THE STATISTICAL ANATOMY OF OCEAN WAVE SPECTRA 



hy 

 Leon E. Bovgman 



I. INTRODUCTION 



In the future, more and more ocean engineering design considerations 

 will involve the wave energy spectrum. Typically, various secondary 

 calculations will be made from the spectral and cross-spectral estimates 

 at and between various space locations. The statistical reliability of 

 the values obtained from the secondary calculations depend critically on 

 the inherent statistical variability of the spectral estimates. 



The estimation of directional wave spectra is obtained by just such 

 secondary calculations on the auto- and cross-spectral densities or 

 corresponding finite Fourier transform coefficients for various wave 

 properties measured at one or more space locations. The reliability of 

 the directional spectrum depends both on the method of computation and on 

 the intrinsic statistical variability of the Fourier coefficients or spec- 

 tral estimates. Such characterizing quantities as the main direction of 

 wave travel for a given wave frequency or some measure of the arc of 

 directions from which waves of a given frequency are coming each have their 

 own confidence intervals which ultimately relate back, through the method 

 of calculation, to the spectral and Fourier coefficient variability. 



Over the years various theoretical probability relations have been 

 derived which apply to linear waves (Pierson, 1955; Goodman, 1957; 

 Blackman and Tukey, 1958). However, engineers are usually concerned with 

 wave heights large enough to make linear assumptions questionable. Waves 

 in hurricanes and other severe storms are prime examples of this situation. 

 Yet it is just in such situations where probability confidence statements 

 for the wave spectra or for derived secondary quantities are needed. 



In the following report, the statistical variations in wave energy 

 spectral estimates for hurricane waves are examined empirically for 12 

 separate intervals of wave record measured during Hurricane Carla (Septem- 

 ber 1961) . The measurements were made on a Chevron Oil Company platform 

 in South Timbalier Block 63, Gulf of Mexico, in a 100-foot water depth. 

 Hurricane waves were chosen for the analysis because they would illustrate, 

 in exaggerated form, the effects of departures from linearity on the 

 statistical variability in spectral estimates. 



Various aspects of the study were reported at the 13th International 

 Conference on Coastal Engineering in Vancouver, B.C., 10 to 14 July 1972, 

 for one 20-minute record (Borgman, 1972). This study gives the analysis 

 for the whole storm and develops certain implications and consequences of 

 the empirical results. 



