.onal Bureau of Standards

N.W. Plds

1964

^ecltniccil <7t©te 9Jo. 219

RADIO PATH LENGTH STABILITY OF

GROUND TO-GROUND MICROWAVE LINKS

M. C. THOMPSON, Jr., and H. B. JANES

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical *92©te 219

Issued November 15, 1964

RADIO PATH LENGTH STABILITY OF

GROUND TO-GROUND MICROWAVE LINKS

M. C. Thompson, Jr., and H. B. Janes

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington, D.C. 20402

Price: 45 cents

Table of Contents

Section Page No,

1. Introduction 1

2. Data Analysis 4

2.1. General 4

2.2. Long-Term Variations 4

2.3. Power Spectrum Analysis 5

2.4. Correlation of Spectral Density Variations with Meteorological Data ... 8

2.5. Signal Amplitude Variations 9

2.6. Comparison of 100 Mc/s and 9400

Mc/s Data 10

2.7. Path Length Difference Data .... 11

3. Conclusions 13

4. Appendix 15

4.1. Tower Motion Study 15

5. References 17

Figures 1 through 50 19 through 68

Radio Path Length Stability of

Ground-to- Ground Microwave Links

M. C. Thompson, Jr., and H. B. Janes

The Lower Atmosphere Physics Section of the

National Bureau of Standards, Troposphere and Space

Telecommunications Division, conducted a series of

eight field experiments in 1958 and 1959 to study the

variation in the apparent path length of ground-toground microwave links (i. e. , the variations in phase

of 9400 Mc/s signals) and the corresponding variations

in radio refractive index and other atmospheric parameters measured at the path terminals. This report

summarizes the results obtained on paths in Colorado

and Florida. It also includes an analysis of long-term

variations in the apparent path length and associated

variables recorded during each experiment, and a power spectrum analysis of short-term variations in

apparent path length and refractivity

.

1 . Introduction

During the period from September 1958 to November 1959 the

Lower Atmosphere Physics Section of the National Bureau of Standards

conducted a series of eight experiments to study the time variations in

the electrical lengths of nearly-horizontal, ground-to-ground, line -of

sight radio links. These were conducted under a variety of environmental conditions such as might be encountered in the operation of

electronic guidance, tracking, and direction-finding systems. The

This work was sponsored, in part, by the U. S. Air Force Ballistic

Missile Division under contract number AF 04(647) - 134.
purpose of the experiments was to study the statistical properties of

the apparent path length variations and their dependence on various

meteorological parameters.

The method used for measuring the apparent path length fluctuations is basically a phase comparison technique which has been described previously [Thompson and Vetter, 1958]. The most impor2

tant atmospheric parameter in this study is the radio refractivity , which was measured in two ways. The long-term variations were

obtained from observations of temperature, pressure, and relative

humidity. The short-term variations were recorded by the use of a microwave refractometer . Standard meteorological techniques were

used to record atmospheric pressure, temperature, relative humidity,

wind velocity, and (in some cases) incident solar radiation (insolation)

at one or both path terminals.

The first of the experiments (referred to hereafter as "runs")

was made over a 15. 2 km path near Boulder, Colorado, during a 40

hour period in September 1958. A map and terrain profile of this

path are shown in figures 1 and 2. The principal objectives were to

study path length variations at 9400 Mc/s over a path having little or

no ground reflection, using both horizontal and vertical polarization.

The second run, in October, was a continuation of the same type of

measurements made in September, but narrower-beam antennas were

used and the length of the run was extended to five days to more adequately study day-to-day variations.

2 m1The radio refractivity, N, is defined by

N = (n - 1) X 10

6

,

where n is the radio refractive index.

-2-
The third run was made at 9400 Mc/s in February 1959, using a 713 m path near Boulder (figures 3 and 4). Simultaneous path length

(phase) variation recordings were made on two paths having one

terminal in common and the other terminals separated vertically,

one near maximum and the other near minimum of the height-gain

pattern. The purpose of this run was to study the effect of ground

reflections on phase stability.

The fourth run was made over a 3. Z km path near Boulder in

June (figures 5 and 6), again using a 9400 Mc/s signal. This run

supplied information on path length stability over a path longer than

that used in February, but one having the same flat terrain and low

antenna heights, thereby ensuring the existence of ground reflections.

The fifth run, in July, used the same 15.2 km path used in the

first two runs. Simultaneous 9400 Mc/s and 100 Mc/s path length

stability recordings were made to test the feasibility of using the

lower frequency and also to provide a comparison of stability recordings made under different ground reflection conditions.

The remaining runs were made on or near the Air Force Missile

Test Center at Cape Canaveral,'" Florida, to gather data under the same

climatic conditions under which actual systems are operated. The

sixth run was made at 9400 Mc/s over a 7. 7 km path over flat terrain

and at approximately grazing incidence to foliage on the path (figures

7 and 8). The seventh run was made over the same path but with path

length variations observed simultaneously at vertically spaced antennas

at one of the terminals; one antenna placed to provide a path slightly

above, and the other slightly below, grazing incidence (figure 8).

The last run was made over a 17. 1 km path extending from Cape

Canaveral to a point north of Cocoa, Florida (figures 9 and 10). The

purpose here was to study the effect of increased path length. Again

* This work was done before the name was changed to Cape Kennedy.

-3-
vertically spaced antennas were used at one terminal, one providing

a path at approximately grazing incidence with the foliage, and the

other below grazing incidence.

2. Data Analysis

2.1. General

In general, the data output from each run consisted of continuous

recordings of apparent path length variations, radio refractive index

at one path terminal using a microwave refractometer, insolation, and

horizontal wind velocity at both terminals. In addition, wet and dry

bulb temperatures and barometric pressure readings were taken at

half -hour intervals. During the last two runs, signal amplitude variations were also recorded continuously.

The path length and refractometer data were divided into two

recording pass-bands: a "low-pass" record covering the spectral

region from to about 1 c/s, and a "band-pass" record extending from

0.03 to 10 c/s. Examples of path length and refr activity data are

shown in figures 11 through 14.

The band-pass data were subjected to an analog power spectrum

analysis to show the shape of the path length and refractivity spectra

in the region from 0.1 to 20 c/s and also to indicate the variation of

spectral density with time and certain atmospheric characteristics.

2.2. Long-Term Variations

The long-term variations in phase, refractivity, and meteorological data are shown in figures 15 through 22. To obtain the graphs

of phase and wind speed and direction, the continuous chart records

were read at half -hour intervals. The effective averaging time for

these variables is estimated to be several seconds except for very

low wind speeds, for which the averaging time may become much larger.

-4-
Temperature, humidity, and pressure graphs are plotted from the

observations of the wet-and-dry bulb thermometers and the barometer

made at half-hourly intervals. In each of these readings the averaging

time is estimated to be about 10 seconds. The refractivity curves are

calculated from these meteorological observations.

It should be noted that in the case of phase and refractometer

recordings no absolute calibrations were available. Thus the data

permit only examination of the relative variations in these parameters.

The data calculated from the barometer and psychrometer readings

provide the absolute measure of refractivity shown in the graphs.

These graphs illustrate the wide variety of path length variations

that can be observed on any path lying at least partially in the lower

troposphere. For example, path length changes of as much as 30

parts per million occurred during a 24-hour period (figures 15 and 22).

These changes generally occur most rapidly near sunrise and sunset.

On occasion, excursions of 5 ppm occurred over a period of 10 minutes.

Conversely, during the night it was not uncommon for the phase to remain within a few parts in 10 million for periods of hours (figure 13).

The path length variations are in most cases well correlated

with refractivity data taken at t. e path terminals. Although the temperature and relative humidity usually exhibited a noticeable diurnal

cycle, the path length data, in general, were dominated by longer-term

variations or "trends" caused by gradually changing weather conditions,

and a diurnal cycle is often not discernible.

2.3. Power Spectrum Analysis

The short-term fluctuations in apparent path length and refractivity were subjected to a power spectrum analysis, which indicates

how much of the variance (mean of the squared deviations from the

sample mean value) is contributed by fluctuations falling into each of

-5-
several narrow bands of fluctuation frequencies. As used here, "shortterm variations" refers to the relatively small and rapid deviations

about the larger long-term trends. The purpose of the spectrum

analysis was to study the behavior of the spectral density (i.e. , variance per unit bandwidth) as a function of time and other parameters.

During runs 1 and 2 (September and October 195 8), all of the

recordings were made on paper charts. The power spectra for these

runs were obtained by digitizing the chart record manually and computing the Fourier transform of the autocovariance function. The

computing method used is essentially that suggested by Blackman and

Tukey [1958]. This analysis has been described in detail previously

[Thompson, Janes, and Kirkpatrick, I960; Thompson and Janes,

1959].

In runs 3 through 8, all band-pass data were recorded on magnetic

tape, which permitted the use of analog spectrum analysis techniques.

In this case, the power spectrum analysis consisted essentially of

passing a voltage proportional to the variable through a very narrow-band

filter and recording the mean squared output as a function of time for

each of several spectral frequencies. A time plot of spectral density

at each frequency was then obtained by dividing the mean squared filter

output by the filter bandwidth. The tape was fed through the analyzer

at a speed 100 times greater than that used in recording. This was done

to reconcile the difference between the frequency ranges of the recording

and analyzing equipment. For example, the 2 c/s filter bandwidth and

frequency range of 3 to 2000 c/s used in the analyses correspond to a bandwidth of 0. 02 c/s and a frequency range of 0. 03 to 20 c/s in recording time. An averaging circuit having a time constant of 4 seconds

(6-2/3 minutes in recording time) was used for averaging the squared

filter output in all cases except the 100 Mc/s data for July 1959. In the

-6-
latter case, a 1-second time constant was used for the lower spectral

frequencies. One disadvantage of this method is that discontinuities

of any kind in the tape data cause large transients in the analyzer output. In scaling the latter for the half-hourly values of spectral density

shown in this report, considerable care was exercised to avoid the

effects of discontinuities.

The results of the analog power spectrum analysis of the 9400

Mc/s path length and refr activity data are summarized in figures 2 3

through 26. They consist of families of spectral-density-versus -time

curves with frequency as the parameter. In general, the power spectra

show a diurnal cycle with increased spectral density during the daylight

hours. In the Florida data this night-to-day increase was on the order

of 10 to 1 in apparent path length, and even larger in refractivity

(figure 25). The Colorado data showed a smaller diurnal variation.

Figure 27 shows the median values of the spectral densities of

refractivity (N) and path length plotted as a function of frequency and

divided into daytime (7:00 a.m. to 6:00 p.m. ) and nighttime data (6:30

p.m. to 6:30 a.m.). Similar curves are shown in figure 28 for run 4

(June 1959). These curves serve to illustrate the slopes of the various

spectra and the size of the day o-night changes in spectral level. It should be noted that there is little or no systematic change in slope in

going from day to night, or from Colorado to Florida.

It would appear that the path length spectral density is significantly higher in Florida than in Colorado. However, it was found that

the particular analog spectrum analysis equipment used here could

yield results that in repeated trials differed in absolute level (i. e. , spectral density) by as much as a factor of 2. However, the relative

accuracy of spectral estimates at the various frequencies within a given run was much better (within about 20 %). Consequently, the

-7-
shapes of the median spectra are considerably more reliable than their

absolute levels. This should be borne in mind in comparing the spectra

obtained in different runs of this series.

2.4. Correlation of Spectral Density Variations

With Meteorological Data

Figures 29 through 34, inclusive, show the spectral density

curves at 1 or 3 c/s taken from the previous graphs compared "with the

corresponding wind speed, temperature, refractivity, and insolation.

The question of correlation between spectral density and the meteorological variables is a difficult one to answer quantitatively. Although

each of these variables was sampled at the rate of two readings per

hour, the effective "pass-bands" of their respective measuring systems

are not necessarily similar. In particular, the smoothness of the

spectral density curves was determined arbitrarily by the choice of

the time constant used in the wave analyzer (6-2/3 minutes in this

case).

However, it appears that of the variables selected for comparison,

the wind speed and temperature are most likely to be significantly

correlated with the apparent path length and refractivity spectral

densities. They all show a similar diurnal cycle with generally higher

spectral levels, temperatures, and wind speeds during the daytime. On

the other hand, it is not hard to find examples of correlation on an

hour-to-hour basis between spectral density and wind speed. In an

effort to describe these apparent correlations quantitatively, the

spectrum of each of the variables was separated into two parts: the

lower frequency variations were isolated by computing a 6. 5-hour

running average of the half-hourly values, while the higher frequency

variations are simply the deviations of the original data about this

running average. The correlation coefficients of both the low-frequency

-8-
and high-frequency variations of spectral density with wind speed and

temperature were computed for the July, Colorado, run and the September, Florida, run. Figures 35 through 38 summarize the results.

During the July run in Colorado, the long-term wind speed lagged

(i.e. , occurred after) the temperature variations by about three hours.

Hence, the correlation curves of wind and temperature versus spectral

density are displaced relative to each other by that amount. It is

interesting to note that the long-term path length spectra correlate

best with average end-point wind speed with very little lag, while the

refractivity spectra correlate best with temperature with no lag. This

would indicate that the path length spectral density lagged the refractivity spectral density by roughly three hours.

2.5. Signal Amplitude Variations

During the runs of October 10-12 and October 30 - November 3,

1959, in Florida, amplitude recordings were made on both the upper

and lower paths. These results are summarized in figures 39 and 40,

which show plots of samples read at 30 -minute intervals. In both runs

and on both paths, regions of rapidly changing field strength were

observed. Between 1300 and 1400 on October 11, the signal received

at the upper antenna increased by nearly 12 db, while that at the lower

antenna increased by almost 9 db. Between 0700 and 0800 of the same

day, the upper path signal increased by 6 db, while the lower was increasing by 12 db. During the early part of October 12, both signals

were some 10 or more db lower for several hours than their average

values and did not recover until after sunrise.

This is believed due to changes in the multipath resulting from

slight changes in the refractivity gradient near the ground. In these

paths, the surface vegetation and terrain combined to make it very

difficult to determine the effective antenna height. However, the

-9-
limited height-gain data which could be obtained indicated that there

was a significant ground-reflected component. The observed range of

signal amplitudes of about 20 db would require (on this basis) a reflection coefficient of about 0.9, which is not unreasonable considering the

very low angle of incidence (practically grazing). Since the paths (both

5

direct and ground-reflected) were about 2x10 X long, a change in

average refractivity of 2. 5 N-units along the path would produce a change of 180 in the phase of the signal arriving over that path. Thus,

a change in signal strength of 20 db would imply, for this path, a change in the refractivity difference of the order of a few N-units over

the vertical separation of about 15-feet. In the area involved, it is

felt that this is not unreasonable in the region immediately above the

terrain.

2. 6. Comparison of 100 Mc/s and 9400 Mc/s Data

Multipath is believed responsible for the major differences noted

in the apparent path length variations at 100 Mc/s and 9400 Mc/s during

run 5. In this case, as shown in figure 19, the 9400 Mc/s phase follows

the refractivity quite closely throughout the entire period, while the

100 Mc/s path length variations show large departures associated with

sunrises and sunsets. This is taken to indicate that the 9400 Mc/s path

is essentially free of ground-reflection (because of the greater effective

roughness at the shorter wavelength), while the 100 Mc/s path includes

a significant reflected component. Again, a change in the vertical differ

ence in refractivity of the order of a few N-units over a height of about

45 meters would be required to produce the observed effect. In view of

the nature of the path, this again is considered a reasonable change to

be expected.

-10-
Comparisons of the spectra of phase fluctuations at 100 Mc/s

and 9400 Mc/s are shown in figures 41 and 42. Since the data at each

frequency have been normalized to parts per million, similar spectral

distributions would be indicated by coincidence of the two sets of curves.

The absence of such coincidence is interpreted to indicate that the

major noise in the measuring system is in the phase measuring section.

Because of the difference in radio frequencies, a given error in the

measurement of path length variance at 100 Mc/s corresponds to an

2

error (94) , or 8800 times as large at 9400 Mc/s. Thus, we should

expect the 100 Mc/s spectrum to flatten out at a level about 4 decades

higher than that of the 9400 Mc/s spectrum. This is, in fact, observed

in figure 42. At the lower frequencies, however, the signal-to-noise

ratio improves and the 100 Mc/s and 9400 Mc/s spectra tend to coincide.

These results are interpreted to indicate that the only significant

effect of frequency (in the region 100 - 9400 Mc/s) is the result of differences in multipath behavior. In other words, in the absence of multipath, the behavior of two frequencies would be very nearly alike. The

introduction of multipath adds a frequency-sensitive mechanism which

can produce significant changes in signal behavior.

2.7. Path Length Difference Data

Run 8, over a 17. 1 km path at Cape Canaveral, involved the use

of two antennas at one terminal, separated vertically by 7 meters.

The upper antenna (19 m above ground) was located at or very near the

radio horizon, while the lower one was probably well below the radio

horizon.

The long-term variations in path (phase) difference are plotted in

figure 43. They are expressed here as variations in apparent elevation

angle in milliradians and in wavelengths of path difference. For purposes of comparison, the surface refractivity is also shown. The range

-11-
of the elevation angle variation over the 2-day period is about 1 milliradian. This appears to be fairly well correlated with the surface

refractivity. Some further analysis of these long-term data has been

made by Bean and Thayer [1963]. Figure 26 shows the power spectrum

of the apparent path length variations occurring on the upper path.

Figure 44 shows the corresponding spectrum for the lower path variations, which were recorded only during the first half of the experiment. Comparison of these two figures shows a very high correlation

in the time variations in the upper and lower path spectra. The corresponding median spectra for both upper and lower paths are plotted in

figure 45. The shapes of the spectra are similar on both paths and

are the same at night as during the day in spite of the sizeable diurnal

variation in the level of both spectra. It would also appear that the

absolute level of variance on the upper path is somewhat higher than

on the lower path, but because of the analysis repeatability problems

mentioned before, it is considered unwise to make closer than orders -

of -magnitude comparisons of absolute spectral density levels observed

on any two variables.

The time varying spectrum of path difference is plotted in figure

46. Since these variations represent changes in the apparent angular

position of the remote site as observed by this 24-foot vertical baseline system, the spectral densities are expressed in terms of milliradians. Figure 47 shows the corresponding median power spectra

for day and night. If the variations on the upper and lower paths were

uncorrelated over the whole passband, the path difference spectrum

would have the same slope and same diurnal variation in level as the

single path spectra. However, the path difference spectrum is relatively low at 0. 1 c/s, indicating that at the lower frequency end there

are components of the single -path variations which are positively

correlated, thereby reducing the variance of their difference.

12-
The diurnal variations pattern of the path difference spectrum is

reversed, with higher spectral densities during the night. This suggests

that the upper and lower path variations were more nearly correlated

during the day than at night. This may be caused by the vertical movement of convective currents during the day which would tend to synchronize refractive index variations on the two vertically separated paths.

On the other hand, horizontal stratification of the atmosphere at night

would tend to reduce the correlation.

3. Conclusions

The results of these experiments suggest the following conclusions:

1. The long-term variations in phase (apparent path

length) are well-correlated with refractivity computed from standard

meteorological data recorded at the path terminals.

2. The spectral density of phase variations in the

fluctuation frequency range from 0. 1 up to 10 cycles per second may

vary as much as an order of magnitude during a 24-hour period, being

generally low at night and high during daytime. The extent of this

effect appears to depend on the particular path, since the diurnal variations observed in Colorado we e much smaller than those observed in

Florida. Of the various meteorological parameters observed, best

correlation appears between the spectral density and the wind speed

averaged from both terminals.

3. The spectra of phase variations from 0. 1 to 10 cycles

per second have slopes (on a log-log graph) of approximately -2. 2;

i. e. , W (f) = kf"

2 ' 2

.

13-
This is somewhat higher than the value of -2. 9 observed in the October

1958 measurements. This slope does not appear to vary significantly

from day to night or from Florida to Colorado.

4. In the same region of fluctuation frequencies, the

intensity of refractivity variations may vary as much as two orders of

magnitude between day and night. Again, the daytime values are higher,

and this effect is much more pronounced in Florida than in Colorado.

5. The form of the refractivity spectra also shows little

effect of time or location, being generally of the form

wN

(f) - k'f'

1 ' 8

Again the exponent is somewhat larger than the average of the October

1958 analyses, e.g. -2.2, but as noted above, this difference probably

can be accounted for within the accuracy of the spectral density estimates.

6. Any dependence of the phase variation data on radio

signal frequency is believed to be the result of the existence of multipath, which introduces a frequency-dependent mechanism.

-14-
4 . Appendix

4. 1. Tower Motion Study

The experiments at Cape Canaveral all involved mounting one or more of the antennas used in the apparent path length measurements on

a tower made of aluminum scaffolding. Since the system is capable of

recording very small changes in apparent path length (on the order of

0. 003 mm), it was necessary to determine the extent to which the data

were effected by motion of the tower itself. To do this, during the

September 1959 run the apparent path length variations occurring over

a short (30 meter) path were recorded simultaneously with those

occurring over the long path. The physical arrangement is shown in

figure 8. The short path extended from the same antenna on the tower

used in the long path measurements to another antenna mounted about

one meter above ground and 30 meters from the base of the tower. The

path was made as short as possible in order to minimize the apparent

changes in length caused by the atmosphere as opposed to actual changes

caused by tower movement.

Figure 48 shows the time variations in the apparent path length

spectrum observed on this short path. Comparing this with the long

path spectrum in figure 25, we i±nd the diurnal pattern is very similar

in both cases, indicating that most of the variations observed on the

short path in this range of spectral frequencies were probably caused by

refractive index variations rather than by tower movement. Figure 49

shows the median spectra of the short path and long path variations, both

plotted in terms of parts per million of the long path. It is evident that

the short path length spectrum is at least an order of magnitude smaller

than the long path spectrum in the frequency range 0.1 to 1 c/s. Between 1 and 10 c/s this margin of safety drops to as low as 3 to 1

.

However, since most of the short path length variations in this frequency

-15-
range appear to be atmospheric in origin, it is very unlikely that the

long path variation data were significantly contaminated by tower movement.

The long-term (hour-to-hour) variations in the short path length,

on the other hand, appear to be more closely correlated with actual

tower movements than with refractive index changes. Figure 50 shows

these variations compared to the corresponding long-term changes in

air temperature and refractivity. The coefficient of correlation between

the short path length and refractivity is 0.16, while the correlation of

path length with air temperature is 0. 66. This" suggests that most of

the long-term path length changes on the short path can be ascribed to

differential thermal expansion of the tower and guy cables.

It should be noted that the maximum change in the short path

7

length was only about 1 mm, or a little over 1 part in 10 of the long

(7.7 km) path. Thus, the tower movements could not have contributed

a readable error to the long-term, long path variations shown in

figure 20.

-16-
5. References

Bean, B. R. , and G. D. Thayer (May - June 1963). Comparison of

observed atmospheric radio refraction effects with values

predicted through the use of surface weather observations,

Radio Sci. J. Res. NBS/USNC-URSI 67D, No. 3, 273-285.

Blackman, R. B., and J. W. Tukey (1958). The measurement of

power spectra from the point of view of communication

engineering, Bell System Tech. J. , Parts 1, 2, 37,

185 and 485.

Thompson, M. C, Jr., H. B. Janes, and A. W. Kirkpatrick

(January I960). An analysis of time variations in tropospheric refractive index and apparent radio path length,

J. Geophys. Res. 65, No. 1.

Thompson, M. C, Jr., and H. B. Janes (July-August 1959).

Measurements of phase stability over a low-level tropospheric path, Radio Sci. J. Res. NBS/USNC-URSI 63D

(Radio Prop. ), No. 1

Thompson, M. C, Jr., and M. J. Vetter (February 1958).

Single -path phase measuring system for three -centimeter

radio waves, Rev. Sci. Instru. 29, No. 2, 148-150.

-17-

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EXAMPLES OF APPARENT PATH LENGTH VARIATIONS OBSERVED

ON 15.2 km (9.4 mi) PATH AT BOULDER, COLORADO

JULY 24, 1959

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-31-
EXAMPLES OF REFRACTIVITY VARIATIONS

CAPE CANAVERAL, FLORIDA SEPTEMBER 4,1959

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-32-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

15.2 km (9.4 mi.) PATH- BOULDER. COLO.-SEPT. 1958

z

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WIND DIRECTION

NORTH TERMINAL

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Figure 15

-33-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

15.2 km (9.4 mi. ) PATH- BOULDER, COLORADO- OCT. 1958

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Figure 16

-34-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

0.7 km (2340 ft.) PATH -BOULDER, COLORADO, FEBRUARY 1959

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Figure 17

-35-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

3.2 km(2mi.) PATH - BOULDER, COLORADO- JUNE 1959

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Figure 18

-36-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

15.2 km (9.4 mi) PATH, BOULDER, COLORADO JULY 1959

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Figure 19

-37-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

7.7 km (4.8 mi.) PATH -CAPE CANAVERAL, FLORIDA - SEPT. 1959

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Figure 20

-38-
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

7.7 km (4.8mi.) PATH- CAPE CANAVERAL, FLA. - OCT. 1959

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Figure 21

-39-

24

1

06 12 10-12-59
LONG-TERM VARIATIONS IN APPARENT PATH LENGTH

AND RELATED VARIABLES

17.1 km( 10.6 mi.) PATH OCT-NOV, 1959 CAPE CANAVERAL. FLORIDA

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Figure 22

-40-
TIME VARIATIONS IN THE POWER SPECTRA

OF APPARENT PATH LENGTH AND REFRACTIVITY

3.2 km (2 Ml.) PATH AT BOULDER, COLORADO

06 12 16 6-7-59

Figure 23

-41-
TIME VARIATIONS IN THE POWER SPECTRA OF

APPARENT PATH LENGTH AND REFRACTIVITY

15.2 km(9.4mi) PATH, BOULDER, COLORADO

12 18 24 7-23-59

06 12 7-25-59

Figure 24

-42-
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TIME VARIATIONS IN THE POWER SPECTRA OF

APPARENT PATH LENGTH AND REFRACTIVITY

17.1 km (10.6 mi.) PATH AT CAPE CANAVERAL, FLORIDA

12 18 24 06 12 18 24 06 12 18 24 06 12 10-30-59 10-31-59 II -1-59 11-2-59

24 06 12 18 11-3-59

Figure 26

-44-
COMPARISON OF SPECTRA OBSERVED IN COLORADO AND FLORIDA

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1.0 3 CYCLES PER SECOND

Figure 27

-45-
MEDIAN POWER SPECTRA OF APPARENT PATH LENGTH

AND REFRACTIVE INDEX

3.2 km. (2 Ml.) PATH AT BOULDER, COLORADO

JUNE 1959

1-2

a.o

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^DAY

NIGHT-^

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INDEX

^^-— DAY

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NIGHT'/

0.3 1.0 3.0 CYCLES PER SECOND20

Figure 28

-46-
APPARENT PATH LENGTH SPECTRAL DENSITY

COMPARED WITH OTHER DATA

15.2 km (9.4 mi.) path, boulder, Colorado

o 10

g- 10'

9400 Mc PATH LENGTH SPECTRAL DENSITY AT 1 cps J hI A.A A t\ A V J V VIVA

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(f) J i\

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A 1 A1 \i V

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25

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IAVERAGE TEMPERATURE AT TERMINALS 1

270

260

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IAVERAGE REFRACTIVITY ATTERMINALSl

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50

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A

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24 06 12 7-25-59

Figure 29

-47-
REFRACTIVITY SPECTRAL DENSITY COMPARED

WITH OTHER DATA TAKEN AT NORTH TERMINAL

15.2 km (9.4mi.) PATH, BOULDER, COLORADO

GO 10 Q.O

CO «3

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i REFRACTIVITY SPECTRAL DENSITY AT 3 cps

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06 12 7-24-59

24 06 12 7-25-59

Figure 30

-48-
APPARENT PATH LENGTH SPECTRAL DENSITY

COMPARED WITH OTHER DATA

7.7 km (4.8 mi.) PATH, CAPE CANAVERAL, FLORIDA

enQ.o

E

CL

Q.

1 1 1 1 1 1 PATH LENGTH SPECTRAL DENSITY AT 1 cps

isr*-*"S. _£lA r ^A1

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1 11 1 1 AVERAGE WIND SPEED AT TERMINALS

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AVERAGE TEMPERATURE AT TERMINALS

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380

370

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06 12 18 24 06 12 18 24 06 12 18 24 9-4-59 9-5-59 9-6-59

Figure 31

-49-
REFRACTIVITY SPECTRAL DENSITY

COMPARED WITH OTHER DATA TAKEN AT NORTH TERMINAL

77km (4.8 mi.) path, cape Canaveral, Florida

n

-2

Q.

hA /

REFRACTIVITY SPECTRAL DENSITY /

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380

370

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24 06 12 18 9-3-59

24 06 12 18 24 9-4-59

6 12 18 24 06 12 18 24 9-5-59 9-6-59

Figure 32

-50-
APPARENT PATH LENGTH SPECTRAL DENSITY

COMPARED WITH OTHER DATA

17.1 km(l0.6mi.) PATH AT CAPE CANAVERAL. FLORIDA

10Q. ~~ 10 Q. 3 io"

p/

1\TH L

1ENGTI

1 1

1

I 1 H SPECTRAL DENSITY AT 1 cps

o

to

AVERAGE WIND SPEED AT TERMINALS

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365

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345

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12 18 24 06 12 18 24 06 12 18 24 06 12 18 24 06 12 18 10-30-59 10-31-59 1 1-1-59 11-2-59 11-3-59

Figure 33

-51-
REFRACTIVITY SPECTRAL DENSITY COMPARED WITH

OTHER DATA TAKEN AT WEST TERMINAL

17.1 km (10.6 mi) PATH AT CAPE CANAVERAL, FLORIDA —i

1 1 1 1 11 r~

REFRACTIVITY SPECTRAL DENSITY AT 3 CPS

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CD

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Figure 34

11-2-59 II -3-59

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9400 Mc SIGNAL AMPLITUDE VARIATIONS

7.7 km (4.8 mi.) PATH, CAPE CANAVERAL, FLA. -OCT. 1959

UPPE R PATH W

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-58-
TIME VARIATIONS IN THE POWER SPECTRA

OF THE APPARENT PATH LENGTH OF 100 MC AND 9400 MC

15.2 km (9.4 mi.) PATH AT BOULDER, COLORADO

100 MC

0.03 Cps

9400 MC

JULY 23

06 12 JULY 24

Figure 41

-59-

24 06 12 18 JULY 25
COMPARISON OF 100 Mc AND 9400 Mc SPECTRA

OBSERVED IN BOULDER, COLORADO

0.3 10 3 CYCLES PER SECOND

10 20

Figure 42

-60-
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-62-
MEDIAN POWER SPECTRA OF PATH LENGTH VARIATIONS

ON TWO VERTICALLY -SEPARATED PATHS

17.1 km. (10.6 Ml.) PATHS AT CAPE CANAVERAL, FLORIDA

OCT 30 - NOV. 1,1959

CO

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Figure 45

-63-
0-

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.64-
MEDIAN POWER SPECTRA OF APPARENT ELEVATION ANGLE (PATH DIFFERENCE)

VARIATIONS 171 km. (10.6 Ml.) PATH AT CAPE CANAVERAL, FLA.

NOVEMBER 1-3, 1959

10"

10"


 10 a.o

(7) Z

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0.1 0.3 CYCLES PER SECOND

Figure 47

-65-
u_OS T Z> 1- £T < 1- LL O

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-66-
MEDIAN POWER SPECTRA OF APPARENT PATH LENGTH VARIATIONS

ON LONG AND SHORT PATHS

SEPTEMBER 1959 CAPE CANAVERAL, FLORIDA

(ORDINATE REFERS TO PARTS PER MILLION ON LONG PATH)

10 -2

10"

en

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10"

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LONG PATH LENGTH

S^_ DAY \^---NIGHT

SHORT PATH LENGTH

DAY NIGHT '

0.1 0.3 10 CYCLES PER SECOND

Figure 49

-67-
AIR TEMPERATURE AND REFRACTIVITY COMPARED TO

APPARENT PATH LENGTH VARIATIONS ON SHORT (30 m) PATH

SEPTEMBER 1959

35

UJo

<£ 30 o

CO

CAPE CANAVERAL, FLORIDA

25

20

AIR TEM PERATUR

SHORT PATH LENGTH

(PATH LONGER)

400

390

3

2

380

370

360,

rJ^r ^REFF? ACTIVITY

ir\iv

06 12 9-3-59

24 06 12 18 9-4-59

06 12 9-5-59

24 06 12

I 9-6-59 I

Figure 50

G PO B4S - 41 -68-