Storm Wave Characteristics
Authors: Robinson R.J. , Brannon H.R. , Kattawar G.W. 
Published: December 2007

Abstract
Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and 98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gull water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given.

Introduction
Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydrodynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire, among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii, establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other area's as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents
- a practical approach to computing wave profiles that depict shapes of waves for use in force calculations,
- a summary of relations for predicting probabilities of wave crest elevations,
- correlations of parameters needed to apply these methods in the Gulf of Mexico and
- examples of application of the techniques.

THEORETICAL BACKGROUND
The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities.