Evaluation method for spatial extreme water level of river network area

Abstract

The invention relates to the technical field of flood risk assessment and defense, in particular to a river network area spatial extremum water level assessment method, which comprises the following steps of: collecting disaster data and spatial data of a river network area water level station, establishing a disaster extremum data sequence, converting the disaster extremum data sequence into unit Frechet distribution, and calculating the spatial extremum water level of the river network area. Different disaster data and spatial data are combined to design complex environmental factor encountering scenes, spatial dependence of extreme water level events between stations is considered, a multivariable spatial extremum model is established, spatial expression of extreme water disasters in different complex environmental factor encountering scenes can be provided, and the extreme water disaster encountering scene model is established. The spatial distribution mode of the extreme water level events of the river network area under different reproduction levels is estimated, the change of the occurrence intensity of flood events of different stations in the river network area in space and event is analyzed, and the composite flood is effectively monitored and evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of flood risk assessment and defense, and more specifically, to a method for assessing spatial extreme water levels in a river network area. Background Art

[0002] The spatial structure of floods is a key factor in determining flood severity. Floods usually affect more than one location, and the most severe floods often affect large areas, resulting in loss of life and severe damage to infrastructure, causing adverse social impacts. Considering the spatial dependence of extreme flood events at multiple locations requires extending the single variable extreme value theory to multivariate. At the same time, understanding the temporal and spatial variations in the probability of extreme floods is very important for regional flood prevention and control.

[0003] Flood frequency analysis in a river network complex area requires consideration of the spatial dependence of extreme flood events between sites under the influence of complex environmental factors. This dependence is often overlooked, which leads to an underestimated risk of extreme floods. Therefore, the model used in regional multivariate frequency analysis should consider the spatiotemporal correlation of flood events, that is, to analyze how the intensity of extreme flood events at different locations varies in space and time in the river network area. The multivariate spatial extreme value model considers the spatial dependence of extreme flood events between sites driven by different environmental factors, and is a hot research direction for composite flood risk assessment.

[0004] The prior art discloses a method for assessing flood disaster risks in different scales. The method collects spatial data of the area to be analyzed and attribute data associated with the spatial data as initial data, compresses the initial data and stores it in a created spatial database; standardizes the initial data and unifies the units; uses the AHP hierarchical analysis method and the entropy weight method coupling model to determine the weight of each factor combination; assesses the flood disaster risk value in the study area, divides the risk level, and generates a flood disaster risk index map. This scheme uses various types of collected natural and social data as input, uses a variety of algorithm coupling models to determine the weight, and finally generates a flood risk level evaluation index map, which improves the accuracy of flood disaster risk assessment. At the same time, it has the advantages of objectivity and efficiency, and more intuitively shows the flood disaster risk situation that the study area may suffer under given conditions. However, the spatial dependence of extreme flood events between water level stations is not considered in this scheme, resulting in the underestimated risk of extreme floods. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiency of the prior art that the risk of extreme floods is underestimated, and to provide a method for assessing the spatial extreme water levels in a river network area, taking into account the spatial dependence of extreme flood events between water level stations, so as to effectively monitor and evaluate compound floods.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A method for evaluating spatial extreme water levels in a river network area is provided, comprising the following steps:

[0008] S1: Collect disaster data and spatial data of water level stations in complex river network areas; disaster data include rainfall, water level, flow, and storm surge data; spatial data include geographical location and elevation data of water level stations, and geographical location includes longitude and latitude;

[0009] S2: Establish a disaster extreme value data sequence based on disaster data; organize the station number, longitude, latitude and elevation data of each water level station into a data matrix based on spatial data;

[0010] S3: Check whether the disaster extreme value data sequence follows the generalized extreme value distribution. If not, proceed to step S4; if yes, proceed to step S5;

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

[0012] S5: Convert the disaster extreme value data series into unit Fréchet distribution;

[0013] S6: Design scenarios for encountering complex environmental factors based on different combinations of disaster data and spatial data;

[0014] S7: Construct 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;

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

[0016] S9: Estimate the spatial distribution patterns of extreme water level events in river networks at different recurrence levels.

[0017] The spatial extreme water level assessment method for a river network area of ​​the present invention collects disaster data and spatial data of water level stations in the river network area, establishes a disaster extreme data sequence, converts the disaster extreme data sequence into a unit Fréchet distribution, combines different disaster data and spatial data to design complex environmental factor encounter scenarios, considers the spatial dependence of extreme water level events between stations, and establishes a multivariate spatial extreme value model. The method can provide a spatial expression of extreme water disasters under different complex environmental factor encounter scenarios, estimate the spatial distribution patterns of extreme water level events in the river network area at different recurrence levels, analyze the changes in the occurrence intensity of flood events at different stations in the river network area in space and events, and effectively monitor and evaluate compound floods.

[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 water level station in the river network area every three days, and finally obtaining the maximum value sequence of the disaster data every three days, that is, 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 as follows: the theoretical marginal distribution function of the maximum value sequence of rainfall, water level, flow and storm surge every three days corresponding to the water level station in the river network area is calculated by the generalized extreme value distribution, and a QQ graph is drawn according to the empirical probability of the maximum water level sequence every three days and the theoretical probability calculated by the generalized extreme value distribution. Finally, whether the extreme value sequence follows the generalized extreme value distribution is judged according to whether the data in the QQ graph is within the 95% confidence region.

[0020] Preferably, if there is a parameter a n (x)>0,b n (x)∈R, satisfies:

[0021]

[0022] Where Z(x) represents the meteorological and hydrological extreme value variable of the water level station for the disaster data x; n represents the length of the extreme value variable time series; Y i (x) represents the maximum value of the disaster data of the i-th time series of the water level station; a n (x) and b n (x) represents the parameter used for normalization; x represents the disaster data; d represents the dimension of Z(x);

[0023] The distribution of Z(x) fitting needs to obey the generalized extreme value distribution. The expression of generalized extreme value distribution is:

[0024]

[0025] In the formula, μ represents the location parameter; τ represents the scale parameter, σ>0; ζ represents the shape parameter; Represents the standardized expression for the generalized extreme value distribution,

[0026] Preferably, in step S5, The marginal distribution function of the generalized extreme value distribution is transformed into the unit Fréchet distribution, and the probability of Z(x)≤q is:

[0027]

[0028] Where Pr[Z(x)≤q] represents the probability of Z(x)≤q; q represents the parameterized boundary of disaster data.

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

[0030] Establish the spatial correlation function ρ(h);

[0031] Based on the spatial correlation function ρ(h), a multivariate spatial extreme value model is constructed:

[0032]

[0033] φ ∑ (ss i )=ρ(h)(ss i );

[0034] Where M(s) represents the multivariate spatial extreme value model, which is used to describe the maximum values ​​at all positions on any surface in Z(x); i represents the i-th point in the point process; l i represents the amplitude of the point process; s represents the spatial position; s i represents the position of a random point; φ ∑ (ss i ) represents the Gaussian distribution density function; ρ(h) represents the spatial correlation function.

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

[0036] (1) Whittle-Marten correlation function:

[0037] c2>0,v>0;

[0038] (2) Cauchy correlation function:

[0039] c2>0, v>0;

[0040] (3) Power exponential correlation function:

[0041] c2>0, v>0;

[0042] (4) Bessel correlation function:

[0043] c2>0,

[0044] (5) Generalized Cauchy correlation function:

[0045]

[0046] Where c2 represents the range parameter of the spatial correlation function; v represents the smoothing parameter of the spatial correlation function; Γ represents the gamma function; K v represents the second kind of modified Bessel function; J vrepresents the first kind of Bessel function; σ represents the scale parameter of the spatial correlation function; λ represents the shape parameter of the spatial correlation function.

[0047] Preferably, in step S8, the spatial dependence of extreme water level events between water level stations in the river network area and the estimated value of the spatial extreme value model are compared using TIC to verify the validity of the spatial extreme value model;

[0048] TIC=-2l pair (ψ)-ktr{J(ψ)H(ψ) -1}, k∈{2,logn};

[0049] In the formula, TIC represents the standard for measuring the spatial extreme value model. The smaller the TIC, the better the spatial extreme value model. pair represents the logarithmic value of the likelihood function; ψ represents the estimated parameter vector, that is, the logarithmic likelihood value of the model; k represents a constant; tr represents the trace operator, which represents the trace of the matrix, that is, the sum of the diagonal elements of the matrix; J(ψ) represents the observed information covariance matrix of the gradient of the likelihood function with respect to the parameter ψ; H(ψ) represents the negative second-order derivative matrix of the likelihood function with respect to the parameter ψ.

[0050] Preferably, the metric for assessing the degree of spatial dependence between water level events in a river network is defined as:

[0051] F(Z(x))=exp(-1 / Z(x));

[0052]

[0053] 1≤θ(h)≤2;

[0054] Where θ(h) represents the extreme water level extreme value coefficient between two water level events in the river network area, which quantifies the correlation of extreme events between locations; ν(h) represents the spatial dependence measure between two locations; E represents the mathematical expectation; F(Z(x)) represents the cumulative distribution function of the unit Fréchet distribution;

[0055] When θ(h) = 1, it means that the spatial dependence between water level events in the river network area is complete dependence;

[0056] When θ(h) = 2, it means that the spatial dependence between water level events in the river network area is independent.

[0057] Preferably, in step S9, a paired likelihood method is used to fit the spatial extreme value model of extreme water level events in the river network area. The paired likelihood method regards all pairs of stations as independent pairs to calculate the likelihood value:

[0058]

[0059] In the formula, l p(w; ψ) represents the paired log-likelihood function; w represents the extreme value data of the water level variable in the river network area; i and j represent different water level stations in the river network area; ∑ i<j Indicates the sum of all position pairs; n ij represents the total number of position pairs; w m (i) represents the extreme value of the water level observed at position i in the mth position pair; w m (j) represents the extreme value of the water level observed at position j in the mth position pair; f(w m (i) ;w m (j) ; ψ) represents the extreme value w at position i under parameter ψ m (i) and the extreme value w at position j m (j) The joint probability density of

[0060] Return period level calculation:

[0061] The bivariate cumulative distribution function of the unit Fréchet distribution is expressed as:

[0062]

[0063] In the formula, Pr[Z(x i )≤q i , Z(x j )≤q j ] represents 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 stations; h represents the Euclidean distance between the i-th water level station and the j-th water level station, h∈R + ; ρ(h) represents the spatial correlation function; q i Represents the disaster data x of the i-th water level station i The parameterized boundary of q j represents the disaster data x of the jth water level station j The parameterized boundary of Z(x i ) represents the water level station about the disaster data x i The meteorological and hydrological extreme value variables, Z(x i ) is the water level extreme value at the i-th water level station in M(s); Z(x j ) represents the water level station about the disaster data x j The meteorological and hydrological extreme value variables, Z(x j ) is the extreme value of the water level at the j-th water level station in M(s);

[0064] Let the parameterized boundary of the disaster data of the i-th water level station and the j-th water level station be the recurrence level of the water level extreme value in year T, that is, The joint probability of the extreme water levels of the i-th water level station and the j-th water level station under the return period of T years can be calculated:

[0065]

[0066]

[0067] In the formula, represents the joint probability of the extreme water level of the i-th water level station and the j-th water level station under the return period of T years; T represents time; y T It represents the recurrence level of extreme water level in year T; μ represents the location parameter; ξ represents the shape parameter; σ represents the scale parameter.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] A spatial extreme value model is established by considering the spatial dependence of extreme flood events between water level stations to effectively monitor and evaluate compound floods. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flow chart of a method for evaluating spatial extreme water level in a river network area in an embodiment of the present invention;

[0071] Figure 2 It is the QQ diagram of the water level station in the third embodiment of the present invention;

[0072] Figure 3 A curve diagram of water level extreme value coefficients for each pair of water level stations when the spatial extreme value model of the Whittle-Marten correlation function is used in the first scenario in the third embodiment of the present invention;

[0073] Figure 4 A curve diagram of water level extreme value coefficients for each pair of water level stations when the spatial extreme value model of the Cauchy correlation function is used in the first scenario in the third embodiment of the present invention;

[0074] Figure 5 A curve diagram of water level extreme value coefficients for each pair of water level stations when the spatial extreme value model of the power exponential correlation function is adopted in the first scenario in the third embodiment of the present invention;

[0075] Figure 6 A water level extreme value coefficient curve diagram of each pair of water level stations when the spatial extreme value model of the Bessel correlation function is adopted in the encounter scenario 1 in the third embodiment of the present invention;

[0076] Figure 7 A curve diagram of water level extreme value coefficients for each pair of water level stations when the spatial extreme value model of the generalized Cauchy correlation function is used in the first scenario in the third embodiment of the present invention;

[0077] Figure 8This is a stability test diagram of the optimal spatial extreme value model in the third embodiment of the present invention when encountering scenario 2;

[0078] Fig. 9 This is a stability test diagram of the optimal spatial extreme value model in the third embodiment of the present invention when encountering scenario three;

[0079] Fig.10 This is a stability test diagram of the optimal spatial extreme value model in Embodiment 3 of the present invention when encountering Scenario 4;

[0080] Fig.11 This is a stability test diagram of the optimal spatial extreme value model in Embodiment 3 of the present invention when encountering Scenario 5;

[0081] Fig.12 Schematic diagram of spatial distribution of extreme water levels at different recurrence levels in Example 3 of the present invention. DETAILED DESCRIPTION

[0082] The present invention will be further described below in conjunction with specific implementation modes.

[0083] Embodiment 1

[0084] This embodiment is the first embodiment of the method for evaluating the spatial extreme water level in a river network area. Figure 1 As shown, the following steps are included:

[0085] S1: Collect disaster data and spatial data of water level stations in complex river network areas; disaster data include rainfall, water level, flow, and storm surge data; spatial data include geographical location and elevation data of water level stations, and geographical location includes longitude and latitude;

[0086] S2: Establish a disaster extreme value data sequence based on disaster data; organize the station number, longitude, latitude and elevation data of each water level station into a data matrix based on spatial data;

[0087] S3: Check whether the disaster extreme value data sequence follows the generalized extreme value distribution. If not, proceed to step S4; if yes, proceed to step S5;

[0088] S4: Clean the disaster extreme value data sequence and return to step S3;

[0089] S5: Convert the disaster extreme value data series into unit Fréchet distribution;

[0090] S6: Design scenarios for encountering complex environmental factors based on different combinations of disaster data and spatial data;

[0091] S7: Construct 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;

[0092] S8: Verify the multivariate spatial extreme value model of extreme water level events in the river network area and select the best spatial extreme value model;

[0093] S9: Estimate the spatial distribution patterns of extreme water level events in river networks at different recurrence levels.

[0094] The above-mentioned method for assessing spatial extreme water levels in river network areas collects disaster data and spatial data of water level stations in river network areas, establishes a disaster extreme data sequence, converts the disaster extreme data sequence into a unit Fréchet distribution, combines different disaster data and spatial data to design complex environmental factor encounter scenarios, considers the spatial dependence of extreme water level events between stations, and establishes a multivariate spatial extreme value model. It can provide a spatial expression of extreme water disasters under different complex environmental factor encounter scenarios, estimate the spatial distribution patterns of extreme water level events in river network areas at different recurrence levels, analyze the changes in the intensity of flood events at different stations in the river network area in space and events, and effectively monitor and evaluate compound floods.

[0095] In step S2, the process of establishing the disaster extreme value data sequence is: selecting the maximum value of the disaster data of the water level station in the river network area every three days, and finally obtaining the maximum value sequence of the disaster data every three days, that is, the disaster extreme value data sequence.

[0096] 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 marginal distribution function of the maximum value sequence of rainfall, water level, flow and storm surge every three days corresponding to the water level station in the river network area is calculated by the generalized extreme value distribution, and a QQ graph is drawn according to the empirical probability of the maximum water level sequence every three days and the theoretical probability calculated by the generalized extreme value distribution. Finally, whether the extreme value sequence follows the generalized extreme value distribution is judged according to whether the data in the QQ graph is within the 95% confidence region.

[0097] If there is a parameter a n (x)>0,b n (x)∈R, satisfies:

[0098]

[0099] Where Z(x) represents the meteorological and hydrological extreme value variable of the water level station for the disaster data x; n represents the length of the extreme value variable time series; Y i (x) represents the maximum value of the disaster data of the i-th time series of the water level station; a n (x) and b n (x) represents the parameter used for normalization; x represents the disaster data; d represents the dimension of Z(x);

[0100] The distribution of Z(x) fitting needs to obey the generalized extreme value distribution. The expression of generalized extreme value distribution is:

[0101]

[0102] In the formula, μ represents the location parameter; τ represents the scale parameter, σ>0; ζ represents the shape parameter; Represents the standardized expression for the generalized extreme value distribution,

[0103] In step S4, the reasons why the disaster extreme value data series does not follow the generalized extreme value include: the data has autocorrelation or seasonality, or the disaster extreme value data series has quality problems such as missing data, short length, and outliers;

[0104] Cleaning includes: removing seasonality and autocorrelation of disaster extreme value data series; checking the quality; transforming the disaster extreme value data series, including logarithmic transformation, square root transformation or power transformation.

[0105] In step S5, The marginal distribution function of the generalized extreme value distribution is transformed into the unit Fréchet distribution, and the probability of Z(x)≤q is:

[0106] q>0;

[0107] Where Pr[Z(x)≤q] represents the probability of Z(x)≤q; q represents the parameterized boundary of disaster data.

[0108] In step S7, the process of constructing a multivariate spatial extreme value model includes:

[0109] Establish the spatial correlation function ρ(h);

[0110] Based on the spatial correlation function ρ(h), a multivariate spatial extreme value model is constructed:

[0111]

[0112] φ ∑ (ss i )=ρ(h)(ss i );

[0113] Where M(s) represents the multivariate spatial extreme value model, which is used to describe the maximum values ​​at all positions on any surface in Z(x); i represents the i-th point in the point process; ι i represents the amplitude of the point process; s represents the spatial position; s i represents the position of a random point; φ ∑ (ss i ) represents the Gaussian distribution density function; ρ(h) represents the spatial correlation function.

[0114] ρ(h) is selected from the following spatial correlation functions (1) to (5):

[0115] (1) Whittle-Marten correlation function:

[0116] c2>0, v>0;

[0117] (2) Cauchy correlation function:

[0118] c2>0, v>0;

[0119] (3) Power exponential correlation function:

[0120] c2>0, v>0;

[0121] (4) Bessel correlation function:

[0122] c2>0,

[0123] (5) Generalized Cauchy correlation function:

[0124]

[0125] Where c2 represents the range parameter of the spatial correlation function; v represents the smoothing parameter of the spatial correlation function; Γ represents the gamma function; K v represents the second kind of modified Bessel function; J v represents the first kind of Bessel function; σ represents the scale parameter of the spatial correlation function; λ represents the shape parameter of the spatial correlation function.

[0126] Embodiment 2

[0127] This embodiment is a second embodiment of a method for evaluating spatial extreme water levels in a river network area. This embodiment is similar to the first embodiment, except that in step S8, TIC is used to compare the spatial dependence of extreme water level events between water level stations in the river network area with the estimated value of the spatial extreme value model to verify the validity of the spatial extreme value model.

[0128] TIC=-2l pair (ψ)-ktr{J(ψ)H(ψ) -1}, k∈{2,logn};

[0129] In the formula, TIC represents the standard for measuring the spatial extreme value model. The smaller the TIC, the better the spatial extreme value model. pairrepresents the logarithmic value of the likelihood function; ψ represents the estimated parameter vector, that is, the logarithmic likelihood value of the model; k represents a constant; tr represents the trace operator, which represents the trace of the matrix, that is, the sum of the diagonal elements of the matrix; J(ψ) represents the observed information covariance matrix of the gradient of the likelihood function with respect to the parameter ψ; H(ψ) represents the negative second-order derivative matrix of the likelihood function with respect to the parameter ψ.

[0130] The F-madogram is used to evaluate the spatial dependence between water level events in the river network, which is defined as:

[0131] F(Z(x))=exp(-1 / Z(x));

[0132]

[0133] 1≤θ(h)≤2;

[0134] Where θ(h) represents the extreme water level extreme value coefficient between two water level events in the river network area, which quantifies the correlation of extreme events between locations; ν(h) represents the spatial dependence measure between two locations; E represents the mathematical expectation; F(Z(x)) represents the cumulative distribution function of the unit Fréchet distribution;

[0135] When θ(h) = 1, it means that the spatial dependence between water level events in the river network area is complete dependence;

[0136] When θ(h) = 2, it means that the spatial dependence between water level events in the river network area is independent.

[0137] In step S9, the paired likelihood method is used to fit the spatial extreme value model of extreme water level events in the river network area. The paired likelihood method regards all pairs of stations as independent pairs to calculate the likelihood value:

[0138]

[0139] In the formula, l p (w; ψ) represents the paired log-likelihood function; w represents the extreme value data of the water level variable in the river network area; i and j represent different water level stations in the river network area; ∑ i<j Indicates the sum of all position pairs; n ij represents the total number of position pairs; w m (i) represents the extreme value of the water level observed at position i in the mth position pair; w m (j) represents the extreme value of the water level observed at position j in the mth position pair; f(w m (i) ;w m (j) ; ψ) represents the extreme value w at position i under parameter ψ m(i) and the extreme value w at position j m (j) The joint probability density of

[0140] Return period level calculation:

[0141] The bivariate cumulative distribution function of the unit Fréchet distribution is expressed as:

[0142]

[0143] In the formula, Pr[Z(x i )≤q i ,Z(x j )≤q j ] represents 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 stations; h represents the Euclidean distance between the i-th water level station and the j-th water level station, h∈R + ; ρ(h) represents the spatial correlation function; q i Represents the disaster data x of the i-th water level station i The parameterized boundary of q j represents the disaster data x of the jth water level station j The parameterized boundary of Z(x i ) represents the water level station about the disaster data x i The meteorological and hydrological extreme value variables, Z(x i ) is the water level extreme value at the i-th water level station in M(s); Z(x j ) represents the water level station about the disaster data x j The meteorological and hydrological extreme value variables, Z(x j ) is the extreme value of the water level at the j-th water level station in M(s);

[0144] Let the parameterized boundary of the disaster data of the i-th water level station and the j-th water level station be the recurrence level of the water level extreme value in year T, that is, The joint probability of the extreme water levels of the i-th water level station and the j-th water level station under the return period of T years can be calculated:

[0145]

[0146] In the formula, represents the joint probability of the extreme water level of the i-th water level station and the j-th water level station under the return period of T years; T represents time; y T It represents the recurrence level of extreme water level in year T; μ represents the location parameter, which is used to describe the central position of the variable; ξ represents the shape parameter, which is used to describe the tail characteristics; σ represents the scale parameter, which is used to describe the extended range of the variable.

[0147] Embodiment 3

[0148] This embodiment is the third embodiment of the method for evaluating the spatial extreme water level in a river network area. 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.

[0149] Collect disaster data and spatial data. The disaster data include rainfall, water level, flow and storm surge data of 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. The spatial data include the geographical location and elevation data of all water level stations in the river network area. The geographical location includes longitude and latitude.

[0150] Based on the collected disaster data, the maximum value of the disaster data every three days is selected to establish a disaster extreme value data sequence, and the longitude, latitude and elevation data are processed into a data matrix.

[0151] The generalized extreme value distribution is selected to calculate the marginal distribution function parameters of the extreme value data series of rainfall, water level, flow and storm surge. Assume that Z(x) is a random field {Y i (x), x∈R d}, if there is a maximum limit process on the n (x)>0,b n (x)∈R, satisfies:

[0152] x∈R d ;

[0153] Then Z(x) is regarded as a maximum stable process, which represents the meteorological and hydrological extreme value variable of the water level station with respect to the disaster data x; x represents the disaster data, which can be rainfall, water level, flow or storm surge; n represents the length of the extreme value variable time series; Y i (x) represents the maximum value of the disaster data of the i-th time series of the water level station; a n (x) and b n (x) represents the parameter used for normalization;

[0154] The marginal distribution should follow the generalized extreme value distribution, and the expression of the generalized extreme value distribution is:

[0155]

[0156] In the formula, μ represents the location parameter; τ represents the scale parameter, σ>0; ζ represents the shape parameter; Represents the standardized expression for the generalized extreme value distribution,

[0157] The maximum likelihood method is used to select the optimal marginal distribution parameters. Assume that Z1, Z2, ... Z n are independent variables that follow the same generalized extreme value distribution function, and the log-likelihood of the generalized extreme value distribution function parameters is given by:

[0158]

[0159] Where l(μ, σ, ξ) represents the log-likelihood function; Indicates judgment Z i Is it less than the upper bound of the distribution? I0(ξ) indicates whether ξ is equal to 0. Indicates judgment Z i Is it less than the lower bound of the distribution? (0，+∞) (ξ) represents an indicator function for judging whether to calculate when ξ is greater than 0.

[0160] make The marginal distribution function of the generalized extreme value distribution is transformed into the unit Fréchet distribution, and the probability of Z(x)≤q is:

[0161] q>0;

[0162] Where Pr[Z(x)≤q] represents the probability of Z(x)≤q; q represents the parameterized boundary of disaster data;

[0163] In order to check whether the disaster extreme value data series follows the generalized extreme value distribution, the QQ diagram of 24 water level stations in the river network area is drawn, as shown in Figure 2 As shown, the empirical probability of the maximum water level at the 24 stations every 3 days and the theoretical probability calculated by the generalized extreme value distribution are on the 45° diagonal, indicating that the fitted marginal distribution is good, the extreme value sequence follows the generalized extreme value distribution, is suitable for the spatial extreme value model, and can be converted to a unit Fréchet distribution.

[0164] Combining different disaster data and spatial data, complex environmental factor encounter scenarios are designed, as shown in Table 1:

[0165] Table 1 Encounter scenarios of different complex environmental factors

[0166]

[0167] In the spatial extreme value model, the spatial marginal distribution is fitted by defining the maximum stable process response surface of the location parameter μ, scale parameter σ and shape parameter ξ of the generalized extreme value distribution. The three spatial variables are considered to predict the generalized extreme value distribution parameters at a fixed location. Among them, the shape parameter usually varies greatly, which can lead to convergence problems in the maximum likelihood estimation. Therefore, the shape parameter remains fixed at each water level station.

[0168] ρ(h) is selected from the following spatial extreme value simulation models (1) to (5):

[0169] (1) Whittle-Marten correlation function:

[0170] c2>0, v>0;

[0171] (2) Cauchy correlation function:

[0172] c2>0, v>0;

[0173] (3) Power exponential correlation function:

[0174] c2>0, v>0;

[0175] (4) Bessel correlation function:

[0176] c2>0,

[0177] (5) Generalized Cauchy correlation function:

[0178]

[0179] Where c2 represents the range parameter of the spatial correlation function; v represents the smoothing parameter of the spatial correlation function; Γ represents the gamma function; K v represents the second kind of modified Bessel function; J v represents the first kind of Bessel function; σ represents the scale parameter of the spatial correlation function; λ represents the shape parameter of the spatial correlation function.

[0180] The spatial extreme value model M(s) is a statistical model used to describe and simulate the spatial distribution of regional extreme value events. The result of calculating M(s) is the spatial distribution map of extreme value events in the region, which is specifically expressed as:

[0181]

[0182] φ ∑ (ss i )=ρ(h)(ss i );

[0183] Where M(s) represents the multivariate spatial extreme value model, which is used to describe the maximum values ​​at all positions on any surface in Z(x); i represents the i-th point in the point process; ι i represents the amplitude of the point process; s represents the spatial position; s i represents the position of a random point; ρ(h) represents the spatial correlation function; φ ∑ (ss i ) represents the Gaussian distribution density function, φ ∑ (ss i ) and ρ(h)(ss i ) have different mathematical forms, but they are both used in spatial modeling to describe the decay process of the correlation between spatial points as the distance increases.

[0184] F-madogram was used as a statistical tool to evaluate the spatial dependence structure of extreme water level events between water level stations in the river network:

[0185] F(Z(x))=exp(-1 / Z(x));

[0186]

[0187] Where θ(h) represents the extreme water level extreme value coefficient between two water level events in the river network area, which quantifies the correlation of extreme events between locations; v(h) represents the spatial dependence measure between two locations; E represents the mathematical expectation; F(Z(x)) represents the cumulative distribution function of the unit Fréchet distribution;

[0188] In disaster scenario 1, the spatial extreme value simulation models (1) to (5) are used to calculate θ(h), as follows: Figures 3 to 7 As shown in the figure, the extreme value coefficient fitting lines obtained by different spatial extreme value simulation models can simulate the observed values ​​of F-madogram well, and the observed values ​​of F-madogram of each pair of water level stations are in the range of 1.0 and 1.6 with the distance between water level stations, indicating that there is spatial dependence of extreme water level events between water level stations. Therefore, the extreme water level events in the river network area are suitable for the spatial extreme value model.

[0189] TIC is used to compare the spatial dependence of extreme water level events between water level stations in the river network and the estimated values ​​of the spatial extreme value model to verify the effectiveness of the spatial extreme value model.

[0190] TIC=-2l pair (ψ)-ktr{J(ψ)H(ψ) -1}, k∈{2,logn};

[0191] In the formula, TIC represents the standard for measuring the spatial extreme value model. The smaller the TIC, the better the spatial extreme value model. pairrepresents the logarithmic value of the likelihood function; ψ represents the estimated parameter vector, that is, the logarithmic likelihood value of the model; k represents a constant; tr represents the trace operator, which represents the trace of the matrix, that is, the sum of the diagonal elements of the matrix; J(ψ) represents the observed information covariance matrix of the gradient of the likelihood function with respect to the parameter ψ; H(ψ) represents the negative second-order derivative matrix of the likelihood function with respect to the parameter ψ.

[0192] The pairwise likelihood method is used to fit the spatial extreme value model of extreme water level events in the river network area. The pairwise likelihood method treats all pairs of stations as independent pairs to calculate the likelihood value:

[0193]

[0194] In the formula, l p (w; ψ) represents the paired log-likelihood function; w represents the extreme value data of the water level variable in the river network area; i and j represent different water level stations in the river network area; ∑ i<j Indicates the sum of all position pairs; n ij represents the total number of position pairs; w m (i) represents the extreme value of the water level observed at position i in the mth position pair; w m (j) represents the extreme value of the water level observed at position j in the mth position pair; f(w m (i) ;w m (j) ; ψ) represents the extreme value w at position i under parameter ψ m (i) and the extreme value w at position j m (j) The joint probability density of .

[0195] like Figures 8 to 11 As shown in the figure, the F-madogram observations of each pair of water level stations in the river network area are close to the theoretical extreme value coefficient equation simulated by the spatial extreme value model, indicating that the selected spatial extreme value model is suitable for spatial modeling of extreme water levels and has high reliability and stability.

[0196] Return period level calculation:

[0197] The bivariate cumulative distribution function of the unit Fréchet distribution is expressed as:

[0198]

[0199] In the formula, Pr[Z(x i )≤q i , Z(x j )≤q j] represents the bivariate cumulative distribution function of the unit Fréchet distribution; h represents the Euclidean distance between the i-th water level station and the j-th water level station, h∈R + ; ρ(h) represents the spatial correlation function; q i Represents the disaster data x of the i-th water level station i The parameterized boundary of q j represents the disaster data x of the jth water level station j The parameterized boundary of Z(x i ) represents the water level station about the disaster data x i The meteorological and hydrological extreme value variables, Z(x i ) is the water level extreme value at the i-th water level station in M(s); Z(x j ) represents the water level station about the disaster data x j The meteorological and hydrological extreme value variables, Z(x j ) is the extreme value of the water level at the j-th water level station in M(s);

[0200] Let the parameterized boundary of the disaster data of the i-th water level station and the j-th water level station be the recurrence level of the water level extreme value in year T, that is, The joint probability of the extreme water levels of the i-th water level station and the j-th water level station under the return period of T years can be calculated:

[0201]

[0202] Where; represents the joint probability of the extreme water level of the i-th water level station and the j-th water level station under the return period of T years; T represents time; y T It represents the recurrence level of extreme water level in year T; μ represents the location parameter; ζ represents the shape parameter; τ represents the scale parameter.

[0203] like Fig.12 As shown, the 50-year and 100-year recurrence intensity distributions of extreme water level events in the river network area calculated by the best spatial extreme value model corresponding to scenarios 2 to 5 are displayed. Visualizing the spatial distribution of extreme water levels under different recurrence levels of complex environmental factors is crucial to improving the ability to identify flood warning signals in complex disaster scenarios.

[0204] In the specific contents of the above-mentioned specific implementation methods, the various technical features can be combined in any non-contradictory manner. In order to make the description concise, not all possible combinations of the above-mentioned technical features are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0205] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for evaluating spatial extreme water levels in a river network area, characterized in that: The following steps are involved: S1: Collect disaster data and spatial data of water level stations in complex river network areas; disaster data include rainfall, water level, flow, and storm surge data; spatial data include geographical location and elevation data of water level stations, and geographical location includes longitude and latitude; S2: Establish a disaster extreme value data sequence based on disaster data; organize the station number, longitude, latitude and elevation data of each water level station into a data matrix based on spatial data; S3: Check whether the disaster extreme value data sequence follows the generalized extreme value distribution. If not, proceed to step S4; if yes, proceed to step S5; S4: Clean the disaster extreme value data sequence and return to step S3; S5: Convert the disaster extreme value data series into unit Fréchet distribution; S6: Design scenarios for encountering complex environmental factors based on different combinations of disaster data and spatial data; S7: Construct 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: Verify the multivariate spatial extreme value model of extreme water level events in the river network area and select the best spatial extreme value model; S9: Estimate the spatial distribution patterns of extreme water level events in river networks at different recurrence levels.

2. The method for evaluating spatial extreme water levels in a river network area according to claim 1, characterized in that: In step S2, the process of establishing the disaster extreme value data sequence is: selecting the maximum value of the disaster data of the water level station in the river network area every three days, and finally obtaining the maximum value sequence of the disaster data every three days, that is, the disaster extreme value data sequence.

3. The method for evaluating spatial extreme water levels in a river network area according to claim 2, characterized in that: 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 marginal distribution function of the maximum value sequence of rainfall, water level, flow and storm surge every three days corresponding to the water level station in the river network area is calculated by the generalized extreme value distribution, and a QQ graph is drawn according to the empirical probability of the maximum water level sequence every three days and the theoretical probability calculated by the generalized extreme value distribution. Finally, whether the extreme value sequence follows the generalized extreme value distribution is judged according to whether the data in the QQ graph is within the 95% confidence region.

4. The method for evaluating spatial extreme water levels in a river network area according to claim 3 is characterized in that: If there is a parameter a n (x)>0,b n (x)∈R, satisfies: Where Z(x) represents the meteorological and hydrological extreme value variable of the water level station for the disaster data x; n represents the length of the extreme value variable time series; Y i (x) represents the maximum value of the disaster data of the i-th time series of the water level station; a n (x) and b n (x) represents the parameter used for normalization; x represents disaster data; d represents the dimension of Z(x); The distribution of Z(x) fitting needs to obey the generalized extreme value distribution. The expression of generalized extreme value distribution is: In the formula, v represents the location parameter; τ represents the scale parameter, σ>0; ζ represents the shape parameter; Represents the standardized expression for the generalized extreme value distribution, 5. The method for evaluating spatial extreme water levels in a river network area according to claim 4, characterized in that: In step S5, Convert the marginal distribution function of the generalized extreme value distribution to the unit Fréchet distribution.

6. The method for evaluating spatial extreme water levels in a river network area according to claim 5, characterized in that: In step S7, the process of constructing a multivariate spatial extreme value model includes: Establish the spatial correlation function ρ(h); Based on the spatial correlation function ρ(h), a multivariate spatial extreme value model is constructed: f ∑ (ss i )=ρ(h)(ss i ); Where M(s) represents the multivariate spatial extreme value model, which is used to describe the maximum values ​​at all positions on any surface in Z(x); i represents the i-th point in the point process; ι i represents the amplitude of the point process; s represents the spatial position; s i represents the position of a random point; φ ∑ (ss i ) represents the Gaussian distribution density function; ρ(h) represents the spatial correlation function.

7. The method for evaluating spatial extreme water levels in a river network area according to claim 6, characterized in that: ρ(h) is selected from the following spatial correlation functions (1) to (5): (1) Whittle-Marten correlation function: (2) Cauchy correlation function: (3) Power exponential correlation function: (4) Bessel correlation function: (5) Generalized Cauchy correlation function: Where c2 represents the range parameter of the spatial correlation function; v represents the smoothing parameter of the spatial correlation function; Γ represents the gamma function; K v represents the second kind of modified Bessel function; J v represents the first kind of Bessel function; σ represents the scale parameter of the spatial correlation function; λ represents the shape parameter of the spatial correlation function.

8. The method for evaluating spatial extreme water levels in a river network area according to claim 7, characterized in that: In step S8, the spatial dependence of extreme water level events between water level stations in the river network area and the estimated values ​​of the spatial extreme value model are compared using TIC to verify the validity of the spatial extreme value model; TIC=-2l pair (ψ)-ktr{J(ψ)H(ψ) -1 }, k∈{2, log n}; In the formula, TIC represents the standard for measuring the spatial extreme value model. The smaller the TIC, the better the spatial extreme value model. pair represents the logarithmic value of the likelihood function; ψ represents the estimated parameter vector, that is, the logarithmic likelihood value of the model; k represents a constant; tr represents the trace operator, which represents the trace of the matrix, that is, the sum of the diagonal elements of the matrix; J(ψ) represents the observation information covariance matrix of the gradient of the likelihood function with respect to the parameter ψ; H(ψ) represents the negative second-order derivative matrix of the likelihood function with respect to the parameter ψ.

9. The method for evaluating spatial extreme water levels in a river network area according to claim 8, characterized in that: A measure to assess the degree of spatial dependence between water level events in a river network, defined as: F(Z(x))=exp(-1 / Z(x)); 1≤θ(h)≤2; Where θ(h) represents the extreme water level extreme value coefficient between two water level events in the river network area, which quantifies the correlation of extreme events between locations; ν(h) represents the spatial dependence measure between two locations; E represents the mathematical expectation; F(Z(x)) represents the cumulative distribution function of the unit Fréchet distribution; When θ(h) = 1, it means that the spatial dependence between water level events in the river network area is complete dependence; When θ(h) = 2, it means that the spatial dependence between water level events in the river network area is independent.

10. The method for evaluating spatial extreme water levels in a river network area according to claim 8, characterized in that: In step S9, the paired likelihood method is used to fit the spatial extreme value model of extreme water level events in the river network area. The paired likelihood method regards all pairs of stations as independent pairs to calculate the likelihood value: In the formula, l p (w; ψ) represents the paired log-likelihood function; w represents the extreme value data of the water level variable in the river network area; i and j represent different water level stations in the river network area; ∑ i<j Indicates the sum of all position pairs; n ij represents the total number of position pairs; w m (i) represents the extreme value of the water level observed at position i in the mth position pair; w m (j) represents the extreme value of the water level observed at position j in the mth position pair; f(w m (i) ; w m (j) ; ψ) represents the extreme value w at position i under parameter ψ m (i) and the extreme value w at position j m (j) The joint probability density of Return period level calculation: The bivariate cumulative distribution function of the unit Fréchet distribution is expressed as: In the formula, Pr[Z(x i )≤q i , Z(x j )≤q j ] represents 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 stations; h represents the Euclidean distance between the i-th water level station and the j-th water level station, h∈R + ; ρ(h) represents the spatial correlation function; q i Represents the disaster data x of the i-th water level station i The parameterized boundary of q j represents the disaster data x of the jth water level station j The parameterized boundary of Z(x i ) represents the water level station about the disaster data x i The meteorological and hydrological extreme value variables, Z(x i ) is the water level extreme value at the i-th water level station in M(s); Z(x j ) represents the water level station about the disaster data x j The meteorological and hydrological extreme value variables, Z(x j ) is the extreme value of the water level at the j-th water level station in M(s); Let the parameterized boundary of the disaster data of the i-th water level station and the j-th water level station be the recurrence level of the water level extreme value in year T, that is, The joint probability of the extreme water levels of the i-th water level station and the j-th water level station under the return period of T years can be calculated: In the formula, represents the joint probability of the extreme water level of the i-th water level station and the j-th water level station under the return period of T years; T represents time; y T It represents the recurrence level of the extreme water level in year T; μ represents the location parameter; represents the shape parameter; τ represents the scale parameter.

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