STATISTICAL ANALYSIS OF DIRECTIONAL SEA STATE PERSISTENCE

Abstract

A statistical model for the long-term distribution of wave height duration is developed in this work. The relationship between directional sea state intensity and sea state duration is obtained by means of a mathematical model that describes the bivariate distribution of significant wave height and the duration of the persistence. The application of the methodology to a particular site on the northern coast of Spain shows that the proposed model can be used to determine the wave climate, improving the results from existing formulations. INTRODUCTION Historically, the evaluation of the wave conditions at a particular site has only focused on frequency analysis of the intensity alone, typically significant wave height, H. Wave measurement programs have contributed to the longer duration of available data sets allowing the study for other climate variables. In port engineering operations and also in offshore and coastal engineering, the duration of persistence (D) of the sea state intensity is of considerable interest since it makes the planning of engineering operations possible from a statistical viewpoint. Recently, the new “Recommendations for maritime and harbour works in Spain (ROM 0.0)” (Puertos del Estado, 2001) establish new conditions for the design of maritime works. This handbook establishes that “All maritime work is constructed to comply, during an interval of time, with specific functions, according to certain requirements of reliability, functionability and operativity”. In particular, the operativity, which defines the working 1 Postdoctoral Researcher, Ocean & Coastal Research Group, Dpto. de Ciencias y Tecnicas del Agua y del Medio Ambiente, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain. mendezf@unican.es 2 Professor, Ocean & Coastal Research Group, Dpto. de Ciencias y Tecnicas del Agua y del Medio Ambiente, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain medinar@unican.es 3 Postdoctoral Researcher, Ocean & Coastal Research Group, Dpto. de Ciencias y Tecnicas del Agua y del Medio Ambiente, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain. lomonaco@puer.unican.es Mendez, Medina, and Lomonaco 1 conditions of the maritime structure, must be defined using three indicators: a) the minimum operativity; b) the average number of admissible technical breakdowns and c) the maximum duration of the technical breakdowns. The minimum operativity is usually expressed in terms of a sea state parameter (in general the significant wave height). The technical breakdown is produced when the significant wave height, H, is greater than a value given by the Recommendations. This information is usually represented by the cumulative distribution function (cdf) of the significant wave height , that is, the long-term distribution. So, for the threshold which defines the technical breakdown, the probability of non-exceedance of significant wave height defines the minimum operativity. ( ) H F H As technical breakdown is defined by the significant wave height, the average number of breakdowns and the maximum duration of technical breakdowns can also be calculated using the significant wave height. Nevertheless, in this case it is necessary to consider the sea state curve. Given a threshold that defines the minimum operativity, there is a number of events N and a duration of exceedance, D, different for each one. Both the significant wave height, H, (or the intensity) and the duration of the exceedance, D, above the threshold H are random variables. Therefore, it will be necessary to obtain the long-term distribution of wave height duration, that is, the joint probability density function pdf fH,D(H,D) (see figure 1).