A method for evaluating spatial extreme water level in river network region

Abstract

The present application relates to the technical field of flood risk assessment and defense, more particularly, to a river network area spatial extreme water level evaluation method, through collecting disaster data and spatial data of river network area water level stations, establishing disaster extreme value data sequence, converting the disaster extreme value data sequence into unit Frechet distribution, combining different disaster data and spatial data to design complex environment factor encounter scene, considering the spatial dependence of extreme water level events between stations, establishing a multivariate spatial extreme value model, which can provide spatial expression of extreme water disasters under different complex environment factor encounter scenes, estimate the spatial distribution pattern of river network area extreme water level events under different recurrence levels, analyze the change of flood event occurrence intensity of different stations in the river network area in space and events, and effectively monitor and evaluate the composite flood.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of flood risk assessment and defense, and more particularly to a river network area spatial extreme water level evaluation method. BACKGROUND

[0002] The spatial structure of flood is a key factor determining the severity of flood. Flood usually affects more than one place, and the most severe flood often affects a large area, causes heavy loss of life and damage to infrastructure, and causes adverse social impact. Considering the spatial dependence of extreme flood events at multiple locations, it is necessary to extend the univariate extreme value theory to multivariate. At the same time, it is very important to understand the probability of occurrence of extreme flood in time and space for regional flood control.

[0003] In the river network composite area, flood frequency analysis needs to consider the spatial dependence of extreme flood events between stations under the influence of complex environmental factors, which is often ignored, which may lead to underestimation of the risk of extreme flood. Therefore, the model used in regional multivariate frequency analysis should consider the temporal and spatial correlation of flood events, that is, how the intensity of extreme flood events at different locations changes in space and time in the river network area. The multivariate spatial extreme value model considers the spatial dependence of extreme flood events between stations driven by different environmental factors, and is a hot research direction for composite flood risk assessment.

[0004] The prior art discloses a method for flood disaster risk assessment in different scale regions, spatial data and attribute data associated with the spatial data of a region to be analyzed are collected as initial data, the initial data is compressed and stored in a created spatial database; the initial data is standardized and the unit is unified; the AHP hierarchical analysis method and the entropy weight method coupling model are used to determine the weight of each factor combination; the flood disaster risk value in the research area is evaluated, the risk level is divided, and a flood disaster risk index map is generated. The scheme uses various natural and social data collected as input, determines the weight by coupling a variety of algorithms, and finally generates a flood risk level evaluation index map, which improves the accuracy of flood disaster risk assessment, and has the advantages of objectivity and efficiency, and more intuitively shows the flood disaster risk situation that the research area may suffer under given conditions. However, the spatial dependence relationship between water level stations is not considered in the scheme, which may lead to underestimation of the risk of extreme flood. SUMMARY

[0005] The present application aims to overcome the underestimation of the risk of extreme flood in the prior art, and provides a river network area spatial extreme water level evaluation method, which considers the spatial dependence relationship between water level stations and effectively monitors and evaluates composite flood.

[0006] To solve the above technical problems, the technical scheme adopted by the present application is:

[0007] A river network area spatial extreme water level evaluation method is provided, comprising the following steps:

[0008] S1: Collecting disaster data and spatial data of water level sites in a complex river network area; wherein the disaster data includes rainfall, water level, flow, storm surge data, and the spatial data includes geographic location and elevation data of the water level sites, and the geographic location includes longitude and latitude;

[0009] S2: Establishing a disaster extreme value data sequence according to the disaster data; and arranging the station number, longitude, latitude and elevation data of each water level site into a data matrix according to the spatial data;

[0010] S3: Checking whether the disaster extreme value data sequence follows a generalized extreme value distribution, if not, going to step S4; if yes, going to step S5;

[0011] S4: Cleaning the disaster extreme value data sequence and returning to step S3;

[0012] S5: Converting the disaster extreme value data sequence into a unit Fréchet distribution;

[0013] S6: Designing complex environmental factor encounter scenarios according to different combinations of disaster data and spatial data;

[0014] S7: Constructing a multivariate spatial extreme value model of river network area extreme water level events according to the designed complex environmental factor encounter scenarios;

[0015] S8: Verifying the multivariate spatial extreme value model of river network area extreme water level events and selecting the best spatial extreme value model;

[0016] S9: Estimating the spatial distribution pattern of river network area extreme water level events under different return levels.

[0017] The river network area spatial extreme water level evaluation method can provide expression of extreme water disasters in space under different complex environmental factor encounter scenarios, estimate the spatial distribution pattern of river network area extreme water level events under different return levels, and effectively monitor and evaluate composite floods by collecting disaster data and spatial data of water level sites in a river network area, establishing a disaster extreme value data sequence, converting the disaster extreme value data sequence into a unit Fréchet distribution, designing complex environmental factor encounter scenarios according to different combinations of disaster data and spatial data, and considering the spatial dependence of extreme water level events between sites to establish a multivariate spatial extreme value model.

[0018] Preferably, in step S2, the process of establishing the disaster extreme value data sequence is: selecting the maximum value of the disaster data of the river network area water level station every three days, and finally obtaining the maximum value sequence of the disaster data every three days, i.e. the disaster extreme value data sequence.

[0019] Preferably, in step S3, the process of checking whether the disaster extreme value data sequence follows the generalized extreme value distribution is: calculating the theoretical edge distribution function of the maximum value sequence of the rainfall, water level, flow and storm surge every three days corresponding to the river network area water level station through the generalized extreme value distribution, drawing a Q-Q plot according to the empirical probability of the maximum water level sequence and the theoretical probability calculated by the generalized extreme value distribution, and finally determining whether the extreme value sequence follows the generalized extreme value distribution according to whether the data in the Q-Q plot is within the 95% confidence region.

[0020] Preferably, if there are parameters , , the following conditions are met:

[0021] , ;

[0022] In the formula, , indicates the meteorological hydrological extreme value variable of the water level station about the disaster data ; , indicates the length of the extreme value variable time sequence; , indicates the maximum value of the disaster data of the water level station at the th time sequence; , and indicate the parameters for standardization; , indicates the disaster data; , indicates the dimension of ;

[0023] The fitted distribution needs to follow the generalized extreme value distribution, and the expression of the generalized extreme value distribution is:

[0024] ;

[0025] In the formula, , indicates the location parameter; , indicates the scale parameter, ; , indicates the shape parameter; , indicates the standardized expression of the generalized extreme value distribution, .

[0026] Preferably, in step S5, let , convert the edge distribution function of the generalized extreme value distribution into a unit Fréchet distribution, then the probability of is:

[0027] ;

[0028] wherein, denotes the probability of the occurrence of an extreme value; denotes a parameterized boundary of the hazard data.

[0029] Preferably, in step S7, the process of constructing a multivariate spatial extreme value model comprises:

[0030] establishing a spatial correlation function ;

[0031] constructing a multivariate spatial extreme value model based on the spatial correlation function :

[0032] ;

[0033] ;

[0034] wherein, denotes a multivariate spatial extreme value model for describing extreme values at all locations on any surface in denotes the th point in the point process; denotes the amplitude of the point process; denotes the spatial location; denotes the random point location; denotes a Gaussian distributed density function; denotes a spatial correlation function.

[0035] Preferably, the spatial correlation function is selected from the following (1) to (5):

[0036] (1) a Whittle-Matern correlation function:

[0037] ;

[0038] (2) a Cauchy correlation function:

[0039] ;

[0040] (3) a power exponential correlation function:

[0041] ;

[0042] (4) a Bessel correlation function:

[0043] ;

[0044] (5) a generalized Cauchy correlation function:

[0045] ;

[0046] wherein, denotes a range parameter of the spatial correlation function; denotes a smoothness parameter of the spatial correlation function; denotes a gamma function; denotes a modified Bessel function of the second kind; denotes a Bessel function of the first kind; denotes a scale parameter of the spatial correlation function; denotes a shape parameter of the spatial correlation function; denotes a spatial dimension.

[0047] Preferably, in step S8, the TIC is used to validate the effectiveness of the spatial extreme value model by comparing the spatial dependence of the extreme water level events between the water level sites in the river network region and the estimated value of the spatial extreme value model;

[0048] , ;

[0049] wherein, the TIC represents a criterion to measure the spatial extreme value model, the smaller the TIC, the better the spatial extreme value model; denotes a log value of the likelihood function; denotes an estimated parameter vector, i.e. the log-likelihood value of the model; denotes a constant; tr denotes a trace operator, which represents the trace of a matrix, i.e. the sum of the diagonal elements of the matrix; denotes an observation information covariance matrix of the gradient of the likelihood function with respect to the parameter ; denotes a negative second derivative matrix of the likelihood function with respect to the parameter .

[0050] Preferably, a measure of the spatial dependence between the water level events in the river network region is evaluated, which is defined as:

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] wherein, denotes an extreme water level extreme coefficient between two water level events in the river network region, which quantifies the extreme event correlation between the locations; denotes a spatial dependence measure between two locations; denotes the mathematical expectation; denotes the cumulative distribution function of the unit Fréchet distribution;

[0056] when represents that the spatial dependence degree between water level events in the river network area is complete dependence;

[0057] when represents that the spatial dependence degree between water level events in the river network area is independence.

[0058] Preferably, in step S9, the spatial extreme value model of the extreme water level events in the river network area is fitted using a pairwise likelihood method, which calculates the likelihood value by regarding all two-by-two combinations of sites as independent pairs:

[0059] ;

[0060] wherein, denotes the pairwise log-likelihood function; denotes the extreme value data of the water level variable of the river network area; and denote different water level sites in the river network area, respectively; the sum is taken over all position pairs; denotes the total number of position pairs; denotes the extreme value of the water level observed at position in the th position pair; denotes the extreme value of the water level observed at position in the th position pair; denotes the joint probability density of the extreme value of position and the extreme value of position under the parameter ;

[0061] Recurrence level calculation:

[0062] The expression of the bivariate cumulative distribution function of the unit Fréchet distribution is:

[0063]

[0064] ;

[0065] wherein, denotes the bivariate cumulative distribution function of the unit Fréchet distribution, which is used to describe the joint probability between the extreme values of two water level sites; denotes the Euclidean distance between the th water level site and the th water level site, ; represents a spatial correlation function; represents the parameterization boundary of the disaster data of the first water level site; disaster data of the water level site the parameterization boundary of the disaster data of the water level site; represents the disaster data of the first water level site; disaster data of the water level site the parameterization boundary of the disaster data of the water level site; represents the meteorological hydrological extreme value variable of the water level site about the disaster data represents the meteorological hydrological extreme value variable of the water level site about the disaster data represents the meteorological hydrological extreme value variable of the water level site about the disaster data represents the meteorological hydrological extreme value variable of the water level site about the disaster data

[0066] Let the parameterization boundary of the disaster data of the first water level site and the second water level site be the return level of the annual low water level extreme value, that is, let , the joint probability of the extreme water level of the first water level site and the second water level site under the return period years can be calculated: , the joint probability of the extreme water level of the first water level site and the second water level site under the return period years can be calculated:

[0067] ;

[0068] ;

[0069] In the formula, represents the joint probability of the extreme water level of the first water level site and the second water level site under the return period years; represents time; represents the return level of the annual low water level extreme value; represents a location parameter; represents a shape parameter; represents a scale parameter. Compared with the prior art, the present application has the beneficial effects that: The spatial extreme value model is established by considering the spatial dependence relationship of extreme flood events between water level sites, and the composite flood is effectively monitored and evaluated.

[0070] BRIEF DESCRIPTION OF DRAWINGS

[0071]

[0072] Figure 1 It is a flow chart of the spatial extreme water level evaluation method of the river network area in the embodiment of the present application;

[0073] Figure 2 It is a Q-Q plot of the water level site in the third embodiment of the present application;​​​​​

[0074] Figure 3 This is a graph showing the water level extreme value coefficients for each pair of water level stations when using the spatial extreme value model of the Whittle-Marten correlation function under the encounter scenario in Embodiment 3 of the present invention.

[0075] Figure 4 This is a graph showing the water level extreme value coefficients for each pair of water level stations in Embodiment 3 of the present invention when the spatial extreme value model of the Cauchy correlation function is used in Scenario 1.

[0076] Figure 5 This is a graph showing the water level extreme value coefficients for each pair of water level stations in Embodiment 3 of the present invention when using a power-law correlation function spatial extreme value model in Scenario 1.

[0077] Figure 6 This is a graph showing the water level extreme value coefficients for each pair of water level stations in the spatial extreme value model of the Bessel correlation function in scenario one of the present invention, according to embodiment three of the present invention.

[0078] Figure 7 This is a graph showing the water level extreme value coefficients for each pair of water level stations in Embodiment 3 of the present invention when the spatial extreme value model of the generalized Cauchy correlation function is used in Scenario 1.

[0079] Figure 8 This is a stability test diagram of the optimal spatial extremum model in scenario two in Embodiment 3 of the present invention;

[0080] Figure 9 This is a stability test diagram of the optimal spatial extremum model in Scenario 3 of Embodiment 3 of the present invention.

[0081] Figure 10 This is a stability test diagram of the optimal spatial extremum model in Scenario 4 of Embodiment 3 of the present invention;

[0082] Figure 11 This is a stability test diagram of the optimal spatial extremum model in Scenario 5 in Embodiment 3 of the present invention;

[0083] Figure 12 This is a schematic diagram of the spatial distribution of extreme water levels under different reproduction levels in Embodiment 3 of the present invention. Detailed Implementation

[0084] The present invention will be further described below with reference to specific embodiments.

[0085] Example 1

[0086] This embodiment is the first embodiment of the spatial extreme water level assessment method for river network areas, such as... Figure 1 As shown, it includes the following steps:

[0087] S1: collecting disaster data and spatial data of water level stations in a complex river network area; wherein the disaster data comprises rainfall, water level, flow, storm surge data, and the spatial data comprises geographic position and elevation data of the water level stations, and the geographic position comprises longitude and latitude;

[0088] S2: establishing a disaster extreme value data sequence according to the disaster data; and arranging the station number, longitude, latitude and elevation data of each water level station into a data matrix according to the spatial data;

[0089] S3: checking whether the disaster extreme value data sequence follows a generalized extreme value distribution, if not, going to step S4; if yes, going to step S5;

[0090] S4: cleaning the disaster extreme value data sequence, and returning to step S3;

[0091] S5: converting the disaster extreme value data sequence into a unit Fréchet distribution;

[0092] S6: designing complex environmental factor encounter scenarios according to different combinations of disaster data and spatial data;

[0093] S7: constructing a multivariate spatial extreme value model of extreme water level events in the river network area according to the designed complex environmental factor encounter scenarios;

[0094] S8: verifying the multivariate spatial extreme value model of extreme water level events in the river network area, and selecting the best spatial extreme value model;

[0095] S9: estimating the spatial distribution pattern of extreme water level events in the river network area under different return levels.

[0096] The above-mentioned river network area spatial extreme water level evaluation method collects disaster data and spatial data of water level stations in the river network area, establishes a disaster extreme value data sequence, converts the disaster extreme value data sequence into a unit Fréchet distribution, designs complex environmental factor encounter scenarios according to different combinations of disaster data and spatial data, considers the spatial dependence of extreme water level events between stations, establishes a multivariate spatial extreme value model, can provide expression of extreme water disasters in space under different complex environmental factor encounter scenarios, estimates the spatial distribution pattern of extreme water level events in the river network area under different return levels, analyzes the spatial and event changes of flood event occurrence intensity of different stations in the river network area, and effectively monitors and evaluates the composite flood.

[0097] In step S2, the process of establishing the disaster extreme value data sequence is as follows: selecting the maximum value of every three-day disaster data of the water level stations in the river network area, and finally obtaining the maximum value sequence of every three-day disaster data, i.e. the disaster extreme value data sequence.

[0098] In step S3, the process of checking whether the disaster extreme value data sequence follows the generalized extreme value distribution is as follows: the theoretical edge distribution function of the three-day maximum value sequence of rainfall, water level, flow and storm surge corresponding to the river network area water level station is calculated through the generalized extreme value distribution, the Q-Q graph is drawn according to the empirical probability of the three-day maximum water level sequence and the theoretical probability calculated by the generalized extreme value distribution, and finally whether the extreme value sequence follows the generalized extreme value distribution is determined according to whether the data in the Q-Q graph is within the 95% confidence region.

[0099] If there are parameters , , satisfying:

[0100] , ;

[0101] In the formula, represents the meteorological hydrological extreme value variable of the water level station about the disaster data ; represents the length of the extreme value variable time sequence; represents the maximum value of the disaster data of the water level station in the th time sequence; and represent the parameters for standardization; represents the disaster data; represents the dimension of ;

[0102] The fitted distribution needs to follow the generalized extreme value distribution, and the expression of the generalized extreme value distribution is:

[0103] ;

[0104] In the formula, represents the location parameter; represents the scale parameter, ; represents the shape parameter; represents the standardized expression of the generalized extreme value distribution, .

[0105] In step S4, the reasons why the disaster extreme value data sequence does not follow the generalized extreme value distribution include: the data has autocorrelation or seasonality, or the disaster extreme value data sequence has data missing, short length, and quality problems of outliers;

[0106] The cleaning includes: removing seasonality and autocorrelation of the disaster extreme value data sequence; checking the quality; and converting the disaster extreme value data sequence, including logarithmic transformation, square root transformation or power transformation.

[0107] In step S5, let Transforming the marginal distribution function of the generalized extreme value distribution into a unit Fréchet distribution, then... The probability is:

[0108] ;

[0109] In the formula, express The probability of; This represents the parameterized boundary of disaster data.

[0110] Step S7, the process of constructing a multivariate spatial extremum model includes:

[0111] Establish spatial correlation functions ;

[0112] Based on spatial correlation function Construct a multivariable spatial extremum model:

[0113] ;

[0114] ;

[0115] In the formula, This represents a multivariable spatial extremum model, used to describe... The local maximum value at all locations on any surface in the middle; The first point in the process of representing points One point; Indicates the magnitude of a point process; Indicates spatial location; Indicates the location of a random point; Represents the Gaussian distribution density function; Represents the spatial correlation function.

[0116] Choose from the following spatial correlation functions (1) to (5):

[0117] (1) Whittle-Marten correlation function:

[0118] ;

[0119] (2) Cauchy correlation function:

[0120] ;

[0121] (3) Power-related functions:

[0122] ;

[0123] (4) Bessel correlation function:

[0124] ;

[0125] (5) Generalized Cauchy correlation function:

[0126] ;

[0127] where, denotes the range parameter of the spatial correlation function; denotes the smoothness parameter of the spatial correlation function; denotes the Gamma function; denotes the second kind modified Bessel function; denotes the first kind Bessel function; denotes the scale parameter of the spatial correlation function; denotes the shape parameter of the spatial correlation function; denotes the spatial dimension.

[0128] Embodiment Two

[0129] This embodiment is the second embodiment of the method for evaluating the spatial extreme water level in a river network area. This embodiment is similar to Embodiment One, except that in step S8, the TIC is used to compare the spatial dependence degree of the extreme water level events between the water level sites in the river network area and the estimated value of the spatial extreme model to verify the effectiveness of the spatial extreme model.

[0130] , ;

[0131] wherein TIC denotes the standard for measuring the spatial extreme model, and the smaller the TIC, the better the spatial extreme model; denotes the log value of the likelihood function; denotes the estimated parameter vector, i.e., the log likelihood value of the model; denotes a constant; tr denotes the trace operator, which denotes the trace of a matrix, i.e., the sum of the diagonal elements of the matrix; denotes the observation information covariance matrix of the gradient of the likelihood function with respect to the parameter ; denotes the negative second derivative matrix of the likelihood function with respect to the parameter .

[0132] The F-madogram is used to evaluate the measure of the spatial dependence degree between the water level events in the river network area, which is defined as:

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] where, denotes the extremal water level coefficient between two water level events in a river network region, quantifying the extremal event correlation between locations; denotes the spatial dependence measure between two locations; denotes the mathematical expectation; denotes the cumulative distribution function of the unit Fréchet distribution;

[0138] When , it represents that the spatial dependence degree between water level events in a river network region is complete dependence;

[0139] When , it represents that the spatial dependence degree between water level events in a river network region is independence.

[0140] In step S9, the spatial extreme value model of the extreme water level events in the river network region is fitted using the pairwise likelihood method, which calculates the likelihood value by regarding all two-by-two combinations of sites as independent pairs:

[0141] ;

[0142] where, denotes the pairwise log-likelihood function; denotes the extreme data of the water level variable in the river network region; and denote different water level sites in the river network region, respectively; the sum is taken over all location pairs; denotes the total number of location pairs; denotes the extreme value observed at location in the th location pair; denotes the extreme value observed at location in the th location pair; denotes the joint probability density of the extreme value of location and the extreme value of location under the parameter ;

[0143] Return period level calculation:

[0144] The expression of the binary cumulative distribution function of the unit Fréchet distribution is:

[0145]

[0146] ;

[0147] In the formula, The bivariate cumulative distribution function representing the unit Fréchet distribution is used to describe the joint probability between extreme values ​​of two water level stations. Indicates the first Water level stations and the The Euclidean distance between water level stations ; Represents the spatial correlation function; Indicates the first Disaster data from water level stations Parameterized boundary; Indicates the first Disaster data from water level stations Parameterized boundary; This indicates data about disasters from water level stations. Meteorological and hydrological extreme variables; This indicates data about disasters from water level stations. Meteorological and hydrological extreme variables.

[0148] Order No. Water level stations and the The parameterized boundary of the disaster data of water level stations is The recurrence level of the annual extreme water level, that is, , then the first Water level stations and the Extreme water levels at water level stations during the recurrence period Joint probability under the year:

[0149] ;

[0150] ;

[0151] In the formula, Indicates the first Water level stations and the Extreme water levels at water level stations during the recurrence period The joint probability under the year; Indicates time; It indicates The annual extreme water level recurrence level; This represents a position parameter, used to describe the center position of the variable; Represents shape parameters used to describe tail characteristics; This represents the scale parameter, used to describe the extended range of the variable.

[0152] Example 3

[0153] This embodiment is the third embodiment of the spatial extreme water level assessment method for river network areas. This embodiment is similar to the second embodiment, except that there are 24 water level stations in the river network area, namely MK, SS, FBC, HP, ZD, DS, SD, LS, SSW, SSJ, GZ, BSW, NH, RQ, NS, MA, JM, HM, SSK, ZY, HS, DLS, BJ and HJ.

[0154] Collect disaster data and spatial data. Disaster data includes rainfall, water level, flow rate, and storm surge data for MK, SS, FBC, HP, ZD, DS, SD, LS, SSW, SSJ, GZ, BSW, NH, RQ, NS, MA, JM, HM, SSK, ZY, HS, DLS, BJ, and HJ. Spatial data includes the geographical location and elevation data of all water level stations in the river network area, including longitude and latitude.

[0155] Based on the collected disaster data, the maximum values ​​of the disaster data for every three days are selected to establish a disaster extreme value data sequence. At the same time, the longitude, latitude and elevation data are processed into a data matrix.

[0156] The marginal distribution function parameters of the disaster extreme value data series of rainfall, water level, flow rate, and storm surge are calculated using the generalized extreme value distribution. It is assumed that... It is a random field The maximum limit process on, if there exists a parameter , ,satisfy:

[0157] , ;

[0158] Then put Considered as a maximum stable process, this represents the data from water level stations regarding disaster data. Meteorological and hydrological extreme variables; Disaster data can be represented as rainfall, water level, flow rate, or storm surge. Indicates the length of the time series of the extreme value variable; Indicates the number of water level stations The maximum value of a time series of disaster data; and Indicates the parameters used for standardization;

[0159] The marginal distribution should follow the generalized extreme value distribution, and the expression for the generalized extreme value distribution is:

[0160] ;

[0161] In the formula, Indicates positional parameters; Indicates the scale parameter. ; denotes the shape parameter; denotes the standardized expression of the generalized extreme value distribution, .

[0162] The maximum likelihood method is used to select the optimal parameters of the marginal distribution, assuming , , are independent variables following the same generalized extreme value distribution function, and the log-likelihood of the parameters of the generalized extreme value distribution function is given by

[0163] ;

[0164] where, denotes the log-likelihood function; denotes the indicator function that determines whether is less than the upper bound of the distribution; denotes the indicator function that determines whether is equal to 0; denotes the indicator function that determines whether is less than the lower bound of the distribution; denotes the indicator function that determines whether is greater than 0.

[0165] Let , the marginal distribution function of the generalized extreme value distribution is converted to the unit Fréchet distribution, then the probability of

[0166] ;

[0167] where, denotes the probability of ; denotes the parameterized boundary of the disaster data;

[0168] In order to check whether the sequence of extreme value data of disasters follows the generalized extreme value distribution, the Q-Q plot of the 24 water level stations in the river network is drawn, as shown in Figure 2 The empirical probability of the maximum water level of the 24 stations every 3 days and the theoretical probability calculated by the generalized extreme value distribution are on the diagonal line, indicating that the fitted marginal distribution is good, the extreme value sequence follows the generalized extreme value distribution, and is suitable for the spatial extreme value model, which can be converted to the unit Fréchet distribution.

[0169] Different disaster data and spatial data are combined to design complex environmental factor encounter scenarios, as shown in Table 1:

[0170] Table 1 Different complex environmental factor encounter scenarios

[0171]

[0172] Fitting spatial extreme value models by defining the location parameter of the generalized extreme value distribution , the scale parameter and the shape parameter of the maximum stable process response surface of the spatial marginal distribution, considering three spatial variables to predict the generalized extreme value distribution parameters at fixed sites, wherein the shape parameter usually changes greatly, resulting in convergence problems in maximum likelihood estimation, therefore, the shape parameter is kept fixed at each water level station.

[0173] Select from the following (1) to (5) spatial extreme value simulation models:

[0174] (1) Whittle-Matern correlation function:

[0175] ;

[0176] (2) Cauchy correlation function:

[0177] ;

[0178] (3) power exponential correlation function:

[0179] ;

[0180] (4) Bessel correlation function:

[0181] ;

[0182] (5) generalized Cauchy correlation function:

[0183] ;

[0184] In the formula, represents the range parameter of the spatial correlation function; represents the smoothness parameter of the spatial correlation function; represents the gamma function; represents the modified Bessel function of the second kind; represents the first kind Bessel function; represents the scale parameter of the spatial correlation function; represents the shape parameter of the spatial correlation function; represents the spatial dimension.

[0185] Spatial extreme value model is a statistical model for describing and simulating the spatial distribution of regional extreme events, and the result of calculation is the spatial distribution map of the regional extreme events, which is specifically expressed as:

[0186] ;

[0187] ;

[0188] where, denotes a multivariate spatial extreme value model, which is used to describe the maxima at all locations on any surface in denotes the th point in a point process; denotes the amplitude of a point process; denotes a spatial location; denotes a random point location; denotes a spatial correlation function; denotes a Gaussian density function, and are mathematically different, but are both used to describe the decay of spatial correlation between points in space as the distance increases.

[0189] The F-madogram is used as a statistical tool to assess the spatial dependence structure of extreme water level events between water level sites in the river network:

[0190] ;

[0191] ;

[0192] ;

[0193] where, denotes the extreme water level extreme value coefficient between two water level events in the river network, which quantifies the correlation of extreme events between locations; denotes the spatial dependence measure between two locations; denotes the mathematical expectation; denotes the cumulative distribution function of the unit Fréchet distribution;

[0194] In disaster scenario one, the spatial extreme value simulation models (1) to (5) are used to calculate As shown in Figures 3 to 7 , the fitting lines of the extreme value coefficients obtained by different spatial extreme value simulation models can well simulate the observed values of the F-madogram, and the observed values of the F-madogram of each pair of water level sites are within the range of 1.0 and 1.6 between the water level sites, indicating that there is spatial dependence between extreme water level events between water level sites. Therefore, the extreme water level events in the river network are suitable for spatial extreme value models.

[0195] The effectiveness of the spatial extreme value model is verified by comparing the spatial dependence degree of extreme water level events between water level sites in the river network area and the estimated value of the spatial extreme value model using TIC;

[0196] , ;

[0197] In the formula, TIC represents the standard of measuring the spatial extreme value model, and the smaller the TIC is, the better the spatial extreme value model is; represents the logarithmic value of the likelihood function; represents the estimated parameter vector, i.e. the logarithmic likelihood value of the model; represents a constant; tr represents a trace operator, which represents the trace of a matrix, i.e. the sum of diagonal elements of the matrix; represents the observation information covariance matrix of the gradient of the likelihood function with respect to the parameter ; represents the negative second derivative matrix of the likelihood function with respect to the parameter .

[0198] The spatial extreme value model of extreme water level events in the river network area is fitted using the pairwise likelihood method, which calculates the likelihood value by regarding all pairs of sites as independent pairs:

[0199] ;

[0200] In the formula, represents the pairwise log-likelihood function; represents the extreme value data of the water level variable in the river network area; and represent different water level sites in the river network area, respectively; The sum is taken over all position pairs; represents the total number of position pairs; represents the water level extreme value observed at position in the th position pair; represents the water level extreme value observed at position in the th position pair; represents the joint probability density of the extreme value of position and the extreme value of position under the parameter .

[0201] As shown in Figures 8 to 11 , the F-madogram observation value of each pair of water level sites in the river network area is close to the theoretical extreme value coefficient equation simulated by the spatial extreme value model, which indicates that the selected spatial extreme value model is suitable for spatial modeling of extreme water levels and has high reliability and stability.

[0202] Calculation of return period level:

[0203] The expression for the bivariate cumulative distribution function of the unit Fréchet distribution is:

[0204]

[0205] ;

[0206] In the formula, The bivariate cumulative distribution function representing the unit Fréchet distribution; Indicates the first Water level stations and the The Euclidean distance between water level stations ; Represents the spatial correlation function; Indicates the first Disaster data from water level stations Parameterized boundary; Indicates the first Disaster data from water level stations Parameterized boundary; This indicates data about disasters from water level stations. Meteorological and hydrological extreme variables; This indicates data about disasters from water level stations. Meteorological and hydrological extreme variables;

[0207] Order No. Water level stations and the The parameterized boundary of the disaster data of water level stations is The recurrence level of the annual extreme water level, that is, , then the first Water level stations and the Extreme water levels at water level stations during the recurrence period Joint probability under the year:

[0208] ;

[0209] ;

[0210] In the formula; Indicates the first Water level stations and the Extreme water levels at water level stations during the recurrence period The joint probability under the year; Indicates time; It indicates The annual extreme water level recurrence level; Indicates positional parameters; representing a shape parameter; representing a scale parameter.

[0211] As Figure 12 The 50-year and 100-year return level intensity distributions of extreme water level events in the river network region calculated by the best spatial extreme value model corresponding to encounter scenarios two to five are shown, as shown in the figure. Visualization of the spatial distribution of extreme water levels under different return levels of complex environmental factors is crucial to improve the ability to identify flood warning signals in complex disaster scenarios.

[0212] In the specific content of the above specific embodiments, each technical feature can be combined arbitrarily without contradiction. In order to make the description simple, all possible combinations of the above technical features are not described, but as long as the combination of these technical features does not exist contradiction, it should be considered as the scope of the present application.

[0213] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application. Based on the above description, those skilled in the art can make other different forms of changes or modifications. Here, it is not necessary and impossible to enumerate all the embodiments. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method for evaluating spatial extreme water level in a river network area, characterized in that, The method comprises the following steps: S1: collecting disaster data and spatial data of water level stations in a complex river network area; wherein the disaster data comprises rainfall, water level, flow, storm surge data, and the spatial data comprises geographical position and elevation data of the water level stations, and the geographical position comprises longitude and latitude; S2: establishing a disaster extreme value data sequence according to the disaster data; and arranging the station number, longitude, latitude and elevation data of each water level station into a data matrix according to the spatial data; S3: checking whether the disaster extreme value data sequence follows a generalized extreme value distribution, if not, going to step S4; if yes, going to step S5; S4: cleaning the disaster extreme value data sequence, and returning to step S3; S5: converting the disaster extreme value data sequence into a unit Fréchet distribution; S6: designing complex environmental factor encounter scenarios according to different combinations of disaster data and spatial data; S7: constructing a multivariate spatial extreme value model of extreme water level events in the river network area according to the designed complex environmental factor encounter scenarios; S8: verifying the multivariate spatial extreme value model of extreme water level events in the river network area, and selecting the best spatial extreme value model; S9: estimating the spatial distribution mode of extreme water level events in the river network area under different return levels.

2. The method according to claim 1, wherein In step S2, the process of establishing the disaster extreme value data sequence is as follows: the maximum value of every three-day disaster data of the water level stations in the river network area is selected, and finally the maximum value sequence of every three-day disaster data, i.e. the disaster extreme value data sequence, is obtained.

3. The method according to claim 2, wherein In step S3, the process of checking whether the disaster extreme value data sequence follows the generalized extreme value distribution is as follows: the theoretical edge distribution function of the maximum value sequence of every three-day rainfall, water level, flow and storm surge of the water level stations in the river network area is calculated through the generalized extreme value distribution, the empirical probability of the maximum water level sequence and the theoretical probability calculated through the generalized extreme value distribution are plotted into a Q-Q graph, and finally whether the extreme value sequence follows the generalized extreme value distribution is determined according to whether the data in the Q-Q graph is within the 95% confidence region.

4. The method according to claim 3, wherein if the parameter , is present, it satisfies: ， ； wherein represents the hydrometeorological extreme variable of the gauging station with respect to the disaster data ; represents the length of the time series of the extreme variable; represents the time index; represents the maximum value of the disaster data of the gauging station for the th time series; and represents the parameter for standardization; represents the disaster data; represents the dimension of The fitted distribution needs to be subject to a generalized extreme value distribution, the expression of which is: ； wherein denotes a location parameter; denotes a scale parameter, ; denotes a shape parameter; denotes a standardized expression of the generalized extreme value distribution, .

5. The method for evaluating spatial extreme water level of river network area according to claim 4, characterized in that, In step S5, let transform the marginal distribution function of the generalized extreme value distribution into the unit Fréchet distribution; represent a parameterized boundary for the disaster data.

6. The method for evaluating spatial extreme water level of river network region according to claim 5, characterized in that, In step S7, the process of constructing the multivariate spatial extreme value model comprises: Establishing spatial correlation function ; Based on spatial correlation function , constructing a multivariate spatial extreme value model: ； ； wherein represents a multivariate spatial extreme value model for describing extreme values at all locations on any of the surfaces in represents the th point in the point process; represents the point process amplitude; represents the spatial location; represents the random point location; represents the Gaussian distribution density function; represents the spatial correlation function.

7. The method for evaluating spatial extreme water level of river network region according to claim 6, characterized in that, selected from the following (1) to (5): (1) Whittle-Matern correlation function: ； (2) Cauchy correlation function: ； (3) power exponent correlation function: ； (4) Bessel correlation function: ； (5) generalized Cauchy correlation function: ； wherein denotes a range parameter of the spatial correlation function; denotes a smoothing parameter of the spatial correlation function; denotes a gamma function; denotes a second kind modified Bessel function; denotes a first kind Bessel function; denotes a scale parameter of the spatial correlation function; denotes a shape parameter of the spatial correlation function; denotes a first kind Bessel function; denotes the Euclidean distance between the water level site and the first water level site; denotes the spatial dimension.

8. The method for evaluating spatial extreme water level of river network region according to claim 7, characterized in that, In step S8, the effectiveness of the spatial extreme value model is verified by comparing the spatial dependence degree of extreme water level events between the water level stations in the river network area and the estimated value of the spatial extreme value model through TIC; ， ； where TIC denotes a criterion to measure the spatial extreme model, the smaller the TIC, the better the spatial extreme model; denotes the log value of the likelihood function; denotes the log-likelihood value of the estimated parameter vector, i.e. the model; denotes a constant; tr denotes the trace operator, which denotes the trace of a matrix, i.e. the sum of the diagonal elements of the matrix; denotes the observation information covariance matrix of the gradient of the likelihood function with respect to the parameters ; denotes the negative second derivative matrix of the likelihood function with respect to the parameters ; denotes the length of the time series of the extreme variable.

9. The method for evaluating spatial extreme water level of river network area according to claim 8, characterized in that, The measure of evaluating the spatial dependence degree of water level events in the river network area is defined as: ； ； ； ； wherein denotes the coefficient of extreme water level extremes between two water level events in a river network region, quantifying the dependence of extreme events between locations; denotes a spatial dependence measure between two locations; denotes the mathematical expectation; denotes the cumulative distribution function of the unit Fréchet distribution; denotes the hydrometeorological extreme variable of a water level site with respect to disaster data ; denotes the hydrometeorological extreme variable of a water level site with respect to disaster data ; denotes the hydrometeorological extreme variable of a water level site with respect to disaster data ; When , represents the degree of spatial dependence between water level events in the river network region is completely dependent; When , the spatial dependence degree between water level events in the river network area is independent.

10. The method for evaluating spatial extreme water level of river network region according to claim 8, characterized in that, In step S9, the pair-wise likelihood method is used to fit the spatial extreme value model of extreme water level events in the river network area, and the pair-wise likelihood method regards all two-by-two combinations of the stations as independent pairs to calculate the likelihood value: ； wherein denotes the pair-wise log-likelihood function; denotes extreme data of water level variables of a river network region; and denote different water level sites of a river network region, respectively; summing over all position pairs; denotes the total number of position pairs; denotes the extreme value of position in position pair observed; denotes the extreme value of position in position pair observed; denotes the joint probability density of the extreme value of position and the extreme value of position under the parameters ; The return period level calculation: The expression of the binary cumulative distribution function of the unit Fréchet distribution is: ； wherein denotes the binary cumulative distribution function of the unit Fréchet distribution, used to describe the joint probability between two water level site extremes; denotes the parameterized boundary of the disaster data at the water level site, ; denotes the spatial correlation function; denotes the parameterized boundary of the disaster data at the water level site; denotes the parameterized boundary of the disaster data at the water level site; denotes the meteorological-hydrological extreme variable of the water level site with respect to the disaster data ; denotes the meteorological-hydrological extreme variable of the water level site with respect to the disaster data ; Let The water level station and the The parametric boundary of the disaster data of the water level station is The return level of the annual minimum water level, i.e. The return level of the annual minimum water level, i.e. The water level station and the The joint probability of the extreme water levels of the water level station and the water level station in the return period ； ； wherein denotes the water level station; joint probability of the extreme water levels at the water level stations under a return level of denotes time; denotes the return level of the extreme water levels under a return period of denotes a location parameter; denotes a shape parameter; denotes a scale parameter.

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