The Application And Research Of Multivate Flood Joint Distribution Based On Copula Theory

Multivariate joint probability distribution is a common method to processfrequency analysis of hydrological multivariate characteristic attributes andcombinatorial calculator of encountered flood events. As a new method, Copula theoryhas the strong flexibility and wide applicability when solving hydrologicalmultivariate joint distribution.This paper constructed the joint distribution of two hydrological variables andapplied this distribution to probability of annual maximum flood occurrence time andthe flood regional compostion. Finally sum up the regularity of the occurrence timeand the scale of flood and a conditional expectation of flood regional compostion,which would provide a new train of thought for flood analysis and calculation. Themain content of this article is as follows:(1) After collecting domestic and overseas relevant literature, managed tograsp the hydrological status quo and progress of the study of multivariate jointdistribution, and summarized the advantages of Copula method compared withtraditional methods.(2) Elaborated the basic concept of Copula Theory、correlation analysis andparameter estimation, then discussed the optimal selection problem of the Copulafunction from the qualitative aspect and quantitative aspect.(3) Introduced the orientation data and its common distribution types to thisarticle, and then expounded the Von Mises distribution, at last emphasize theparameter estimation of the unimodal and bimodal mixture of Von Mises distribution.(4) After determining the marginal distributions of the annual maximum floodscale and its occurring time, then gave an approach to find the optimal Copula function,finally established the joint distribution modal of two variables of annual maximumflood with using this best Copula function.(5) Applied the above model to the study of Yichang’s flood data, andestablished the joint distribution of annual maximum flood peak and its occurringtime、the joint distribution of annual maximum volume of60days and its happened starting time, according to this model, discussed the regularity between annualmaximum flood and its occurrence time.(6) Applied the same model to the study of flood regional composition ofJingJiang River, and established the joint distribution of Yichang and regional floodvolume, finally calculate conditional expectation of regional flood.