Three-dimensional Copula multivariable combined sudden drought identification method

Abstract

The invention relates to a three-dimensional Copula multivariable combined sudden drought recognition method. Relates to the technical field of drought identification. The method comprises the following steps: acquiring rainfall, potential evapotranspiration, soil humidity and runoff data; selecting an optimal probability distribution function to respectively fit soil humidity and runoff series processes to obtain a marginal distribution function of soil humidity and runoff; fitting the rainfall and potential evapotranspiration difference value by using three parameters log-logistic to obtain a marginal distribution function of the rainfall and potential evapotranspiration difference value; based on the marginal distribution function of the soil humidity and the runoff volume and the marginal distribution function of the rainfall and the potential evapotranspiration difference value, combined distribution is constructed, and a comprehensive sudden drought index is obtained based on the combined distribution; based on the comprehensive drought index, identifying a time sequence of a drought event by using a percentile method; a drought feature is identified based on the time series of drought events. According to the invention, the accuracy and reliability of sudden drought identification can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of drought identification, and in particular to a three-dimensional Copula multivariate joint identification method for sudden drought. Background Art

[0002] Against the backdrop of climate change and frequent extreme weather events, droughts, especially flash droughts, pose a major challenge to ecosystem and water resource management. Flash drought events are closely related to temperature, precipitation, soil moisture, runoff, etc. At present, flash drought identification mainly includes three methods: the first is the drought index method, which uses drought indices to identify flash droughts, such as the evaporative stress index (ESI), the standardized evaporative stress ratio (SESR), the evaporative demand drought index (EDDI), etc.; the second is the multi-indicator threshold method, which comprehensively judges flash droughts based on multiple indicator anomaly thresholds, such as when the anomalies of multiple variables such as soil moisture anomaly, evapotranspiration anomaly, and temperature anomaly reach a certain threshold, it is considered that a flash drought has occurred; the third is the soil moisture percentile method, which judges the occurrence of a flash drought based on the soil moisture percentile decline rate or the duration of drought. In general, most current studies only consider a single meteorological element or soil moisture to identify flash droughts, which cannot fully reflect the complex drought process and the interaction between different variables.

[0003] In terms of multivariate drought identification research, the focus is currently on long-term drought events, while multivariate joint identification of sudden droughts, which are sudden and short-term droughts, is still relatively scarce. In addition, most existing multivariate joint identification methods for drought events rely on linear analysis, which makes it difficult to effectively capture the complex nonlinear relationship between variables in sudden drought events. For example, linear methods cannot fully reflect the asymmetry and tail dependence between different variables in sudden drought events, which may lead to insufficient accuracy in sudden drought identification.

[0004] In summary, there are still several key issues to be solved in the identification of sudden droughts, including how to comprehensively consider the impact of factors such as precipitation, runoff and soil moisture on sudden drought events, and how to scientifically and accurately evaluate and identify the onset, termination and development process of sudden droughts. Summary of the invention

[0005] This application proposes a three-dimensional Copula multivariate joint identification method for sudden droughts. The three variables of precipitation and potential evapotranspiration, soil moisture and runoff are used to construct a multivariate joint distribution through a three-dimensional C-Vine Copula model. The purpose is to propose a more accurate sudden drought identification scheme, which will combine the dependency structure of multiple variables and enrich the judgment criteria for sudden drought events, thereby improving the accuracy and reliability of sudden drought identification.

[0006] In order to achieve the above purpose, the technical solution adopted in this application is:

[0007] A three-dimensional Copula multivariate joint drought identification method, characterized by comprising:

[0008] Obtain precipitation, potential evapotranspiration, soil moisture, and runoff data;

[0009] The optimal probability distribution function is selected to fit the soil moisture and runoff series processes respectively, and the marginal distribution functions of soil moisture and runoff are obtained;

[0010] The three-parameter log-logistic method is used to fit the difference between precipitation and potential evapotranspiration to obtain the marginal distribution function of the difference between precipitation and potential evapotranspiration; wherein the difference between precipitation and potential evapotranspiration is the difference between precipitation and potential evapotranspiration;

[0011] Based on the marginal distribution function of the soil moisture and runoff and the marginal distribution function of the difference between precipitation and potential evapotranspiration, a joint distribution is constructed, and a comprehensive sudden drought index is obtained based on the joint distribution;

[0012] Based on the comprehensive sudden drought index, the time series of sudden drought events are identified using the percentile method;

[0013] Based on the time series of sudden drought events, sudden drought characteristics are identified; wherein the sudden drought characteristics include sudden drought frequency, duration and occurrence time.

[0014] Furthermore, the optimal probability distribution function is selected to fit the soil moisture and runoff series processes respectively, and the marginal distribution functions of soil moisture and runoff are obtained, including:

[0015] Taking every eight days as the unit, we select eight days of data corresponding to the same time in each year to construct a multi-year eight-day scale data series;

[0016] Selecting a plurality of univariate probability distribution types as preselected marginal distribution functions; wherein the plurality of univariate probability distribution types include gamma distribution, Rayleigh distribution, normal distribution, exponential distribution, lognormal distribution, Weibull distribution, extreme value distribution, generalized extreme value distribution, log-logistic distribution, logistic distribution, and t-location scale distribution;

[0017] The Kolmogorov-Smirnov test and the Akaike information criterion are used as the judging criteria to select a marginal distribution function that best fits the soil moisture and runoff of each eight-day time series from the preselected marginal distribution functions.

[0018] Furthermore, the three-parameter log-logistic fitting of the difference between precipitation and potential evapotranspiration was used to obtain the marginal distribution function of the difference between precipitation and potential evapotranspiration, including:

[0019] The marginal distribution of the difference between precipitation and potential evapotranspiration is simulated using the three-parameter Log-logistic method. The probability density function expression is:

[0020]

[0021] Where: f(x) is the probability density function expression, α, β, γ are scale, shape and starting parameters respectively, x is a random variable, which refers to the difference between precipitation and potential evapotranspiration;

[0022] The parameter estimates are calculated using the following linear moment method formula:

[0023]

[0024] Where: w s is the probability weight moment, S = 0, 1, 2, is the sequence number of the probability weight moment, w0, w1, w2 represent three different probability weight moments respectively; Γ() is the Gamma function of β; l is the sequence number of the cumulative water deficit sequence X in ascending order; X i' is the i'th cumulative water deficit in the cumulative water deficit sequence, n' is the total number of cumulative water deficits in the cumulative water deficit sequence;

[0025] The cumulative probability F(x) of a given time scale is calculated using the three-parameter log-logistic probability distribution function as follows:

[0026]

[0027] Furthermore, based on the marginal distribution function of the soil moisture and runoff and the marginal distribution function of the difference between precipitation and potential evapotranspiration, a joint distribution is constructed, and a comprehensive sudden drought index is obtained based on the joint distribution, including:

[0028] The joint distribution of the marginal distribution functions of soil moisture and runoff and the marginal distribution functions of the difference between precipitation and potential evapotranspiration is constructed using the multidimensional C-Vine copula, which is expressed as:

[0029]

[0030] Where n is the dimension of the multivariate variable; j is the level of the vine structure tree; i is the number of nodes in each tree layer; f 1,2…n represents variables x1,…,x n The joint marginal distribution function of k For variable x k Marginal distribution function of, k = 1, 2, ..., n, c j,j+1|1,…,j-1 is the conditional Copula function, x j is the jth variable, x j-1 is the j-1th variable, F(xj |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable x j The conditional cumulative probability distribution function, F(x j+i |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable x j+i The conditional cumulative probability distribution function of ;

[0031] Three different tree structures are used, each structure contains two layers of tree decomposition; three random variables X1, X2, X3 are set, and the joint distribution function of the three random variables X1, X2, X3 is Break it down this way:

[0032]

[0033] Where F1(x1), F2(x2), and F3(x3) are the marginal distribution functions of random variables X1, X2, and X3, respectively. 12 is the two-dimensional Copula function between X1 and X2, C 13|2 It is the conditional Copula function of X1 and X3 given X2;

[0034] The first tree structure is a two-dimensional Copula C structure for constructing variables X1 and X2. 12 , calculate the joint distribution of the two variables based on their marginal distributions F1(x1) and F2(x2); the second layer of the tree structure constructs the conditional Copula C of X1 and X3 given X2. 13|2 , and according to F 1|2 (x1|x2) and F 3|2 (x3|x2) computes the conditional joint distribution;

[0035] The joint distribution function The comprehensive sudden drought index is obtained by converting the cumulative probability value of percentiles into parameter-free statistics. The calculation formula is as follows:

[0036]

[0037] In the formula, CFDI is the cumulative probability of the i-th data point after sorting, i is The sequence number of the sorted data point ranges from 1 to n, where n is the length of the data sequence.

[0038] Further, based on the comprehensive sudden drought index, the time series of sudden drought events is identified using the percentile method, including:

[0039] The comprehensive sudden drought index is reassembled in time sequence to form a continuous long time series, and the time series of sudden drought events is identified in the continuous long time series by the following method:

[0040] On an eight-day time scale, the average quantile drops sharply from above 40% to below 20%, and the average rate of decline is at least 5%. This time period is identified as the sudden drought occurrence stage;

[0041] If the soil moisture quantile rises above 20% and lasts for at least 16 days, the drought is confirmed to be over.

[0042] Further, based on the time series of the sudden drought events, identifying sudden drought characteristics includes:

[0043] Based on the pixel scale, the total number of sudden droughts during the entire study period was obtained as the number of sudden droughts, and the average number of sudden droughts per year was taken as the frequency of sudden droughts;

[0044] The average duration of sudden drought was calculated as the ratio of the total duration of sudden drought to the number of sudden droughts during the study period.

[0045] The average time required for the comprehensive sudden drought index to drop rapidly from more than 40% to less than 20% is taken as the sudden drought occurrence time.

[0046] The benefits of this application are:

[0047] This application integrates key variables including precipitation, potential evapotranspiration, soil moisture and runoff information to construct a comprehensive sudden drought index that can provide a more comprehensive perspective and identify more accurate sudden drought events, so as to solve the problem that a single variable is often difficult to fully capture complex sudden drought events. In addition, compared with linear methods such as entropy weight method and principal component analysis, this application is based on C-Vine Copula, which can capture complex nonlinear relationships and tail dependencies between variables, making it more effective in dealing with the multivariate dependency structure of sudden drought influencing factors. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0049] Figure 1 A flowchart of a method for identifying sudden drought provided in an embodiment of the present application;

[0050] Figure 2 A combined tree diagram of the three-dimensional C-Vine copula provided in the embodiment of the present application;

[0051] The above drawings have shown clear embodiments of the present application, which will be described in more detail later. These drawings and text descriptions are not intended to limit the scope of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0052] The following examples are only for better explanation of the present invention, but the content of the present invention is not limited to the application in the examples. Therefore, those skilled in the art can make non-essential improvements and adjustments to the implementation scheme according to the above content of the invention and apply them to other examples, which are still within the protection scope of the present invention.

[0053] The present invention will now be further described with reference to the accompanying drawings.

[0054] The present application embodiment provides a three-dimensional Copula multivariate joint drought identification method. Figure 1 A flowchart of a three-dimensional Copula multivariate joint drought identification method provided in an embodiment of the present application. The drought identification method can be implemented based on an electronic terminal. The drought identification method uses C-Vine Copula to combine the marginal distribution function of precipitation and potential evapotranspiration difference (P-PET), soil moisture (SM) and runoff (R) to construct a time series of droughts on grid pixels, and develop a new method for three-dimensional Copula multivariate joint drought identification. In the embodiment, the implementation process of the method is described in detail using the global grid pixels from 1981 to 2023 as the study area, such as Figure 1 As shown, the method specifically includes steps S100 to S600.

[0055] Step S100, obtaining precipitation, potential evapotranspiration, soil moisture and runoff data.

[0056] In this embodiment, the global daily and pixel-by-pixel precipitation (P), potential evapotranspiration (PET), soil moisture (SM) and runoff data (R) are collected from 1981 to 2023, and the four daily data sets are further averaged to an eight-day scale. Among them, with a day as the step length, the soil moisture data is the 0-100cm soil layer soil moisture data generated by superimposing the 0-7cm, 7-28cm and 28-100cm soil layers, and the potential evapotranspiration is calculated using meteorological elements such as solar radiation, air temperature, humidity and wind speed, using the Penman-Monteith formula of the Food and Agriculture Organization of the United Nations (FAO).

[0057]

[0058] Where: PET is the potential evaporation (mm / day); R nis the net radiation (MJ / (m2 day); G is the soil heat flux (usually negligible in daily calculations); Δ is the slope of the saturated water vapor pressure curve (kPa / ℃); r is the hygrometer constant (kPa / ℃); T is the daily average temperature at 2 meters (℃); u2 is the wind speed at 2 meters (m / s); e s is the saturated water vapor pressure (kPa); e a is the actual water vapor pressure (kPa).

[0059] Step S200, selecting the optimal probability distribution function to fit the soil moisture and runoff series processes respectively, and obtaining the marginal distribution functions of soil moisture and runoff.

[0060] In this embodiment, eight days of data corresponding to the same time in each year are selected in units of eight-day scales to construct eight-day scale data sequences from 1981 to 2023. Eleven univariate probability distribution types widely used in the field of hydrological frequency analysis are selected as marginal distribution functions, including gamma distribution, Rayleigh distribution, normal distribution, exponential distribution, lognormal distribution, Weibull distribution, extreme value distribution, generalized extreme value distribution, log-logistic distribution, logistic distribution, tLocationScale distribution, and Kolmogorov-Smirnov test and Akaike Information Criterion (AIC) are used as evaluation criteria to select the marginal distribution function of soil moisture and runoff that best suits the eight-day time series.

[0061] Step S300, using three-parameter log-logistic fitting to obtain the marginal distribution function of the difference between precipitation and potential evapotranspiration; wherein the difference between precipitation and potential evapotranspiration is the difference between precipitation and potential evapotranspiration.

[0062] In this embodiment, the difference between precipitation and evapotranspiration (expressed as P-PET, i.e., precipitation minus potential evapotranspiration) represents the water surplus or deficit of a region in a specific period. The three-parameter Log-logistic distribution can allow the existence of negative values ​​by introducing a location parameter, thereby overcoming the limitation of the standard Log-logistic distribution. The present invention uses the three-parameter Log-logistic to simulate the marginal distribution of P-PET. Its probability density function expression is:

[0063]

[0064] Where: f(x) is the probability density function expression, α, β, γ are scale, shape and starting parameters respectively, x is a random variable, which refers to the difference between precipitation and potential evapotranspiration;

[0065]

[0066] Where: w s is the probability weight moment, S = 0, 1, 2, is the sequence number of the probability weight moment, w0, w1, w2 represent three different probability weight moments respectively; Γ() is the Gamma function of β; l is the sequence number of the cumulative water deficit sequence X in ascending order; X i' is the i'th cumulative water deficit in the cumulative water deficit sequence, n' is the total number of cumulative water deficits in the cumulative water deficit sequence;

[0067] Through the three-parameter log-logistic probability distribution function, the cumulative probability F(x) for a given time scale can be calculated as follows:

[0068]

[0069] Step S400: construct a joint distribution based on the marginal distribution function of the soil moisture and runoff and the marginal distribution function of the difference between precipitation and potential evapotranspiration, and obtain a comprehensive sudden drought index based on the joint distribution.

[0070] In this embodiment, in steps S200 and S300, by analyzing 46 time series every eight days during the period from 1981 to 2023, the marginal distribution functions of the difference between precipitation and potential evapotranspiration (P-PET), flow (SM) and runoff (R) are obtained, and their joint distribution is further constructed using the multidimensional C-Vine copula:

[0071]

[0072] Where n is the dimension of the multivariate variable; j is the level of the vine structure tree; i is the number of nodes in each tree layer; f 1,2…n represents variables x1,…,x n The joint marginal distribution function of k For variable x k Marginal distribution function of, k = 1, 2, ..., n, c j,j+1|1,…,j-1 is the conditional Copula function, x j is the jth variable, x j-1 is the j-1th variable, F(x j |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable xj The conditional cumulative probability distribution function, F(x j+i |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable x j+i The conditional cumulative probability distribution function of .

[0073] In the process of constructing the three-dimensional C-Vine Copula, three different tree structures (such as Figure 2 As shown in Figure 2, each structure contains two layers of tree decomposition. Specifically, there are three random variables X1, X2, and X3, and their joint distribution function is This can be broken down in the following way:

[0074]

[0075] Among them, F1(x1), F2(x2), F3(x3) are the marginal distribution functions of random variables X1, X2, X3 (i.e., P-PET, SM and R), C 12 is the two-dimensional Copula function between X1 and X2, C 13|2 It is the conditional Copula function of X1 and X3 under the given condition of X2. The first layer of tree structure is the two-dimensional Copula C that constructs variables X1 and X2 12 , calculate the joint distribution based on the marginal distributions F1(x1) and F2(x2) of the two variables. The second layer of the tree structure constructs the conditional CopulaC of X1 and X3 given X2. 13|2 , and according to F 1|2 (x1|x2) and F 3|2 (x3|x2) calculates the conditional joint distribution. In order to ensure the accuracy of modeling the multivariate dependency structure, various Copula functions including Gaussian Copula, Student t Copula, Clayton Copula, Gumbel Copula, Frank Copula, etc. are compared, and the fitting effect of each two-dimensional Copula is evaluated by calculating the Akaike Information Criterion (AlC), and the optimal Copula model is selected to construct the multidimensional dependency structure.

[0076] The joint distribution function The parameter-free statistics can be further converted into the cumulative probability value of percentile (Formula 9), and the Composite Flash Drought Index (CFDI) is obtained:

[0077]

[0078] In the formula, CFDI is the cumulative probability (percentile value) of the i-th data point after sorting. i is The sequence number of the sorted data point ranges from 1 to n. n is the length of the data sequence.

[0079] Step S500: Based on the comprehensive sudden drought index, the time series of sudden drought events is identified using the percentile method.

[0080] In this embodiment, the comprehensive sudden drought index CFDI constructed based on C-Vine copula in step S400 is reassembled in chronological order to form a continuous long time series. Combined with existing studies, the criteria for defining sudden drought events are as follows: (1) On an eight-day time scale, the average quantile drops sharply from above 40% to below 20%, and the average decline rate is at least 5%. This stage is defined as the sudden drought occurrence stage. (2) The termination of the sudden drought event occurs when the soil moisture quantile rises back to above 20% and lasts for at least 16 days (2 8-day periods), at which time the sudden drought ends. (3) The duration of the sudden drought event must be at least 24 days (3 8-day periods) to exclude short-term drought periods that have no significant impact on the ecosystem. At the same time, the duration of the sudden drought event should not exceed 64 days (8 8-day periods) to distinguish it from seasonal drought events on a longer time scale.

[0081] Step S600: identifying sudden drought characteristics based on the time series of the sudden drought events; wherein the sudden drought characteristics include sudden drought frequency, duration and occurrence time.

[0082] In this embodiment, based on the sudden drought event identification result of step S500, the sudden drought characteristics are identified, including the frequency of occurrence of sudden droughts, the duration and the time of occurrence of sudden droughts. Based on the pixel scale, the number of sudden droughts is the total number of sudden droughts that occur during the entire study period, and the sudden drought frequency is the average number of sudden droughts that occur each year, reflecting the frequency of sudden droughts. The average duration of sudden droughts refers to the ratio of the total duration of sudden droughts during the study period to the number of sudden droughts. The time of sudden drought occurrence is defined as the average time required for the comprehensive sudden drought index to drop rapidly from more than 40% to less than 20%.

[0083] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some or all of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and should all be included in the scope of the claims and specification of the present invention.

Claims

1. A three-dimensional Copula multivariate joint drought identification method, characterized in that: include: Obtain precipitation, potential evapotranspiration, soil moisture, and runoff data; The optimal probability distribution function is selected to fit the soil moisture and runoff series processes respectively, and the marginal distribution functions of soil moisture and runoff are obtained; The three-parameter log-logistic method is used to fit the difference between precipitation and potential evapotranspiration to obtain the marginal distribution function of the difference between precipitation and potential evapotranspiration; wherein the difference between precipitation and potential evapotranspiration is the difference between precipitation and potential evapotranspiration; Based on the marginal distribution function of the soil moisture and runoff and the marginal distribution function of the difference between precipitation and potential evapotranspiration, a joint distribution is constructed, and a comprehensive sudden drought index is obtained based on the joint distribution; Based on the comprehensive sudden drought index, the time series of sudden drought events are identified using the percentile method; Based on the time series of sudden drought events, sudden drought characteristics are identified; wherein the sudden drought characteristics include sudden drought frequency, duration and occurrence time.

2. The method according to claim 1, characterized in that The optimal probability distribution function is selected to fit the soil moisture and runoff series processes respectively, and the marginal distribution functions of soil moisture and runoff are obtained, including: Taking every eight days as the unit, we select eight days of data corresponding to the same time in each year to construct a multi-year eight-day scale data series; Selecting a plurality of univariate probability distribution types as preselected marginal distribution functions; wherein the plurality of univariate probability distribution types include gamma distribution, Rayleigh distribution, normal distribution, exponential distribution, lognormal distribution, Weibull distribution, extreme value distribution, generalized extreme value distribution, log-logistic distribution, logistic distribution, and t-location scale distribution; The Kolmogorov-Smirnov test and the Akaike information criterion are used as the judging criteria to select a marginal distribution function that best fits the soil moisture and runoff of each eight-day time series from the preselected marginal distribution functions.

3. The method according to claim 1, characterized in that The three-parameter log-logistic method is used to fit the difference between precipitation and potential evapotranspiration, and the marginal distribution function of the difference between precipitation and potential evapotranspiration is obtained, including: The marginal distribution of the difference between precipitation and potential evapotranspiration is simulated using the three-parameter Log-logistic method. The probability density function expression is: Where: f(x) is the probability density function expression, α, β, γ are scale, shape and starting parameters respectively, x is a random variable, which refers to the difference between precipitation and potential evapotranspiration; The parameter estimates are calculated using the following linear moment method formula: Where: w s is the probability weight moment, S = 0, 1, 2, is the sequence number of the probability weight moment, w0, w1, w2 represent three different probability weight moments respectively; Γ() is the Gamma function of β; l is the sequence number of the cumulative water deficit sequence X in ascending order; X i' is the i'th cumulative water deficit in the cumulative water deficit sequence, n' is the total number of cumulative water deficits in the cumulative water deficit sequence; The cumulative probability F(x) for a given time scale is calculated using the three-parameter log-logistic probability distribution function as follows:

4. The method according to claim 3, characterized in that Based on the marginal distribution function of the soil moisture and runoff and the marginal distribution function of the difference between precipitation and potential evapotranspiration, a joint distribution is constructed, and a comprehensive sudden drought index is obtained based on the joint distribution, including: The joint distribution of the marginal distribution functions of soil moisture and runoff and the marginal distribution functions of the difference between precipitation and potential evapotranspiration is constructed using the multidimensional C-Vine copula, which is expressed as: Where n is the dimension of the multivariate variable; j is the level of the vine structure tree; i is the number of nodes in each tree layer; f 1,2…n represents variables x1,…,x n The joint marginal distribution function of k For variable x k Marginal distribution function of, k = 1, 2, ..., n, c j,j+1|1,…,j-1 is the conditional Copula function, x j is the jth variable, x j-1 is the j-1th variable, F(x j |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable x j The conditional cumulative probability distribution function, F(x j+i |x1,…,x j-1 ) is given x1,…,x j-1 Under these conditions, the variable x j+i The conditional cumulative probability distribution function of ; Three different tree structures are used, each structure contains two layers of tree decomposition; three random variables X1, X2, X3 are set, and the joint distribution function of the three random variables X1, X2, X3 is Break it down this way: Where F1(x1), F2(x2), and F3(x3) are the marginal distribution functions of random variables X1, X2, and X3, respectively. 12 is the two-dimensional Copula function between X1 and X2, C 13|2 It is the conditional Copula function of X1 and X3 given X2; The first tree structure is a two-dimensional Copula C structure for constructing variables X1 and X2. 12 , calculate the joint distribution of the two variables based on their marginal distributions F1(x1) and F2(x2); the second layer of the tree structure constructs the conditional CopulaC of X1 and X3 given X2 13|2 , and according to F 1|2 (x1|x2) and F 3|2 (x3|x2) computes the conditional joint distribution; The joint distribution function The comprehensive sudden drought index is obtained by converting the cumulative probability value of percentiles into parameter-free statistics. The calculation formula is as follows: In the formula, CFDI is the cumulative probability of the i-th data point after sorting, i is The sequence number of the sorted data point ranges from 1 to n, where n is the length of the data sequence.

5. The method according to claim 4, characterized in that Based on the comprehensive sudden drought index, the percentile method is used to identify the time series of sudden drought events, including: The comprehensive sudden drought index is reassembled in time sequence to form a continuous long time series, and the time series of sudden drought events is identified in the continuous long time series by the following method: On an eight-day time scale, the average quantile drops sharply from above 40% to below 20%, and the average rate of decline is at least 5%. This time period is identified as the sudden drought occurrence stage; If the soil moisture quantile rises above 20% and lasts for at least 16 days, the drought is confirmed to be over.

6. The method according to claim 5, characterized in that Based on the time series of sudden drought events, identifying sudden drought characteristics, including: Based on the pixel scale, the total number of sudden droughts during the entire study period was obtained as the number of sudden droughts, and the average number of sudden droughts per year was taken as the frequency of sudden droughts; The average duration of sudden drought was calculated as the ratio of the total duration of sudden drought to the number of sudden droughts during the study period. The average time required for the comprehensive sudden drought index to drop rapidly from more than 40% to less than 20% is taken as the sudden drought occurrence time.

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