1074 
pate part of the following discussion (p. 1075, eq. (12)), 
the Bowen formula can be derived in a simple manner. 
If the eddy coefficients for diffusion of water vapor 
and conduction of heat are assumed to be identical, 
the upward fluxes of latent energy of water vapor and 
of heat can be written 
0.621 de 
Corea dt p A dz 
and 
de 
Qn — — CA Gs’ 
where p is the atmospheric pressure, A the eddy con- 
ductivity (or diffusivity), c, the specific heat of the air, 
and @ the air temperature. To be exact, potential tem- 
perature should have been used, but near the sea 
surface, where the vertical temperature gradient is 
large, only a small error is mtroduced by using the 
ordinary temperature. It follows that 
ee Qi, Cp dd/dz 
Q. 0.621 L de/dz ~ 
Replacing the ratio of the differentials by the ratio 
(@; — a)/(eé: — ea) and imtroducing the numerical 
values c, = 0.240, p = 1000 mb, and LZ = 585, one 
obtains R, the Bowen ratio: 
Bs OM 2a (8) 
Cs — Ca 
The Bowen ratio has been used extensively by Cum- 
mings and Richardson (see, for example, [6]) in the 
study of evaporation from lakes, and by Jacobs [8] 
in his examination of the energy exchange between the 
ocean and the atmosphere. 
For the North Atlantic and the North Pacific Oceans, 
Jacobs determined the Bowen ratio as a function of 
latitude. In both cases R increased with latitude, but 
the values found for the North Atlantic were con- 
sistently smaller than those for the North Pacific. 
In the Atlantic even small negative values were found 
near the equator, mdicating that there the average air 
temperature is slightly higher than the sea-surface 
temperature. The reality of this feature must be ques- 
tioned. Careful observations from specially equipped 
ships have demonstrated that in the tropics of the 
Atlantic Ocean the air temperature is about 0.8C lower 
than the sea-surface temperature, but the values found 
on climatological charts show a smaller difference or 
even a higher air temperature. The reason for this is 
that the climatological charts are based on routine 
observations on board ship, in which errors due to the 
ship’s heat or faulty exposure of the thermometer have 
not been eliminated. In his computations of R, Jacobs 
[8] used data from climatological charts and, therefore, 
his & values are probably too small in low latitudes, 
but in higher latitudes they are more nearly correct. 
Taking the average for the two northern oceans one 
obtains: 
MARINE METEOROLOGY 
North Latitude R R R 
(deg) (Jacobs) (Corrected) (in intervals 
of latitude) 
70 0.53 0.53 
60 0.37 0.37 os 
50 0.25 0.25. 0. 1 
40 0.18 0.18 0 15 
30 0.08 0.13 0 11 
20 0.02 0.10 0. 10 
10 0.00 0.10 0 40 
0 0.00 0.10 
The mcrease with increasing north latitude is in part 
an effect of the continents from which cold air flows 
out over the oceans in winter. In the Southern Hemi- 
sphere the effect is absent or weak, and therefore we 
shall assume that R increases only to 0.25 at 70°S. 
Results. In revising the computation of evaporation 
on the basis of energy considerations we shall make use 
of Schmidt’s values of the radiation surplus and of 
Jacobs’ values of R m the Northern Hemisphere after 
application of an estimated correction in the tropics. 
For the Southern Hemisphere we shall mtroduce esti- 
mated values. For the latent heat of vaporization, 
values will be used corresponding to the average sea- 
surface temperature in the different latitudes. All values 
used and the results obtained are shown in Table J, 
which also contains the evaporation observed on board 
ship reduced to true evaporation (p. 1072) and average 
values according to Jacobs. 
If we take into consideration the ocean areas between 
parallels of latitude, the average annual evaporation 
between latitudes 70°N and 70°S is found to be 99 cm 
per year. The error of this value is probably less than 
+10 cm per year. 
EVAPORATION FROM THE OCEANS COMPUTED 
FROM METEOROLOGICAL ELEMENTS 
History. In evaporation studies one of the aims has 
long been the establishment of relationships that would 
permit computation of evaporation from the meteoro- 
logical elements recorded on board ship, that is, from 
air temperature, humidity, wind velocity, and baro- 
metric pressure, and from knowledge of the sea-surface 
temperature. Prior to about 1920 several empirical 
equations were developed on the basis of pan measure- 
ments on shipboard or on land (see for example equation 
(3)), but these equations give only the empirical rela- 
tion between the evaporation from the pan and certain 
meteorological elements and they cannot be expected 
to give correct values of the evaporation from the sea 
surface. This point of view had not been generally 
recognized [7, 11] but had been emphasized by Schmidt 
[21], who strongly recommended the detailed examina- 
tion of humidity, temperature, and wind conditions 
in the very lowest layers of the air directly above the 
sea surface in order to establish a basis for reducing 
the evaporation measurements on board ship to the 
sea surface. 
Wiist [29] carried out a limited number of such 
measurements (see p. 1072), but used them only for 
a reduction of the averages and not for the establish- 
ment of a new relationship. Recent advances have 
been made by following the entirely different procedure 
