A method for analyzing characteristic quantities of abrupt changes from drought to flood and vice versa

Abstract

The present invention discloses a method for analyzing characteristic quantities of rapid alternation events between drought and flood. First, precipitation data is collected, the SWAP index is calculated, and the intensity and duration characteristics are extracted; then, it is checked whether the time series of the two characteristics are consistent; sometimes, a probability distribution model is used for fitting and evaluated by the SBC and AIC criteria, otherwise a generalized additive model is used for fitting, and finally the marginal distribution functions of the intensity and duration are obtained; then, the Copula function likelihood ratio method is used to check the consistency of the two marginal distribution functions; furthermore, a Copula joint distribution function with constant or time-varying parameters is used to simulate the joint distribution function of the two characteristics; finally, according to the joint distribution function, the joint return periods of "or" and "and" for the duration and intensity are calculated, and the most probable combination method is used to derive the joint design values of the duration and intensity, and this design value is the risk threshold. The present invention can timely evaluate the risk of characteristic values of rapid alternation events between drought and flood, and has very important significance for the analysis and prevention of rapid alternation disasters between drought and flood.

Description

Technical Field

[0001] The present invention relates to the field of hydrological water resources applications, and particularly relates to a method for analyzing characteristic quantities of drought-flood abrupt alternation events. Background Art

[0002] Drought-flood abrupt alternation refers to the situation where a certain region or basin is continuously dry in the early stage and then experiences concentrated heavy rainfall in the later stage, resulting in rapid rises in rivers, urban waterlogging, etc., and changing from a drought state to a flood state in a short period of time, reflecting the coexistence of drought and flood extreme events in the short term. Against the background of global warming, increasing extreme precipitation, and enhanced water vapor circulation, the stability of the climate system decreases. Affected by climate change and human activities, the uneven temporal and spatial distribution of precipitation is further aggravated, and the frequency and intensity of global droughts, floods and other extreme disasters continue to increase. The frequency and intensity of drought-flood abrupt alternation events also continue to increase worldwide and have attracted more and more extensive attention from domestic and foreign scholars in recent years.

[0003] Since drought-flood abrupt alternation events and their characteristic changes are spatiotemporally discontinuous, frequency analysis of the characteristics of drought-flood abrupt alternation events is helpful for formulating flood control and drought prevention measures and plans, providing a theoretical basis for drought-flood abrupt alternation disaster prevention in areas with unbalanced temporal and spatial distribution of water resources, and is of great significance in regional water resources planning and management. Many studies have shown that the characteristics such as the intensity, duration, and frequency of drought and flood disasters have obvious changing trends under the drive of a non-uniform climate background (such as global warming). Therefore, when conducting frequency analysis of drought and flood disasters, it is necessary to diagnose whether there are change points in the univariate time series or multivariate dependence. In the case of consistency, estimate the constant parameters of the variable; in the case of non-consistency, estimate the time-varying parameters of the variable. However, current research lacks consideration of the non-consistent changes in drought-flood abrupt alternation events. Under the background of a changing environment, it is necessary to discuss and discriminate the detected non-consistency in the attributes of drought-flood events, and conduct multivariate frequency analysis of drought-flood abrupt alternation considering potential non-consistency, which is of great significance for meteorological disaster research and prevention. Summary of the Invention

[0004] The present invention considers the time-varying statistical characteristics of hydrological sequences, constructs a method for analyzing characteristic quantities of drought-flood abrupt alternation events under a non-uniform background, analyzes the characteristic quantities of drought-flood abrupt alternation events, thereby obtaining more reliable risk prevention information, and timely evaluating the risk of characteristic values of drought-flood abrupt alternation events, which is of great significance for the analysis and prevention of drought-flood abrupt alternation disasters.

[0005] The technical solution of the present invention is as follows:

[0006] A method for analyzing characteristic quantities of drought-flood abrupt alternation events, comprising the following steps:

[0007] S1: Determine the study area and collect daily-scale precipitation data within the basin;

[0008] S2: Based on the precipitation data of the basin, calculate the standardized weighted average precipitation SWAP index, identify the dry-wet abrupt transition process of the basin, and extract the intensity and duration characteristics of the dry-wet abrupt transition events;

[0009] S3: Use ADF (Augmented Dickey-Fuller unit root test) to test whether the time series of the intensity characteristics and the duration characteristics are consistent respectively;

[0010] When the time series consistency holds, use the probability distribution model with constant parameters to fit the intensity characteristics and the duration characteristics respectively, and based on the evaluation of the SBC (Schwarz Bayesian information criterion) criterion and the AIC (Akaike Information Criterion) criterion, obtain the intensity marginal distribution function and the duration marginal distribution function;

[0011] When the time series consistency does not hold, use the Generalized Additive Models for Location, Scale and Shape (GAMLSS) to fit the intensity characteristics and the duration characteristics respectively, and obtain the intensity marginal distribution function and the duration marginal distribution function;

[0012] S4: Use the Copula-based likelihood-ratio test (CLRtest) to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds;

[0013] When the consistency hypothesis holds, use the Copula joint distribution function with constant parameters to simulate and obtain the joint distribution function of the duration and the intensity;

[0014] When the consistency hypothesis does not hold, use the Copula joint distribution function with time-varying parameters to simulate and obtain the joint distribution function of the duration and the intensity;

[0015] S5: Based on the joint distribution function of the duration and the intensity, calculate the joint return periods of "or" and "and" of the duration and the intensity, and use the Most-likely weight function to derive the joint design value of the duration and the intensity, and take this design value as the risk threshold for the disaster prevention and control of the dry-wet abrupt transition events.

[0016] Furthermore, the calculation process of the standardized weighted average precipitation SWAP index in step S2 is as follows:

[0017] The SWAP index is based on the premise that the drought and flood status on the current day is affected by the previous drought and flood status and the precipitation on the current day. Its calculation method assumes that the weighted average precipitation (WAP) sequence on the same day follows a Gamma distribution. The weighted average precipitation sequence is fitted by the Γ distribution, and finally, the cumulative probability distribution is standardized. The calculation formula of the weighted average precipitation sequence is as follows:

[0018]

[0019] w n =(1 - a)a n-1

[0020] In the formula, WAP i represents the weighted average precipitation sequence, P n represents the precipitation on the nth day, w n represents the weight of P n , a is the parameter for the weight decay over time, a n is the parameter for the weight decay over time on the nth day, N is the number of days affected by the previous precipitation. The selection of a and N depends on the local soil - water system in the study area. Take a = 0.9 and N = 45.

[0021] Furthermore, in step S2, based on the calculated SWAP index, the run - theory is used to identify and extract the drought - flood abrupt transition process in the basin. The specific steps are as follows:

[0022] For a certain drought - flood index time series, set the index critical values X0, X1 and the time - length critical values D0, D1 and D2. When the time that the index continuously remains below X0 is not less than D0, it is considered that drought occurs; when the time that the index continuously remains above X1 is not less than D1, it is considered that flood occurs; when the time interval between drought and flood is not greater than D2, it is considered that a drought - flood abrupt transition event is formed. According to the drought - flood index classification standard, select the values corresponding to the upper bound of the drought level and the lower bound of the moderate flood level as X0 and X1, that is, X0 = - 1 and X1 = 1; referring to the run - theory identification process of various abrupt transition event identifications, determine the identification duration threshold D0 = D1 = 10 days based on the daily - value index, and the abrupt transition period duration threshold D2 = 8 days between the drought state and the flood state. According to the extracted drought - flood abrupt transition events, obtain the duration and intensity of each drought - flood abrupt transition event.

[0023] Furthermore, in step S3, when the time - series consistency holds, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows;

[0024] Select the probability distribution models commonly used in meteorological and hydrological research as alternative models, specifically including Exponential (exp), Gamma, Generalized gamma with three parameters (gamma3), Normal, Log-normal (lnorm), Logistic (logis), and Weibull, a total of 7 probability distribution models. Fit the intensity characteristics and duration characteristics respectively through these 7 alternative models, and evaluate the goodness of fit of the above 7 alternative models through the SBC criterion;

[0025] The calculation formula of SBC is as follows:

[0026] SBC = GD + log(ξ) × df = -2 log L(θ) + log(ξ) × df

[0027] In the formula, GD is the global fitting deviation, df is the number of degrees of freedom, θ and ξ represent the estimated values of the probability distribution parameters and the number of parameters respectively, and L(·) represents the value of the log-likelihood function;

[0028] To avoid overfitting of the distribution, and also consider evaluating the goodness of fit of the above 7 alternative models through the AIC criterion;

[0029] The calculation formula of AIC is as follows:

[0030] AIC = 2ξ - 2 log L(θ)

[0031] Finally, among all the alternative models that pass the test, select the distribution model that minimizes the calculated values of AIC and SBC simultaneously as the relatively optimal model, and use this relatively optimal model as the intensity marginal distribution function or duration marginal distribution function.

[0032] Furthermore, for the alternative Normal and Log-normal probability distribution models, their defined interval for variables is [-∞, +∞], while the intensity characteristics and duration characteristics to be tested are both greater than 0. Therefore, it is necessary to correct the defined interval of the above 2 alternative models to the positive value interval, and use the following formula to represent the corrected cumulative probability:

[0033]

[0034] In the formula, f(x|θ) is the probability density function, and θ is the probability distribution parameter.

[0035] Furthermore, in step S3, when the time series consistency does not hold, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows;

[0036] The Generalized additive models for location, scale and shape (GAMLSS) that can comprehensively consider location, scale and shape parameters are used for marginal distribution fitting. In the generalized additive model, it is assumed that the independent observations of the response variable Y follow the probability distribution f(y i |Θ i );

[0037] where Θ i =(μ i , σ i , v i , τ i ) is a vector composed of probability distribution parameters. μ and σ are location and scale parameters, and v and τ are shape parameters, which respectively characterize the skewness and kurtosis of the distribution;

[0038] The relationship between the probability distribution parameters and their explanatory variables is established through a link function, and the expression is:

[0039]

[0040] That is:

[0041]

[0042] In the formula, g k (·) represents the link function; θ k , μ, σ, v, τ are column vectors with a length of ;

[0043] X k is a known matrix, corresponding to the explanatory variable values of time periods; k represents the serial number of the sequence to be analyzed; is the parameter vector to be solved, with a dimension of J k ; Z jk is a known design matrix; γ jk is a column vector composed of random variables.

[0044] In the present invention, the identified time of the rapid alternation between drought and flood (Drought onset) is used as an explanatory variable to establish a functional relationship between the duration of the rapid alternation, the parameters of the intensity probability distribution, and the time of the rapid alternation between drought and flood. The semi-parametric cumulative form of the GAMLSS model is adopted to express the probability distribution parameters as cubic spline functions of the starting time of the rapid alternation between drought and flood, which is conducive to capturing possible non-linear relationships. The present invention aims to maximize the likelihood function, calculates the time-varying parameters of the alternative probability distributions, and screens the optimal intensity marginal probability function and duration marginal probability function from 7 alternative distribution models according to the SBC criterion and the AIC criterion.

[0045] Furthermore, in step S4, the process of using the Copula function likelihood ratio method to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds is as follows;

[0046] The basic assumption of the Copula function likelihood ratio method is that, with the Copula function type fixed, the change point of the dependence structure intensity of the multi-variable hydrological sequence is analyzed by detecting the change of its parameter θ c ;

[0047] Given that y1, y2,..., y d is a time series composed of the observed values of a d-dimensional random variable, where y i =(y 1,i , y 2,i ,..., y n,i ), i = 1, 2,..., d, the overall population where the observed values are located follows the probability distributions F(y1|θ c,1 ), F(y2|θ c,2 ),..., F(y n |θ c,n ), θ c,i is the Copula function parameter corresponding to different time periods. In the Copula function likelihood ratio test, the null hypothesis is that there is no change point in the dependence structure of the multi-variable (i.e., all observed values follow the same probability distribution), and the expression formula is as follows:

[0048] H0: θ c,1 = θ c,2 =... = θ c,n = η0

[0049] The alternative hypothesis H1 is: there exists k * and such that θ c,1 = θ c,2 =... = θ c,k* = η1, and θ c,k* =... = θ c,n = η2, and at the same time η1 ≠ η2; construct the likelihood ratio Λ based on the Copula functionk When Λ k is less than a given threshold, the null hypothesis H0 is rejected, and it is considered that there is a change point k in the multivariate dependence structure * ;

[0050]

[0051] where L n (·) represents the likelihood function of the entire sample sequence; L k (·) and are the likelihood functions before and after the test point k respectively; u i represents the marginal distribution probability of the bivariate sequence; c(·) represents the Copula probability density function; and are the maximum likelihood estimates of the Copula function parameters η0, η1, and η2 respectively. Rewrite Λ k in logarithmic form to obtain:

[0052]

[0053] Furthermore, construct the logarithmic statistical test statistic as follows:

[0054]

[0055] When Z n is greater than the threshold corresponding to the given significance level, the null hypothesis H0 is rejected, and the likelihood ratio statistic follows an asymptotic distribution:

[0056]

[0057] where z represents the given threshold. When z approaches infinity, h = l = [ln(n)] 3 / 2 ;

[0058] h, l, O represent the parameters of the asymptotic distribution; p is the number of parameters of the Copula function with one change point; Substitute into the above formula. If the calculated P-value is less than the threshold, the null hypothesis is rejected at the significance level of this threshold, and the consistency hypothesis does not hold; otherwise, it holds.

[0059] Furthermore, in step S4, the joint distribution function of duration and intensity established according to the Copula function is expressed as:

[0060] P(D,S) = C(u D , u S |θ c )

[0061] where D and S represent intensity and duration respectively; uD , u S represents the marginal distributions of intensity and duration;

[0062] Similar to the GAMLSS model, to estimate the time-varying parameters of the Copula, explanatory variables are introduced to describe the functional relationship between the time-varying parameters of the Copula and the explanatory variables;

[0063] g(θ c ) = β0 + Xβ1

[0064] where g(θ c ) represents the link function when the copula parameter is θ c ;

[0065] θ c = (θ c,1 , θ c,2 ,..., θ c,n ) T is a column vector composed of the time-varying parameters of the Copula;

[0066] X = (X1, X2,..., X n ) T represents n observations of the explanatory variables; β0 and β represent the parameter vectors to be solved;

[0067] Next, according to whether the consistency assumption of the relationship between duration and intensity holds or not, the expression of the link function is given in different cases:

[0068] (1) When the relationship between the two variables remains consistent, the Copula parameter is a constant value that does not change with time, and the link function is expressed as:

[0069] g(θ c ) = constant

[0070] (2) When the consistency assumption is violated, the Copula parameter is a function that changes with time. Therefore, the occurrence time time of the drought event is introduced as an explanatory variable, and the link function is rewritten as:

[0071] g(θ c ) = β0 + time·β1

[0072] Furthermore, the marginal function inference method is adopted to solve the Copula parameter θ c,t by maximizing the log-likelihood function. The formula is as follows:

[0073]

[0074] where u D,i represents the marginal distribution of intensity in the i-th period; u S,iDenote the duration marginal distribution of the $i$-th period; $D$ i Denote the intensity of the $i$-th period; $S$ i Denote the duration of the $i$-th period; $\theta$ D Denote the parameter of the intensity marginal distribution; $\theta$ S Denote the parameter of the duration marginal distribution; $\theta$ D,i Denote the parameter of the intensity marginal distribution of the $i$-th period; $\theta$ S,i Denote the parameter of the duration marginal distribution of the $i$-th period; $c(\cdot)$ is the probability density function of Copula; $f$ D $(\cdot)$ and $f$ S $(\cdot)$ respectively represent the probability density functions of the duration and intensity marginal distributions; In the Inference Function for Margins (IFM), since the maximum values of the second and third terms on the right side of the above formula have been obtained by fitting the marginal distributions of the duration and intensity previously, so only need to maximize the first term on the right side of the equation to obtain the optimal $\beta_0$ and $\beta_1$, and substitute the estimated values of $\beta_0$ and $\beta_1$ into the calculation of the estimated value of the Copula function;

[0075]

[0076] In the formula, time i Denote the occurrence time of the $i$-th period.

[0077] According to the differences in the dependence structures between variables under the description of the limit conditions in the present invention, the commonly used Copula functions can be divided into Elliptical Copula, Archimedean Copula, Extreme Value Copula, and Mixed Copula, etc. At present, the Elliptical Copula and Archimedean Copula are more widely used in the hydrological field. The present invention adopts a total of one Elliptical Copula (Gaussian Copula) and four Archimedean Copula functions (Clayton Copula, Frank Copula, Gumbel Copula, and Joe Copula), a total of five Copula functions as alternative single-parameter alternative Copula functions. After fitting, it is necessary to conduct a goodness-of-fit test on the selected Copula function. According to the Bayesian Information Criterion (BIC), select the function with the smallest BIC value as the optimal joint distribution Copula function to establish the joint distribution function of the duration and intensity.

[0078] Further, in step S5, the process of calculating the joint return periods of "OR" and "AND" of the duration and intensity is as follows:

[0079] The univariate characteristic of the rapid alternation of drought and flood $P(x\geq x$* ) The recurrence period is calculated as follows:

[0080]

[0081] where T is the recurrence period of the drought-flood abrupt alternation event, and F(x * ) is the event probability function of x * ; interval is the average time interval between all drought-flood abrupt alternation events, in years, that is, the time length from the start of one drought-flood abrupt alternation event to the start of the next drought-flood abrupt alternation event; if N year drought-flood abrupt alternation events are sampled within N alter years, the formula for interval is:

[0082]

[0083] The multivariate drought-flood abrupt alternation frequency analysis has multiple combinations of joint recurrence periods, including the "OR" joint recurrence period and the "AND" joint recurrence period. The "OR" joint recurrence period refers to the recurrence period calculated when one or more of the random variables of the drought-flood abrupt alternation event exceed a given threshold, denoted by the OR operator "∨"; the "AND" joint recurrence period refers to the recurrence period calculated when all the random variables of the drought-flood abrupt alternation event exceed a given threshold. Therefore, the "AND" recurrence period is also called the "joint exceedance recurrence period" or the "co-occurrence recurrence period", denoted by the AND operator "∧";

[0084] The recurrence period calculation formulas from different perspectives are as follows;

[0085] From the perspective of univariate:

[0086]

[0087]

[0088] In the formula, T S , T D are the recurrence periods from the perspective of univariate of duration and intensity respectively, and F S (s) and F D (d) represent the probabilities of the occurrence of duration and intensity respectively;

[0089] From the perspective of bivariate:

[0090]

[0091]

[0092] In the formula, represents the "OR" joint recurrence period from the perspective of the two variables of duration and intensity, Denote the "AND" joint return period from the perspectives of duration and intensity as F S,D (s, d) is the joint occurrence probability of duration and intensity;

[0093] Based on the above formulas, the "OR" and "AND" joint return periods of duration and intensity are calculated.

[0094] Furthermore, in step S5, the process of obtaining the joint design values of duration and intensity by using the most probable combination method is as follows:

[0095] The joint design value of drought-flood rapid transition events refers to the multivariate combination (u ml , v ml ) when the rapid transition joint density f(u, v) composed of rapid transition characteristics reaches the maximum value at a certain design return period level, that is, the possibility of this combination occurring is the greatest. Therefore, it is solved by constructing the following equation:

[0096] [u ml , v ml = argmax f(u, v)

[0097] f(u, v) = c(u, v) · f(u) · f(v)

[0098] where f(u, v) is the joint probability density function of rapid transition bivariate variables, c(u, v) is the probability density function of the corresponding joint Copula distribution, f(u), f(v) are the marginal density functions of variables, and [u ml , v ml is the joint design value combination of the multivariate variables to be obtained;

[0099] The calculation steps of obtaining the joint design value by using the most probable combination method are as follows:

[0100] (1), Based on the Copula joint distribution function, use the Monte Carlo method to simulate multiple groups of variable combinations (u ml , v ml ), and the number of groups taken is 100000;

[0101] (2), According to the calculation formulas of the "OR" and "AND" return periods, find the joint return periods corresponding to the bivariate combinations in the previous step;

[0102] (3), According to the determined return period level, screen the variable combinations that meet the accuracy requirements (e = 10 -4 ), and the variable combination with the largest joint probability density value is the joint design value to be obtained.

[0103] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0104] The present invention provides a method for analyzing the characteristic quantities of drought-flood abrupt alternation events based on the non-consistency theory. By using the time-varying parameter Copula function, a joint distribution between the duration and intensity with strong dependence of drought-flood abrupt alternation characteristics under the non-consistency background is established, and the joint design values of drought-flood abrupt alternation characteristics at each recurrence period are calculated. Taking this joint design value as the risk threshold for drought-flood abrupt alternation events, a further assessment of the risk of characteristic values of drought-flood abrupt alternation events can be made, which is of great significance for meteorological disaster research and prevention. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 It is a schematic flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0106] The drawings are only for illustrative purposes and cannot be construed as limiting the present patent; for better illustrating the embodiments, some components in the drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual products; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted. The positional relationships described in the drawings are only for illustrative purposes and cannot be construed as limiting the present patent.

[0107] Embodiment 1:

[0108] As Figure 1 shown, a method for analyzing the characteristic quantities of drought-flood abrupt alternation events includes the following steps:

[0109] S1: Determine the study area and collect the daily-scale precipitation data within the basin.

[0110] S2: Based on the precipitation data of the basin, calculate the standardized weighted average precipitation SWAP index, identify the drought-flood abrupt alternation process of the basin, and extract the intensity and duration characteristics of the drought-flood abrupt alternation events.

[0111] S3: Use ADF (Augmented Dickey-Fuller unit root test) to test whether the time series of intensity characteristics and duration characteristics are consistent respectively.

[0112] When the time series consistency holds, use the probability distribution model with constant parameters to fit the intensity characteristics and duration characteristics respectively, and based on the evaluation of the SBC (Schwarz Bayesian information criterion) and AIC (Akaike Information Criterion), obtain the intensity marginal distribution function and the duration marginal distribution function.

[0113] When the time series consistency does not hold, use the generalized additive model for location, scale and shape (GAMLSS) to fit the intensity characteristics and duration characteristics respectively, and obtain the intensity marginal distribution function and the duration marginal distribution function.

[0114] S4: Use the Copula-based likelihood-ratio test (CLRtest) to examine whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds;

[0115] When the consistency hypothesis holds, use the Copula joint distribution function with constant parameters to simulate the joint distribution function of duration and intensity;

[0116] When the consistency hypothesis does not hold, use the Copula joint distribution function with time-varying parameters to simulate the joint distribution function of duration and intensity;

[0117] S5: Based on the joint distribution function of duration and intensity, calculate the joint return periods of "OR" and "AND" for duration and intensity, and use the Most-likely weight function to derive the joint design values of duration and intensity. Take these design values as the risk thresholds for disaster prevention and control of drought-flood rapid alternation events.

[0118] The meteorological data used in this embodiment can be sourced from the product "Daily Value Dataset of Surface Climate Data in China (V3.0)" of the National Meteorological Science Data Center. The selected river basin can be the Pearl River Basin, and the daily precipitation data of 75 meteorological stations within the Pearl River Basin from 1961 to 2020 are collected.

[0119] In this implementation, the calculation process of the standardized weighted average precipitation SWAP index in step S2 is as follows:

[0120] The SWAP index is based on the premise that the drought-flood state on the current day is affected by the previous drought-flood state and the precipitation on the current day. Its calculation method assumes that the weighted average precipitation (WAP) sequence on the same day follows a Gamma distribution, fits the weighted average precipitation sequence through the Γ distribution, and finally performs standard normalizing processing on the cumulative probability distribution. The calculation formula for the weighted average precipitation sequence is as follows:

[0121]

[0122] w n =(1 - a)a n-1

[0123] In the formula, WAP i represents the weighted average precipitation sequence, P n represents the precipitation on the nth day, w n represents the weight of P n , and a is the parameter for the decay of the weight over time, a nis the decay parameter of the weight over time on the nth day. N is the number of days affected by previous precipitation. The selection of a and N depends on the local soil-water system in the study area. Take a = 0.9 and N = 45.

[0124] In this implementation, in step S2, based on the calculated SWAP index, the run theory is used to identify and extract the dry-wet abrupt transition process of the basin. The specific steps are as follows:

[0125] For a certain dry-wet index time series, set the index critical values X0, X1 and the time length critical values D0, D1 and D2. When the time that the index continuously is lower than X0 is not less than D0, it is considered that drought occurs; when the time that the index continuously is higher than X1 is not less than D1, it is considered that flood occurs; when the time interval between drought and flood is not greater than D2, it is considered that a dry-wet abrupt transition event is formed; according to the dry-wet index division standard, select the values corresponding to the upper bound of the dry grade and the lower bound of the medium flood grade as X0 and X1, that is, X0 = -1 and X1 = 1; referring to the run theory identification process of various abrupt transition event identifications, determine the identification duration threshold D0 = D1 = 10 days based on the daily value index, and the abrupt transition period duration threshold D2 = 8 days between the drought state and the flood state. According to the extracted dry-wet abrupt transition events, obtain the duration and intensity of each dry-wet abrupt transition event.

[0126] In this implementation, in step S3, when the time series consistency holds, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows;

[0127] Select the probability distribution models commonly used in meteorological and hydrological research as alternative models, specifically including 7 probability distribution models: Exponential (exp), Gamma, Generalized gamma with three parameters (gamma3), Normal, Log-normal (lnorm), Logistic (logis), and Weibull. Fit the intensity characteristics and duration characteristics through these 7 alternative models respectively, and evaluate the goodness of fit of the above 7 alternative models through the SBC criterion;

[0128] The calculation formula of SBC is as follows:

[0129] SBC = GD + log(ξ) × df = -2 log L(θ) + log(ξ) × df

[0130] In the formula, GD is the global fitting deviation, df is the number of degrees of freedom, θ and ξ represent the estimated values of the probability distribution parameters and the number of parameters respectively, and L(·) represents the value of the log-likelihood function;

[0131] To avoid overfitting of the distribution and also consider evaluating the goodness of fit of the above 7 alternative models using the AIC criterion;

[0132] The calculation formula of AIC is as follows:

[0133] AIC = 2ξ - 2logL(θ)

[0134] Finally, among all the alternative models that pass the test, select the distribution model that minimizes the calculated values of AIC and SBC simultaneously as the relatively optimal model, and use this relatively optimal model as the intensity marginal distribution function or the duration marginal distribution function.

[0135] In this implementation, for the alternative normal and lognormal probability distribution models, their defined interval for variables is [-∞, +∞], while the intensity characteristics and duration characteristics to be tested are all greater than 0. Therefore, the defined intervals of the above 2 alternative models need to be corrected to the positive value interval, and the corrected cumulative probability is represented by the following formula:

[0136]

[0137] In the formula, f(x|θ) is the probability density function, and θ is the probability distribution parameter.

[0138] In this implementation, in step S3, when the time series consistency does not hold, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows;

[0139] Use the Generalized additive models for location, scale and shape (GAMLSS) that can comprehensively consider location, scale and shape parameters to perform marginal distribution fitting. In the generalized additive model, assume that the independent observations of the response variable Y i |Θ i ) follow the probability distribution f(y

[0140] where Θ i =(μ i ,σ i ,v i ,τ i ) is a vector composed of probability distribution parameters, μ and σ are location and scale parameters, ν and τ are shape parameters, which respectively characterize the skewness and kurtosis of the distribution;

[0141] Establish the connection between the probability distribution parameters and their explanatory variables through the link function, and the expression is:

[0142]

[0143] That is:

[0144]

[0145] In the formula, g k (·) represents the connection function; θ k , μ, σ, ν, τ are column vectors of length ;

[0146] X k is a known matrix, corresponding to the explanatory variable values of time periods; k represents the serial number of the sequence to be analyzed; is the parameter vector to be solved, with a dimension of J k ; Z jk is a known design matrix; γ jk is a column vector composed of random variables.

[0147] In this implementation, the identified time of drought-flood abrupt transition (Drought onset) is used as an explanatory variable to establish the functional relationship between the abrupt transition duration, the intensity probability distribution parameters, and the time of drought-flood abrupt transition. The semi-parametric additive form of the GAMLSS model is adopted to express the probability distribution parameters as a cubic spline function of the starting time of drought-flood abrupt transition, which is beneficial to capturing possible non-linear relationships. The present invention aims to maximize the likelihood function, calculate the time-varying parameters of the alternative probability distributions, and screen the optimal intensity marginal probability function and duration marginal probability function from 7 alternative distribution models according to the SBC criterion and the AIC criterion.

[0148] In this implementation, in step S4, the process of using the Copula function likelihood ratio method to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds is as follows;

[0149] The basic assumption of the Copula function likelihood ratio method is that, with the Copula function type fixed, the change point of the dependence structure strength of the multivariate hydrological sequence is analyzed by detecting the change of its parameter θ c ;

[0150] It is known that y1, y2,..., y d is a time series composed of the observed values of d-dimensional random variables, where y i =(y 1,i , y 2,i ,..., y n,i ), i = 1, 2,..., d, and the population where the observed values are located follows the probability distributions F(y1|θ c,1 ), F(y2|θ c,2 ),..., F(y n |θ c,n ), θc,i They are the Copula function parameters corresponding to different time periods. In the Copula function likelihood ratio test, the null hypothesis is that there is no change point in the dependence structure of multiple variables (i.e., all observed values follow the same probability distribution), and the expression formula is as follows:

[0151] H0: θ c,1 = θ c,2 =... = θ c,n = η0

[0152] The alternative hypothesis H1 is: there exists k * and such that θ c,1 = θ c,2 =... = θ c,k* = η1, and θ c,k* =... = θ c,n = η2, and at the same time η1 ≠ η2; construct the likelihood ratio Λ k based on the Copula function. When Λ k is less than the given threshold, reject the null hypothesis H0 and consider that there is a change point k in the dependence structure of multiple variables * ;

[0153]

[0154] In the formula, L n (·) represents the likelihood function of the entire sample sequence; L k (·) and are the likelihood functions before and after the test point k respectively; u i represents the marginal distribution probability of the bivariate sequence; c(·) represents the Copula probability density function; and are the maximum likelihood estimates of the Copula function parameters η0, η1, and η2 respectively. Rewrite Λ k in logarithmic form to get:

[0155]

[0156] Furthermore, construct the following logarithmic form of the statistical test statistic:

[0157]

[0158] When Z n is greater than the threshold corresponding to the given significance level, reject the null hypothesis H0, and the likelihood ratio statistic follows an asymptotic distribution:

[0159]

[0160] where z represents a given threshold value. When z approaches infinity, h = l = [ln(n)] 3 / 2 ;

[0161] h, l, and O represent the parameters of the asymptotic distribution; p is the number of parameters of the Copula function with a change point; Substituting into the above formula, if the calculated P-value is less than the threshold, the null hypothesis is rejected at the significance level of this threshold, and the consistency hypothesis does not hold; otherwise, it holds.

[0162] In this implementation, in step S4, the joint distribution function of duration and intensity established according to the Copula function is expressed as:

[0163] P(D,S) = C(u D ,u S |θ c )

[0164] where D and S represent intensity and duration respectively; uD and uS represent the marginal distributions of intensity and duration;

[0165] Similar to the GAMLSS model, in order to estimate the time-varying parameters of the Copula, explanatory variables are introduced to describe the functional relationship between the time-varying parameters of the Copula and the explanatory variables;

[0166] g(θ c ) = β0 + Xβ1

[0167] where g(θ c ) represents the link function when the copula parameter is θ c ;

[0168] θ c = (θ c,1 ,θ c,2 ,...,θ c,n ) T is a column vector composed of the time-varying parameters of the Copula;

[0169] X = (X1,X2,...,X n ) T represents n observations of the explanatory variables; β0 and β represent the parameter vectors to be solved;

[0170] The following gives the expression of the link function in different cases according to whether the consistency hypothesis of the relationship between duration and intensity holds:

[0171] (1) When the relationship between the two variables remains consistent, the Copula parameter is a constant value that does not change with time, and the link function is expressed as:

[0172] g(θ c ) = constant

[0173] (2) When the consistency assumption is violated, the Copula parameter is a function that varies with time. Therefore, the occurrence time time of the drought event is introduced as an explanatory variable, and the copula function is rewritten as:

[0174] g(θ c ) = β0 + time·β1

[0175] Furthermore, the marginal function inference method is adopted. By maximizing the log-likelihood function, the Copula parameter θ is solved c,t , and the formula is as follows:

[0176]

[0177] In the formula, u D,i represents the intensity marginal distribution in the i-th period; u S,i represents the duration marginal distribution in the i-th period; D i represents the intensity in the i-th period; S i represents the duration in the i-th period; θ D represents the parameter of the intensity marginal distribution; θ S represents the parameter of the duration marginal distribution; θ D,i represents the parameter of the intensity marginal distribution in the i-th period; θ S,i represents the parameter of the duration marginal distribution in the i-th period; c(·) is the probability density function of the Copula; f D (·) and f S (·) represent the probability density functions of the duration and intensity marginal distributions respectively; in the marginal function inference method (IFM), since the maximum values of the second and third terms on the right side of the above formula have been obtained by fitting the marginal distributions of the duration and intensity previously, only the first term on the right side of the equal sign needs to be maximized to obtain the optimal β0 and β1, and the estimated values of β0 and β1 are substituted into the calculation of the estimated value of the Copula function;

[0178]

[0179] In the formula, time i represents the occurrence time in the i-th period.

[0180] According to the differences in the dependence structures between variables under extreme conditions described in the present invention, common Copula functions can be classified into Elliptical Copula, Archimedean Copula, Extreme Value Copula, and Hybrid Copula, etc. Among them, Elliptical Copula and Archimedean Copula are currently widely used in the hydrological field. The present invention uses a total of one Elliptical Copula (Gaussian Copula) and four Archimedean Copula functions (Clayton Copula, Frank Copula, Gumbel Copula, and Joe Copula), a total of five Copula functions as alternative Copula functions for single parameters. After fitting, the goodness-of-fit test needs to be performed on the selected Copula function. According to the Bayesian Information Criterion (BIC), the function with the smallest BIC value is selected as the optimal joint distribution Copula function to establish the joint distribution function of duration and intensity.

[0181] In this embodiment, in step S5, the process of calculating the joint return period of "OR" and "AND" of duration and intensity is as follows:

[0182] The return period calculation of the univariate characteristic P(x≥x * ) of the rapid alternation of drought and flood is as follows:

[0183]

[0184] Among them, T is the return period of the rapid alternation of drought and flood events, and F(x * ) is the event probability function of x * ; interval is the average time interval for all rapid alternation of drought and flood events to occur, in years, that is, the time length between the start of one rapid alternation of drought and flood event and the start of the next rapid alternation of drought and flood event; if N year rapid alternation events are sampled within a time period of N alter years, the calculation formula for interval is:

[0185]

[0186] The frequency analysis of abrupt alternation of drought and flood with multiple variables has multiple combinations of joint return periods, including the "or" joint return period and the "and" joint return period. The "or" joint return period refers to the return period calculated when one or more of the random variables of the abrupt alternation of drought and flood events exceed a given threshold, which is represented by the OR operator "∨"; the "and" joint return period refers to the return period calculated when all the random variables of the abrupt alternation of drought and flood events exceed a given threshold. Therefore, the "and" return period is also called the "joint exceedance return period" or the "co-occurrence return period", which is represented by the AND operator "∧".

[0187] The calculation formulas for the return periods from different perspectives are as follows;

[0188] From the perspective of single variable:

[0189]

[0190]

[0191] In the formula, T S , T D are the return periods from the perspective of single variable of duration and intensity respectively, and F S (s) and F D (d) represent the probabilities of the occurrence of duration and intensity respectively;

[0192] From the perspective of two variables:

[0193]

[0194]

[0195] In the formula, represents the "or" joint return period from the perspective of the two variables of duration and intensity, represents the "and" joint return period from the perspective of the two variables of duration and intensity, and F S,D (s,d) is the joint occurrence probability of duration and intensity;

[0196] Based on the above formulas, the joint return periods of "or" and "and" for duration and intensity are calculated.

[0197] In this implementation, in step S5, the process of obtaining the joint design values of duration and intensity by using the most probable combination method is as follows:

[0198] The joint design value of the abrupt alternation of drought and flood events refers to the multi-variable combination (u ml , v ml ) when the joint density f(u,v) of the abrupt alternation composed of the abrupt alternation characteristics reaches the maximum value at a certain design return period level, that is, the possibility of this combination occurring is the greatest. Therefore, it is solved by constructing the following equation:

[0199] [u ml , v ml = argmax(u, v)

[0200] f(u, v) = c(u, v)·f(u)·f(v)

[0201] where f(u, v) is the joint probability density function of the sharp-turn bivariate variables, c(u, v) is the probability density function of the corresponding joint Copula distribution, f(u) and f(v) are the marginal density functions of the variables, and [u ml , v ml is the joint design value combination of the required multivariate variables;

[0202] The calculation steps for obtaining the joint design value by using the most probable combination method are as follows:

[0203] (1) Based on the Copula joint distribution function, use the Monte Carlo method to simulate multiple groups of variable combinations (u ml , v ml ), and the number of groups taken is 100,000;

[0204] (2) According to the calculation formulas of the "or" and "and" return periods, find the joint return periods corresponding to the bivariate combinations in the previous step;

[0205] (3) According to the determined return period level, screen the variable combinations that meet the accuracy requirements (e = 10 -4 ), and the variable combination with the largest joint probability density value is the joint design value obtained.

[0206] The present invention provides a method for analyzing the characteristic quantities of drought-flood sharp-turn events based on the non-stationarity theory. By using the time-varying parameter Copula function, a joint distribution between the duration and intensity with strong dependence of drought-flood sharp-turn characteristics under the non-stationarity background is established, and the joint design values of drought-flood sharp-turn characteristics at each return period are calculated. Taking this joint design value as the risk threshold for drought-flood sharp-turn events, a further assessment of the risk of drought-flood sharp-turn event characteristic values can be made, which is of great significance for meteorological disaster research and prevention.

[0207] Example 2:

[0208] This embodiment provides a device for analyzing the characteristic quantities of drought-flood sharp-turn events, including a collection module, a feature extraction module, a screening module, an inspection module, and an output module that are sequentially connected for communication;

[0209] Among them, the collection module: is used to collect daily-scale precipitation data within the basin;

[0210] Feature extraction module: Based on the data of the acquisition module, calculate the standardized weighted average precipitation (SWAP) index, identify the rapid alternation process of drought and flood in the basin, and extract the intensity and duration characteristics of the rapid alternation events of drought and flood.

[0211] Screening module: Used to respectively test whether the time series of the intensity characteristics and the duration characteristics are consistent by using ADF (Augmented Dickey-Fuller unit root test) according to the intensity characteristics and the duration characteristics obtained by the feature extraction module.

[0212] When the time series consistency holds, use the probability distribution model with constant parameters to fit the intensity characteristics and the duration characteristics respectively, and based on the evaluation of the SBC (Schwarz Bayesian information criterion) and AIC (Akaike Information Criterion), obtain the intensity marginal distribution function and the duration marginal distribution function.

[0213] When the time series consistency does not hold, use the generalized additive model for location, scale and shape (GAMLSS) to fit the intensity characteristics and the duration characteristics respectively, and obtain the intensity marginal distribution function and the duration marginal distribution function.

[0214] Testing module: Used to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds by using the Copula-based likelihood-ratio test (CLR test) according to the intensity marginal distribution function and the duration marginal distribution function obtained by the screening module.

[0215] When the consistency hypothesis holds, use the Copula joint distribution function with constant parameters to simulate and obtain the joint distribution function of duration and intensity.

[0216] When the consistency hypothesis does not hold, use the Copula joint distribution function with time-varying parameters to simulate and obtain the joint distribution function of duration and intensity.

[0217] Output module: Based on the joint distribution function of duration and intensity obtained by the testing module, calculate the joint return periods of "OR" and "AND" of duration and intensity, and use the most-likely weight function to derive the joint design values of duration and intensity. Finally, output this design value as the risk threshold for disaster prevention and control of rapid alternation events of drought and flood.

[0218] Among them, the above modules can be integrated in a system for implementation, and finally the results are output through the output port to be displayed on the display screen.

[0219] Example 3:

[0220] This embodiment provides an electronic device, including a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete communication with each other through the communication bus; the memory is used to store a computer program; the processor is used to execute the program stored on the memory to implement the method for analyzing the characteristic quantities of drought-flood rapid transition events in the above-mentioned Embodiment 1.

[0221] This embodiment also provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the method for analyzing the characteristic quantities of drought-flood rapid transition events described above is implemented.

[0222] Obviously, the above-mentioned embodiments of the present invention are only examples for clearly explaining the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made on the basis of the above description. It is not necessary and impossible to list all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for analyzing characteristic quantities of rapid alternation events between drought and flood, characterized in that, It includes the following steps: S1: Determine the research area and collect daily-scale precipitation data within the basin; S2: Based on the precipitation data of the basin, calculate the standardized weighted average precipitation SWAP index, identify the dry-wet abrupt transition process of the basin, and extract the intensity and duration characteristics of the dry-wet abrupt transition events; S3: Use ADF to test whether the time series of the intensity characteristics and the duration characteristics are consistent respectively; When the time series consistency holds, use the probability distribution model with constant parameters to fit the intensity characteristics and the duration characteristics respectively, and based on the evaluation of the SBC criterion and the AIC criterion, obtain the intensity marginal distribution function and the duration marginal distribution function; When the time series consistency does not hold, use the generalized additive model to fit the intensity characteristics and the duration characteristics respectively, and obtain the intensity marginal distribution function and the duration marginal distribution function; S4: Use the Copula function likelihood ratio method to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds; When the consistency hypothesis holds, use the Copula joint distribution function with constant parameters to simulate and obtain the joint distribution function of the duration and the intensity; When the consistency hypothesis does not hold, use the Copula joint distribution function with time-varying parameters to simulate and obtain the joint distribution function of the duration and the intensity; S5: Based on the joint distribution function of the duration and the intensity, calculate the joint return periods of "or" and "and" of the duration and the intensity, and use the most likely combination method to derive the joint design values of the duration and the intensity, and use this design value as the risk threshold for the prevention and control of dry-wet abrupt transition event disasters.

2. The method for analyzing characteristic quantities of rapid alternation events between drought and flood according to claim 1, characterized in that, The calculation process of the standardized weighted average precipitation SWAP index in step S2 is as follows: The SWAP index is an index based on the premise that the dry-wet state of the current day is affected by the dry-wet state of the previous period and the precipitation of the current day. Its calculation method is to assume that the weighted average precipitation sequence on the same day follows a Gamma distribution, fit the weighted average precipitation sequence through the Γ distribution, and finally perform standard normal transformation on the cumulative probability distribution. The calculation formula of the weighted average precipitation sequence is as follows: w n = (1 - a)a n-1 Where, WAP i represents the weighted average precipitation series, P n represents the precipitation on the nth day, w n represents the weight of P n , a is the parameter for the decay of the weight over time, a n is the decay parameter of the weight over time on the nth day, N is the number of days of the influence of the previous precipitation, and the selection of a and N is determined according to the local soil-water system in the study area. Take a = 0.9 and N = 45.

3. The method for analyzing characteristic quantities of rapid alternation events between drought and flood according to claim 2, characterized in that, In step S2, based on the calculated SWAP index, use the run theory to identify and extract the dry-wet abrupt transition process of the basin. The specific steps are as follows: For the time series of the dry-wet index, set the index critical values X0, X1 and the time length critical values D0, D1 and D2. When the time that the index continuously is lower than X0 is not less than D0, it is considered that drought occurs; when the time that the index continuously is higher than X1 is not less than D1, it is considered that flood occurs; when the time interval between drought and flood is not greater than D2, it is considered that a dry-wet abrupt transition event is formed; according to the dry-wet index division standard, select the values corresponding to the upper bound of the dry grade and the lower bound of the medium flood grade as X0 and X1, that is, X0 = -1 and X1 = 1; determine the identification duration threshold D0 = D1 = 10 days based on the daily value index, and the abrupt transition period duration threshold D2 = 8 days between the dry state and the flood state. According to the extracted dry-wet abrupt transition events, obtain the duration and intensity of each dry-wet abrupt transition event.

4. The method for analyzing characteristic quantities of rapid alternation events between drought and flood according to claim 1, characterized in that, In step S3, when the time series consistency holds, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows; Seven probability distribution models, namely exponential, gamma, three-parameter generalized gamma, normal, lognormal, logistic, and Weibull, were selected as alternatives. These seven alternative models were used to fit the intensity characteristics and duration characteristics respectively, and the goodness of fit of the above seven alternative models was evaluated by the SBC criterion; The calculation formula of SBC is as follows: SBC = GD + log(ξ) × df = -2log L(θ) + log(ξ) × df In the formula, GD is the global fitting deviation, df is the number of degrees of freedom, θ and ξ represent the estimated values of the probability distribution parameters and the number of parameters respectively, and L(·) represents the value of the log-likelihood function; At the same time, the goodness of fit of the above seven alternative models was also evaluated by the AIC criterion; The calculation formula of AIC is as follows: AIC = 2ξ - 2logL(θ) Finally, among all the alternative models that passed the test, the distribution model that minimized the calculated values of AIC and SBC simultaneously was selected as the relatively optimal model, and this relatively optimal model was used as the intensity marginal distribution function or the duration marginal distribution function.

5. The method for analyzing characteristic quantities of rapid alternation events between drought and flood according to claim 4, characterized in that, For the alternative normal and lognormal probability distribution models, the defined interval of their variables is [-∞, +∞], while the intensity characteristics and duration characteristics to be tested are both greater than 0. Therefore, the defined intervals of the above two alternative models need to be corrected to the positive value interval, and the corrected cumulative probability is expressed by the following formula: In the formula, f(x|θ) is the probability density function, and θ is the estimated value of the probability distribution parameter.

6. The method for analyzing characteristic quantities of rapid alternation events between drought and flood according to claim 4, characterized in that, In step S3, when the time series consistency does not hold, the specific process of fitting the intensity marginal distribution function and the duration marginal distribution function is as follows; Use the generalized additive model to fit the marginal distribution. In the generalized additive model, assume that the independent observations y i of the response variable Y follow the probability distribution f(y i |Θ i ); where, Θ i = (μ i , σ i , v i , τ i ) is a vector composed of probability distribution parameters, μ and σ are location and scale parameters, and v and τ are shape parameters, representing the skewness and kurtosis of the distribution, respectively; The relationship between the probability distribution parameter and its explanatory variable is established through the link function, and the expression is: That is: where g k (·) represents a connection function; θ k , μ, σ, v, τ are column vectors of length ; X k is a known matrix, corresponding to the explanatory variable values for each time period; k represents the sequence number of the sequence to be analyzed; is the parameter vector to be solved, with dimension J k ; Z jk is a known design matrix; γ jk is a column vector composed of random variables.

7. A method for analyzing characteristic quantities of drought-flood abrupt alternation events according to claim 6, characterized in that, In step S4, the process of using the Copula function likelihood ratio method to test whether the consistency hypothesis between the intensity marginal distribution function and the duration marginal distribution function holds is as follows; The basic assumption of the Copula function likelihood ratio method is that, with the Copula function type fixed, the change point of the dependence structure strength of the multivariate hydrological series is analyzed by detecting the change of its parameter θ c ; Given \(y_1,y_2,\cdots,y\) d is a time series composed of observed values of \(d -\)dimensional random variables, where \(y\) i =\((y\) 1,i ,y\) 2,i ,\cdots,y\) n,i ), \(i = 1,2,\cdots,d\). The population where the observed values are located follows the probability distributions \(F(y_1|\theta\) c,1 ), \(F(y_2|\theta\) c,2 ),\cdots,F(y\) n |\theta\) c,n ). \(\theta\) c,i are the Copula function parameters corresponding to different time periods. In the Copula function likelihood ratio test, the null hypothesis is that there is no change point in the dependence structure of multivariate variables, and the expression formula is as follows: H0:θ c,1 = θ c,2 =... = θ c,n = η0 The alternative hypothesis H1 is: there exists k * and such that θ c,1 = θ c,2 =... = θ c,k* = η1, and θ c,k* =... = θ c,n = η2, and at the same time η1 ≠ η2; construct the likelihood ratio Λ k based on the Copula function. When Λ k is less than the given threshold, reject the null hypothesis H0 and consider that there is a change point k * ; where L n (·) represents the likelihood function of the entire sample sequence; L k (·) and are the likelihood functions before and after the checkpoint k respectively; u i represents the marginal distribution probability of the bivariate sequence; c(·) represents the Copula probability density function; and are the maximum likelihood estimates of the Copula function parameters η0, η1, and η2 respectively. Rewrite Λ k in logarithmic form to obtain: Furthermore, the following logarithmic statistical test quantity is constructed: When Z n is greater than the threshold corresponding to the given significance level, the null hypothesis H0 is rejected, and the likelihood ratio statistic follows an asymptotic distribution: Wherein, z represents a given threshold value. When z approaches infinity, h = l = [ln(n)] 3 / 2 ; h, l, and O represent the parameters of the asymptotic distribution; p is the number of parameters of the Copula function with one change point; Substitute into the above formula. If the calculated P-value is less than the threshold, the null hypothesis is rejected at the significance level of this threshold, and the consistency hypothesis does not hold; otherwise, it holds.

8. A method for analyzing characteristic quantities of drought-flood abrupt alternation events according to claim 7, characterized in that, In step S4, the joint distribution function of duration and intensity established according to the Copula function is expressed as: P(D,S) = C(u D ,u S |θ c ) where D and S represent intensity and duration respectively; u D , u S represent the marginal distributions of intensity and duration; In order to estimate the time-varying parameters of the Copula, explanatory variables are introduced to describe the functional relationship between the time-varying parameters of the Copula and the explanatory variables; g(θ c ) = β0 + Xβ1 where, g(θ c ) represents the copula function when the copula parameter is θ c ; θ c = (θ c,1 , θ c,2 ,..., θ c,n ) T is a column vector composed of time-varying parameters of the Copula; X = (X1, X2,..., X n ) T represents n observations of the explanatory variables; β0 and β represent the parameter vectors to be solved; According to whether the consistency hypothesis of the relationship between duration and intensity holds or not, the expression of the link function is given in different cases: (1) When the relationship between the two variables remains consistent, the Copula parameter is a constant value that does not change with time, and the link function is expressed as: g(θ c ) = constant (2) When the consistency hypothesis is violated, the Copula parameter is a function that changes with time. Therefore, the occurrence time time of the drought event is introduced as an explanatory variable, and the link function is rewritten as: g(θ c ) = β0 + time·β1 Furthermore, the marginal function inference method is adopted to solve the Copula parameter θ by maximizing the log-likelihood function c,t , and the formula is as follows: where \(u\) D,i represents the intensity marginal distribution in the \(i\)-th period; \(u\) S,i represents the duration marginal distribution in the \(i\)-th period; \(D\) i represents the intensity in the \(i\)-th period; \(S\) i represents the duration in the \(i\)-th period; \(\theta\) D represents the parameter of the intensity marginal distribution; \(\theta\) S represents the parameter of the duration marginal distribution; \(\theta\) D,i represents the parameter of the intensity marginal distribution in the \(i\)-th period; \(\theta\) S,i represents the parameter of the duration marginal distribution in the \(i\)-th period; \(c(\cdot)\) is the probability density function of the Copula; \(f\) D \((\cdot)\) and \(f\) S \((\cdot)\) represent the probability density functions of the duration and intensity marginal distributions respectively; in the marginal function inference method, since the maximum values of the second and third terms on the right side of the above formula have been obtained by fitting the marginal distributions of the duration and intensity previously, only the first term on the right side needs to be maximized to obtain the optimal \(\beta_0\) and \(\beta_1\), and the estimated values of \(\beta_0\) and \(\beta_1\) are substituted into the calculation of the estimated value of the Copula function; where time i represents the occurrence time of the i-th period.

9. A method for analyzing characteristic quantities of drought-flood abrupt alternation events according to claim 8, wherein, In step S5, the process of calculating the joint return periods of "or" and "and" for duration and intensity is as follows: The recurrence period calculation of the single-variable feature P(x≥x * ) for the rapid alternation of drought and flood is as follows: Among them, T is the recurrence period of the drought-flood abrupt alternation event, and F(x * ) is the event probability function of x * ; interval is the average time interval between all drought-flood abrupt alternation events, in years, that is, the time length between the start of one drought-flood abrupt alternation event and the start of the next drought-flood abrupt alternation event; if N year drought-flood abrupt alternation events are sampled within a time period of N alter years, the calculation formula for interval is: The calculation formulas of the return periods from different perspectives are as follows; From the perspective of a single variable: Where, T S and T D are the return periods from the univariate perspectives of duration and intensity respectively, F S (s) and F D (d) represent the probabilities of the occurrence of duration and intensity respectively; From the perspective of a bivariate variable: In the formula, represents the "or" combined return period from the perspectives of the two variables of duration and intensity, represents the "and" combined return period from the perspectives of the two variables of duration and intensity, F S,D (s, d) is the combined occurrence probability of duration and intensity; Based on the above formulas, the joint return periods of "or" and "and" for duration and intensity are calculated.

10. A method for analyzing characteristic quantities of drought-flood abrupt alternation events according to claim 9, wherein, In step S5, the process of obtaining the joint design values of duration and intensity by using the most probable combination method is as follows: The combined design value of drought-flood rapid alternation events refers to the multivariate combination (u ml , v ml ) at which the combined density f(u, v) of rapid alternation characteristics reaches the maximum under a certain design recurrence period level, that is, the possibility of this combination occurring is the greatest. Therefore, it is solved by constructing the following equation: [u ml ,v ml ) = argmax f(u, v) f(u, v) = c(u, v) · f(u) · f(v) Among them, f(u, v) is the joint probability density function of the sharp-turn double variables, c(u, v) is the probability density function of the corresponding joint Copula distribution, f(u) and f(v) are the marginal density functions of the variables, and [u ml , v ml is the joint design value combination of the multi-variables to be obtained; The calculation steps for obtaining the combined design value by using the most probable combination method are as follows: (1), Based on the Copula joint distribution function, the Monte Carlo method is used to simulate multiple groups of variable combinations (u ml , v ml ), and the number of groups is taken as 100,000; (2) According to the calculation formulas for the return periods of "or" and "and", find the combined return period corresponding to the bivariate combination obtained in the previous step; (3) According to the determined return period level, screen the variable combinations that meet the accuracy requirements (e = 10 -4 ). The variable combination with the largest joint probability density value is the jointly designed value obtained.

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