154 TECHNICAL SURVEY 
decrease of humidity with height (—de/dh), where e 
is the water vapor pressure in millibars. (e can be 
found from meteorological tables when relative 
humidity and temperature are known.) The ordinate 
is the rate of increase of temperature with height 
(dT /dh).The slanting lines represent various values of 
temperature and relative humidity at some particular 
height h. The lines passing through the same point 
at the upper right of the diagram correspond to the 
same mean temperature; lines of different slopes 
represent different mean relative humidities. 
In order to determine the rate of change of M at 
a given level, find the point in the diagram corre- 
sponding to the actual rates of change of moisture 
and temperature. Also pick out the straight line 
representing the actual mean values of temperature 
and humidity in the layer considered. If the point 
is at the lower right relative to this straight line, M 
decreases with height in the layer chosen; that is, a 
duct exists. If the point is at the upper left of the 
straight line, M increases with height and there is 
no duct. 
The rate of change of M, (dM/dh), may be 
obtained from the diagram by measuring the hori- 
zontal distance from the point to the line and 
multiplying by the function of the temperature f(T) 
given in the table on Figure 27. The result is the 
value of dM/dh, the rate of change of M, in M units 
per 100 m. This quantity is negative when the point 
is to the right of the line and positive when the point 
is to the left of the line. 
It is seen at once from the diagram that for small 
values of the moisture lapse an extremely steep 
temperature gradient is required in order to produce 
a duct (lower left part of the diagram). In cold air 
such as is found in the arctic the total moisture is 
small, and hence the moisture gradient will in general 
be quite small. Ducts will then only occur when a 
very strong temperature inversion exists. 
Strong temperature inversions occur only under 
special meteorological conditions which will be 
discussed below. Ordinarily the temperature of the 
air decreases with height; and this will put our 
representative point into the upper part of Figure 
27. A duct can then exist only when the moisture 
lapse is large enough, so that the representative 
point falls to the right of the appropriate slanting 
line. Such ‘conditions are common in the lower 
atmosphere. This leads to a wet duct, which is 
determined almost completely by the moisture lapse. 
Physical Causes 
of Stratification— Turbulence 
There are three basic meteorological factors which 
tend to modify the temperature and moisture distri- 
butions in the lowest layers of the atmosphere. These 
are: (1) advection, (2) nocturnal cooling (over land), 
and (8) subsidence. 
Advection is a meteorological term used to desig- 
nate the horizontal displacement of air having 
particular properties. Advection is of great interest 
in propagation problems particularly because it leads 
to an exchange of heat and moisture between the air 
and the underlying ground or sea surface and thus 
affects the physical structure of the lowest layers. 
Nocturnal cooling over land is caused by a loss of 
heat from the ground by infrared (heat) radiation. 
The cooling of the ground is communicated to the 
lower layers of air and leads to the establishment of 
a low-level temperature inversion. 
Subsidence means a slow vertical sinking of air 
over a very large area. It is most likely to be found 
in regions where barometric Highs are located. 
Subsidence tends to produce a temperature inversion 
and also produces very dry air which, spreading out 
over a humid surface, creates a situation which is 
favorable for the formation of a duct. 
The processes (1) and (2) change the physical 
characteristics of the air through transfer of heat 
or moisture between the air and the underlying 
surface of the ground or sea. The operating factor 
in this exchange is turbulence. The main features 
of turbulence in the lower atmosphere are outlined 
briefly below. 
Convection occurs spontaneously whenever the 
decrease of temperature with height exceeds a value 
of about 1 C per 100 m. This convective condition 
is usually produced as a result of the heating of the 
ground by the sun’s rays. Even with a cloudy sky 
the diffuse daylight often is strong enough to produce 
moderate convection. On a hot summer day convec- 
tion over land extends to great heights. Convection 
mixes the air thoroughly and thus causes a uniform 
distribution of moisture and a uniform decrease of: 
temperature with height of about 1 C per 100 m. 
Hence even moderate convection tends to produce a 
smooth M curve which varies linearly with height. 
Standard conditions may therefore be assumed to 
prevail on clear summer days (and not infrequently 
on clear days in the cooler seasons) from the hours 
of late morning until late afternoon, during which 
time convection is most active. 
Frictional turbulence occurs frequently in the lower 
atmosphere even in the absence of convective condi- 
tions. It is caused by the wind and requires the 
presence of at least light winds, but with moderate 
or strong winds the effect is more pronounced. In 
conditions of calm or with a gentle breeze, frictional 
turbulence is confined to the lowest strata. Moderate 
or strong winds develop a layer of intense turbu- 
lence, caused by friction of the air at the irregularities 
of the ground. This layer is usually quite well defined 
in height and extends to an average elevation of 
about 1,000 m over land. Over a relatively smooth 
sea where friction is small the height of the layer is 
-much reduced. In this frictional layer the air becomes 
thoroughly mixed; the vertical temperature gradient 
