CN114756817A - Copula function-based combined probability analysis method for composite flood disasters - Google Patents
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Abstract
The invention is applicable to the field of joint probability analysis, and provides a combined probability analysis method of composite flood disasters based on Copula function, which aims to provide a flood control construction basis of the composite rain disasters, can reflect the functions of influencing the overflow and storage capacity characteristic quantity of flood facilities by establishing a joint probability distribution function of 'tide level' and 'rainfall peak value', and solves the problem that the risk rate is difficult to be used as a reference value of an actual engineering defense standard by designing a quantile combination which enables the joint probability density to reach the maximum value as a design value of a rain tide combination, thereby providing a reasonable selection for engineering design and a risk management and control standard and providing a reliable basis for flood control construction.
Description
Technical Field
The invention belongs to the field of joint probability analysis, and particularly relates to a Copula function-based combined probability analysis method for composite flood disasters.
Background
The Copula function is actually a function which connects variable edge distribution functions and combined distribution of the variable edge distribution functions, is also called as a connection function, can accurately calculate the risk rate of multiple disaster factors under combination according to actual conditions, is widely used for calculating the combined probability of rainfall and hydrological events, but lacks comprehensive consideration of rainfall peak values and tide levels for characterizing rainfall characteristics in the aspect of rain and tide combined disaster analysis at present, and the method for selecting the edge distribution has limitations, so that the good edge distribution cannot always obtain the accurate combined distribution, and the risk rate cannot be directly applied to engineering design as a reference value of engineering defense standards, thereby providing a construction basis for flood control engineering.
Disclosure of Invention
The invention aims to provide a Copula function-based combined probability analysis method for composite flood disasters, and aims to solve the problems that the rainfall peak value and the tide level for characterizing rainfall characteristics lack of comprehensive consideration in the aspect of rain and tide composite disaster analysis at present, the method for selecting edge distribution has limitations, the good edge distribution is often inconsistent, accurate combined distribution can be obtained, and the risk rate cannot be directly applied to engineering design as a reference value of an engineering defense standard, so that construction basis is provided for flood control engineering.
The invention provides a Copula function-based combined probability analysis method for composite flood disasters, which comprises the following steps of:
selecting representative tide level stations and rainfall stations for analyzing coastal cities, wherein the representative tide level stations are positioned at the river section sea entrance and obtain tide level series data; the representative rainfall stations are positioned in the downstream drainage basin of the analysis river reach and acquire rainfall data of the downstream drainage basin, and a corresponding number of rainfall stations are selected according to the area of the downstream drainage basin of the analysis river reach;
carrying out consistency correction on the tide level series data;
aiming at the rainfall station, a rainfall intensity method is adopted to divide a continuous rainfall time sequence into rainfall events, rainfall data is divided, the rainfall time sequence is divided into different rainfall fields, and then a characteristic variable rainfall peak value for representing the rainfall type is counted;
Sampling the rainfall peak value by adopting a maximum annual value method: sampling a maximum rainfall peak value sample in each year according to different regional characteristics;
calculating the rainfall peak value of the drainage basin surface aiming at the maximum rainfall peak value sample;
respectively calculating the marginal probability distribution of the tide level series and the rainfall peak value series, and selecting various distribution line types in the hydrological frequency analysis to respectively perform curve fitting on the tide level and the rainfall peak value;
determining two edge distribution line types with the best fitting effect with each variable data series by adopting a plurality of fitting goodness test methods;
adopting Frank, Gumbel and Clayton Copula functions to respectively construct the joint probability distribution of extreme tide level and rainfall characteristic variable;
evaluating the goodness of fit of the Copula function by selecting an AIC (information index) information criterion method, a BIC (bit information criterion) method and a K-S (K-S) inspection method, and selecting optimal joint probability distribution;
constructing a recurrence period risk rate model based on the optimal joint probability distribution, and constructing a recurrence period model through the recurrence period risk rate model;
and according to the recurrence period model, under the condition of setting a recurrence period, taking a quantile combination which can enable the joint probability density of the Copula function to reach the maximum value as a design value of an engineering design and risk management and control standard.
Further, the recurrence period risk rate model comprises a co-occurrence recurrence period risk rate model, a joint recurrence period risk rate model and a recurrence period risk rate model of a Kendall distribution function.
Further, sampling the peak rainfall value by adopting a maximum annual value method in the step: sampling maximum rainfall peak value samples in each year according to different regional characteristics, selecting the rainfall peak value samples with the design duration of 24 hours, namely adopting annual maximum daily rainfall as the rainfall peak value samples, and adopting storm water gain corresponding to the annual maximum daily rainfall as a tide level sample.
Further, constructing the co-occurrence recurrence period risk rate model under an AND scenario:
according to the definition of the Copula function, the formula of the two-dimensional joint distribution is as follows:
F(x，y)＝P(X≤x，Y≤y)＝C[FX(x)，FY(y)]＝C(u，v) (1)
in the formula (1), F (x, y) is a cumulative distribution function of (x, y), FX(x) As a function of the distribution of the precipitation edges, FY(Y) is a storm water-increase edge distribution function, X is a precipitation threshold, Y is a storm water-increase threshold, X is precipitation, Y is storm water-increase, u is a precipitation edge distribution function, and v is a storm water-increase edge distribution function;
P((R＞r)∩(T＞t))＝1-FX(x)-FY(y)+C[FX(x)，FY(y)]＝1-u-v+C(u，v) (2)
in the formula (2), u is an edge distribution function of precipitation, v is an edge distribution function of storm water increment, C (u, u) is a Copula function of combined distribution of precipitation and storm water increment, P (R > R) # n (T > T)) is a co-occurrence recurrence period risk ratio of precipitation and storm water increment, R is precipitation, R is a precipitation threshold, T is storm water increment, and T is a storm water increment threshold.
Further, including, obtaining a co-occurrence period by solving an inverse of the co-occurrence period:
T∩＝(1-u-v+C(u，v))-1 (3)
in the formula (3), u is the edge distribution function of precipitation, v is the edge distribution function of storm water increase, C (u, v) is the joint distribution Copula function of precipitation and storm water increase, T∩Is the co-occurrence reproduction period.
Further, constructing a joint recurrence period risk rate model under an OR scenario:
P((R＞r)∪(T＞t))＝1-C[FX(x)，FY(y)]＝1-C(u，v) (4)
in the formula (4), u is an edge distribution function of precipitation, v is an edge distribution function of storm water increase, C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, P (R > R) U (T > T)) is a combined recurrence period risk rate of precipitation and storm water increase, R is precipitation, R is a precipitation threshold, T is storm water increase, and T is a storm water increase threshold.
Further, a joint recurrence period is obtained by solving the reciprocal of the joint recurrence period, as follows:
T∪＝(1-C(u，v))-1 (5)
in the formula (5), C (u, v) is a Copula function of the joint distribution of the precipitation and the storm water increase, T∪Is a joint recurrence period.
Further, constructing a recurrence period risk rate model of the Kendall distribution function under the Kendall scenario includes:
in the formula (6), t is a combined value based on the cumulative probability of the Copula function,
a function is generated for the Copula,
is composed of 
The right derivative of (a).
Further, the Kendall distribution function recurrence period is obtained by solving the reciprocal of the recurrence period risk rate of the Kendall distribution function, and the method specifically comprises the following steps:
TKendall＝(1-KC(t))-1 (7)
in formula (7), TKendallFor the recurrence period of the Kendall distribution function, KC(t) is the recurrence period risk ratio of the Kendall distribution function.
Further, the calculation method of the combination of quantiles for maximizing the joint probability density of Copula function is as follows:
(ud，vd)＝argmax(f(u，v)) (8)
in the formula (8), (u)d，vd) Designing a value for a combination of rain tide, wherein f (u, v) is a joint probability density, u is an edge distribution function of precipitation, and v is an edge distribution function of storm water increment;
f(u，v)＝c(u，v)f(u)f(v) (9)
in the formula (9), f (u, v) is the joint probability density, c (u, v) is the probability density function of two-dimensional Copula, f (u) is the marginal probability density of precipitation, and f (v) is the marginal probability density of storm water increment.
Further, the multiple profiles in the hydrological frequency analysis are respectively: gamma distribution curves Gamma, Burr distribution curves, lognormal distribution curves lognormal, and generalized extremum distribution curves GEV.
The invention has the beneficial effects that:
(1) the invention not only establishes the Copula function aiming at evaluating better edge distribution, but also selects two better distribution line types in the edge distribution, establishes a plurality of joint probability distributions through different combinations, and then optimizes the construction method with the best performance, thereby avoiding the defect that the optimal edge distribution can not obtain good joint distribution.
(2) According to the method, through edge function optimization and Copula function fitting goodness inspection, a rain tide and wind tide combined disaster combined risk analysis model is constructed, the encountering risk probability of extreme rainfall and wind storm tides in different joint reproduction periods is quantitatively evaluated, the functions of influencing the overflowing and storage capacity regulating capacity of flood facilities can be reflected, a reliable basis is provided for flood control construction, and the method has important guiding significance for flood control and disaster reduction of coastal cities in China.
(3) According to the invention, under the condition of setting a recurrence period, a quantile combination which enables the joint probability density to reach a maximum value is designed as a design value of a rain tide combination, so that the problem that the risk rate is difficult to serve as a reference value of an actual engineering fortification standard is solved, and a reasonable choice is provided for engineering design and a risk management and control standard.
Drawings
FIG. 1 is an edge distribution function of precipitation provided by an embodiment of the present invention;
FIG. 2 is an edge distribution function of storm water augmentation provided by an embodiment of the present invention;
fig. 3 is a combined probability distribution diagram of precipitation and storm water increase provided by the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The following detailed description of specific implementations of the invention is provided in conjunction with specific embodiments:
the embodiment is as follows:
based on the maximum daily precipitation in 1979-2014(36a) of a certain coastal city and the corresponding storm water increase of a certain tide station of the coastal city, the implementation process of the Copula function-based composite flood disaster joint probability analysis method provided by the embodiment of the invention is shown below, for convenience of description, only the parts related to the embodiment of the invention are shown, and the details are as follows:
s1, selecting and analyzing representative tide level stations and rainfall stations of the coastal city, wherein the representative tide level stations are positioned at the river section sea entrance and acquiring tide level series data; the representative rainfall stations are positioned in the downstream drainage basin of the analysis river reach and acquire rainfall data of the representative rainfall stations, and a corresponding number of rainfall stations are selected according to the area of the downstream drainage basin of the analysis river reach;
s2, carrying out consistency correction on the tide level series data obtained in S1;
s3, aiming at each representative rainfall station selected in the S1, a rainfall intensity method is adopted to divide the continuous rainfall time sequence into rainfall events, rainfall data are divided, the rainfall time sequence is divided into different rainfall fields, and then the characteristic variable rainfall peak value representing the rainfall type is counted;
S4, sampling the rainfall peak value obtained in the S3 by adopting a maximum annual value method: sampling a maximum rainfall peak value sample in each year according to different regional characteristics;
in the embodiment of the invention, a rainfall peak value sample is selected with the design duration of 24 hours, namely, the rainfall of the annual maximum day is adopted as the rainfall peak value sample, and storm water increment corresponding to the annual maximum day rainfall is adopted as a tide level sample;
s5, calculating the rainfall peak value of the drainage basin surface according to the maximum rainfall peak value sample in the S4;
s6, respectively calculating the edge probability distribution of each series aiming at the rainfall peak value and the tide level series, and respectively performing curve fitting on the tide level and the rainfall peak value by selecting a Gamma distribution curve Gamma, a Burr distribution curve, a lognormal distribution curve lognormal and a generalized extreme value distribution curve GEV in hydrological frequency analysis, wherein the edge distribution function of precipitation is shown in figure 1, and the edge distribution function of storm water increment is shown in figure 2;
s7, determining two edge distribution line types with the best fitting effect with each variable data series by adopting three fitting goodness testing methods, namely a K-S testing method, an AIC information criterion method and a BIC information criterion method, wherein the specific methods are as follows:
The results of fig. 1 and 2 show that the Burr, Gamma, GEV and lognomal distributions have a better fit to precipitation, while the Burr and GEV distributions have a better fit to storm water augmentation. According to the precipitation goodness-of-fit statistic of table 1, the K-S statistic of GEV distribution is minimum, and AIC and BIC of Lognormal distribution have better goodness-of-fit. Therefore, the invention takes the GEV distribution as an edge distribution function of the precipitation. For storm water increase, the GEV and the Burr are consistent in K-S statistics and are both 0.1010, and the AIC and BIC goodness tests of the GEV and the Burr are not greatly different, and in conclusion, the GEV distribution is selected as an edge distribution function.
TABLE 1 rainfall and storm water goodness of fit statistic
S8, adopting Frank, Gumbel and Clayton Copula functions to respectively construct the joint probability distribution of extreme value tide level and rainfall characteristic variable,
the method comprises the following specific steps:
after the optimal edge distribution functions of precipitation and storm water are optimized, Gumbel Copula, Clayton Copula and Frank Copula functions are respectively adopted to deduce the combined distribution of precipitation and storm water, as shown in FIG. 3.
S9, selecting an AIC information criterion method and a BIC information criterion method, evaluating the goodness of fit of the Copula function, and selecting the optimal joint probability distribution, wherein the method specifically comprises the following steps:
After the parameter values of all Copula functions are calculated, the fitted combined distribution is compared with the empirical distribution, and therefore the K-S test, the AIC criterion and the BIC of the 3 groups of Copula functions are calculated. As shown in Table 2, the tau correlation coefficients of Gumbel, Clayton and Frank Copula functions are 0.2995, 0.2770 and 0.2908 respectively, which shows that the two functions have a certain positive correlation. Through comparing 3 test statistics of 3 groups of Copula functions, the Frank Copula function K-S test statistics are found to be smaller than Gumbel and Clayton Copula functions, and the Frank Copula function can express typical characteristics of the coastal city rain tide disaster event combined distribution better. After the optimal Copula function is optimized, a joint distribution function of the precipitation and storm water increase can be obtained, as shown in fig. 3. As shown in Table 2 below, the coastal city rain tide encountered the optimal joint distribution of Frank Copula with parameters θ of 2.8149, and K-S, AIC and BIC of 3.5672, -126.4207 and-121.2537, respectively.
TABLE 2 Copula function parameters and test statistics
S10, constructing a recurrence period risk rate model based on the optimal joint probability distribution in S9, and constructing the recurrence period model through the recurrence period risk rate model, wherein the method specifically comprises the following steps:
constructing a joint recurrence period risk rate model under the OR scene:
P((R＞r)∪(T＞t))＝1-C[FX(x)，FY(y)]＝1-C(u，v) (4)
In the formula (4), u is an edge distribution function of precipitation, v is an edge distribution function of storm water increase, C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, P (R > R) U (T > T)) is the risk rate of the combined recurrence period of precipitation and storm water increase, R is precipitation, R is a precipitation threshold, T is storm water increase, and T is a storm water increase threshold;
and (3) solving a joint recurrence period model through the joint recurrence period risk rate, wherein the joint recurrence period model comprises the following steps:
T∪＝(1-C(u，v))-1 (5)
in the formula (5), C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, T∪A combined recurrence period;
table 3 shows that at 5, 10, 20, 50 and 100a (a represents year) rain tide combined recurrence periods, the combined probabilities of rain tides encountered are: 0.3219, 0.1764, 0.0934, 0.0388, and 0.0197.
TABLE 3 Combined probability of water decline and storm water increase during different reproduction periods
S11, according to the recurrence period model in S10, under the condition of setting the recurrence period, taking quantile combination which can enable the joint probability density of the Copula function to reach the maximum value as a design value of the engineering design and risk management and control standard, specifically as follows:
(ud，vd)＝argmax(f(u，v)) (8)
in the formula (8), (u)d，vd) Designing a value for a combination of rain tide, wherein f (u, v) is a joint probability density, u is an edge distribution function of precipitation, and v is an edge distribution function of storm water increment;
f(u，v)＝c(u，v)f(u)f(v) (9)
In equation (9), f (u, v) is the joint probability density, c (u, v) is the probability density function of two-dimensional Copula, f (u) is the marginal probability density of precipitation, and f (v) is the marginal probability density of storm water increase.
In the actual fortification standard, a corresponding fortification standard reference can be made according to the rain tide recurrence period. Table 4 shows the design values for different combinations of heavy precipitation and storm water augmentation at different joint recurrence periods. It can be seen that the corresponding precipitation and storm water increase of the Gumbel function are both smaller than the Clayton function and the Frank function in the reproduction period from 5a to 100a, and are particularly more obvious in the reproduction periods from 50a and 100 a; overall, the design values for rain tide combinations for the Clayton function and Frank function are comparable, with precipitation and storm water at 233mm and 2.7m at 50a recovery period; in the 100a joint reproduction period, precipitation and storm water increase are about 276mm and 3.5m, which indicates that a flood control wall of at least 3.5m is designed and constructed on the basis of considering astronomical flood tide in coastal cities for preventing strong precipitation or storm water increase in one hundred years.
TABLE 4 rain tide combined engineering design values at different reproduction periods
Further, the multiple profiles in the hydrological frequency analysis in S6 are: gamma distribution curves Gamma, Burr distribution curves, lognormal distribution curves lognormal, and generalized extremum distribution curves GEV.
Further, the three goodness-of-fit test methods in S7 include an AIC information criterion method, a BIC information criterion method, and a K-S test method.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (11)
1. A Copula function-based combined probability analysis method for composite flood disasters is characterized by comprising the following steps:
selecting representative tide level stations and rainfall stations for analyzing coastal cities, wherein the representative tide level stations are positioned at the river section sea entrance and obtain tide level series data; the representative rainfall stations are positioned in the downstream drainage basin of the analysis river reach and acquire rainfall data of the representative rainfall stations, and a corresponding number of rainfall stations are selected according to the area of the downstream drainage basin of the analysis river reach;
carrying out consistency correction on the tide level series data;
aiming at the rainfall station, a rainfall intensity method is adopted to divide a continuous rainfall time sequence into rainfall events, rainfall data is divided, the rainfall time sequence is divided into different rainfall fields, and then a characteristic variable rainfall peak value representing the rainfall type is counted;
Sampling the rainfall peak value by adopting a maximum annual value method: sampling a maximum rainfall peak value sample in each year according to different regional characteristics;
calculating the rainfall peak value of the drainage basin surface aiming at the maximum rainfall peak value sample;
respectively calculating the marginal probability distribution of the tide level series and the rainfall peak value series, and selecting various distribution line types in the hydrological frequency analysis to respectively perform curve fitting on the tide level and the rainfall peak value;
determining two edge distribution line types with the best fitting effect with each variable data series by adopting a plurality of fitting goodness test methods;
adopting Frank, Gumbel and Clayton Copula functions to respectively construct the joint probability distribution of extreme tide level and rainfall characteristic variable;
evaluating the goodness of fit of the Copula function by selecting an AIC (information index) information criterion method, a BIC (bit information criterion) method and a K-S (K-S) inspection method, and selecting optimal joint probability distribution;
constructing a recurrence period risk rate model based on the optimal joint probability distribution, and constructing a recurrence period model through the recurrence period risk rate model;
and according to the recurrence period model, under the condition of setting a recurrence period, taking quantile combination which can enable the joint probability density of the Copula function to reach the maximum value as a design value of an engineering design and risk management and control standard.
2. The Copula-function-based combined probability analysis method for composite flooding disasters according to claim 1, wherein the recurrence period risk model comprises a co-occurrence recurrence period risk model, a combined recurrence period risk model and a recurrence period risk model of a Kendall distribution function.
3. The Copula function-based combined probability analysis method for composite flooding disasters according to claim 2, characterized in that the annual maximum value method is adopted in the step to sample the rainfall peak: sampling maximum rainfall peak value samples in each year according to different regional characteristics, selecting the rainfall peak value samples with the design duration of 24 hours, namely adopting annual maximum daily rainfall as the rainfall peak value samples, and adopting storm surge corresponding to the annual maximum daily rainfall as a tide level sample.
4. The Copula-function-based combined probability analysis method for composite flooding disasters according to claim 3, comprising the steps of constructing the co-occurrence recurrence period risk rate model under an AND scenario:
according to the definition of the Copula function, the formula of the two-dimensional joint distribution is as follows:
F(x，y)＝P(X≤x，Y≤y)＝C[FX(x)，FY(y)]＝C(u，v) (1)
in the formula (1), F (x, y) is a cumulative distribution function of (x, y), F X(x) As a function of the distribution of the precipitation edges, FY(Y) is a storm water-increase edge distribution function, X is a precipitation threshold, Y is a storm water-increase threshold, X is precipitation, Y is storm water-increase, u is a precipitation edge distribution function, and v is a storm water-increase edge distribution function;
P((R＞r)∩(T＞t))＝1-FX(x)-FY(y)+C[FX(x)，FY(y)]＝1-u-v+C(u，v) (2)
in the formula (2), u is an edge distribution function of precipitation, v is an edge distribution function of storm water increase, C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, P ((R > R) # n (T > T)) is a co-occurrence recurrence period risk ratio of precipitation and storm water increase, R is precipitation, R is a precipitation threshold, T is storm water increase, and T is a storm water increase threshold.
5. The Copula-function-based combined probability analysis method for composite flood disasters according to claim 4, wherein the co-occurrence periods are obtained by solving the reciprocal of the co-occurrence periods:
T∩＝(1-u-v+C(u，v))-1 (3)
in the formula (3), u isThe edge distribution function of precipitation, v is the edge distribution function of storm water increase, C (u, v) is the joint distribution Copula function of precipitation and storm water increase, T∩Is the co-occurrence reproduction period.
6. The Copula-function-based combined probability analysis method for composite flooding disasters according to claim 3, characterized by comprising the steps of constructing a combined recurrence period risk rate model under an OR scenario:
P((R＞r)∪(T＞t))＝1-C[FX(x)，FY(y)]＝1-C(u，v) (4)
In the formula (4), u is an edge distribution function of precipitation, v is an edge distribution function of storm water increase, C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, P ((R > R) U (T > T)) is a combined recurrence period risk rate of precipitation and storm water increase, R is precipitation, R is a precipitation threshold, T is storm water increase, and T is a storm water increase threshold.
7. The Copula-function-based combined probability analysis method for composite flooding disasters according to claim 6, wherein the combined recurrence period is obtained by solving the reciprocal of the combined recurrence period, and specifically the following is obtained:
T∪＝(1-C(u，v))-1 (5)
in the formula (5), C (u, v) is a Copula function of combined distribution of precipitation and storm water increase, T∪Is a joint recurrence period.
8. The Copula-function-based combined probability analysis method for the composite flooding disasters according to claim 3, wherein the construction of the recurrence period risk rate model of the Kendall distribution function under the Kendall scenario comprises:
in the formula (6), t is a combined value based on the cumulative probability of the Copula function,
a function is generated for the Copula,
is composed of
The right derivative of (c).
9. The Copula-function-based combined probability analysis method for the composite flooding disaster, according to claim 8, is characterized in that a Kendall distribution function recurrence period is obtained by solving an inverse of a recurrence period risk rate of the Kendall distribution function, and specifically, the method comprises the following steps:
TKendall＝(1-KC(t))-1 (7)
In formula (7), TKendallFor the recurrence period of the Kendall distribution function, KCAnd (t) is the recurrence period risk ratio of the Kendall distribution function.
10. The Copula-function-based combined probability analysis method for composite flood disasters according to claim 1, wherein the calculation method of the quantile combination for maximizing the joint probability density of Copula functions is as follows:
(ud，vd)＝argmax(f(u，v)) (8)
in the formula (8), (u)d，vd) Designing a value for a combination of rain tide, wherein f (u, v) is a joint probability density, u is an edge distribution function of precipitation, and v is an edge distribution function of storm water increment;
f(u，v)＝c(u，v)f(u)f(v) (9)
in the formula (9), f (u, v) is the joint probability density, c (u, v) is the probability density function of two-dimensional Copula, f (u) is the marginal probability density of precipitation, and f (v) is the marginal probability density of storm water increment.
11. The Copula-function-based combined probability analysis method for composite flooding disasters according to claim 1, wherein the multiple distribution lines in the hydrologic frequency analysis are respectively: gamma distribution curves Gamma, Burr distribution curves, lognormal distribution curves Iognormal, and generalized extremum distribution curves GEV.
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| CN117634325A (en) * | 2024-01-26 | 2024-03-01 | 水利部交通运输部国家能源局南京水利科学研究院 | Method and system for identifying extremum event of data-limited estuary area and researching composite flood disasters |
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| CN117634325A (en) * | 2024-01-26 | 2024-03-01 | 水利部交通运输部国家能源局南京水利科学研究院 | Method and system for identifying extremum event of data-limited estuary area and researching composite flood disasters |
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