| Summary: | Summary: This paper provides some probabilistic properties of the deep water wave steepness and the spectral wave steepness by using distributions based on data from the Norwegian continental shelf. Here the average statistical properties represented by the mean value and the standard deviation of the two steepness parameters are considered. Examples of results for the wave steepness are given for a Phillips spectrum and a family of JONSWAP spectra for wind sea, and for sea states described by a joint frequency table of significant wave height and mean zero-crossing wave period for combined wind sea and swell. The results for the spectral wave steepness are obtained by using a joint distribution of significant wave height and spectral wave steepness, and the average statistical features are given for joint frequency tables of significant wave height and mean zero-crossing wave period from three locations on the Norwegian continental shelf. Keywords: Wave steepness, Spectral steepness parameter, Phillips spectrum, JONSWAP spectrum, Joint frequency tables, Wave statistics
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