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The effect of travelling ionospheric disturbances on the group path, phase path, amplitude and direction of arrival of radio waves reflected from the ionosphere
The effect of travelling ion~p~~~ disturbances cmthe group path, phase path, amplitude and direction of arrival of radio waves reflected from the ionosphere R.N.
E. BAULCH*and E. C. BUTCHER
Division of Theoretical and Space Physics, La Trobe University, Bundoora, Victoria 3083, Australia (Received injnalform
10 November 1984)
Abstract-A fixed frequency amplitude rn~ulat~ transmission was reflected from the ionosphere and changes in the group path, phase path, signal amplitude and directions of arrival ofthis transmission caused by travelhng ionospheric disturbances were measured. These measurements enabled approximate determinations of the horizontal wavelength, period and horizontal phase velocity of the disturbances, which were compared with the theory of disturbances for atmospheric waves. A simple model is proposed to explain the phase relationships between the TfDs observed in the group and phase paths, and the faster decrease in power of the phase path than the other measured parameters indicated by spectral analysis. 1. INTRODU~ION
There have been many studies of travelIing ionospheric disturbances (TIDs) since MARTYN(1948) explained anomalous variations in ionograms obtained from spaced ionosondes in terms of a travelling wave. A few of these studies have used the technique of spaced sensors to determine the horizontal phase velocity and direction of TIDs, e.g. GEORGES(1968) (spaced HF Doppler .measurements) and MORTON(1978) (spaced Total Electron Content me~urements). There are, however, problems with determining the direction and phase velocities in this way, since it has been observed that the characteristics of the resultant travelling wave may change considerably over short distances (GEORGFS, 1968). Corrugation models of the ionosphere have been used to determine the tilts in electron density gradients induced by TIDs (BRAMLEY,1953) and to explain Doppler shift and amplitude variations caused by them (LYON, 1979). In a previous paper BAULCHand BUTCHJX(1978) used a corrugation model to relate the angles of arrival of a CW oblique transmission reflected from the E-region to the tilts along (yL)and across (yc) the transmission path. It is the purpose of this paper to use the corrugation model to determine properties of TIDs from measurements ofdirection of arrival, group path, phase path and amplitude made over a slightly oblique path for both E- and F-region reflections.
system with a carrier frequency of 3399 KHz and a modulation frequency of 2 KHz was used to determine the group path P’ by measuring the rate of change of phase path P as a function of frequencyf, i.e. dP p’ = p+fdf The signal was transmitted over a path length of about 102 km and the phase path was determined by obtaining the phase change of the carrier over an interval of time and the signal amplitude of the carrier was determined by the A3 method (e.g. DAVIES,1969). The direction of arrival was measured by obtaining the phase difference between spaced antennae (3 crossed dipoles which formed a right angled isosceles triangle whose sides were 80 m long) in an Adcock type finder (Ross et al. 1951). For an E-region reflection a zenith angle of approximately 27” was obtained, while for the F-region a zenith angle of about lo” was obtained. Measurements were made on the ordinary mode of the transmission and several examples of the variations obtained with this system have been presented in a previous paper (BAULCHet al., 1984).
3. RESULTS
Figure I shows a night-time F-region recording where the data has been passed through a high pass filter to remove long term trends to show variations in the measured parameters and it is seen that there are 2. METHOD oscillatory effects in all the parameters. Several features The experimental equipment is described elsewhere are apparent. (1) The oscillations in the amplitude (BAULCHet al., 1984). Briefly, an amplitude modulated always tend to die away during the night-time period, reappearing again in early morning. (2) The amplitudes * Present address : Division of Textile Physics,CAIRO, 338 of the group height variations are usually greater (by an order of magnitude or more) than those in the phase Blaxland Road, Ryde, NSW 2112, Australia. 653
654
R. N. E. BAULCH and
E. C. BUTCHER
40 GROUP PATHtkm)
20 2
PHASE PATtt(km) ZENITHtDEG)
, D]&
AZWvlUTH(DEG) 201~------
0800
0400
0000
2000
1600
A.E.T
Fig. 1.Changes in the group path, phase path, directions of arrival and amplitude for the night-time reflection 24/9/1981-25/9/1981.
height. (3) The phase difference between the osciilations in the group and phase paths may be zero, 180” or 90”. These properties are characteristic of most recordings obtained. The second and third points may be seen more clearly from the F-region example shown in Fig. 2. In this example only the group path, phase path and signal amplitude have been passed through a high pass filter. (These filters had a cut off frequency of 0.02 min- ’ . No such filter has been applied to the direction of arrival.) For these TIDs (which have a period N 15 min) the group and phase path variations at first appear
to be out of phase (15151600),
then in phase (16201710) and then about 90” out of phase for a couple of cycles (1715-1745), with the group path variations leading the phase path. There are also times when there seems to be no resemblance between the variations in the group path and phase path (18~1830). The signal ampIitude appears to be roughly in phase with the phase path for much of the time, but this is not always the case. The zenith and azimuth angle variations do not appear to be consistently correlated with any of the other variations measured, but there is a gradual 9o*out inphase
p$fw 1
I
AMPLITUDE (DB) 2
PHASE PATH 0
I 1500
1600
1700
1800
1900
A.E.T.
Fig. 2. Changes in the amplitude, phase path, group path, zenith angle and azimuth angle for the day-time Fregion reflection for 18/8/1979.
Effect of travel@
655
ionospheric disturbances on radio waves
GROUP PATH(km)
PHASE PATH(km)
ZENITH(DEG)
A,,,,PL,TUDE(DS)
1800
1900
2000
2100
A.E.T
Fig. 3. Changes in the group path, phase path, zenith angle, azimuth and amplitude for the day-time F-region reflection for 28/g/1981.
decrease in zenith angle between 1515 and 1730. Another example is shown in Fig. 3. In this case the oscillations in group and phase path change from in phase, to out of phase, to 90” phase difference, again with the group path leading. In both examples the disturbances could not be classified as large scale, since they only produced very slight inflexions to ionograms taken at Beveridge (37’S, 145”E), which was located approximately 6 km from the mid-point of the oblique path. Analysis of the data showed that a whole range of periods of TIDs were possible. For short period irregularities in the F-region (r 5 40 min) it was found that almost 40% of the records of oscillations in the group and phase paths had a phase difference of + 90 and on about 40% of the records they had a phase difference of 0” or 180”. (These records were obtained mostly between 1600 and 0800 AET). For the longer period disturbances most had phase differences of 0” or 180”(with 0” being predominant) and these occurred on about 40% of the records. For the E-region it was found for most TIDs that a phase difference of + 90” occurred and such variations were present on about 50% of the
records. On about 10% of the E-region records the phase difference was 0” or 180”. ROBINSON and DY.WN(1977) showed that changes in the group path, AP’, due to an irregularity may be related to changes in the phase path, AP, due to the irregularity by Ap’= AP+fd$ where f is the frequency of the radio wave. For the observed TIDs the magnitude of the changes in the group path ranged from being approximately the same as the changes in the phase path (AP) to up to twenty times greater than the changes in the phase path, indicating that at times both the AP and the f(dAP/df) terms in equation (1) may be important to describing the changes in the group path. ROBIN~C~N and DYSON(1977) showed that for an irregularity in the electron density profile the phase path change, AP, was always out of phase with the ionization change, AN, the maximum change in the phase path occurring just above the maximum in the electron density perturbation. Thus, for a monotonic profile, equation
R. N. E. BAULCHand E. C. BUTCHER
6.56
(1) may be used to relate the group path changes to a perturbation in the electron density profile, Although changes in phase path are determined by contributions along the whole path, the major contribution will be due to those changes that occur near the reflection level. If it is assumed that the oscillatory nature of AP is caused mainly by a similar small oscillatory variation in AN, then for a given probing frequency (i.e. given altitude) theobserved variations in AParesinusoidal in nature and may be written AP = A sin (wt+#,
(2)
where # (= k-r) may be a function of height and position (k = ?kk,+ fik,, r = ii f&z}. Then from equation (1) we expect the group path variation to be of the form AP’= B sin(wt+(b+q) where
(3)
B = (a2 + bz)l’z a=
(A+fAaf>
l?=Af$ tan r~= b/a and any variation in the oscillation frequency, o, with wave frequency f has been ignored. It may be seen that the relative amplitudes and phases of the oscillations in AP and AP’ depend on the relative magnitudes of the terms in equation (3) and therefore on the shape of the perturbation profile, as well as the height ofreflection of the radiowave within the perturbation. In view of the results presented in Figs. 2 and 3 the following situations may be considered. (a) If a >>b, q - 0” or - 180”, the value of tl depends on the variation of A withf: If
(A+fE>
z-0,
af
then rf - 0 and if
(A+fg>co, Q - 180”. The latter case may only occur when aA/af is negative. Whether Q is -0” or - 180” would therefore depend on which part of the profile the radio wave was reflected. As the reflection level moves up or down the profile 1 may change from - 0” to - 180” or vice versa. Since for many of the observed oscillations B >>A when g - 0” or - MO”,this implies that reflection occurs in a region wheref(aA/af) >>A. This situation is indicated schematically in Fig. 4 using a simple sinusoidal
irregularity in AN(z). Referring to Fig. 2, between 1.515 and 1600 AP and AP’ are out of phase with the amplitude of AP’ being much larger than that in AP. This would be equivalent to a reflection from level L in Fig. 4 withf(dA/af) >>A. Between 1600 and 1615 the oscillation in AP’ has effectively disappeared and the amplitude of the oscillation in AP is a maximum. This corresponds to a reflection from level M. Between 1620 and 1710 the oscillation in AP and AP’ are in phase, which corresponds to a reflection from level N. Thus over the period 1515 to 1710, the reflection level has moved downward through the lower part of the irregularity. (b) If a cc b, q - f90”, when afpjaf is positive, the oscillation in AP’ will lead that in AP. The condition a <
AND GRAVITY
WAVES
It is usually assumed that TIDs are a manifestation of atmospheric gravity waves. The dispersion relation for atmospheric waves in a non-isothermal atmosphere (without dissipation or Doppler shift) has been given by EINAULXand HINES(1970) as
k,2 = ($
-I)k:+(y),
(4)
Effect of travelling ionospheric disturbances on radio waves
657
AN
TIME
.
Fig. 4. Schematic diagram showing the instantaneous perturbations in the electron density N as a function of frequency and the associated changes in phase path P and group path P’. The expected variations in P and P’ as a function of time at various levels are shown on the right, assuming that the amplitude in I? varies
sinusoidalfy with time. Group path (----), where
frequency
of the atmosphere,
C = (Hgy)“’ is the velocity of sound in the atmosphere, g is the acceferation due to gravity, y is the ratio of specific heats H is the scale height, and tu is the angular frequency of the wave. This equation is also atmosphere where 3H
-
aZ
= 0, @B =
valid
WI
and
for an
phase path (-)_
If it is assumed that the TIDs observed here are associated with gravity waves, a value of k, may be estimated, since w may be determined and an approximate value for the horizontal wave number, k,, for a disturbance may be obtained using the group path and the tilts in the ionosphere derived from the direction of arrival measurements. (The group path is used since it is related to the zenith angle [Martyn’s theorem (1935)]). If it is assumed that the properties of the socillations in AP indicate the properties of the associated wave, at least with respect to period and phase, then for a = k *r equation (3) gives
-$AP
= Bk, cos (cot + kg + q).
(5)
isothermal
OS < 0,.
Plots of w as a function of k, may be obtained for different values of k, using equation (4). If any two of the parameters w, k, and k, are known these plots may be used to find the third parameter.
This has a maximum value ofBk, which may be related to the tilts in the ionosphere. The magnitude of the tilt is given by BALJLCH and BUTCHER(1978) as Y = Cv:+rt3”2, where yL=2
1
#d-t+tan-’ (
1 C2 tan f$,--tan #* >>
R. N. E. BAULCHand E. C. BUTCHER
658
Equation (4) may be written in terms of the horizontal phase speed (HINES, 1974) as
is the tilt along the propagation path and yc = tan-’
(sin(B-8Jtan
4)
1/ = C(wi--0” se? f?)l’* PX (0,” _w2)112 ’
is the tilt across the path and tan #d = tan b, cos (5- 5,), Hand d, being the measured azimuth and zenith angles and 0, and 4, the expected azimuth and zenith angles assuming a horizontally stratified ionosphere. The tangent of the maximum tilt, Y,,,,then equals the maximum gradient i.e. tan y, = Bk, or
(6)
tan yrn k, = 7 In any length of data a whole spectrum of waves may be present to produce a given TID. Several lengths of data were analysed and the periods of those waves present were obtained by performing a spectral analysis of the data and then obtaining the variations of a given period using bandpass filters. In most cases the amplitude of AP’ was greater than AP. Table 1 shows those wave properties deduced from the TIDs present on the night of 10/S/81 to 11/9/81 for an F-region reflection. It is seen that the longest perioddisturbances (190and210min) hadlonghorizontalwavelengths(630 and 1000 km, respectively) and small horizontal phase speeds, whereas, with one or two exceptions, those disturbances with periods from 12-36 min had shorter horizontal waveIengths (between 300 and 700 km) and larger horizontal phase speeds.
where B = tan ’ (k&J is the elevation angle of phase propagation relative to the horizontaf. It is seen that for an isothermal atmosphere, (we = Weand og < 0,) for a constant 0 one would expect V,, to increase as the period of the wave T (= 271/0_$ increased. This is clearly not so for the TIDs whose properties are given in Table 1, as may be seen from the plot of log V, versus log T given in Fig. 5. For these TIDs is it seen that the points appear to separate into two lines, which are represented by the relation VP, = AT” (where n - -0.75 for both data sets). This result is similar to that obtained by HERRON(1973) for TIDs in the night-time F-region measured using a spaced CW Doppler array. In order to explain the difference between his results and those expected from equation (7) for an isothermal atmosphere and fixed 0, Herron proposed that the TIDs he observed were hydromagnetic waves travelling in the ionosphere with dispersive characteristicsofelectromagneticwavesinahighconductivity medium. However, HINES{1974) showed that there was no difficulty in explaining the sense of the dispersion reported by Herronforthefollowing twocases.(a)Fora fixed Oin a non-isothermal atmosphere where wB cos 8 > w,. This condition could be applied if 0 was made sufficiently small. (b) For 0 to be a suitable function of o rather than being fixed. KLOSTERMEYER (1974) also showed that Herron’s results were in agreement with that expected for gravity waves if the dissipative effects of thermal conductivity, viscosity and ion drag were
Table 1. Measured period, phase path amplitude (A), group path amplitude (B), peak-peak value of the radio-wave amplitude, horizontal wavelength (Ax)and horizontal phase velocity (V,) for some F-region disturbances. Period (min) 210 190 36 33 27 27 26 21 18 16 15 15 14 12
Time (AET) 1700 2100 2200 0500 0100 0300 1700 1830 0630 0500 OOOO 1830 2200 1700
(7)
(kk)
(k:)
10 4.5 0.6 0.4 0.7 0.3 1.2 1.0 0.3 0.2 0.8 0.7 0.3 0.8
17.5 21 12 6 13 16 9.5 20 11 10 11 I7 8 11
P-PAmp. (db) 10 15 IO 7
1 9 18 4 10 7 4 6 10 20
V
1, (km)
(m s”fl)
IWO 630 670 320 630 380 370 620 390 530 360 330 280 340
80 55 310 160 390 230 240 490 360 550 400 370 330 470
659
Effect of travelling ionospheric disturbances on radio waves
Table 2. Vertical waveien~s c&&a&d From the data of Table 1 for an isothermal atmosphere assuming both dissipation and non-dissipation.
I.51 1 t.0
’
1
’
’ 1.5
’
’
1
/
’
’
(
8
2.0
1
Period (min)
A (km) No dissipation
210 190 36 33 27 27 26 21 18 16 15 15 14 12
48 33 217 105 302 161
a 2.5
LOG 1 oT
2%@@ Dissipation .125 104 222 121 304 168 171 473 307 697 397 351 329 723
:z 306 698 396 350 328 724
Fig. 5. Measured dispersion for the waves observed in the night-time F-region 10/9/1981-~1/9/f981.
of #s = O.Q1+4 s”’’ (T, = 10.03 min) and o, = 0.0107 s-l (r, = 9.83 min). For calculation (2) the US Standard (1966) Atmosphere was used with an assumed night-time Chapman F-region which had a maximum electron density of 3 x 10’ ’ m- 3 at 300 km. The caiculation was made for waves at 200 km. The results ofthis ~~~u~ation are shown in Table 2, where it is seen that the values of 2, determined are comparable for both caIculatiuns,except at the Iongest periods. This seems to indicate that it is only at the longest periods observed here that dissipation becomes important, It is also seen that 6 (= tan- ’ kJk,) is not constant, but varies with period. This may be seen in Fig. 6, where 0 is determined using the k, values obtained using calculations (2) above (with dissipation). Also shown values
taken into account, since for any given wave period and height the gravity waves have an attenuation minimum at a certain horizontal phase speed and waves having the lowest attenuation predominate. Values of k, (and hence B) were calculated for the TIDs given in Tabte 1 using : (1) the isothermd form of equation (4) faB = w,) with no dissipation; (2) a calculation by M. P. &key (private communication) based on that given by FRANCIS(f%‘3) for an isothermal atmosphere where the dissipative effects of thermal conductivity, viscosity and ion drag have been included For both calculations the values g = 9.2 m se2, H = 33.88 km and y = 1.67 (equivalent to an atomic oxygen atmosphere) were taken, which gave
I,
50
*.
,
I,,
100 T
,
,,I,
1,
160
‘
I,,
200
inins)
Fig. 5. Measured elevation angle ofpropagation(@)relative to the Borizontal as a fun&an of period for the waves observed in the night-time F-regi5~ lQ~~lP~~-~l/P~lP8~.
660
R. N. E. BAULCHand E. C. BUTCHER Table 3. Measured period, phase path amplitude (A), group path amplitude (B), peal-peak value of the radio-wave amplitude, horizontal wavelength (AX)and horizontal phase velocity (I&) for some E-region disturbances. P-P Amp. (db)
Period (min)
Time (APT)
(k:)
(k:)
28 25 9 8
1200 1030 1130 1030
0.2 0.7 0.3 0.3
2.5 6.0 8.0 8.0
(solid line) is a plot of the approximate dispersion relation cos 0 = T,/T which is valid in an isothermal atmosphere if ki D co,‘/C’ (HINES, 1960). In the case
considered here o,jC - 1.48 x 10m5 m-i, so this condition will only hold for values of nz <<(425)’ km’. Given the values of 1, determined, the agreement of the experimental results with this relationship is quite good. Therefore it is seen that the dispersion observed may be explained by assuming that 6 is a suitable function of w, and that the waves are propagating in an approximately isothermal atmosphere with *ome dissipation at the longer periods. The properties of waves deduced from an E-region TID on 25/9/81 are shown in Table 3. Again the horizontal phase speed decreases with increasing period and the values of 1, have been determined as before. Both equation(4) and the calculation includingdissipation (with an E-peak electron density of 2 x 10” mm3 at 120 km, with H = 11.6 km and for waves at the peak) gives values of 1, - 16 and 100 km for the periods of 28 and 25 min, respectively, but whereas equation (4) gives values of 1, - 200 km for both shorter period waves, the calculation including dissipation indicates they are evanescent.
1.5 1.0 1.5 4.0
71 350 380 600
50 230 700 1200
assumed to fall in all records as approximately F” (n negative), where F is the frequency of the TID, then a plot of the logarithm of the amplitude against frequency will allow a value of n to be determined. Two graphs show such a plot for E- and F-region irregularities (Figs. 7 and 8). Although some of these plots show an oscillatory nature, particularly at high frequencies, a value of n may be estimated from the general trend and Table 4 shows the approximate powers of n for the 20 different spectra over the period from 24/9/1981 to 21/10/1981. Although the value of n varied slightly through the frequency range and from record to record,
_o.6i
B
GRO,UP ;ATH
‘BASE
,
PATH
1
,
““““‘I”
L
b
5. SPECTRALANALYSISOF THE TIDs Tables 1 and 3 show, as an example, properties of gravity waves associated with a number ofirregularities from two different records. To observe trends in such records, spectral analysis of over twenty records was performed. In general all spectra showed that over a record length of approximately 8 h, irregularities with a large number of different periods were present. This is similar to the spectral analysis results obtained by BAULCHand BUTCHER(1978) on TIDs observed in the direction of arrival of a 2.5 MHz signal. In most cases the largest periods had the largest amplitude, but it is interesting to note that while the largest period disturbances dominated all records, the amplitude in the different spectra decreased at different rates as a function of the frequency ofthe disturbance for different measurements. If the amplitudes of the spectra were
-1.6
-0.6
I
AMPLITUDE
LOG, of -1.6
-0.6
Fig. 7. Log-log plots of amplitude spectra for the group path, phase path, azimuth angle, zenith angle and amplitude for a night-time F-region reflection on 24/9/1981. The ordinate is log,, (amplitude) measured relative to the maximum value.
661
E&et of travelhrtg ionospheric ~s&urban~s on radio waves Table 4. Values of&e ccx.f?iciats n d&&w.% from the ~p~tude spectra by fitting the data to the Jaw A cc F” for the group path, phase path, amplitude, zenith angle and azimuth angle.
F-Xe$iOtl E-region
Group path
Phase path
-0.18+0.02 -0.14*0.03
-0.36+0.05 -0.56+0.06
~~l~~de -0.1540.03 -0.21 fO.66
A?&nutb
zenith -0.12+0.02 -0.20+0.03
-0.lifO.02 -0.19*0.02
in all cases n was larger for the phase path t&n any other ~~~~~r~~~t and was smallest for the directions of arrival. The ualue of n for the azimuth and zenith angles was similar and of the same order of that for the grcmp path, as would be expected for the zenith angle from MhRTrY&stheorem (f935) For F-region irregul~ities the data indicates A K F--0.9” sfnd
-1.3
Therefore the dithxent power law in the graup and phase path variations is caused by a variation with F of dA/df,i.e. thesba~~fthe~storti~~~ro~l~f~r theTIDs is resident on the period trf the TIE). For the E-r&m the difference in the value of n for M and dP is even larger than for the F-region and indicates a different variation with TID period dthe perturbation profile in the two regions. In view of the different properties of TIDs in the two regions (e.g. period, amplitude, vertical wavelengths this may not be surprising.
-0.3
-0.5-1.3
-0.3
Fig 8. Log-log plots u~~~ljtude
spectra for the group path, phase path, azimuth angle, zenith angle and amptitude for a day-time E-region refleotion on 29/9/1981. The ordinate is log,, (amplitude) measured relative to the maximum value.
~~~~u~l~~g~n~s-~e wish to thank Mr M. P, HICKIIYfor ~~l~u~at~~the values of 1, including dissipation and for many interesting discussions of the properties ofgravity waves, This work was supported by a grant from the Radio Research Board of Australia. RNEB acknowledges the receipt of an Australian Commonwealth Postgraduate Scholarship during the period of this work.
BAWLCS R. N. E. 2UIdi%JTCRBR fi c Bnutctr R. N. E, and BUTCHERE. C. Baurxw R. N. E,, BUTCHER E. C., DEWN J. C, and HAMMERP, R. BRAMLEY E. N. DAVIES
K.
DXWN P. L. and Bn~rr J, A. EINAUDZ F. and HINESC. 0. FRANCIS8. H. GEORGE~ T. M. HERRON T. J. HINESC. 0. HINESC. 0. KmTeftMFYERJ*
1979 1970 1973
1968 1973 1960 1974 1972
Company. J. atmos. terr. P&s_ 41,367. Can. J. P&s. 48,1458, J7,~~~~hys. Res. T&2278. J. atmos. terr. Phys. 3@, 735. .I. atmos. ten. Phys. 35, 101. Can. J. Phys. 25, I44 3, iltm@s.&ST*Phys. 35,120% 3. atmw, terr* P&s. 38, I393.
662
R. N. E. BAULCHand E. C. BUTCHER
KL~STFXMEYER J. LYONG.F. MARTYND. F. MARTYN D. F. ROBINSON I. and DYSONP. L. Ross W., BRAMLEYE. N. and ASHWELLG. E. TE~TUDJ. and VASSEUR G.
1974 1979 1935 1948 1977 1951 1969
.I. atmos. terr. Phys. 36, 1995. J. atmos. terr. Phys. 41, 5. Proc. Phys. Sot. 41,323. Proc. R. Sot. A194,429. J. atmos. terr. Phys. 39,263. Proc. IEE 98,294. Annls Giophys. 25,525.
1967 1978
ESSA Technical Report IER 57. M.Sc. Thesis, La Trobe University.
Reference is also made to the following unpublished material: GEOGREST. M. MORTONF.
E. BAULCH*and E. C. BUTCHER
Division of Theoretical and Space Physics, La Trobe University, Bundoora, Victoria 3083, Australia (Received injnalform
10 November 1984)
Abstract-A fixed frequency amplitude rn~ulat~ transmission was reflected from the ionosphere and changes in the group path, phase path, signal amplitude and directions of arrival ofthis transmission caused by travelhng ionospheric disturbances were measured. These measurements enabled approximate determinations of the horizontal wavelength, period and horizontal phase velocity of the disturbances, which were compared with the theory of disturbances for atmospheric waves. A simple model is proposed to explain the phase relationships between the TfDs observed in the group and phase paths, and the faster decrease in power of the phase path than the other measured parameters indicated by spectral analysis. 1. INTRODU~ION
There have been many studies of travelIing ionospheric disturbances (TIDs) since MARTYN(1948) explained anomalous variations in ionograms obtained from spaced ionosondes in terms of a travelling wave. A few of these studies have used the technique of spaced sensors to determine the horizontal phase velocity and direction of TIDs, e.g. GEORGES(1968) (spaced HF Doppler .measurements) and MORTON(1978) (spaced Total Electron Content me~urements). There are, however, problems with determining the direction and phase velocities in this way, since it has been observed that the characteristics of the resultant travelling wave may change considerably over short distances (GEORGFS, 1968). Corrugation models of the ionosphere have been used to determine the tilts in electron density gradients induced by TIDs (BRAMLEY,1953) and to explain Doppler shift and amplitude variations caused by them (LYON, 1979). In a previous paper BAULCHand BUTCHJX(1978) used a corrugation model to relate the angles of arrival of a CW oblique transmission reflected from the E-region to the tilts along (yL)and across (yc) the transmission path. It is the purpose of this paper to use the corrugation model to determine properties of TIDs from measurements ofdirection of arrival, group path, phase path and amplitude made over a slightly oblique path for both E- and F-region reflections.
system with a carrier frequency of 3399 KHz and a modulation frequency of 2 KHz was used to determine the group path P’ by measuring the rate of change of phase path P as a function of frequencyf, i.e. dP p’ = p+fdf The signal was transmitted over a path length of about 102 km and the phase path was determined by obtaining the phase change of the carrier over an interval of time and the signal amplitude of the carrier was determined by the A3 method (e.g. DAVIES,1969). The direction of arrival was measured by obtaining the phase difference between spaced antennae (3 crossed dipoles which formed a right angled isosceles triangle whose sides were 80 m long) in an Adcock type finder (Ross et al. 1951). For an E-region reflection a zenith angle of approximately 27” was obtained, while for the F-region a zenith angle of about lo” was obtained. Measurements were made on the ordinary mode of the transmission and several examples of the variations obtained with this system have been presented in a previous paper (BAULCHet al., 1984).
3. RESULTS
Figure I shows a night-time F-region recording where the data has been passed through a high pass filter to remove long term trends to show variations in the measured parameters and it is seen that there are 2. METHOD oscillatory effects in all the parameters. Several features The experimental equipment is described elsewhere are apparent. (1) The oscillations in the amplitude (BAULCHet al., 1984). Briefly, an amplitude modulated always tend to die away during the night-time period, reappearing again in early morning. (2) The amplitudes * Present address : Division of Textile Physics,CAIRO, 338 of the group height variations are usually greater (by an order of magnitude or more) than those in the phase Blaxland Road, Ryde, NSW 2112, Australia. 653
654
R. N. E. BAULCH and
E. C. BUTCHER
40 GROUP PATHtkm)
20 2
PHASE PATtt(km) ZENITHtDEG)
, D]&
AZWvlUTH(DEG) 201~------
0800
0400
0000
2000
1600
A.E.T
Fig. 1.Changes in the group path, phase path, directions of arrival and amplitude for the night-time reflection 24/9/1981-25/9/1981.
height. (3) The phase difference between the osciilations in the group and phase paths may be zero, 180” or 90”. These properties are characteristic of most recordings obtained. The second and third points may be seen more clearly from the F-region example shown in Fig. 2. In this example only the group path, phase path and signal amplitude have been passed through a high pass filter. (These filters had a cut off frequency of 0.02 min- ’ . No such filter has been applied to the direction of arrival.) For these TIDs (which have a period N 15 min) the group and phase path variations at first appear
to be out of phase (15151600),
then in phase (16201710) and then about 90” out of phase for a couple of cycles (1715-1745), with the group path variations leading the phase path. There are also times when there seems to be no resemblance between the variations in the group path and phase path (18~1830). The signal ampIitude appears to be roughly in phase with the phase path for much of the time, but this is not always the case. The zenith and azimuth angle variations do not appear to be consistently correlated with any of the other variations measured, but there is a gradual 9o*out inphase
p$fw 1
I
AMPLITUDE (DB) 2
PHASE PATH 0
I 1500
1600
1700
1800
1900
A.E.T.
Fig. 2. Changes in the amplitude, phase path, group path, zenith angle and azimuth angle for the day-time Fregion reflection for 18/8/1979.
Effect of travel@
655
ionospheric disturbances on radio waves
GROUP PATH(km)
PHASE PATH(km)
ZENITH(DEG)
A,,,,PL,TUDE(DS)
1800
1900
2000
2100
A.E.T
Fig. 3. Changes in the group path, phase path, zenith angle, azimuth and amplitude for the day-time F-region reflection for 28/g/1981.
decrease in zenith angle between 1515 and 1730. Another example is shown in Fig. 3. In this case the oscillations in group and phase path change from in phase, to out of phase, to 90” phase difference, again with the group path leading. In both examples the disturbances could not be classified as large scale, since they only produced very slight inflexions to ionograms taken at Beveridge (37’S, 145”E), which was located approximately 6 km from the mid-point of the oblique path. Analysis of the data showed that a whole range of periods of TIDs were possible. For short period irregularities in the F-region (r 5 40 min) it was found that almost 40% of the records of oscillations in the group and phase paths had a phase difference of + 90 and on about 40% of the records they had a phase difference of 0” or 180”. (These records were obtained mostly between 1600 and 0800 AET). For the longer period disturbances most had phase differences of 0” or 180”(with 0” being predominant) and these occurred on about 40% of the records. For the E-region it was found for most TIDs that a phase difference of + 90” occurred and such variations were present on about 50% of the
records. On about 10% of the E-region records the phase difference was 0” or 180”. ROBINSON and DY.WN(1977) showed that changes in the group path, AP’, due to an irregularity may be related to changes in the phase path, AP, due to the irregularity by Ap’= AP+fd$ where f is the frequency of the radio wave. For the observed TIDs the magnitude of the changes in the group path ranged from being approximately the same as the changes in the phase path (AP) to up to twenty times greater than the changes in the phase path, indicating that at times both the AP and the f(dAP/df) terms in equation (1) may be important to describing the changes in the group path. ROBIN~C~N and DYSON(1977) showed that for an irregularity in the electron density profile the phase path change, AP, was always out of phase with the ionization change, AN, the maximum change in the phase path occurring just above the maximum in the electron density perturbation. Thus, for a monotonic profile, equation
R. N. E. BAULCHand E. C. BUTCHER
6.56
(1) may be used to relate the group path changes to a perturbation in the electron density profile, Although changes in phase path are determined by contributions along the whole path, the major contribution will be due to those changes that occur near the reflection level. If it is assumed that the oscillatory nature of AP is caused mainly by a similar small oscillatory variation in AN, then for a given probing frequency (i.e. given altitude) theobserved variations in AParesinusoidal in nature and may be written AP = A sin (wt+#,
(2)
where # (= k-r) may be a function of height and position (k = ?kk,+ fik,, r = ii f&z}. Then from equation (1) we expect the group path variation to be of the form AP’= B sin(wt+(b+q) where
(3)
B = (a2 + bz)l’z a=
(A+fAaf>
l?=Af$ tan r~= b/a and any variation in the oscillation frequency, o, with wave frequency f has been ignored. It may be seen that the relative amplitudes and phases of the oscillations in AP and AP’ depend on the relative magnitudes of the terms in equation (3) and therefore on the shape of the perturbation profile, as well as the height ofreflection of the radiowave within the perturbation. In view of the results presented in Figs. 2 and 3 the following situations may be considered. (a) If a >>b, q - 0” or - 180”, the value of tl depends on the variation of A withf: If
(A+fE>
z-0,
af
then rf - 0 and if
(A+fg>co, Q - 180”. The latter case may only occur when aA/af is negative. Whether Q is -0” or - 180” would therefore depend on which part of the profile the radio wave was reflected. As the reflection level moves up or down the profile 1 may change from - 0” to - 180” or vice versa. Since for many of the observed oscillations B >>A when g - 0” or - MO”,this implies that reflection occurs in a region wheref(aA/af) >>A. This situation is indicated schematically in Fig. 4 using a simple sinusoidal
irregularity in AN(z). Referring to Fig. 2, between 1.515 and 1600 AP and AP’ are out of phase with the amplitude of AP’ being much larger than that in AP. This would be equivalent to a reflection from level L in Fig. 4 withf(dA/af) >>A. Between 1600 and 1615 the oscillation in AP’ has effectively disappeared and the amplitude of the oscillation in AP is a maximum. This corresponds to a reflection from level M. Between 1620 and 1710 the oscillation in AP and AP’ are in phase, which corresponds to a reflection from level N. Thus over the period 1515 to 1710, the reflection level has moved downward through the lower part of the irregularity. (b) If a cc b, q - f90”, when afpjaf is positive, the oscillation in AP’ will lead that in AP. The condition a <
AND GRAVITY
WAVES
It is usually assumed that TIDs are a manifestation of atmospheric gravity waves. The dispersion relation for atmospheric waves in a non-isothermal atmosphere (without dissipation or Doppler shift) has been given by EINAULXand HINES(1970) as
k,2 = ($
-I)k:+(y),
(4)
Effect of travelling ionospheric disturbances on radio waves
657
AN
TIME
.
Fig. 4. Schematic diagram showing the instantaneous perturbations in the electron density N as a function of frequency and the associated changes in phase path P and group path P’. The expected variations in P and P’ as a function of time at various levels are shown on the right, assuming that the amplitude in I? varies
sinusoidalfy with time. Group path (----), where
frequency
of the atmosphere,
C = (Hgy)“’ is the velocity of sound in the atmosphere, g is the acceferation due to gravity, y is the ratio of specific heats H is the scale height, and tu is the angular frequency of the wave. This equation is also atmosphere where 3H
-
aZ
= 0, @B =
valid
WI
and
for an
phase path (-)_
If it is assumed that the TIDs observed here are associated with gravity waves, a value of k, may be estimated, since w may be determined and an approximate value for the horizontal wave number, k,, for a disturbance may be obtained using the group path and the tilts in the ionosphere derived from the direction of arrival measurements. (The group path is used since it is related to the zenith angle [Martyn’s theorem (1935)]). If it is assumed that the properties of the socillations in AP indicate the properties of the associated wave, at least with respect to period and phase, then for a = k *r equation (3) gives
-$AP
= Bk, cos (cot + kg + q).
(5)
isothermal
OS < 0,.
Plots of w as a function of k, may be obtained for different values of k, using equation (4). If any two of the parameters w, k, and k, are known these plots may be used to find the third parameter.
This has a maximum value ofBk, which may be related to the tilts in the ionosphere. The magnitude of the tilt is given by BALJLCH and BUTCHER(1978) as Y = Cv:+rt3”2, where yL=2
1
#d-t+tan-’ (
1 C2 tan f$,--tan #* >>
R. N. E. BAULCHand E. C. BUTCHER
658
Equation (4) may be written in terms of the horizontal phase speed (HINES, 1974) as
is the tilt along the propagation path and yc = tan-’
(sin(B-8Jtan
4)
1/ = C(wi--0” se? f?)l’* PX (0,” _w2)112 ’
is the tilt across the path and tan #d = tan b, cos (5- 5,), Hand d, being the measured azimuth and zenith angles and 0, and 4, the expected azimuth and zenith angles assuming a horizontally stratified ionosphere. The tangent of the maximum tilt, Y,,,,then equals the maximum gradient i.e. tan y, = Bk, or
(6)
tan yrn k, = 7 In any length of data a whole spectrum of waves may be present to produce a given TID. Several lengths of data were analysed and the periods of those waves present were obtained by performing a spectral analysis of the data and then obtaining the variations of a given period using bandpass filters. In most cases the amplitude of AP’ was greater than AP. Table 1 shows those wave properties deduced from the TIDs present on the night of 10/S/81 to 11/9/81 for an F-region reflection. It is seen that the longest perioddisturbances (190and210min) hadlonghorizontalwavelengths(630 and 1000 km, respectively) and small horizontal phase speeds, whereas, with one or two exceptions, those disturbances with periods from 12-36 min had shorter horizontal waveIengths (between 300 and 700 km) and larger horizontal phase speeds.
where B = tan ’ (k&J is the elevation angle of phase propagation relative to the horizontaf. It is seen that for an isothermal atmosphere, (we = Weand og < 0,) for a constant 0 one would expect V,, to increase as the period of the wave T (= 271/0_$ increased. This is clearly not so for the TIDs whose properties are given in Table 1, as may be seen from the plot of log V, versus log T given in Fig. 5. For these TIDs is it seen that the points appear to separate into two lines, which are represented by the relation VP, = AT” (where n - -0.75 for both data sets). This result is similar to that obtained by HERRON(1973) for TIDs in the night-time F-region measured using a spaced CW Doppler array. In order to explain the difference between his results and those expected from equation (7) for an isothermal atmosphere and fixed 0, Herron proposed that the TIDs he observed were hydromagnetic waves travelling in the ionosphere with dispersive characteristicsofelectromagneticwavesinahighconductivity medium. However, HINES{1974) showed that there was no difficulty in explaining the sense of the dispersion reported by Herronforthefollowing twocases.(a)Fora fixed Oin a non-isothermal atmosphere where wB cos 8 > w,. This condition could be applied if 0 was made sufficiently small. (b) For 0 to be a suitable function of o rather than being fixed. KLOSTERMEYER (1974) also showed that Herron’s results were in agreement with that expected for gravity waves if the dissipative effects of thermal conductivity, viscosity and ion drag were
Table 1. Measured period, phase path amplitude (A), group path amplitude (B), peak-peak value of the radio-wave amplitude, horizontal wavelength (Ax)and horizontal phase velocity (V,) for some F-region disturbances. Period (min) 210 190 36 33 27 27 26 21 18 16 15 15 14 12
Time (AET) 1700 2100 2200 0500 0100 0300 1700 1830 0630 0500 OOOO 1830 2200 1700
(7)
(kk)
(k:)
10 4.5 0.6 0.4 0.7 0.3 1.2 1.0 0.3 0.2 0.8 0.7 0.3 0.8
17.5 21 12 6 13 16 9.5 20 11 10 11 I7 8 11
P-PAmp. (db) 10 15 IO 7
1 9 18 4 10 7 4 6 10 20
V
1, (km)
(m s”fl)
IWO 630 670 320 630 380 370 620 390 530 360 330 280 340
80 55 310 160 390 230 240 490 360 550 400 370 330 470
659
Effect of travelling ionospheric disturbances on radio waves
Table 2. Vertical waveien~s c&&a&d From the data of Table 1 for an isothermal atmosphere assuming both dissipation and non-dissipation.
I.51 1 t.0
’
1
’
’ 1.5
’
’
1
/
’
’
(
8
2.0
1
Period (min)
A (km) No dissipation
210 190 36 33 27 27 26 21 18 16 15 15 14 12
48 33 217 105 302 161
a 2.5
LOG 1 oT
2%@@ Dissipation .125 104 222 121 304 168 171 473 307 697 397 351 329 723
:z 306 698 396 350 328 724
Fig. 5. Measured dispersion for the waves observed in the night-time F-region 10/9/1981-~1/9/f981.
of #s = O.Q1+4 s”’’ (T, = 10.03 min) and o, = 0.0107 s-l (r, = 9.83 min). For calculation (2) the US Standard (1966) Atmosphere was used with an assumed night-time Chapman F-region which had a maximum electron density of 3 x 10’ ’ m- 3 at 300 km. The caiculation was made for waves at 200 km. The results ofthis ~~~u~ation are shown in Table 2, where it is seen that the values of 2, determined are comparable for both caIculatiuns,except at the Iongest periods. This seems to indicate that it is only at the longest periods observed here that dissipation becomes important, It is also seen that 6 (= tan- ’ kJk,) is not constant, but varies with period. This may be seen in Fig. 6, where 0 is determined using the k, values obtained using calculations (2) above (with dissipation). Also shown values
taken into account, since for any given wave period and height the gravity waves have an attenuation minimum at a certain horizontal phase speed and waves having the lowest attenuation predominate. Values of k, (and hence B) were calculated for the TIDs given in Tabte 1 using : (1) the isothermd form of equation (4) faB = w,) with no dissipation; (2) a calculation by M. P. &key (private communication) based on that given by FRANCIS(f%‘3) for an isothermal atmosphere where the dissipative effects of thermal conductivity, viscosity and ion drag have been included For both calculations the values g = 9.2 m se2, H = 33.88 km and y = 1.67 (equivalent to an atomic oxygen atmosphere) were taken, which gave
I,
50
*.
,
I,,
100 T
,
,,I,
1,
160
‘
I,,
200
inins)
Fig. 5. Measured elevation angle ofpropagation(@)relative to the Borizontal as a fun&an of period for the waves observed in the night-time F-regi5~ lQ~~lP~~-~l/P~lP8~.
660
R. N. E. BAULCHand E. C. BUTCHER Table 3. Measured period, phase path amplitude (A), group path amplitude (B), peal-peak value of the radio-wave amplitude, horizontal wavelength (AX)and horizontal phase velocity (I&) for some E-region disturbances. P-P Amp. (db)
Period (min)
Time (APT)
(k:)
(k:)
28 25 9 8
1200 1030 1130 1030
0.2 0.7 0.3 0.3
2.5 6.0 8.0 8.0
(solid line) is a plot of the approximate dispersion relation cos 0 = T,/T which is valid in an isothermal atmosphere if ki D co,‘/C’ (HINES, 1960). In the case
considered here o,jC - 1.48 x 10m5 m-i, so this condition will only hold for values of nz <<(425)’ km’. Given the values of 1, determined, the agreement of the experimental results with this relationship is quite good. Therefore it is seen that the dispersion observed may be explained by assuming that 6 is a suitable function of w, and that the waves are propagating in an approximately isothermal atmosphere with *ome dissipation at the longer periods. The properties of waves deduced from an E-region TID on 25/9/81 are shown in Table 3. Again the horizontal phase speed decreases with increasing period and the values of 1, have been determined as before. Both equation(4) and the calculation includingdissipation (with an E-peak electron density of 2 x 10” mm3 at 120 km, with H = 11.6 km and for waves at the peak) gives values of 1, - 16 and 100 km for the periods of 28 and 25 min, respectively, but whereas equation (4) gives values of 1, - 200 km for both shorter period waves, the calculation including dissipation indicates they are evanescent.
1.5 1.0 1.5 4.0
71 350 380 600
50 230 700 1200
assumed to fall in all records as approximately F” (n negative), where F is the frequency of the TID, then a plot of the logarithm of the amplitude against frequency will allow a value of n to be determined. Two graphs show such a plot for E- and F-region irregularities (Figs. 7 and 8). Although some of these plots show an oscillatory nature, particularly at high frequencies, a value of n may be estimated from the general trend and Table 4 shows the approximate powers of n for the 20 different spectra over the period from 24/9/1981 to 21/10/1981. Although the value of n varied slightly through the frequency range and from record to record,
_o.6i
B
GRO,UP ;ATH
‘BASE
,
PATH
1
,
““““‘I”
L
b
5. SPECTRALANALYSISOF THE TIDs Tables 1 and 3 show, as an example, properties of gravity waves associated with a number ofirregularities from two different records. To observe trends in such records, spectral analysis of over twenty records was performed. In general all spectra showed that over a record length of approximately 8 h, irregularities with a large number of different periods were present. This is similar to the spectral analysis results obtained by BAULCHand BUTCHER(1978) on TIDs observed in the direction of arrival of a 2.5 MHz signal. In most cases the largest periods had the largest amplitude, but it is interesting to note that while the largest period disturbances dominated all records, the amplitude in the different spectra decreased at different rates as a function of the frequency ofthe disturbance for different measurements. If the amplitudes of the spectra were
-1.6
-0.6
I
AMPLITUDE
LOG, of -1.6
-0.6
Fig. 7. Log-log plots of amplitude spectra for the group path, phase path, azimuth angle, zenith angle and amplitude for a night-time F-region reflection on 24/9/1981. The ordinate is log,, (amplitude) measured relative to the maximum value.
661
E&et of travelhrtg ionospheric ~s&urban~s on radio waves Table 4. Values of&e ccx.f?iciats n d&&w.% from the ~p~tude spectra by fitting the data to the Jaw A cc F” for the group path, phase path, amplitude, zenith angle and azimuth angle.
F-Xe$iOtl E-region
Group path
Phase path
-0.18+0.02 -0.14*0.03
-0.36+0.05 -0.56+0.06
~~l~~de -0.1540.03 -0.21 fO.66
A?&nutb
zenith -0.12+0.02 -0.20+0.03
-0.lifO.02 -0.19*0.02
in all cases n was larger for the phase path t&n any other ~~~~~r~~~t and was smallest for the directions of arrival. The ualue of n for the azimuth and zenith angles was similar and of the same order of that for the grcmp path, as would be expected for the zenith angle from MhRTrY&stheorem (f935) For F-region irregul~ities the data indicates A K F--0.9” sfnd
-1.3
Therefore the dithxent power law in the graup and phase path variations is caused by a variation with F of dA/df,i.e. thesba~~fthe~storti~~~ro~l~f~r theTIDs is resident on the period trf the TIE). For the E-r&m the difference in the value of n for M and dP is even larger than for the F-region and indicates a different variation with TID period dthe perturbation profile in the two regions. In view of the different properties of TIDs in the two regions (e.g. period, amplitude, vertical wavelengths this may not be surprising.
-0.3
-0.5-1.3
-0.3
Fig 8. Log-log plots u~~~ljtude
spectra for the group path, phase path, azimuth angle, zenith angle and amptitude for a day-time E-region refleotion on 29/9/1981. The ordinate is log,, (amplitude) measured relative to the maximum value.
~~~~u~l~~g~n~s-~e wish to thank Mr M. P, HICKIIYfor ~~l~u~at~~the values of 1, including dissipation and for many interesting discussions of the properties ofgravity waves, This work was supported by a grant from the Radio Research Board of Australia. RNEB acknowledges the receipt of an Australian Commonwealth Postgraduate Scholarship during the period of this work.
BAWLCS R. N. E. 2UIdi%JTCRBR fi c Bnutctr R. N. E, and BUTCHERE. C. Baurxw R. N. E,, BUTCHER E. C., DEWN J. C, and HAMMERP, R. BRAMLEY E. N. DAVIES
K.
DXWN P. L. and Bn~rr J, A. EINAUDZ F. and HINESC. 0. FRANCIS8. H. GEORGE~ T. M. HERRON T. J. HINESC. 0. HINESC. 0. KmTeftMFYERJ*
1979 1970 1973
1968 1973 1960 1974 1972
Company. J. atmos. terr. P&s_ 41,367. Can. J. P&s. 48,1458, J7,~~~~hys. Res. T&2278. J. atmos. terr. Phys. 3@, 735. .I. atmos. ten. Phys. 35, 101. Can. J. Phys. 25, I44 3, iltm@s.&ST*Phys. 35,120% 3. atmw, terr* P&s. 38, I393.
662
R. N. E. BAULCHand E. C. BUTCHER
KL~STFXMEYER J. LYONG.F. MARTYND. F. MARTYN D. F. ROBINSON I. and DYSONP. L. Ross W., BRAMLEYE. N. and ASHWELLG. E. TE~TUDJ. and VASSEUR G.
1974 1979 1935 1948 1977 1951 1969
.I. atmos. terr. Phys. 36, 1995. J. atmos. terr. Phys. 41, 5. Proc. Phys. Sot. 41,323. Proc. R. Sot. A194,429. J. atmos. terr. Phys. 39,263. Proc. IEE 98,294. Annls Giophys. 25,525.
1967 1978
ESSA Technical Report IER 57. M.Sc. Thesis, La Trobe University.
Reference is also made to the following unpublished material: GEOGREST. M. MORTONF.