PART I 
METEOROLOGY 
Chapter 1 
METEOROLOG Y—THEORY* 
MODIFICATION OF WARM AIR BY 
A COLD WATER SURFACE» 
Ta OF THE COMMONEST TYPES of M curves which 
produce nonstandard propagation are the S-shaped 
curve and the simple trapping curve where M decreases 
from the surface to 200 ft, say. The S-shaped curve 
occurs in regions of subsidence, for example, in the 
extensive subtropical anticyclones. The forecasting 
of this phenomenon will not be presented in this dis- 
cussion which is confined to the simple trapping case. 
During 1943 the question arose regarding the 
feasibility of forecasting the change in the temperature 
and vapor pressure distribution as warm air flows over 
a cold water surface. Through practice, considerable 
success had already been obtained in forecasting the 
M curve a few miles offshore in Boston Harbor. How- 
ever, it was suggested that a general method be de- 
vised whereby the M curve could be predicted for 
greater distances from the shoreline and for different 
regions of the world. In order to solve this forecast 
problem the Boston Harbor soundings were investi- 
gated in the light of turbulence theory. 
Two factors had to be kept in mind, namely: 
1. The Boston Harbor soundings of temperature 
and vapor pressure were scant. A more serious diffi- 
culty was the total absence of data at distances in 
excess of 15 miles from the land. 
2. Since forecasting techniques were the primary 
aim it was necessary to find a solution which was 
suitable for field use. 
Diffusion Equation 
The differential equation for turbulent mass ex- 
change may be written 
=) 
oz] ~ 
ar _ 2(x 
ot 0z 
If K, the coefficient of eddy diffusion, is assumed con- 
(1) 
See also Parts II.and III of Chapter 17, Volume 1, Com- 
mittee on Propagation. ; 
bRy J. M. Austin, Meteorology Department, MIT. 
197 
stant, then 
pl oad = # (4) = 
elie \/4Kt 
where # = error function, that is, 
2 [Fw 
E(é =~ [i dz, 
1, (2) 
T’ = temperature at a level z over the ocean, 
T = initial temperature at z over the land, 
T,, = initial air temperature over land at z — 0, 
T. = water temperature, 
t = time. 
Values of K were then computed from the observa- 
tional data by evaluating the ratio (Z’—T) /(T,.—T ») 
for different evaluations and different times. These 
values were averaged for each level and the results 
shown in Table 1 were obtained. After plotting K 
TaBLE 1. Values of K. 
Eleva- 
tion 
in ft 20 50 100 200 300 
K 0.014 x10! | 0.07 x10 | 0.18 x 104 | 0.38 x 104 | 0.67 x 104 
against elevation, the approximate linear variation 
of K was extrapolated to give values of K for eleva- 
tions up to 700 ft. This level of 700 ft lies well within 
the limit of 250 m which was indicated by Mildner* 
to be the level where K reaches its maximum. 
These values of K were then used to construct Table 
2, which gives (7’—7')/(Lo—Tw) for all levels in 
terms of the time that the air has been over the water. 
The same values of K were obtained from the analysis 
of vapor pressure changes; hence the same table can 
be used to evaluate the ratio (e’—e)/(e¢—é»). From 
this table it is a simple matter to reconstruct the M 
curve at any distance over the ocean, provided the 
initial state of the air is known. An example of the 
changes in the M curve are given in Figure 1. 
Discussion of Procedure 
Summarizing the favorable aspects of this study, 
it can be stated that: 
1. The values of K were almost identical for vapor 
