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ANALYSIS OF IONOSPHERIC VERTICAL

SOUNDINGS FOR ELECTRON DENSITY

PROFILE DATA

I. FACILITIES FOR CONVENIENT MANUAL

REDUCTION OF IONOGRAMS

BY J. W. WRIGHT AND R. B. NORTON

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL BUREAU OF STANDARDS

technical ^flote.

14

July , 1959

Analysis of Ionospheric Vertical Soundings for Electron

Density Profile Data

I. Facilities for Convenient Manual Reduction of Ionograms

by

J.W. Wright and R.B. Norton

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ANALYSIS OF IONOSPHERIC VERTICAL SOUNDINGS

FOR ELECTRON DENSITY PROFILE DATA

I. Facilities for Convenient Manual Reduction of Ionograms

by

J. W. Wright and R. B. Norton

Abstract

Facilities for manual reduction of ionospheric vertical soundings to true heights are prepared using the "10 point" ratios of Ventrice

and Schmerling. A study of the effects of the earth's magnetic field

on true height calculations permits selection of five sets of these

ratios assuring equal accuracy of application for any part of the world.

The facilities available are in the form of transparent overlays and

matching special graph paper.

ANALYSIS OF IONOSPHERIC VERTICAL SOUNDINGS

FOR ELECTRON DENSITY PROFILE DATA

I. Facilities for Convenient Manual Reduction of Ionograms

I. Introduction

Of the several methods available for the determination of

electron density vs. height profiles from ionospheric vertical soundings, those which lend themselves best to large scale, frequent application invariably involve the use of electronic computers. A need

exists, however, for a method of comparable accuracy which can be

applied quickly and with a minimum of equipment. The method of Kelso,

(in which a true height is obtained as the simple average of the virtual heights at 5 or 10 frequencies selected according to a definite

law) satisfies these requirements, but has the disadvantage that no

account is taken of the influence of the earth's magnetic field.

2 Recently, by modifying the matrix method of Budden , Schmerling-^ has determined sampling ratios similar to Kelso's, but with the

effect of the earth's magnetic field included. Ventrice and Schmerling

have presented tables of the sampling ratios with which Ionograms obtained anywhere in the world may be analysed.

A method has been devised at the National Bureau of Standards

for the determination of world zones of approximately equal magnetic

field error. The Schmerling coefficients applying most closely to the

characteristics of magnetic dip and gyrofrequency in each such zone
have been selected. Over.lays incorporating the selected coefficients

have been devised; they may "be used to analyze ionograms quickly and

conveniently in the manner described below.

II. Description of Facilities

The "Ten Point" ratios for each zone are given in Table I.

These are the ratios which the sampling frequencies bear to -the frequency ("index frequency") at which the true height is desired. Since,

within a zone, the sampling ratios vary only slightly with frequency,

the same set of ratios may be used over a considerable portion of the

frequency range. Only one set of ratios is necessary for the lowest

dip/gyrofrequency zone, reflecting the fact that here the effect of

the earth's magnetic field on the true height calculation is small.

In the intermediate latitudes, two sets of ratios are needed, and at

the higher latitudes three sets are necessary to preserve the same

accuracy throughout the frequency range

.

Scaling overlays and graph paper have been prepared specifically for the reduction of logarithmic ionograms obtained with KBS C-2,

C-3j and C-^ ionosondes, but they may be applied to any virtual height

curve traced or drawn onto the graph paper. The overlays may also be

applied directly to the projected image of logarithmic ionograms, but

it is essential that the frequency scale of the overlay and of the

ionogram correspond exactly.

-2-
In the design of the overlays , advantage is taken of the

logarithmic frequency scale of the ionogram. This is done by choosing

a single index frequency of 25. Mc (indicated by "fN" on the overlays)

for all zones - and all frequency ranges to be covered. The 10 point

ratios have then been located on the logarithmic frequency scale as

fractions of this index frequency. Because of the logarithmic scale

the same overlay can be used at any point on the ionogram for which the

10 point ratios are appropriate. Where two or three sets of ratios are

necessary within a zone to treat adequately the entire frequency scale

they all appear together on the same overlay, and use the same index.

An example of one of the overlays available, and of the graph

paper, are shown in reduced size in Figs. 1 and 2. A transparent overlay for any zone and a supply of graph paper can be provided to bona fide

workers upon request to World Data Center A, Rational Bureau of Standards,

Boulder, Colorado, USA.

III. Specification of World Zones

The world has been divided into five zones such that the

variation of the magnetic field effect is satisfactorily small within

each zone. The division is carried out in terms of the magnetic parameters that affect true height calculations- -dip and field strength.

A graph of the boundaries within which fall all values of the

earth's magnetic dip and field strength (represented by gyrofrequency)

-3-
is shown in Fig. 3- Five zones of equal magnetic field error are also

shown. To determine the zone appropriate for an ionospheric observatory

(and hence the group of 10 point coefficients to be used there) it is

necessary to know only the magnetic dip and the gyrofrequency at 200 km

(=2.552F, where F is the total field strength at ground in cgs units).

The study of errors due to the magnetic field, and the resulting

delimitation of world zones, have been accomplished by computing the

errors produced by using inappropriate magnetic field parameters in the

calculation of the true height curves from a single virtual height curve.

In the present case, the errors have been characterized by their magnitudes at 95 »5 Per cent of the penetration frequency of the parabolic

layer best fitting the computed true height curves. Since the errors

generally increase nearer the penetration frequency, our estimates should

provide a reliable guide to the magnitude and world-wide variations of

these errors.

When the proper set of coefficients for any zone and frequency

range are used, the largest errors at 95-5 per cent of the penetration

frequency, incurred within the zone, will be 0.025 of the semi-thickness

of the best fitting parabolic layer. The errors will be larger nearer

the penetration frequency. Also, at the highest dip angles (near 90 )

the above factor may approach 0.07- In a typical case of a parabolic

layer with a 10 Mc penetration frequency and of 200 km half thickness,

the magnetic error at 9-55 Mc will be 5 km or less within the zone.

-h-
IV. Method of Analysis

It is recommended that the ordinary virtual height curve be

first obtained on the graph paper to assure correspondence of the

frequency scales and to permit easy measurement of heights at the sampling frequencies. This may be done in two ways:

A. The ionogram image may be projected from film onto the

graph paper supplied. The h

1 (f ) curve for the ordinary ray is traced

onto the paper; any corrections necessary to assure proper correspondence

of the height and frequency markers with the corresponding scales of the

paper should be made continuously along the curve

B. Alternatively, virtual heights may be plotted onto the

graph paper, either directly from the "B-Scan" presentation of the

ionosonde (especially valuable for rapid or "real time" analyses), or

from ionograms obtained on non- logarithmic equipment. Enough heights

must be plotted to permit the h

1 (f ) curve to be drawn fairly accurately.

The tracing or graph of virtual height must now be "completed."

Several steps are necessary:

(1) An extrapolation of the virtual height graph to low

frequencies is usually necessary, since often the lower sampling points

fall well below the 1.0 Mc lower limit of the ionogram. In general,

little harm results from assuming that the height of reflection below

1.0 Mc is constant, except perhaps at sunrise and sunset, and in cases

of night E.

(2) Large gaps in the virtual height curve due to deviative

absorption (near penetration frequencies) or to equipment insensitivity,

should be filled In by careful estimates of the most reasonable curve.

(3) Parts of the virtual height curve obscured by blanketing

sporadic E should be filled in with a reasonable curve

-5-
More detailed consideration of the treatment of difficult cases

is given to guide the systematic scaling of virtual height data for

analysis by the Budden matrix method, in informal memoranda from the

National Bureau of Standards.

The overlay permits the determination of the true height of

reflection at any frequency chosen on the ordinary virtual height curve.

The number of heights to determine, and their distribution in frequency

are matters of individual choice, and will depend on the purpose for

which the work is to be done. To define adequately the true height

profile, five to ten individual determinations will usually suffice,

unless great detail near penetration frequencies is desired. Often a

useful first value to get is the true height of the F2 layer maximum,

corresponding to foF2.

In any case, the analysis using these overlays proceeds as

follows

The overlay is placed on the ionogram tracing so that its

height lines are parallel to those on the tracing, and so that the

line indicated by fN (the index frequency) falls on the frequency at

which the true height is desired. (To find h max F2, the line fN should

be aligned with foF2.) At the intersections of the h' (f) curve with

each of the sampling points indicated on the overlay, the virtual heights

are scaled and added together. Any of the points that fall below 1.0 Mc

must be represented in the sum by making an appropriate assumption about

the virtual heights at low frequencies. The overlay should not be moved

6-
until all ten values have been obtained. One tenth of the sum is then

the true height of reflection at the chosen frequency. It should be

remembered that for certain of the world zones,, the sampling points

depend upon the frequency at which the true height is to be derived.

The overlays for these zones have the two or three sets of sampling ratios

plotted on the same overlay. The user must select the set appropriate

to the point of the frequency scale (value of fN) under analysis.

V. Example of Application

To illustrate the results obtained by application of an overlay to a typical ionogram, the 10 point ratios of Zone III were used to

analyse a few points on the virtual height curve shown in Fig. k. This

curve, obtained at the U.S. Army Signal Corps White Sands (New Mexico)

station, is typical of nighttime conditions; with such ionograms true

height determinations may be made quite accurately. The magnetic dip

(60. k ) and gyrofrequency (1.3^-3 Mc at 200 km) at White Sands place

this station near the northern boundary of Zone III.

The true heights calculated at 0.2 Mc intervals using the

Budden matrix method may be compared on the figure with four heights

determined using the 10 point ratios of Zone III. The numerical values

obtained by both methods agree within 2 km.

7-
References

1. Kelso, J. M. Journal of Geophysical Research, JjjJ, 357 (1952).

2. Budden, K* G. "A Method for Determining the Variation of Electron

Density with Height (N(z) curves) from Curves of Equivalent

Height Against Frequency ( (h'f) curves)" Report of the

Physical Society Conference on the Physics of the Ionosphere,

Cavendish Laboratory, Cambridge, 1955* Page 332.

3- Schmerling, E. R. Journal of Atmospheric and Terrestrial Physics , 12 , 8, (1958).

k. Ventrice, C. A. and Schmerling, E. R. , Scientific Report No. 106

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