INTRODUCTION 
N ORDER to forecast sea and swell from 
weather data it is necessary to know the charac- 
ter of the waves produced by a given wind that 
blows for a known length of time over a known 
stretch of water, the fetch. Prior to 1942 such 
knowledge was based on empirical relationships 
many of which were inconsistent among them- 
selves. In the fall of 1942 a need for sea and swell 
forecasts arose in connection with the planned 
invasion of North Africa. In order to improve 
the basis for forecasting, the authors began their 
studies at the request of the Oceanographic Divi- 
sion of the Directorate of Weather, Army Air 
Forces. 
Preliminary conclusions were helpful in the 
African and Mediterranean operations but con- 
sistent results were not achieved until the summer 
of 1943. By that time all oceanographic work 
had been transferred to the United States Navy. 
Under contracts with the United States Hydro- 
graphic Office and the Bureau of Ships, the studies 
of sea, swell, and surf were carried on at an 
accelerated pace. 
In this paper a close combination of theoretical 
conclusion and empirical knowledge is attempted. 
From a study of the processes by which energy is 
transmitted from wind to waves, certain energy 
equations are derived which relate wave height and 
velocity to wind velocity, duration of wind, and 
fetch. In order to solve these equations it is 
necessary to make certain formal .assumptions. 
The physical significance of these assumptions are 
as yet obscure but the solutions obtained are in 
some cases in agreement with empirical relation- 
ships and in other cases they remove inconsisten- 
cies which have arisen because the relative import- 
ance of the different variables had not been clearly 
recognized. 
The present paper is a revision of a report, 
Wind Waves and Swell; A Basic Theory for 
Forecasting, which was submitted to the Hydro- 
graphic Office in September 1943, but which could 
not be released because of wartime restrictions. 
In the revision a few changes in the theory have 
been made, partly because some of the original 
assumptions were too arbitrary and partly because 
some new approaches have been stimulated by 
C.-G. Rossby’s recent studies of wave motion. 
When the original paper was prepared it was 
believed that the results would apply to “the 
larger waves present” but no attempt was made to 
describe these larger waves more specifically. It 
is now proposed to introduce a statistical term and 
to define ‘the larger waves’ as waves having 
“average height and period of the one-third 
highest waves.’’ The waves described by these 
averages are called “significant waves,’’ because 
experience gained so far indicates that a careful 
observer who attempts to establish the character 
of the higher waves will tend to record the signifi- 
cant waves as defined here. The concept of 
“significant waves’ is important because only 
the significant waves are known empirically, and 
because for these waves the classical requirement 
that crests are conserved is not fulfilled. There- 
fore, the growth and decay of significant waves 
do not obey the laws that would apply to the 
waves of the classical theory, but take place 
according to other laws that will be developed 
in this paper. 
All solutions which relate waves to wind can 
be represented as relations between nondimen- 
sional parameters, but because the empirical data 
available in 1943 were too incomplete to be shown 
in this form, nondimensional presentations could 
not be used for comparison between theory and 
observations. Through the efforts of agencies 
partaking in wave research new and more com- 
prehensive material has now made it possible to 
check the nondimensional relationships against 
observations. 
As a whole, the changes are few considering the 
intensity with which wave research has been 
carried out since 1943. The basic numerical 
relationships between wave height and period as 
functions of wind velocity, fetch, duration, and 
distance of decay differ only slightly from those 
proposed in 1943 and used subsequently with 
considerable success in sea and swell forecasting 
during the war. 
