The distribution of individual wave heights in shallow water has been shown by many workers to differ from the Rayleigh distribution This chapter describes the detailed comparison of storm wave data measured at the West Sole Field in the southern North Sea with a variety of distributions and the identification of the most appropriate distribution for design purposes To achieve this each selected distribution was expressed as a Weibull function of the form: (formula available in full paper) where P is the probability that the height, x, exceeds the value Ho.
The Gluhovski distribution simplified for the local conditions can be described by equation (1) with¿ = 2.2006 and f = 9 9724, for data normalized using the rms sea surface elevation Of the distributions used this was found to provide the best fit to the normalized cumulative probability data. The consequences of using this distribution for the calculation of the most likely wave in a even period are examined further.
Time series of sea surface elevation measured using a calibrated wavestaff were recorded on paper charts The ten most severe storms during the period March 1974 to July 1986 were selected using wave, wind and fetch information. In general, wave records are 17 07 min long and digitized at 2 Hz to eve 2048 data points for further analysis. Because the West Sole chart records are only 10 min long, digitization was carried out at a rate of 4 Hz (in terms of the time series) over a period of 8 53 min to produce the required 2048 data points. Sixteen 8 53 minute samples, recorded at three-hourly intervals, centred on the peak of each storm were digitized, giving a total of 160 digital records. The digital data range was ± 15 24 in with a resolution of 0 73 cm. The storm periods used are summarized in Table I. The wavestaff calibrations were then applied to convert the digital samples from ‘recorded height’ to ‘true height’.
Time series and wave spectra were plotted in order to identify records less than 8.53 min long, noisy records, and records containing errors as a result of the digitization process. The wave data were also flagged automatically to give an indication of the number of failures of quality control checks on each data sample The data were checked for deviation from the sample mean and standard deviation, change in steepness, and breaking waves. A total of 16 invalid records were identified and these were removed from the data base, giving a total of 144 valid records.
The time series records were analysed by hand using the Tucker-Draper method (refs 1 and 2). Computerized analyses were also used to calculate the root mean square of the sea surface elevation and other commonly used spectral and deterministic parameters, the analysis of which is not discussed here.
The raw wave data were normalized by dividing each data value by the rms value of the 8.53 minute sample.
TABLE I Storm data periods (Available in full paper