EVAPORATION FROM THE OCEANS 
of computing evaporation directly from a knowledge 
of humidity and wind conditions in the lowest layer. 
A first attempt in this direction was made by Wagner 
[28], who had to confine himself to general considera- 
tions and the use of empirical relations established 
over land because the type of studies urged by Schmidt 
had not been made. 
Even today there are available only a few series of 
measurements of temperature, humidity, and wind at 
various levels in the vicinity of the sea surface. The 
interpretation of these few observations has, however, 
helped to throw light on the problem of evaporation, 
but clear-cut results have not been obtained. It is 
necessary to review the manner in which the problem 
has been dealt with by different authors and to evaluate 
the empirical evidence that supports or contradicts 
the different conclusions. 
Theoretical Considerations. When one is dealing with 
evaporation, the moisture content of the air is best 
deseribed by the specific humidity g. The moisture 
concentration (water vapor per unit volume) is then 
equal to pq, and this concentration will be considered a 
conservative property, that is, a property which is 
altered locally (except at the boundaries) by processes 
of diffusion and advection only: 
deg) _ 9 (coe) a (2 a 
ot Ox \p Ox oy\ p oy 
sige ie ue (9) 
0z\p 02 
iy 9 
Ox 
Here A./p, A,/p, and A./p represent the diffusion 
coefficients (of dimensions L? T—!) which are supposed 
to be different in different directions, p is the density 
of the air, and w,, w,, and w, are the velocity com- 
ponents. The definition implies that the following con- 
siderations are not valid if droplets are present in such 
numbers that condensation on or evaporation from 
these droplets cannot be neglected. 
Equation (9) has been used in very simplified forms. 
If we assume stationary conditions (0(pq)/dt = 0), 
motion along the x-axis only (w, = w. = 0), and 
neglect horizontal diffusion (Az 0(pq)/dx = A, 0(pq)/oy 
= 0), equation (9) is reduced to 
f) C 7 _ 9(pqws) 
dz\p a2 Gap 
In this form it has been applied by Sutton [22] to the 
problem of evaporation from a limited body of water. 
His theoretical conclusions are in good agreement with 
the results of experiments in the laboratory and con- 
ditions observed in the field. Other similar studies have 
been carried out and have led to the clarification of 
experimental results, but they are not applicable to 
the problem of evaporation from the ocean because the 
ocean surface must be considered as a water surface 
of infin'te extension, directly above which the hori- 
zontal gradients of moisture content are negligible. 
Very near the sea surface the vertical velocity can be 
(pqw.) — = (pqwy) — = (pqwz) . 
(10) 
1075 
neglected in all circumstances and the density can be 
considered constant. Equation (9) is then reduced to 
d dq\ _ 
Liag)=a 
A a = const, 
which simply expresses the fact that near the boundary 
surface the vertical flux of water vapor, expressed in 
units of mass per area and time, is independent of 
height. In the cgs system the flux is expressed in g 
em? sect. 
If the vertical flux is directed upwards, dq/dz must 
be negative. In this case the flux must equal the evap- 
oration from the water surface, and therefore 
or 
(11) 
E=-—A ai (g em~ sec“). (12) 
dz 
Thus the problem of evaporation is reduced to the 
problem of finding the vertical flux of water vapor. 
This may appear to be an easy matter, because in 
the air the eddy diffusivity A can be considered to be 
practically known from wind observations. However, 
difficulties arise because, very close to the surface, 
diffusivity and viscosity are not identical, and because 
different assumptions as to the character of the diffu- 
sivity close to the surface lead to widely different results. 
The eddy viscosity increases with height and, fur- 
thermore, depends upon the stability of the stratifica- 
tion and the character of the sea surface, whether hy- 
drodynamically smooth or rough. At indifferent stratifi- 
cation or slight instability, conditions which prevail 
over the sea, the eddy viscosity is a lmear function of 
height. 
In anticipation of material which follows, it can be 
stated that at some distance from the surface 
A & pkowez, (13) 
where ky and wx are defined as below. Since A dq/dz = 
const, it follows that g must vary with the logarithm of 
height, and Montgomery [16] has therefore introduced 
an evaporation coefficient I, defined by 
1 dq 
== ; 14 
y Gd: —~qdlnz oo) 
Introducing (13) and (14) into (12) we obtain 
E = kopwxT (qs — q)- (15) 
It is this expression which we shall attempt to evaluate 
for smooth and rough conditions; that is, we shall 
determine the evaporation coefficient I which is the 
unknown factor. 
Over a smooth surface there exists, next to the surface, 
a thin boundary layer in which the flow is laminar and 
where ordinary viscosity acts. Above this laminar layer 
the turbulent layer begins. Placing the origin of the 
vertical axis at the top of the laminar layer, we have in 
