486 
slightly Jess than the critical angle, the lower fre- 
quencies will be reflected more strongly from the 
layer. In addition, any deviation of the layer from 
the horizontal plane will affect the higher frequency 
radiation more than the lower frequencies. This is 
manifested by the greater fading range of the 547- 
me signal as shown in Figure 3. 
Consider the case where the layer is 330 ft thick. 
Since the angle at which the radiation will be inci- 
dent upon the layer will depend upon its elevation, 
it is possible to compare the experimental data with 
theoretically calculated reflection ratios. In Figure 2, 
‘the curves indicate the theoretically predicted varia- 
tion of field strength as the layer rises. The absolute 
decibel scale does not apply to the theoretical curves; 
only the slope is significant. The actual layer thick- 
‘ness and the effective change of the index of refraction 
through the layer varied around the values used, and 
so an exact correspondence between theory and experi- 
ment should not be expected. However, the agreement 
is fair. In addition, at any given time the reflecting 
stratum is a warped surface which changes shape with 
time. This condition complicates any theoretical treat- 
ment of the problem. 
The analysis thus far indicates that the variation in 
actual index of refraction through the layer has to 
be used to explain the magnitude of the fields observed 
on the one-way link. When the layer is thin the longer 
wave radiation might,be expected to leak more readily 
through the stratum and thus show less trapping at 
the greater distances. Actually, the vertical sections 
of field strength taken in the plane (Figures 8 and 9) 
show rather large fields above the layer at the longer 
ranges. This might be interpreted in favor of the 
modified index over the measured index of refraction. 
However, on the other hand it could be diffraction due 
to the low elevation of the layer, or a storage field when 
the actual index of refraction is used. A study of the 
attenuation along the path should clear up this last 
point. 
Vertical Field Strength Sections 
Two typical sets of field strength data. are shown 
in Figure 8 and in Figure 9, Figure 8 illustrates a 
ease for which there was definite trapping predicted 
by the modified index criterion. It will be noted that 
the 63-me radiation shows little variation in field 
strength with altitude. In most cases it shows even 
less variation with time at a given altitude. The higher 
frequencies show more variation of signal with alti- 
tude, and the field strength distribution varies more 
with time. This variation with time is in complete 
agreement with the data taken on the San Pedro to 
San Diego one-way link. The minimum field above the 
minimum point of the M curve, as predicted by ray 
theory, is certainly missing at the lower frequencies 
and rather uncertain at the higher frequencies. 
Figure 9 in the following paper shows field strength 
sections for a day when the reflecting layer was at an 
elevation of around 3,000 ft. Here the solid line rep- 
resents the first run and the dotted line the repeat sec- 
tion. The time interval between sections was from an 
hour to an hour and a half. The sections at about 75 
miles from the laboratory show results compatible with 
the one-way link data. At low elevations the lower 
frequencies show stronger fields than the higher fre- 
quencies. This again is in agreement with reflection 
theory. 
SumMary 
The modified index of refraction, in conjunction 
with ray theory, is a poor criterion for trapping. 
Strong fields are observed well below the horizon when 
the observed modified index would indicate that no 
trapping would be taking place. The vertical distribu- 
tion of field strength for the lower frequencies appears 
to have little in common with the fields predicted by 
ray tracing methods where the energy is assumed to 
follow the rays. 
There is no apparent correlation between the experi- 
mental data and the simple wave guide analysis. 
APPENDIX 
Treating the elevated refracting stratum as a plane 
reflecting layer seems to agree in general with experi- 
ence, for the following reasons. (1) The observed fre- 
quency sensitivity of the reflecting layer is predicted. 
(2) The observed fading characteristics of the differ- 
ent frequencies is again in the right direction, the 
higher the frequency the greater the fading. (3) 
Strong fields well below the horizon under conditions 
of high layers cannot be explained on the basis of 
refraction alone. 
THE CORRELATION OF CALCULATED 
AND MEASURED FIELD STRENGTHS? 
Since the time of issue of reference 3, the impor- 
tance of further experimental check against the cal- 
culated patterns has been fully realized. 
The field strength cross sections recently obtained 
by airplane-borne receivers have made possible such 
a check. 
For anything more than a rough qualitative corre- 
lation it was sqon apparent that quantitative field 
strength analyses were needed for the actual observed 
meteorological conditions. 
Because of the clearly apparent influence of high 
ievel inversion layers on the observed radiation fields, 
this type of condition was selected. Consider, for ex- 
ample, the M curve at 50-mile range obtained on 
September 29 reduced to three linear segments as 
shown in Figure 9.° It is clear that the M curves at 
10 and 100 miles are not seriously different. 
We thus have a condition in which M@— WM, de- 
creases by 50 units in a 200-ft interval of altitude 
attaining the minimum yalue of +50 at 3,000-ft 
elevation. 
Figure 10 shows the ray diagram constructed for 
the analysis. The diagonal lines below 4,000 ft rep- 
resent the positions at which field strengths were 
measured and calculated. 
The actual size of the ray diagrams is 27x40 in. 
Rays in the region of standard refraction have a 58-in. 
radius. Through the transition layer the radius is 4 
in. The above radii are determined by the vertical and 
horizontal scaling factors and are approximately one 
ten millionth of the curvature as given by dM/dh. 
Note that the downward curvature of the earth and 
upward curvature of rays in the standard propaga- 
tion regions are made equal, thus reducing the slopes 
of the rays and resulting errors inherent with de- 
formed scale graphical methods. 
Since the tangent ray (shown with short dashes) 
intercepts only a small part of the fourth and none 
of the fifth section of measurements, the analysis 
methods employed in radar coverage diagrams had 
to be extended. Specifically, the coverage diagram 
analysis at NRSL has applied to fields between 85 and 
100 db below that at a distance of one meter from the 
transmitter. This largely excludes consideration of 
any but interference and trapping zones. 
The measurements with which correlation was de- 
sired extended to about 30-db weaker fields so that 
partial reflection and diffraction fields were involved. 
Proceeding with the ray tracing analysis, the in- 
terference field was calculated at points of intersec- 
tion of the direct and sea-reflected rays. Path differ- 
ences were determined using a map measure and a 
planimeter as explained in reference 4. Ray densities 
were measured for the direct and reflected compo- 
nents, and the associated fields were added with re- 
spect to the phase. The diffraction field below the 
tangent ray was calculated by Norton’s method. 
Reflected rays fromthe layer were introduced as 
originating at the center of the layer. The reflection 
coefficients for the angles of incidence wete calculated 
as described in reference 5 for the case of a mono- 
tonic transition layer in which the refractive index 
decreases by 50°X 10~. In the terms of field intensity 
»By F. R. Abbott, U. S. Navy Radio and Sound Labo- 
atory, San Diego, California. 
See discussion of Figure 9. 
the reflection coefficient values ranged from 0.2 to 
0.1 at 63 me and from 0.01 to 0.003 at 524 me. 
In Figure 9 the calculated normal interference 
and diffraction fields are shown dotted beside the 
measured values except at 3,250 me on which the 
30- and 45-mile sections have been displaced for 
clarity. At 63 me there is an apparent displacement 
of about 3 db which is probably associated with the re- 
duction in measurements to the decibels below the field 
at a distance of 1 m from the transmitter. Note that 
at 60 miles the interference pattern of the diffraction 
and partial reflection fields as calculated appears with 
a phase displacement of about 180 degrees from the 
observed field. The phase relationship depends, of 
course, on an assumed value of 90 degree change of 
phase on reflection. 
At 170 me there is a displacement of about 10 db 
due to difficulty of reduction in measurements. In- 
troducing a 10-db correction, alt values at 170 me 
agree closely, including the field at 130- miles, due 
solely to partial reflection. No attempt was made to 
calculate the detailed variation with altitude. 
The agreement between calculated and observed 
fields at 524 mc is excellent above, but poor below, the 
tangent ray. At 130 miles 20- to 30-db difference ap- 
pears. Note that the measured field is about 20 db 
greater than the 170-me field at that range. This 
contradicts the trend of the calculated reflection coef- 
ficients which should decrease exponentially with rela- 
tive thickness of the layer measured in wavelengths. 
The observed 524-mc fields at 130 miles on some other 
days of pronounced high-level inversions were well 
below the 170-me fields and thus in qualitative agree- 
ment with theory. At 3,250 mc there is again good 
agreement above the tangent ray, but again, in the 
region below, the observed fields were high though the 
calculated values became very small. 
Thus a preliminary check of analysis versus meas- 
urements indicates: 
1. Discrepancy of absolute values except where the 
field at the maximum of a lobe was measured. 
2. Excellent agreement as to variation with range: 
and altitude above the geometric tangent as well as 
in the diffraction-partial reflection zoné, except that, 
at 524 me and 325 me strong fields were observed 
below 4,000 ft to 130 miles in contradiction with 
theory. 
ARIZONA. 
ATMOSPHERIC REFRACTION UNDER 
CONDITIONS OF A RADIATION 
INVERSION: 
x INVESTIGATION of propagation of high-frequency 
radio waves under conditions of a nocturnal tem- 
perature inversion was made in Arizona over a short 
period in December 1944. Climatic conditions in this 
Tegion permitted testing the dependency of refractive 
index in the lower troposphere on the temperature 
lapse rate, since the water vapor content was expected 
to remain relatively constant. 
During the day in this area. the soil heats rapidly, 
producing vertical instability and convection mixing 
near the ground and hence a temperature lapse rate 
in the lower atmosphere approaching the dry adia- 
batic rate. After sunset the soil temperature drops 
rapidly, cooling the layer of air adjacent to the sur- 
face and prdducing a low-level radiation inversion 
during the night. 
It was thought that the progression of this low- 
level inversion would at times cause the lapse rate of 
refractive index to vary between slightly positive and 
zero, which would be the case of greatest interest. If 
during such a variation of lapse rate field strength 
observations are made with a receiving antenna which 
under standard conditions is in the earth shadow re- 
“By J. B. Smyth, U. 8. Navy Radio and Sound Laboratory., 
