1086 
attenuation. The comparison suggests that travel time 
be computed on the basis of the decay distance and the 
group velocity of the swell at the end of the decay dis- 
tance. The effect of a following wind during decay is to 
give lower swell arriving earlier, and the effect of an 
opposing wind is the opposite. The results for travel 
WAVE STEEPNESS AGAINST RATIO WAVE VELOCITY TO WIND VELOCITY 
12 2 LEGEND 
" PARIS © KRUMMEL 
ie D EHRING © BERKELEY 
Z 10 1 9 METEOR © U.S.S. AUGUSTA 
ts GIBSON © ZIMMERMANN 
a 9 CORNISH © GASSENMAYRS 
me DOVER @ U.S. ENGINEERS 
=a:) SCHOTT  @ H.M.S. FORRESTER 
mm © OFFICERS U.S. NAVY 
“7 
n 
B6 COORDINATES 
w 
= 
we 
f= 
bh 4 
i 
3 
a 
ae) 
! 
Oo. 2.3 4 5 6 7 86 9 LO Ll 12 13 14 15 16 17 LB 
WAVE AGE, B 
Fig. 4.—Wave steepness plotted against wave age. The 
dashed lines represent the part of the theoretical relationship 
which must be modified to conform to empirical evidence. 
time, following wind, and opposing wind are incorpo- 
rated into the forecasting method. 
Groen and Dorrestein [7] attribute the decay and the 
period increase of swell to a selective damping by eddy 
viscosity. The eddy-viscosity coefficient used depends 
on the size of the systems under consideration, and the 
coefficient is larger for long waves than for short ones. 
Groen and Dorrestein point out that it is improbable 
that the values of the sheltering coefficient would be 
the same for swell and wind waves as Sverdrup and 
Munk [24] have assumed. 
TABLE I. PREDICTED AND OBSERVED WAVE 
CHARACTERISTICS 
Per cent 
of cases 
Predicted height within 1 ft of observed 
LASKid nL eee oie cite Pants eR ai Cero Soe 53 
Predicted height within 2 ft of observed 
JeVSeAct eee d Seats Ga POO bios aero ona eee rote es 80 
Predicted period within 2 sec of observed 
Soles rik o{o Mee ahr ptt teeta acta chat teointe d scan ences AS On bleen oct 63 
Predicted arrival time within 6 hr of ob- 
SELVECGtIME! corse tie ene ots Ee 69 
Tsaacs and Saville [10] have compared forecasts made 
according to the method in its present form with 
records from wave meters at Point Sur, California, and 
Heceta Head, Oregon. The results of the comparison 
for a total of more than 200 forecasts for each station 
during the period April to December, 1947, are given in 
Table I. The predicted heights are appropriately cor- 
rected for the transformation from deep water to the 
position of the wave meter. They do not show any 
MARINE METHOROLOGY 
tendency to be higher or lower than the observed 
heights. The predicted arrival times, however, show a 
tendency to be too early and the periods to be too low. 
According to Isaacs and Saville, “97 per cent of the 
recorded significant increases in wave height were fore- 
cast, but 23 per cent of the forecast wave trains failed 
to arrive. The rather large proportion of non-arrivals 
apparently resulted from the erroneous selection of 
fetches... .”” They conclude that the forecasting tech- 
nique “results in a high degree of reliability for fore- 
casting the arrival of significant imcreases in wave 
height, and prognosticating the wave heights,” but that 
“the forecast of wave period and arrival time of the 
peaks of the wave trains does not display the same 
degree of reliability... .’’ Bates [8] reviews the fore- 
casting of sea, swell, and surf for landing operations in 
World War II and concludes that the forecasts were 
basically correct. 
Suthons [20] presents graphs for the forecasting of sea 
and swell, but the empirical data on which they are 
based and the exact methods of preparation are not 
indicated. Predicted wave periods for sea are longer 
from these graphs than from the first method, and 
wave heights lower. If a 6,6-relationship is derived 
from Suthons’ graphs, the agreement with the observa- 
tional data mentioned above (Fig. 4) is not good over a 
wide range of 6 values. Suthons attributes the increase 
in wave period to the downward transport of wave 
energy by molecular and eddy viscosity, but no quan- 
titative discussion of the mechanism is presented. 
The Wave Spectrum 
The great complexity of the waves in the sea ob- 
secures the exact meaning of earlier wave observations 
which form the empirical basis for the forecasting meth- 
ods discussed in the preceding section. Only recently 
has it been possible, by analyzing records from pressure- 
type wave meters, to clarify the relation of the pre- 
dicted wave height and period to the irregular pattern 
actually recorded. 
An individual wave record shows a wide range of 
heights and periods. For many practical applications, 
such as the landing of craft, wave action on structures, 
and sand movement, only the heights and periods of 
the higher waves in the record are significant. The terms 
significant wave height and significant wave period have 
accordingly been defined as the average height and 
period, respectively, of the highest one-third of the 
waves, after ripples and waves of height less than one 
foot are eliminated from consideration [23]. 
Experience shows that observers who attempt to de- 
t_rmine visually the characteristics of waves tend to 
record heights and periods which are approximately 
those of the significant waves rather than of the average 
waves. Since the forecasting method is based on such 
visual observations, one might expect that the pre- 
dicted wave heights and periods are to be considered 
significant heights and periods. This expectation has 
subsequently been confirmed [10]. 
The characterization of a wave record in terms of the 
