DTIC ADA183143: A Mid-Latitude Scintillation Model.

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MICROCOPY RESOLUTION TEST CHART
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AD-A183 143

A MID-LATITUDE SCINTILLATION MODEL

R. E. Robins
J. A. Secan
E. J. Fremouw

Northwest Research Associates, Inc.

P. 0. Box 3027

Bellevue, WA 98009-3027

31 October 1986

Technical Report

CONTRACT No. DNA 001-85-C-0017

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11. TITLE (Include Security Classification)

A MID-LATITUDE SCINTILLATION MODEL

PROGRAM
ELEMENT NO.

62715H

PROJECT

TASK

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from 851101 to861031

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Robins, Robert E-: Secan, James A.; Fremouw, E.J. __

13a. TYPE OF REPORT |l3b. TIME COVERED 114. DATE OF REPORT (Year, Month, Day) |lS. PAGE COUNT

Technical from 851101 to861Q31 I 861031 _ 78 _

16. SUPPLEMENTARY NOTATION

This work was sponsored by the Defense Nuclear Agency under RDT&E RMC Code

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17. __ COSATI CODES _ 18. SUBJECT TERMS (Continue on reverie if necessary end identify by block number)

field group subgroup Structured High-altitude Plasmas Transionospheric Radio

13 _2_Radiowave Scintillation and Radar Channels

2 8 _ Mid-latitude Scintillation

19. ABSTRACT ( Continue on reverse if necessary and identify by block number)

Radiowave scintillation in the presence of ionospheric disturbances has the
potential to disrupt numerous transionospheric radio and radar systems. This report
describes development of a model characterizing the plasma-density irregularities
that produce scintillation in the naturally disturbed mid-latitude F layer. The model
will be incorporated into Program WBM0D, which includes subroutines for computing both
link geometry and scintillation indices, the latter by means of phase-screen dif¬
fraction theory. Earlier versions of WBMOD.i which are operational at USAF Global
Weather Central and at several other user locations, 1 ‘were based on extensive analysis
of scintillation data collected in the auroral and equatorial zones in-ONA'$ Wideband
Satellite Mission. The model described herein is based on similarly extensive analy¬
sis of Wideband data from one mid-latitude station and of data collected from DNA's
Hi La t satellite at another mid-latitude station. The model describes irregularities

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19. ABSTRACT (Continued)

at an effective height of 350 km that are isotropic across the geomagnetic field and
elongated by a factor of 10 along the field and whose one-dimensional spatial power
spectrum obeys a single-regime power law with a (negative) spectral index of 1.5. The
height-integrated spectral strength of the irregularities is modeled as a function of
magnetic apex local time, solar epoch (sunspot number), and the F-layer magnetic apex
latitude of the point. The report highlights a disagreement by a factor of approxi¬
mately three between irregularity strength inferred from the two satellites in a
region of overlap between the two mid-latitude stations. Whether this difference
results from processing artifacts or geophysical processes/is still open to investiga¬
tion.

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CONVERSION TABLE

Conversion factors for U.S. customary
to metric (SI) units of measurement.

To Convert From

To

Multiply By

angstrom

meters (m)

1.000 000 X E -10

atmosphere (normal)

kilo pascal (kPa)

I 013 25 X E +2

bar

kilo pascal (kPa)

1.000 000 X E *2

bam

meter* (m*)

1.000 000 X E -28

British thermal unit (thermochemical)

joule (J)

1.054 350 XE.3

calorie (thermochemical)

joule (J)

4. 184 000

cal (thermochemicaD/cm**

mega joule/m 3 (MJ/m 3 )

4. 184 000 X E -2

degree (angle)

radian (rad)

1. 745 329 X E -2

degree Fahrenheit

degree kelvin (K)

= (ff ♦ 459. 67)/1.8

electron volt

Joule (J)

1.602 19 X E -19

erg

joule (J)

1.000 000 X E -7

erg/second

watt (W)

1.000 000 X E -7

foot

meter (m)

3 048 000 X E -1

foot-pound -force

joule (J)

1.355 813

gallon (U.S. liquid)

meter (m )

3. 785 412 X E -3

inch

meter (m)

2. 540 000 X E -2

jerk

joule (J)

1 000 000 X E *9

kip (1000 Ibf)

newton IN)

4.44 8 222 X E +3

kip/lnch 2 (kai)

kilo pascal (kPa)

6 894 7 57 X E +3

ktap

new ton-second/m 2
(N-*/m‘j

1.000 000 X E .2

micron

meter (m)

1 000 000 X E -6

mil

meter Im)

2. 540 000 X E -5

mile (International)

meter (m)

1.609 344 X E +3

ounce

kilogram (kg)

2. 834 952 X E -2

pound-force (lbs avoirdupois)

newton (N)

4.448 222

pound-force inch

newton-meter (N*m)

1. 129 849 X E -1

pound -force/inch

newton /meter (N/m)

1. 751 266 X E *2

pound -force Aoot 3

kilo pascal (kPa)

4. 798 026 X E -2

pound -force/inch" (psi)

kilo pascal (kPa)

6. 894 757

pound-mass (Ibm avoirdupois)

kilogram (kg)

d.3535 924 X E -1

pound-mass-foot (moment of inertia)

kilogram-meter
(kg • m^)

4. 214 011 X E -2

pound-mass/fool 3

kilogram/meter
(kg/m 1 *)

1 601 846 X E 4l

roentgen

coulomb Al log ram
(C/kg)

2 579 7G0 X E -4

shake

second (s)

1 000 000 X E -8

• lug

kilogram (kg)

1.459 3 90 X E . 1

torr (mm Hg, 0* C)

kilo pascal (kPa)

l. 333 22 X £ -1

. ,.—.. .... - .... ■ ... . .

.

, s

TABLE OF CONTENTS

,

Section

Page

CONVERSION TABLE

iii

LIST OF ILLUSTRATIONS

V

■*;

LIST OF TABLES

ix

•»

'£

V

1

INTRODUCTION

1

*>

N

2

METHOD

3

2.1 Stanford Data

3

*

2.2 Bellevue Data

6

V

2.3 Review of Modeling Procedure

9

3

DRIFT, SHAPE FACTORS, AND HEIGHT

15

*4

3.1 Drift Velocity

15

s

3.2 Cross-field Isotropy

15

3.3 Along-field Axial Ratio

16

*

3.4 Spectral Index

16

>!

3.5 Height of the Equivalent Phase Screen

16

$

4

IRREGULARITY STRENGTH MODEL

19

H

4.1 Procedure

19

i’

4.2 Results

21

’»

«

4.2.1 Latitudinal Variation

21

4.2.2 Diurnal Variation

23

4.2.3 Sunspot-number Dependence

23

4.2.4 /C^L Lead Constant

23

5

CONCLUSION

28

•a

•e

5.1 Efficacy of WBMOD

28

♦a

3

5.2 Summary

28

7«

6

LIST OF REFERENCES

37

Appendices

38

A Replacement of C $ L with C^L

39

1

1

i.

B Partial Resolution of Stanford/Bellevue Discrepancy

iv

49

>■>

<•

LIST OF ILLUSTRATIONS

re

Scatter plots of F layer (350 km) penetration points from the Stanford
Wideband data base. Points are plotted in (a) on a grid of geographic
latitude and longitude, and in (b) are on a grid of apex latitude and
longitude. In both plots, the receiver location is shown as a small
circle. Penetration points fell into six nighttime (Nl, N2....N6) and five
daytime (01, 02,...05) corridors. Nighttime passes traversed from north
to south and daytime passes from south to north.

Scatter plots of rms phase fluctuation, a , vs apex
nighttime data from the Stanford Wideband data base,
anomalous pass are shown as small circles.

latitude, A , for

a

Points from an

Scatter plots of F layer (350 km) penetration points from the Bellevue
HiLat data base for (a) 0800-1600 apex local time and (b) 2000-0400 apex
local time. Points are plotted on a grid of apex latitude and apex
longitude.

Scatter plots from Bellevue HiLat data base of (a) apex latitude vs apex
local time and (b) apex local time vs day of year.

Scatter plot from Bellevue HiLat mid-latitude data base (apex latitude £
54° and K p <5) of apex local time vs day of year.

Scatter plots from Bellevue HiLat mid-latitude data base with bin-average
plots superimposed: (a) K p vs day of year, demonstrating the lack of K p
dependence on season; (b) Sunspot number vs day of year, exhibiting a peak
which implies a possible coupling of the plotted variables; (c) K p vs apex
local time, demonstrating the lack of K p dependence on local time; (d)
Sunspot number vs apex local time, demonstrating that sunspot number does
not depend on apex local time; (e) K p vs sunspot number, demonstrating that
K p does not depend on sunspot number.

Bin-average plots of the ratio of intensity scintillation index, S^, to

phase scintillation index, o,, vs apex latitude, for Stanford observations

<p

(solid lines) and WBM0D simulations (dashed lines). Simulation results

LIST OF ILLUSTRATIONS (Continued)

yj

&

Figure

are shown for phase-screen heights of 250, 350, and 450 km. Figures 7(a),
7(b) and 7(c) are for night and day, night only, and day only, respec¬
tively. Latitude bins are 2° wide, and bins containing fewer than 100
points for (a) and (b) and 50 points for (c) are not shown.

Histograms of (a) data and (b) log data for the Bellevue HiLat

data base.

Scatter plots of log vs apex latitude for the Stanford Wideband (a)

nighttime and (b) daytime data bases. Bin-average plots are superimposed.

Scatter plot of log /C^L vs apex local time for the Bellevue HiLat mid¬
latitude data base. Bin-average (jagged line) and best fit sinusoidal
(smooth line) plots are superimposed. The peak to peak amplitude of the
sinusoid is 0.30.

Scatter plot of log /C^L vs sunspot number (SSN) for the Bellevue HiLat
mid-latitude data base. The log mean and the apex local time varia¬
tion have been subtracted from the log /C'^L data. A bin-average plot
(jagged line) and a best fit straight line are superimposed. The best fit
is computed for the SSN range 0-70.

Scatter plot of log /CjT vs day of year for the Bellevue HiLat mid-latitude
data base. A bin-averaged plot and the zero level are superimposed.
Subtracted from the log /C^l data are the log vCjT mean and the previously
computed best fits for apex local time and sunspot number variations. The
plot shows the absence of any seasonal variation.

'catter plots of Briggs-Parkin angle vs magnetic apex latitude, \ , for
nighttime data corridors N2, N3, N4, and N5. Plots are shown in (a), (b),
(c), and (d), respectively.

Scatter plots of Briggs-Parkin angle vs magnetic apex latitude, \ , for

3

daytime data corridors 01, D2, D3, 04, and D5. Plots are shown in (a),
(b), (c), (d), and (e), respectively.

Bin-average plots of nighttime yvs \ for (a) the two most nearly overhead
corridors (N3 and N4) and (b) two lower-elevation corridors (N2 and N5).

LIST OF ILLUSTRATIONS (Continued)

Figure p age

Solid lines show results from observations, and dotted lines show results
from WBMOD simulations. Latitude bins are 2° wide, and bins containing
fewer than 30 points for (a) and 15 points for (b) are not shown.

16 Bin-average plots of daytime a, vs A, for (a) the two most nearly overhead 35

0 a

corridors (D2 and D3), and (b) three lower-elevation corridors (Dl, D4 and
D5). Solid lines show results from observations, and dotted lines show
results from WBMOD simulations. Latitude bins are 2° wide, and bins

containing fewer than 30 points for (a) and 15 points for (b) are not
shown.

17 Relationship between bin averages of phase spectral index, p, measured 42

with Rover at Bellevue and four measures of irregularity strength derived

from spectral strength, T, of VHF phase scintillation. Also shown are
occurrence distributions for the four strength measures. (a): CL com¬
puted from Eq. (18), employing measured values of p in the transformation.

(b): C^L computed from Eq. (18), employing a fixed value (2.5) of p in the
transformation, (c): C^L computed from Eq. (22), employing measured values
of p. (d): C|0 computed from Eq. (22), employing a fixed value (2.5) of p.

Note that only the first procedure results in a consistent trend between p
and the strength parameter.

18 Relationship between bin averages of phase spectral index, p, and spectral 44

strength, T, of VHF phase scintillation directly measured at Bellevue.

Occurrence distribution of T also is shown.

19 Occurrence distribution of VHF phase spectral index measured at Bellevue 45
between Day 109 of 1984 and Day 107 of 1986 (same population as in all
other figures containing observed data).

20 Relationships between phase spectral index, p, and two measures of irregu- 46

larity strength for observed (broken) and simulated (solid) data sets.

(a): C $ L computed from Eq. (18). (b): C^L computed from Eq. (22). In both

cases, the simulated data sets contained absolutely no correlation between

p and the parameter, T, from which the strength measure was computed. The

distribution of T was uniform (and truncated). Transformation to C L has

s

vi i

LIST OF ILLUSTRATIONS (Concluded)

Ev:

Figure

altered the distribution to resemble that of p (which was a Gaussian fit to
Figure 19, while transformation to C^L has preserved the uniform distri-

21

24

25

26

27

bution except at the truncation edges.

Variation of log /C^L with apex latitude from the Stanford Wideband and
Bellevue HiLat data bases, (a) shows a scatter plot, where crosses denote
Stanford data and dots denote Bellevue data; (b) shows bin average plots
for each data set.

22 Comparison of the values 10 log T calculated from a (p = 2.5) to the

<}>

values 10 log T extracted from the phase SDF, computed for five representa¬
tive Stanford Wideband passes. The straight line is a least-squares fit to
the data, constrained to have a slope of unity.

23 Comparison of the values 10 log T calculated from o (p - 2.85) to the

<J>

values 10 log T extracted from the phase SDF computed for five representa¬
tive Stanford Wideband passes. This figure differs from Figure 22 only in

the value of p used to calculate T from a..

<P

Bin-average plots of log /C^L vs apex latitude for the Stanford Wideband
and the Bellevue HiLat data bases. Solid lines are identical to the solid
lines in Figure 21b. Dotted line shows the effect of calculating log vC^T
for the Stanford data using p = 2.85 and a 0.8 adjustment factor.

(a) VHF (upper plots) and UHF c (lower plots ) channels for Wideband pass

ST-01-49. Top plot in each pair is log intensity, bottom plot is phase

detrended at 0.1 Hz. (b) Scatter plot of c^at UHF c against at VHF for

Wideband pass ST-01-49, (c) Plot of VHF (upper) and UHF c (lower) log vs

time for Wideband pass ST-01-49.

(a) VHF (upper plots) and UHF c (lower plots) channels for Wideband pass ST-

02-25. Top plot in each pair is log intensity, bottom plot is phase

detrended at 0.1 Hz. (b) Scatter plot of a, at UHF aqainst a ± at VHF for

<t> c 3 <t>

Wideband pass ST-02-25, (c) Plot of VHF (upper) and UHF (lower) log o vs

c cf>

time for Wideband pass ST-02-25.

Variation of /C^L and /CjT cos

with apex latitude for the Stanford and

8ellevue data bases.

vm

Page

50

52

53

55

56

58

61

LIST OF TABLES

Table

1 Idealized Analysis Procedure

2 Actual Analysis Procedure

3 Night and Day Means for Stanford data satisfying 35°£ X £45°.

4 Stanford/Wideband Passes Reprocessed

Page

13

13

27

54

ix

SECTION 1

INTRODUCTION

A recent report (Fremouw and Robins, 1985) described a scintillation model for
equatorial regions. This model was incorporated into the computer program WBMOD to
complement a previously developed scintillation model for auroral regions (Fremouw
and Lansinger, 1981; Secan and Fremouw, 1983a). Both models were based on extensive
analysis of data from DNA's Wideband Satellite (Rino et al , 1977; Fremouw et al,
1978).

In this report we describe the determination of a mid-latitude scintillation
model. The model is based on Wideband data taken at Stanford, CA, and on a subset of
the data taken at Bellevue, WA, from the DNA Hilat satellite (Fremouw et al, 1985).
The Wideband mid-latitude data set is significantly smaller than the Wideband equa¬
torial and auroral data sets, since mid-latitude data were obtained only for the first
four months (May 1976 to Sept. 1976) of the Wideband experiment. The Stanford
receiver subsequently was moved to Kwajalein to obtain equatorial data for the
duration of the experiment (until Sept. 1979).

In spite of the limited data base available from Stanford, we were able to use it
to obtain useful parameterizations of the irregularity-1ayer height, latitudinal
dependence, and average strength. The mid-latitude data taken with the transportable
HiLat receiver, "Rover," while located at Bellevue, WA, during the period April 1984
through February 1986 were used to obtain the diurnal variation and to determine the
solar-cycle dependence of the scintillation level at mid-latitudes. Representations
of mid-latitude convective drift and along-field axial ratio were determined from
published results.

In Section 2 we describe the Stanford and Bellevue data bases and briefly review
the modeling approach, which was described in detail in the previous report (Fremouw
and Robins, 1985). In Section 3 we explain our choices for mid-latitude plasma-drift
velocity, shape factors, and height of the equivalent phase screen. In Section 4 we
describe our determination of the model for the height-integrated spectral strength of
irregularities. We depart from the approach used for equatorial and auroral modeling
in two ways. First, instead of expressing spectral strength in terms of the familiar
C L , we use the quantity C.L, defined by

C|<L ,(I|°0 neters jl*P

( 1 )

where p is the phase power-law spectral index. The reason for this change is dis¬
cussed in Appendix A. Second, as we discuss further in Section 4, the statistics of
the data have led us to model log C^L rather than C^L. In Section 5 we conclude by
showing some model vs data comparisons to demonstrate the utility of the model, and by
summarizing our work.

SECTION 2

METHOD

2.1 STANFORD DATA.

The Wideband receiver at Stanford was located at 37°26'N, 122 10'W (apex latitude
and longitude* of 43.14°N and 299.93°E, respectively). From May 28 to September 10,
1976, data from 87 passes were received; 63 of these passes (2536 points) were at
night (2300 to 0050) and 24 passes (941 points) were during the day (0945 to 1125).
Figures 1(a) and 1(b) show scatter plots of F layer- (350 km) penetration point
locations for all passes in the Stanford data base except for three. (Two night and
one day pass were deleted for reasons explained below.) In both plots, the receiver
location is shown as a small circle. Figure 1(a) shows the penetration point distri¬
bution on a grid of geographic latitude and longitude and Figure 1(b) shows it on a
grid of apex latitude and longitude. The data fall into distinct corridors, which we
have labeled N1, N2, N3, N4, N5, and N6 for nighttime passes and D1, D2, D3, D4, and D5
for daytime passes. The direction of the nighttime passes was from north to south and
for the daytime passes was from south to north.

Two passes were deleted because of severe tracking errors. Because the number of
daytime passes was relatively small, two daytime passes with less severe tracking
errors were retained. (Errant penetration points from these passes are evident
between corridors D1 and D2.) A third pass was dropped because of unusually large
(rms phase fluctuation) values. Figure 2 shows a scatter plot of nighttime o vs X

(J) d

(apex latitude) points, with points from the third deleted pass shown as small
circles. The K p value at the time of the anomalous pass was 4+ (4.33) and, 1.5 hours
after the pass, it was 7- (6.67), which was the highest value that occurred during
the Stanford campaign. This coincidence of high and high is quite suggestive
that magnetic storm activity was an influence on the unusually strong phase scintilla¬
tion. In any case, the pass was deleted from the data set to prevent it from biasing
the various scintillation statistics.

The result of the above pass deletions and the removal of two additional bad
points was to leave the Stanford data base with 61 nighttime passes containing 2447

S' 50

-o

CL

<T3

L, 30-

CD

O

OJ

CD

\ ,=r . ! X •••

\ \ \ .;•••'
vW -.i? =si*/ ,‘v"

V ,*r\ .'SSN jS?' /.V V .*//

V. - & ■■■,4? *■ .%?

\| i .*» ‘j.i, v; fc : •

N2 N6

I 30

Geographic Longitude (deg)

, 03 “ ....

' « •.* V# • *

, VJ5 % *;

x: ■ :i.%, J N # /

s M/ v rn : m l,„ it si

Ml

Apex Longitude (deg)

Figure 1. Scatter plots of F-layer (350 km) penetration points from the Stanford
Wideband data base. Points are plotted in (a) on a grid of geographic
latitude and longitude, and in (b) are on a grid of apex latitude and
longitude. In both plots, the receiver location is shown as a small
circle. Penetration points fell into six nighttime (Nl, N2....N6) and
five daytime (Dl, D2....D5) corridors. Nighttime passes traversed from
north to south and daytime passes from south to north.

points and 23 daytime passes containing 896 points. In practice, the first and last
points of each pass were not used, leaving the actual modeling data base with 2325
nighttime and 850 daytime points.

2.2 BELLEVUE DATA.

When at Bellevue, the HiLat transportable receiver, "Rover," is located at
47°36.5 1 N and 122°11.5'W (53.45°N, 296.35°E apex latitude and longitude). The data
used in this report were collected from 16 April 19,84 through 19 April 1986, with a
ten-week break from 24 August through 3 November 1984 when Rover was deployed to
Hanscom AFB, MA. Although Rover typically locks to HiLat's signals within a few
degrees above the horizon, routine processing of beacon data begins at 10° elevation,
and the first and last data points so obtained were ignored in our analysis. Figures
3(a) and 3(b) illustrate the coverage provided at Bellevue by HiLat during this
period. Both are scatter plots of the apex latitude and longitude of the F-layer
penetration point (350km altitude). Figure 3(a) showing coverage in the daytime sector
(0800-1600 MLT) and Figure 3(b) showing coverage in the nighttime sector (2000-0400
MLT). Ascending passes on these plots are roughly parallel to the magnetic meridian
and descending passes are roughly at 45° to the magnetic meridian.

The magnetic local-time (defined in the apex coordinate system) coverage is
illustrated in Figures 4(a) and 4(b). Figure 4(a) is a scatter plot of apex latitude
and magnetic local time for the entire data set. As can be seen, all local times are
well (and reasonably evenly) sampled. HiLat was able to sample all local times due to
precession of its orbit. The effect of this can be seen in Figure 4(b), a scatter plot
of apex local time vs day-of-year. The broad streaks in this figure are descending
passes and the dots are ascending passes. As can be seen, each magnetic local time has
been sampled eight times and each season has been sampled four times (with the
exception of the period when the receiver was at Hanscom AFB). The entire Bellevue
data base for this period contains 27,780 data points from 1304 passes.

A subset of this data base was used for the modeling described in this report. In
order to remove any auroral effects from the data base to allow us to focus on mid¬
latitude behavior, only those data points below apex latitude 54° and having K p -5
were used. This selection reduced the number of points to 3146 points from 774
passes. (Note: Roughly six weeks of observations also were removed due to a cutoff at
28 February 1986 in the available data base on planetary magnetic activity index, K ,

and raw sunspot number, SSN.) The effect of this reduction on the overall magnetic
local time coverage was minimal, as can be seen from Figure 5, which is a repeat of
Figure 4(b) for the reduced data set.

As the modeling procedures used to specify the behavior of C^L require an assump¬
tion that the variations of C.L with time, season, K , and SSN are independent of one

k P

another, several scatter plots were generated to check for inadvertent correlations
between these parameters, which could bias the modeling results. Figures 6(a) through
6(e), scatter plots of with day of year, SSN with day of year, with magnetic
local time, SSN with magnetic local time, and with SSN, show that there was, for the
most part, little correlated variation between these various parameters.

The strongest correlation found was in the relationship between SSN and day of
year (Figure 6(b)), which shows a distinct peak in the early summer due to high SSN
values at the start of the HiLat observations in 1984. In order to separate and
distinguish between SSN and seasonal variations, our strategy was to remove the SSN
variation from C^L prior to any seasonal modeling. In fact, as shown in Section
4.2.3, there is no further seasonal variation once the SSN variation is accounted for.

2.3 REVIEW OF MODELING PROCEDURE.

In the report on equatorial modeling, an idealized procedure was described for
determining the following irregularity parameters: (horizontal vector drift velo¬
city of the irregularities), b (cross-field axial ratio), 6(sheet orientation angle),
a (field-aligned axial ratio), q ( in-situ spectral index), h (effective phase-screen
height), and C s L (now changed to C^L). These parameters were to be determined from
the following observables: (diffraction-pattern velocity derivable from inter¬
ferometer measurements), p(x,y) (ground measured spatial autocorrelation function -
also derivable from interferometer measurements), geometrical enhancement, p
(observed phase spectral index), S^/o + (where S^ is the normalized standard deviation
of intensity and is the standard deviation of phase), and o A . Table 1, repeated
from the previous report, summarizes the idealized procedure.

For the mid-latitude case, the same approach is applicable, but as in the equa¬
torial case, we have departed from the idealized procedure. Our actual approach is
outlined in Table 2, the elements of which are discussed in Sections 3 and 4.

One other parameter, the outer scale of scinti11 ation-producing ionospheric
irregularities, is required by the model but is not obtainable from scintillation
measurements. We have followed our past practice (Fremouw and Lansinger, 1081; Secan

year

Scatter plots from Bellevue HILat mid-latitude data base with bin-
average plots superimposed: (a) K vs. day of year, demonstrating the
lack of K dependence on season; p (b) Sunspot number va. day of year,
exhibiting a peak which implies a possible coupling of the plotted
variables; (c) K vs. apex local time, demonstrating the lack of K
dependence on local time; (d) Sunspot number vs. apex local time,
demonstrating that sunspot number does not depend on apex local time; (e)
K vs. sunspot number, demonstrating that K does not depend on sunspot
namber. p

Interferometer

Measurements

Table 1. Idealized analysis procedure
Physical Parameters

"d

p(x,y)

Geometrical

Enhancement

Table 2. Actual analysis procedure.

Physical Parameters

b 6 a

Richmond <U night:east 20 m/s
al (1980) day:west 20 m/s

No Extended
Enhancement

( 0 )

Sinno and
Minakoshi

(1983)

10

Oefatilt

1.5

4

and Fremouw, 1983a; and Fremouw and Robins, 1985) of setting to a large constant
value, 1000 km. This value can be overridden by users of WBMOD, and it should soon be
refinable by analysis of in-situ measurements in the DNA high-altitude effects
community.

cw

-vv« A

SECTION 3

DRIFT, SHAPE FACTORS, AND HEIGHT

3.1 DRIFT VELOCITY.

As in the case of the equatorial scintillation model, lack of interferometer
results from Wideband led us to deviate from the idealized procedure outlined in Table
1 and to devise a model for convective drift of F-layer irregularities from published
incoherent-scatter radar observations.

After reviewing the recent literature, we chose the work of Richmond et al (1980)
as the basis for WBMOD's description of mid-latitude F-layer drift. Richmond et al
present results from an empirically calibrated pseudo-electrostatic potential model.
The measurements underlying their model are from the facilities at Millstone Hill, St.
Santin, Arecibo, and Jicamarca. For V^, the eastward component of V^, we chose a
close approximation to the published results at 40°N apex latitude, namely the
diurnally cyclic variation,

V dy = 20 sin[(t - 13) 2 /24] (2)

where t is magnetic local time. The other components of V^, and V rfz , were set to
zero.

Transition to the equatorial drift model is provided by means of an error
function centered at 20° apex latitude. Transition to the auroral drift model is
established by means of an error function centered at the apex latitude of the high-
latitude scintillation boundary,

\ b = 71.8 - 1.5 K p - 5.5 cos (t - 2) 2^/24, (3)

where K p is the standard 3-hour planetary magnetic activity index.

3.2 CROSS-FIELD ISOTROPY.

To determine the cross-field axial ratio, b, and the orientation angle, 6 , we
again followed the example of the equatorial model. As in the case of the data from
Ancon and Kwajalein, we observed no extended enhancement along the intersection of any
plane with the F layer. We thus set the axial ratio, b, to unity, and the (now
inconsequential) orientation angle, o, to zero. Transition to the auroral value of b
again is provided by an error function centered at the high-latitude scintillation
boundary. Since the equatorial value of b also is unity and the auroral and equa¬
torial values of • also are zero, no transitions are needed for these values.

ma*. 1

15

3.3 ALONG-FIELD AXIAL RATIO.

To determine a value for the along-field axial ratio, a, we turned to the work of
Sinno and Minakoshi (1983). In their paper, the authors present a study of the effect
of geometrical enhancement on the scintillation of VHF signals received at five
locations in Japan from the geostationary satellite ETS-II. The five receiver
stations provide a range of 0.6° to 17.0° for the angle, '-T'gp, between the radiowave
propagation vector and the geomagnetic field. The data exhibit increasing scintilla¬
tion (as measured by the index) for decreasing ii/ , and hence demonstrate that
geometrical enhancement (which should maximize for = 0 ) does in fact produce
increased scintillation. Furthermore, Sinno and Minakoshi show that the data agree
quite well with theoretical vs 4 ; p curves computed for an along-field axial ratio,
a, of 10. We therefore selected 10 as the WBMOD mid-latitude value of a. Transition
to equatorial and auroral values of a are treated as for drift velocity (see Section
3.1).

3.4 SPECTRAL INDEX.

Although spectral information was not computed for the Wideband Stanford data,
the indication from the HiLat Bellevue data was that the mid-latitude value of the
spectral index, q, is about 1.85 (see Appendix B). This result was somewhat sur¬
prising since examination of the equatorial and auroral Wideband data had led in each
case to a choice of 1.5 for q. As discussed in Appendix B, it appears that Wideband-
vs-HiLat processing differences are at least partially responsible for this observed
difference. Suggestive though the Bellevue results may be, we have decided for the
time being to set the mid-latitude value of q to 1.5, the equatorial and auroral
value, pending completion of our examination of the processing and geophysical
influences on measured spectral index.

3.5 HEIGHT OF THE EQUIVALENT PHASE SCREEN.

With the irregularity shape parameters, a, b, and *, set, we were able to

determine the equivalent phase-screen height, h, from values of the ratio S./o (where

4

S^ is the standard deviation of intensity normalized by the mean intensity and is
the standard deviation of phase). Figure 7(a) shows plots of average S./- vs \ for

4 ^ 3

the entire Stanford data base. The solid line is for the observed value’s, and the
dashed lines are for point-by-point simulations of the data base using choices for the
equivalent phase screen height, h, of 250, 350, and 450 km. The simulations were done

with a modified version of WBMOD, using the parameter choices described in the pre¬
vious sections.

Figure 7(a) suggests that a reasonable choice for h lies in the range 250 to 350
km. Figures 7(b)and 7(c) show nighttime and daytime data, respectively, and are
otherwise identical to Figure 7(a). Figure 7(b) suggests a choice for h of about 350
km, but Figure 7(c) indicates a value for h of less than 250 km. The latter indication
suggests that the E layer is an important contributor to overall observed daytime
scintillation. Since WBMOD is a model of F-layer-produced scintillation, we are
guided by the nighttime results to choose the WBMOD mid-latitude value of h to be 350
km, the same value selected for equatorial and auroral regions.

SECTION 4

IRREGULARITY STRENGTH MODEL

4.1 PROCEDURE.

In the previous sections we have described the determination of all parameters in
the mid-latitude scintillation model except for the height-integrated strength of
irregularities, the modeling of which is described in this section. In previous
versions of WBMOD the irregularity strength for equatorial and auroral regions has
been modeled in terms of the quantity /C ’L. For reasons explained in Appendix A, we
are changing from C $ L to the quantity C^L. C^L is given by equation (1) which we
repeat here:

C kL .(ifO metersj’^CjL

where p is the phase spectral index. We have further decided, for reasons explained
below, actually to model the ouantity log /C^L.

Figures 8(a) and 8(b) shew histograms of .TJT and log vTTjT, respectively, for
the Bellevue HiLat database. The distribution of log ►T ) T is approximately normal,
while the * C^L distribution is strongly skewed. We have thus decided to model log
i ’£| < L rather than v C^L in order to take advantage of the desirable statistical
properties of normally distributed data.

Our basic assumption regarding the quantity log 'C k L is that it can be rep¬
resented as the sum.

log *'C k L = C + M' a ) + f T (t) + f R ( R) (4)

where C is a lead constant, and f., f^ and f are functions depending respectively on
the apex latitude ■ , the magnetic (apex) local time t (hours), and R, the sunspot
number.

Data bases of log > C^L values were obtained for Stanford (from ,)and Bpllevue
(from T and p), using the relations described in Appendix A. We then used the Stanford
data to find the functional form for f , the Bellevue data to find the forms for f and
f R » and finally, the Stanford data for the value of C. It is worth noting that even
though we have set the model value of the in-situ spectral index, q, to l.S, we have

used the measured phase spectral index p = 2.85 for the purpose of computing the mid¬
latitude irregularity strength for the Bellevue data. (See Appendix B.)

4.2 RESULTS.

The significant details in our determination of the three functions and the lead
constant in the representation for log >'C^L will now be described.

4.2.1 Latitudinal Variation.

Shown in Figures 9(a) and 9(b) are scatter plots of log > C. L vs • with line
plots of bin-averaged log /C^L vs X superimposed, for the Stanford Wideband data
base. Figure 9(a) shows nighttime, and Figure 9(b) shows daytime data. The Bellevue
data base was not used because its latitudinal range did not extend far enough
equa forward.

It can be seen from Figures 9(a) and 9(b) that there is an increasing trend in log
vC.L toward the lower and upper extents of the observed ■ range. Appendix B
discusses several aspects of this behavior, including the possibility that the scat¬
tering-theory assumption of a thick (with respect to irregularity correlation length)
irregularity layer does not hold. At the same time, it is clear that for ' in the

a

range of 35 to 45° there is little or no trend in /CL as a function of - .

Juxtaposing this observation with the uncertainties surrounding the trends in V T^I for

35 and • 45°, we have decided to take a conservative approach and set f. (’■ ) to

a a 1 a

zero. We do, however, need to mesh the mid-latitude model with the equatorial and
auroral models. We do so by assuming an error function decay to zero for the mid¬
latitude contribution as 1 approaches the equatorial and auroral regions. The half-
maximum points of the error functions are set at the equatorial transition point, *

3

= 20’, and at the high-latitude scintillation boundary, * b , given by equation (3).
The error function decay rates are chosen to match the decay rates of the apex-
latitude-dependent terms in the equatorial and auroral scintillation models.

An additional feature in the mid-latitude model is a plasmapause term given by

' = c P p K p 7 ( 1 * cos tI)

t 5 i

where C is a lead constant, is the magnetic index, t is magnetic ^apex^ time, ^
is apex latitude, and ■ is the plasmapause location given by ■ ^ ^ being the
th« scintillation boundary given by equation '3'. This tern ; s J'sruss-'d by Fremouw
1 i o^/i ' _

V.

k&LUM

4.2.2

Diurnal Variation.

Figure 10 shows a scatter plot of log / C^L vs apex local time from the Bellevue
data base for 54° and K <5; a line plot of bin-averaged log is superimposed
(jagged line). We favor the Bellevue data over Stanford for determining the time
dependence because the time window for the Stanford data was too narrow, being only
110 minutes at night and 100 minutes during the day. Noting a data maximum near
midnight and a minimum near noon, we obtained a best sinusoidal fit (shown by the
smooth line in Figure 10) to the Bellevue data, the peak-to-peak amplitude being 0.30.
Thus, we set fy(t) to 0.15 cos For the Stanford data the difference between the
nighttime and daytime averages of log / is 0.24, which is similar to the Bellevue
peak-to-peak value.

4.2.3 Sunspot Number Dependence.

Figure 11 shows a scatter plot of log vs sunspot number for the previously
defined Bellevue data set with the diurnal variation and the mean log ,'C^L subtracted
out; a line plot of bin-average log /C^L is superimposed (jagged line). The slope of
a best-fit linear approximation to these data (shown by the straight line in Figure
11) is 0.002, and we have set f R (R) to 0.002 R.

Figure 12 shows a scatter plot of log vs day of year (bin-agerage plot and
zero level superimposed) after the diurnal and sunspot number dependencies and a mean
level are removed from the data. A lack of seasonal dependence is evident, and so the
previously observed (Figure 6b) possible coupling between sunspot number and season is
of no concern.

4.2.4 >T^E Lead Constant.

Since our model-vs-data evaluation tests are performed for Stanford data corri¬
dors (see Section 5.1), and since the Stanford/Bellevue discrepancy is not completely
resolved (see Appendix B), we decided to use the Stanford data to evaluate the lead
constant in our model for log vXjT. In the previous sections we have shown that a
suitable mid-latitude model for log .T^T can be written as

log .TjT = C + 0.15 cos —— + 0.00? R.

? 3

A A-\ '■ f -

a aV. j-.

tin

Apex Local Time (hours)

Figure 10. Scatter plot of log y£7T vs apex local time for the Bellevue HiLat mid¬
latitude data base. Bin-average (jagged line) and best fit sinusoidal
(smooth line) plots are superimposed. The peak to peak amplitude of the
sinusoid is 0.30.

log /CTT

Sunspot Number

Figure 11. Scatter plot of log /C. L vi sunspot num ber (SSN) for the Bellevue HiLat
mid-latitude data base. The log /C.L mean and the apex local time
variation have been subtracted from the log /C^L data. A bin-average
plot (jagged line) and a best fit straight line are superimposed. The
best fit is computed for the SSN range 0-70.

Scatter plot of log vC,L vs day of year for the Bellevue HiLat mid¬
latitude data base. A bin-average d pl ot and the zero level are super¬
imposed. Subtracted from the log /C^L data are the log /CTT mean and the
previously computed best fits for apex local time and sunspot number
variations. The plot shows the absence of any seasonal variation.

The lead constant can be evaluated by taking averages over the Stanford data base on
both sides of this equation. Since it is actually /C^L that is required by WBMOD to
obtain and S^, we rewrite the above equation, prior to taking averages, as

2nt

v'fjT = K 10 0 - 15 C0S 24 10°- 002R . ( 6 )

By taking averages on both sides of this equation, we can obtain K, the log of which is
the lead constant, C.

Since the Stanford data are not evenly distributed over time of day, we take

separate night and day averages. We restrict ourselves to the latitude band 35°<.

X, 145°, since it was data from this region that motivated our decision to set f (x )
a 3 x a'

= 0 (see Section 4.2.1). The following table summarizes the results:

Table 3. Night and day means for Stanford data satisfying 35° £ X < 45°.

V

1 q 0 *15 cos ,,4

1 Q 0.0002R

1.697 E15

1.403

1.0646

1.090 E15

0.730

1.0617

Treating day and night equally, we obtain
mean (/CjT) = 1.3935 E15
and mean (io°- 002R ) = 1.063.

We set the diurnal mean of 0.15 cos to unity, the ideal result for data uniformly
distributed in time. It then follows from equation ( 6 ) that K is 1.311 E15 and the
lead constant C is 15.12.

SECTION 5

CONCLUSION

5.1 EFFICACY OF WBMOD.

The results from the previous sections were incorporated into WBMOD, and evalua¬
tion tests of the new mid-latitude scintillation model were performed. Results of
model/data comparisons for the Stanford data corridors defined in Figures 1(a) and
1(b) (see Section 2.1) are presented below.

To increase the statistical significance of our results, we found it advantageous
to combine certain data corridors. Figures 13(a) through 13(d) show scatter plots of
Briggs-Parkin angle, t^gp, vs apex latitude, X , for nighttime data corridors N2, N3,
N4, and N5, respectively. It can be seen that the \p Dn vs X, behavior is similar for N3

Dr a

and N4, the two more nearly overhead corridors. Namely, for each of these corridors,
Vgp reaches a minimum between 10° and 20° at an apex latitude close to that of the
receiver. The scatter plots for corridors N2 and N5 also are qualitatively similar.
We therefore grouped corridor N3 with N4 and N2 with N5 for comparisons between model
results and data. In a similar manner. Figures 14(a) through 14(e) support the
grouping of daytime data corridor D2 with D3 (most nearly overhead), and D1 and D2
with D5.

To perform the model/data comparison presented below, we used a modified version
of WBMOD to simulate the satellite geometry and each data point of each pass. Figures
15(a) and (b) show the comparisons for the nighttime data and Figures 16(a) and (b)
show the comparisons for the daytime data. Most satisfying is that the geometrical
enhancement peaks for both night and day overhead corridor groups are reproduced by
WBMOD with reasonable accuracy. For all corridors the model/data agreement for '

a

between 35° and 45° is quite good, as we should expect, since that is where the absence
of latitudinal variation in model C^L is consistent with the lack, of latitudinal
variation in the C^L data. North and south of this interval the observed scintilla¬
tion strength generally exceeds the model results. It is hoped that further observa¬
tions from HiLat and Polar BEAR will help to explain these trends, at least in the
latitude regime for which • .

5.2 SUMMARY.

From contributions to the literature, the limited data base collected at Stanford
during the first four months of the DNA Wideband experiment, and a subset of the

28

Briggs-Parkin Angle (deg) Briggs-Parkin Angle (deg)

Angle (deg)

05

X .

/

y

Apex Latitude (deg)

Figure 14. Scatter plots of Briggs-Parkin angle vs magnetic apex latitude, X fc
daytime data corridors 01, 02, D3, D4, and D5. Plots are shown in (a)
(b), (c), (d), and (e), respectively (Concluded).

$

Bellevue HiLat data, we have determined a characterization of mid-latitude amb'ent F-
layer radiowave scintillation and will include it in WBMOD, our global scintillation
model. A general procedure presented in a previous report on the equatorial component
of WBMOD has been used as a guide for mid-latitude model development.

As indicated in Table 2, our model describes the scinti11 ation-producing irregu¬
larities as having cross-field isotropy, elongation along the magnetic field by a
factor of 10, a single-regime power-law spectrum with an in-situ spectral index of
1.5, and representation by a phase-modulating screen located at an F-layer altitude of
350 km. In accord with an empirically based model of plasma drift, the i rregularities
are taken to drift eastward at night at speeds up to 20 m/sec and westward in the
daytime at the same speeds.

The model describes the height-integrated spectral strength of the irregulari¬
ties, log »'C. L, by means of the following formulation:

(7)

log .T^U~= C + fy(t) + fp(R)

where t = local apex time (hours),

and R = smoothed Zurich sunspot number;

2-t

and where fj = 0.15 cos

f R (R) = 0.002 R, (Q)

and = 14.50.

We have introduced no apex-latitude dependence for mid-latitude C^L and have used
error functions to merge the mid-latitude model with the equatorial and auroral
models.

The mid-latitude model in WBMOD produces representative average scintillation
levels for 35":_’. 1.45 and successfully characteri zes the effects of geometric
enhancement for radiowave transmissions having Briggs-Parkin angles approaching zero.
No attempt is made to model.increasing scintillation trends observed in the Stanford
data for 35 and • ^45"’. We await further observations from DNA's HiLat and

data for 35 and • ’ > 45\ We await further observations from DNA's HiLat and

3 3

Polar BEAR satellites to understand better scintillation activity occurring at apex
latitudes falling between those represented by the auroral 'Poker Flat' and the mid¬
latitude data. The transition between mid-latitude and equatorial 'Ancon and
kwajalein) behavior remains to be explored.

SECTION 6

LIST OF REFERENCES

Fremouw, E.J. '19841, "Improvements in Operational Codes Describing the Ambient Iono¬
sphere," Defense Nuclear Agency, Progress Report No. 9 , Contract DNA001-83-C-
0097, Physical Dynamics, Inc., Bellevue, WA.

Fremouw, E.J. and J.M. Lansinger (1981), "A Computer Model for High-Latitude Phase
Scintillation Based on Wideband Satellite Data from Poker Flat," DNA Report
^686£, Contract DNA001-79-C-0372, Physical Dynamics, Inc., Bellevue, WA.

Fremouw, E.J. and R.E. Robins (1985), "An Equatorial Scintillation Model," Final
Report for DNA Contract DNA001-83-C-0097, Physical Dynamics, Inc. Report No. PD-
NW-85-342R, Bellevue, WA.

Fremouw and Secan, (19861, "Support of "Rover" Ground Station for DNA's HiLat Satel¬
lite," Progress Report for DNA Contract No. DNA001 -85-C-0017, Physical Dynamics,
Inc., Bellevue, WA.

Fremouw, E.J., R.L. Leadabrand, R.C. Livingston, M.D. Cousins, C.L. Rino, B.C. Fair,
and R.A. Long r 1978), "Early Results from the DNA Wideband Satellite Experiment -
Complex-signa1 Scintillation," Rad. Sci. , I 3 ( 1 ), 167-187.

Fremouw, E.J., H.C. Carlson, T.A. Potemra, P.F. Bythrow, C.L. Rino, J.F. Vickrey,
R.L. Livingston, R.E. Huffman, C.I. Meng, D.A. Hardy, F.J. Rich, R.A. Heelis,
W.B. Hanson and L.A. Wittwer (1985), "The HiLat Satellite Mission," Rad. Sci., 20
'3\ 416-424. —

L’vings ton, R.C., C.L. Rino, J.P. McClure, and W.B. Hanson (1981), "Spectral

Characteristies of Medium-Scale Equatorial F-Region Irregularities,"
J. Gcophys, Res., 86 '41 2421-2428.

Richmond, A.D., M. Blanc, B.A. Emery, R.H. Wand, B.G. Fejer, R.F. Woodman, S.
Ganguly, D . Amayenc, R.A. Behnke, C. Calderon, and J.V. Evans (1980), "An
Empirical Model of Quiet-Day Ionospheric Electric Fields at Middle and Low Lati¬
tudes," J. Geophys. Res. , 85 (A91, 4658-4664.

^ino, C.L. '19791, "A Power Law Phase Screen Model for Ionospheric Scintillation. 1.
Weak Scatter," Rad. Sci., 14 '6), 1135.

Pino, C.L., E.J. Fremouw, R.C. Livingston, M.D. Cousins, and B.C. Fair (1977), "Wide¬
band Satellite Observations ," DNA Report 4399F , Contract DNA001-75-C-0111, SRI
International , Menlo Park, CA.

Secan, J.A. and E.J. Fremouw '1 983a), "Improvement of the Scinti11 at ion-1rregularity
Mod^1 in WBMOD," DNA Report TR-81-241 . Contract DNA001-81 -C-0092 , Physical Dyna¬
mics, Inc., Bellevue, WA.

Secan, J.A. and r .F. Fremouw '1 983b'', "Improvements in Operational Codes Describing
the Ambient Ionosphere," Defense Nuclear Agency, Progress Report No. 2 , Contract
DNA901-8' > -C-0 r '97 1 Physical Dynamics, Inc., Bellevue, WA.

S’nno, v . and H. Minakoshi ' 1 983' , "Experimental Results on Satellite Scintillations
Due to F 1 eld-A1 ’gned Irregul arities at Mid-Latitudes," J. Atmos. Terr. Phys.,

AC fQ/Cl'CC'iCC'? ——

APPENDIX A

REPLACEMENT OF C L WITH C. L

S k

In developing power-law scintillation theory, Rino (1979) chose to characterize
irregularity and phase-scintillation strength in spectral terms, owing to the practi¬
cal indeterminacy of the ionospheric outer scale. As a measure of irregularity
strength, he defined the quantity *

<*'*>** r(¥)/i*r) <n,

electron-density variance
outer-scale wavenumber
two-dimensional (phase) power-law index.

iical meaning of is a bit obscure, although it is mathemati¬
cally well defined. An approximate physical definition is that it is "numerically
equal to" the spatial power spectral density (PSD) at a wavenumber of unity (i.e., at
a scale size of 1 m/rad). It is to be recognized that C $ does not have the usual
three-dimensional spatial PSD units, but rather units of (el ) 2 /n/ 4+p ^. Of more
practical significance, its defining wavenumber is far outside the scintillation-
producing spectrum and probably outside any true power-law regime.

C s * 8

3/2

where

<*.>

the

k =
o

the

and

P =

the

The

precise

phy

For reasons soon to be demonstrated, we define a new irregularity strength
parameter, C^, very closely related to C $ , explicitly as the three-dimensional PSD of
electron density at a wavenumber k. That is, first we use Eqs. (5) and (6) of Rino
(1979) to write the spectrum as

S N (k) = S~ 3/2

i

2=1

2

< AN e >

2\ o

MP-2)

( 12 )

(k 8 ♦

where anisotropy has been taken up in the definition of the wavenumber, k, and then we
defi ne

' ( 2 ± 1 \ k (P-2)

C k - 8"

3/2

t2=l\

^(k? ♦ k ?)fP +1 > /2

(13)

so that C, = C,/(k 2 + k?)^ p+1 ' /2

(14)

39

c

PREVIOUS PAGE
IS BLANK

and has true PSD units of (el/m 3 ) 2 /(rad/m) 3 = el 2 /m 3 . For >> k Q , we have

C k * 8 ' t

3/2 \ 2

«>

? ^ p ' 2>

2 \ 0

k k (p+l) k k (p+l)

Next, we choose k k to be 2V10 rad/m (i.e. a scale size of 1 km/cycle). We then have,
to a good approximation.

C k = 4 v TT X 10'

-3 n -l2±l)

I 10 V 1 2 j

V 2 -T ; TJfT)

2\ t,(P~2)

\ e / o

/ 10 8 \ ^^

or C k = ( 2— meterS ) 1

The simple rescaling represented by Eq. (17) accomplishes two things. First, it
produces a strength parameter, C k> which is a true PSD. More important, it character¬
izes the strength in a portion of the spectrum relevant to scintillation research (a
scale size of 1 km rather than one on the order of a meter). Using C s instead of C k
causes an irregularity-strength data base derived from phase-scintillation measure¬
ments to be unrealistically sensitive to variations in spectral index, p, whether
those variations are ordered or random and whether they are real or arise from
experimental or numerical inaccuracies. That sensitivity stems from the "long lever
arm" that one effectively is employing in extrapolating a measurement made in the
kilometer-scale range to a characterization defined in the meter-scale range. We
shall see that converting phase-scintillation measurements to C $ introduces a mis¬
leading dependence of the irregularity strength parameter on p.

To complete a consistent procedure, we also define a new (in principle) parameter
for characterizing the strength of phase scintillation, starting with that defined by
Rino (1979) as

T

sec 0 ) GC s

v (p-n

e

where r = classical electron radius,

= radio wavelength,

L = thickness of the irregular layer,

= incidence angle of the propagation vector on the layer,
and = the effective (anisotropic) scan velocity.

( 18 )

Again T is approximately numerically equal to but not identical with a PSD, namely the
temporal PSD of phase at a fluctuation frequency of 1 Hz. It has units of rad^/Hz^'
P) •

2

Analagous to C^, we define explicitly as the PSD of phase (in rad /Hz) at fluctua¬
tion frequency ^, namely

t 2.2

T 1 = V

where „ = V

c / k 2 + .2.(p+l)/2

-HE/2)_ ( L sec *) GC --- 0 k ' v (p - 1}

(p+l)-/£+l.^ (L ° k , 2 + 2»p/2 V e

v ' o ' r

o e 2~ *

From Eqs. (13), (18), and (19), we have, obviously,

T 1 ■ T '< l * •

Again in the 1arge-outer-scale limit, we have

L. L (P + 1)

T, r‘.‘ --- U ■'.) C G V (p_1) •» (21)

1 * „P ' k e p

and, defining ^ at 1 Hz, we can obtain C^L to a good approximation from
C ,. L - (10 3 ) (P+1 M^) cos

- rv (P-D (2?)

\2/ r e GV e

where = (1 Hz) p T.

Experimental ly, the parameter usually referred to as T really is T., the two being
numerically equal (in the large-outer-scale limit). We shall make no further dis¬
tinction between them. The distinction between and is of considerable practical
importance, however, as we shall now see.

Repeatedly, it is reported that the spectral index, p (and its one-dimensional
counterpart, q = p-1), decreases (portrays a shallower spectrum) as irregularity
strength, characterized by (or its height-integrated counterpart CL), increases.
In dealing with the HiLat data from Rover, we again found this dependence, as illus¬
trated in Figure 17a. The sample distribution of the contributing data population
also is shown. The trend is very consistent for all log^C data bins hav’ing more
than about 100 samples.

T. *. S . *-

NO. DATA POINTS

NO. DATA POINTS

o

o

o

o

o

o

o

o

o

if)

o

w

o

o

CM

C\J

—

—

if)

o

o

o

o

o

o

o

o

o

o

o

o

if)

o

if)

o

o

CO

CM

<\l

—

if)

13 tO E TD <4- O
Of- CJ <U O i-
<4- <C X CL

“O <4- QJ 4->

C • 00 13 00

03 C r 03 L-

o ' fo -i-

cu •>- • cn > 4-

34 J ac

> 03 LU •*— “O <1)

CU i— >> CD SZ

•— i— £ O S- +->

.— -r~ O r— r3

oj - 4 —> S— cl to >>

CD E <D|-

•r- QJ QJ C

+j 0*0 E O

ro oo <D *■

•M ^ 03+^

L- 0) 3 CO C (ID

qj oo Q- f—< -i— _cr

> (T3 E "— >>-*->

o x: o • o

o: au cr.— cu

LU CL4->

x: u 1 E O

*-> m i/)E cu z

> O

o s-

S- Qj

<4- ^

*4— •" *■ ■ 4->

r ,

*0 0—1
QJ *

OJ Cl QJ

•J

“O CM E

L- *

QJ '*—- 03

O

13 h-

-P> O S-

to

3 • 03

H

OC.

03 •'tO

CL CT^- CL

QJ x: QJ

E LU LO

o

(0

EP L

o • xi

cn o

U ECMP

CD

n

r C (O

O'-— CD

CL QJ 03

_J S- C

u

i

S- QJ

(0*4— QJ QJ

—i

•P E

C_J D L

X to

TJ -- P

QJ x:
•Of— -P>

C res cn

s_ c

4-> 0J

<— u L
03 QJ-P
S- Q_ to
4-> tO

__QJ 03 CO

_o t: >

3 . 13 QJ

CL -O X!
E QJ -P
• O X

c O -r- -a

O *4— C

r- _J 03

4-> -X 03
03 <_) CL

E cn
L- C C

O

o

o

o

o

o

o

o

o

if)

o

if)

o

o

CM

CM

—

—

10

o

o

o

o

o

*4—

QJ

aj

O ^-r- QJ
*P U >i QJ

o

o

o

o

o

O

to ~0

x:

<o^O 5

o

if)

o

u>

o

O

03 QJ

4->

c r— 4->

CO

hi

CM

..1.1

CM

..In

, .7. ■

i.7m

U>

.ill.

o

i I 1 oo

XI >
CL T-

3P

03 • CL QJ

L- C E JC

*4— QJ *4—

o ~o

to

ior c
qj p o
cn cn-r-
ra C P
S- CU 13
QJ S- -Q
> P’f

03 tO S-

XI 03 QJ
p E CM L
S- CM 4->
C O '—"

-f- Q— 4->
to • C
cl c cr qj

03 LU P
*4— L- to
O -M E •»-
O to
tO QJ S- C

qj x: <4- o

CO CM

X 30 NI “IVdl 33 dS 35 VHd

d 'X30NI lVdl33dS 3SVMd

qj x: <4- o

3 +-> tj

r— T3

03 C QJ 03
> i- 4->

13 C
-a a. a_-r-
QJ E

L P O 1/3
Z3 O U 4->

tO i—

i 03 —I 13

QJ LO -X tO
l E • CJ QJ
C\J S-

1 cn-—^

C QJ

CUC, i-

=3 Z3

■Or— “O

r— 03 • QJ

i a > a u

p * /. ,* / s -■

■L

42

T M’W V'*'V ^ TW » V W *TTF V ' 1H ■ LT ■ ^ "V* V"

fS

S

V%

.v;

i * *
\\
'j\
' %

Indeed, our geophysical intuition suggests that the trend in Figure 17a is "too
good to be true." Accordingly, we checked for the same trend in T, the observable from
which the derived quantity C s L was obtained. The empirical relationship between p and
> T cos - and the corresponding sample distribution are shown in Figure 18. A trend is
evident only for bins with relatively few points, albeit still a goodly number.

Believing now that the consistent trend in Figure 17a was introduced in the
conversion from T to C $ L, we checked for it in the empirical relationship between the
measured p values and the latter quantity derived using a representative but fixed
value of p (2.5) instead of the measured values. The result is shown in Figure 17b,
from which the consistency of the trend in Figure 17a again is absent, reinforcing our
disbelief in its underlying significance.

Next, we employed Eq. (22) to obtain C^L, using the measured values of p for the
conversion, and plotted its relationship with p in Figure 17c. Its similarity to
Figure 17b makes us believe that it represents more nearly the true relationship
between irregularity strength and spectral index in the Rover data population than the
simple trend in Figure 17a. This belief is further reinforced by Figure 17d, which
was obtained from Eq. (22) using a fixed value of p (2.5) for the conversion. That is,
out of the four procedures represented in Figure 17, only the one employing the long
lever arm of extrapolation imposed by solving Eq. (18) for produces the clean trend
often reported as the relationship between irregularity strength and spectral index.

"*VV,

We shall now demonstrate that employing the C s "lever arm" introduces the

reported clean trend into a data set having absolutely no underlying relationship

between observed scintillation strength and spectral slope. To do so, we produced a

simulated data population of p and T cos 0 values, the sample distribution of the

former being modeled after that actually observed in the Rover data population, and

-5 -3 2

the distribution of the latter being uniform between 10 and 10 rad /Hz. Figure 19
shows the distribution of p values actually measured at VHF in Bellevue. For the
simulation, we employed a gaussian fit to this distribution, having a mean value of
2.7 and a standard deviation of 0.71. We produced the simulated data set by applying
the Gaussian p distribution repeatedly to points within each of the equally populated
T bins. Thus, there was no correlation between p and T.

• We then used Eq. (18) to compute C^L from the simulated data base, employing
fixed values of 1.0 for G and 1500 m/sec for V . The relationship between the input p
values and the output C^L values is indicated by the solid curve in Figure 20a. It is
represented very well by a straight line with a slope of -0.59, as obtained from a best

43

NO. DATA POINTS

at the truncation edges.

fit over the range 10 £ log ((^L)* 5 — 12. This is essentially identical to the
relationship between p and log (CL) with a slope of -0.3 reported by Livingston et al
(1981) and with the trend displayed in Figure 17a, which is repeated as the broken
curve in Figure 20a. The histogram in Figure 20a illustrates the distribution of C s L
values resulting from application of Eq. (18) to a uniformly distributed (albeit
truncated) population of T values, given a p distribution such as the observed one
illustrated in Figure 19.

Finally, we converted our simulation data base from T to C^L, using Eq. (22).
Those results are displayed in Figure 20b along with the corresponding relationship
between p and C^L from the observed data base. The uniform distribution of input T
values from the simulated data population has survived transformation to C^L, except
near its truncation edges, as indicated by the histogram. A few T values near the
edges have been converted preferentially to the smallest (largest) C^L values by large
(small) p values, as indicated by the solid curve. The relationship between measured
p and C k L derived from the measured T values displays a somewhat similar behavior, as
indicated by the broken curve.

We conclude from the forego-ing that the relationship between irregularity
strength and spectral index often reported from measurements of phase scintillation
is, at least, strongly amplified by the "lever arm" of extrapolation from measurements
in the km-scale regime to characterization, by means of C $ from Eq. (18), in the
meter-scale regime. We have, therefore, abandoned use of C s L in characterizing
irregularity strength in favor of C^L, obtained from the simple scaling indicated by
Eq. (17).

APPENDIX B

PARTIAL RESOLUTION OF STANFORD/BELLEVUE DISCREPANCY

The first step in combining the results from the Stanford Wideband data set and
the Bellevue (Rover) HiLat data set was to plot the apex latitude variation of log
^CjT from the two data sets (Figure 21(a) shows scatter plots and Figure 21(b) shows
bin-average plots.) As can be seen, there is a discrepancy of over half an order of
magnitude between the »'C^'L values at the northern end of the Stanford data set and the
southern end of the Bellevue data set. Two possible sources of this discrepancy were
investigated:

1. Errors in the code developed to convert raw phase data to C^L.

2. Differences in the methods used to calculate CL from phase ( o. for the

k "t

Stanford data set and the spectral parameters T and p for the Bellevue data
set).

Regarding number 1, the implementations of the theory used in the conversion were
checked carefully, and hand calculations for a selected number of points were compared
to calculations from the software. No errors or problems were found in this area.

Regarding number 2, the equation for C^L as a function of the phase spectral
parameters T and p developed in Appendix A (Equation (22)) was used to calculate C^L
from the Bel levue/HiLat data base. This approach could not be used directly for the
Stanford/Wideband data base, as the T and p parameters were not generated for this
data set. However, the RMS phase parameter, can be converted to an equivalent T
value. This equivalence follows from the assumption that the phase spectral density
function (SDF) can be modeled in terms of the two parameters T (spectral power at 1 Hz)
and p ^spectral slope) as

SDF = Tf~ P . (23)

2

Since the phase variance, , is the integral of this function over all fre¬
quencies such that f f where is the low-frequency cutoff 'set in the Stanford
data by the 0.1 Hz detrender cutoff’ 1 , we get

PREVIOUS PAGE
IS BLANK

+ Stanford
• Bellevue

ui

I1v3p.y

;

MTf*.

f:

*v--

T>‘

3*8

>■ vs:

Apex Latitude (deg)

J

St dnford

Apex Latitude (deg)

Variation of log /C^L with apex latitude from the Stanford Wideband and
Bellevue HiLat data bases. (a) shows a scatter plot, where crosses
denote Stanford date and dots denote Bellevue data; (b) shows bin average
plots for pach daia set.

2

2T

-(p-1)

(24)

l

> 3 *

k*‘- v

‘vOv

0

,’v V

fck^.

K£

<v

&¥

4> (p-1) C

or

T = 0.5(p-l)f c {p ' 1) o^ 2 •

(25)

The major uncertainty in Equation (25) is the value to use for p. For the calculations
used in creating Figure 21, a value of 2.5 was used; this choice was based on analysis
of other Wideband data sets (Fremouw and Lansinger, 1981; Fremouw and Robins, 1985).
The value of T calculated from Equation (25) and the assumed value of p can then be
used to calculate C^L.

In order to test this calculation, five Stanford/Wideband passes (listed in Table
4) were reprocessed to provide values for T and p as well as o Figure 22 is a
scatter plot of the T values calculated from the values using Equation (25) with p
= 2.5, plotted against the corresponding T values obtained from a log-linear fit to
the actual phase SDF. The straight line is a linear least-squares fit to the data con¬
strained to have a slope of 1.0.

Initially, the offset found from Figure 22 was to be used as an empirical
correction to the Stanford T values, but a more detailed study of discrepancies
between the spectral results from the Wideband data sets and those from the HiLat data
sets (Fremouw and Secan, 1986) found that the p values from the Wideband data sets are
artificially low. The Stanford passes were reprocessed using the standard HiLat
processing, which yielded an average value for p of 2.85, which agrees well with the
average p found in the low-latitude end of the Bellevue/HiLat data set.

Figure 23 is a scatter plot of the data in Figure 22, this time using p = 2.85 in
calculating T from o The offset is much smaller now, with a residual multiplicative
correction of 0.8 to convert T calculated from o^to the corresponding T extracted from
the phase SDF. (Note: This residual probably is tied to the consistent steepening of
the phase SDF reported in several recent reviews of both Wideband and HiLat data. As
this tie is still under investigation, we have not attemped to resolve the issue here
but have simply carried forward the correction factor).

10 log T (from PRMS)

Stanford (P = 2.5)

A A /

t ‘‘$A

A

Figure 22<

10 log T (from SDF)

Comparison of the values 10 log T calculated from r; (p = 2.5) to the
values 10 log 7 extracted from the phase SDF, computed for five
representative Stanford Wideband passes. The straight line is a least-
squares fit to the data, constrained to have a slope of unity.

10 log T (from PRMS)

Stanford (P = 2.85)

Figure T. Comparison of the values 10 log T calculated from (p = 2.85) to the
values 10 log T extracted from the phase SDF computed' for five
representative Stanford Wideband passes. This figure differs from
Figure only in the value of p used to calculate T from -

Table 4. Stanford/Wideband Passes Reprocessed.

Pass ID

Date

GMT

ST-01-41

1 Jul 76

17:31

ST-01-49

8 Jul 76

18:39

ST-02-25

6 Aug 76

06:55

ST-02-47

27 Aug 76

08:41

ST-10-04

4 Sep 76

07:00

Figure 24 is a repeat of the bin-averages in Figure 21(b) with an additional

curve showing the new latitudinal variation for Stanford using a p value of 2.85

and the correction factor of 0.8. Although the Stanford and Bellevue curves are now

closer together, they still differ by a factor of ~3. To explain this discrepancy, we

hypohesized that the increase in C^L with latitude at the high-latitude end of the

Stanford data set was due to urban radio noise from the San Francisco/Oakland area

north of Stanford interfering with the VHF signal. To investigate this, both VHF and

UHF c (the center UHF channel) for the five Stanford passes listed in Table 4 were

reprocessed, and the a, values for the two frequencies were compared. Any noise

<P _1

contamination in only the VHF channel would cause a departure from the f scaling

expected in the observed a x values.

<P

Figures 25(a)-(c) and 26(a)-(c) show the results of the foregoing analysis for

ft

ft

Vi

A

passes ST-01-49 and ST-02-25. The upper two plots in Figures 25(a) and 26(a) are the

log intensity and detrended (at 0.1 Hz) phase for the VHF channel, and the bottom two

plots are the log intensity and detrended phase for the UHF channel. Note that the

c -1

ordinate scales on the VHF and UHF c detrended phase plots reflect the theoretical f

scaling, which in this case is a factor of 3 between the Wideband VHF and UHF c
channels.

Figures 25(b) and 26(b) are scatter plots of c from UHF against o from VHF,

^ '$

and Figures 25(c) and 26(c) show the variation of log n for both VHF and UHF through
the pass. Note that the axis scales on the scatter plots in Figures 25(b) and 26(b)
have been set so that all points following the f’ 1 scaling fall along the diagonal
from the lower left to upper right of the plot.

These foregoing figures, which are representative of the five passes re¬
processed, show little evidence of a systematic noise contamination in the VHF data.

■- .•«
.'-V-.Vi'.V,

Intens

) VHF
-02-25
detrended .
Wideband d

time

Ut

'IaHSI

0.0

0.3

0.6

0.9

VHF RMS Phase Fluctuation (rad)

Universal Time (HMM)

Figure 26. (a) VHF (upper plots) and UHF (lower plots) channels for Wideband pass

ST-02-25. Top plot in each pair is log intensity, bottom plot is phase
detrended at 0.1 Hz. (b) Scatter plot of cu at UHF r against a, at VHF for

Wideband pass ST-02-25. (c) Plot of VHF (upper) C and UHF (lower) log

vi time for Wideband pass ST-02-25 (Concluded). c

While there is some scatter from the f behavior expected, the departures are not
great, and the largest departures shown in the two figures are at the end points of the
passes and are attributable to detrender effects. Therefore, short of reprocessing a
larger number of Stanford passes (note that five passes constitute roughly six percent
of the entire Stanford/Wideband data base), we do not feel that there is strong
evidence that the residual difference in shown in Figure 24 is due to external
noise interference on the VHF channel.

Two features in the overall shape of the latitudinal variation of ,r^T for both
the Stanford and Bellevue d-+a sets in Figure 24 suggested another possible contri¬
bution to the discrepancy: (i) both curves "kink" at latitudes very close to the
latitude of the station from which the data were collected, and (ii) the slopes of the
high-latitude end of both curves are nearly identical. In examining the data, we
found that the kinks occurred at the latitude where the minimum in the longitude-
averaged value of the F-layer incidence angle, occurred. Although any variations
with should be accounted for in the theory that gives T in terms of C^L, we
nevertheless replotted the data from Figure 24 as vT^L cos , as shown in Figure 27.
The discrepancy still has not been accounted for, but it has been reduced, and the
kink in the Stanford data has disappeared.

One possible explanation for this observed sec -dependence in the C^L data would
be a break-down in the assumption, made in the theory that gives T in terms of C^L,
that the irregularity layer is thick with respect to the correlation lengths of the
irregularities. This assumption leads to a variation of T with the product of sec

and C.L. If this assumption is not valid, which would imply a coherent integration of

K 2
the effects of the irregularities on the phase, a sec variation would result.

3

While this does not agree with the sec • variation suggested in the Stanford C^L
behavior in Figure 27, it is in the correct direction and may imply that the thick-
screen assumption is invalid for this data set.

ses

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