Research On POT-Copula Method In The Calculation Of Extreme Water Level And Its Application

The return period value of extreme water level is an important marine hydrological parameter.The accurate predictability of the extreme water level is the basis for the formulation of coastal protection standards and the design of marine engineering,and is of great significance to the safety and economy of the project.At present,sampling method of annual maximum series was used in these major countries.This method does not have a high data utilization rate,and requires a continuous sample long enough to ensure the accuracy of the result.If the annual maximum value is missing,it cannot be applied;in addition,the annual maximum method directly processes the water level data formed by the combined effect of astronomical tide and storm surges.As a univariate frequency analysis method,the impact of each variable on the water level change is not reflected in the calculation process.In order to overcome the limitation of traditional water level calculation method,based on the grouping sampling method and composite extremum theory,this thesis discusses the compound distribution model of return period value of extreme surges.The Copula function is used to construct the joint distribution of astronomical tide and random surges and calculate the water level in the return period.The main work and results of the thesis are as follows:(1)On the basis of the commonly used grouping method time window method and double threshold method,time window with a small threshold grouping method suitable for water level data processing is proposed.The method has clear steps and strong operability,and can quickly obtain independent samples that meet the requirements of the over-threshold model.(2)Based on the time window sampling method with a small threshold and the multivariate compound extremum theory,the P-GP(Poisson-Generalized Pareto)composite distribution method for the calculation of return period level of surges is obtained.In the process of thresholding,the theory of change point is introduced,and the method of thresholding the average life graph is improved.The compound distribution method was compared with the annual maximum method to verify feasibility(3)Using the Copula function to construct the joint distribution of the annual extreme water level series and the annual extreme surge series,make parameter estimation and goodness-of-fit evaluation for the four types of Archimedean Copula functions.Finally,the joint distribution of annual extreme water level series fitted with Frank Copula function and the joint distribution of annual extreme surge series fitted by G-H Copula function are obtained.Compared with the traditional two-dimensional distribution model,the use of Copula function processing to construct a joint distribution is simple,breaking through the limitation of same the edge distribution,and broadening the application range of the P-GP type of over-threshold model as an edge distribution to deal with multivariate problems.(4)The calculation method of extreme water level is discussed through the joint distribution of astronomical tide and random surges based on Copula function,and compared with the traditional method.For the joint distribution of annual extreme value water level series,the high water level of the recurrence period is obtained by the joint probability method;for the joint distribution of annual extreme value water level series,the high water level of the recurrence period is obtained by the conditional probability method.The method in this thesis overcomes the shortcomings of the return period obtained by different fitting distributions in the single-factor annual extreme value method.Compared with other methods,the calculation results are stable.The results of this thesis show that the method of Copula function with over-threshold method to find the high water level in the recurrence period has the advantages of high data utilization rate,flexible joint distribution construction,stable calculation results,etc.compared with other methods.In the absence of the situation,it has good application prospects.