Joint probability analysis of marine environmental elements

Abstract Reasonably determining the fortification criterion is one of the important links in the design of breakwaters and flood walls, and it is directly related to the construction cost and protection efficiency of these engineering works. Wave height is one of the most important element of the marine environment determined by the breakwater and flood protection standards. Based on the stochastic process theory, this paper gives a mathematical description of the stochastic process that can reflect the deeper level of statistical characteristics regarding the wave heights. By regarding the number of typhoons in a certain sea area as a Poisson process, this paper establishes a new model for the joint probability analysis of marine environmental elements: the nested random composite distribution model, and it gives the display expression of the new model. We also take typhoon data, wave height, and water increase data under typhoon influence from Weizhou Hydrological Station in western Guangdong, China from 1990 to 2016 as samples, and use the Gumbel-Pareto distribution as the edge distribution to apply the nested random composite distribution model to typhoon-affected sea areas. The joint recurrence period under different time combinations is calculated, and the joint statistical characteristics of the same element or different elements in different periods are also given.