TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 155 
caused by convection is about —1 C per 100 m, and 
the moisture lapse is steady and rather small. 
Standard refraction will therefore prevail when winds 
are moderate to strong over land, and over the ocean 
also when the winds are sufficiently strong. 
Temperature inversions occur when the temperature 
of the surface (sea or land) is appreciably lower than 
the temperature of the air. The transition from the 
ground temperature to the free air temperature takes 
the form shown in Figure 28. The heat and moisture 
T GROUND T 
Ficure 28. Air temperature versus height for an 
inversion. 
transfer caused by turbulence in a temperature inver- 
sion is less simple than that in a frictional layer. 
The turbulent processes active in inversion regions 
are highly complex and are not yet very well 
explored.It is known, however, that the intensity of 
the vertical transfer of heat and moisture is greatly 
reduced as compared to the rate of transfer with 
frictional turbulence. The reduction is the more 
pronounced, the steeper the vertical increase of tem- 
perature; in a steep inversion the rate of transfer 
may be many times less than in a frictional layer. 
This tends to produce a vertical stabilization of the 
air layers in the inversion region. As soon, therefore, 
as a temperature inversion has begun to form, the 
rapid mixing in the lowest layers, usually effected 
by frictional turbulence, stops and is replaced by a 
much more gradual diffusion. 
Assume now, for instance, that the rate of diffusion 
has become so slow that the transfer of moisture over 
a height of a few hundred feet takes many hours or, 
perhaps, a day or two. When the air in the inversion 
is dry to begin with and flows over ground capable 
of evaporation (the sea or moist land) there will be 
established, in such an air mass, a steep moisture 
lapse, since the water vapor that has been taken up 
by the air near the ground will only gradually diffuse 
into the dry air aloft. Conditions are then favorable 
for the formation of an evaporation duct, in addition 
to whatever tendency toward duct formation may 
be caused by the temperature inversion itself. 
Advective Ducts—Coastal Conditions 
Advective formation of ducts may occur both over 
land and over sea, but this process is most important 
over the ocean near coasts. The most common illus- 
tration is that of air above a warm land surface 
flowing out over a cooler sea. Over the land the air 
will usually have acquired a convective or nearly 
convective temperature gradient of —1 C per 100 m. 
When this air flows out over the cool water surface, 
a temperature inversion is rapidly formed which 
grows in height as the process of turbulent transfer 
progresses. The temperature inversion does not, in 
itself, give rise to a pronounced duct because the 
effect of a temperature gradient upon the M curve 
is relatively small; but when the air is dry, evapora- 
tion from the sea surface takes place simultaneously 
with the heat transfer, and a moisture lapse rate is 
established in the lowest layers. The combination of 
temperature inversion and moisture lapse rate is 
most favorable for the formation of a duct off shore. 
The gradual formation of this type of duct is 
illustrated in Figure 29. This shows M curves, corres- 
eer ai y/) Re tas 
600 
rape el eel Pr san AmAI a oi 
ea al an 
z 
300 
is 200 
A aces 
ZONES 
fo} 
[o) 10 20 30. 40 50 60 70 im 30 =i 
M-Mo 
Ficure 29. Development of duct off coast. Initial state 
corresponds to air at coast line. 14 hr, 14 hr, etc., refer 
to time air has been over water. Initial conditions for 
this set of curves: unmodified air Tp = 32 C, e = 12.3 
mb; water 7 = 22 C, e» = 26.5 mb saturation. 
ponding to the simple surface type of trapping (see 
Figure 20, curve II) for a series of time intervals 
(and distances) as the air moves out over the water. 
The top of the duct is given by the elevation of the 
minimum value of the M curve. It will be noticed 
that the duct acquires a maximum depth some time 
after the air has touched the cold water surface; 
thereafter the depth decreases. The cause of this 
behavior is found in the progressive decrease in 
moisture and temperature differences which is the 
final result of the diffusion process. Thus the final 
stage of this transformation is an air mass whose 
temperature and moisture distributions are in equi- 
librium with the underlying water surface and no 
longer show a rapid variation with height. 
Duct formation in such a case depends on two 
quantities: (1) the excess of the unmodified air 
temperature above that of the water and (2) the 
