A MODEL FOR THE DISTRIBUTION FUNCTION 
FOR SIGNIFICANT WAVE HEIGHT 
by 
Edward F. Thompson 
I. INTRODUCTION 
The long-term distribution of significant wave height at a site can be 
estimated from empirical data or by either of two empirical models in the 
Shore Protection Manual (SPM), Section 4.332 (U.S. Army, Corps of Engineers, 
Coastal Engineering Research Center, 1977)!. Where sufficient data are avail- 
able, direct use of empirical data is usually preferable to either SPM model. 
However, proper estimation of the long-term distribution of significant height 
requires the use of an integral number (preferably 3 or more) of reasonably 
complete years of data. This requirement is often difficult to meet because 
of intermittent failure to obtain observations and limited number of years of 
data collection at a site. 
Tt is often convenient to model an observed distribution of significant 
wave height. A model provides a simple parameterization of the observed dis- 
tribution as well as a systematic method for extrapolating to probabilities 
beyond the data (although extrapolations are always much more uncertain than 
the part of the distribution well supported by data because of long-term 
variability in storms producing extreme wave conditions). Since there is no 
compelling physical basis for favoring any particular model, models are chosen 
to fit observed distributions of significant height. The models in the SPM 
were proposed as a tool for representing the distribution of the highest 50 to 
80 percent of observed significant heights. The model presented in equation 
4-6 of the SPM is a two-parameter modified exponential distribution which is 
further simplified in equation 4-9 of the SPM to a one-parameter distribution. 
The model presented in this report is based on a three-parameter Weibull 
distribution function. The three-parameter model can better fit observations 
than either the one- or two-parameter models in the SPM. Parameters are eval- 
uated to optimize the fit to empirical data from a gage at Nags Head, North 
Carolina. The model is formulated in dimensionless terms so that the effect 
of mean significant wave height level is removed. The advantages of using 
dimensionless terms are that more complete use is made of available data and 
that general characteristics of the distribution of significant height in 
addition to the mean can be readily examined. The dimensionless distribution 
function may be relatively invariant compared to mean significant height vari- 
ations along a short section of coast. Hence, the model presented in this 
report is believed to provide a more general representation than the models 
in the SPM. 
ly.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 
Protection Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1, 
U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp. 
