Long-Term Wave Probabilities Based on Hindcasting of Severe Storms
Authors: Jahns H.O. , Wheeler J.D. 
Published: December 2007

In these new procedures for estimating long-term wave probabilities, special emphasis is placed oil wave-crest statistics. An analysis of data from Gulf of Mexico hurricanes indicates that for some water depths extreme crest heights may be more frequent than would be predicted on the basis of random noise wave theory.

Introduction
Offshore operators are becoming increasingly aware of the statistical nature of environmental conditions that enter into design considerations for offshore structures. Foremost among these considerations is the determination of a "design wave" that the structure must be able to withstand without drainage. Several recent publications' -- discuss the problem of selecting such design waves in accordance with a specified risk level, usually expressed in terms of a recurrence interval. This statistical approach is based on the implicit assumption that it is not possible to determine a useful, or meaningful, upper limit of wave conditions that may be encountered at a given location over a long period of years. Therefore, it may be assumed that any wave condition that can reasonably be selected for deign purposes has a finite probability, however small, of being exceeded during the life of the structure. The designer is faced with selecting the design conditions so that this probability is small enough to be acceptable in view of the safety requirements and environmental and economic factors that may be involved in each particular case. Several authors base the selection of design-wave criteria on estimated recurrence intervals for the maximum sea state* generated by severe storms. The frequency of extreme sea states can be estimated by oceanographic "hindcasting" based on historical weather records, usually in the form of synoptic maps showing barometric pressure and wind velocities. Inherent in this approach is one basic difficulty, which results from the statistical nature of storm waves: The design sea state with a given recurrence interval is not sufficient to define a design waive for a given recurrence interval, Usually, a design-wave height is simply obtained by multiplying, the significant wave height of the design sea state by some factor, typically in the range of 1.8 to 2.0. Random noise theory can be used to estimate the probability that this design-wave height will be exceeded when the design sea state is experienced for a given length of time. However, the design-wave height may also be exceeded in other sea states, both lower and higher than the design sea state. Thus, there is a range of sea states that contribute to the probability that a wave higher than the design wave will be experienced, and this whole range should be taken into account if the recurrence interval for a given wave height is to be estimated. Proper evaluation of long-term wave-height probability requires that the wave-height distribution probability requires that the wave-height distribution function for a given sea state be integrated over the distribution of sea states. This approach has been followed by several authors. Their methods are based on actual wave observations, which are used to obtain the distribution of sea states. While this is the most direct approach, it is often difficult to apply because of a lack of reliable wave data.
JPT
P. 473