VLF radio transmissions at sunrise

Press.Printedin Northern Ireland Journalof Atmospheric andTerrestrial Physics,1974,Vol.36,pp.489-499.Pergamon

VLF radio transmissions at sunrise C. A. SCHOUTE-VANNECK Department of Physics, University of Durban-Westville,

Durban, South Africa

(Received 21 June 1973) Al&&--The effective reflection coefficient of the D-region for VLF radio waves during sunrise is calculated by applying a full-wave technique to a model of the temporal distribution of free electrons in the lower ionosphere. Estimations are made of the field strength of signals propagated from a distant transmitter by a process of multiple reflections between the Earth and the ionosphere as the propagation path progressively comes under solar influence. The calculated fields are compared with observations made in the U.S.A. of transmissions from Panama (24 kHz) and Hawaii (23.4 kHz). The results indicate that variations in the field strength of VLF transmissions may be interpreted satisfactorily in terms of changes in the free electron content of the D-region during sunrise. 1. INTRODUCTION

sunrise the field strength of VLF radio waves observed at large distances from a transmitter shows characteristic variations. Several suggestions have been put forward to account for these fluctuations. Interference phenomena at sunrise from continuous VLF transmissions are known to occur and progress has been made in the interpretation of interference patterns in terms of interference between first and second order modes of the waveguide mode theory (CROMBIE, 1964, 1965, 1966; MEARA, 1973). However, the explanation of the observed amplitude variations in terms of modal interference only is not satisfactory, especially where variations in the integrated field strength of atmospherics originating in randomly distributed thunderstorms are concerned. The field variations at sunrise of VLF atmospherics have been shown to be intimately related to ionospheric phenomena (SCHOUTE-VANNECK and WRIGHT, 1968). The causes of the observed field variations should thus be sought primarily in that region of the ionosphere which is the most influential in the propagation of VLF waves, the D-region. Now that a better understanding of the structure of the D-region is emerging, it is becoming increasingly practicable to estimate the effects of changes in the constitution of the D-region on VLF radio transmissions. It is the purpose of this paper to demonstrate that the essential qualitative features of the field variations of signals from a distant VLF transmitter during sunrise may be derived from a consideration of the changes which take place in the distribution of electrons in the D-region. A dynamic model of the D-region during sunrise is assumed and from it the effective reflection coeliicient of the ionosphere for different solar angles is calculated. By regarding radio waves to be propagated by a process of successive reflections between the ionosphere and the terrestrial surface, the field strength at a receiver is estimated as each effective reflecting region comes under solar influence. The relative field strengths thus calculated are then compared with recordings made in Littleton (near Denver), U.S.A. of VLF transmissions from Panama and Hawaii. DURING

489

C. A. SCHOUTE-VANNECK

490

2. CALCULATION OF REFLECTIONCOEFFICIENTS Full-wave calculations of ionospheric reflection coefficients are generally complicated and time consuming, but where essentially semi-quantitative results are sought several simplifications may be introduced to facilitate computations. In this project it is assumed that the ionosphere is horizontally stratified and isotropic, the only particles involved in the propagation of VLF energy being electrons whose motions are damped by collisions with heavier particles. When used for qualitative purposes, an isotropio ionosphere is acceptable since it has been shown that for VLF waves computations in which the Earth’s magnetic field is neglected are not seriously in error (BARR, 1971). The effective reflection coefficient of the ionosphere may then be calculated by the second method given by BUDDEN(1965). A plane wave, polarised with its electric vector in the plane of incidence, is assumed to be obliquely incident from below on the horizontally stratified isotropic ionosphere. The variation of the reflection coefficient, R, with increasing altitude, x, is then given by

aR -?f ax=c i ( $(l

-R)2cose

- --&

(1 -@$)(I

+ R)e)

(1)

where i = 1/-i, f = frequency of radiation, c = velocity of electromagnetic waves in free space, 8 = angle of incidence, n = complex refractive index of the ionosphere, given by n2 = 1 - X/(1 - iZ) where X and 2 are magneto-ionic quantities expressed in rationalised units by and and N = number density of free electrons, e = electron charge, m = electron mass, Q = dielectric constant of free space, v = frequency of collisions of electrons with heavier particles. The reflection coeffioient for the ionosphere is computed by choosing an initial value of R, say R,, applicable to a point high in the ionosphere and then integrating the equation by a step-by-step process from the initial value until a point below the ionosphere is reached. The resulting value of R at this point is then the reflection coefficient for the specified wave and ionospheric structure. BUDDEN(1955) has described a method for obtaining the initial value R, for oblique incidence. The reflection coefficient for vertical incidence, given by

R, = (n - l)/(n + l), is used as a starting value, the X and 2 parameters from which n is calculated being selected to be appropriate for a point high in the ionosphere. A preliminary integration of equation (1) using this starting value and holding X and 2 constant is done and continued downwards through an ionosphere of infinite extent until aRl& reaches an insignificantly small value, i.e. R remains sensibly constant. This value of R is adopted as the required initial value R,. The main integration of equation (1) is then performed with this initial value and the value of R reached at a point below

VLF radio transmissions at sunrise

491

the ionosphere is taken as the reflection coefficient of the ionosphere. It should be noted that as the integration proceeds towards the terrestrial surface in the negative z-direction, a negative sign for llRl&must be adopted in the numerical work. 3. D-REGION PARAMETERS AT SUNRISE

The variation in the distribution of electrons in the D-region during sunrise may be seen from the results of wave interaction experiments described by SMITHet al.

55y

01

I’

’

1 Electron

I I

,I

” IO

density,

,,,I 100

I

cm-3

Fig. 1. Electrondensityproties duringsunrise. (1967) and from measurements of reflection and transmission coefficients given by THOMASand HARRISON(1970). The patterns described are similar to the sequence of profiles obtained from rocket-borne probes (SMITHet al., 1966; MECHTLYand SMITH,1968; SECHRIST,1968) determined during a period of sunspot minimum. It is therefore accepted that profiles based on these measurements are representative of the general changes which take place in the distribution of electrons at sunrise. The electron number density profiles assumed for sunrise during a quiet sun period are shown in Fig. 1. These profiles were obtained by combining the results given by SMITHet al. (1967) with those of SMITHet al. (1966). Below 65 km the data is incomplete and speculative extrapolations were made to obtain profles from which the calculations could be terminated. The electron density for the night-time D-region is shown in Fig. 2. It was obtained by combining the results of Knapp (JOHLER,1967), SMITHet al. (1967), DEEES (1966) and WAEAI (1967). The reflection coefficient for the D-region at noon was calculated from the profile given in Fig. 2 which was compiled from results quoted by BELROSEand BOURNE

C. A. SCHOUTE-VANNECK

492

Collision

frequency

u ,

see-’

130-

Q

60 50 40-

14

Electron

density

N,

cme3

Fig. 2. Electron density profiles at night and at noon together with the collision frequency.

(1967) and BELROSEet ab. (1967), extrapolations being made at low altitudes. The frequency of collisions of electrons with heavier particles at different altitudes is shown in Fig. 2 which is based on the results given by PIGGOTTand THRANE(1967) and COOKSand LORENTS(1961). 4.

COMPUTATIONAL PROCEDURE

The D-region reflection coefficients for 27 kHz waves at an angle of incidence of 80’ were computed on a Hewlett-Packard Model 91OOBprogrammable calculator, using three separate programmes. With N and v appropriate for a selected solar zenith angle and altitude, n and R, were calculated first. The second programme determined the appropriate initial value of R, by an iterative process which continued until @RI < 1.5 x 10e4. The third programme then calculated the reflection coefficient, using equation (1). The integration was performed step-by-step in equal increments of Sx = -0.5 km until the base of the ionosphere at which n = 1 was reached. The size of the altitude increments conforms to the criterion suggested by BUDDEN(1955), i.e. where the electron density does not vary very rapidly with height, a step of about l/25 of the free space wavelength of the exploring wave is suitable.

493

VLF radio transmissions at sunrise

This procedure was followed for all the profiles shown in Fig. 1 and noon and night conditions shown in Fig. 2. The variation of the reflection coefficient R(X) with x, the solar zenith angle as measured from a point on the Earth’s surface directly below the ionospheric region being investigated, is shown in Fig. 3.

o Calculated

0

I 110

I

I 100

Solar

I

I

90

zenith

angle

X,

value

1

so

I

1

degrees

Fig. 3. Calculated D-region reflection coefficient during sunrise.

5.

COMPBRISON OF REFLECTION COEFFICIENTS

It is of interest at this stage to compare the results of the present calculations of reflection coefficients for night and day conditions with those obtained by other workers. During 1949 (sunspot maximum), BAIN et al. (1952) observed for f = 16 kHz, 8 = 75’, that for vertically polarised waves R = O-6 ati night and R = O-32 at noon. From a postulated electron density distribution during equinox and sunspot minimum, DEEKS (1966) found that for the same frequency and angle of incidence R = 0.42 at night and R = 0.38 at noon. If it is assumed that reflection coefficients for different frequencies and angles of incidence are approximately the same providing f cos 8 is the same (DEEKS, 1966), then the reflection coefficient for f = 27 kHz, 8 = 80’ would be approximately equal to that for a frequency off = 16 kHz and 6 = 73”. The reflection coefficients calculated in this investigation apply to sunspot minimum and are R (night) = O-58

and

R (noon) = 0.33.

These figures may be compared directly with the observed values quoted above for 16 kHz and 0 = 75’. The similarities between the results quoted above support the view that the calculated reflection coefficients are not seriously affected by the assumptions which were made to simplify the calculations.

494

C.

A. SCHOUTE-VANNECK

6. PROPAGATION MECHANISM OF VLF

RADIO WAVES

In the analysis which follows it is assumed that radio energy from a VLF transmitter is propagated to a distant receiving station by a number of reflections which take place successively at the ionosphere and the surface of the Earth. By a reflecting region is implied that section of the lower ionosphere which is effective in returning VLF radiation to Earth. The curvature of the surface of the Earth and the effective height of the ionospheric region combine to set a limit to the minimum number of reflections which are possible in the distance between the transmitter and any particular receiver. The field at the receiver results from the combination of waves which have undergone a different number of Earth-ionosphere reflections. During sunrise, the ionospheric reflection regions successively come under solar influence and the effective reflection coefficient for each region varies with time according to the results depicted in Fig. 3. The received signal strength at any time is thus given by the combination of all the possible multi-reflection modes, due allowance being made for the reflection coefficient of each one of the reflection regions, depending on the extent to which it is under solar influence at that particular time. Measurements are made most conveniently in terms of the solar zenith angle as observed from the receiver. In order that the field strength may be evaluated in terms of this angIe, the argument x in R(X), the reflection coefficient shown in Fig. 3, should be expressed in terms of the solar angle at the receiver rather than in terms of the angle at a point directly below the reflecting region. Let x, XR, denote the respective solar zenith angles measured at a point directly below an ionospheric reflecting region and at the receiver locality, both situated on the Earth’s surface; let T be the solar angle at the transmitter at the instant of ground sunrise at the receiver. If there are n successive equally spaced ionospheric reflecting regions along the propagation path from the transmitter to the receiver, then for any one of these regions x = XR + (2??8+ I)(27 - 60°)/2m

(2)

where m relates to the particular reflection region being considered and m takes the values (n - l), (*n - 2), , . . 2, 1, 0 for the lst, 2nd, . . . nth successive region respectively, count,ing from the transmitter to the receiver. The reflection coefficient, at a time specified by XR, of one of these regions identified by the value of m will be given by the reflection coefficient derived from Fig. 3 which has (2) as argument, i.e. reflection coefficient = R(XR + (2m + l)(T - 60*)/2n). In the case of a multi-hop transmission of n hops, the received field strength depends on the product of the reflection coefficients of the active reflecting regions; it is thus

where E, is the stren@h of the incident field applicable to the particular propagation path and R, is the reflection coefficient of the terrestrial surface for the frequency considered.

VLF radiotransmissions at sunrise

495

The observed field strength at the receiver is the result of the combination of all fields produced at the receiver by all possible multi-hop transmissions. If interference effects are neglected and the approximation is made that the incident energy is equally distributed among all the possible effective propagation paths, then the field strength at the receiver is given by E(xR) = E, “zw [m=fi’ R(xR + (2m + l)(T - 90")/2n)] ?l=nminn&;-o

(3)

where nmin is the minimum number of hops possible between the transmitter and the receiver and R, is taken as unity for VLF radiation (JORDAN,1953). It has been found that in practice only low order multi-hop transmissions need be considered since the high orders contribute little to the total received field strength on account of the multiplicative effect of the ionospheric reflection coefficient. 7. FIXED STATIONCONTINUOUSWAVE TRANSMISSIONS A test of the validity of the foregoing considerations for determining the variations in the field strength of a transmitter at sunrise as predicted by (3)combined with the reflection coefficients of Fig. 3 is afforded by comparing calculated values with measurements of the field strength produced by a distant transmitter during sunrise. Mr. Keith L. Strait of the American Association of Variable Star Observers (Solar Division) has for some time been recording the relative field strength in Littleton (near Denver), Colorado, U.S.A., of the VLF transmitters NBA (24kHz) and NPM (23.4kHz) located in Panama and Hawaii respectively. He has very kindly selected typical sunrise records and made them available for this analysis. 7.1 Transmissions

from NBA, Panama to Littleton

Geographical co-ordinates : Transmitter frequency:

NBA, Panama

09'04'N; 79’39’W

Littleton

39'50'N; 104’57’W.

24 kHz.

The great circle distance from Panama to Littleton is estimated as 4150 km. Assuming that during sunrise the altitude of the effective reflecting region of the ionosphere is 80 km and that the Earth’s radius is 6371 km, the minimum number of hops for the transmission path is two. For the transmission considered, the transmitter undergoes sunrise before the receiver. The reflection coefficients for different solar angles shown in Fig. 3 apply to an angle of incidence of the transmitted wave of 80". Angles of incidence for the different transmission modes were calculated assuming transmission to be over a curved Earth. Where the angle of incidence differed from 80'for different multi-hop modes, a correcting factor was applied. This factor was derived from the dependence of the reflection coefficient on incidence angle shown graphically by DEEKS (1966), but modified to apply to the frequency of NBA by assuming that the reflection coefficients are numerically the same for different frequencies and incident angles providing f cos 0 is the same (DEEKS, 1966). Although these correcting factors were obtained from reflection coefficients at noon, they were considered to be sufficiently reliable for the present semi-quantitative analysis.

C. A. SCHOUTE-VANNECK

496

I 1000

/ 1100

I

I

I

1200

1300-

1000

Universal

Fig. 4. Field strength

Time,

1100

I

I

I200

1300

hr

of 24-kHz transmitter NBA (Panama) Littleton, Colorado, U.S.A.

as recorded in

The relative field strength at the receiver for each degree of zenith angle was calculated by combining (3) with the results given in Fig. 3. Contributions by propagation modes involving more than four hops were ignored as their contribution to the received field strength was found to be insignificant. Tracings of the records made in Littleton are shown in Fig. 4. The observed and calculated field strength variations during sunrise on 6 June 1970, are shown in Fig. 5 in which the observed curve has been smoothed and the calculated results, for ease

6 June 1970

In 0 .E L 115

II0

105

100

95

Solar

zenith

angle

at

so

receiver,

85

80

75

X, degrees

Fig. 6. Comparison of observed and calculated field strengths during sunrise for the Panama to Littleton transmission.

VLF radio transmissions at sunrisa

497

of comparison, have been normalised to the observed field strength at the arbitrarily chosen solar zenith angle of XR = 107’. When the calculated and observed field strength variations are compared, several interesting features appear : (1) The general pattern of the variation in field strength at sunrise consists of a slight increase in the field at about layer sunrise, followed by a sudden large decrease which reaches a minimum at about the time of ground sunrise at the transmitter. The field then increases gradually to a maximum at the time of ground sunrise at the receiver. This general pattern is reproduced by the theoretical results. (2) The gradients of the main field variations are the same for both observed and calculated curves. (3) An unexpected feature is the appearance in the calculated curve of the small peak which is superimposed on the minimum at about the time of sunrise at the transmitter. This peak is not apparent in the observed record of 6 June, but it is prominent in the record of 4 June and less so, but still definite, in the records of 5 and 7 June. (4) The observed curves all show a marked rise in field strength to a peak occurring at the receiver ground sunrise and then a decline. The calculated curve shows the increase satisfactorily, but the decline is much more gradual than that observed. This indicates that the decline in the calculated R(X) curve of Fig. 3 after about x = 87’ should be more rapid than shown; the implication is that the electron densities in the lowest reaches of the D-region are somewhat different from those assigned in the numerical model used. (5) When the theoretical curve is normalised to the observed curve the ordinates of the two curves for all abscissae are of comparable magnitudes. 7.2 Transmissions from NPiW, Hawaii to Littleton Geographical co-ordinates :

NPM, Hawaii

21’25’N;

158’09’W

Littleton

39”50’N;

104’57’W.

Transmitter frequency : 23.4 kHz. Tracings of recordings made in Littleton of the relative field strength during sunrise are shown in Fig. 6. The great circle distance from Hawaii to Littleton was taken as 5300 km and with the altitude of the effective ionospheric region at 80 km the minimum number of hops possible is three. Since t,he transmitter is situated west of the receiver, the transmitter undergoes ground sunrise after the receiver. The field at the receiver was calculated by the same method as that used for the Panama-Littleton transmissions, the field being taken as the summation of the 3-, 4- and 5-hop transmissions, contributions by higher order transmissions being unimportant. The results obtained are shown in Fig. 6 where the calculated results have been superimposed on the observed records after scaling so that the field strengths before the main sunrise decreases are of the same magnitude. General similarity between the observed and calculated curves is again apparent, especially in the times of occurrence of the field maxima and minima. The gradients of the field variations are also in agreement. However, certain discrepancies do exist 8

C. A. SCHOUTE-VANNECK

498

0

I ~~

40 I 1300

I 1400

I 1600

1 1500

Universal

Time,

I 1700

I I600

hr

Fig. 6. Field strength of 23*4-kHz transmitter NPM (Hawaii) as recorded in Littleton, Colorado, U.S.A. with calculated field strengths for the same transmissions superimposed for comparison.

and warrant comment. The low field observed prior to sunrise at the receiver on 2 October 1969 is not normal; the more usual field is depicted in the record of 11 October 1969. The calculated curves do not show the prominent sharp field maxima observed at about XR = 80” and between 60” and 70”, but give a broad peak with subsidiary minima. This is probably due to the calculated curves being based on idealised conditions in which reflections for only certain specific angles of incidence associated with a number of discrete multihop modes are considered. In reality, a multihop mode transmission would be possible for a range of incident angles clustered around the incident angle defined by the number of hops and the distance between the transmitter and the receiver. An allowance for these transmissions would have the effect of smoothing out the discrete secondary maxima and minima shown by the calculated curves. 8. CONCLUSIONS (1) Meaningful theoretical results on the propagation of VLF radio waves at sunrise may be derived by assuming that the waves are propagated by a process of multiple reflections between the ionosphere and the terrestrial surface, where the ionospheric reflection coefficients are derived from an isotropic ionosphere.

VLF radio transmissions at sunrise

499

(2) VariaCions in the field strength of VLF waves at sunrise may be interpreted in terms of changes which take place in the free electron content of the D-region as it comes under solar influence. (3) The

general

pattern

of the

distribution

of free

electrons

in bhe D-region

sunrise as represented by the assumed model is satisfactory but the numerical values adopted for electron number densities at the 1owesCaltitudes after about the time of ground sunrise appear to be inaccurate. during

author wishes to express his gratitude to Mr. K. L. STRAITof Littleton, Colorado, U.S.A. for making his VLF records available for this investigation. The research was supported by the University of Durban-Westville.

Acknowledgements-The

REFERENCES BAIN W. C., BRACEWELL R. N., STRAKER T. W. and WESTCOTT C. H. BARR R. BELROSE J. S. and BOURNE I. A.

1953

Proc.

1971 19G7

J. atmos. terr. Phys. 33, 343. Proc. Conf. Ground-based Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canada, p. 79. Proc. Conf. Ground-based Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canuda, p. 167. Proc. R. Sot. MT, 516. J. Res. NBS 68D, 27. Proc. IEEE 53, 2027. Radio Sci. 1, 47. Proc. R. Sot. A291, 413. Proc. Conf. Ground-based Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canada, p. 399. Electromagnetic Waves and Radiating Systems, Chap. 16. Constable, London. J. atmos. terr. Phys. 35, 305. J. atmos. terr. Phys. 30, 363. Proc. Conf. Ground-baaed Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canada, p. 607. J. atmos. terr. Phys. 30, 609.

BELROSE J. S., BO~RNE I. A. and HEWITT J.

1967

BUDDEN K. G. CROMBIE D. D. CROMBIE D. D. CROMBIE D. D. DEEES D. G. JOHLER J. R.

1955 1964 1965 1966 1966 1967

JORDAN E. C.

1953

MEARA L. A. MECECTLYE. E. and SMITH L. G. PIGGOTT W. R. and THRA~ E. V.

1973 1968 1967

SCHOUTE-VANNECK C. A. and WRIGHT A. G. SECHRIST C. F. SMITH R. A., COYNE T. N. R., LOCH R. G. and BOURNE I. A.

1968

7’1x.x~~ L. and HARRISON

M. D.

WAKAI N.

Reference

1968 1967

1970 1967

Inst.

elect. Engrs

99, 250.

J. atmos. terr. Phys. 30, 371. Proc. Conf. Ground-baaed Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canada, p. 335. J. atmos. terr. Phys. 32, 1. Proc. Copbf. Ground-based Radio Wave Prop. Studies of the Lower Ionosphere. Def. Res. Board, Canada, p. 552.

is also made to the following unpublished material:

COOK C. J. and LORENTS D. C.

1961

SMITH L. G., WEEKS L. H. and MCKINNON P. J.

1966

Final Tech. Rept. 6, SRI Project PAU3340. Stanford Res. Inst., Menlo Park, California, U.S.A. NASA Rept. No. CR-391.