200 RADIO WAVE PROPAGATION EXPERIMENTS 
power law is not a law of nature. A complete so.ution 
of the problem would involve a theory giving K as 
a function of temperature gradient. A start has been 
made on this for the case of still air which is agitated 
by thermal turbulence originating from heating on 
its lowest level. The value of K so calculated is small 
compared with that for a light wind. It seems likely 
that the effect of an inversion on K will also be small. 
To sum up, radar personnel should be warned that 
the diffusion theory is at present in a highly unsatis- 
factory state ; any conclusions drawn from it should be 
treated with the greatest reserve, and some calcula- 
tions already published are based on assumptions 
which have no meteorological foundations. 
PRELIMINARY RESULTS OF METEOR- 
OLOGICAL MEASUREMENTS IN 
MASSACHUSETTS BAY? 
The modification produced in land air when it 
passes out over water is known to be particularly effec- 
tive in producing nonstandard microwave propaga- 
tion. The preliminary results of this study are covered 
in the present report; they are necessarily incomplete 
and tentative. 
Modification of Air Flowing 
over Water 
To begin with, some basic considerations will be 
presented. Figure 2 shows an airplane sounding in air 
which is warm and dry relative to the underlying 
water. Before leaving land the air was vertically 
homogeneous; that is, potential temperature and 
specific humidity were constant. This may be seen 
by comparing the observed temperature and vapor 
pressure with the broken straight lines drawn for 
OCTOBER 19,1944 1141-1203 c-23! 
5 MILES NORTH OF PROVINCETOWN, MASS O FIRST ASCENT 
+ SECOND ASCENT 
SURFACE WIND WEST 4B 
HEIGHT IN FEET 
te) Oo o Z b 
23466171689 BF9MWHI2I314 O 10 20 30 40 SO 
TEMPERATURE 
IN DEGREES C 
VAPOR PRESSURE M-Mo 
IN MILLIBARS 
Figure 2. Typical airplane sounding, giving temper- 
ature and water vapor variation with height. 
homogeneous air. The straight line of modified index 
of refraction M is constructed for homogeneous air; 
it is close to standard. The air is being modified by 
loss of heat to the water and by evaporation. 
At the common boundary the temperatures of air 
and water are identical. he vapor pressure also is 
given by the water temperature; over sea water the 
4By R. B. Montgomery, Radiation Laboratory, MIT. 
vapor pressure is 98 per cent of the saturation value 
corresponding to the water temperature. It follows 
that the modified index at the surface is determined 
by the water temperature alone. 
Figure 2 illustrates in a striking manner the simi- 
larity in shape of the three curves. The ratio of the 
change from unmodified value at any height to the 
change at the surface is the same for all three quan- 
tities. 
Modification of air over water is due largely to 
turbulent mixing, which transports heat and water 
vapor in exactly the same manner (the eddy dif- 
fusivity is identical for both). Next to the water 
boundary there is always a laminar layer, through 
which heat is transported to the turbulent layer by 
true conduction while the water vapor is transported 
by true diffusion ; the coefficients for these two related 
processes happen to be nearly the same, so heat and 
water vapor are transported vertically to nearly the 
same relauve degree. he temperature distribution is 
modified by radiation also, but for an initial period 
of a few hours this is unimportant compared with the 
processes just mentioned. 
When initially homogeneous air flows over water of 
constant temperature, a necessary result is therefore 
that the curves of temperature and water vapor pres- 
sure are similar. Furthermore the M curve is similar 
also, because within the range of any sounding the 
modified index is approximately a linear function of 
temperature, vapor pressure, and height. 
The extent of similarity revealed in Figure 2 is 
unusual. Often the three curves have very different 
shapes. In the latter case the deviation from simi- 
larity can be ascribed (1) to lack of homogeneity in 
the unmodified air, (2) to varying water temperature 
along the air’s trajectory, or (3) to radiation during ~ 
prolonged over-water modification. 
The M Deficit 
The distances on the base line from the straight 
broken line to the arrow are the temperature excess 
and humidity deficit respectively. There is obviously 
a corresponding quantity pertaining to index of re- 
fraction. The M deficit may be defined as the value 
of the modified index at the water surface less the 
representative surface value in the unmodified air. 
Temperature excess, humidity deficit, and M deficit 
are related, so any two fully determine the difference 
between unmodified air and air at the water surface. 
The two of most direct significance are M deficit and 
temperature excess. Forecasting is simplified by their 
use: Temperature excess is necessary in drawing the 
temperature curve; similarity and M deficit then give 
the M curve directly. Another advantage in using 
M deficit is that whether it is positive, zero, or nega- 
tive determines at once whether the modified air is 
probably characterized by an M inversion (layer 
where modified index of refraction decreases upward) 
