Etrapolation of Historical Storm Data for Estimating Design Wave Heights

Abstract

ABSTRACT An improved method is presented for using a small amount of available wave height information to estimate extreme value statistics for selecting offshore platform design waves. The method permits flexibility in choice of distribution functions through use of computerized procedures, estimates extrapolated wave height uncertainty due to small sample size, and includes criteria for judging whether or not given wave height values can be represented by one or more of the distributions implemented in the method The relevance of-uncertainty to selection of design wave heights, is discussed and illustrated. INTRODUCTION The problem of selecting design wave heights for offshore platforms has many facets, ranging from the development of oceanographic data to the selection of the prudent level of engineering risk for a particular installation. This paper describes an improved method for using a small available amount of wave height information to estimate the extreme-value statistics and associated uncertainties for the large storm waves that have a very low probability of occurrence. Hindcast wave height information for design wave studies usually covers a period of historical record that is shorter than the return period selected for acceptable engineering risk. Return periods commonly used for selection of design waves are, 100years or more, but good meteorological data, on which the calculated wave heights are based, can rarely be obtained for periods covering more than 50–60 years. As a consequence, extrapolations to longer return periods are necessary. Present methods for making the extrapolation employ probabilistic models through the use of special probability graph papers on which a family of distribution functions plot as straight lines. The wave heights are plotted versus their "plotting-position" return period, and a straight line fitted to the plotted data is extended beyond the data to estimate extreme wave heights for return periods of interest. The methods are described in numerous technical papers and books; references 1 through 5 are examples. The shortcomings of the present commonly used methods are:the straight line drawn through the data is in most cases visually fitted to the data, thus is subject to error; andno information is available on the uncertainty of the resulting extrapolation. These shortcomings have been discussed by many authors, and many of their concepts influenced this studyl-4. The improved method presented in this paper offers:greater flexibility in the choice of distributions through computerized procedures,guidelines for picking the "best" distribution from several implemented in the method, andprocedures for estimating the uncertainty of extrapolated wave heights. PART I - EXTRAPOLATION METHOD Two types of probability models are used in the extrapolation method one, a conditional probability estimating maximum wave heights, given that a storm exceeding a specified wave height threshold occurred; the other, the Poisson distribution estimating the number of storms that exceeded the specified threshold in a given time interval.