is used to collect gridded temperature and precipitation data of the study area, extract binary time series of heat wave events and extreme precipitation events from the gridded 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 is used to establish a single-layer heat wave network and a single-layer extreme precipitation network according to the nonlinear adjacency matrix, respectively. By calculating the interlayer connection between the heat wave layer and the precipitation layer, a double-layer coupled heat wave-extreme precipitation network is constructed, and the single-layer network coefficient and the double-layer network coefficient are calculated. The detection module is used to obtain stable community classification results based on the dual-layer coupled heat wave-extreme precipitation network by employing a community clustering method that combines 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, characterized in that, When the processor executes the program, it implements the community structure detection method for concurrent extreme climate events in space as described in any one of claims 1 to 8.

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