FORECASTING OCEAN WAVES 
significant waves gives a useful description of the 
record.* Wiegel [25] finds that the daily average height 
of the highest ten per cent of the waves bears a rela- 
tively constant rel: ionship to the significant height at 
the locations on the Pacific Coast of the United States. 
This fact is of practical importance because less time is 
required to compute the average for the highest ten jer 
cent. A good correlation between the maximum waves 
recorded each day and the significant waves is also 
noted, and Seiwell [17] finds at Cuttyhunk and Bermuda 
that the ratio of the daily average height of all waves to 
the highest one-third is relatively constant. These re- 
sults (Table II) taken collectively indicate that in gen- 
TasieE II. Ratios or Mpan Wave Hercut AnD or AVERAGE 
or Hieuest 10 Per Cent TO Sianiricant Wave HEIGHT 
Observation Point 
Satppet| Pomme, | Beets | Potak | Gut | Ber 
(swell) | Sur [25] [25] [25] | (17) (17) 
Interval over which averages xe: 
onmed bere tes sscyjae 46 three 20-min intervals | 2-min intervals 
waves per day 
Ratio of mean to 
significant ees 0.67 0.64 | 0.64 
Ratio of highest 10% 
to significant...... 1.27 | 1.30 | 1.30 
eral a similar distribution of wave heights prevails in 
the waves generated in different storms although the 
absolute magnitude varies. 
A more detailed interpretation is obtained by sub- 
jecting the records to harmonic analysis. Barber and 
Ursell [2] have pioneered in the development of instru- 
ments for obtaining the Fourier amplitude spectrum. 
The spectra are taken to indicate that a storm pro- 
duces a mixture of trains of waves of all lengths up to a 
maximum which depends on the greatest wind strength. 
The component trains act independently during decay, 
and each travels at the group velocity appropriate to 
its period. In an individual spectrum at a very distant 
station the swell covers a narrow range of periods, but 
at a closer station the wave band is wider and broadens 
rapidly toward shorter periods. Seiwell and Wadsworth 
[18], on the other hand, take issue with such an in- 
terpretation of the component periods in the Fourier 
amphtude spectrum. From a computation of the auto- 
correlation function they reach the following rather 
surprising conclusions which are quoted from their 
summary: 
(1) Periodogram analyses performed on oceanic wave 
records do not appear to give correct geophysical information. 
The numerous wave periods, and bands of periods, indicated 
by this type of analysis do not necessarily possess physical 
significance. 
(2) Application of the hypothesis of generalized harmonic 
4. W. H. Munk, ‘Proposed Uniform Procedure for Observ- 
ing Waves and Interpreting Instrument Records.” Scripps 
Institution of Oceanography Wave Report No. 26, December 
12, 1944 (unpublished). 
1087 
analyses to western North Atlantic wave records indicates 
that ocean wave patterns are not complex interference pat- 
terns resulting from combinations of many wave frequencies, 
but frequently consist of a single sinusoidal wave on which is 
superimposed an oscillatory component... . 
This question of the interpretation of records is funda- 
mental in the consideration of wave generation and 
propagation, and it merits further study. 
_ Problems in Forecasting 
Three main stages in the study of forecasting ocean 
waves from storms can be recognized. In the earliest 
stage the forecasting was based on empirical ‘‘engineer- 
ing rules,’”’ mutually inconsistent and often incomplete. 
The well-known Stevenson’s law, for example, relates 
wave height to fetch without regard to wind speed. The 
second stage was the development during World War 
II of consistent, dimensionally correct relationships. 
These relationships have made it possible to forecast 
the significant waves to an accuracy sufficient for many 
practical applications. Most of the foregoing discussion 
deals with this stage of the development. The relation- 
ships are strengthened by the application of hydro- 
dynamic theory, although the theoretical basis is not 
at all secure. The third stage, and one which we are now 
entering, centers about the British studies of the wave 
spectrum [2, 5], and some recent attempts to forecast 
the entire spectrum [4]. 
According to Deacon [4], 
The width of the spectrum when waves are being generated 
by a rising wind suggests that the energy begins to be dis- 
tributed over a range of wave lengths as soon as the waves are 
formed, some being communicated to the longer wave lengths 
before the shorter ones are fully energized. Each spectrum has 
an optimum band in which the waves are highest. Waves 
shorter than this optimum period are lower, presumably be- 
cause they have a smaller capacity for absorbing energy with- 
out becoming unstable; and longer waves are lower, probably 
because their speed, which is nearly equal to that of the wind, 
allows them less opportunity of absorbing energy. ... The 
period of the highest waves is approximately 25 per cent less 
than the period of the longest waves. 
From this point of view the forecasting of significant 
waves 1s closely related to the forecasting of the opti- 
mum band. An increase in significant wave height with 
fetch, or with wind speed, corresponds to an increase in 
the maximum energy contained in this band, and an 
increase in the period of the significant waves repre- 
sents a shift of the optimum band towards longer pe- 
riods. Since the characteristic of this optimum band 
depends closely on the character of the component wave 
trains longer and shorter than those of the band, it is 
not possible to develop a satisfactory physical theory 
for forecasting the optimum band without regard to 
the remaining portion of the spectrum. Nor is it de- 
sirable to do so, for there are many practical problems 
for which the character of the optimum band is only 
incidental. In the study of the acoustic and optical 
properties of the sea surface the short-period portion of 
