summation of a number of short-term distributions. Oceanographers have held that the short- 

 term* distribution of wave heights x is approximately of the Rayleigh type (a narrow power 

 spectrum is assumed) for which, 



P(.)- 2- e~ x2/Ei 



where E ■ is the mean square of all the individual wave heights x corresponding to sea condi- 

 tion i. Note that numerically the value of E computed for wave height will be four times the 

 value of E computed for wave amplitude because wave height is taken equal to twice the wave 

 amplitude. See References 8 and 10 for a discussion of the distribution of wave heights in 

 terms of the power spectrum concept. 



In Reference 9, it was suggested that the long-term distribution of wave heights and 

 wave periods is of the log-normal type, that is, that the logarithms of these heights and peri- 

 ods are approximated by a normal distribution. Thus 



p (log a>)rf (logs) = _Le-( !ogI -"» 2/2a2 <i(lo^) 

 a v/2 n 



log a; 



P(x) = P(loga;) = / p(logce) c?(loga;) 



logx =-c 



where p(log;r) is the probability density of the variate, log x, 

 u is the mean value of log x, and 

 a 2 is the variance of log x. 

 Then the parameters u and a define this distribution completely. 



In this report log-normal distributions are fitted to the characteristic wave heights and 

 periods reported by the Weather Bureau. The resultant graphs represent long-term distributions 

 and give the probability with which a given value of the variate x will or will not be exceeded 

 in an average year.** 



*The short-term distribution is approximately valid if measurements are taken over a relatively short period of 

 time, of the order of one hour, during which interval the sea conditions do not change appreciably. It can be shown 

 that this distribution is the same as that representing the wave heights, in the area under consideration, at one 

 instant of time. 



**Although the distributions given here are for a six-year period, study of the distributions for the individual 

 years making up the six-year period indicates that a single year gives a typical sample of the distribution obtained 

 for many years. Therefore, the six-year distribution may be considered valid for an average year. 



