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Ionospheric response to internal gravity waves observed at Delhi
JournalofAtmospheric andTerrestrial Physics,1973,Vol.35, pp. 1351-1381. PergamonPress. Printedin NorthernIreland
Ionospheric response to internal gravity waves observed at Delhi C. S. G. K. SETTY, ANURAG B. GUPTA and 0. P. NAGPAL Department of Physics and Astrophysics, University of Delhi, Delhi-7, India (Received
6 March
1972;
in revised form 29 November 1972)
Abstract-Measurements of small scale fluctuations in the day time P-region critical frequency over Delhi have revealed the presence of internal gravity waves in the P-region of the ionosphere with periods ranging from 8 to 70 min. The amplitude spectrum of these fluctuations is not uniform but contains two maxima and a minimum. The minimum is found to lie between 25 and 35 min period. It is suggested that this apparent dip in the spectrum is not due to some mechanism which filters out the gravity waves of these particular periods but represents the manner in which the gravity waves manifest themselves in the ionosphere over Delhi (dip angle 42.4’). This view, suggested by Sterling, Hooke and Cohen from their recent studies, is confirmed by the above experimental findings at Delhi.
(KENT, 1970) have been used to observe a class of wavelike irregularities in the ionosphere known as the travelling ionospheric disturbances (TID’s). The most successful explanation of these observations (MUNRO, 1950, 1958; VALVERDE, 1958; CHAN and VILLARD, 1962; TITHERIDGE, 1963, 1968; GEORQES, 1967; DAVIS and DA ROSA, 1969; KENT and GUPTA, 1971; REDDY and RAO, 1971) is that which attributes the TID’s to the corresponding disturbances of the neutral gas associated with the passage of atmospheric gravity waves (HINES, 1960; PITTEWAY and HINES, 1965; HINES and REDDY, 1967; HOOKE, 1968; TESTUD and FRANCOIS, 1971). Theoretical work of HOOKE (1968, 1970) has shown that the internal gravity waves produce TID’s through photochemical and dynamical means and that the ionospheric response to these waves should vary with the geoSome of these observations have been verified magnetic and geographic latitude. using incoherent scatter radar technique (TESTUD and VASSEUR, 1969; VASSEUR and WALDTEUFEL, 1969). The purpose of this paper is to report certain characteristics of the travelling ionospheric disturbances, observed at Delhi, where the magnetic inclination is 42.4”. Observations on FB-region critical frequency were made every minute to observe the small fluctuations in the electron concentration at the F2-region peak. The experimental set-up consists of a single vertically radiating variable frequency ionosonde. The technique and the method of observation have been described earlier (KENT and GUPTA, 1971) in which paper some preliminary results of the F2-region critical frequency were reported and the observed fluctuations were attributed to the presence of gravity waves in the F2-region. An average spectrum of these waves was also presented. Studies were further made to determine the speed of these disturbances and their vertical wavelengths. The direction of propagation has not been determined uniquely-only a component in the magnetic meridian plane is evaluated using the ray tracing technique. Frequencies reflected from different heights provide several points in the ionosphere which are separated both horizontally and vertically
A NUMBER of radio techniques
1351
1352
C. S. G. K.
SETTY,ANTIRAQB. GTJFTAand 0. P. XA~PAL
in the magnetic meridian plane. Advantage is taken of the fact that the O-mode deviates towards the north while the X-mode decays towards the south. Further observations on the FZ-region critical frequency fluctuations were made in continuation of the ones reported above. In this paper we wish to discuss some characteristics of these fluctuations in detail. The theory developed by HOOKE (1970), and by STERLINGet ab. (1971), in order to explain their observations of TID’s, shows that the amplitudes of the fractional pert~bations in electron ~on~ntration occurring during a wave passage at the height of the _ziZ-layerpeak should vary with the magnetic inclination and exhibit a minimum or a maximum for a meridionally propagating wave. It is shown by these authors that the ionosphere response to the propagating atmospheric gravity waves is ~~erent at different latitud~s~ A wave which produces siguiflcant perturbat,ion at the Equator may not cause an observable change at temperate latitudes. We wish to highlight this particular ar~ment and support it by our expe~mental observations.
Measurements of critical frequency used in the present investigation were made during the daytime (~~~~~~09 h LT) to avoid the large variations in the critical frequency due to productio~l and loss of ionization and by transport elects (D~uP~~ and NISB~T, 1968). Plots of critical frequency vs. time provide an effectively instantaneous picture of the changes in the electron concentration. Several wavelike perturbations were normally visible on each plot. Short term changes of smaller amplitude of the order of 1OOkHz were usually superimposed on larger periods (greatep than 2 hr) and were frequently periodic with quasi-periods from 10 min upwards, On many occasions the records show a sustained wave motion, with a period and amplitude which are reasonably constant up to several complete cycles. The records obtained over a period of 2 years at Delhi were examined for the occurrence of such events and were analysed to find the spectrum of the critical freque~ey Auctuations. Linear trends and spectral components comparable to the record length were removed from the data before the spectral analysis was carried out. The observed periods spread from 10 min to about 70 min. The larger periods were, however, difficult to observe because the diurnal changes in the ionosphere usually dominated over the longer period perturbations. The average height of the .FZ-layer peak, at which the fluctuations were observed, was found to be near 300 km. A typical record, taken on 8 February 1971, is shown in Fig. 1. The thick curve represents the time variation of the BY-region critical frequency, and the thin curve is the detrended version showing the fluctuations in the critical frequency. Two disturbances of 20 and 60 min periods, superimposed an each other, are clearly visible. Several cycles of osculations of 20 min period can be seen. Also shown is the computed spectrum which shows two maxima corresponding to 20 and 60 min periods of oscillations. A distinct dip in the amplitude spectrum at 30 min period can be seen. The spectrum has been normalized to show contribution from l-min intervals (r.m.s. values are used). The electron density ~uctuations for a mean F2-region critical frequency of Il.5 MHz.
are ca~eulated
Ionospheric s%aponse to ir&er~m;lgravity waves obsarved at lIM& -
TIME
V&RtATIONS
1353
OF f,FZ f,
WE& of the spectra showed two maxima and one minimum, aIthough they were not identical for deferent occasions but tended to develop a marked peak arwnd 20 TX& and then around 60 min w%h a marked dip between 25 and 35 min. &Eean spectra, weighted according to record length, were calculated for all the data taken to determine the average seasonal behaviour. These spectra for summer, equinox a,nd winter, respectively, are shown in Fig. 2. The following two main features of these spectra may be pointed out: (a) ~~xin~a around 36 and 66-min periods. (b) Minimum around 30 min, although not so pronounced in the average spectra, this minimum is very conspicuous in the individual spectra. The significant observable difference in the spectra is the low period cut off which appears to be increasing towards the summer. Apart from measuring the arn~~~t~deand period of the ~~~~u~t~o~sIt is also possible to measure their vertical ~ave~~n~~bswithin a limited aceuraoy by recording the critical frequencies and the frequencies corresponding to given, large group heighm near the peak of the PZ-region for both 0- and X-modes. This provides severa. points in the ionosphere where these ~~~~~a~~o~~ are recorded and these points are separated both in the ho~~on~a~ and vertical planes by dista,nces which vary from 10 to 40 km. ~xam~atio~ of these records shows that they are almost identical to the f,E2 and &I!‘2 records and show time delays of the order of a minute or more, Tbis time delay between the various records vi”ascapsulated with the help of the cross-correlation technique. In l?ig. 3 are shown Bornetypical records of this
1354
C. S. G. K. SETTY,
s
IO
50
Period,
A.NURAG
B. GUIFTA and 0. P.
NAGPAL
100
min
Fig. 2. Mean spectra of the critical frequency fluctuations averaged separately for summer, winter and equinox. The spectra are normalized in the same manner as that of Fig. 1.
1
I 10
Local time.
hr
Fig. 3. A typical record of the f,P2 and f,P2 fluctuations made on 18 JuIy 1970. Also shown are the records of frequency fluctuations at large, iixed group heights of 500, 550 and 600 km. The f~(600), for example, represents the frequency fluotuations for the O-mode of radio waves reflected from a group height of 600 km.
kind made on 18 July 1970. Each record is labelled to indicate whether it is a critical frequency record (~~~2 or f,F2) or the frequency record made at fixed group heights of 500, 550 and 600 km. The separation in the horizontal and the vertical planes is calculated by raytracing method. Ionograms taken during the time of observation are reduced to obtain true-height profiles and the ray tracing ~aleulations are made to obtain the ray paths for the radio waves. These ray paths for the frequencies corresponding
Ionospheric
response to internal gravity waves observed at Delhi
1355
and f,RZ at 1230 h LT, are shown in Fig. 4. The frequencies f,(600) represented by fo(500) and f,,(600) are reflected from different heights and the vertical component of the speed is then obtained by dividing their vertical separation by the average time delay between them. The estimate of the component of the vertical speed together with the observed dominant periods obtained by spectral analysis of the record enables us to calculate the vertical component of the wavelength (A,) of Table 1 summarises some of the results obtained in this the travelling disturbances. manner. Each record revealed more than one dominant period as is, for example, seen
to f,(~OO),
18 July 1970 1230 hr
320
f0 (600)
f, F2
300
f,(500) E x f .P I"
260
260
240
220
200
N---D
!lC, c--s 16
8
6
0 Ground
range,
16
24
km
Fig. 4. Some ray paths for radio waves at 1230 hr on 18 July 1970. Ray-tracing is done in the actual ionospheric model obtained by true-height analysis of the ionogram taken at 1230 hr LT. Collision frequency in the P2-region is taken to be 2.5 x 103/sec.
on the record made on 8 February 1971 (Fig. 1). The values of the vertical wavelengths, A,, are calculated for each dominant period assuming that they are travelling with the same speed. Cross-spectrum analysis was made of these records to determine the relative phase and speeds of the dominant periods and it is, in fact, found that these speeds are practically the same. DISCUSSION The measured periods for the daytime disturbances were mostly between lo-60 min. The upper limit is not so well defined and is affected to some extent by the difficulty of separating long-period variations from the diurnal changes and to some extent by the limited length of the records which do not permit accurate estimation of long-period oscillations. Similar results were reported by the Australian group of workers (MUNRO, 1950, 1953, 1958; MUNRO and HEISLER, 1956; HEISLER, 1958, 1963, 1964) who also noted preferred periods within this range. TITHERID~E (1968) interpreted that the range of values of 15-60 min for the period of the travelling wave disturbances, with a low period cut-off at 15 min to be in fair agreement with the expected values of the gravity waves at the F®ion level. The upper limit
1356
C. S. G. K.
SETTY, ANURAG B. GUPTA and 0.
P. NAGPAL
Table 1 Dominant periods (min)
Vertical wavelength
290
20 60
134 403
1 April 1970
320
20 40
124 247
20 June 1970
340
16 30 70
70 131 307
18 July 1970
325
28 60
260 547
12 October
290
15 33
95 208
Height Date
(km)
8 February
1971
1970
2.2 (km)
for gravity wave periods is probably set by the hydromagnetic viscosity giving a gradual cut-off at periods of the order of 60 min (HINES, 1960), and by the ion drag which becomes an effective damping mechanism for gravity waves with periods greater than 30 min (CLARK et al., 1970). HINES (1968) has also suggested that the amplitude and phase of the travelling disturbances are strongly controlled by the molecular dissipation processes. The problem of ionospheric response to the meridionally propagating internal gravity waves at the FZ-region heights has been studied by HOOKE (1970). His equation (7) is reproduced here as equation (1) for ready reference
(y) ((k-1,) + i(l,
f+L
* 1,)
[A +-&(ln N,,)]]
(1)
eo
where N,’ is the perturbation of the electron density N, N,, is the unperturbed value of N, U represents the neutral gas velocity induced by gravity wave propagation lbis the unit vector in the direction of magnetic induction 1,is the unit vector in the vertical direction k is the wave vector i2 Ezz-1 H is the scale-height of the neutral gas and cu is the circular wave frequency. The term d/d.+ N,,) in (1) vanishes at the peak of the FB-layer and since we are concerned with the peak of the FB-layer, we shall drop this term. The term 1/2H can be neglected under the condition 4kz2 > l/Hz. This condition is found to be satisfied for the spectrum of fluctuations observed on 8 February 1971, as shown in Fig. 1. The same is true for all those observed disturbances for which it was possible to calculate the vertical wave number. Thus, neglecting the last two terms of (l),
Ionospheric response to internal gravity waves observed at Delhi
1357
the amplitude A of the fractional perturbation in electron concentration occurring during a wave passage is given by
A=i
(k
-lJ(u-la),
It is thus seen from (2) that the amplitude of the instantaneous fractional perturbation A depends on the two factors (U +l,), the component of the gravity waveinduced neutral gas velocity and (k * l,), the component of the wave vector in the
Pole I‘,'I,,,,,,,,,,,,r
Equator rr;,,,
Fig. 5. Illustrating the competition between the requirements that both U . 11, and k . lb be large if an internal gravity wave were to produce a large amplitude ionospheric irregularity. In the above case U . lb is the largest when the wave propagates equator-ward,but in this event k . lb is so small that the wave produces a relatively small ionospheric response. When the wave propagates poleward, U . lb is small, but k . lbis so much greater that the wave produces a significantly larger response (after HOOKE, 1970, Fig. 2).
direction of the magnetic induction. Figure 5 illustrates the effects of these two factors on the ionospheric response to the gravity wave propagation. It is thus concluded that it is the tilt of the wave front relative to the geoma~etio ~olination f that is primarily responsible for determining the shape of the ionospheric response to the atmospheric gravity waves. The following approximate dispersion relation which relates the tilt of the wave front to the wave period, equation (3), is given by HINES (1960, equation (4)) a,2 = (r2 - T,2) a,yQ.
(3)
Using equations (2) and (3), STERLING et al. (1971) have obtained the following expression (equation (4)) for A, for nearly transverse internal gravity waves propagating meriodionally A =
u ’ Tg i
r:
)
(T/T,) sin (2 sin-i (T,/T) - 21).
Here there are new symbols: il is the wavelength An,1, are the horizontal and vertical components of A, respectively
(4)
1358 7g
C. S. G. K. SETTY, ANURAUB. GUPTA and 0. P. NAUPAL
is the Brunt period for isothermal atmosphere 300 km level in our calculations.
These authors have considered
and is taken to be 16 min at the
four waves, all having the same value (U/A) but
different periods T = 10~,, 5rg, ~57, and l-17,, respectively. The response of the FB-region ionosphere to these waves varies with I in the manner as shown in Fig. 6 (after Fig. 5 of SrEnLrNa et al., 1971). It may be noted that the response changes with the value of I and 7. A wave which may be very significantly affecting the ionosphere
Delhicdip angle 42.4”) -
-_6=
16min
30 Dip angle,
degrees
50
Period,
Fig. 6.
; ,I
70
!
min
Fig. 7.
Fig. 6. Variation in the response of the PZ-region ionosphere to various internal gravity waves, propagating meridionally toward the Equator, as a function of magnetic inclination I. The figures on the curves represent the wave periods in minutes. Fig. 7. Variation in the response of the P&-region ionosphere at Delhi (dip angle 42.4’) to internal gravity waves (T = 16-90 min) propagating meridionally towards the Equator, as a function of wave period. Solid line shows the spectrum when 7g = 16 min and the broken line when 79 = 13 min.
at temperate latitudes becomes unobservable near the Equator, although the wave amplitude as such remains constant. To make the situation clearer, we have drawn Fig. 7, relevant to our station (dip angle 42.4”) and represents the ionospheric response to waves as a function of period. It is noticed that the response is minimum at T = 24 min and increases as the period increases away from 24 min. It appears that the ionospheric response will increase indefinitely as the period increases. This is clearly because the theory neglects the damping effects of thermal conductivity, molecular viscosity, ion drag etc. A theory which takes these factors into account is expected to predict a rapid fall in the amplitude of the higher period waves bringing the theoretical spectrum closer to the observed ones. HOOKE (1968) has studied the effects of gravity waves on photoionisation and chemical loss rates. He suggests that if these factors become important the observed
Ionospheric response to internal gravity waves observed at Delhi
1359
dip in the spectrum will tend to vanish. These effects are not important at the F2-region heights because the ion life-times are much greater than the wave period. The lower cut-off is determined by the Brunt period which is typically 16 min at 300 km level for an isothermal atmosphere. A theory modified to include the effect of temperature gradients will predict the fall of Brunt period and the amount of this fall will depend on the magnitude of the temperature gradient. Although it is not intended to examine the variation of the dip in the observed spectra in relation to the Brunt period, it may, nevertheless, be pointed out from equation (4), that the Brunt period will have a positive effect on the response of the ionosphere. Figure 7 shows the responses to gravity waves propagating in two different model atmospheres with different Brunt periods. It is seen that the dip in the spectrum shifts from T = 24 min (for 7g = 16 min, solid line curve) to that at 7 = 19 min (for 78 = 13 min, broken line curve). CONCLUSIONS
Results presented in this paper show that the gravity waves of periods between 10 and 70 min show a selective amplification around 20- and 60-min periods and attenuation around 30 min period. Since there is no experimental limitation to account for such behaviour, it seems likely that the spectra of Fig. 2 reflect the manner in which gravity waves manifest themselves at Delhi at the F2-region heights. Our observations agree well qualitatively with the theoretical predictions of STERLING et al. (1971) except for a small shift in the observed periods; while the theory predicts, for meridionally propagating waves, a dip in the spectrum at 24 min over Delhi, the observed values lie between 25 and 35 min. It should be pointed out, however, that the equation used for determining A is derived from a rather idealised theory, wherein the equations of motions are linearised by assuming that the variables are only of perturbation magnitude and that the atmosphere is described as isothermal. These
Delhi (Dipangle Azimuth = 66
42.4)
3-
Q
e-
I
-
30
50 Period,
70
90
min
Fig. 8. Variation in the response of the P2-region ionosphere at Delhi to internal gravity waves (7 = 16-90 min), propagating at an azimuth of 60°, as a function of wave period.
1360
C. S. G.
K. SEXY,
Ama
B. GUPTA and 0.
P. NAUPAL
assumptions, it is believed, may lead to some disparities while comparing the theoretically calculated spectra with those measured experimentally. It may be further pointed out that the theoretical spectrum of Fig. 7 is derived on the assumption that the wave propagation is meridional. It is expected that apparent dip in Fig. 7 will shift from 24 min period when the waves are travelling at some angle with the meridian plane. In fact, using the same idealised theory with suitable modifications, it is observed that this dip varies between 24 and 80 min as the azimuth varies from 0 to 80 degrees west of north and between 17 and 24 min when it varies from 0 to 80 degrees west of south. Figure 8 is an example of such a spectrum when the waves are propagating at an azimuth 60” west of north assuming all other parameters to be the same. In this case, the dip appears at 34 min period. Hence, it is quite possible that the fluctuations we have observed represent the gravity waves propagating at We have also seen that any change different azimuths and not strictly meridionally. in the Brunt period of the atmosphere changes the ionosphere response to gravity waves and the position of the dip in the spectrum is shifted to a lower value. This is because the effect of the temperature gradients at the F2-region heights are such as to lower the value of the Brunt period which, in effect, lowers the position of the dip in the spectrum. AckraowZedgementsThe authors would like to thank Drs. K. DAVIES, W. H. HOOKE and R. COHEN of Environmental Research Laboratories, Boulder, for stimulating discussions. Thanks The research reported in this paper are also due to Prof. F. C. AULUCK for encouragement. was supported by a PL-480 Grant through the ESSA Laboratories, the Department of Commerce, U.S.A., under contract E-128-69 (N). REFERENCES CHAN K. L. and VILLA~D 0. G., JR. DAVIS M. J. and DA ROSA A. V. DOUPNIE J. R. and NISBET J. S. GEORCES T. M. HEISLER L. H. HEISLER L. H. HEISLER L. H. HINES C. 0. HINES C. 0. HINES C. 0. and REDDY C. A. HOOKE W. H. HOOKE W. H. KENT G. S. KENT G. S. and GUPTA A. B. MUNRO G. H. MU~RO G. H. M~NRO 0. H. MUNRO G. H. and HEISLER L. H. PITTEWAY M. L. V. and HINES C. 0. REDDY C. R. and RAO B. R. STERLING D. L., HOOKE W. H. and COHEN R. TESTUD J. and VASSEUR G. TESTUD J. and FRANCOIS P.
1962 1969 1968 1968 1958 1963 1964 1960 1968 1967 1968 1970 1970 1971 1950 1953 1958 1956 1965
J. geophys. Rea. 67, 973. J. geophys. Res. 74, 5721. J. atmos. terr. Phys. 30, 931. J. atmos. terr. Phys. 30, 735. Aust. J. Phys. 11,79. J. atmos. tew. Phys. 25, 71. J. geophys. Res. 69, 5105. Can. J. Phys. 38,1441. J. atmos. terr. Phys. 30, 845. J. geophys. Res. 72, 1015. J. atmos. tew. Phys. 30, 795. J. geophys. Res. 75, 5535. Rev. Geophys. Space Phys. 3, 228. J. atmos. terr. Phys. 33,281. Proc. R. Sot. A202, 208. Proc. R. Sot. A219, 447. Aust. J. Phys. 11,91. Aust. J. Phys. 9,343. Can. J. Phys. 43, 2222.
1971 1971
J. atmos. terr. Phys. 33, 251. J. geophys. Res. 76,3777.
1969 1971
An& Gdophys. 25, 525. J. atmos. terr. Phys. 33,765.
Ionospheric
response to internal gravity waves observed at Delhi
TITHERIDGE J. E. TITHERIDGE J. E. VASSE~~ G. and WALDTEUFEL P.
1963 1968 1969
Reference is also made to the following unpblished CLARK R. M., YEH K. LIU C. H. VALVERDE J. F.
C. and
1970 1958
1361
J. geophys. Res. 68, 3399. J. geaphys. Res. 73, 243. J. atmos. tern. Phys. 31, 885. material: Tech. Rept. No. 39, Ionosph. Res. Lab., University of Illinois, Urbana. Sci. Rept. No. 1, Stanford Laboratories.
Ionospheric response to internal gravity waves observed at Delhi C. S. G. K. SETTY, ANURAG B. GUPTA and 0. P. NAGPAL Department of Physics and Astrophysics, University of Delhi, Delhi-7, India (Received
6 March
1972;
in revised form 29 November 1972)
Abstract-Measurements of small scale fluctuations in the day time P-region critical frequency over Delhi have revealed the presence of internal gravity waves in the P-region of the ionosphere with periods ranging from 8 to 70 min. The amplitude spectrum of these fluctuations is not uniform but contains two maxima and a minimum. The minimum is found to lie between 25 and 35 min period. It is suggested that this apparent dip in the spectrum is not due to some mechanism which filters out the gravity waves of these particular periods but represents the manner in which the gravity waves manifest themselves in the ionosphere over Delhi (dip angle 42.4’). This view, suggested by Sterling, Hooke and Cohen from their recent studies, is confirmed by the above experimental findings at Delhi.
(KENT, 1970) have been used to observe a class of wavelike irregularities in the ionosphere known as the travelling ionospheric disturbances (TID’s). The most successful explanation of these observations (MUNRO, 1950, 1958; VALVERDE, 1958; CHAN and VILLARD, 1962; TITHERIDGE, 1963, 1968; GEORQES, 1967; DAVIS and DA ROSA, 1969; KENT and GUPTA, 1971; REDDY and RAO, 1971) is that which attributes the TID’s to the corresponding disturbances of the neutral gas associated with the passage of atmospheric gravity waves (HINES, 1960; PITTEWAY and HINES, 1965; HINES and REDDY, 1967; HOOKE, 1968; TESTUD and FRANCOIS, 1971). Theoretical work of HOOKE (1968, 1970) has shown that the internal gravity waves produce TID’s through photochemical and dynamical means and that the ionospheric response to these waves should vary with the geoSome of these observations have been verified magnetic and geographic latitude. using incoherent scatter radar technique (TESTUD and VASSEUR, 1969; VASSEUR and WALDTEUFEL, 1969). The purpose of this paper is to report certain characteristics of the travelling ionospheric disturbances, observed at Delhi, where the magnetic inclination is 42.4”. Observations on FB-region critical frequency were made every minute to observe the small fluctuations in the electron concentration at the F2-region peak. The experimental set-up consists of a single vertically radiating variable frequency ionosonde. The technique and the method of observation have been described earlier (KENT and GUPTA, 1971) in which paper some preliminary results of the F2-region critical frequency were reported and the observed fluctuations were attributed to the presence of gravity waves in the F2-region. An average spectrum of these waves was also presented. Studies were further made to determine the speed of these disturbances and their vertical wavelengths. The direction of propagation has not been determined uniquely-only a component in the magnetic meridian plane is evaluated using the ray tracing technique. Frequencies reflected from different heights provide several points in the ionosphere which are separated both horizontally and vertically
A NUMBER of radio techniques
1351
1352
C. S. G. K.
SETTY,ANTIRAQB. GTJFTAand 0. P. XA~PAL
in the magnetic meridian plane. Advantage is taken of the fact that the O-mode deviates towards the north while the X-mode decays towards the south. Further observations on the FZ-region critical frequency fluctuations were made in continuation of the ones reported above. In this paper we wish to discuss some characteristics of these fluctuations in detail. The theory developed by HOOKE (1970), and by STERLINGet ab. (1971), in order to explain their observations of TID’s, shows that the amplitudes of the fractional pert~bations in electron ~on~ntration occurring during a wave passage at the height of the _ziZ-layerpeak should vary with the magnetic inclination and exhibit a minimum or a maximum for a meridionally propagating wave. It is shown by these authors that the ionosphere response to the propagating atmospheric gravity waves is ~~erent at different latitud~s~ A wave which produces siguiflcant perturbat,ion at the Equator may not cause an observable change at temperate latitudes. We wish to highlight this particular ar~ment and support it by our expe~mental observations.
Measurements of critical frequency used in the present investigation were made during the daytime (~~~~~~09 h LT) to avoid the large variations in the critical frequency due to productio~l and loss of ionization and by transport elects (D~uP~~ and NISB~T, 1968). Plots of critical frequency vs. time provide an effectively instantaneous picture of the changes in the electron concentration. Several wavelike perturbations were normally visible on each plot. Short term changes of smaller amplitude of the order of 1OOkHz were usually superimposed on larger periods (greatep than 2 hr) and were frequently periodic with quasi-periods from 10 min upwards, On many occasions the records show a sustained wave motion, with a period and amplitude which are reasonably constant up to several complete cycles. The records obtained over a period of 2 years at Delhi were examined for the occurrence of such events and were analysed to find the spectrum of the critical freque~ey Auctuations. Linear trends and spectral components comparable to the record length were removed from the data before the spectral analysis was carried out. The observed periods spread from 10 min to about 70 min. The larger periods were, however, difficult to observe because the diurnal changes in the ionosphere usually dominated over the longer period perturbations. The average height of the .FZ-layer peak, at which the fluctuations were observed, was found to be near 300 km. A typical record, taken on 8 February 1971, is shown in Fig. 1. The thick curve represents the time variation of the BY-region critical frequency, and the thin curve is the detrended version showing the fluctuations in the critical frequency. Two disturbances of 20 and 60 min periods, superimposed an each other, are clearly visible. Several cycles of osculations of 20 min period can be seen. Also shown is the computed spectrum which shows two maxima corresponding to 20 and 60 min periods of oscillations. A distinct dip in the amplitude spectrum at 30 min period can be seen. The spectrum has been normalized to show contribution from l-min intervals (r.m.s. values are used). The electron density ~uctuations for a mean F2-region critical frequency of Il.5 MHz.
are ca~eulated
Ionospheric s%aponse to ir&er~m;lgravity waves obsarved at lIM& -
TIME
V&RtATIONS
1353
OF f,FZ f,
WE& of the spectra showed two maxima and one minimum, aIthough they were not identical for deferent occasions but tended to develop a marked peak arwnd 20 TX& and then around 60 min w%h a marked dip between 25 and 35 min. &Eean spectra, weighted according to record length, were calculated for all the data taken to determine the average seasonal behaviour. These spectra for summer, equinox a,nd winter, respectively, are shown in Fig. 2. The following two main features of these spectra may be pointed out: (a) ~~xin~a around 36 and 66-min periods. (b) Minimum around 30 min, although not so pronounced in the average spectra, this minimum is very conspicuous in the individual spectra. The significant observable difference in the spectra is the low period cut off which appears to be increasing towards the summer. Apart from measuring the arn~~~t~deand period of the ~~~~u~t~o~sIt is also possible to measure their vertical ~ave~~n~~bswithin a limited aceuraoy by recording the critical frequencies and the frequencies corresponding to given, large group heighm near the peak of the PZ-region for both 0- and X-modes. This provides severa. points in the ionosphere where these ~~~~~a~~o~~ are recorded and these points are separated both in the ho~~on~a~ and vertical planes by dista,nces which vary from 10 to 40 km. ~xam~atio~ of these records shows that they are almost identical to the f,E2 and &I!‘2 records and show time delays of the order of a minute or more, Tbis time delay between the various records vi”ascapsulated with the help of the cross-correlation technique. In l?ig. 3 are shown Bornetypical records of this
1354
C. S. G. K. SETTY,
s
IO
50
Period,
A.NURAG
B. GUIFTA and 0. P.
NAGPAL
100
min
Fig. 2. Mean spectra of the critical frequency fluctuations averaged separately for summer, winter and equinox. The spectra are normalized in the same manner as that of Fig. 1.
1
I 10
Local time.
hr
Fig. 3. A typical record of the f,P2 and f,P2 fluctuations made on 18 JuIy 1970. Also shown are the records of frequency fluctuations at large, iixed group heights of 500, 550 and 600 km. The f~(600), for example, represents the frequency fluotuations for the O-mode of radio waves reflected from a group height of 600 km.
kind made on 18 July 1970. Each record is labelled to indicate whether it is a critical frequency record (~~~2 or f,F2) or the frequency record made at fixed group heights of 500, 550 and 600 km. The separation in the horizontal and the vertical planes is calculated by raytracing method. Ionograms taken during the time of observation are reduced to obtain true-height profiles and the ray tracing ~aleulations are made to obtain the ray paths for the radio waves. These ray paths for the frequencies corresponding
Ionospheric
response to internal gravity waves observed at Delhi
1355
and f,RZ at 1230 h LT, are shown in Fig. 4. The frequencies f,(600) represented by fo(500) and f,,(600) are reflected from different heights and the vertical component of the speed is then obtained by dividing their vertical separation by the average time delay between them. The estimate of the component of the vertical speed together with the observed dominant periods obtained by spectral analysis of the record enables us to calculate the vertical component of the wavelength (A,) of Table 1 summarises some of the results obtained in this the travelling disturbances. manner. Each record revealed more than one dominant period as is, for example, seen
to f,(~OO),
18 July 1970 1230 hr
320
f0 (600)
f, F2
300
f,(500) E x f .P I"
260
260
240
220
200
N---D
!lC, c--s 16
8
6
0 Ground
range,
16
24
km
Fig. 4. Some ray paths for radio waves at 1230 hr on 18 July 1970. Ray-tracing is done in the actual ionospheric model obtained by true-height analysis of the ionogram taken at 1230 hr LT. Collision frequency in the P2-region is taken to be 2.5 x 103/sec.
on the record made on 8 February 1971 (Fig. 1). The values of the vertical wavelengths, A,, are calculated for each dominant period assuming that they are travelling with the same speed. Cross-spectrum analysis was made of these records to determine the relative phase and speeds of the dominant periods and it is, in fact, found that these speeds are practically the same. DISCUSSION The measured periods for the daytime disturbances were mostly between lo-60 min. The upper limit is not so well defined and is affected to some extent by the difficulty of separating long-period variations from the diurnal changes and to some extent by the limited length of the records which do not permit accurate estimation of long-period oscillations. Similar results were reported by the Australian group of workers (MUNRO, 1950, 1953, 1958; MUNRO and HEISLER, 1956; HEISLER, 1958, 1963, 1964) who also noted preferred periods within this range. TITHERID~E (1968) interpreted that the range of values of 15-60 min for the period of the travelling wave disturbances, with a low period cut-off at 15 min to be in fair agreement with the expected values of the gravity waves at the F®ion level. The upper limit
1356
C. S. G. K.
SETTY, ANURAG B. GUPTA and 0.
P. NAGPAL
Table 1 Dominant periods (min)
Vertical wavelength
290
20 60
134 403
1 April 1970
320
20 40
124 247
20 June 1970
340
16 30 70
70 131 307
18 July 1970
325
28 60
260 547
12 October
290
15 33
95 208
Height Date
(km)
8 February
1971
1970
2.2 (km)
for gravity wave periods is probably set by the hydromagnetic viscosity giving a gradual cut-off at periods of the order of 60 min (HINES, 1960), and by the ion drag which becomes an effective damping mechanism for gravity waves with periods greater than 30 min (CLARK et al., 1970). HINES (1968) has also suggested that the amplitude and phase of the travelling disturbances are strongly controlled by the molecular dissipation processes. The problem of ionospheric response to the meridionally propagating internal gravity waves at the FZ-region heights has been studied by HOOKE (1970). His equation (7) is reproduced here as equation (1) for ready reference
(y) ((k-1,) + i(l,
f+L
* 1,)
[A +-&(ln N,,)]]
(1)
eo
where N,’ is the perturbation of the electron density N, N,, is the unperturbed value of N, U represents the neutral gas velocity induced by gravity wave propagation lbis the unit vector in the direction of magnetic induction 1,is the unit vector in the vertical direction k is the wave vector i2 Ezz-1 H is the scale-height of the neutral gas and cu is the circular wave frequency. The term d/d.+ N,,) in (1) vanishes at the peak of the FB-layer and since we are concerned with the peak of the FB-layer, we shall drop this term. The term 1/2H can be neglected under the condition 4kz2 > l/Hz. This condition is found to be satisfied for the spectrum of fluctuations observed on 8 February 1971, as shown in Fig. 1. The same is true for all those observed disturbances for which it was possible to calculate the vertical wave number. Thus, neglecting the last two terms of (l),
Ionospheric response to internal gravity waves observed at Delhi
1357
the amplitude A of the fractional perturbation in electron concentration occurring during a wave passage is given by
A=i
(k
-lJ(u-la),
It is thus seen from (2) that the amplitude of the instantaneous fractional perturbation A depends on the two factors (U +l,), the component of the gravity waveinduced neutral gas velocity and (k * l,), the component of the wave vector in the
Pole I‘,'I,,,,,,,,,,,,r
Equator rr;,,,
Fig. 5. Illustrating the competition between the requirements that both U . 11, and k . lb be large if an internal gravity wave were to produce a large amplitude ionospheric irregularity. In the above case U . lb is the largest when the wave propagates equator-ward,but in this event k . lb is so small that the wave produces a relatively small ionospheric response. When the wave propagates poleward, U . lb is small, but k . lbis so much greater that the wave produces a significantly larger response (after HOOKE, 1970, Fig. 2).
direction of the magnetic induction. Figure 5 illustrates the effects of these two factors on the ionospheric response to the gravity wave propagation. It is thus concluded that it is the tilt of the wave front relative to the geoma~etio ~olination f that is primarily responsible for determining the shape of the ionospheric response to the atmospheric gravity waves. The following approximate dispersion relation which relates the tilt of the wave front to the wave period, equation (3), is given by HINES (1960, equation (4)) a,2 = (r2 - T,2) a,yQ.
(3)
Using equations (2) and (3), STERLING et al. (1971) have obtained the following expression (equation (4)) for A, for nearly transverse internal gravity waves propagating meriodionally A =
u ’ Tg i
r:
)
(T/T,) sin (2 sin-i (T,/T) - 21).
Here there are new symbols: il is the wavelength An,1, are the horizontal and vertical components of A, respectively
(4)
1358 7g
C. S. G. K. SETTY, ANURAUB. GUPTA and 0. P. NAUPAL
is the Brunt period for isothermal atmosphere 300 km level in our calculations.
These authors have considered
and is taken to be 16 min at the
four waves, all having the same value (U/A) but
different periods T = 10~,, 5rg, ~57, and l-17,, respectively. The response of the FB-region ionosphere to these waves varies with I in the manner as shown in Fig. 6 (after Fig. 5 of SrEnLrNa et al., 1971). It may be noted that the response changes with the value of I and 7. A wave which may be very significantly affecting the ionosphere
Delhicdip angle 42.4”) -
-_6=
16min
30 Dip angle,
degrees
50
Period,
Fig. 6.
; ,I
70
!
min
Fig. 7.
Fig. 6. Variation in the response of the PZ-region ionosphere to various internal gravity waves, propagating meridionally toward the Equator, as a function of magnetic inclination I. The figures on the curves represent the wave periods in minutes. Fig. 7. Variation in the response of the P&-region ionosphere at Delhi (dip angle 42.4’) to internal gravity waves (T = 16-90 min) propagating meridionally towards the Equator, as a function of wave period. Solid line shows the spectrum when 7g = 16 min and the broken line when 79 = 13 min.
at temperate latitudes becomes unobservable near the Equator, although the wave amplitude as such remains constant. To make the situation clearer, we have drawn Fig. 7, relevant to our station (dip angle 42.4”) and represents the ionospheric response to waves as a function of period. It is noticed that the response is minimum at T = 24 min and increases as the period increases away from 24 min. It appears that the ionospheric response will increase indefinitely as the period increases. This is clearly because the theory neglects the damping effects of thermal conductivity, molecular viscosity, ion drag etc. A theory which takes these factors into account is expected to predict a rapid fall in the amplitude of the higher period waves bringing the theoretical spectrum closer to the observed ones. HOOKE (1968) has studied the effects of gravity waves on photoionisation and chemical loss rates. He suggests that if these factors become important the observed
Ionospheric response to internal gravity waves observed at Delhi
1359
dip in the spectrum will tend to vanish. These effects are not important at the F2-region heights because the ion life-times are much greater than the wave period. The lower cut-off is determined by the Brunt period which is typically 16 min at 300 km level for an isothermal atmosphere. A theory modified to include the effect of temperature gradients will predict the fall of Brunt period and the amount of this fall will depend on the magnitude of the temperature gradient. Although it is not intended to examine the variation of the dip in the observed spectra in relation to the Brunt period, it may, nevertheless, be pointed out from equation (4), that the Brunt period will have a positive effect on the response of the ionosphere. Figure 7 shows the responses to gravity waves propagating in two different model atmospheres with different Brunt periods. It is seen that the dip in the spectrum shifts from T = 24 min (for 7g = 16 min, solid line curve) to that at 7 = 19 min (for 78 = 13 min, broken line curve). CONCLUSIONS
Results presented in this paper show that the gravity waves of periods between 10 and 70 min show a selective amplification around 20- and 60-min periods and attenuation around 30 min period. Since there is no experimental limitation to account for such behaviour, it seems likely that the spectra of Fig. 2 reflect the manner in which gravity waves manifest themselves at Delhi at the F2-region heights. Our observations agree well qualitatively with the theoretical predictions of STERLING et al. (1971) except for a small shift in the observed periods; while the theory predicts, for meridionally propagating waves, a dip in the spectrum at 24 min over Delhi, the observed values lie between 25 and 35 min. It should be pointed out, however, that the equation used for determining A is derived from a rather idealised theory, wherein the equations of motions are linearised by assuming that the variables are only of perturbation magnitude and that the atmosphere is described as isothermal. These
Delhi (Dipangle Azimuth = 66
42.4)
3-
Q
e-
I
-
30
50 Period,
70
90
min
Fig. 8. Variation in the response of the P2-region ionosphere at Delhi to internal gravity waves (7 = 16-90 min), propagating at an azimuth of 60°, as a function of wave period.
1360
C. S. G.
K. SEXY,
Ama
B. GUPTA and 0.
P. NAUPAL
assumptions, it is believed, may lead to some disparities while comparing the theoretically calculated spectra with those measured experimentally. It may be further pointed out that the theoretical spectrum of Fig. 7 is derived on the assumption that the wave propagation is meridional. It is expected that apparent dip in Fig. 7 will shift from 24 min period when the waves are travelling at some angle with the meridian plane. In fact, using the same idealised theory with suitable modifications, it is observed that this dip varies between 24 and 80 min as the azimuth varies from 0 to 80 degrees west of north and between 17 and 24 min when it varies from 0 to 80 degrees west of south. Figure 8 is an example of such a spectrum when the waves are propagating at an azimuth 60” west of north assuming all other parameters to be the same. In this case, the dip appears at 34 min period. Hence, it is quite possible that the fluctuations we have observed represent the gravity waves propagating at We have also seen that any change different azimuths and not strictly meridionally. in the Brunt period of the atmosphere changes the ionosphere response to gravity waves and the position of the dip in the spectrum is shifted to a lower value. This is because the effect of the temperature gradients at the F2-region heights are such as to lower the value of the Brunt period which, in effect, lowers the position of the dip in the spectrum. AckraowZedgementsThe authors would like to thank Drs. K. DAVIES, W. H. HOOKE and R. COHEN of Environmental Research Laboratories, Boulder, for stimulating discussions. Thanks The research reported in this paper are also due to Prof. F. C. AULUCK for encouragement. was supported by a PL-480 Grant through the ESSA Laboratories, the Department of Commerce, U.S.A., under contract E-128-69 (N). REFERENCES CHAN K. L. and VILLA~D 0. G., JR. DAVIS M. J. and DA ROSA A. V. DOUPNIE J. R. and NISBET J. S. GEORCES T. M. HEISLER L. H. HEISLER L. H. HEISLER L. H. HINES C. 0. HINES C. 0. HINES C. 0. and REDDY C. A. HOOKE W. H. HOOKE W. H. KENT G. S. KENT G. S. and GUPTA A. B. MUNRO G. H. MU~RO G. H. M~NRO 0. H. MUNRO G. H. and HEISLER L. H. PITTEWAY M. L. V. and HINES C. 0. REDDY C. R. and RAO B. R. STERLING D. L., HOOKE W. H. and COHEN R. TESTUD J. and VASSEUR G. TESTUD J. and FRANCOIS P.
1962 1969 1968 1968 1958 1963 1964 1960 1968 1967 1968 1970 1970 1971 1950 1953 1958 1956 1965
J. geophys. Rea. 67, 973. J. geophys. Res. 74, 5721. J. atmos. terr. Phys. 30, 931. J. atmos. terr. Phys. 30, 735. Aust. J. Phys. 11,79. J. atmos. tew. Phys. 25, 71. J. geophys. Res. 69, 5105. Can. J. Phys. 38,1441. J. atmos. terr. Phys. 30, 845. J. geophys. Res. 72, 1015. J. atmos. tew. Phys. 30, 795. J. geophys. Res. 75, 5535. Rev. Geophys. Space Phys. 3, 228. J. atmos. terr. Phys. 33,281. Proc. R. Sot. A202, 208. Proc. R. Sot. A219, 447. Aust. J. Phys. 11,91. Aust. J. Phys. 9,343. Can. J. Phys. 43, 2222.
1971 1971
J. atmos. terr. Phys. 33, 251. J. geophys. Res. 76,3777.
1969 1971
An& Gdophys. 25, 525. J. atmos. terr. Phys. 33,765.
Ionospheric
response to internal gravity waves observed at Delhi
TITHERIDGE J. E. TITHERIDGE J. E. VASSE~~ G. and WALDTEUFEL P.
1963 1968 1969
Reference is also made to the following unpblished CLARK R. M., YEH K. LIU C. H. VALVERDE J. F.
C. and
1970 1958
1361
J. geophys. Res. 68, 3399. J. geaphys. Res. 73, 243. J. atmos. tern. Phys. 31, 885. material: Tech. Rept. No. 39, Ionosph. Res. Lab., University of Illinois, Urbana. Sci. Rept. No. 1, Stanford Laboratories.