The data from the sea surface profiles worked up by the Hydrographic Office were 

 used further to obtain the mean square of the wave height, E. These quantities are also 

 listed in Table 4. In order to check the utility of the theoretical method of Reference 8 for 

 the prediction of wave heights, the Hydrographic Office also computed the mean square of the 

 wave height E on the basis of the distribution of wind velocities for the sea area and sea sur- 

 face profile in question; these values are listed in the last column of Table 4. Graphs of 

 these various quantities are presented and discussed in Appendix B, Figures 34 through SB- 

 STATISTICAL BACKGROUND 



Wave heights and wave periods estimated from the Weather Bureau data for ten ocean 

 stations are presented in the form of their distribution functions. For example, all wave 

 heights reported by the shipboard observers are considered to be members of a statistical 

 "population" of wave heights. The distribution function of wave heights indicates the rela- 

 tive probability of encountering a wave of a given height as a function of that height. Figure 

 5 illustrates this distribution function. The area under the curve to a value x- is the integral 

 of the function up to x i and is equal to the fraction of all members of the population of wave 

 heights which have a height less than a?.. Mathematically 



X oo 



P (x) = I pdx and P (x -» oo) = I pdx = 1 

 



0.18 



0.16 

 0.14 



0.12 



c 

 Q 0.10 



o0.08 

 o 

 a 

 0.06 





















































<~ 



\ 

















f 





^ 



\ 













/ 



' 







I 



Experimental 

 X Data 









/ 









4 













0.02 



J 







< 













/ 



12,365 observations \ 1 

 each of which represents N, 

 a given sea state. 











4 8 12 16 20 24 28 32 



x = Significant Wave Height in feet 

 Figure 5 - Distribution Function 



where p is the probability density and P is 

 a function of x designated as the cumulative 

 distribution function of x. P (x) is numeri- 

 cally equal to the probability that a value 

 chosen at random from the population is 

 less than x. 



A detailed discussion of the statisti- 

 cal methods utilized in this report is given 

 in Reference 9. Only a few of the major 

 concepts will be described here. The dis- 

 tribution applicable to a given sea condition 

 is here called a "short-term" distribution, 

 whereas the distribution applicable when 

 the sea conditions are allowed to vary over 

 a wide range, such as over a year's time, 

 is called a "long-term" distribution. Thus 

 the long-term distribution is the result of a 



