CN108009127A - The analysis method that a kind of typhoon characterization factor influences sea wave height - Google Patents
The analysis method that a kind of typhoon characterization factor influences sea wave height Download PDFInfo
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Abstract
The invention discloses the analysis method that a kind of typhoon characterization factor influences sea wave height.The analysis method is that a continuous variable representated by 3 discrete variables representated by three typhoon factors and wave height or water level is combined into a new distribution pattern.The present invention, come analyzed vortex influencing mechanism, and then establishes 3 d-dem Compound Extreme Value model using mathematical statistics method, and Return period Design Wave value is calculated by this model, so as to the more comprehensive substantive rule of reflection environmental element.
Description
Technical Field
The invention relates to an analysis method for influence of typhoon characteristic factors on wave height of sea waves.
Background
In some sea areas (especially estuary sea areas), typhoon and heavy waves are superposed above storm surge water levels and flood water levels, and astronomical heavy waves can make wave surface water levels abnormally high so as to destroy and cross wave guards and flood dams and submerge large lands together with local flood to cause huge disasters, so that the storm surge has huge harm to the construction of coastal cities, ocean coast engineering, aquaculture and the like and is the first disaster in coastal areas. Because the influence of typhoon on wave height of sea waves is the result of mutual and common influence of all characteristic factors of typhoon, the research on the influence mechanism of the characteristic factors of typhoon on the sea waves is very necessary. The research on various characteristic factors of typhoon which influences the wave height of the sea waves and how the characteristic factors influence the wave height of the sea waves are less in domestic and foreign research results.
The influence of a plurality of characteristic factors of typhoon on the wave height of sea waves is comprehensively considered from a mathematical statistical method, the intrinsic mechanism of the typhoon influencing the wave height of the sea waves is analyzed, the typhoon influence mechanism is analyzed by the mathematical statistical method, a three-dimensional discrete composite extreme value model is further established, and the model is used for calculating the design wave height value for many years, so that the essential rule of the environmental elements can be more comprehensively reflected.
Disclosure of Invention
The invention aims to provide a method for analyzing the influence of typhoon characteristic factors on wave height of sea waves.
In order to solve the technical problems, the invention adopts the technical scheme that the typhoon characteristic factors are an analysis method for the influence of the typhoon characteristic factors on the wave height of the sea waves, wherein the typhoon characteristic factors are the landing frequency of the typhoon in an observation sea area, the maximum wind speed near the center of the bottom layer of the typhoon and the shortest distance from the center of the typhoon to an observation point respectively; that is, the intensity of typhoon itself, the distance from the observation sea area to the center of typhoon and the frequency of typhoon happening in the sea area all affect the extreme wave height and the extreme water level; the invention compounds 3 discrete variables represented by three typhoon characteristic factors and a continuous variable represented by wave height or water level into a new distribution mode;
deriving a three-dimensional discrete-maximum entropy composite extreme value model according to the three characteristic factors of the typhoon;
the theorem is set as xi, eta m (m =0, L, 6) is a continuous type random variable, and η m Obey distribution Q m (x) Xi obeys the distribution G (x), let y 1 ，y 2 ，y 3 Is equal to η m (m =0, L, 6) and xi are all independent random variables with non-negative integers, and xi is recorded ijk Is xi when y 1 ＝i,y 2 ＝j，y 3 Current observed value of = kMemory for recording
p ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 ＝k)，i,j,k＝0,1,2,...,
Define random variable ζ
The distribution function of ζ is then:
is easy to see F (x) = F 0 (x)-ε(x)，
F 0 (x) Is exactly the sum of m A three-dimensional discrete composite extremum distribution consisting of the distribution of (m =0, l, 6) and the distribution of ξ;
definition (y) 1 ,y 2 ,y 3 ) Is a three-dimensional discrete random vector with probability distribution as follows: p is a radical of ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 K), ξ obey a continuous profile G (x), remembering
Scale F 0 (x) A composite distribution formed by the two distributions;
in practical situations, three characteristic factors of typhoon must be all greater than 1 to affect sea waves; if one of the measuring points is zero, for example, when the typhoon intensity is zero and the frequency of the typhoon is not zero, the shortest distance from the center to the measuring point cannot exist; therefore ε (x) is apparently 0; thus solving for
F (x) = R, F may be substituted 0 (x) R, while neglecting ∈ (x), so that the problem can be simplified;
in practical engineering applications, the selection of typhoon landing frequency follows the distribution of sessions, and therefore (y) is selected 1 ,y 2 ,y 3 ) Obeying a three-dimensional mission distribution; through analysis, the correlation coefficients of the typhoon intensity, the shortest distance from the typhoon center to the measuring point and the typhoon occurrence frequency are very small, so that three variables can be approximately regarded as being correlated and independent, and the distribution obeyed by the three characteristic factors is as follows:
wherein, lambda, mu and eta are three unknown parameters which can be estimated by the measured data;
because the wave height under the influence of typhoon is in accordance with continuous distribution, in order to reduce the priori of the wave height of the design, the wave height xi is selected to obey the maximum entropy distribution; the derivation of the maximum entropy distribution function has a better theoretical basis, the function comprises four parameters, existing data can be fitted more finely and flexibly, and the four parameters respectively appear in the positions of coefficients, powers and indexes;
assuming that the random variable X is the wave height, assuming that the wave height conforms to the distribution f (X), the entropy function of the wave height X
Is composed of
The maximum entropy distribution of the wave height X is:
euler equation of
The maximum entropy probability density function of X is of the form:
x represents wave height under the influence of typhoon; f (x) satisfies the following constraint
The mathematical expectation of the extreme wave height X is recorded as E (X), the variance is recorded as D (X), and then the formula (3-5) is substituted into the three constraint conditions for calculation to obtain the product
With A m Marking the m-th origin moment, i.e.Can obtain the product
Order toAnd with B k S and K respectively represent K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution, and according to definition and the relation between the origin moment and the central moment, the K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution have
Gamma and zeta can be obtained by solving the equation set (3-9), beta can be obtained by substituting the gamma and zeta into the formula (3-7), and alpha can be obtained by substituting the gamma, zeta and beta into the formula (3-6); therefore, as long as the expected E (X), the variance D (X), the skewness S and the kurtosis K are calculated (estimated) by the extreme wave height sequence, 4 undetermined parameters in the maximum entropy distribution function (3.5) can be obtained by solving an equation system;
both gamma and zeta in the equation set (3-9) are contained in the gamma-function, and an explicit solution cannot be obtained, and the solution needs to be completed through numerical calculation and an iterative method, wherein an iterative relation is established through Newton iteration, and an iterative process is controlled through a Euclidean algorithm to obtain the numerical solution of gamma and zeta; a. The m Obtained from the arithmetic mean of the measured data;
therefore, after the three-dimensional discrete distribution and the continuous distribution are determined, the three-dimensional discrete composite extreme value model can be obtained:
the distribution function has seven unknown parameters, so that the influence of typhoon on the wave height of the sea waves can be more carefully reflected, and the result is more scientific and reasonable.
Preferably, the distribution function of ζ is
The following was demonstrated:
note book
The invention has the beneficial effects that:
a typhoon influence mechanism is analyzed by utilizing a mathematical statistic method, a three-dimensional discrete composite extreme value model is further established, and a design wave height value once many years is calculated through the model, so that the substantial rule of the environmental elements can be reflected more comprehensively.
Drawings
The invention is described in further detail below with reference to the drawings and the detailed description.
Fig. 1 is a variation trend chart of the lowest air pressure at the center of the typhoon and the maximum wind speed at the center of the bottom layer in the embodiment of the analysis method for the influence of the typhoon characteristic factors on the wave height of the sea waves.
Fig. 2 is a correlation coefficient diagram of each typhoon characteristic quantity and wave height in the embodiment of the analysis method for the influence of the typhoon characteristic factors on the wave height of the sea waves.
Detailed Description
In the embodiment, the influence of a plurality of characteristic factors of typhoon on the wave height of sea waves is comprehensively considered from a mathematical statistical method, before the influence of the typhoon on the wave height of sea waves is analyzed, the influence mechanism of typhoon is analyzed by using the mathematical statistical method, a three-dimensional discrete composite extreme value model is further established, and the designed wave height value for many years is calculated through the model, so that the essential rule of environmental elements can be more comprehensively reflected.
In this embodiment, theoretical results are described by using a research method combining theoretical research with empirical analysis and by combining chart display. The innovation of the embodiment mainly comprises the following aspects:
(1) And aiming at the typhoon forming development rule, performing correlation analysis on each characteristic factor in the typhoon by using a new mathematical analysis method. And analyzing the relation among the characteristic factors of the typhoon so as to more scientifically analyze the mechanism of the marine disaster caused by the typhoon. The calculation model is improved aiming at the traditional design wave height without considering the influence of typhoon factors or only considering the influence of typhoon frequency, and the influence of each characteristic factor of typhoon on extreme wave height is comprehensively considered, so that the calculation model is more practical, scientific and reasonable.
(2) The rank correlation coefficient analysis method is adopted to obtain the correlation relation of the typhoon characteristic factors on the ocean factors influenced by the typhoons, so that different degrees of influence of the typhoon characteristic factors on the ocean factors can be obtained, and the important influence factors can be selected for mathematical modeling. The harmonious measurement, namely the rank correlation coefficient, is a more flexible and robust correlation analysis tool, is widely applied to the field of non-parameter statistics, is particularly used for researching the correlation among random variables, and avoids a plurality of defects of the traditional linear correlation analysis.
(3) Through rank correlation analysis, three typhoon characteristic factors which have the largest influence on sea waves are selected, the three characteristic factors are relatively independent, the comprehensive influence of the typhoon on the sea waves can be reflected more comprehensively, and the three variables are typhoon frequency, the maximum wind speed near the center of the typhoon bottom layer and the shortest distance from the typhoon center to an observation point. Because the occurrence frequency of the typhoon is a discrete random variable, the collected data of the other two characteristic factors of the typhoon are subjected to discretization processing. According to a new tropical cyclone classification grade standard issued by the China weather bureau, the maximum wind speed near the center of the typhoon bottom layer is taken as a standard for classifying, the times of typhoons in different grades in 2 years in the yellow sea area are calculated, and obviously, the typhoons are changed into a discrete random variable after being processed in such a way; by taking reference to the standard for dividing the distance from the center of the typhoon to the measuring point of Fang Zhongsheng and the like, the distance from the center of the typhoon to the measuring point in the yellow sea area is divided into 7 classes, the number of times that the typhoon enters each class in 27 years is calculated, and the variable is discretized. Therefore, three discrete variables influencing the wave height of the sea waves are determined, and the comprehensive influence of the typhoon on the sea waves can be comprehensively reflected through the three variables.
(4) After three discrete variables of the typhoon are selected, a three-dimensional discrete-maximum entropy composite extreme value model is deduced on the basis, typhoon landing frequency is set, the three-dimensional discrete vector, namely the maximum wind speed near the center of the bottom layer and the shortest distance from the center to a measuring point, obeys three-dimensional Possion distribution, and continuous random variable wave height distribution is selected as maximum entropy distribution. Therefore, the new model can reflect the influence of a plurality of characteristic quantities of the typhoon on the wave height, maintain the uncertainty to the maximum extent and better accord with the actual rule.
(5) The new model is checked using the measured data. The design wave height values of 20-year first chance, 50-year first chance, 100-year first chance and 200-year first chance are respectively calculated. Comparing the obtained result with the result obtained by the previous model, and comparing with the actual data. The advantages of the new method were analyzed.
1 typhoon characteristic factor correlation analysis and influence thereof on sea waves
1.1 correlation analysis of characteristic factors of typhoon
Typhoon occurrence has many data records, and the record of the data reflects the characteristics of typhoon and the influence on sea areas. According to typhoon data information given in the typhoon yearbook, seven characteristic factors, namely the lowest central air pressure, the maximum wind speed near the center of the bottom layer of the typhoon, the maximum wind speed radius of the typhoon, the moving speed of the typhoon, the closest distance between the center of the typhoon and a measured point, the frequency of the typhoon and the moving direction angle of the typhoon, are selected for analysis.
The characteristic factors are discussed in groups, the effect of the lowest air pressure of the typhoon center and the maximum wind speed near the bottom center on the extreme wave height of sea waves is always concerned, in a numerical forecasting model, simulating the wind speed generated by the typhoon in a typhoon field generally needs the lowest central air pressure of the typhoon, the maximum wind speed near the typhoon bottom center, the maximum wind speed radius of the typhoon and the moving speed of the typhoon, and the four parameters have obvious correlation, so that the four parameters are discussed as a group of influence factors. The minimum distance from the typhoon center to the research sea area and the moving direction of the typhoon are two parameters describing the influence of the typhoon on the research sea area, and are discussed together. In addition, the frequency of typhoon occurrence has a great influence on sea waves, and the frequency of typhoon occurrence is also used in a model for researching the influence of typhoon on extreme wave height in the current practical application, so that the typhoon occurrence frequency is analyzed independently.
1.1.1 typhoon intensity and moving speed influence analysis on wave height of sea waves
The influence of the combination of the lowest air pressure of the center of the typhoon, the maximum wind speed near the center of the bottom layer of the typhoon and the shifting speed of the typhoon on the wave height and water increase of the sea waves is analyzed.
When the typhoon moves fast, the combined action of the low air pressure at the center of the typhoon and the extremely high wind speed can often cause a large storm surge, the water is rapidly increased, and a large disaster is easily caused; when the moving speed is slow, the life cycle of the device is long, the caused heavy rain is violent, and the water is rapidly increased by the sea waves, so that the great wave height is caused. The storm surge is violent, and the damage of billow and storm with the height of several meters to the landing area is very strong.
It should also be noted that the speed of movement of the typhoon is closely related to the wave height. This is because the speed of typhoon movement determines the duration of the same wind direction in the sea area. Namely, when the typhoon moves fast, the acting time of the wind in the same direction is short, the wave height is small, and the distribution range of the large wave area is small; on the contrary, when the typhoon moves slowly, the wind in the same direction acts for a long time, and the wave height and the large wave area are also large in distribution range.
When the typhoon intensity and the typhoon are determined, the more the distance between the typhoon center and the observation sea area is, the bigger the typhoon waves are, and of course, the different moving direction angles of the typhoon have different influences on the sea area.
1.1.2 typhoon center distance to the sea area under study and typhoon moving direction
Of the seven characteristic parameters of typhoon, the distance from the center of typhoon to the research sea area and the moving direction of typhoon are two parameters which can well describe the influence of typhoon on the research sea area.
Under the condition that the typhoon intensity is the same, the closer the observation point is to the center of the typhoon, the larger the disaster caused by the typhoon. The moving direction of the typhoon is characterized by the moving direction angle of the typhoon, namely the azimuth angle of the connecting line of the center of the typhoon and the measuring point relative to the advancing direction of the typhoon. The azimuth reflects the effect of typhoon on the direction of the waves.
1.1.3 landing on Chinese typhoon frequency
Extreme sea conditions generally occur in the typhoon process, for Qingdao areas, storm weather systems with the coastal wave height of more than or equal to 510cm are all typhoons or are related to typhoons, and the paths and times of the typhoons are different every year, so that the typhoons affecting various places are different in frequency.
The typhoon landing frequency of China is higher than that of other countries, obviously, the occurrence of typhoon can inevitably lead to larger wave height, and therefore, the higher the typhoon landing frequency is, the more easily the extreme value wave height appears.
The section analyzes the characteristics of each characteristic factor of the typhoon and the influence mechanism on the wave height of the sea waves. In the next section, the relation between the typhoon characteristic factors is analyzed by a mathematical means, and then the influence degree of the characteristic factors on the sea waves is analyzed.
1.2 Harmonious measures of random variables (rank correlation coefficient)
Generally, when the correlation relationship between two variables is analyzed, the correlation coefficient of product moment of Pearson is obtained,
it reflects the linear correlation between two random variables X, Y, obviously | ρ | ≦ 1, and the equal sign holds only when X and Y are linear, hence also called linear correlation coefficient, sometimes simply referred to as correlation coefficient. When rho is larger than 0, the random variables are positively correlated; rho is less than 0, called negative correlation; and ρ =0, it is called uncorrelated. When the correlation coefficient between X and Y needs to be emphasized, it is also denoted as ρ (X, Y). Balance
Is a sample (X) i ,Y i ) I = linear correlation coefficient of 1,l, n, which is an estimate of the overall correlation coefficient ρ.
Through analysis, a harmonious measure, namely a rank correlation coefficient and a measuring method thereof are introduced in the embodiment to solve the defects of Pearson linear correlation coefficients and analyze the influence of typhoon characteristic quantity on sea waves.
1.2.1 Harmonious metric-rank correlation coefficient derived from copula function
For the disadvantages of the conventional linear correlation analysis method, the present embodiment introduces a harmony measure-rank correlation coefficient derived from the Copula function as a tool for correlation analysis and multivariate statistical analysis.
Sklar's theorem: for a distribution F with a unary edge 1 L F N The joint distribution function of (2) has a Copula function, and meets the following requirements:
F(x 1 ,L,x n ,L,x N )＝C(F(x 1 ),L,F(x n ),L,F(x N ))
if F 1 ,L F N Continuously, C is uniquely determined; and if F 1 ,L F N For edge distribution of random variables, the function F defined by the above equation is F 1 ,L F N The joint distribution function of (1). Here, N edge functions F (x) 1 ),L,F(x n ),L,F(x N ) Can belong to different distribution types, which is a great advantage of adopting Copula function to construct multivariable joint distribution function. An important characteristic of the Copula junction function is that it is invariant to strict monotonically increasing transformations of random variables, and assuming that the Copula function of random variables X, Y is C (u, v), T (X), T (Y), and is a strictly increasing continuous transformation, then (X, Y) and (T (X, T (Y)) have the same Copula. With this property, two very important inferences can be drawn: firstly, a Copula function reflects a correlation structure between random variables; this correlation structure is independent of the unit of measure of each random variable; the correlation index derived by the Copula function is more suitable for the requirements of people than the commonly used Pearson correlation coefficient of people, because the Pearson correlation coefficient is a constant correlation index under linear transformation, and if the correlation of a nonlinear function is involved, an incorrect conclusion can be derived.
Another random variable Y also tends to appear large if X appears large, or small when X appears smallAt values, Y also tends to appear small, and X and Y are said to be harmonious. Let (x) i ,y i ) And (x) j ,y j ) Are two observations of a continuous random vector (X, Y) if (X) i -x j )(y i -y j ) If > 0, then it is called (x) i ,y i ) And (x) j ,y j ) Is harmonious; if (x) i -x j )(y i -y j ) If < 0, then it is called (x) i ,y i ) And (x) j ,y j ) Is discordant. Two Copula functions are introduced below to derive a harmonious relevance metric: kendall τ and Spearman ρ s 。
Defining: is provided with (X) 1 ,Y 1 ) And (X) 2 ,Y 2 ) Are independent and equally distributed random vectors called
τ(X,Y)＝Pr((X 1 -X 2 )(Y 1 -Y 2 )＞0)-Pr((X 1 -X 2 )(Y 1 -Y 2 )＜0)
And the correlation coefficient is Kendall rank and is abbreviated as tau.
Copula expression of Kendall rank correlation coefficient:
if (X, Y) is a continuous random vector and the correlation structure function is C, then
Defining: is provided with (X) 1 ,Y 1 )，(X 2 ,Y 2 ) And (X) 3 ,Y 3 ) Are independent and equally distributed random vectors called
τ(X,Y)＝3(Pr((X 1 -X 2 )(Y 1 -Y 3 )＞0)-Pr((X 1 -X 2 )(Y 1 -Y 3 )＜0))
Is a Spearman rank correlation coefficient, abbreviated as rho s 。
Copula function expression of Spearman rank correlation coefficient:
if (X, Y) is a continuous random vector and the correlation structure function is C, then
In this embodiment, the correlation analysis of each characteristic factor of typhoon is performed by this method.
1.2.2 parameters Kendall τ and Spearman ρ s Is estimated by
Is (X) 1 ,Y 1 ),L,(X n ,Y n ) Is a sample of a continuous random vector (X, Y) and is further provided with X n,n ≤L≤X 1,n Is (X) 1 ,L,X n ) If X is the order statistic of i ＝X k,n Then call X i In (X) 1 ,L,X n ) The rank of medium from large to small is k. With R i And Q i Respectively represent X i ，Y i In (X) 1 ,L,X n ) And (Y) 1 ,L,Y n ) Rank of (2). Sample Kendall rank correlation coefficient is defined as
In fact, from n pairs of observations (x) 1 ,y 1 ),L(x n ,y n ) Two pairs of (x) at any place in i ,y i ) And (x) j ,y j ) I ≠ j, consensusDifferent extraction methods are adopted, whether the two pairs of extracted observations are harmonious or not is considered, and if the two pairs of extracted observations are harmonious, the result is (R) i -R j )(Q i -Q j ) Is greater than 0; if not harmonious, (R) i -R j )(Q i -Q j ) < 0, thereforeCan also be expressed as
Wherein c represents the number of harmonious observation pairs and d represents the number of discordant observation pairs, andif there is no case with the same observation.
Define the sample Spearman rank correlation coefficient as
Wherein the content of the first and second substances,it can be seen thatAnd withIn the same form except that (X) i ,Y i ) Rank (R) i ,Q i ) Instead of (X) i ,Y i ). It is noted that
By simple operation, canIs simplified into
Rank correlation coefficientAndin fact, the correlation coefficients between the magnitude orders of the observations are not the correlation coefficients of the observations themselves, and the single increment transform does not change the magnitude order of the observations and therefore does not change the rank correlation coefficients. And they may describe non-linear correlations between variables.
1.3 correlation analysis of each characteristic factor of typhoon and influence on wave height
The section selects and analyzes the typhoon data of twenty-six years which has influence on the sea area of the yellow sea. The method comprises the steps of the lowest air pressure of the center of the middle typhoon, the maximum wind speed of the center of the bottom layer, the moving speed of the typhoon, the maximum wind speed radius of a seven-level wind ring, the shortest distance from the center of the typhoon to an observation sea area and the landing frequency of the typhoon in the observation sea area.
Because the magnitude and dimension of the typhoon characteristic factors are different, the original data of the five typhoon characteristic factors are processed without dimension, and the influence caused by the difference in magnitude or dimension among the variables is eliminated, so that the average value of each variable is 0, and the variance is 1. The transformation formula is as follows:
wherein the content of the first and second substances,is the mean of the given data and σ is the variance of the given data.
Since the influence of the typhoon moving direction angle on the sea waves mainly influences the wave direction, but hardly influences the height, and the data is difficult to accurately obtain, the data analysis is only performed on other six typhoon characteristic factors. Let the lowest pressure of the center of the typhoon be p and the maximum wind speed of the center of the bottom be v 1 The typhoon moving speed is v 2 The maximum wind speed radius of the seven-level wind ring is R, the shortest distance from the center of the typhoon to the observation sea area is R, and the landing frequency of the typhoon in the observation sea area is n.
The following is to use typhoon and wave data of 27 years in the yellow sea area to the Neislandic observation station (1963-1989), and to use the rank correlation coefficient analysis method to perform unconventional correlation analysis on the five variables. Since the five characteristic factors are the influence factors directly influencing the wave height of the sea wave and are the five parameters which can most characterize the typhoon characteristics, correlation analysis is specially carried out on the five variables. And a more reasonable and accurate correlation value than the traditional correlation analysis result is obtained by utilizing the rank correlation coefficient. The method for calculating the rank correlation coefficient by using the second section calculates the following table of the correlation coefficients among the characteristic factors:
TABLE 2.2 TABLE of rank correlation coefficients between the characteristic factors of typhoons
As can be seen from Table 2.2, the correlation coefficient between the lowest pressure at the center of the typhoon and the maximum wind speed at the center of the bottom layer is-0.9182, which indicates that the harmony is high. It can be seen from fig. 1 that when the air pressure is low, the wind speed is correspondingly high, and the degree and magnitude of the change are equally large, i.e. if the smaller value of either of the two occurs, the probability that the other tends to occur with a large value is very high. Therefore, when one occurs, the other must occur accordingly, and the harmony of the two is high. They can be seen as an influencing variable, and all the characteristics can be reflected by only selecting one characteristic factor.
Rank correlation coefficients of the typhoon center lowest air pressure and the bottom layer center maximum wind speed and the typhoon center moving speed are-0.0472 and 0.0584 respectively, and it can be obviously shown that the typhoon center moving speed and the first two characteristic factors are almost independent.
From Table 2.2, the rank correlation coefficients of the typhoon center lowest air pressure and the bottom layer center maximum wind speed and the maximum wind speed radius are-0.5325 and 0.5634 respectively, and the harmonious degree is higher. The lower the typhoon central air pressure is, the larger the maximum wind speed of the bottom layer center is, the larger the maximum wind speed radius is, and the larger the influence range on the research sea area is. The great wave height is easy to generate and the water is increased.
The rank correlation coefficients of the central lowest air pressure and the bottom layer central maximum wind speed and the shortest distance between the typhoon center and the observation sea area are 0.3527 and-0.3298, and the correlation degree is very low. Tables 2-4 show that when the relationship between the typhoon central air pressure and the maximum wind speed and the distance between the center and the measuring point is not large, the typhoon central air pressure and the maximum wind speed are approximately regarded as independent.
The rank correlation coefficient of the typhoon center moving speed and the typhoon maximum wind speed radius is-0.0908, and obviously, the two characteristic factors are almost independent. Therefore, the center moving speed of the typhoon is almost independent of the center minimum air pressure, the center maximum wind speed of the bottom layer, and the maximum wind speed radius, and should be discussed separately.
The influence on the wave height of the sea waves is analyzed by combining the harmony degree among the typhoon characteristic factors. Considering that six meteorological elements such as the lowest air pressure of a typhoon center, the maximum air speed of a bottom layer center, the moving speed of the typhoon, the maximum air speed radius, the shortest distance between the typhoon center and an observation sea area, the landing frequency of the typhoon in the observation sea area and the like have different degrees of influence on the wave height of the sea waves, and influence mechanisms of the six meteorological elements are different, and correlation analysis research is performed on the six characteristic parameters of the typhoon and the corresponding wave height of the sea waves respectively.
Let typhoon wave height be b, the following table is rank correlation coefficient of six typhoon characteristic factors and wave height:
TABLE 2.3 rank correlation coefficient of typhoon eigenfactor and wave height
As is evident from Table 2.3, the rank correlation coefficients of the lowest pressure in the center of the typhoon and the maximum wind speed and wave height near the center of the basement are-0.8161 and 0.8888, and the harmonious degree is very high. Meanwhile, the harmony between the two typhoon characteristic factors is also very consistent through the conclusion, so that the influence degree of the two typhoon characteristic factors on the wave height of the sea waves can be completely reflected by only considering one of the typhoon characteristic factors when selecting the variables. The influence degree of the typhoon moving speed and the wave height of the sea waves is 0.0798, and the correlation is very low. In practice, the moving speed of the typhoon is also 20-30 kilometers and is not very high. Therefore, it can be concluded that the moving speed of typhoon is incompatible with the wave height of sea waves in the research sea area. The rank correlation coefficient between the shortest distance from the center of the typhoon to the research sea area and the wave height of the sea waves is-0.8042, namely the smaller the distance is, the greater the influence on the wave height of the sea waves is, and therefore the characteristic factor is used as an influence factor. The harmonic degree of the maximum wind speed radius of the typhoon and the wave height is higher, and the harmonic degree is used as an influence factor of the wave height in the embodiment. The rank correlation coefficient of the typhoon frequency and the wave height is 0.5762, which is also high and should be used as an influence factor for analysis.
From fig. 2, the correlation between the maximum wind speed near the center of the typhoon and the wave height is the largest, the negative correlation between the lowest air pressure at the center and the wave height and the shortest distance from the center to the measuring point and the wave height is the largest, and then the maximum wind speed radius and the moving speed. And then, through the analysis of the characteristic quantities of the typhoon in the front, the three variables of the maximum wind speed of the center of the bottom layer, the shortest distance between the center of the typhoon and the observation sea area and the landing frequency of the typhoon in the observation sea area are selected, so that the more comprehensive influence of the typhoon on the wave height of the sea waves can be well reflected. A new model is built and deduced by utilizing the three variables, and the extreme wave height sub under the influence of a plurality of characteristic factors of typhoon is predicted all the year round.
1.4 summary of this chapter
In the chapter, the interrelationship among all the characteristic factors of the typhoon is firstly analyzed in detail, and different influence mechanisms and joint influence mechanisms of all the characteristic factors on the sea waves are analyzed. The result shows that the generation of the wave height of the extremely large sea is not the result of single factor action in the typhoon characteristic factors but the result of combined influence of a plurality of characteristic factors.
In order to clarify the degree of correlation between them, this chapter uses a Copula function-based correlation measure, that is, a measure of harmony of random variables — rank correlation coefficient method. And (3) calculating the rank correlation coefficient among all the characteristic factors of the typhoon by using a rank correlation coefficient method, reflecting that the harmony degree between the lowest air pressure of the center of the typhoon and the maximum wind speed of the typhoon is highest, and the other correlation degrees are lower. It also reflects that the correlation between the typhoon center moving speed and other characteristic factors is the lowest. On the basis, the characteristic factors of typhoon and the corresponding maximum wave height value caused by the typhoon are analyzed by a rank correlation coefficient method, and the rank correlation analysis is carried out, and the result shows that: the rank correlation coefficient of the lowest air pressure of the typhoon center and the maximum wind speed near the bottom center and the wave height is highest, the harmony degree of the maximum wind speed radius of the typhoon and the wave height is higher, the typhoon frequency is higher than 0.5, and the influence degree of the typhoon moving speed and the wave height of the sea wave is the lowest, and the typhoon moving speed and the wave height are almost regarded as irrelevant.
According to the calculation results, three variables of the maximum wind speed of the center of the bottom layer, the shortest distance between the center of the typhoon and the observation sea area and the landing frequency of the observation sea area are finally selected, and the typhoon characteristic factors under the influence of the plurality of characteristic factors of the typhoon are predicted all the year round. Therefore, the comprehensive influence of typhoon on sea waves can be reflected.
2 design wave height calculation new mode for reflecting typhoon characteristic factor influence
The important and basic measures for preventing typhoon marine disasters are to establish necessary breakwaters and flood dams along the related shore, and one of the key technical problems for implementing the measures is how to reasonably determine the defense standard. Therefore, a joint distribution function of extreme values of wave height and storm surge water level (or flood and storm surge water increasing in estuary sea area) meeting the actual situation needs to be established according to a certain theory, and accordingly, a joint extreme value (or joint recurrence period of the extreme value) is calculated for many years, so that a basis is provided for determining the design standard of the breakwater and the flood bank.
2.1 derivation of theoretical model
In this section, a three-dimensional discrete-maximum entropy composite extreme value model is derived according to the three characteristic factors of the typhoon selected in the previous chapter.
Definition (y) 1 ,y 2 ,y 3 ) Is a three-dimensional discrete random vector with probability distribution as follows: p is a radical of ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 K), ξ obey a continuous profile G (x), remembering
We call F 0 (x) A composite distribution is formed for the two distributions.
The theorem is set as xi, eta m (m =0, L, 6) is a continuous type random variable, and η m Obey distribution Q m (x) Xi obey the distribution G (x), let y 1 ，y 2 ，y 3 Is equal to η m (m =0, L, 6) and xi are all independent random variables with non-negative integers, and xi is recorded ijk Is xi when y 1 ＝i,y 2 ＝j，y 3 When observed value of = k, note p ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 ＝k)，i,j,k＝0,1,2,...,
Define random variable ζ
The distribution function of ζ is:
and (3) proving that:
note the book
Is easy to see F (x) = F 0 (x)-ε(x)，
F 0 (x) Is exactly the sum of m And (m =0, L, 6) and ξ. In practical situations, the three characteristic factors of typhoon must all be greater than 1 to have an effect on the waves. If one of them is zero, for example, when the typhoon intensity is zero and the frequency of the typhoon is not zero, the condition can not exist. So ε (x) is apparently 0. Therefore, we solve for
F (x) = R, F may be substituted 0 (x) = R, and ∈ (x) is ignored, so that the problem can be simplified. It proves that the process is similar to the one-dimensional discrete composite extremum distribution situation.
In practical engineering application, the typhoon landing frequency is selected to comply with the distribution of the sites, so the embodiment selects (y) 1 ,y 2 ,y 3 ) Obeying a three-dimensional session distribution. The second chapter analyzes typhoon intensity, and correlation coefficients between the shortest distance from a typhoon center to a measuring point and typhoon occurrence frequency are small, so that three variables can be approximately regarded as relevant and independent, and the distribution obeyed by the three characteristic factors is as follows:
where λ, μ, η are three unknown parameters that can be estimated from the measured data, see section below.
To reduce the priori nature of the desired design wave height, the present embodiment chooses wave height ξ to obey the maximum entropy distribution. The derivation of the maximum entropy distribution function has a good theoretical basis, the function comprises four parameters which respectively appear at the positions of coefficients, powers and exponents, and existing data can be fitted more finely and flexibly.
The wave height under the influence of typhoon is consistent with the continuous distribution. Assuming that the wave height conforms to the distribution f (x), the wave height is set to be randomThe quantity X, of course, the wave heights are all positive values, f (X) is a probability density function of X, the entropy function of which is
x represents the wave height under the influence of typhoon. f (x) satisfies the following constraint
The first two constraints (d) (e) are descriptions of accepted facts and are not specified a priori. Constraint (f) means an arbitrary order of statistical momentAre present.
According to the maximum entropy principle, our task is to find the f (x): h (X) is maximized under the above three constraints. This is a conditional variational problem whose Eular equation is
Where f = f (x), and λ, β, γ, ξ are undetermined constants. By the formula
Wherein α = e λ-1 Still to be determined constant, then we get the maximum entropy probability density function form of X.
In practical application, X may be a wave height, a water level, or other marine environmental factors, in this embodiment, the wave height, and the corresponding distribution function is
The mathematical expectation of the extreme wave height X is recorded as E (X), the variance is recorded as D (X), and then the formula (3-5) is substituted into the three constraint conditions for calculation to obtain the product
With A m Marking the m-th moment of origin, i.e.Can obtain the product
Order toAnd with B k S and K respectively represent K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution, and according to definition and the relation between the origin moment and the central moment, the K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution have
Thereby is provided with
Gamma and zeta can be obtained by solving the equation set (3-9), beta can be obtained by substituting gamma and zeta into the formula (3-7), and alpha can be obtained by substituting gamma, zeta and beta into the formula (3-6). It can be seen that if the expected E (X), the variance D (X), the skewness S and the kurtosis K are calculated (estimated) from the extreme wave height sequence, 4 undetermined parameters in the maximum entropy distribution function (2.3) can be obtained by solving the equation system.
Both γ and ζ in the equation set (3-9) are contained in the Γ -function, and an explicit solution thereof cannot be obtained, and the solution needs to be completed through numerical calculation and an iterative method.
The parameters are then calculated using the above equation. The parameter of f (x) can be represented by A m M =1,2,3l, n, where n can be chosen to be any integer greater than 3, in practice a, similarly to the method used in general statistics m Estimated from
Wherein x is i Represents the ith observation of X,represents A m N is the total number of observations, when A is determined m F (x) can be determined completely by evaluating the selected variables.
Thus, after the three-dimensional discrete distribution and the continuous distribution are determined, the three-dimensional discrete composite extreme value model can be obtained:
the distribution function has seven unknown parameters, so that the influence of typhoon on the wave height of the sea waves can be more carefully reflected, and the result is more scientific and reasonable.
2.2 application of the model
In this embodiment, the typhoon wave data of 27 years from the observation station to the continental island in the yellow sea area is used to estimate parameters of the established new model, and the wave heights under the influence of three characteristic factors of typhoon are subjected to one-time value of 20 years, 50 years, 100 years and 200 years, and compared with the results obtained by the traditional model.
2.2.1 discretization and parameter estimation of typhoon characteristic factor data
Because the extreme condition of the wave height of the sea waves is considered, the probability statistical analysis is carried out by utilizing typhoon data appearing in the yellow sea area for 27 years and the maximum value of the wave height of the sea waves caused by typhoons every year in the section.
Through the analysis in the previous chapter, the maximum wind speed of the bottom layer center of the typhoon, the shortest distance from the center of the typhoon to an observation point and the occurrence frequency of the typhoon are selected as three discrete variables in the model. Now discretization is performed based on the given data material.
Because the maximum value of the sea waves under extreme conditions is considered, typhoon data which influences the strength of the yellow sea area to the maximum degree every year is selected for analysis
According to the grades divided by the Chinese weather service bureau typhoons, the typhoons are divided into 6 grades according to the maximum wind speed near the center of the bottom layer of the typhoons, and the table 3-1 shows the typhoon frequency occurring in different grades.
TABLE 3-1 discretization table for maximum wind speed near center of typhoon bottom and parameter estimation value
According to the longitude and latitude of the yellow sea area towards the measuring point of the island, the shortest distance r (nautical miles) from the typhoon center to the measuring point is divided into 7 types: the distance between the maximum typhoon center and the measuring point in twenty-seven years is classified and counted as shown in the table 3-2, wherein the seven intervals are marked as 1 to 7 grades, and the seven intervals are less than or equal to 100, 100-200, 200-300, 300-4OO, 4OO-500, 500-600 and more than 600.
TABLE 3-2 discretization table of shortest distance from typhoon center to measuring point and parameter estimation value
TABLE 3-3 typhoon incidence frequency and parameter estimation
Through the tables 3-1,3-2,3-3, the maximum wind speed from the center of the typhoon bottom layer, the shortest distance from the typhoon center to the measuring point and the occurrence frequency of the typhoon are three-dimensional vectors (y) of discrete random variables 1 ,y 2 ,y 3 ) The display expression for which the three-dimensional probability distribution function is found is
2.2.2 comparison of parameter estimates of wave height and their distribution function
When the design wave height calculation is carried out on the annual extreme value wave height formed under the influence of typhoon, the distribution of the design wave height is generally assumed to conform to Gumbel, weibull or Pearson-III extreme value distribution, so that the function is reasonably set to be generalized extreme value distribution when the design parameters are met for many years through the past epitaxial calculation; however, in the past, the empirical factors are too many, and the artificial interference factors are too many, so the maximum entropy distribution is selected by the present embodiment. As can be seen from tables 3-4, the K-S test performed on the maximum entropy function and the Gumbel distribution function both passed the hypothesis test when the function was extrapolated at a significance level of 0.05. It is reasonable to choose the maximum entropy to fit the extreme wave height data.
Tables 3-5K-S test values for maximum entropy distribution and Gumbel distribution
Fitting calculation is carried out on the maximum entropy distribution function of the wave height, the Gumbel distribution function and actual wave height data, and it can be seen that the fitting condition of the maximum entropy distribution is obviously better than that of the Gumbel function.
2.2.3 use of the new model to calculate the design wave height over the years
From the given typhoon wave data, all function related parameter values are calculated as in tables 3-6. Thus, the display expressions of all functions are expressed.
Tables 3-6 three-dimensional Session distribution parameters, maximum entropy and Gumbel distribution function parameter estimates
Based on the parameters sought, the present example finds the different levels of recurrence for the four different composite distributions, as shown in tables 3-6.
Tables 3-6 design wave height values of different reproduction periods calculated by different design models
As can be seen from tables 3 to 6. The design wave height is slightly higher than other methods and is much higher than other methods in years under the influence of the three characteristic factors of typhoon. In fifty years, one in one hundred and two in one hundred, the designed wave height value is respectively 9.92%,9.46% and 7.78% higher than the two-dimensional Poisson maximum entropy distribution; the ratio of the distribution of the maximum entropy to the distribution of the maximum entropy is respectively 10.45 percent, 11.30 percent and 8.65 percent; the maximum entropy distribution is higher by 15.25%,16.04% and 11.83%; obviously, the wave height value of the design obtained by the three-dimensional session-maximum entropy distribution in many years is larger than that of the other three distributions, so that the conclusion that the three-dimensional session-maximum entropy distribution contains all the information of the two-dimensional composite distribution and the one-dimensional composite distribution can be obtained. Meanwhile, according to the analysis of the chapter II, the future development of the typhoon strength is strengthened, so that the caused extreme wave height is higher and higher, and the result shows that the influence of the typhoon on the extreme wave height is effectively considered by the three-dimensional Poisson maximum entropy composite distribution method, and the design wave height is stricter when the reproduction period is longer, which is favorable for considering the extreme condition of ocean engineering; meanwhile, the traditional single-factor method is slightly low in design extreme wave height and possibly brings certain hidden danger to coastal engineering, and the new model achieves good compromise in two important aspects of safety and economy in ocean construction. Therefore, the model provides a reliable theoretical basis in the construction of protective measures such as breakwater and breakwalls in coastal engineering and offshore platform operation. Is very valuable for practical application.
3 conclusion
The embodiment firstly analyzes the interrelation of each characteristic factor of the typhoon in detail, and analyzes different influence mechanisms and joint influence mechanisms of each characteristic factor on the sea waves. Analysis results show that the generation of the wave height of the extremely large sea waves is not a result of single factor action in the typhoon characteristic factors but a result of combined influence of a plurality of characteristic factors.
In order to clarify the degree of correlation between them, the present embodiment uses a rank correlation coefficient method to find the rank correlation coefficient between each characteristic factor of the typhoon, which reflects that the harmony between the lowest air pressure in the center of the typhoon and the maximum wind speed of the typhoon is the highest, and the other correlations are lower. It also indicates that the correlation between the typhoon center moving speed and other characteristic factors is the lowest. On the basis, the characteristic factors of typhoon and the corresponding maximum wave height value caused by the typhoon are analyzed by a rank correlation coefficient method, and the rank correlation analysis is carried out, and the result shows that: the rank correlation coefficient of the lowest air pressure of the center of the typhoon and the maximum wind speed near the center of the bottom layer and the wave height is highest, the harmonious degree of the maximum wind speed radius of the typhoon and the wave height is higher, the typhoon frequency is higher than 0.5, and the influence degree of the typhoon moving speed and the wave height of the sea wave is the lowest, so that the typhoon moving speed and the wave height are almost irrelevant.
According to the calculation results, three variables of the maximum wind speed of the center of the bottom layer, the shortest distance between the center of the typhoon and the observation sea area and the landing frequency of the observation sea area are finally selected, and the typhoon characteristic factors under the influence of the plurality of characteristic factors of the typhoon are predicted all the year round. Therefore, the comprehensive influence of typhoon on sea waves can be reflected.
And finally, on the basis of a composite extreme value theory, a composite extreme value distribution model in which discrete variables are formed by three-dimensional discrete mission distribution and continuous variables are formed by maximum entropy distribution is deduced by utilizing a probability measure correlation theory. The new model can embody the influence of three main characteristic factors of typhoon on the wave height of sea waves, and is more comprehensive and more reasonable than the previous one-dimensional discrete composite distribution model only considering typhoon frequency.
And estimating parameters in the new model by using typhoon and wave height data of the yellow sea area 27. The specific distribution function of the model is determined and a distribution function graph is drawn. The maximum wave height values of 10 years, 20 years, 50 years and 100 years are respectively calculated. And comparing and analyzing with the evaluation value of the one-dimensional discrete composite extreme value distribution. The results show that the design wave height is slightly higher than that of other methods and is much higher than that of other methods in consideration of the influence of three characteristic factors of typhoon in years. According to the analysis of chapter II, the future development of the typhoon strength is enhanced, so that the caused extreme wave height is higher and higher, and the result shows that the composite entropy method effectively considers the influence of the typhoon on the extreme wave height, and the design wave height when the recurrence period is longer is stricter, which is favorable for the consideration of extreme conditions of ocean engineering; meanwhile, the method also shows that the traditional single-factor method is slightly low in design extreme wave height and may bring certain hidden danger to coastal engineering. Therefore, the model provides a reliable theoretical basis in the construction of protective measures such as breakwater and breakwalls in coastal engineering and offshore platform operation. Is very valuable for practical application.
In the embodiment, all characteristic factors in the typhoon generating process are firstly analyzed, the mechanism of the influence of the characteristic factors on the wave height of the sea waves is researched and analyzed, and the influence mechanism is clearly analyzed. And then, the characteristic factors are combined with actually measured data of the observation station to perform correlation analysis in the non-traditional sense. And then, carrying out correlation analysis on the characteristic factors of the typhoon and the wave height of the sea waves under the influence of the characteristic factors by using a rank correlation coefficient analysis method, and selecting the typhoon characteristic factors which are inconsistent with each other and have high correlation degree with the wave height of the sea waves as the characteristic factors for establishing the model. And finally, by deducing a new model and utilizing the measured data, the established model is checked. The method is based on long-time typhoon data statistical analysis and utilizes a new model to predict the extreme value wave height caused by typhoon, and has certain guiding significance for coastal zone planning and coastal engineering protection. The calculation result of the established calculation model provides a basis for the defense standards of oceans, coastal engineering and disaster prevention departments.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (2)
1. A method for analyzing influence of typhoon characteristic factors on wave height of sea waves is characterized by comprising the following steps:
the analysis method is characterized in that 3 discrete variables represented by three typhoon characteristic factors and a continuous variable represented by wave height or water level are compounded into a new distribution mode;
the three typhoon characteristic factors are respectively the landing frequency of the typhoon in an observation sea area, the maximum wind speed near the center of the bottom layer of the typhoon and the shortest distance from the center of the typhoon to an observation point; that is, the intensity of typhoon itself, the distance from the observation sea area to the center of typhoon and the frequency of typhoon happening in the sea area all affect the extreme wave height and the extreme water level;
deriving a three-dimensional discrete-maximum entropy composite extreme value model according to the statistical characteristics of the three typhoon characteristic factors;
theorem set xi, eta m ,Is a continuous type random variable, and η m Obey distribution Q m (x) Xi obey the distribution G (x), let y 1 ，y 2 ，y 3 Is equal to η m ,Xi is a random variable with independent value of nonnegative integer, and xi is memorized ijk Is xi when y 1 ＝i,y 2 ＝j，y 3 Current observed value of = k
p ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 ＝k)，i,j,k＝0,1,2,...,
Define random variable ζ
The distribution function of ζ is then:
is easy to see F (x) = F 0 (x)-ε(x)，
F 0 (x) Is exactly the sum of m ,The distribution of the peak and the distribution of the xi form three-dimensional discrete composite extreme value distribution;
definition (y) 1 ,y 2 ,y 3 ) Is a three-dimensional discrete random vector with probability distribution as follows: p is a radical of ijk ＝P(y 1 ＝i,y 2 ＝j,y 3 K), ξ obey a continuous profile G (x), remembering
Scale F 0 (x) A composite distribution formed by the two distributions;
in practical situations, three characteristic factors of typhoon must be all greater than 1 to affect sea waves; if one of the measuring points is zero, for example, when the typhoon intensity is zero and the frequency of the typhoon is not zero, the shortest distance from the center to the measuring point cannot exist; therefore ε (x) is apparently 0; thus solving for
F (x) = R, F may be substituted 0 (x) R, while neglecting ∈ (x), so that the problem can be simplified;
in practical engineering applications, the selection of typhoon landing frequency follows the distribution of sessions, and therefore (y) is selected 1 ,y 2 ,y 3 ) Obeying a three-dimensional mission distribution; through analysis, the correlation coefficients of the typhoon intensity, the shortest distance from the typhoon center to the measuring point and the typhoon occurrence frequency are very small, so that three variables can be approximately regarded as being correlated and independent, and the distribution obeyed by the three characteristic factors is as follows:
wherein lambda, mu and eta are three unknown parameters which can be estimated from the measured data;
because the wave height under the influence of typhoon is in accordance with continuous distribution, in order to reduce the priori of the wave height of the design, the wave height xi is selected to obey the maximum entropy distribution; the derivation of the maximum entropy distribution function has a better theoretical basis, the function comprises four parameters, existing data can be fitted more finely and flexibly, and the four parameters respectively appear in the positions of coefficients, powers and indexes;
assuming that the random variable X is the wave height, assuming that the wave height conforms to the distribution f (X), the entropy function of the wave height X
Is composed of
The maximum entropy distribution of the wave height X is:
euler equation of
The maximum entropy probability density function of X is of the form:
x represents wave height under the influence of typhoon; f (x) satisfies the following constraint
(d)
(e)
(f)
The mathematical expectation of the extreme wave height X is recorded as E (X), the variance is recorded as D (X), and then the formula (3-5) is substituted into the three constraint conditions for calculation to obtain the product
With A m Marking the m-th origin moment, i.e.Can obtain the product
Order toAnd with B k S and K respectively represent K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution, and according to definition and the relation between the origin moment and the central moment, the K-order central moment, skewness (skewness) and kurtosis (kurtosis) of extreme value wave height distribution have
Gamma and zeta can be obtained by solving the equation set (3-9), beta can be obtained by substituting gamma and zeta into the formula (3-7), and alpha can be obtained by substituting gamma, zeta and beta into the formula (3-6); therefore, as long as the expected E (X), the variance D (X), the skewness S and the kurtosis K are calculated (estimated) by the extreme wave height sequence, 4 undetermined parameters in the maximum entropy distribution function (3.5) can be obtained by solving an equation system;
both gamma and zeta in the equation set (3-9) are contained in the gamma-function and are not explicit solutions, and the solutions need to be completed through numerical calculation and an iterative method, wherein an iterative relation is established through Newton iteration, an iterative process is controlled through an Euclidean algorithm, and the numerical solutions of gamma and zeta are obtained; a. The m Obtained from the arithmetic mean of the measured data;
therefore, after the three-dimensional discrete distribution and the continuous distribution are determined, the three-dimensional discrete composite extreme value model can be obtained:
the distribution function has seven unknown parameters, so that the influence of typhoon on the wave height of the sea waves can be more carefully reflected, and the result is more scientific and reasonable.
2. The analytical method of claim 1, wherein: the distribution function of the zeta is
The following was demonstrated:
note the book
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