484, 
is high more often than the S and at any given time 
usually reaches a higher level. Radar ranges on sur- 
face targets are extended by as much as 20 to 25 per 
cent above normal, and again X band experiences 
more effect. These increases in signal strength can 
be of great importance for communications, beacons, 
or any other application involving one-way transmis- 
sion of microwaves, such as countermeasure. It should 
also be remembered whenever secrecy is required. 
2. Substandard conditions may be present for sev- 
eral days at a time if the air is warm and moist. The 
reduction in signal strengths and radar ranges on 
surface targets which accompanies substandard con- 
ditions does not seem to be markedly frequency sensi- 
tive. It should be stressed that variations in one-way 
signal strength of at least 90 db have been observed. 
The radar ranges have also varied from roughly 10 or 
15 miles up to at least 280 miles. These changes are 
not rare oecurrences; deviations from the- standard 
account for the major percentage of the time, especial- 
ly during warm weather, and at the higher frequencies 
even during the fall. 
TRANSMISSION CHARACTERISTICS 
OF AN OVER-WATER PATH? 
Results were previously reported of some prelim- 
inary analyses of one-way radio transmission on a 41- 
mile over-water path from Provincetown to Gloucester, 
with terminals well below the horizon. S- and X-band 
radiations were transmitted over the double paths in- 
dicated in Figure 9 to both “high” and “low” receivers, 
and 11%-me radiation over only the high path. Numer- 
ous meteorological surface measurements and low-level 
soundings were made, and essentially through compar- 
isons with these measurements the following correla- 
tions for microwave transmission and surface Mf curves 
were obtained. 
With positive M deficits, or M inversions, two cases 
were found. 
1. Low ducts, less than 50 ft thick, resulted in a very 
steady signal at levels well above standard. The in- 
crease in signal level took place although the terminals 
were as much as 100 ft above the top of the M inver- 
sion. Such low ducts caused greater increases in the 
signal level on X band than on S band. 
2. High ducts, 100 ft thick or more, resulted in very 
high signal levels on the average, but with deep fad- 
ing. The signal level did not continue to increase witt 
increasing duct height but instead “saturated” near 
the free space level. No frequency diversity between 
S and X bands was found in this case. 
With negative M deficits, or substandard M curves, 
the signal was always below standard. 
In November 1944 no correlations with M curves 
had been obtained for the 11%-me signal, and a clear 
lack of correlation with the microwaves had been 
noted. 
A detailed analysis has since been undertaken 
which is as yet far from complete. This paper describes 
the method in use and presents some additional results. 
In studying the fundamental phenomena of propa- 
gation the method employed was to tie the complete 
representative M curve to the observed transmission 
results by means of the wave theory. A threefold at- 
tack was used: 
1. The meteorologists studied each situation in de- 
tail to determine a representative M curve and its 
changes with position and time. 
2. Theoretical field strengths were found by put- 
ting the representative M curve, or a close approxi- 
mation to it, back into the wave equation. These theo- 
retical yalues were then compared with the observa- 
tions. 
3. Empirical correlations were then made between 
the M curves and the transmission results. This was 
done because the theory is applicable only to the sim- 
plest M curves and to uniform conditions. 
4By P. J. Rubenstein and W. T. Fishback, Radiation Lab 
oratory, MIT. 
APPENDIX 
This approach was employed in an effort to find 
parameters in terms of which predictions of range o 
field strength can he made for operational use. It is 
not considered a suitable method in itself for use in 
the field. 
The meteorological part of the program has not in 
general received sufficient attention. Spot measure- 
ments at a given time and place do not necessarily 
give an adequate description of prevailing conditions. 
A thorough meteorological analysis of the entire period 
of transmission is therefore under way. For each case 
the synoptic situation is studied to find the trajectory 
of the air over the path at the time in question. Radio- 
sondes, surface measurements, winds aloft, measured 
water temperatures, and all available low-level sound- 
ings are studied and the characteristics of the air over 
the water determined. Then representative low-level 
soundings are constructed. Such so-called synthetic 
soundings for the path midpoint are being drawn for 
6-hour intervals for each day of operation. In addition, 
estimates are made of the departures from uniformity 
over the path and of the times of occurrence of marked 
changes. 
All the radio analysis has been based upon these 
synthetic soundings and the accompanying discussion. 
The meteorological analysis is at first made completely 
independent of the radio data, with minor revisions 
when necessary after consideration of the transmis- 
sion data. It is believed that full use of transmission 
data can be made only through such close cooperation 
of the persons engaged in both the meteorological and 
the radio work, not only in the measurements but also 
in the analysis. 
Perhaps the most striking information which has 
so far resulted from the detailed analysis is the em- 
pirical correlation of the 117-me performance with 
M curves. Increases in signal level above the standard 
are found to result from either large surface ducts 
(200 ft or more thick) or elevated superstandard 
layers which do not necessarily show overhanging M 
curves. Such layers occur frequently over Massachu- 
setts Bay, mainly as a result of nocturnal cooling over 
land. Those which affect the 117-me transmission 
oceur below about 1,500 ft. Their strength is usually 
doubtful in view of the lack of accurate information 
on conditions over land in radiation inversions. 
Figure 10 shows the correlation diagrams obtained 
when, first, all points are included, and second, all 
cases of elevated superstandard M layers are omitted. 
(Standard values are —120 db for 117 me and —80 
db for S band.) The first diagram obviously shows no 
correlation and is the sort of diagram obtained last 
fall. The second, however, is just what should be ex- 
pected for the correlation with surface phenomena. 
The S-band signal rises to the free space value as the 
duct height goes up to about 100 ft and then “satu- 
rates” for higher ducts. The 117-me signal, however, 
is affected only by ducts considerably more than 100 
ft high. Similarly, only a thin substandard layer is 
required to affect the S-band signal, but not until the 
layer is rather thick is the low frequency affected by it. 
In the period so far studied (960 hours total) the 
signal level was above standard 49 per cent of the 
time, standard 38 per cent of the time, and substand- 
ard 13 per cent of the time, Of the superstandard 
period 46 per cent has been correlated with elevated 
superstandard M layers, 36 per cent with thick sur- 
face ducts, and 4 per cent with situations in which 
elevated layers and thick surface ducts coexisted. Only 
14 per cent of the time remains in doubt, and this in- 
cludes many periods of exceedingly complex meteoro- 
logical situations for which the analysis was incon- 
clusive. In addition to correlation of field strengths 
with M curves, comparisons have been made between 
measured and theoretical values of field strengths. The 
theoretical values were calculated on the assumption of 
bilinear modified index curves, that is, curves made 
up of two straight-line segments. The M curve is taken 
to be standard above the joint, and two parameters are 
used: the height of the joint, or duct thickness, g, and 
the ratio s of the slope. The straight lines are drawn 
not in terms of M deficits but to give the best possible 
fit to the actual M curve. For the range of values of 
these parameters for which the contribution of the first 
mode only is of importance the curves of field strength 
shown in the following two figures are representative. 
Figure 11 shows the effect of changing duct height. 
0 to 500 ft, on the 117-me field strength for various 
values of the slope of the lower segment. The field 
strength is measured relative to free space value and 
—33 db is standard. (s = —3 corresponds to a value 
of dM /dh about —100/100 ft; s = —2 is —30 per 106 
ft, ete.) Note that for the bilinear model, unless the 
slope of the bottom portion be extreme, the duct height 
must be of order 200 ft or higher before there is any 
appreciable effect at this frequency. 
Figure 12 is a similar theoretical diagram for the 
high S-band path. The scale in this case is 0 to 100 ft. 
At X band the corresponding changes occur over a 
height range of only about 30 ft. For the low paths 
at any given frequency the curves are similar, but the 
increases in field strength occur more rapidly, so that 
the free space value is reached at essentially the same 
duct height for both high and low paths. 
In a few special cases for S and X bands contribu- 
tions of a number of modes (as many as 18 in one case) 
have been added in phase. In no case did the calculated 
field strength reach a value more than 15 db above the 
free space value, and in most cases it was between 
—5 and +10 db. 
The calculations check well with observations in a 
qualitative way in spite of the fact that the bilinear 
curve is not in general a good approximation to the 
true M curve and that the assumption of a uniform M 
curve along the entire transmission path is an ex- 
treme idealization. They show the order of magnitude 
of duct heights at which appreciable increases in field 
strength first occur at a given frequency. They demon- 
strate also the important fact that the field strength 
is increased even at considerable heights above the 
duct. This is so because with a leaky mode the height- 
gain function does not decrease with height above the _ 
duct but instead becomes practically constant over an 
appreciable range. This is illustrated in Figure 13, 
where the normalized height-gain function for a leaky 
case is compared with the standard. The decrease in! 
absolute value of the height gain is compensated by 
the reduction in-the attenuation. It is thus clearly 
not necessary to put a transmitter inside the low duct 
in order to take advantage of it; nor does the first 
mode need to be actually trapped as indicated by ray 
tracing, but merely less attenuated than the standard 
As to character of the signal, the theory suggests 
that steady signal is obtained with low ducts because 
only a single mode is important. With large ducts fad- 
ing may be eaused by interference among many modes 
which change rapidly in amplitude and phase with 
small changes in refraction. Even with very large 
ducts, for terminals well above the duct, steady signal 
might again be expected because the field strength 
there would probably again result from a single leaky 
mode, in this case not the first mode. 
Finally, the calculations agree with observations in 
showing that even when many modes are strongly 
trapped, the field strength at a fixed point does not 
reach the high value one might expect on the basis of 
an attenuation proportional to 1/R but rather remains 
near the ordinary free space value. This results from 
the fact that coincident with the reduction in attenua- 
tion which occurs with trapping, there is also an ap- 
preciable reduction in the height-gain function within 
the duct, as shown in Figure 14. The balance of the 
two countereffects prevents extreme increases in field 
strengths at all ranges of practical interest for micro- 
waves. 
To sum up, the 117-me transmission is noticeably 
affected both by thick surface ducts or substandard 
layers and by elevated superstandard layers up to 1,500 
ft altitude, which need. not necessarily overhang. The 
wave theory for elevated layers is not yet sufficiently 
