METEOROLOGY — THEORY 223 
Tape 13, Critical wavelengths in meters for 7’ = 280°A. 
AU (meters per second) 
AT (C) 0 2 4 6 8 10 12 14 
0 Ps a) Cs) Cs) C) co i) ) 
0 339 677 1016 1354 1693 2031 2370 
2 0 180 718 1616 2872 4488 6463 8796 
0 159 493 860 1225 1584 1938 2287 
A 0 90 359 808 1486 2244 3231 4398 
0 87 317 632 985 13851 1720 2087 
6 0 60 239 539 958 1496 2155 2933 
0 59 226 479 782 1121 1478 1843 
8 0 45 180 404 718 1122 1616 2199 
0 44 174 375 684 985 1264 1612 
10 0 36 144 323 574 898 1293 1759 
0 36 140 308 529 793 1090 1413 
12 0 30 120 269 479 748 1077 1465 
0 30 118 260 451 684 952 1247 
14 0 26 103 231 410 641 923 1256 
0 26 101 225 393 600 841 1110 
Upper value: incompressible, homogeneous fluids. Lower value: com- 
preasible, isothermal fluids. 
versions, and there are some ten cases on record where 
wavelengths of the billows as well as values for the 
temperature and wind velocity differences have been 
observed. In these cases the maximum difference be- 
tween observed wavelength and critical wavelength was 
48 per cent. In only three cases was the difference 
greater than 15 per cent.*®> 
Other weather phenomena have been observed whicl 
indicate stable wave motion in the atmosphere. In 
1936, quite regular fluctuations were measured in 
ceiling height at San Diego on two occasions. The 
amplitude of the fluctuations averaged 25 to 30 m in 
the two cases, with periods of about 15 to 20 min over 
time intervals of 4 or 5 hours.?° In 1934 at the Blue 
Hill Observatory in Massachusetts, there occurred 
wave-like fluctuations in the pressure record, which 
were analyzed by Haurwitz.?’ In these cases upper-air 
data were not sufficiently accurate to compute wave- 
lengths quantitatively by means of the critical wave- 
length formula, but it appeared from approximate 
values of wind shear and density difference that the 
critical wavelengths might well be occurring. 
If it is desired, then, to predict what wavelengths 
will occur with a given inversion, the critical values 
would seem in the light of these observations to give 
a good estimate of the order of magnitude. 
Assuming that these wavelengths are the ones which 
occur, one can discuss the velocities and periods of 
the wave motion. For these critical wavelengths, the 
velocity of the wave motion is the mean of the veloci- 
ties of the air masses above and below the inversion. 
Hence the period can be estimated by dividing the 
wavelength given in the table by this valye. As an 
example, for a mean velocity of 5 m per second, the 
periods vary from about 6 sec to about 8 min, de- 
pending on the wind shear and density difference. 
The vertical velocity at the inversion cannot be 
determined, since an arbitrary constant is involved. 
However, it can be said that this vertical velocity will 
be reduced to one-tenth its inversion value at a height 
d equal to 37 per cent of the wavelength above the in- 
version. This holds strictly only for thé incompres- 
sible, homogeneous case but is approximately correct 
for the other case as well. 
It is known, then, from theoretical considerations 
and some observational material, that wave motion is 
apt to occur at a layer in the atmosphere where there 
is a temperature inversion accompanied by wind shear. 
When such inversions are believed to be of impor- 
tance in affecting the propagation of radio waves, it 
should be remembered that there may well be wave 
motion occurring and that the interface is not neces- 
sarily a level surface. It remains to be determined 
whether this fact will help to explain the observed 
very high frequency fading. An estimate of wave- 
length, period, and velocity of the atmospheric wave 
motion, as given by Table 13, may be of assistance 
in testing this possibility. 
ANALYSIS OF DUCTS IN THE TRADE 
WIND REGIONS* 
This report is an analysis of the frequency and 
magnitude of low-level and elevated ducts as indi- 
cated by meteorological observations over the trade 
wind areas of the Atlantic and Pacific Oceans. Mete- 
orological soundings of the Meteor expedition,” taken 
during 1925 to 1927 over the Atlantic Ocean were 
utilized in analyzing elevated ducts. Climatological 
data of the Atlantic and Pacific Oceans were employed 
in study of low-level ducts. A qualitative analysis of 
95 soundings of the Meteor expedition had previously 
been made in reference 23. 
Elevated Ducts 
TRADE WIND AND DoLpRUMS AREAS 
A semipermanent high-pressure system is located 
over the oceans at about 30 degrees of latitude. The 
northeast trade winds blow from 30°N to about 5°N. 
Between the equator and 30°S the southeast trade 
winds prevail. The doldrums, a region of light winds 
and heavy rainfall, appears between the two wind 
systems. 
Ducts IN THE TRADE WIND REGION 
In the trade winds a warm, dry subsiding air mass 
exists over a cool, moist ground layer. The transition 
zone between the two air masses is characterized by 
a temperature inversion (increase with height) and 
a sharp decrease of the water vapor content of the 
air. It is this transition layer which coincides with 
the duct, which in this paper is defined as a layer in 
which the curvature of the path of high-frequency 
electromagnetic waves exceeds the curvature of the 
kBy Raymond Wexler, Signal Corps Ground Signal Agency. 
