APPENDIX B 

 COMPARISON OF WAVE STATISTICS 



It is of interest to utilize the wave data obtained during the sea tests of the VALLEY 

 FORGE and the UNIMAK to gain some insight into the validity of a few of the assumptions 

 often made in the forecasting and analysis of ocean waves. For this purpose the following 

 items were computed: 



(a) The characteristic wave height was determined from the wave profiles. 



(b) The wave profiles were analyzed according to the method outlined in Appendix A to 

 obtain the frequency distribution of individual wave heights and of the corresponding wave 

 lengths above a certain cutoff length.* 



(c) The mean value of the squares of all individual wave heights corresponding to waves 

 longer than the cutoff length was determined from the data obtained under Item (b). This value 

 is denoted by the symbol E. 



(d) The average value of the upper third of the waves having the largest magnitudes 

 (significant wave height) was determined from the data obtained under Item (b). 



(e) The average value of the characteristic wave heights determined by the shipboard ob- 

 servers was tabulated. 



( f) The Hydrographic Office computed** a theoretical value of E on the basis of the dis- 

 tribution of wind velocities that generated the sea. The method of Reference 8 was used, ac- 

 cording to which E is proportional to the area under the power spectrum of the sea. These 

 values are also given in Table 4. 



In Figure 6, Item (a) is plotted against Item (e). In Figure 34, Item (c) is plotted 

 against Item (f ). In Figure 35, Item (a) is plotted against the square root of Item (f ). In Fig- 

 ure 36, Item (d) is plotted against Item (e). 



Figure 6 indicates that trained shipboard observers can, on the average, estimate the 

 heights of the predominant waves reasonably well. 



The value of E determined from the wind data should agree with the E obtained from the 

 wave profiles provided the theory of Reference 7 is valid, a narrow sea spectrum exists, swell 

 is a negligible factor, and the stereophotograph covered a representative area of the ocean. 

 One may expect considerable deviations from these assumptions; for example, the sea surface 

 profiles sometimes indicate considerable deviation from a narrow spectrum as well as the 



*The cutoff length is that wave length below which lies three percent of the area under the power spectrum. 

 For a detailed description of the power spectrum concept and a method for computing E from wind data, see Ref- 

 erence 7. The numerical values of E given in this report are four times those of Reference 7, since we are deal- 

 ing with crest-to-trough wave heights rather than with wave amplitudes. 



**This computation does not take account of swell that may have been present in the wave system. 



45 



