FORECASTING 
to be made more easily and with greater certainty than 
most types of meteorological forecasts. 
The present status of wave forecasting is that there 
are available methods which permit useful predictions 
of certain wave characteristics from synoptic meteoro- 
logical observations. The theoretical basis of the meth- 
ods does not adequately explain the physical mechanism 
of wave generation and decay. We shall consider wave 
forecasting, the deficiencies of the methods, and some 
of the unsolved problems. 
Sea, Swell, and Surf 
The categories sea, swell, and surf form a natural 
division of the topic of wave forecasting. The latter, or 
more generally, the transformation of waves in shallow 
water, is dealt with by methods which are somewhat 
different from those used in the study of sea and swell. 
The essential features of the surf problem have been 
accounted for physically, whereas this is not the case 
for sea and swell, as previously mentioned. Sea is de- 
termined by the nature of the winds, and the forecast- 
ing of sea depends therefore upon the current and pre- 
dicted synoptic meteorological situation. Swell depends 
to a lesser extent upon the synoptic situation, but its 
characteristics can still be altered by a following or an 
opposing wind during the course of decay. Surf is de- 
termined by factors which are largely nonmeteorologi- 
cal, and we confine our consideration of surf to this 
section, where we note some of the important physical 
factors in the problem. 
As waves move into shallow water the wave length 
and wave velocity decrease. Waves moving at an angle 
to the bottom contours are subject to refraction. The 
wave crests tend to orient themselves parallel to the 
bottom contours. Changes in wave-crest orientation are 
associated with convergence and divergence of energy 
along the crest [11]. As a result, waves over a subma- 
rine canyon are relatively low compared to waves on 
either side of the canyon; the pattern is reversed for a 
submarine ridge. These changes can all be quantita- 
tively accounted for by the lmear-wave theory, 
assuming conservation of energy and constancy of wave 
period [22]. An exception occurs where the waves travel 
over great stretches of shallow water such as exist 
along the coast of the Gulf of Mexico and the shelf east 
of Long Branch, New Jersey. In such eases the effects 
of bottom friction [14] and percolation [13] should be 
taken into account. 
As the waves approach the breaking point the height 
increases rather suddenly, and the wave breaks at 
a depth approximately equal to 44 the wave height. 
Adequate predictions can be based on the application 
of the solitary-wave theory [12]. Waves breaking at an 
angle to the shore set up longshore currents whose 
average velocity can be roughly estimated when bot- 
tom contours are straight and parallel [15]. In the case 
of nearly normal wave approach, longshore currents are 
variable in direction and form an integral part of a 
system of currents, called rip currents [19], which in- 
clude narrow zones of fast flow away from shore. 
Active research is being conducted on the near-shore 
OCEAN WAVES 1083 
circulation [19], including rip currents, on orbital ve- 
locities, and on the important role played by waves, 
particularly breakers, in beach erosion and in the design 
of engineering structures. 
Although a number of characteristics of surf are 
predictable if the deep-water wave characteristics and 
the bottom topography are known [9], it must be noted 
that the basic relationships apply only approximately, 
and even large deviations are to be expected. More re- 
search on surf is indicated, particularly on the problem 
of the mechanism of breaking. 
Forecasting Significant Waves 
The notations given below will be used in the dis- 
cussion which follows. 
F—length of wind fetch (subscript F denotes value of 
variable at end of fetch); 
D—decay distance (subscript D denotes value of 
variable at end of decay distance); 
H—wave height; 
C—phase velocity of wave; 
T—wave period; 
L—wave length; 
6—H/L (wave steepness) ; 
H—nmean energy of wave per unit area; 
x—horizontal distance coordinate; 
é—time; 
tz—duration time of wind; 
U—wind velocity at about 8 m above surface; 
B—C/U (wave age); 
7— tangential stress of wind on sea surface; 
Uy'—mean surface mass transport velocity; 
Ry—mean rate of energy transfer to wave as a result 
of normal wind pressure; 
Rr—mean rate of energy transfer to wave as a result 
of tangential wind stress; 
g—acceleration of gravity; 
s—sheltermg coefficient; 
p—density of air; 
y’—tesistance coefficient applicable to wind. 
The outstanding characteristic of sea and swell is its 
irregularity, and a complete description of the sea sur- 
face requires the introduction of statistical terms. 
Nevertheless, a practical purpose can be served by 
dealing only with the most prominent, or “significant,” 
waves. A definition of the term “significant” is given in 
the following section. One of the major achievements 
of wartime wave forecasting was the development of 
operationally useful methods, one with a theoretical- 
empirical basis [24], and the other primarily empirical 
[20]. We next consider the results and basis of the first 
method, and make a brief comparison with the second. 
Observers have noted that as the wind blows over a 
limited fetch, the wave height and period over the up- 
wind part of the fetch reach a steady state after a 
limited interval of time. As time passes the steady- 
state region expands over the whole fetch. The wave 
height and period at the end of the fetch are determined 
from the wind velocity, fetch, and duration. The rela- 
tionships given below, in terms of nondimensional par- 
ameters, follow from the forecasting theory. 
