ANALYSIS OF DATA 

 DISTRIBUTION PATTERNS 



Examination of Figures 1 through 4 shows that all have a similar type of frequency 

 distribution, that is, distributions peak towards the lower wave heights. Similar distributions 

 presented in Figure 11 of Reference 6 also showed such patterns. The data presented there^ 

 were compiled from charts of observations made by Japanese merchant ships in the North 

 Pacific during the 15-yr period from 1924 through 1938. These charts^ are available at the 

 U.S. Hydrographic Office at Suitland, Maryland. Areas of observations were broken down into 

 2-deg squares, that is, 2 deg latitude by 2 deg longitude. A study of these charts, which 

 present the data in the form of histograms, leads to the conclusion that, in general, these 

 histograms are also peaked in the direction of the lower wave heights. 



On the basis of a study of the experimental data thus far available to the author, there 

 is a strong indication that the frequency distributions of wave heights may be approximated 

 by a straight line when plotted on logarithmic probability paper. Figure 5 shows some of the 

 patterns obtained from the data of Figures 1, 2, and 3 and Reference 6. This approximation 

 of the wave-height distributions by a straight line means that they approach a logarithmically 

 normal distribution, that is, if the frequency is plotted as a function of the logarithm of wave 

 height, the distribution will be normal. 



FITTING MATHEMATICAL CURVES TO FREQUENCY DISTRIBUTION 



In addition to the log-normal curve two other types of curves have been fitted to the 

 Weather Bureau data (Figure 1) in order to find a suitable mathematical function which might 

 be used to represent the observations. The Weather Bureau data were chosen because they 

 appeared to have been obtained by the most reliable and consistent sampling procedure. The 

 fitted curves are shown in Figures 6 and 7. The first is a Pearson Type I Curve whose shape 

 is based on the values of the moments fi- of the given fi-equency distribution and whose origin 

 is taken at the mode computed from the measured distribution. The curve is defined by the 

 equation given in Figure 6 and discussed in Appendix 1. The second fitted curve. Figure 7, 

 is of the form known as the "random walk" distribution. It has been shown^ that if the sea 

 elevation ^ may be represented by a narrow spectrum, the probability that at any fixed location 

 the wave height A lies between h and h + dh is approximately 



P(h)dh-^e ^^ dh [1] 



where hP- is the mean of h?. If the sea has a narrow spectrum, the elevations ^ of the wave 

 surface have a normal distribution, see Figure 8. 



