INTERPRETATION OF WAVE ENERGY SPECTRA 
by 
Edward F. Thompson 
I INTRODUCTION 
The ocean usually has more than one independent train of waves propagating 
along its surface in U.S. coastal areas. The common practice of using a single 
significant height and period for a sea state can be misleading because no indi- 
cation is given to the existence or characteristics of other trains. On the 
other hand, an estimate of the wave energy spectrum provides more information 
than is generally used in coastal engineering. The spectrum can be reduced to 
estimates of significant wave height and period for all major wave trains pres- 
ent. A knowledge of these characteristics for major wave trains is often im- 
portant to coastal engineers. 
Spectra are becoming widely available through various field wave measurement 
programs, laboratory tests with programable wave generators, and numerical wave 
hindeasting projects. Because of the availability and applications of spectra, 
practicing coastal engineers should become familiar with spectra and their 
interpretation. 
II. PRIMARY GOAL OF SPECTRAL ANALYSIS 
A fundamental parameter for characterizing a wave field is some measure of 
the periodicity of the waves. For many years a significant period, which could 
be subjectively estimated in various ways, was used. However, the ocean surface 
often has waves characterized by several distinct periods occurring simultane- 
ously. A record of the variation of sea-surface elevation with time, commonly 
called a time series, frequently appears confusing and is difficult to interpret. 
Developments in computer technology and in mathematical analysis of time 
series have provided a practical approach to an objective, more comprehensive 
analysis of periodicity in wave records. The approach is to express the time 
series as a sum of periodic functions with different frequency, amplitude, and 
phase. The simplest functions to apply are the trigonometric sine and cosine 
functions. Thus, the time series of sea-surface deviations from the mean sur- 
face, n(t), is expressed by equation (3-11) in the Shore Protection Manual 
(SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) 
as 
my Gt) a aj Cos (wjt-o3) (1) 
J 
where 
a; = amplitude 
w7 = frequency in radians per second 
$j = phase 
t=) ‘tame 
