I urn NOV 2 1970

^ecltnical vtote ^Zo. 339

OBSERVED PHASE-FRONT DISTORTION IN SIMULATED

EARTH-TO- SPACE MICROWAVE TRANSMISSIONS

H. B. JANES AND M. C. THOMPSON, JR.

'-'$%&* "'"foNr ' WSi%. '"

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical ^Tlete 339

ISSUED May 12, 1966

OBSERVED PHASE -FRONT DISTORTION IN SIMULATED

EARTH -TO -SPACE MICROWAVE TRANSMISSIONS

H. B. Janes and M. C. Thompson, Jr. Institute for Telecommunication Sciences and Aeronomy :

Environmental Science Services Administration

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.

Formerly the Central Radio Propagation Laboratories of the National Bureau of standards.

CRPL was transferred to ESSA in October, 1965 but will continue to use NBS

publications series pending inauguration of their own.

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

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TABLE OF CONTENTS

1. Introduction

2. General Description of the Experiment

3. Analysis of Results

4. Summary and Conclusions

5. Appendix

6. References

Figures 1 through 73

Table II Table III Table IV

Table V

1

3

5

15

18

19

20-92

93

94

95

96

Observed Phase -Front Distortion in Simulated

Earth-to- Space Microwave Transmissions

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

An experimental study has been made of the time and

space statistics of the phase -front distortion of microwave

signals sent from a ground terminal to an elevated terminal. These phase -front characteristics are important in

systems involving phase measurements between a ground

station and a moving air -borne or space terminal. To isolate atmospheric errors from random motion of the upper

terminal, the latter was simulated by a series of mountaintop antenna arrays. Phase-front distortion was analyzed in

terms of time variations in radio range on a single path and

in first and second range differences from pairs of paths.

The cross-correlations of (1) range variations on adjacent

paths, and (2) range difference variations on both adjoining

and separated pairs of paths are investigated, including the

strong dependence of correlation on the portion of the power

spectrum included in the data. The effect of the mountaintop terrain on the spatial homogeneity of the phase -front was

examined and found to be insignificant. A diurnal pattern in

the variance of 15-minute range difference samples was

observed, with minimum variance in the early morning hours.

This pattern was not observed in the range variances, nor

were the range and range difference variances significantly

correlated with refractive index, air temperature, pressure

or wind speed data at the lower terminal.

1. Introduction

A microwave signal transmitted through the troposphere is subjected to random retardations because of space and time variations in

the atmospheric refractive index along the radio path. These retardations

result in random variations of the phase -of-arrival of the signal, and are

an important source of error in radio measurements of range and/ or angular position.
Several experimental studies of range and range difference (angular

position) variations caused by the atmosphere have been conducted over

the past several years on slant paths to simulate ground-to- space transmissions [Norton, et al. , 1961; and Janes and Thompson, 1964]. To

minimize contamination of the data from geometric variations in range,

these tests were all made on geometrically-stable paths with the upper

terminal on a mountain.

Extension of these fixed-path data to the moving beam case in which

the lateral movement of the upper terminal imparts a non-zero angular

velocity to the propagation path requires a knowledge of the spatial statistics of the phase -of -arrival along the horizontal path of the moving

upper terminal. In effect, the phase -front of a signal originating at the

lower terminal will be distorted or "crinkled" by the time it arrives at

the line of travel of the upper terminal and the time variability of the

observed phase will be a function of the spatial wave-front statistics and

the velocity of the upper terminal.

In June and July of 1964, the Central Radio Propagation Laboratory

of the National Bureau of Standards performed an experiment under the

sponsorship of the United States Air Force Avionics Laboratory to

study the time and space statistics of this elevated phase -front. In particular, the objective was to obtain a detailed statistical description of

time and space variations in the phase -front to serve as a basis for predicting atmospheric errors in microwave range and/ or angular position

measurements involving a moving upper terminal.

; 'Tn this discussion, we assume for convenience that the signal is originating at the lower terminal and the phase is being observed at the upper

terminal, but the transmitting and receiving roles could, of course, be

interchanged without changing the results.

**On October 11, 1965, the CRPL was redesignated the Institute for

Telecommunication Sciences and Aeronomy of the Environmental Science

Services Administration.

*** Project 4108, Task 4108 02, D. O. AF(33-657) 63-391

-2-
The purpose of this report is to describe the experiment, the data

obtained, and the results of the statistical analysis.

2. General Description of the Experiment

2. 1 Propagation paths, antenna arrangements

In principle, the best experimental arrangement would have included

a moving terminal (e.g. , an aircraft or satellite) sweeping with a perfectlydetermined trajectory across the sky to measure the phase-front characteristics of a ground-based signal. However, this possibility was ruled

out at the outset for compelling technological reasons. It was decided to

substitute an array of fixed mountain-top antennas for the moving terminal,

and make phase -of -arrival and phase -difference recordings at several

points on the array simultaneously. This arrangement, illustrated in

figure 1, isolates the purely atmospheric effects from the random motion

of any practical airborne terminal and permits the collection of statistically large data samples of phase -front behavior.

The site chosen is on the Island of Maui, Hawaii, with propagation

paths extending from a point 25 meters above sea level at the abandoned

Puunene airport to an array of four antennas approximately 3000 meters

above sea level at the summit of Mt. Haleakala. The paths were from

24. 5 to 24. 9 km in length and were tilted at an angle of 7 degrees from

the horizontal. A map and terrain profile are shown in figures 2 and 3.

All phase measurements were made at a radio frequency of 9. 4 GHz.

Parabolic antennas 122 cm in diameter were used at both upper and lower

sites. At the latter site the antenna was mounted 163 cm above ground

and the upper antennas were mounted 91 cm above local terrain. In both

cases,- the antenna beams were sufficiently narrow to avoid ground

reflections.

The phase measurement equipment used was a modification of a basic system described previously [Thompson and Vetter, 1958].

-3-
The experiment was divided into 9 "runs" or periods of continuous

recording activity, each approximately 24 hours long. Each run was

characterized by a particular arrangement of the 4 antennas at the upper

site. The several arrangements were chosen to give as wide a variety

of path separations as possible. Two basic configurations were used,

and these are shown in a sketch in figure 4. Configuration A provided

two pairs of adjacent paths, the antenna separation of one pair (A, C and

C,D) being twice that of the other (A,B and B,C). In addition, path pair

A,D provided a separation twice that of A , C and C,D. Configuration B

provided two path pairs with equal antenna separations, the pairs in turn

being separated by various distances up to a maximum of 790 meters.

Table I gives the inclusive times and antenna arrangement for each

run. The "antenna locations" noted in the table refer to the positions of

the four upper-site antennas in use in each run as identified by the circled

numbers on the topographic map of the Haleakala site in figure 5.

2. 2 Data Output

The principal data consist of continuous recordings of time variations of 1) the phase-of-arrival of signals sent over one (and in some

cases two) of the four paths in use at any one time, 2) the difference in

the phase-of-arrival observed on pairs of paths, and 3) the second

difference, or the difference of two phase difference variables observed

on two pairs of paths.

Although these data were originally calibrated in terms of phase-ofarrival at the radio frequency of 9. 4 GHz, the results are discussed here

in terms of variations in the apparent or radio path lengths, and their

first and second differences, and will be referred to as range (R), range

2 difference (AR), and second range difference (A R), respectively. This

permits description of the phase front in terms of spatial deviations or "crinkling" of an imagined surface of constant phase.

4-
The range and first and second range difference data were recorded

as continuous variables on magnetic tape and on paper strip charts. The

pass -band of the measuring and tape recording system extended from

to about 10 Hz. Some typical paper chart recordings of range and range

difference are shown in figures 6, 7, and 8.

Secondary data consisted of magnetic tape and paper chart recordings

of atmospheric refractivity at 1. 5 meters above ground at the lower site,

paper chart recordings of wind speed and direction measured at 3.7 meters

above ground at the upper site, and 6. 4 meters above ground at the lower

sites, and paper chart recordings of refractivity at 1. 5 meters above

ground at from 2 to 4 points on the upper antenna array. In addition,

hourly or half-hourly readings of wet and dry bulb temperature and barometric pressure were taken at both sites. To record cloudiness, 35 mm

pictures of the path were taken at both sites at hourly or half -hourly

intervals.

3. Analysis of Results

The objective of the data analysis was to describe as completely as

possible the time and space variability of the phase -front after being

"crinkled" or distorted in its passage from the lower site to the mountaintop antenna array. In the analysis the time behavior of the phase -front

observed at several points was first examined. The resulting time (and

frequency) statistics were then used to study 1) the degree of spatial

homogeneity of the data gathered along the phase-front, and 2) the spatial

covariance of the phase (range) variable, R, and of its spatial differential,

£R. The correlations of these phase -front statistics with time of day and

with several meteorological parameters were finally investigated.

-5-
The basic input to the analysis consisted of continuous data from

45 fifteen -minute sample periods -- 5 samples from each of the 9 runs. The only criteria used in selecting the samples were that all variables be

free of recording defects and that the sample times be distributed as evenly as possible around the clock. Each sample was digitized at the

rate of 25 to (in some cases) 30 points per second, giving a total of 22, 000

to 27, 000 discrete points per sample per variable. The basic output of

the analysis consists of variances, power spectra and cross-correlation

coefficients arranged to illustrate the statistical characteristics of the

phase-front.

3. 1 The variance and power spectrum

A few preliminary comments on these statistics may be helpful in

interpreting the results.

The power density spectrum (i.e. , the Fourier cosine transform

of the autocovariance function) is a widely-used statistical tool for

analyzing the variability of a given quantity as well as the covariability

of two quantities. It indicates the amount of variance (i. e. , mean- squared

deviation from the sample mean) contributed by the fluctuations lying in a given band of fluctuation frequencies. Its integral over all fluctuation

frequencies is the total sample variance. In the case of discrete data,

this relationship is given by

2 1 n — 2 1 m_1 1 S (X) = ^T ill < X

i

" X> " t 2

W <fo> + ftW(V

+

1

W(fm

)] Af '

2 where s (X) = sample variance of X, determined from n values of X,

W(f .) = power density (in units of variance per unit bandwidth) in a frequency band of width Af centered on f . , and

m = number of non-zero frequencies at which W(f) is estimated in a given computation. (In this analysis m = 100, although for

graphical clarity, not all values are plotted. )

-6-
In the case of two variables, one can obtain the normalized cospectral density, i.e. , the coefficient of cross-correlation of fluctuations

occurring in the frequency increment Af centered on f . If W (f), W (f),

and W 7\(^) are the spectral densities of the two variables and of their

( 1 - L)

difference, respectively, the normalized cospectral density is given by

W(f) +W (f) - W (f)

C(f) =

l [ ' ZyjW^i) W

2

(f)

If W (f) = W (f ) =W(f), a valid assumption in most cases discussed in

this report, this simplifies to

W

d-2)

(f)

C(f) = 1 - U L)

2W(f)

In this report, most of the variance and correlation data are represented by two sets of values for each sample. One set of results, computed from the "raw" data, includes the entire pass -band of the input data

from zero to 1. 5 Hz or (in some cases) 1. 25 Hz. (The two upper

frequency limits resulted from a change-over to new digitizing equipment.

Since it has no significant effect on the results, the upper limit is given

simply as "approximately 1.4 Hz. ") The second set of values, labeled

"approximately 0. 007 to 1. 4 Hz, " was obtained by integrating the power

spectra over the specified frequency range, i.e. , it consists of only that

part of the total variance contributed by the frequency band covered by the

computed power spectrum. This computation is analogous to passing the

continuous data through an infinitely sharp band-pass filter. These

"filtered" data variances are of interest because longer-term trends

which often dominate the "raw" data have been, in effect, removed

prior to the computation of variances, correlation coefficients, etc.

-7-
3. 2 Range variations

Examples of time variations in range as seen at one antenna are

shown in figures 6, 7, and 8. (The abrupt shifts in level occurring whenever the trace nears either edge of the chart are the result of an automatic

scale -shift device used to insure that the level stays within the range of

the recorder while at the same time permitting maximum resolution. ) The power spectra of all 15 -minute range data samples are plotted in

figures 9 to 17, inclusive. They are shown here to illustrate the wide

variability in magnitude of spectral density. For example, the spectral

-4 2.

density at 0. 1 Hz ranges from about 0. 2 to 3 x 10 cm /Hz. On the

other hand, the slope of the spectrum varies only slightly from sample

to sample, and is approximately -2. 5, the same value that has been

obtained repeatedly in previous experiments [Thompson, Janes and

Kirkpatrick, I960; Thompson and Janes, 1964; Janes, Kirkpatrick,

Waters, and Smith, 1965]. (In this context, a slope of -2.5 means that

-2. 5

the spectral density is proportional to f . ) In these graphs, a distinction is made between day and night samples

to illustrate any persistent diurnal effect. However, with the exception

of run 2, no such effect was clearly seen. (The dependence of variance

on time of day will be discussed in a later section. ) The curve in each figure joins median values and will serve as representative range spectra for comparison with other spectra.

Having examined the spectral characteristics of range variations at

each of several locations, we find the next question to be investigated

is whether these characteristics are influenced by the particular location

of the upper terminal. The map in figure 5 illustrates the very rugged

terrain over which the antennas were distributed on Mt. Haleakala, and

it would not be unreasonable to ask if the phase -front structure was

distorted by the local terrain. To illustrate the spatial homogeneity of
the phase -front, the range variances observed simultaneously at pairs of

points on the array are compared in figure 18. It can be seen that despite

the wide range of variance levels, the variances are highly correlated on

paths separated by as much as 790 meters. This suggests that if the

mechanisms causing the range variations are influenced by the presence

of the mountain, they are at least being influenced uniformly over the

800-meter segment of the phase-front.

One of the most important characteristics of the phase-front is the

so-called spatial correlation of range at an instant of time as a function of

separation. In the absence of a continuous record of range versus position along the phase-front, this spatial correlation function can be estimated by the time cross-correlation of range variations observed at pairs

of points as a function of separation.

Some caution must be exercised in making this estimation of spatial

correlation from time correlation, however. This is because the coefficient of cros s -correlation of time variations in range is a function not

only of path separation but also of the spectral frequency pass -band over

which the data are being examined. For example, figure 19 shows the

correlation coefficients of range versus upper terminal separation, using

first "raw" data (nominal pass-band to 1.4 Hz) and then the "filtered"

data (using only the pass -band covered by the power spectra, i. e. , about

0. 007 to 1.4 Hz). The line segments join median values of correlation

at each separation. The necessity for specifying the data pass -band is

obvious in this figure. It should also be borne in mind that the finite

sample length itself acts as a high-pass filter in that it removes variance

contributions from frequencies that are low compared to the reciprocal

of the sample length. For example, if one -hour sample periods had been

used instead of 15 minutes, the "raw" data correlations (0 to 1.4 Hz)

would have, in general, been higher than those shown.

9-
The spectral distribution of correlation can be examined by comparing the power spectra of range (R) and range difference (AR), as explained in section 3. 1. This is done in figures 20, 21, and 22, using

the median spectra from the range spectrum graphs discussed previously,

along with the corresponding median spectra of range difference data.

(The individual AR spectra from which the latter were obtained are shown

in figures 38 to 46, inclusive. ) Keeping in mind that the extent to which the AR spectrum falls below

twice the level of the R spectrum is a measure of the correlation of the

two R variables (section 3. 1), two characteristics of phase-front variations are shown clearly in these figures. Firstly, the correlation of the

two R variables at a given separation decreases with increasing spectral

frequency until a critical frequency is reached beyond which the AR

spectral density is approximately equal to twice that of R, indicating a complete lack of correlation. (Because of random sampling errors and

the use of median spectra, these spectral density relationships are only

approximately fulfilled in these graphs. ) Secondly, the minimum frequency

above which the ranges are uncorrelated and the degree of correlation at

any lower frequency are both inverse functions of path separation. Note,

for example, that the range variations on paths separated by 1. 25 meters

(run 3, figure 20) are well correlated over the entire spectrum frequency

range, 0. 01 to about 1. 5 Hz, while those at separations of 790 meters

(run 6, figure 21) show no correlation whatever in the same two-decade

band. At a separation of 10 meters (runs 1 and 2, figure 20) the critical

frequency dividing correlated and uncorrelated regions appears to be

about 0. 1 Hz.

10-
3. 3 Range difference variations

An analysis somewhat analogous to the range analysis can be made

of the range difference (AR) data, which represent time variations in the

space differential of the phase-front. It was seen in connection with the

correlation analysis in the previous section that the spectral density of

AR at low frequencies decreases with decreasing path separation. The

corresponding dependence of AR variance on path separation is shown in

figure 23, where again the "raw" or total variances are compared to the

"filtered" variances computed only for the frequency band covered by the

spectra. It is not surprising that the latter process, which in effect

removes low frequency trends from the data before computing the variance,

produces a relatively larger reduction in variance at the large separations,

where trends are more evident, than at the small separations. This

effect shows up as a reduction in the slope of the points in the right-hand

graph in figure 23.

It is interesting to note that if the deviation of the observed phase -

front from a non-crinkled (free-space) phase-front could be depicted by

a simple wedge-shaped distortion that prevailed over the whole phase -front,

the points would fall on a line with slope of + 2. It is clear that the data

in both graphs fail to conform to this simple model, and if the data had been

filtered further to remove more low-frequency variance (e. g. , by using

shorter samples) the departure of the data from this model would have

been even greater. This again emphasizes the caution that must be

exercised in deriving spatial statistics from time data.

Figures 24, 25, and 26 show a comparison of pairs of range difference variances obtained simultaneously at different parts of the phase

front. As in the case of the range data, there appears to be good spatial

homogeneity in the phase difference data. In other words, these graphs

suggest that the AR data were not contaminated in any persistent way by

local terrain features along the mountain top.

-11-
The question of correlation of range difference variations at different points on the phase-front is complicated by a spectral frequencydependence similar to that already observed in the range data. To illustrate this, a comparison is made in figure 27 of the power spectra of

2

range differences (Ml) and of the difference of two AR variables (A R),

using medians of the individual spectra in both cases. Here again,

correlation is indicated by the amount by which the A R spectrum falls

below twice the AR spectrum (see section 3. 1). In this figure all AR data

were recorded on adjoining path pairs, i. e. , one path was common to

both pairs. The 1. 25- and 2. 5-meter pairs in run 3 show high correlation

at the lower frequencies, but none of the other pairs show definite correlation over this spectral frequency region, with the possible exception of

the 10-meter pair in run 1. Figure 28 shows a similar comparison for

separated path pairs, and it is clear that the correlation is negligible

-2

over the entire two decades from 10 to 1 cycle per second.

The cross-correlation coefficients computed from the 15-minute

AR samples are plotted in figure 29 for both "raw" and "filtered" data.

The abscissa is the separation of the path pairs, measured from their

centers. Comparing these spatial correlation functions for AR with the

corresponding graphs for the range data (figure 19), it can be seen that

the AR correlations decrease more rapidly with increasing separation.

It is also interesting to note that "filtering" the data has less effect on

the range difference correlation function than on the range correlation

functions. This is because the AR variances are not as dominated by low

frequency contributions, and hence eliminating the latter before computing

the correlation coefficient has relatively less effect on the result.

-12-
A significant feature of the range difference correlation functions

is that the correlation is negligible for all spacings (between centers of

path pairs) greater than about 20 meters, regardless of the antenna separation within each pair. (Note that for all spacings of 20 meters or less

the path pairs adjoin, i. e. , one path was common to each pair. ) It should

be borne in mind that in general, reducing the sample length below the

15 minutes used here would reduce the correlation further. Since any

system involving a moving air -borne or space terminal would probably

have considerably less than 15 minutes available to make an angle determination from AR data, the correlations shown here are almost certainly

higher than could be realized in an operational situation.

3. 4 Variances of R and AR versus

time of day and/ or meteorological parameters

It has been evident throughout this investigation that the variances

of the 15-minute samples of range and range difference vary widely from

sample to sample. Although this variability is to be expected in any

sampling process, it should be determined how much of this variability

in sample variances can be traced to a dependence on time of day or on

various meteorological data. Any such dependence would be valuable in

predicting periods of increased phase-front distortion.

In figure 30, the range variances of all 15-minute samples are

plotted versus time of day. As before, both "raw" and "filtered" data

(pass bands: to 1.4 and 0.007 to 1.4 Hz, respectively) are shown.

Neither variance shows a clear-cut diurnal pattern, except for a slight

reduction in the spread or range of variance values from about 0800 to

1400. In the case of the filtered data, there also appears to be a reduction

in the variance level around 0600.

-13-
The corresponding range difference variances are plotted versus

time of day in figures 31 and 3 2. Here a slightly more definite diurnal

pattern can be seen. In both the raw data of figure 31 and the filtered

data in figure 3 2, there is a tendency for the variances to increase gradually during the daylight hours, reach a maximum in late afternoon, and

then subside slowly during the evening. For example, at the smaller

separations (1. 25 to 10 meters) the average variance increases by a

factor of about 10 from early morning to mid-afternoon.

The search for relationships between range or range difference

variance and refractive index or other meteorological variables was

considerably less fruitful. Since the radio range is proportional to the

average refractive index along the path, the range variance might be

expected to be proportional to the refractive index variance observed at a point on the path. To check this possibility, in figure 33, the range

variances are compared to the corresponding variances of refractive

index (expressed in refractivity (N) units) recorded at the lower site.

It is clear from these graphs that no close relationship exists in these

sample statistics.

Similarly, in figures 34 to 37, inclusive, the range variances and

the difference variances for three representative path separations are

compared with air temperature, refractivity and wind speed observed

at the upper and lower sites. The temperature and refractivity values

were estimated by interpolation of the meteorological data read at halfhour intervals at the upper site and hourly at the lower. The wind speeds

were taken from the continuous anemometer recordings by visually

estimating the average speed during each of the 15-minute sample periods,

(The data pass-bands noted in the figures refer, of course, only to the

radio data. )

-14-
The purpose of these graphs is to illustrate any obviously strong

correlations. The number of data points available, especially in the

case of the range differences, is too small to justify a sophisticated

search for subtle correlations, especially since weak correlations would

be of little value operationally. The strongest correlations appear to be

between variance and wind speed at the lower site, and even these are not

impressive. The correlation coefficients of the logarithm of variance

versus wind speed in each case is listed below:

Radio data pass -band

Variable to 1.4 Hz 0. 007 to 1. 4 Hz

Range +0.42 +0.60

Range Difference

5-meter path separation +0. 52 +0. 36

40-meter path separation +0. 21 +0. 56

750-790-meter path separation +0. 54 +0. 07

4. Summary and Conclusions

In this experiment a study has been made of the statistical structure

of the elevated phase -front of a ground -based microwave signal that has

been distorted by propagation through the lower layers of the troposphere.

Time statistics of phase -front variations (in terms of radio slant range

and range difference) have been examined with the spacing of the several

phase sensors along the phase -front as a parameter.

The principal results can be summarized as follows:

1. Although the antennas for the phase measurements at the upper

site were mounted on very uneven terrain on a mountain summit, the

results obtained at various points of the array indicated no significant

bias as a function of sensor antenna location. Although it is probable

that the presence of the mountain did have some effect on the data, it

appears that any such effect was uniform over the entire segment of the

15-
phase-front "seen" by the mountain-top array. Although the influence of

the mountain is difficult to assess quantitatively, results obtained in a companion experiment at this site sponsored by the U. S. Air Force

Electronic Systems Division lend support to a belief that such an influence

was small in at least some respects. In the latter experiment a comparison was made of the refractive index profiles measured with an airborne

refractometer in vertical ladder flights near the lower terminal as opposed

to profiles from slant descent flights directly down the radio path. No

systematic difference was found between these two types of profile, indicating that the mountain had no significant effect on long-term (e. g. , hour-to-hour) changes in average refractive index along the radio path.

Its effect on short-term phase statistics, however, is unknown.

2. The cross-correlation of range variations at separated points

on the phase -front was investigated as a function of path separation.

Although spatial correlation functions are shown, it is emphasized that

the cross -correlation of range variations on two paths is not only a

function of their separation but also of the sample length and the

fluctuation frequency pass -band of the range data. For this reason,

application to a particular system will require careful modification of

these results to fit the effective pass -band of the system.

3. Similarly, the cross -correlation of range difference variations

on both adjoining and separated pairs of paths was studied. It was found

to drop off more rapidly with increasing separation than did the range

data, although here again the spectral frequency dependence of the

correlation was evident. Using 15-minute samples, the correlation of

range difference variables was negligible when the distance between path

pairs exceeded about 20 meters regardless of the path separation within

each pair. Reducing the sample length further would, in general, have

reduced the correlation at a given separation accordingly.

-16-
4. An analysis of the range and range difference variances of

15-minute samples revealed little or no significant dependence on several

meteorological parameters (i. e. , temperature, pressure, refractive

index, wind speed at both terminals). The range variance was not found

to be correlated with time of day or with the variance of refractive index

observed at the lower terminal. On the other hand, the range difference

variances (especially for small antenna separations) did show a definite

diurnal pattern, with values during the afternoon hours on the order of

10 times larger than night-time values.

-17-
5. Appendix

In addition to the material discussed in preceding sections of this

report, there were other data recorded and processed in the course of

the experiment which are not discussed in detail here but which may prove

helpful in further interpretation of the results, and are of interest from

the standpoint of basic radio propagation research.

Figures 38 through 46 show the power spectra of all range difference samples, plotted to distinguish between day-time and night-time

samples. The medians of these sample spectra, represented by the line

through the points in each graph, were used in comparing range and range

difference spectra in section 3. 2.

Figures 47 through 55 show long-term variations in range observed

at one point on the phase-front along with refractivity and relative humidity computed from meteorological data taken at each site. The corresponding air temperature, pressure and wind velocity data are plotted in

figures 56 through 64.

To show cloud activity during (or near) each of the day-time sample

periods, the appropriate path photographs taken at each path terminal

are shown in figures 65 through 73. The locations of upper and lower

sites are indicated on figure 69.

Tables II through V list variances of range and first and second

range differences computed from all of the 15-minute sample periods.

These tables include "raw" variances (pass-band: approximately to

1.4 Hz) computed directly from the digitized data, and "filtered" variances (pass-band: approximately 0. 007 to 1. 4 Hz) computed by integrating the power spectra over that frequency range.

-18-
6. References

Janes, H. B. , A. W. Kirkpatrick, D. M. Waters, and D. Smith (Apr.

12, 1965) Phase and amplitude diversity in over -water transmissions

at two microwave frequencies, NBS Technical Note 307.

Janes, H B. , and M. C. Thompson, Jr. (Nov. 1964) Errors induced by

the atmosphere in microwave range measurements, Radio Sci.

J. Res. NBS/USNC-URSI, 68D, No. 11, 1229-1235.

Norton, K. A., J. W. Herbstreit, H. B. Janes, K. O. Hornberg, C. F.

Peterson, A. F. Barghausen, W. E. Johnson, P. I. Wells, M. C.

Thompson, Jr., M. J. Vetter, and A. W. Kirkpatrick ( 1961),

An experimental study of phase variations in line-of-sight microwave transmissions, NBS Monograph 33.

Thompson, M. C. , Jr., H. B. Janes, and A. W. Kirkpatrick (Jan. I960),

An analysis of time variations in tropospheric refractive index and

apparent radio path length, J. Geophy. Res. 65, No. 1, 193-201.

Thompson, M. C.,Jr., and H. B. Janes (Nov. 15, 1964), Radio path

length stability of ground-to-ground microwave links, NBS

Technical Note 219.

Thompson, M. C. , Jr., and M. J. Vetter (Feb. 1958), Single path

phase measuring system for three-centimeter radio waves, Rev.

Sci. Instru. 29, No. 2, 148-150.

-19-
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ANTENNA AND ANEMOMETER ARRANGEMENTS AT UPPER (HALEAKALA) TERMINAL

CONFIGURATION 'A' (RUNS I, 2, 3)

CONFIGURATION 'B' (RUNS 4 THRU 9)

SS^

TABLE I Schedule of Recording Periods

Run Period (local time) Config- S

uration

1 1000 June 29 - 1020 June 30 A 10. m

2 1355 June 30 - 1415 July 1 A 2.5

3 1749 July 1 - 1645 July 2 A 1.25

4 0855 July 7 - 0811 July 8 B 40-

5 1302 July 9 - 1300 July 19 B 10.

6 0800 July 15 - 0615 July 16 B 185.

7 1300 July 16 - 1630 July 17 B 90.

8 1528 July 21 - 1400 July 22 B 20.

9 1553 July 22 - 1500 July 23 B 5.

D Antenna

Locations

7,9,13,14

9,11,12,13

9,10,11,12

105. m 7, 14, 16, 18

165. 7,9,17,18

605. 1,5,7,18

660. 1,4,6,15

'770. 1,3,7,13

785. 1,2,7,8

-23-
24-
0.32 cm-*

SAMPLE CHART RECORDINGS FROM RUN 1

RANGE

0.32 cm -a

RANGE DIFFERENCE - ANTENNA SEPARATION: 40 m

I -aTWO RANGE

i DIFFERENCES - ANTENNA. i SEPARATION

:

20 m

1 VY

0.32 cm

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TWO RANGE DIFFERENCES - ANTENNA SEPARATION: 5 m

0.32 cm

1430

g ..

A i

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JUNE 29, 1964

Figure 6

, *.f. A.

1420

25-
SAMPLE CHART RECORDINGS FROM RUN 2

RANGE

BS

0.32 cm a

V I

RANGE DIFFERENCE - ANTENNA SEPARATION: 10 m

0.32 cm

TWO RANGE DIFFERENCES - ANTENNA SEPARATION: 5 m

0.32 cm - a a

. ^

- - *

TWO RANGE DIFFERENCES -ANTENNA SEPARATION: 2.5 m

0.32 cm ViAA%NvnAvw^^^^

^^f%('f'-^

v

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, ....- Vy^WS/^J^^yAj

1505 1500 JUNE 30, 1964

Figure 7

-26-

1455
SAMPLE CHART RECORDINGS FROM RUN 6

RANGE

RANGE DIFFERENCE - ANTENNA SEPARATION: 790 m

0.32 cm

RANGE DIFFERENCE - ANTENNA SEPARATION: 185 m

0.32 cm

JULY 15, 1964

Figure 8

27-
RANGE POWER SPECTRA

PUUNENE-HALEAKALA PATH

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-28-
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-29-
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-30-
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Figure 13

-32-
RANGE POWER SPECTRA

PUUNENE-HALEAKALA PATH

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-33.
RANGE POWER SPECTRA

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-34-
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36-
COMPARISON OF RANGE VARIANCES ON ADJACENT PATHS

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Figure 18

-37-
CORRELATION OF RANGE VARIATIONS vs ANTENNA SEPARATION

AT UPPER TERMINAL

(COMPUTED FROM 15-MINUTE SAMPLES)

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Figure 19

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Figure 23

-42-
COMPARISON OF RANGE DIFFERENCE VARIANCES

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Figure 24

-43-
COMPARISON OF RANGE DIFFERENCE VARIANCES

ON SEPARATED PAIRS OF PATHS

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04 08 12 JUNE 30, 1964

-66-
RANGE, REFRACTIVITY AND HUMIDITY DATA FROM

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-67-

12 16 JULY 1, 196420
RANGE, REFRACTIVITY AND HUMIDITY DATA FROM

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08 12 JULY 2, 1964

20

-68-
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-69-

04 08 12 JULY 8, 1964
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RUN 5

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12 JULY 10, 1964

-70.
RANGE, REFRACTIVITY AND HUMIDITY DATA FROM

RUN 6

RANGE

v

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Figure 52

-71-

04 08 16 JULY 16, 1964
RANGE, REFRACTIVITY AND HUMIDITY DATA FROM

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RANGE

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3

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1 JULY 17, 1964

Figure 53

-72-
RANGE, REFRACTIVITY AND HUMIDITY DATA FROM

RUN 8

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in

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Figure 55

-74-

20
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN

35

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-75-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 2

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16 20 JUNE 30, 1964

00 04 08 12 JULY I, 1964 Figure 57

-76-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 3

35

30

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16 20 00 JULY 1, 1964 !

04 08 JULY 2, 1964 Figure 58

-77-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 4

30

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08 16 JULY 7, 1964

20 00 Figure 59

04 08 JULY 8, 1964

-78-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 5

35

30 =—

25

20

TEMPERATURE

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1016 £ 1014 <5, 1012

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WIND DIRECTION

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16 20 JULY 9. 1964

04

Figure 60

•79-

n 12 JULY 10, 1964
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 6

35

25

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 TEMPERATURE

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20 00 04 08 JULY 16, 1964 Figure 61

-80-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 7

TEMPERATURE

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16 20 JULY 16, 1964

00 04 Figure 62

-81-

08 12 JULY 17, 1964
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 8

TEMPERATURE

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UPPER SITE

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16 20 JULY 21, 1964

08 12 JULY 22, 1964 Figure 63

-82-
TEMPERATURE, PRESSURE AND WIND DATA FOR RUN 9

35

30

25

„- 20

oro

UJo

TEMPERATURE

^~ ,'"'-\

V LOWER SITE y

v.—

UPPER SITE

1016

1014

1012

1010

1008

1

1 PRESSURE

UPPER SITE(SCALE AT RIGHT)

LOWER^ITEJSCALE AT LEFT) -— "" -^..^ *"" ^m ^*1 "" ^>»

o<_> UJCO

s.CO

cr

20 00 JULY 22, 1964

04 08 12 JULY 23, 1964 Figure 64

-83-

20
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN I FROM LOWER FROM UPPER

SITE SITE

l-l

(JUNE 29, 1016-1031)

1-2

(JUNE 29,1418-1433)

1-3

(JUNE 29, 1815-1830)

1759

Figure 65

-84-
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 2

FROM LOWER

SITE

FROM UPPER

SITE

2-1

(JUNE 30, 1452-1507)

2-2

(JUNE 30,1930-1945)

2-4

(JULY 1,0531 -0546)

2-5

(JULY I, 1001 -1016)

Figure 66

-85-
PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 3

FROM LOWER

SITE

FROM UPPER

SITE

3 -I

(JULY I, 1800-1815)

3 -4

(JULY 2, 0815-0830)

for * ^W

3-5

(JULY 2, 1238-1253)

Figure 67

-86.
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 4

FROM LOWER FROM UPPER

SITE SITE

4-1

(JULY 7, 0930-0945)

4 -2

(JULY 7, 1350-1405)

4-5

(JULY 8, 0615-0630),

Figure 68

-87-
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 5

FROM LOWER FROM UPPER

SITE SITE

5 -I

(JULY 9, 1700-1715;

5-4

(JULY 10,0700-0715)

5-5

(JULY 10,1100-1115)

Figure 69

-88-
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 6

FROM LOWER FROM UPPER

SITE SITE

6-1

(JULY 15,0830-0845)

6-2

(JULY 15, 1 100 -1115)

6-3

(JULY 15, 1500-1515)

Figure 70

-89
PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 7

ASSOCIATED

SAMPLE

FROM LOWER

SITE FROM UPPER

SITE

7-1

(JULY 16,1800-1815)

7-4

(JULY 17, 1130-1145)

7-5

(JULY 17, 1500-1515)

Figure 71

-90-
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 8

FROM LOWER

SITE FROM UPPER

SITE

8-1

(JULY 21, 1550-1605

Figure 72

1600

8-4

(JULY 22,0530-0545)

8-5

(JULY 22, 1003-1018)

-91
ASSOCIATED

SAMPLE

PATH PHOTOGRAPHS TAKEN AT TIMES INDICATED

RUN 9

FROM LOWER

SITE

FROM UPPER

SITE

9-1

(JULY 22, 1629-1644)

9-4

(JULY 23, 0615-0630)

9-5

(JULY 23, 1120- 1 135

)

Figure 73

-92-
w

pqH

Ity ^ C -« 81^ 5 Q g

a;

u

Pi Oh

co co

ftf o

+J "° « a ° o

CO

R

CO T> ,jQ

fi I (C en +j en m fo ^ Oh •H

Pn -

CO T3 CD

<u S

bo cd

COO

CM c 2m

en T3

CD (1)

PI 3 3 ° > Si o3

cm

ffj

CM

V

tf

42

CO

<3

<3

T3

CO

<3

ti

Pi q;

CO

CD

+->CO Q

ft

CO £

oni co1 1 * 1 i i l 1 iLT> uni LO LT) 1 1 1 or—1 o.—1 o

cm 00

co ON

CM

CMCM

oO ^o

i-H OO nO CO CM

<—i -vO ""I <f) CM xO oo CM i-h i—i

LO ^ —< CM

—i

T3O ..

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oo CM OO CO «*

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r- 1—1

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on oo •* ^ ^ LO LT) ~v

LT) CO 2 - —i o ^* —i

oO

CM

LO i—t

CO i—i ^ CM* CM* vO 00* IT)

oo oO oo co ^ i i I i i M ^ ^ 7f ^ I I I I I LO -^ LO LT) ^ I I I I I r- "tf r- o oo o o oo cm r- v • a a 9 r—4

f*. i—I i—I

CM

OvO CO 00 00

CO LO i-H rf

O

>—I oO CM

—I —i

00 uO

O

O •—i hh oo oo o o o CM CM

CO CO 0O CO -"tf" I I I I I oo -* un rt* -^ i i i i i ^ -s}H LO LO rtf I I I I I H ^ T}l H f» O nO oo O CM

(M [^ CM —( CO

in o o m

n

OO O"^ CT^

—• LO i—i oO vD '—I '—i

vD

O CO U0 00

LO -^ -^ ^ O

—t CM ^ CM CM

oo CM CO oo -^ l I I i l CO CO <HH ^jH ^ I I I I I ^ ^ Tf LO "^ I I I I I 00 CM 00 CM -^

"^

O CO CM LO vO •—> *& CO O

vO CM

—i if)h

r-< o o r~ ^o

•HH r-H OvJ CM -st< ^ -h ^ 00 CM O —i -h O O • a a o d ^ f~- r^ LO 00

CO1 CM1 CO1 CO1 1 CO1 CO1 ^H •* i 1 1 * LO1 1 LO O * CO o co <* r 1 o 00 ^ LT> CO CM LO i—1

CM i—i o r- r- CO v£> r~ 0O LO r—1

CO lO i—1 O CM r^- CO oo ^ r—I

OO 0O LO ^ oo - sD o

CMl CMl CMi oo1 COi CMl CO1 CO ' 1 i 00 CO1 CO1 "* l CO

cm o o oo r-

—t if) 00

O 00 9 9 o cm o —i r~ cm

CM CM -h I I I 00 LO n£> 00 sO ^ 00 vD oo oo 9 9 9 9 H l> vfj f» (M

vO oo if) if) ifi

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nO vO sD nD sD o o o o o

CM CM CM CM oo

r^ oo 00 LO r~ LO 00 LO vO 00

i—i lo lo r>-

>—<

r~- o oo oo cm o o vO r^ fi 9 9 • » • LO CM ^O oO i—I

CM

OO —* ^h LO CO O oo O

^f

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<—i .—i O

O

—i

vD ^>D ^ ^ ^ \wf) ^ \0 o o ~-«. -^. -^

CO CO —I i—I '—I O vO sO r~ vD O vO H 00 H

CO CM T^ r-H OO

00 "—I O LO "HH O 00 CM O LO • • • 9 9 —i

i—i

r~ co oo

OO LO LO 00

O CO •—* i-H CO

00 CM oo 00 CM —t CM O O r-t

^^ ^* ^^ ^* ^^ vO vD xD vO xO

O ^O sO sD

O

—* CM CO -hh lO I I I I I

xD vO r~ r^ r- —i CM CO ^ lO I I I I I CM CM CM CM CM

hh

N

N

N

r~ r~ r^ r^ r-

-h

N ro ^ if) I I I I I 00 CO CO CO CO

CM

LO

CM

CO

CMI LO

CM

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enu

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a,

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CJ

Pi

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COa,

enu

CD 43

-93-
TABLE III 2 Variances, in (cm) , of Range and First and Second Range Difference Data

(Computed from 15-minute samples; pass-band: to approximately 1.4 Hz)

Sample

No. Date

Starting

Time

R R AR AR

ab

AR

cd

A

2P

ab, cd

4-1

4-2

4-3

4-4

4-5

5-1

5-2

5-3

5-4

5-5

6-1

6-2

6-3

6-4

6-5

7-1

7-2

7-3

7-4

7-5

8-1

8-2

8-3

8-4

8-5

9-1

9-2

9-3

9-4

9-5

7/7/64

7/7/64

7/7/64

7/8/64

7/8/64

7/9/64

7/9/64

7/10/64

7/ 10/64

7/10/64

7/ 15/64

7/15/64

7/15/64

7/15/64

7/16/64

7/16/64

7/17/64

7/17/64

7/17/64

7/17/64

7/21/64

7/21/64

7/22/64

7/22/64

7/22/64

7/22/64

7/22/64

7/23/64

7/23/64

7/23/64

0930

1350

2015

0000

0615

1700

2200

0400

0700

1100

0830

1100

1500

2100

0130

1800

0000

0500

1130

1500

1550

2015

0100

0530

1003

1629

2100

0145

0615

1120

1. 18

6.63(-l)

2. 88

8.01(-1)

1.99

1. 22

7. 29(-l)

1.67

7.13(-1)

1.94

7.79(-l) 9.41(-1)

2.32(-l) 2.03(-l)

3.89(-l) 3.90(-l)

1.09(-1) 1.17(-1)

2.91 3.66

1. 20

1. 47

3.08

1. 54

1.71

1. 52

9.67(-l)

2. 04(-l)

6. 02(-l)

2. 50

1. 07(+l)

8. 03(-l)

1. 09

1. 23

6.09

1.43

2.55

2.73

1.83

1.81

1.81

7. 19(-

1. 22(-

2.42

2.63

1)

1)

1.05( + 1) 5.25(-l)

1.39

1. 25

7.63

9.25(-l) 9.49(-l)

1. 16 1.41

2.09(-l) 1.42(-1)

1.08(-1) 1.56(-1)

2.36 2.87

1. 16(-1)

2. 86(-l)

2.71(-1)

1. 10(-1)

3.77(-2)

1.76

6. 55(

1. 94

2.99

1)

2. 26

2.49(-l)

2. 85(-l)

2.72

2.73(-l)

2. 14

3.49

4.73

2. 11

3.81

1.87(-1) 4.56

2. 00(-2) 2.54

2. 68(-2) 2.18

2. 36(-2) 1.18

7.09(-l) 6.55

1. 58

2.04

6.40

8.88

5.75(-l) 1.44

58

60

33

23

07

1.86 1.70

5.15(-1) 8.26

1.57 2.32

1.04(-1) 8.83

1. 26

1.98 2.64

6.02(-l) 1.26

2.90(-l) 2.16

1.20(-1) 2.57

3.00(-l) 6.43

8. 38 (-3)

(-2 ) 9. 30 :-2)

(-2 i 3.79 (-2)

(-2 i 2.63 -2)

(-2 i 5.78 (-3)

(-3 ) 5.01 (-3)

(-4 ) 2.52 -4)

(-4 I 2.04 (-4)

(-3 ) 1. 09 -3)

(-3 ) 8.41 -3)

(-1 ) 4. 28 !-i)

(-1 1 2.74 -1)

(-1 ) 5.94 -1)

(-1 7.96 -1)

(-1 3.23 -1)

(-1 3.64 -1)

(-2 1. 18 -1)

(-2 8. 26 -3)

(-1 3.911 -1)

(-1 3. 18 -2)

(-2 2. 17 -2)

(-3 7. 12| -3)

(-2 7. 84 -3)

(-4 -- (-2 1. 551 -2)

(-3) 2. 26| -3)

(-3) 2.47) -3)

(-4; 4.79( -4)

(-4; 2. 63( -4)

(-4; 4. 53{ -4)

1.07(-1)

8.77(-2)

5.62(-2)

1.07(-2)

5. 10(-4)

4. 23(-4)

2. 32(-3)

1. 31(-2)

6.73(-l)

5.61(-1)

1. 26

1.44

3. 30(-l)

1. 16

2.78(-l)

1.84(-2)

1.61

1.37(-1)

1. 68(- 1) 1.64(-2)

3.07(-2)

2. 10(-3)

2. 80(-2)

5.63(-3)

3.45(-3)

6. l6(-4)

5. 02(-4)

1.47(-3)

numbers in parentheses indicate powers of 10, i. e. , 3. 25(-2) = 3. 25 x 10

94-
o

OJ

a

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i—( 1 1 1 1

00o

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ro oo ^ <? ^ OO i ^ ^

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oo

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roj oo 1 -—1

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m ^ i i i i i i r- oj o- r~- no

oO •—I 00 0O r—i

0J CO vO CO lO ^ -^ m m rf i i i i i m o Is- ^t1 o O vD Tf OO IT)

r-H 00 ^H ,—I

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m un oo co ^ 00

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CO

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OO OJ oO ^ xh CO •* ^ ^ ^ ^ -*

m

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C!-i o 1—1

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eq

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r—1

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m <tf oo* 0J OJ* Is- ^°

r- CT* vO sO S T) a) <] H PI05 i—i a

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4->pi

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^-( OJ1 00 001

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in -xi \0

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^T N^ ^* ^* ^^ \D ^i) \D \0 \D

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oj oo oo oj oo ^O \D ^O \0 vO

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oo

m c> co \0 o a • • a O- i—* vD O- CO

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r—I O

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wvO ^ ^ ^ ^ ^ \D vO O O \ \ -^

CO oo

—i i—i >—i o nD o- r~ r~- —i oo co ^ m i i i i i 00 00 00 OJ OJ

^f o ^t

m o

t^ If) iH ^ H

i—i ^ s£> oo

m o o m ir> oo O CO i—i i—i

CO 00 OJ CO 00 0J

<—\ OJ o O—i ^ "^ "^ T^ ^

sD vD sD vD ^O

^H •—< 00 00 00

t^ o- r^ r^ oi—i oj oo ^ m i i i i i CO CO CO CO CO

ooI m

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Pi

-95-
TABLE V

Variances, in (cm) , of Range and First and Second Range Difference Data

(Computed from 15-minute samples; pass-band: approximately 0.007 to 1.4 Hz )

Sample

No. Date

Starting R

Time

R AR

ac AR

ab

AR

cd *

2R

ab, cd

4-1

4-2

4-3

4-4

4-5

5-1

5-2

5-3

5-4

5-5

6-1

6-2

6-3

6-4

6-5

7-1

7-2

7-3

7-4

7-5

8-1

8-2

8-3

8-4

8-5

9-1

9-2

9-3

9-4

9-5

7/7/64

7/7/64

7/7/64

7/8/64

7/8/64

7/9/64

7/9/64

7/10/64

7/ 10/64

7/10/64

7/15/64

7/15/64

7/ 15/64

7/15/64

7/16/64

7/16/64

7/17/64

7/17/64

7/17/64

7/17/64

7/21/64

7/21/64

7/22/64

7/22/64

7/22/64

7/22/64

7/22/64

7/23/64

7/23/64

7/23/64

0930

1350

2015

0000

0615

1700

2200

0400

0700

1100

0830

1100

1500

2100

0130

1800

0000

0500

1130

1500

1550

2015

0100

0530

1003

1629

2100

0145

0615

1120

2.04

3.72

4.41

2.02

6. 17

5. 29

3. 32

4. 15 8.64

4.46

6. 23

4.69

3.44

4.43

5.65

6.47

2. 54

3.45

5.41

2. 34

8.73

4.44

1. 20

9. 86

8. 17

8. 06

4.45

9.43

4. 80

9. 52

2) 1.69

•2) 3.15

2) 4.02

• 2) 2.22

•3) 6.57

• 2)

•3)

•3) 3)

2)

.2) 2)

1) •1) 2)

4.83

2.60

2.79

7. 38

3.90

1.02

5.90

2. 22

3.44

7.64

-2) 4.36

2) 2. 13

3) 1.64

2) 7.02

2) 2.81

•2) 6.57

2) 4.74

1) 4.91

3) 6.83

•2) 5.31

•2)

•2) 3)

3)

3)

7.20

6. 32

1. 29

8. 10

9.75

2)

2)

•2)

•2)

•3)

2)

3)

3)3)

2)

1)

2)

1)

1)2)

2)2)

3)

2)

2)

9. 26

5.09

5.87

2.46

4.43

6.07

4.80

3.76

1. 12

3. 20

1. 30

1. 23

4.90

8. 58

1. 65

1. 05

3.98

4.84

1. 50

4. 00

•2) 1.47

•2) 7.46

•2) 1.04

3) 1.65

2) 1.50

2)

2)2)

3)3)

1. 31

9.74

2.00

1. 18

1.61

-3) 9.60 (-3 1 2.58 (-3

-2) 1.52 I-2

1 2.90 ;-2 I 3.78(

-2) 2.96 -2) 1.87 -2 > 4. 83(

-2) 1.53 (-2, 1. 33 [-2 1 3. 14(

-3) 3.91 -3 1.80 -3 1

-2) 3. 38 [-3] 4. 38 i-3 7.45(

-3) 2. 12 -4- 2. 28 ;-4 4. 63(

-3) 1. 83 .-4) J. 52 ;-4 3. 56(

-2) 1. 10 ;-3 1. 09 ^-3 2. 51(

-2) 2. 62 -3) 5. 30 -3 8. 86(

-1) 4. 38 -2) 1. 05 (-1 1.62(

-1) 7. 87 -2) 9.49 -2 1.95(

-1) 2.67 -1 2. 63 -1 4. 36(

-1) 5.62 ,-1) 4.65 ,-i 9. 12(

-1) 1.03 -1) 1. 21 -1 2. 26(

-1) 1. 5| -1) 4. 38 -2 1.63(

-2) 2.40{ -2) 2.94 -2 5.61(

-3) 1. 15 -3) 1. 15 -3 2. 19(

-1) 8.40( -2) 7. 92 -2 2. 12(

-2) 1. 52 -2) 9. 50 -3] 2. 47(

-1) 1. 37 -2) 9. 31 -3 2. 61(

-2) 8. 13( -3; 5.97 ^-3) 1.54(

-1) 1.90- -2: 5. 21 -3) 2. 34(

-2) 6. 38| -4) -- 1. 37(

-1) 6. 301 -3) 8.591 -3) 1.79(

-1) 2. 17( -3) 1.70| -3) 3.89(

-2) 1. 17i -3! 2. 65i -3) 3. 58(

-2) 1. 84( -4; 4.75( -4; 6. 35(

-2) 2. 30| -4; 2. 69' -4; 4. 85(

-2) 3.70( -4; 2. 98| -4; 7.60(

2)

•2)

•2)

-3)

-4)

-4)

-3)

-3)

-1)

-1)

-1)

-1)

-1)

-1)

-2)

-3)

-1)

-2)

-2)

-2)

-2)

-3)

-2}

-3)

-3)

-4)

-4)

-4)

numbers in parentheses indicate powers of 10, i. e. , 3. 25(-2) = 3. 25 x 10

-2

96- GPO 858-469

U.S. DEPARTMENT OF COMMERCE

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U.S. DEPARTMENT OF COMMERCE