OCEAN WAVES AS A METEOROLOGICAL TOOL! 
By W. H. MUNK 
University of California, Scripps Institution of Oceanography and Institute of Geophysics 
Introduction 
Since ancient times seafarmg men have recognized 
the significance of ocean waves as a sea-borne storm 
warning. However, their interpretation was intuitive, 
based upon the experience gained in a lifetime at sea. 
The first attempt to apply this ancient art as an aid 
in weather forecasting appears to have been made in 
New Zealand around the turn of the century.2 Yet no 
quantitative methods were developed until World War 
Il. We shall describe the three general methods which 
present themselves at this time. Hach of these has its 
advantages and disadvantages, but it is too early to 
state whether these methods will find widespread appli- 
cation. 
The Height-Period Method Applied to Visible Swell 
This method is based on the relationships established 
for forecasting sea and swell from weather maps [15, 
16].° It consists of computing the wind speed U in a 
storm area, the distance D from the storm area, and 
the travel time ¢> of a swell, making use of measure- 
ments of the swell height H> and period 7’p. A discus- 
sion of these quantities is found in another paper.’ 
Wave height and period refer to deep water, and to the 
significant waves, that is, the average of the highest 
one-third of all waves present. Observations from ship- 
board can therefore be taken without further modifica- 
tion. In the case of land-based observations the wave 
1. Contribution from the Scripps Institution of Oceanogra- 
phy, New Series No. 512. Many of the results discussed here 
are based on research carried out for the Hydrographie Office, 
the Office of Naval Research, and the Bureau of Ships of the 
Navy Department, under contract with the University of Cali- 
fornia. 
2. Prof. C. EH. Palmer, in a letter to the author, writes, ‘In 
the early days of weather forecasting in New Zealand (towards 
the end of the last century) no information from Australia was 
available, consequently the only meteorological warning of 
storms coming from the west was the local fall in the barometer. 
In an endeavor to get more advanced warnings, Captain Edwin, 
who was then in charge of a very small weather forecasting 
organization in the Marine Department, used the observations 
of sea and swells from light houses to supplement the data on 
the synoptic maps. These old maps are still in the archives of 
the New Zealand Meteorological Service and I have studied 
them with some interest because the reconstruction of the 
storm positions and tracks by means of the ocean observations 
seems remarkably good.”’ 
3. Consult “Forecasting Ocean Waves” by W. H. Munk-and 
R.S. Arthur, pp. 1082-1089 in this Compendium. 
4. In estimating wave heights from visual observations 
there is a tendency to arrive at values well in excess of the mean 
heights for all waves present. The definition of significant 
waves given above has been found in accord with the estimates 
of most observers. 
period can be determined at any depth since it does not 
change as waves enter shallow water. Along steep coast- 
lines or exposed beaches with simple bottom topography 
the deep water wave height can, for practical purposes, 
be taken as the wave height one or two wave lengths 
outside the breaker zone. Otherwise it is necessary to 
take into account, by means of specially constructed 
“refraction diagrams” [7, 12], the effect of bottom to- 
pography and of the configuration of the coastline. 
The nondimensional relationships given below follow 
from the forecasting theory [16]: 
U2 1 1 al (1) 
gHp ie 2a orp op : 
D 3 2) | 
a ; = (22 2 
iT 1.72 X 10 E ie (2) 
> _ 916 x 10! E = ey | (3) 
Tp : . Or ? 
I 
Qa Hp 
op = @ T (4) 
dr = dr(Br), (5) 
Br = Br(gt/U), (6) 
where g is gravity, and ¢ the storm duration. The rela- 
tionships (5) and (6) are very complicated analytically, 
and are here presented in graphical form (Fig. 1). Equa- 
tions (1) to (6) contain seven unknowns, and the quan- 
tities U, D, and ty are therefore not uniquely determined 
from measurements of swell height and period. To ob- 
tain a complete solution a relation 
i= t(U) (7) 
will be assumed between the duration of the storm and 
its intensity, based on the common experience that 
high winds are usually of short duration. For two spe- 
cific relationships, a storm of unusual duration (line 
A in Fig. 2 inset), and a short-lived storm (line B), 
equations (1) to (7) have been solved and the results 
shown graphically (Fig. 2), using practical units. The 
examples in Table I illustrate that D and tp do not 
depend very critically upon the nature of the relation- 
ship ¢(U) and can be determined with greater certainty 
than U. To obtain greater accuracy the forecaster may 
attempt an interpolation between Cases A and B, based 
on his experience with the duration of storms over par- 
ticular regions. It should be noted that the results ob- 
5. Equation (8) has been revised according to equation (1) 
in R. 8. Arthur, “Revised Wave Forecasting Graphs and Pro- 
cedure.”’ Scripps Institution Wave Report 73, March 1948 (un- 
published). 
1090 
