156 TECHNICAL SURVEY 
humidity deficit, that is, the difference of the satura- 
tion vapor pressure corresponding to the water tem- 
perature minus the actual water vapor pressure in 
the unmodified air. If these quantities are large, 
especially the humidity deficit, a duct will develop. 
A great variety of local conditions may, however, 
be encountered in problems of this type, and empiri- 
cal rules developed for one locality may not at all 
apply to others. 
Advective processes may also occur over land, but 
the conditions required for duct formation are likely 
to be found much less frequently. Evaporation over 
land need by no means be small unless the land 
surface is very arid (desert) ; in fact, evaporation over 
a moist soil or a ground covered with vegetation may 
be comparable to, or even larger than, evaporation 
from a sea surface. A duct may therefore be formed 
when dry, warm air flows over a colder ground surface 
capable of evaporation. The temperature excess and 
humidity deficit may again be defined as above. 
Land and sea breezes often produce ducts near 
coastal regions. These winds are of thermal origin 
and are produced by temperature differences between 
land and sea. The mechanism is illustrated in Figure 
30. During the day, when the land gets warmer than 
WARM COLD COLD WARM 
LAND SEA LAND SEA 
SEA BREEZE LAND BREEZE 
Ficure 30. Land and sea breezes. 
the sea, the air rises over the land and descends over 
the sea and causes an air circulation in which the 
wind blows from sea to land (sea breeze) in the lowest 
levels. Vice versa, if during the night the land becomes 
colder than the sea, a circulation in the opposite 
direction arises. This is the land breeze. As a rule, 
this type of phenomenon is extremely shallow, and 
the winds do not extend above a few hundred feet 
at the most. Often there is a reverse wind in the 
layer above the land or sea breeze layer. A sea breeze 
may modify the advective conditions described above 
in various ways, and extremely strong ducts have 
been observed repeatedly under sea breeze condi- 
tions. The land and sea breezes are of a strictly local 
nature and in some cases will extend only a few 
kilometers to both sides of the shore. Nevertheless 
this region may be an important part of the trajec- 
tory of radiation. These breezes develop only under 
fairly calm conditions; under conditions of moder- 
ately strong wind, the sea and land breeze will be 
perceptible only as a slight modification of the 
existing wind. Because of their limited extent, fore- 
casting of these breezes requires a study of the local 
wind and temperature conditions. 
Advective ducts caused in the manner described 
here are often quite limited horizontally. This is 
especially true if a sea breeze is involved. The 
assumption made throughout this report, namely 
that the stratification of the air is of infinite extent 
horizontally, will no longer be valid, and superrefrac- 
tion may be restricted to a stretch along the coast. 
Ducts over the Open Ocean 
A type of duct that is somewhat similar to the 
advective duct described above is found over the 
open ocean where the air has had an extensive over- 
water trajectory. It has been studied in experiments 
carried out at the island of Antigua in the West 
Indies. The subsequent description refers to this 
particular location, but on the basis of experience 
gained operationally and in other experiments it may 
be presumed that similar conditions prevail in 
numerous other regions of the world, particularly in 
the trade wind regions. 
At Antigua, in winter and early spring when these 
tests were made, the wind is usually from the north- 
east since the island is situated at the southeastern 
fringe of the so-called Bermuda High, a large semi- 
permanent circulation system over the North 
Atlantic, extending from about 10° to 30° North 
latitude. The air at Antigua has thus had an ocean 
trajectory of thousands of miles. The relative hum- 
idity is of the order of 60 to 80 per cent, indicating 
that in spite of the long passage over the sea no 
diffusion equilibrium has been established between 
the sea surface and the moisture in the lower atmos- 
phere. On the other hand, there is little difference 
between the air and sea temperature, the latter 
being rather constant at 25 C and the former varying 
between 23 and 26 C. The air is, therefore, nearly 
in convective thermal equilibrium with the sea sur- 
face, and no appreciably “dry” duct can develop. 
The duct is caused by the moisture variation in the 
lowest layers. 
A typical M curve is:shown in Figure 31. 1t may 
200 
MIXED | rf 
> ro 
ho a 
DS 
° 
HEIGHT IN FEET ——e 
) 
fe) 
40 
M MODIFIED INDEX —————— 
Figure 31. M curve over West Indian Ocean. 
