Flood frequency analysis method for non-uniform regions based on Bayesian theory

Abstract

The present invention relates to the field of flood prediction technology, and in particular to a method for analyzing the frequency of non-uniform regional floods based on Bayesian theory. The method comprises the following steps: obtaining flood sequence data, meteorological data, and basin characteristic data of hydrological stations within a basin; performing regional flood dynamic change analysis on the flood sequence data and meteorological data to generate regional flood time-series dynamic change data; extracting flood characteristic parameters of hydrological stations within the basin from the basin characteristic data based on the regional flood time-series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region; deriving prior information of flood distribution parameter regression coefficients from the flood characteristic parameters of hydrological stations within the region to obtain maximum likelihood estimates of the distribution parameters of individual hydrological stations. The present invention improves the accuracy and applicability of flood frequency analysis based on Bayesian theory by introducing Bayesian theory, spatial correlation analysis, and spectrum analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of flood prediction, and in particular to a method for analyzing flood frequency in inconsistent regions based on Bayesian theory. Background Art

[0002] Initially, flood frequency analysis relied on classical statistical methods, such as extreme value theory and linear regression models. These methods assumed that flood events were consistent across regions, meaning that flood probability and intensity were similar across the entire study area. However, this assumption often overlooked regional geographical variations, climate change, and other influencing factors, leading to biased frequency analysis results in practical applications. With the development of statistics, particularly the rise of nonparametric statistical methods and geostatistics, researchers have gradually recognized that flood events can exhibit significant regional inconsistency. To better capture this regional variation, models based on Bayesian theory have been proposed. Bayesian methods can flexibly integrate historical data, expert knowledge, and other prior information to analyze regional flood frequency uncertainty. However, traditional flood frequency analysis methods often assume that flood characteristics are similar across regions. In reality, geographical characteristics, climate conditions, and precipitation patterns vary significantly across regions. Furthermore, traditional methods typically analyze flood distribution parameters independently for each hydrological station, ignoring potential spatial correlations between stations. This results in low accuracy and applicability of Bayesian-based flood frequency analysis. Summary of the Invention

[0003] Based on this, it is necessary to provide a method for analyzing the frequency of floods in inconsistent regions based on Bayesian theory to solve at least one of the above technical problems.

[0004] To achieve the above purpose, a method for analyzing flood frequency in inconsistent regions based on Bayesian theory is provided, the method comprising the following steps:

[0005] Step S1: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin; perform regional flood dynamic change analysis on the flood sequence data and meteorological data to generate regional flood time series dynamic change data; extract flood characteristic parameters of hydrological stations within the basin from the basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region;

[0006] Step S2: Derivation of prior information of flood distribution parameter regression coefficients for flood characteristic parameters of hydrological stations in the region to obtain maximum likelihood estimates of distribution parameters of individual hydrological stations; importing the maximum likelihood estimates of distribution parameters of individual hydrological stations and watershed characteristic data into a preset regional regression model to perform prior probability distribution calculation to obtain prior probability distribution data of regression coefficients of individual stations;

[0007] Step S3: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; derive the posterior information of the flood distribution parameter regression coefficient from the flood distribution likelihood function using Bayesian theory, thereby generating a Bayesian estimate of the regression coefficient of a single station;

[0008] Step S4: constructing a spatial association network based on the Bayesian estimation of the regression coefficient of a single site to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation of the regression coefficient of a single site to generate site flood spatial association data;

[0009] Step S5: perform spatial regional flood data collection on the site flood spatial correlation data to obtain inconsistent regional flood collection data; perform fast Fourier transform on the inconsistent regional flood collection data to generate inconsistent regional flood spectrum data; perform cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the single site regression coefficient and the Bayesian estimate of the single site regression coefficient to generate a regional flood frequency distribution map.

[0010] By acquiring flood sequence data, meteorological data, and basin characteristic data from hydrological stations within a basin and conducting a dynamic change analysis of regional floods, the present invention can fully understand the temporal changes and regional characteristics of floods, provide accurate basic data for the subsequent extraction of flood characteristic parameters, and ensure the accuracy of the analysis. Prior information on the regression coefficients of the flood characteristic parameters of the hydrological stations is derived, and the prior probability distribution of the regression coefficients of a single station is calculated in combination with the basin characteristic data. This effectively combines the spatial characteristics of the basin with the statistical laws of flood occurrence, improves the accuracy of the regression coefficient estimation in flood frequency analysis, and reduces uncertainty. By constructing a likelihood function and applying Bayesian theory to derive posterior information on the regression coefficients, the estimation of the regression coefficients can be updated more accurately. Combining prior information with actual observations of flood sequence data enhances the accuracy and credibility of the flood frequency analysis results. By constructing a spatial association network of stations and conducting flood correlation analysis, the spatial relationship between stations and the mutual influence of floods can be revealed, helping to better capture the spatiotemporal distribution characteristics of floods at the regional level and providing more comprehensive data support for regional flood frequency analysis. Using fast Fourier transforms to process flood data from non-uniform regions, generating flood spectrum data, and combining this with Bayesian estimates for cross-flood frequency verification, this method helps address differences in flood characteristics across complex regions, improves comprehensive analysis of regional flood frequencies, and generates more accurate regional flood frequency distribution maps. Therefore, by introducing Bayesian theory, spatial correlation analysis, and spectrum analysis, this invention improves the accuracy and applicability of flood frequency analysis based on Bayesian theory.

[0011] Preferably, step S1 includes the following steps:

[0012] Step S11: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin;

[0013] Step S12: performing data preprocessing on the flood sequence data, meteorological data, and watershed characteristic data to generate standard flood sequence data, standard meteorological data, and standard watershed characteristic data, wherein the data preprocessing includes data cleaning, data denoising, data missing value filling, and data standardization;

[0014] Step S13: performing regional flood dynamic change analysis on the standard flood sequence data and the standard meteorological data to generate regional flood time series dynamic change data;

[0015] Step S14: extracting flood characteristic parameters of hydrological stations within the basin from the standard basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region.

[0016] This invention improves data quality and consistency through preprocessing (including cleaning, denoising, missing value filling, and standardization) of flood sequence data, meteorological data, and watershed characteristic data, ensuring the accuracy of subsequent analysis and calculations, and providing a highly reliable data foundation for scientific research. By analyzing regional flood dynamics using flood sequence and meteorological data, we can comprehensively understand regional flood temporal trends, identify potential flood risk points, and provide data support for watershed management and disaster warning. Extracting flood characteristic parameters for hydrological stations within a watershed based on regional flood temporal dynamics effectively captures the dynamic characteristics of watershed characteristics, providing refined support for regional hydrological simulation, flood forecasting, and disaster prevention and mitigation decision-making. Each sub-step is interconnected, forming a complete closed-loop process from data collection to parameter extraction. Its clear logic and modular design facilitate operation and expansion, adapting to the needs of diverse flood data analysis in different regions and types. By combining dynamic data with watershed characteristic data, the accuracy of extracting flood characteristic parameters within a watershed is enhanced, providing a more scientific basis for flood risk forecasting and management. It integrates data from three dimensions: flood sequences, meteorological conditions, and river basin characteristics, providing a multi-angle analytical perspective, helping to reveal the causes and patterns of regional floods in greater depth, and offering strong technical support for studying the mechanisms of flood evolution.

[0017] Preferably, step S13 includes the following steps:

[0018] Step S131: performing time series decomposition on the flood sequence data to generate flood sequence time series decomposition data; performing random fluctuation component separation on the flood sequence time series decomposition data to generate flood sequence random fluctuation component data;

[0019] Step S132: performing meteorological change pattern analysis on the meteorological data to generate short-term meteorological pattern data and long-term meteorological pattern data; performing extreme meteorological flood change analysis on the random fluctuation component data of the flood sequence based on the short-term meteorological pattern data to generate extreme meteorological flood change data;

[0020] Step S133: performing common meteorological flood change analysis on the random fluctuation component data of the flood sequence using long-term meteorological model data to generate common meteorological flood change data; performing change peak extraction on the extreme meteorological flood change data to obtain extreme meteorological flood change peak data;

[0021] Step S134: extract the change mean of ordinary meteorological flood change data to obtain ordinary meteorological flood change mean data; analyze the regional flood meteorological linkage effect based on the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data to generate regional flood time series dynamic change data.

[0022] By performing temporal decomposition and separation of random fluctuation components on flood sequence data, this method refines the characteristics of flood variation, providing more accurate data support for analyzing the complex dynamic changes of floods, especially when addressing uncertain and random flood fluctuations. By analyzing meteorological variation patterns and dividing meteorological data into short-term and long-term patterns, this not only helps capture the impact of short-term extreme weather events on floods, but also reveals the role of long-term meteorological trends in flood variation, providing refined support for flood prediction and management at different time scales. Analysis and peak extraction of flood variations under extreme weather conditions can accurately identify the characteristics of extreme flood variations, providing key data for flood risk warning and emergency response, and improving the timeliness and relevance of disaster prevention and mitigation. Extracting the mean of flood variation under normal weather conditions can summarize the average variation patterns of floods, revealing the stability and predictability of floods under non-extreme conditions, and providing a reference for long-term monitoring and management of hydrological patterns within a basin. Regional flood-meteorological linkage effect analysis based on peak data of extreme weather flood variations and mean data of normal weather flood variations helps to fully understand the multidimensional impact of weather changes on flood formation and evolution, providing a scientific basis for comprehensive basin management and the formulation of flood control measures. The resulting regional flood dynamics data integrates flood change information across multiple levels, time scales, and meteorological conditions, providing a high-quality, dynamic data foundation for subsequent hydrological model optimization, watershed management, and flood forecasting. The logical connections between each sub-step are clear, functionally independent, and highly interconnected. This data is not only suitable for analyzing flood dynamics under different meteorological conditions, but also facilitates its widespread application across different watersheds or regions, demonstrating its versatility and scalability.

[0023] Preferably, the regional flood-meteorological linkage effect analysis based on the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data includes:

[0024] The flood-meteorological linkage effect index was calculated using the linkage effect quantification formula for the peak data of extreme meteorological flood changes and the mean data of ordinary meteorological flood changes to obtain the flood-meteorological linkage effect index. Based on the flood-meteorological linkage effect index, the regional sensitivity analysis of the linkage effect of hydrological stations in the basin was conducted to generate regional flood linkage sensitivity data.

[0025] Based on the regional flood linkage sensitivity data, the flood-meteorological linkage effect index is ranked by regional effects to generate regional sensitivity ranking data; the flood intensity change trend of extreme meteorological flood change peak data and ordinary meteorological flood change mean data are analyzed through regional sensitivity ranking data to generate regional flood time series dynamic change data.

[0026] By using a quantitative formula for linkage effects to calculate the flood-meteorological linkage effect index, this method can quantitatively reveal the impact of extreme and normal meteorological conditions on flood changes, providing scientific and systematic indicator support for flood management and early warning systems. By performing regional sensitivity analysis on the linkage effect index, the sensitivity of different hydrological stations to meteorological changes can be accurately identified, providing a basis for developing targeted prevention and control measures and regional flood risk assessments, and helping to improve regional flood control capabilities. By ranking regional flood linkage sensitivity data, the differences in flood-meteorological linkage effects across regions can be revealed, providing support for refined regional flood risk management and resource allocation. Highly sensitive areas can be prioritized to effectively optimize the allocation of flood control resources. Based on the regional sensitivity ranking data, flood intensity trend analysis of extreme meteorological flood peak change data and normal meteorological flood mean change data can accurately identify future flood intensity trends, helping decision makers prepare emergency plans in advance and improving disaster response efficiency. The generated regional flood time series dynamic change data can comprehensively reflect the temporal characteristics of flood changes under extreme and normal meteorological conditions, providing strong data support for optimizing flood prediction models and future watershed management, further improving prediction accuracy and decision-making effectiveness. This process can not only be flexibly applied to different meteorological conditions and regions, but also adapt to the needs of various river basins through modular design. It has high application value in actual flood warning, disaster management, and coordinated analysis of meteorology and hydrology.

[0027] Preferably, the linkage effect quantification formula is used to calculate the flood-meteorological linkage effect index for the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data. The linkage effect quantification formula is as follows:

[0028]

[0029] Where, Expressed as flood-meteorological linkage effect index, Expressed as the peak value of extreme meteorological floods, Expressed as the average value of ordinary meteorological floods, Expressed as the mean temperature under extreme meteorological conditions, It is expressed as the mean temperature under normal meteorological conditions. Expressed as extreme rainfall, Expressed as normal rainfall, Expressed as the duration of extreme rainfall, Expressed as the duration of normal rainfall, Expressed as the impact weight of flood peak, Expressed as the impact weight of temperature change, Expressed as the impact weight of rainfall change, Expressed as the impact weight of rainfall duration.

[0030] This paper analyzes and integrates a linkage effect quantification formula based on the changes in flood characteristics under different meteorological conditions (extreme and normal weather conditions), considers the impact of meteorological factors (temperature, rainfall, and rainfall duration) on flood changes, and quantifies these effects into a linkage effect index. The numerator of the formula (reflecting the changes in floods) is: Indicates flood peaks under extreme weather conditions Compared with the average flood value under normal weather conditions The difference between them represents the magnitude of flood changes and reflects the direct impact of extreme meteorological conditions on floods. Indicates temperature under extreme weather conditions Temperature under normal weather conditions The difference between the two reflects the indirect impact of temperature changes on floods. Temperature changes can indirectly change flood conditions by affecting precipitation, evaporation, snowmelt and other processes. The denominator (reflecting changes in meteorological factors): Indicates rainfall under extreme meteorological conditions Precipitation under normal weather conditions The difference between the two shows the driving effect of rainfall changes on floods. Rainfall is the direct cause of floods, and extreme rainfall can significantly increase the intensity and frequency of floods. Indicates the duration of rainfall under extreme meteorological conditions Duration of normal rainfall The difference between the two reflects the impact of rainfall duration changes on floods. The duration of rainfall directly affects the accumulation of ground water, thereby affecting the occurrence and change of floods. The impact weight of flood peak value indicates the contribution of the change of flood peak value under extreme meteorological conditions to the linkage effect. If the flood peak value changes greatly under extreme weather conditions, it means that the area is more sensitive to extreme weather changes. The impact weight of temperature change indicates the impact of temperature change on flood changes. If the temperature changes significantly, it may trigger heavier precipitation or snowmelt, thus affecting the formation of floods. The magnitude of reflects the indirect impact of temperature change on floods. The impact weight of rainfall change represents the direct impact of rainfall change on floods. The greater the rainfall, the higher the intensity and frequency of floods may be. The larger the value, the more important the rainfall is in flood generation. The impact weight of rainfall duration changes, indicating the impact of rainfall duration on floods. If the rainfall duration is longer, it usually means a higher flood risk. The weight indicates the degree of influence of rainfall duration on floods. When using the conventional linkage effect quantification formula in this field, the flood-meteorological linkage effect index can be obtained. By applying the linkage effect quantification formula provided by the present invention, the flood-meteorological linkage effect index can be calculated more accurately. This linkage effect quantification formula comprehensively considers the linkage relationship between flood changes and meteorological factors, and uses weight parameters to quantify the impact of each factor on flood risk, thereby providing a multi-dimensional and comprehensive flood-meteorological linkage effect index. By accurately calculating flood changes under different meteorological conditions, it can provide an important basis for flood warning, risk assessment, and disaster prevention and mitigation.

[0031] Preferably, step S2 includes the following steps:

[0032] Step S21: Calculate the maximum likelihood estimate of the flood sequence distribution parameters for the flood characteristic parameters of the hydrological stations in the region to obtain the maximum likelihood estimate of the distribution parameters of a single hydrological station. The formula for calculating the maximum likelihood estimate of the flood sequence distribution parameters is as follows:

[0033] ;

[0034] Where, is the regression coefficient of the flood sequence distribution parameter, represents the distribution parameter estimated based on the flood series of a single station only, Indicates the i Site distribution parameters H non-consistent covariates, and denote the link functions of the first and second distribution parameters, respectively, is a linear function;

[0035] Step S22: constructing a regional regression model; performing a matrix representation of the regional regression model to obtain a matrixed regional regression model; wherein the construction formula of the regional regression model is as follows:

[0036]

[0037] ; ;

[0038] Where, Indicates the i Sites The variance of the error caused by the sample estimate of , Indicates a site i With site j The correlation coefficient between the sample errors is the same as that under the consistency condition;

[0039] The formula for the model matrix representation is as follows:

[0040] ;

[0041] Where X is given by K Site C Regional covariates K ×( C +1) order matrix; The first flood sequence λ Regional regression coefficients of distribution parameters; Indicates t Time by C The vector of random effect terms of the basin characteristic indicators is assumed to have a mean of 0, and the covariance matrix is The multivariate normal distribution of Indicates t Time by K The flood sequence of the station λ A vector of regional regression model errors consisting of distribution parameters; Indicates t Time by K The flood sequence of the station λ A vector of sample errors for the estimated values ​​of the distribution parameters; Indicates t The total error at time is and The sum of .

[0042] Step S23: importing the maximum likelihood estimation value of the distribution parameter of a single hydrological station and the watershed characteristic data into the matrixed regional regression model to perform prior probability distribution calculation to obtain the prior probability distribution data of the regression coefficient of the single station;

[0043] The formula for calculating the prior probability distribution is as follows:

[0044] ;

[0045] Where, Data expressed as prior probability distributions of regression coefficients for individual sites.

[0046] This method uses the maximum likelihood estimation (MLE) method to calculate the distribution parameters of flood series for each hydrological station. These parameters reflect the flood characteristics of a specific station under different climatic conditions. The regression coefficients, etc., shown in the formula, represent the impact of different non-uniform covariates (such as precipitation and temperature) in the station's flood series on flood variability. These regression coefficients help quantify how these factors influence flood events and estimate the likelihood and magnitude of floods based on historical data. The regional regression model integrates flood data from multiple hydrological stations to create a regional model that captures inter-station correlations. The model's construction formula represents the error covariance structure between different stations, where errors between stations may be correlated (represented by the correlation coefficient ρ_ij). Matrixing the regional regression model facilitates combining the estimated distribution parameters for each station with regional characteristic data, enabling more comprehensive flood prediction. The distribution parameters and watershed characteristic data obtained from individual hydrological stations are input into the matrixed regional regression model to calculate the prior probability distribution. The calculation of the prior probability distribution helps derive prior information about the regression coefficients for individual stations. This information will serve as the basis for further flood predictions, and the model prediction effect will be optimized by fusing data and prior information through Bayesian methods.

[0047] Preferably, step S3 includes the following steps:

[0048] Step S31: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; the construction formula of the likelihood function is as follows:

[0049] ;

[0050] Where, Expressed as flood distribution likelihood function;

[0051] Step S32: Using Bayesian theory to derive the flood posterior probability distribution function from the flood distribution likelihood function, thereby obtaining the posterior probability distribution data of the regression coefficient of a single station; the formula for deriving the flood posterior probability distribution function is as follows:

[0052] ;

[0053] Where, Expressed as the posterior probability distribution data of the regression coefficient of a single site, The value range of

[0054] Step S33: Performing Bayesian estimation calculation on the prior probability distribution data of the regression coefficient of the single site using the posterior probability distribution data of the regression coefficient of the single site to obtain the Bayesian estimation value of the regression coefficient of the single site; wherein the Bayesian estimation value calculation is as follows:

[0055] .

[0056] The present invention combines the prior probability distribution data of the regression coefficients of a single station with the flood series data to construct a likelihood function for the flood distribution. The likelihood function represents the probability of the observed flood series data given a given regression coefficient. This function obtains the likelihood of the entire flood series by multiplying the probability values ​​at all time points. By constructing the likelihood function, the model's fit to the observed data can be quantified, providing a basis for subsequent Bayesian updates. The likelihood function helps understand how specific regression coefficients affect the performance of the flood prediction model. Applying Bayesian theory, the posterior probability distribution of the flood regression coefficient is derived using the likelihood function and the prior probability distribution. The Bayesian formula combines prior knowledge (i.e., the prior distribution) with observed data (i.e., the likelihood function) to obtain the posterior probability distribution of the regression coefficient given a given flood series. The posterior probability distribution fully accounts for prior information and new observations, providing a more accurate estimate of the regression coefficient. Bayesian methods can handle uncertainty, providing more comprehensive results than point estimates, making them suitable for problems with high uncertainty, such as flood prediction. In this step, the posterior probability distribution is used to calculate the Bayesian estimate of the regression coefficient. The Bayesian estimate takes a weighted average of all possible values ​​of the regression coefficient, where the weights are given by the posterior distribution, to obtain the most likely estimate of the regression coefficient. Bayesian estimation provides a comprehensive estimate of the regression coefficient and is more robust than simple maximum likelihood estimation. Bayesian estimation can more accurately predict the probability and characteristics of floods, especially when the sample size is small or the data is incomplete, providing more reliable results.

[0057] Preferably, step S4 includes the following steps:

[0058] Step S41: constructing a site feature vector based on the Bayesian estimation value of the regression coefficient of a single site to generate site feature matrix data;

[0059] Step S42: performing parameter space search on the site feature matrix data to generate prior parameter set data;

[0060] Step S43: constructing a spatial association network for the prior parameter set data to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation value of the regression coefficient of a single site to generate site flood spatial association data.

[0061] This method constructs a site feature vector using the Bayesian estimates of the regression coefficients of individual sites, ultimately generating a site feature matrix. The site feature matrix combines the regression coefficients with other relevant site characteristics to provide a complete description for subsequent analysis. The generation of the site feature matrix comprehensively reflects multiple relevant characteristics of a site, providing foundational data for subsequent analysis. It helps integrate information from different sources, correlates the site's regression coefficients with other characteristics (such as geographic location and historical flood records), and enhances the model's multidimensional analytical capabilities. A parameter space search is performed on the site feature matrix data to generate priori parameter set data. This process involves systematically searching the possible parameter space to find the most optimal parameter configuration for the current flood prediction model. Parameter space search optimizes model parameter selection, ensuring that the selected parameters are optimal for the current data characteristics, thereby improving model accuracy. This search method can find an appropriate parameter set within a broad parameter space, avoiding local optimal solutions and providing more comprehensive optimization results. Using the priori parameter set data, a site spatial correlation network is constructed, and flood correlation analysis is performed on the Bayesian estimates of the regression coefficients of individual sites, ultimately generating site-flood spatial correlation data. The construction and analysis of spatial correlation networks helps identify the relationships between different sites and their impact on flooding. By constructing a site spatial correlation network, we can better understand the spatial relationships between different sites and provide intuitive data support for analyzing the mutual impact between sites. Flood correlation analysis can reveal similarities and differences in flood occurrence patterns across different sites, helping to optimize model predictions, especially when there is a certain degree of spatial dependence. This step helps improve the accuracy of the model's spatial distribution, resulting in more accurate flood risk predictions at different geographical locations.

[0062] Preferably, constructing a spatial association network for the prior parameter set data includes:

[0063] Perform multi-scale decomposition on the prior parameter set data to generate eigendecomposition data; perform time series window processing on the eigendecomposition data to generate time series feature data; perform spatial mapping processing on the time series feature data to generate eigendecomposition matrix data; perform coordinate transformation on the eigendecomposition matrix data to generate standardized coordinate data;

[0064] Perform distance calculation on the standardized coordinate data to generate distance matrix data; perform weight assignment on the distance matrix data to generate spatial distance feature data; perform triangulation on the spatial distance feature data to generate initial network data; perform spatial partitioning on the initial network data to generate partition structure data;

[0065] The degree distribution of the partition structure data is processed to generate network topology structure data; based on the graph neural network algorithm, the spatial association network of the network topology structure data is constructed to generate a site spatial association network.

[0066] This invention uses multi-scale decomposition to help extract multi-level information from data, enhancing the model's ability to process features at different scales. This enables the model to identify relationships at different scales, helping to capture potential spatial patterns and trends. Time series window processing can extract dynamic patterns and trends in time series, helping to identify short-term or long-term patterns of change. This helps improve the model's predictive capabilities, especially when the data exhibits distinct time series characteristics. Spatial mapping combines time series and spatial features, enhancing the model's analytical capabilities in both spatial and temporal dimensions. This helps further identify temporal variations in spatial distribution, especially in complex geographic environments. Coordinate transformation helps ensure spatial consistency between different datasets, avoiding analytical errors caused by differences in coordinate systems. This improves the standardization of data processing and facilitates subsequent spatial correlation analysis. The distance matrix provides spatial relationship data between sites, revealing the relative positions of different sites and helping to determine the scope of influence and the strength of associations. This provides a quantitative basis for spatial analysis, facilitating subsequent calculations and network construction. Weight assignment adjusts the strength of associations between sites based on spatial distance, improving the accuracy of spatial correlation networks. This makes the relationships between sites more dynamic, allowing adjustments based on actual distance and degree of influence. Triangulation lays the foundation for subsequent network analysis and helps form a preliminary spatial association network. Triangulation makes the network structure closer to the actual spatial distribution, improving the authenticity of the network. Spatial partitioning can help analyze the differences in relationships within and outside the region, improving the performance of the spatial association network in different regions. It provides a clear data framework for subsequent network optimization and regional analysis. Through degree distribution analysis, key nodes in the network can be identified and the contribution of different sites to the entire network can be understood. This step helps optimize the network structure and improve network stability and efficiency. Graph neural network algorithms can effectively capture the complex spatial relationships between sites and optimize the network's spatial reasoning capabilities by learning the associations between different nodes. Graph neural networks can enhance the adaptability and flexibility of the network and improve the spatial association network's ability to process new data.

[0067] Preferably, step S5 includes the following steps:

[0068] Step S51: performing spatial regional flood data collection on the site flood spatial correlation data to obtain non-uniform regional flood collection data; performing fast Fourier transform on the non-uniform regional flood collection data to generate non-uniform regional flood spectrum data;

[0069] Step S52: performing cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the regression coefficient of a single station and the Bayesian estimation value of the regression coefficient of a single station, and generating verified regional flood spatial distribution data;

[0070] Step S53: Visualize the flood frequency of the verified regional flood spatial distribution data to generate a regional flood frequency distribution map.

[0071] By specifically collecting data from areas of inconsistency, this method can effectively identify regions with complex patterns and unusual behavior, helping to increase focus and analysis accuracy in specific areas. FFT transforms flood data from the time domain to the frequency domain, extracting frequency signatures from flood events and revealing periodic or repetitive patterns. The generation of spectral data simplifies the representation of flood data and provides efficient numerical representation for subsequent analysis, reducing the burden of big data processing. Combining prior probability distributions with Bayesian estimation allows for precise correction of flood spectral data, making it more reliable and statistically meaningful. This not only improves data accuracy but also enhances the robustness of the model. Cross-validation reduces bias caused by data inconsistencies or noise, improving the reliability and accuracy of spectral validation. The resulting validated regional flood spatial distribution data facilitates analysis of regional flood variations and supports accurate forecasting and regional flood management. Generating flood frequency distribution maps clearly displays flood frequency distribution across regions, helping decision makers identify high-risk areas and optimize resource allocation and emergency management. Visualized data makes complex statistical and spectral analysis results easier to understand and apply, facilitating more effective flood forecasting and planning. Frequency distribution maps provide a visual estimate of the probability of future floods, making prediction models more accurate and enabling early warning of potential risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 A schematic diagram of the steps of a method for analyzing flood frequency in inconsistent regions based on Bayesian theory;

[0073] Figure 2 for Figure 1 Detailed implementation steps of step S2 in FIG.

[0074] Figure 3 for Figure 1 Detailed implementation steps of step S3 in FIG.

[0075] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0076] The following is a clear and complete description of the technical method of the present invention in conjunction with the accompanying drawings. It is obvious that the embodiments described are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative efforts are within the scope of protection of the present invention.

[0077] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor and / or microcontroller approaches.

[0078] It should be understood that although the terms "first," "second," and the like may be used herein to describe various elements, these elements should not be limited by these terms. These terms are used solely to distinguish one element from another. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element, without departing from the scope of the exemplary embodiments. The term "and / or" as used herein includes any and all combinations of one or more of the listed associated items.

[0079] To achieve this, please refer to Figures 1 to 3 , a method for analyzing flood frequency in inconsistent regions based on Bayesian theory, the method comprising the following steps:

[0080] Step S1: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin; perform regional flood dynamic change analysis on the flood sequence data and meteorological data to generate regional flood time series dynamic change data; extract flood characteristic parameters of hydrological stations within the basin from the basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region;

[0081] Step S2: Derivation of prior information of flood distribution parameter regression coefficients for flood characteristic parameters of hydrological stations in the region to obtain maximum likelihood estimates of distribution parameters of individual hydrological stations; importing the maximum likelihood estimates of distribution parameters of individual hydrological stations and watershed characteristic data into a preset regional regression model to perform prior probability distribution calculation to obtain prior probability distribution data of regression coefficients of individual stations;

[0082] Step S3: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; derive the posterior information of the flood distribution parameter regression coefficient from the flood distribution likelihood function using Bayesian theory, thereby generating a Bayesian estimate of the regression coefficient of a single station;

[0083] Step S4: constructing a spatial association network based on the Bayesian estimation of the regression coefficient of a single site to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation of the regression coefficient of a single site to generate site flood spatial association data;

[0084] Step S5: perform spatial regional flood data collection on the site flood spatial correlation data to obtain inconsistent regional flood collection data; perform fast Fourier transform on the inconsistent regional flood collection data to generate inconsistent regional flood spectrum data; perform cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the single site regression coefficient and the Bayesian estimate of the single site regression coefficient to generate a regional flood frequency distribution map.

[0085] By acquiring flood sequence data, meteorological data, and basin characteristic data from hydrological stations within a basin and conducting a dynamic change analysis of regional floods, the present invention can fully understand the temporal changes and regional characteristics of floods, provide accurate basic data for the subsequent extraction of flood characteristic parameters, and ensure the accuracy of the analysis. Prior information on the regression coefficients of the flood characteristic parameters of the hydrological stations is derived, and the prior probability distribution of the regression coefficients of a single station is calculated in combination with the basin characteristic data. This effectively combines the spatial characteristics of the basin with the statistical laws of flood occurrence, improves the accuracy of the regression coefficient estimation in flood frequency analysis, and reduces uncertainty. By constructing a likelihood function and applying Bayesian theory to derive posterior information on the regression coefficients, the estimation of the regression coefficients can be updated more accurately. Combining prior information with actual observations of flood sequence data enhances the accuracy and credibility of the flood frequency analysis results. By constructing a spatial association network of stations and conducting flood correlation analysis, the spatial relationship between stations and the mutual influence of floods can be revealed, helping to better capture the spatiotemporal distribution characteristics of floods at the regional level and providing more comprehensive data support for regional flood frequency analysis. Using fast Fourier transforms to process flood data from non-uniform regions, generating flood spectrum data, and combining this with Bayesian estimates for cross-flood frequency verification, this method helps address differences in flood characteristics across complex regions, improves comprehensive analysis of regional flood frequencies, and generates more accurate regional flood frequency distribution maps. Therefore, by introducing Bayesian theory, spatial correlation analysis, and spectrum analysis, this invention improves the accuracy and applicability of flood frequency analysis based on Bayesian theory.

[0086] In the embodiment of the present invention, reference Figure 1 FIG. 1 is a flow chart of the steps of a method for analyzing flood frequency in inconsistent regions based on Bayesian theory according to the present invention. In this example, the method for analyzing flood frequency in inconsistent regions based on Bayesian theory includes the following steps:

[0087] Step S1: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin; perform regional flood dynamic change analysis on the flood sequence data and meteorological data to generate regional flood time series dynamic change data; extract flood characteristic parameters of hydrological stations within the basin from the basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region;

[0088] In this embodiment of the present invention, long-term flood series data is collected from various hydrological stations within a river basin. This data should include parameters such as the time of flood occurrence, flood flow, and water level. This data can be obtained from national or regional meteorological and water conservancy departments, or through remote sensing technology to obtain relevant hydrological data. Meteorological data within the river basin is collected, particularly parameters such as precipitation, temperature, and humidity. This data is typically provided by meteorological stations, but can also be obtained through remote sensing satellite data or regional meteorological bureaus. Meteorological data should cover long time spans within the river basin, especially data on extreme meteorological events related to floods, such as heavy rainfall events. Geographical data of the river basin is obtained, including drainage area, land use type, slope, soil type, and hydroclimatic conditions. Geographic Information Systems (GIS) can be used to obtain elevation data and land use data within the river basin. Time series analysis is performed on the flood series data to identify trends and cyclical characteristics of regional floods. Trend analysis of flood data is performed using methods such as the autoregressive moving average model (ARMA), the sliding mean method (SMA), and the Hopkins method to identify patterns such as seasonal and interannual variations. Analyze extreme flood events in flood series to identify potential flood risk points. Develop a flood time-series dynamics model based on flood series data, taking into account factors influencing flood variability (such as precipitation and climate change). Use machine learning algorithms such as regression analysis, neural networks, and support vector machines to perform time-series modeling to predict future regional flood dynamics. The generated regional flood time-series dynamics data should reveal trends and fluctuations in flood variability at different time scales, helping to understand long-term and short-term flood variability. Extract relevant flood characteristic parameters from flood series data. These parameters include, but are not limited to, peak flood discharge (maximum flood discharge), flood frequency (probability of exceeding a certain discharge threshold), flood duration (length of flood duration), flood probability (frequency of flood occurrence), and flood risk index (a flood risk assessment parameter that comprehensively considers multiple factors). Based on the data obtained from the regional flood time-series dynamics analysis and combined with watershed characteristic data, quantitatively extract flood characteristics for each hydrological station. For example, the peak method can be used to extract the maximum flood discharge, or statistical methods (such as least squares fitting) can be used to analyze long-term flood trends and extract flood characteristics for different hydrological stations. Flood characteristic parameters for each hydrological station within the basin can be derived through regression analysis or other parameterization methods, based on time-series dynamic data and meteorological data. By combining basin characteristic data (such as drainage area, slope, and land use) with regional flood time-series dynamic data, multiple regression analysis and weighted averaging can be used to extract characteristic parameters closely related to flood occurrence. GIS tools can be used for spatial analysis, combining hydrological models with the spatial distribution characteristics of the basin to extract station-specific geographic and hydrological characteristic parameters.

[0089] Step S2: Derivation of prior information of flood distribution parameter regression coefficients for flood characteristic parameters of hydrological stations in the region to obtain maximum likelihood estimates of distribution parameters of individual hydrological stations; importing the maximum likelihood estimates of distribution parameters of individual hydrological stations and watershed characteristic data into a preset regional regression model to perform prior probability distribution calculation to obtain prior probability distribution data of regression coefficients of individual stations;

[0090] In this embodiment of the present invention, flood characteristic parameters, such as peak flood flow, flood frequency, and flood duration, are obtained from each hydrological station in the region in step S1. These flood characteristic parameters are used in subsequent regression analysis. An appropriate probability distribution function is selected to describe the distribution of flood flow or water level data. Common flood distribution functions include Weibull distribution, Gumbel distribution, and Log-normal distribution. A maximum likelihood estimation method is used to calculate the maximum likelihood estimate based on the flood characteristic parameter data of each hydrological station. Basin characteristic data (such as basin area, land use, and climate conditions) are combined with the maximum likelihood estimate of a single hydrological station as input to construct a regression model. The basin characteristic data serves as an explanatory variable in the regression model. A regional regression model (such as linear regression, polynomial regression, or other appropriate regression model) is designed to calculate the regression coefficient for each station. The regression model uses the obtained maximum likelihood estimates of the distribution parameters of the single station and the basin characteristic data to calculate the prior probability distribution. Prior distributions can be estimated using methods such as Bayesian inference or Markov Chain Monte Carlo (MCMC). Using regional regression models and Bayesian inference, prior probability distribution data for the regression coefficients at each hydrological station are obtained. This data provides prior information for subsequent flood model parameter estimation.

[0091] Step S3: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; derive the posterior information of the flood distribution parameter regression coefficient from the flood distribution likelihood function using Bayesian theory, thereby generating a Bayesian estimate of the regression coefficient of a single station;

[0092] In this embodiment of the present invention, flood data is modeled by selecting an appropriate probability distribution function (such as the Weibull distribution, Gumbel distribution, or Log-normal distribution) based on the prior probability distribution data of the regression coefficients at individual hydrological stations generated in step S2 and combined with historical flood series data. The likelihood function describes the likelihood of the regression coefficient parameters given the observed data (such as flood series data). By combining the prior distribution of the regression coefficients for individual hydrological stations derived in step S2, the relationship between flood distribution parameters, such as the likelihood function parameters, and the observed flood series data can be further refined, resulting in a specific likelihood function. Within the Bayesian statistical framework, the posterior distribution of the regression coefficient can be derived from the prior distribution and the likelihood function using Bayes' theorem. By combining the prior probability distribution and the likelihood function, the posterior distribution is calculated using the Bayesian formula. For Bayesian estimation, maximum a posteriori (MAP) estimation is generally used to calculate the most likely regression coefficient, i.e., to maximize the posterior distribution. This posterior distribution can be maximized using optimization algorithms (such as gradient descent and MCMC sampling). If detailed information about the distribution of regression coefficients is required, Markov Chain Monte Carlo (MCMC) methods can be used to sample the posterior distribution, obtaining multiple samples of regression coefficients. These samples reflect the potential uncertainty of the regression coefficients. The Bayesian estimate (i.e., the posterior mean) can be used as the optimal estimate of the regression coefficients. If the posterior distribution is Gaussian, its mean can be directly taken as the Bayesian estimate. Bayesian estimation not only provides the optimal value of the regression coefficient but also reveals the distribution of the regression coefficients, revealing the uncertainty of the parameters. The variance or standard deviation of the posterior distribution can be used to assess uncertainty, which helps analyze the credibility of the model predictions.

[0093] Step S4: constructing a spatial association network based on the Bayesian estimation of the regression coefficient of a single site to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation of the regression coefficient of a single site to generate site flood spatial association data;

[0094] In this embodiment of the present invention, each hydrological station in a region is treated as a node in a network. The attributes of each node include the station's estimated Bayesian regression coefficient, geographic coordinates (such as latitude and longitude), and the station's watershed characteristic data (such as watershed area and slope). A preliminary association weight is calculated based on the geographic distance between nodes. A distance formula (such as Euclidean distance) is generally used to calculate the spatial distance between two stations. The closer the distance, the greater the association weight. The association weight is further refined based on the similarity between the station's Bayesian regression coefficient estimates. The closer the regression coefficients, the greater the similarity in flood characteristics between the two stations. By combining the geographic distance weights and the regression coefficient similarity weights, a comprehensive association weight between stations is generated to quantify the strength of spatial association between stations. Based on the comprehensive association weights between stations, a station spatial association matrix is ​​constructed. Each element in the matrix represents the strength of spatial association between two stations, with the main diagonal elements of the matrix being zero (i.e., the association between a station and itself is zero). Based on the station spatial association matrix, it is converted into a network structure to generate a station spatial association network. The nodes in the network represent stations, and the edge weights represent the strength of association between stations. In the site spatial correlation network, flood characteristic correlation indicators between sites are calculated through time series analysis of flood series data. Specifically, the temporal correlation of site flood series (such as the Pearson correlation coefficient) is used to quantify the degree of correlation between flood characteristics between two sites. Based on these analysis results, the flood series correlation is combined with the weights of the spatial correlation network to generate flood spatial correlation data between each pair of sites. The analysis results are compiled to generate a complete dataset that records the spatial correlation strength and flood characteristic correlation strength between each pair of sites, as well as the possible correlation paths or impact ranges.

[0095] Step S5: perform spatial regional flood data collection on the site flood spatial correlation data to obtain inconsistent regional flood collection data; perform fast Fourier transform on the inconsistent regional flood collection data to generate inconsistent regional flood spectrum data; perform cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the single site regression coefficient and the Bayesian estimate of the single site regression coefficient to generate a regional flood frequency distribution map.

[0096] In this embodiment of the present invention, target sites within a region are screened based on spatial correlation data of site floods. Flood sequence data are collected through historical records and real-time observations. The collected flood sequence data from each site is spatially integrated to form a basic dataset of regional flood dynamics. Non-uniform regions with significantly different flood characteristics are identified, and flood data from these regions is extracted to form flood data collected in the non-uniform regions. The flood data collected in the non-uniform regions is detrended (e.g., removing long-term trends or outliers) to ensure the accuracy of frequency domain analysis. A fast Fourier transform is performed on the pre-processed flood data sequence to obtain a frequency domain representation of the flood data and generate flood spectrum data for the non-uniform regions. The dominant frequency components and energy distribution in the spectrum are extracted to analyze the temporal periodicity and burstiness of flood events. The prior probability distribution data of the regression coefficients for each site and the Bayesian estimate of the regression coefficients for each site are used as input parameters for frequency validation. By jointly analyzing the Bayesian estimate, the flood spectrum data for the non-uniform regions, and the prior distribution of the regression coefficients, a cross-validation model is constructed to assess the reliability of flood frequency characteristics. Compare the predicted frequency distribution with the actual spectrum data, adjust the frequency verification model, and generate verified regional flood spatial distribution data. Based on this verified regional flood spatial distribution data, perform spatial visualization mapping of flood frequency characteristics. The horizontal axis represents spatial location (e.g., longitude and latitude). The vertical axis, or color depth, represents the magnitude of flood frequency or characteristic values. Combined with GIS (Geographic Information System) tools or frequency distribution mapping algorithms, the flood frequency distribution is presented as a regional frequency distribution map, visually demonstrating the differences in flood risk across different regions within the basin.

[0097] Preferably, step S1 includes the following steps:

[0098] Step S11: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin;

[0099] Step S12: performing data preprocessing on the flood sequence data, meteorological data, and watershed characteristic data to generate standard flood sequence data, standard meteorological data, and standard watershed characteristic data, wherein the data preprocessing includes data cleaning, data denoising, data missing value filling, and data standardization;

[0100] Step S13: performing regional flood dynamic change analysis on the standard flood sequence data and the standard meteorological data to generate regional flood time series dynamic change data;

[0101] Step S14: extracting flood characteristic parameters of hydrological stations within the basin from the standard basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region.

[0102] In this embodiment of the present invention, historical flood data, including information such as flood occurrence time, flow rate, and duration, is obtained from hydrological monitoring stations within the basin. Meteorological data, such as precipitation, temperature, wind speed, and humidity, is collected for the basin area. This data can be obtained from meteorological stations or remote sensing data. This data includes information such as the basin's topography, soil type, land use, and vegetation cover. This data can be obtained from a geographic information system (GIS) or remote sensing data source to help understand the basin's hydrological behavior. Erroneous or incomplete data points are identified and deleted. For example, missing timestamps or outliers are processed. For continuous meteorological data or flood series data, filtering techniques (such as low-pass filtering) are used to remove random noise and ensure data smoothness and reliability. Interpolation methods (such as linear interpolation and k-nearest neighbor interpolation) are used to fill in missing values ​​and ensure the continuity of time series data. Various data types (such as flood flow and precipitation) are normalized or standardized to eliminate unit differences, facilitating subsequent analysis and modeling. Time series analysis is performed based on flood series data and meteorological data. Time series modeling methods (such as ARIMA and LSTM) can be used to analyze the relationship between flood patterns and meteorological factors. This analysis generates time-series data describing regional floods, such as flood frequency, intensity, and duration. Based on the regional flood time-series dynamics data from step S13, flood characteristic parameters are extracted for each hydrological station within the basin. For example, by analyzing the spatiotemporal distribution, intensity, and frequency of floods at different stations, flood characteristics such as peak flow and flow duration can be extracted. The flood characteristic parameters for each hydrological station within the basin are integrated to generate regional flood characteristic parameters, providing basic data for subsequent flood warning and forecasting efforts.

[0103] Preferably, step S13 includes the following steps:

[0104] Step S131: performing time series decomposition on the flood sequence data to generate flood sequence time series decomposition data; performing random fluctuation component separation on the flood sequence time series decomposition data to generate flood sequence random fluctuation component data;

[0105] Step S132: performing meteorological change pattern analysis on the meteorological data to generate short-term meteorological pattern data and long-term meteorological pattern data; performing extreme meteorological flood change analysis on the random fluctuation component data of the flood sequence based on the short-term meteorological pattern data to generate extreme meteorological flood change data;

[0106] Step S133: performing common meteorological flood change analysis on the random fluctuation component data of the flood sequence using long-term meteorological model data to generate common meteorological flood change data; performing change peak extraction on the extreme meteorological flood change data to obtain extreme meteorological flood change peak data;

[0107] Step S134: extract the change mean of ordinary meteorological flood change data to obtain ordinary meteorological flood change mean data; analyze the regional flood meteorological linkage effect based on the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data to generate regional flood time series dynamic change data.

[0108] In an embodiment of the present invention, flood series data is decomposed into long-term trends, seasonal variations, and random fluctuation components using time series analysis methods (such as STL decomposition and Hodrick-Prescott filtering). This step helps identify long-term trends and cyclical fluctuations in the data. Using random fluctuation component separation techniques (such as wavelet transform or empirical mode decomposition (EMD)), short-term random fluctuation components are extracted from the flood series. This data is used to capture abnormal fluctuations during floods, particularly those caused by extreme weather or emergencies. Statistical analysis or machine learning methods (such as principal component analysis (PCA) and factor analysis) are used to extract patterns in meteorological data. Short-term meteorological pattern data (such as daily or monthly patterns) and long-term meteorological pattern data (such as interannual variations or climate change trends) are generated. Based on the short-term meteorological pattern data, the random fluctuation component data of the flood series is analyzed, focusing specifically on extreme meteorological conditions (such as extreme precipitation and high winds). The impact of these meteorological changes on floods is assessed, and extreme weather flood variation data is generated to reveal the relationship between floods and extreme weather. Based on long-term meteorological pattern data (such as seasonal and annual climate variations), we analyze the random fluctuation component data of flood series, identify the impact of meteorological factors (such as seasonal precipitation and temperature variations) on flood fluctuations, and generate data on common meteorological flood fluctuations. Peak values ​​are extracted from extreme meteorological flood fluctuation data, focusing on events with particularly unusual flood intensity or duration. These peak values ​​help identify the most extreme fluctuations and influencing factors in floods. We calculate the mean of common meteorological flood fluctuation data to obtain the mean flood fluctuation under long-term meteorological conditions, reflecting the characteristics of flood fluctuations under normal meteorological conditions. By combining the extreme meteorological flood peak value data with the common meteorological flood mean data, we use linkage analysis methods (such as multivariate regression and correlation analysis) to analyze the interactions and influences between meteorological factors and flood occurrence, generating regional flood time series dynamic variation data. This data reveals the dynamic patterns of regional floods under different meteorological patterns.

[0109] Preferably, the regional flood-meteorological linkage effect analysis based on the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data includes:

[0110] The flood-meteorological linkage effect index was calculated using the linkage effect quantification formula for the peak data of extreme meteorological flood changes and the mean data of ordinary meteorological flood changes to obtain the flood-meteorological linkage effect index. Based on the flood-meteorological linkage effect index, the regional sensitivity analysis of the linkage effect of hydrological stations in the basin was conducted to generate regional flood linkage sensitivity data.

[0111] Based on the regional flood linkage sensitivity data, the flood-meteorological linkage effect index is ranked by regional effects to generate regional sensitivity ranking data; the flood intensity change trend of extreme meteorological flood change peak data and ordinary meteorological flood change mean data are analyzed through regional sensitivity ranking data to generate regional flood time series dynamic change data.

[0112] In an embodiment of the present invention, a formula for the linkage effect between floods and meteorological factors is established using a mathematical model or regression analysis method. Peak data for extreme meteorological floods and mean data for normal meteorological floods are substituted into the formula. Weighting coefficients are determined through statistical analysis and modeling to obtain a flood-meteorological linkage effect index for each hydrological station or region. Based on the flood-meteorological linkage effect index, sensitivity analysis methods (such as local sensitivity analysis and Monte Carlo simulation) are used to assess the sensitivity of different hydrological stations or regions to meteorological changes. The flood-meteorological linkage effect index is compared with meteorological and hydrological data from each hydrological station in the region to evaluate each station's response to flood changes under extreme and normal meteorological conditions. A sensitivity score is assigned to each station to generate a sensitivity value for each hydrological station. The flood-meteorological linkage effect index for each hydrological station is ranked to generate sensitivity ranking data for different hydrological stations within the region. The linkage effect index can be ranked using a ranking method or ranking algorithm (such as the Kendall rank correlation coefficient or Spearman rank correlation analysis). The resulting regional sensitivity ranking data reflects which areas are most sensitive to flood-meteorological changes, helping to identify high-risk areas of priority concern. Combining regional sensitivity ranking data with flood change data, we conduct trend analysis of regional flood intensity through regression analysis or time series forecasting (such as ARIMA models and LSTM). Prioritize areas for analysis based on the rankings, and use peak data for extreme weather floods and mean data for common weather floods to conduct trend forecasts. We identify regional flood intensity trends, analyze rising or falling flood intensity trends, and analyze their correlation with meteorological changes. Combining trend analysis results with regional sensitivity ranking data generates regional flood time series dynamic change data, describing flood patterns in different regions under varying meteorological conditions. This data is then provided to decision makers for flood warning and disaster prevention planning.

[0113] Preferably, the linkage effect quantification formula is used to calculate the flood-meteorological linkage effect index for the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data. The linkage effect quantification formula is as follows:

[0114]

[0115] Where, Expressed as flood-meteorological linkage effect index, Expressed as the peak value of extreme meteorological floods, Expressed as the average value of ordinary meteorological floods, Expressed as the mean temperature under extreme meteorological conditions, It is expressed as the mean temperature under normal meteorological conditions. Expressed as extreme rainfall, Expressed as normal rainfall, Expressed as the duration of extreme rainfall, Expressed as the duration of normal rainfall, Expressed as the impact weight of flood peak, Expressed as the impact weight of temperature change, Expressed as the impact weight of rainfall change, Expressed as the impact weight of rainfall duration.

[0116] This paper analyzes and integrates a linkage effect quantification formula based on the changes in flood characteristics under different meteorological conditions (extreme and normal weather conditions), considers the impact of meteorological factors (temperature, rainfall, and rainfall duration) on flood changes, and quantifies these effects into a linkage effect index. The numerator of the formula (reflecting the changes in floods) is: Indicates flood peaks under extreme weather conditions Compared with the average flood value under normal weather conditions The difference between them represents the magnitude of flood changes and reflects the direct impact of extreme meteorological conditions on floods. Indicates temperature under extreme weather conditions Temperature under normal weather conditions The difference between the two reflects the indirect impact of temperature changes on floods. Temperature changes can indirectly change flood conditions by affecting precipitation, evaporation, snowmelt and other processes. The denominator (reflecting changes in meteorological factors): Indicates rainfall under extreme meteorological conditions Precipitation under normal weather conditions The difference between the two shows the driving effect of rainfall changes on floods. Rainfall is the direct cause of floods, and extreme rainfall can significantly increase the intensity and frequency of floods. Indicates the duration of rainfall under extreme meteorological conditions Duration of normal rainfall The difference between the two reflects the impact of rainfall duration changes on floods. The duration of rainfall directly affects the accumulation of ground water, thereby affecting the occurrence and change of floods. The impact weight of flood peak value indicates the contribution of the change of flood peak value under extreme meteorological conditions to the linkage effect. If the flood peak value changes greatly under extreme weather conditions, it means that the area is more sensitive to extreme weather changes. The impact weight of temperature change indicates the impact of temperature change on flood changes. If the temperature changes significantly, it may trigger heavier precipitation or snowmelt, thus affecting the formation of floods. The magnitude of reflects the indirect impact of temperature change on floods. The impact weight of rainfall change represents the direct impact of rainfall change on floods. The greater the rainfall, the higher the intensity and frequency of floods may be. The larger the value, the more important the rainfall is in flood generation. The impact weight of rainfall duration changes, indicating the impact of rainfall duration on floods. If the rainfall duration is longer, it usually means a higher flood risk. The weight indicates the degree of influence of rainfall duration on floods. When using the conventional linkage effect quantification formula in this field, the flood-meteorological linkage effect index can be obtained. By applying the linkage effect quantification formula provided by the present invention, the flood-meteorological linkage effect index can be calculated more accurately. This linkage effect quantification formula comprehensively considers the linkage relationship between flood changes and meteorological factors, and uses weight parameters to quantify the impact of each factor on flood risk, thereby providing a multi-dimensional and comprehensive flood-meteorological linkage effect index. By accurately calculating flood changes under different meteorological conditions, it can provide an important basis for flood warning, risk assessment, and disaster prevention and mitigation.

[0117] As an example of the present invention, refer to Figure 2 As shown, in this example, step S2 includes:

[0118] Step S21: Calculate the maximum likelihood estimate of the flood sequence distribution parameters for the flood characteristic parameters of the hydrological stations in the region to obtain the maximum likelihood estimate of the distribution parameters of a single hydrological station. The formula for calculating the maximum likelihood estimate of the flood sequence distribution parameters is as follows:

[0119] ;

[0120] Where, is the regression coefficient of the flood sequence distribution parameter, represents the distribution parameter estimated based on the flood series of a single station only, Indicates the i Site distribution parametersH non-consistent covariates, and denote the link functions of the first and second distribution parameters, respectively, is a linear function;

[0121] Step S22: constructing a regional regression model; performing a matrix representation of the regional regression model to obtain a matrixed regional regression model; wherein the construction formula of the regional regression model is as follows:

[0122]

[0123] ; ;

[0124] Where, Indicates the i Sites The variance of the error caused by the sample estimate of , Indicates a site i With site j The correlation coefficient between the sample errors is the same as that under the consistency condition;

[0125] The formula for the model matrix representation is as follows:

[0126] ;

[0127] Where X is given by K Site C Regional covariates K ×( C +1) order matrix; The first flood sequence λ Regional regression coefficients of distribution parameters; Indicates t Time by C The vector of random effect terms of the basin characteristic indicators is assumed to have a mean of 0, and the covariance matrix is The multivariate normal distribution of Indicates t Time by K The flood sequence of the station λ A vector of regional regression model errors consisting of distribution parameters; Indicates t Time by K The flood sequence of the station λ A vector of sample errors for the estimated values ​​of the distribution parameters; Indicates t The total error at time is and The sum of .

[0128] Step S23: importing the maximum likelihood estimation value of the distribution parameter of a single hydrological station and the watershed characteristic data into the matrixed regional regression model to perform prior probability distribution calculation to obtain the prior probability distribution data of the regression coefficient of the single station;

[0129] The formula for calculating the prior probability distribution is as follows:

[0130] ;

[0131] Where, Data expressed as prior probability distributions of regression coefficients for individual sites.

[0132] In the embodiment of the present invention, based on the given flood series data and covariates, the maximum likelihood estimation (MLE) method is used to calculate the flood series distribution parameters of a single hydrological station using a regression model. The model is set as: , obtain time series flood data and related meteorological covariate data from each hydrological station in the region. For each hydrological station, use the maximum likelihood estimation method to perform regression analysis and calculate the optimal regression coefficient of each distribution parameter. Using the above formula, the maximum likelihood estimate of the flood series distribution parameter of each hydrological station is obtained. A multi-station, multi-covariate regression model is used to combine the distribution parameters of the hydrological stations with the characteristics of the watershed to construct a regional regression model. The construction formula is: ; ; Here, Indicates the i The sample error of a hydrological station at time t is, For the correlation coefficients between different sites, a matrix representing the regional regression model is constructed by using the estimated distribution parameters of all hydrological sites. The regression coefficients of each site are and random effects As variables, a matrix representation is formed that includes all basin characteristics and regional covariates. The error terms and covariance matrices of all hydrological stations are calculated and matrixed to obtain the matrix representation of the regional regression model. Based on the regression coefficients of the hydrological stations and the basin characteristic data, the prior probability distribution of the regression coefficients is calculated. The prior probability distribution calculation formula is: = Prior distribution model, where The regression coefficients describe the relationship between hydrological stations and regional characteristics. The distribution parameters and watershed characteristic data obtained through maximum likelihood estimation are then imported into the regional regression model. The model then calculates prior distribution data for the regression coefficients. This data is then used for further Bayesian inference or other statistical analysis methods to assess future flooding trends.

[0133] As an example of the present invention, refer to Figure 3 As shown, in this example, step S3 includes:

[0134] Step S31: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; the construction formula of the likelihood function is as follows:

[0135] ;

[0136] Where, Expressed as flood distribution likelihood function;

[0137] Step S32: Using Bayesian theory to derive the flood posterior probability distribution function from the flood distribution likelihood function, thereby obtaining the posterior probability distribution data of the regression coefficient of a single station; the formula for deriving the flood posterior probability distribution function is as follows:

[0138] ;

[0139] Where, Expressed as the posterior probability distribution data of the regression coefficient of a single site, The value range of

[0140] Step S33: Performing Bayesian estimation calculation on the prior probability distribution data of the regression coefficient of the single site using the posterior probability distribution data of the regression coefficient of the single site to obtain the Bayesian estimation value of the regression coefficient of the single site; wherein the Bayesian estimation value calculation is as follows:

[0141] .

[0142] In this embodiment of the present invention, a likelihood function is used to describe flood distribution based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data. The likelihood function is used to measure the probability of the observed data (flood sequence) when the regression coefficient is given. Formula: ;in Expressed as flood distribution likelihood function, is the flood data with a given regression coefficient The probability density function under . Using Bayesian theory, combined with the prior probability distribution and the likelihood function, the posterior probability distribution function of the flood distribution is derived. The posterior probability distribution function represents the updated distribution of the regression coefficient based on the observed data. ,in Expressed as the posterior probability distribution data of the regression coefficient of a single site, The value range of The prior distribution of the regression coefficient is expressed as . Using the posterior probability distribution, the Bayesian estimate of the regression coefficient for each station is calculated. This process uses the posterior distribution to weight the regression coefficients to obtain the most likely regression coefficient. ,in is the Bayesian estimate of the regression coefficient for a single site.

[0143] Preferably, step S4 includes the following steps:

[0144] Step S41: constructing a site feature vector based on the Bayesian estimation value of the regression coefficient of a single site to generate site feature matrix data;

[0145] Step S42: performing parameter space search on the site feature matrix data to generate prior parameter set data;

[0146] Step S43: constructing a spatial association network for the prior parameter set data to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation value of the regression coefficient of a single site to generate site flood spatial association data.

[0147] In this embodiment of the present invention, relevant data is collected from each site, including meteorological data (such as precipitation and temperature), geographic information (such as altitude and land use type), and historical flood data. This information is converted into a feature vector using Bayesian estimates. Each site's feature vector may include precipitation, temperature variations, land use type, river basin information, and Bayesian estimates of regression coefficients. The feature vectors for all sites are integrated into a site feature matrix. This matrix is ​​used for subsequent analysis and modeling. Based on the site feature matrix, a parameter space is defined, encompassing various factors such as possible regression coefficients, flood probability, precipitation patterns, and soil type. A search algorithm (such as particle swarm optimization, grid search, or simulated annealing) is used to search within this parameter space. This process identifies a set of prior parameters that best describes the relationship between site characteristics and flood occurrence. Through optimization using the search algorithm, a satisfactory set of prior parameters is obtained. These parameters provide the basis for constructing a spatial correlation network. This spatial correlation network is constructed using geographic information and flood patterns between sites. Graph theory methods can be used, where each site represents a node in the graph, and the edges between nodes represent the spatial correlation between sites (such as geographical distance or similarity of hydrological characteristics). The relationship between sites is represented by constructing an adjacency matrix or weight matrix. The correlation between floods between sites is analyzed using a site spatial association network, combined with Bayesian estimates of regression coefficients and flood series data. Methods such as correlation analysis, cluster analysis, or spatial regression models can be used to assess the similarity of flood occurrence between sites. Based on the analysis results, site flood spatial association data are generated. These data can help understand the spatiotemporal patterns of flood occurrence between different sites and how to improve flood warnings and risk assessments using data from adjacent sites.

[0148] Preferably, constructing a spatial association network for the prior parameter set data includes:

[0149] Perform multi-scale decomposition on the prior parameter set data to generate eigendecomposition data; perform time series window processing on the eigendecomposition data to generate time series feature data; perform spatial mapping processing on the time series feature data to generate eigendecomposition matrix data; perform coordinate transformation on the eigendecomposition matrix data to generate standardized coordinate data;

[0150] Perform distance calculation on the standardized coordinate data to generate distance matrix data; perform weight assignment on the distance matrix data to generate spatial distance feature data; perform triangulation on the spatial distance feature data to generate initial network data; perform spatial partitioning on the initial network data to generate partition structure data;

[0151] The degree distribution of the partition structure data is processed to generate network topology structure data; based on the graph neural network algorithm, the spatial association network of the network topology structure data is constructed to generate a site spatial association network.

[0152] In this embodiment of the present invention, a priori parameter sets (such as regression coefficients and precipitation data) are decomposed into features at multiple scales using wavelet transforms, Fourier transforms, or similar multi-scale analysis methods. Multi-scale decomposition is performed on each parameter set to extract feature information at different scales. For example, for precipitation data, wavelet transforms can be used to decompose the data into high-frequency and low-frequency components, representing detailed information and overall trends, respectively. Multi-scale feature data is output for further analysis. Based on the temporal characteristics of the data, an appropriate time window is defined. For example, a fixed time span (such as a week or a month) can be selected as the window length. Time series window processing is performed on the feature-decomposed data, segmenting the data by time period to obtain data within each window. Features (such as mean, variance, and trend) are extracted within each time window. A time series feature vector is generated for each time window, representing the changing characteristics within that time period. The time series feature data is mapped to a spatial coordinate system based on the geographic coordinates and feature information of the station. Interpolation methods or mapping algorithms such as Lagrange interpolation and Kriging interpolation can be used. Map the temporal feature data of each site onto spatial coordinates to form a feature matrix in a spatial coordinate system. The resulting matrix data, obtained through spatial mapping, contains spatiotemporal information and can be further processed. The spatial coordinate data is converted to a standardized coordinate system through linear transformation or coordinate standardization methods. Common methods include normalization and Z-score standardization. Each site's coordinates are processed using a conversion formula or method to obtain standardized coordinate data. This standardized coordinate data will be used for subsequent distance calculations and network construction. Based on the site's geographic coordinates, an appropriate distance metric is selected. Commonly used methods include Euclidean distance and Manhattan distance. Distances are calculated between all sites to generate a symmetric distance matrix. Each element represents the spatial distance between two sites. The resulting distance matrix provides the basis for subsequent weight assignment and spatial association analysis. Based on the distance matrix, weights are assigned to each pair of sites using a specific function (such as the Gaussian kernel function or inverse distance weighting). Generally, closer sites receive larger weights. Spatial weights are calculated for each pair of sites. Weights can generally be calculated using the following formula: ;in, For site and sites The distance between is the scaling factor for the weights. By assigning weights, a matrix is ​​generated to represent the spatial distance characteristics between sites. The Delaunay triangulation algorithm is used to generate an initial network structure based on the spatial coordinates of the sites. Delaunay triangulation ensures that the incenter of each triangle does not contain other sites, thus avoiding illogical connections between data. Sites are connected through triangulation to form a preliminary spatial network. The resulting initial network data represents the preliminary spatial connectivity relationships between sites. Spectral clustering algorithms or community detection algorithms (such as the Louvain algorithm) can be used to divide the initial network into several functional regions. Sites are divided into different regions based on their spatial location and network structure. Partitioned structure data is output, with each region containing several sites, representing the spatial relationships within that region. The degree of each site (i.e., the number of connections with other sites) is calculated, and the degree distribution is analyzed. A degree distribution graph can be plotted to analyze the importance of sites in the network. Based on the degree distribution data, a topological structure between sites is established to identify sites with high connectivity and which are hubs in the network. The final network topology data is obtained and used for subsequent spatial association network construction. Select an appropriate GNN model, such as GCN (Graph Convolutional Network) or GAT (Graph Attention Network), to learn the relationships between nodes (sites) in the network. Use network topology data to train the GNN model to learn the spatial correlations and flooding correlations between sites. After training, use the model to generate a final site spatial correlation network, revealing the spatial flooding correlations between sites.

[0153] Preferably, step S5 includes the following steps:

[0154] Step S51: performing spatial regional flood data collection on the site flood spatial correlation data to obtain non-uniform regional flood collection data; performing fast Fourier transform on the non-uniform regional flood collection data to generate non-uniform regional flood spectrum data;

[0155] Step S52: performing cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the regression coefficient of a single station and the Bayesian estimation value of the regression coefficient of a single station, and generating verified regional flood spatial distribution data;

[0156] Step S53: Visualize the flood frequency of the verified regional flood spatial distribution data to generate a regional flood frequency distribution map.

[0157] In this embodiment of the present invention, flood-related inconsistency areas are identified based on spatial correlation data from site floods. These areas may have inconsistent flood characteristics due to factors such as topography, climate, and urbanization. Site data within these inconsistency areas is collected to obtain time-series flood data for the region. The collected data may include precipitation, flow, and water level. The collected flood data is preprocessed, including removing outliers, filling in missing data, and smoothing. This ensures the temporal and spatial consistency of the data and enables spectral analysis. A fast Fourier transform (FFT) is performed on the processed flood data to convert it from the time domain to the frequency domain. The FFT can help reveal periodic characteristics in the data, such as the frequency, period, and amplitude of flood events. The output is a spectral dataset describing the frequency distribution characteristics of flood events within the inconsistency areas. Analysis of the spectral data can reveal the periodicity and variation patterns of flood events at different time scales. The resulting flood spectral data is cross-validated against a Bayesian estimated prior distribution. This step verifies the accuracy of the model by comparing flood frequency data from different sites. After cross-validation, a corrected regional flood spatial distribution dataset is generated. This data describes the frequency and distribution of floods at each station within the region, taking into account Bayesian estimates for each station. This data can be used to further analyze flood risk across different regions and help decision makers understand the spatial patterns of flooding. Use appropriate visualization tools (such as heat maps, spatial distribution maps, and spectrum plots) to display the frequency distribution of regional floods. GIS software (such as ArcGIS) or programming libraries (such as Matplotlib, Seaborn, and Plotly) can be used for graphical rendering. Convert the validated regional flood spatial distribution data into a visual chart. Color intensity can be used to indicate flood frequency, or symbol size can be used to indicate the flood risk level at different stations. For example, a heat map can be used to indicate flood frequency, while a gradient of regional colors can be used to display flood frequency at different stations. The resulting regional flood frequency distribution map clearly demonstrates the frequency of floods across different regions and stations, providing intuitive visual support for regional flood risk assessment. This map can aid in post-disaster reconstruction, early warning systems, and regional flood prevention decision-making.

Claims

1. A method for analyzing flood frequency in inconsistent regions based on Bayesian theory, characterized in that: The following steps are involved: Step S1: Obtain flood sequence data, meteorological data, and basin characteristic data from hydrological stations within the basin; perform regional flood dynamic change analysis on the flood sequence data and meteorological data to generate regional flood time series dynamic change data; Based on the regional flood time series dynamic change data, the flood characteristic parameters of the hydrological stations in the basin are extracted from the basin characteristic data to obtain the flood characteristic parameters of the hydrological stations in the region; Step S2: Derivation of prior information of flood distribution parameter regression coefficients for flood characteristic parameters of hydrological stations in the region to obtain maximum likelihood estimates of distribution parameters of individual hydrological stations; importing the maximum likelihood estimates of distribution parameters of individual hydrological stations and watershed characteristic data into a preset regional regression model to perform prior probability distribution calculation to obtain prior probability distribution data of regression coefficients of individual stations; Step S3: construct a likelihood function based on the prior probability distribution data of the regression coefficient of a single station and the flood sequence data to obtain a flood distribution likelihood function; derive the posterior information of the flood distribution parameter regression coefficient from the flood distribution likelihood function using Bayesian theory, thereby generating a Bayesian estimate of the regression coefficient of a single station; Step S4: construct a spatial association network based on the Bayesian estimation value of the regression coefficient of a single site to generate a site spatial association network; The site spatial correlation network is used to perform flood correlation analysis on the Bayesian estimation value of the regression coefficient of a single site to generate site flood spatial correlation data; step S4 includes the following steps: Step S41: constructing a site feature vector based on the Bayesian estimation value of the regression coefficient of a single site to generate site feature matrix data; Step S42: performing parameter space search on the site feature matrix data to generate prior parameter set data; Step S43: constructing a spatial association network for the prior parameter set data to generate a site spatial association network; using the site spatial association network to perform flood correlation analysis on the Bayesian estimation value of the regression coefficient of a single site to generate site flood spatial association data; constructing a spatial association network for the prior parameter set data includes: Perform multi-scale decomposition on the prior parameter set data to generate eigendecomposition data; perform time series window processing on the eigendecomposition data to generate time series feature data; perform spatial mapping processing on the time series feature data to generate eigendecomposition matrix data; perform coordinate transformation on the eigendecomposition matrix data to generate standardized coordinate data; Perform distance calculation on the standardized coordinate data to generate distance matrix data; perform weight assignment on the distance matrix data to generate spatial distance feature data; perform triangulation on the spatial distance feature data to generate initial network data; perform spatial partitioning on the initial network data to generate partition structure data; Perform degree distribution processing on the partition structure data to generate network topology data; construct a spatial correlation network on the network topology data based on the graph neural network algorithm to generate a site spatial correlation network; Step S5: perform spatial regional flood data collection on the site flood spatial correlation data to obtain inconsistent regional flood collection data; perform fast Fourier transform on the inconsistent regional flood collection data to generate inconsistent regional flood spectrum data; perform cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the single site regression coefficient and the Bayesian estimate of the single site regression coefficient to generate a regional flood frequency distribution map.

2. The method for analyzing flood frequency in inconsistent regions based on Bayesian theory according to claim 1 is characterized in that: Step S1 includes the following steps: Step S11: Obtain flood sequence data, meteorological data, and basin characteristic data of hydrological stations within the basin; Step S12: performing data preprocessing on the flood sequence data, meteorological data, and watershed characteristic data to generate standard flood sequence data, standard meteorological data, and standard watershed characteristic data, wherein the data preprocessing includes data cleaning, data denoising, data missing value filling, and data standardization; Step S13: performing regional flood dynamic change analysis on the standard flood sequence data and the standard meteorological data to generate regional flood time series dynamic change data; Step S14: extracting flood characteristic parameters of hydrological stations within the basin from the standard basin characteristic data based on the regional flood time series dynamic change data to obtain flood characteristic parameters of hydrological stations within the region.

3. The method for analyzing the frequency of flood in inconsistent regions based on Bayesian theory according to claim 2 is characterized in that: Step S13 includes the following steps: Step S131: performing time series decomposition on the flood sequence data to generate flood sequence time series decomposition data; performing random fluctuation component separation on the flood sequence time series decomposition data to generate flood sequence random fluctuation component data; Step S132: performing meteorological change pattern analysis on the meteorological data to generate short-term meteorological pattern data and long-term meteorological pattern data; performing extreme meteorological flood change analysis on the random fluctuation component data of the flood sequence based on the short-term meteorological pattern data to generate extreme meteorological flood change data; Step S133: performing common meteorological flood change analysis on the random fluctuation component data of the flood sequence using long-term meteorological model data to generate common meteorological flood change data; performing change peak extraction on the extreme meteorological flood change data to obtain extreme meteorological flood change peak data; Step S134: extract the change mean of ordinary meteorological flood change data to obtain ordinary meteorological flood change mean data; analyze the regional flood meteorological linkage effect based on the extreme meteorological flood change peak data and the ordinary meteorological flood change mean data to generate regional flood time series dynamic change data.

4. The method for analyzing the frequency of flood in inconsistent regions based on Bayesian theory according to claim 3 is characterized in that: The analysis of regional flood-meteorological linkage effects based on the peak data of extreme meteorological flood changes and the mean data of ordinary meteorological flood changes includes: The flood-meteorological linkage effect index was calculated using the linkage effect quantification formula for the peak data of extreme meteorological flood changes and the mean data of ordinary meteorological flood changes to obtain the flood-meteorological linkage effect index. Based on the flood-meteorological linkage effect index, the regional sensitivity analysis of the linkage effect of hydrological stations in the basin was conducted to generate regional flood linkage sensitivity data. Based on the regional flood linkage sensitivity data, the flood-meteorological linkage effect index is ranked by regional effects to generate regional sensitivity ranking data; the flood intensity change trend of extreme meteorological flood change peak data and ordinary meteorological flood change mean data are analyzed through regional sensitivity ranking data to generate regional flood time series dynamic change data.

5. The method for analyzing the frequency of flood in inconsistent regions based on Bayesian theory according to claim 4 is characterized in that: The quantitative formula for linkage effect is used to calculate the flood-meteorological linkage effect index for the peak data of extreme meteorological flood changes and the mean data of ordinary meteorological flood changes. The quantitative formula for linkage effect is as follows: Where, Expressed as flood-meteorological linkage effect index, Expressed as the peak value of extreme meteorological floods, Expressed as the average value of ordinary meteorological floods, Expressed as the mean temperature under extreme meteorological conditions, It is expressed as the mean temperature under normal meteorological conditions. Expressed as extreme rainfall, Expressed as normal rainfall, Expressed as the duration of extreme rainfall, Expressed as the duration of normal rainfall, Expressed as the impact weight of flood peak, Expressed as the impact weight of temperature change, Expressed as the impact weight of rainfall change, Expressed as the impact weight of rainfall duration.

6. The method for analyzing flood frequency in inconsistent regions based on Bayesian theory according to claim 1, characterized in that: Step S5 includes the following steps: Step S51: performing spatial regional flood data collection on the site flood spatial correlation data to obtain non-uniform regional flood collection data; performing fast Fourier transform on the non-uniform regional flood collection data to generate non-uniform regional flood spectrum data; Step S52: performing cross-flood frequency verification on the inconsistent regional flood spectrum data based on the prior probability distribution data of the regression coefficient of a single station and the Bayesian estimation value of the regression coefficient of a single station, and generating verified regional flood spatial distribution data; Step S53: Visualize the flood frequency of the verified regional flood spatial distribution data to generate a regional flood frequency distribution map.

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