A theoretical basis for the occurrence of rare wave groups is developed. The work is not limited to a successive threshold crossing criteria, only that a derived Gaussian process, based on the wave elevation, has a maximum value in a given exposure time. The theory is compared with numerical Monte Carlo simulations in addition to physical oceanographic data. The wave groups, in run length, shape, and amplitude, are shown to be dependent on the wave spectrum and its spectral moments, a prescribed exposure time, and a pre-selected mean wavegroup period.@en

This paper addresses the existence of rare wave groups by examining time series data from the Pt. Reyes buoy. The buoy is operated by the Coastal Data Information Program (CDIP), University of California San Diego. The definition of rare wave groups, as defined by Kim and Troesch, used in this paper differs from the more commonly used wave group definition based on threshold crossings. With the time series data from the Pt. Reyes buoy, these rare wave groups are shown to be a naturally occurring phenomenon. The essential features of the data are examined, as well as the analysis methods and findings. By sifting through 17 years of wave elevation data from the Pt. Reyes buoy, this preliminary work addresses not only the question to what extent rare wave groups exist in nature but also what their probability of occurrence is.@en