Characteristics of ionospheric irregularities capable of producing quasi-horizontal traces on ionograms

Characteristics of ionospheric irregularities capable of producing quasi-horizontal traces on iouograms P. L. DY.WN and D. L. ROBERTS Physics Department, La Trobe University, Bundoora, Victoria 3083, Australia (Received in final form

16Notjember 1988)

Abstrac&-This paper presents simulated ionograms calculated for a parabolic ionospheric layer containing irregularities in the form of smaii amplitude waves. With small amplitudes, ~rturbation techniques can be used enabling results for the irregular ionospheres to be calculated from the results for smooth ionospheres. This approach is relatively straightforward and avoids having to ray trace new paths each time the irregularity parameters are changed. It is, however, restricted to irregularities which do not cause multiple echoes. Irregularities with vertical wavelengths of up to a few kilometres can produce significant changes in the ionosphere over height intervals smaller than those involved in reflecting a single pulse. Consequently, in the simulation procedure, it is essential to consider not just the carrier frequency but the complete frequency spectrum of the pulse. Irregularities with vertical wavelengths of the order of 10 km or more can produce ripples in an ionogram trace. These will, of course, be more evident on ionograms with high frequency resolution. Irregularities with vertical wavelengths of up to several kilometres and amplitudes up to a few per cent can produce significant pulse spreading and splitting. The actual effects depend not just on the irregularity properties but also on the ionosonde pulse width, gain and frequency and height resolutions. Some simulations show trace splitting and quasi-horizontal traces similar in many respects to effects observed by BOWMAN(1987, J. atmos. terr. Pkys. 49, 1007) and BOWMANef al. (1988, J. atmos.terr. Phy~. 50, 797). Consequently it is suggested that, at least in some cases, small amplitude (< 3%) and small scale (<4 km) irregularities produce the spread-F reported by these authors. 1. INTRODUCTION

expression for the electric field, E,, of a pulse received at the ground after reflection at vertical incidence. The expression may be written as :

In recent years there have been very significant improvements in the capabilities of ionosondes which

have led to new detailed measurements of ionospheric irregularities. Of particular relevance to this paper are the observations of spread-F obtained by Bowman and co-workers (BOWMAN, 1987 ; BOWMAN et al., 1988) using a Disonde (BOWMAN et al., 1986). One of the features of their instrument is that it can be operated with much higher frequency and range resolutions than a normal ionosonde. When observations are then made of spread-F, discrete quasi-horizontal traces, #IT, are often observed. The purpose of this paper is to show that small scale perturbations in electron concentration can produce effects very similar to the QHTs. ROBRWN and DYKIN (1977b) showed that small scale irregularities could produce pulse spreading of ionosonde echoes and they suggested that this could contribute to unresolved spread-F. This idea is extended in this paper and it is shown that trace splitting can occur on ionograms with high frequency resolution.

E,(t) =

I’ Wf-fJ i -n

ew CW[~--fYfY4

d.6 (1)

where t is time, P(f) is the phase path at frequency J M(f-,f;) is the frequency spectrum of a pulse with carrier frequency f,, c is the speed of light. Budden further showed that the electron density gradient in the ionosphere distorts the shape of reflected pulses, with steeper gradients producing greater distortion. As is evident from equation (I), the distortion is due to the different components of the pulse being reflected from different heights, thus causing the phase path, P(f), to vary with frequency. RORINSON and DY.WN (1977b) used Budden’s approach and considered irregularities with vertical extents smaller than the range of reflection heights involved in the reflection of a pulse. As a consequence, different components of a pulse could be reflected from the underside of different irregularities, thus giving rise to pulse spreading or splitting. As a first approximation, if a pulse of bandwidth Af is reflected from a region of the ionosphere in which the gradient in the plasma frequency is df,/dh, then the components of the pulse are reflected over a

2. THEORY

In high resolution measurements using pulsed sounders it is important to consider the effects of the ionosphere on pulse shape. The basic theory has been considered by BUDDEN (1961) who derived an 279

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P. L. DYSONand D. L. ROBERTS

height range of approximately Af /(df,/dh). Consequently, irregularities with vertical extents smaller than, and comparable to, this value can have significant effects on the pulse shape. Note that if the bandwidth of the transmitted pulses is increased in order to transmit narrower pulses, the range of heights over which reflection takes place is increased, and a greater range of irregularity sizes could affect the pulse shape significantly. It is not a straightforward matter to consider, in a general way, the effects of ionospheric irregularities on echoes observed by an ionosonde. The main reasons are that with irregularities present, echoes are no longer confined to vertical incidence and several echoes may occur at a single frequency. Extensive three-dimensional ray tracing is then required to determine the number and properties of echoes. However, BENNETTand DYSON(1986) have shown that the effects of small scale amplitude irregularities can be determined by considering perturbations to the vertical incidence echoes of the undisturbed ionosphere. Furthermore, by ignoring the Earth’s magnetic field, they were able to derive analytical expressions for the effects of irregularities in several different types of background layer. This paper is concerned with demonstrating effects which small scale irregularities can have on ionograms so it is not crucial that the Earth’s magnetic field be included. Consequently analytical results given by Bennett and Dyson should be adequate for our purposes. To confirm this, separate calculations using these analytical approximations and a more involved numerical integration procedure were compared for several ionogram simulations and in all cases negligible differences were found. It is important to note that on a VAX8820 computer the integration procedure took between 2-25 h of CPU time, whereas only 3-5 min were required for the analytical approximation. For the bottomside ionosphere it is most appropriate to use a parabolic layer as a representative model. We will consider such a layer as the background ionosphere upon which irregularities are superimposed. For the background ionosphere the variation of plasma frequency, &,, with height and the phase path, P,,(f), at vertical incidence are then given by (e.g. BUDDEN,1961):

=,:[l-(yq]

f‘?%

(2)

P&f) =h”,-$‘-+‘(+-$log($+); f
(3)

where h, is the height of the layer peak, f, is the peak plasma frequency and y, is the layer semi-thickness. Following BENNETTand DYSON(1986) consider a multiplicative irregularity which perturbs the background ionosphere so that the variation of plasma frequency with height, &(h), is now given by :

flZ = fl[l +Wit>l.

(4)

Various types of irregularity function could be considered, but it is convenient to consider a sinusoidal irregularity described by BENNETTand DYSON(1986) : (5)

Af,$ = AA exp [i(wt-k~-k,y-k,z+~)],

where AA is the irregularity amplitude, k = (k,, k,, k,) is the irregularity wavenumber, M;is the angular frequency of the wave and JI is the phase. When the irregularity is included, the phase path, P(f), may be written as : J’(f) = pdf> +Wf),

(6)

where the perturbation to the phase path, P(f), by (BENNETTand DYSON,1986) is :

Wf)

=

given

exp i

wt-k,x+$+

;sgn(k,)-kzh,

)I

AA,

(7)

where h, is the reflection height of the background layer. Combining equations (6) and (1) enables the electric field strength of ionospheric echoes to be calculated.

3. IONOGRAMSIMULATIONS In order to investigate the effects of different irregularities, ionograms were synthesized in the following way. A background parabolic ionosphere was specified and the parameters of the sinusoidal perturbation selected. The bandwidth of the transmitted pulses was chosen and equations (1) and (6) used to calculate the electric field strength of echoes over a range of carrier frequencies. The effects of the receiver were then simulated by using a Butterworth filter function with appropriate bandwidth to match that of the simulated transmitted pulses (ROBINSONand DYSON, 1977b). Other effects, such as antenna gain, are not directly relevant to pulse shape calculations. It was also assumed that the output of the receiver detector is proportional to power. Figure 1 shows results of simulations for a typical

Characteristics of ionospheric irregularities

ionosonde, using a pulse bandwidth of 15 kHz and a logarithmic frequency sweep. Figure l(a) shows the ionogram for a single parabolic layer without irregularities. The layer has a critical frequency of4.01 MHz, peak height of 250 km and semi-thickness of 128 km. As expected, the echo trace increases monotonically with frequency. At each frequency the pulse is well defined with a single power maximum in the middle of the pulse. As the critical frequency is approached the echo range increases rapidly and the limited frequency resolution of the simulated ionograms becomes apparent. The other ionograms in Fig. 1 show the effects of irregularities on the background ionosphere. For the perturbation calculations, the horizontal wavelength of irregularities is not important because it is apparent from equation (7) that the k, term only produces a constant phase term for a single ionogram simulation. Of course, this is not the case for some other echo parameters, such as the angle of arrival (BENNETTand DYSON,1986). Figures l(b) and (c) show small amounts of pulse spreading near the critical frequency due to irregularities with a vertical wavelength of 2 km and amplitudes of 0.1% and 0.25%, respectively. This is consistent with the results of ROBINSONand DY.WN (1977b). In Fig. l(d) the vertical wavelength is sufficiently large so that pulse spreading is no longer obvious, nevertheless a ripple due to the irregularity is apparent near the critical frequency. Features of this type do appear on topside and bottomside ionograms and have been studied by ROBINSONand DYSON (1977a) and DYEGON and BENNETT(1987). Many modern ionosondes can be operated with much higher frequency and range resolutions than are used in routine sounding. Figure 2 shows simulated high resolution ionograms restricted to a frequency band near the critical frequency. Ionograms (a), (b) and (c) are for the same ionospheres as their counterparts in Fig. 1, with case (a), an ionosphere without irregularities, simply showing the trace expected from a smooth ionosphere. It is apparent that with the higher resolution, considerable structure is now evident in the echo traces. Case (d) helps illustrate that the effects depend on both the irregularity wavelength and the background ionosphere. At lower frequencies there is little pulse spreading but the irregularity produces ripples in the echo trace. As the critical frequency is approached, the background electron density gradient increases so that there is an increase in the height interval involved in reflecting a pulse. As a consequence, the echoes begin to spread and the ripple in the echo traces is replaced by a more complicated structure. To investigate whether these effects may be related

281

to the observations of BOWMANet al. (1988), the same background parabolic layer as for Figs. 1 and 2 has been used together with a pulse bandwidth of 35 kHz. These parameters are reasonably appropriate for the observations shown in their fig. 5. Simulated ionograms obtained for various irregularity sizes are shown in Fig. 3. It is apparent that a variety of effects can be produced with various types of striations occurring in the traces and even splitting into more than one trace. The simulations considerd so far produce significant effects near the critical frequency. Similar effects can be produced at lower frequencies but larger amplitudes are required because of the decreased gradient in the background ionosphere. Some examples, shown in Fig. 4, indicate very pronounced QHTs at both the leading and trailing edges of the pulse with a more complicated quasi-horizontal structure evident towards the centre. This splitting shows the pulse is being resolved into more than one trace. Since some traces are weaker than others the actual effects observed will depend on the dynamic range of the receiver and display system. Finally, Fig. 5 shows simulated fixed frequency ionograms for the situation in which the wave irregularity is moving. Rather than specify a particular velocity (in which case the horizontal axis would be time), the irregularity has been advanced in phase by uniform steps. Consequently, the horizontal axis is radians. Obviously, for a wave of period T, this axis could be transformed to time by multiplying by T/27r. This figure shows that for a moving irregularity, fixed frequency observations would produce a fringe pattern. The periodicity of the irregularity is related to the horizontal spacing of the most intense echoes, not the spacing of the weaker striations. The period of the irregularities could therefore be determined from a careful comparison of the trace between echoes of comparable strength. 4. DISCUSSION There are many reports in the literature of observations which indicate that unresolved spread-F can be made up of a number of closely spaced, but discrete echo traces. A summary of these has been given by BOWMANet al. (1988). The simulations presented in Fig. 1 show that small amplitude wave irregularities with vertical wavelengths of a few kilometres can produce small amounts of spreading. Note that in Fig. 1, the virtual height scale is not as compressed as on real ionograms, and hence the actual spreading effect will not be as pronounced. Thus, as pointed out by ROBINSON and DYSON (1977b), pulse spreading is not an

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Fig. 1. (a-b) Ionogram simulations for a typical ionosonde with pulse width of 15 kHz and a logarithmic frequency sweep. (a) Single parabolic layer without irregularities. (b) Parabolic layer containing irregularities with vertical wavelengths of 2 km and amplitude of 0.1%.

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Fig. 1 (1.4). (c) Parabolic layer containing irregularities with vertical wavelengths of 2 km and ampritude of 0.25%. (d) Parabolic layer containing an irregularity with vertical wavelength of 16 km with amplitude of &IS%*

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Fig. 2. Simulated high resolution ionograms restrioted to a frequency band near the critical frequency. Ionograms (a), (bf and fc) are for the same ionospheres as their Fig. 1 conterparts. (d) Farabolic iayer condoning irregularity with vertical wavelength of 4 km and amplitude of 0.175%.

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Fig. 3. (a-d) Ionograms simulated for a modern high resolution ionosonde, with a pulse width of 35 kHz as is used by F&-N ef al.(1988). (a) Background parabolic layer. The other plots show irregularities of(b) 2 km vertical extent, 0.15% ~plitude; (c) 2 km, 0.25% ; (d) 4 km, 0.075%.

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alternative explanation of unresolved spread-F, but complementary. If a range of irregularity sizes is present, as often appears to be the case (DYSONet al., 1974), larger scale irregularities can produce spreading of individual traces. Many of the observations reported by BOWMANet al. (1988) are cases for which spread-F could only be detected by a high resolution ionosonde. This, in itself, suggests that the irregularities involved are of relatively small amplitude. The fact that the spread-F appears as quasi-horizontal traces suggests that the irregularities also have small scale sizes. The reason is that irregularities of small amplitude, but of relatively large scale, can be expected to produce smooth, rather than discontinuous, changes in the echo traces. Results shown in Fig. 2, and others given by DYSON and BENNETT(1987), indicate that irregularities of a few per cent in amplitude, and wavelengths of about 10 km or more do produce smoothly varying changes in echo traces. Consequently, it seems likely that the irregularities involved are small in amplitude and vertical extent. BOWMANet al. (1988) also concluded that

the quasi-horizontal structure was most likely due to small scale vertical structure in the ionosphere. Once the vertical structure of irregularities is comparable to the height interval required to reflect the components of a radio pulse, it is obvious that any attempt to model the effects of irregularities must take this into account. In the E-region, electron density gradients can be very steep so that reflection of radio pulses generally may be regarded as occurring at a sharp interface, even for irregularities or layers with vertical extents of the order of a kilometre. However, this is not so in the F-region. The simulations presented in the previous section show that a variety of effects, including quasi-horizontal traces, can be produced depending on the irregularity size and amplitude, and the bandwidth and resolution of the ionosonde. Figure 3(d) shows quite prominent quasihorizontal traces very similar to those shown in figs. 5(a) and (c) of Bowman et al. The grey scale in the simulated ionograms shows different power levels. In filmed ionograms, the echo traces often have little grey scale. Certainly the reproductions in Bowman et d’s

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paper do not have a grey scale. It is apparent from Fig. 3 that patterns observed on actual ionograms

could be influenced by the threshold level of echo detection. If the level is raised, the intense QHTs in Fig. 3(d) could become more pronounced. The simulated ionograms in Figs. 3(b) and (c) resemble Figs. 5(b) and (d) of Bowman et al. in that there is splitting into two main traces, with each trace containing QHTs. Consequently, dual traces with QHT structure could occur just due to the presence of small scale irregularities. Of course, the two main traces could be produced by a large irregularity causing echoes at different angles of arrival, with small scale irregularities responsible for just the QHT structure. The calculations show that the effects produced by the small scale irregularities depend, not just on the properties of the irregularities, but also on the characteristics of the ionosonde making the observations. In particular the bandwidth, dynamic range and the

frequency and range resolutions are all important. Consequently, an ionosonde for which all these parameters can be varied would enable definitive measurements to be made on the role of small scale irregula~ties in producing quasi-ho~zontal traces. One further point is that we have considered the effects of irregularities on a single echo trace only. The results therefore apply to wave irregularities which are propagating vertically or which have a sufficiently large horizontal wavelength so that overlapping echoes do not occur. The actual horizontal wavelength will be a function of the irregularity vertical wavelength and amplitude. If overlapping echoes do occur, there will be further complications in echo structure due to interference. For travelling waves, the perturbation theory predicts that one hop multiple echoes occur for : (#J2P’AP,

2 1,

(8)

where AP, is the amplitude of the phase path fluc-

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PHASEOF IRREGULARITY(Rad) Fig. 5. Simulated fixed frequency ionograms for the situation in which the irregularity is moving, for a carrier of 3.7 MHz. (a) 2 km, 0.25% ; (b) 4 km, 9.5%.

tuations given in equation (7) (BENNETT, 1988). Typical parameters used in this paper are P’ = 350 km, AA = 0.001, 1, = 4 km, y = 128 km and f = 0.96s. With these values, equation (8) gives 1, ,< 272 km. Thus, the results presented here apply to vertically propagating waves.

5.

CONCLUSIONS

Ionogram simulations show that small scale irregularities, with vertical wavelengths of up to several kilometres and amplitudes of up to a few per cent, can produce considerable echo trace structure which should be evident on high resolution ionograms

obtained with modern ionosondes. Multiple trace effects, resembling quasi-horizontal traces, and main trace duplication are produced. Patterns similar to some of those observed by BOWMAN et al. (1988) have been simulated suggesting that they have detected small scale irregularities of the type discussed in this paper. Future studies combining the simulation technique with observations should enable a more direct determination of irregularity properties. Acknowledgements-This work has been supported by the Australian Research Grants Scheme. We acknowledge discussions with J. A. BENNETTand G. G. BOWMAN.

REFERENCES BENNETTJ.

A. and BOWMAN G. G.

E~OWMAN

DYSON P.

L.

G. G., CLARKE R. H. and MEEHAND. H.

1986 1987

J. atmos. terr. Phys. 49, 1007.

1988

J. atmos. terr. Phys. 50,797.

Radio Sci. 21, 375.

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Characteristics of ionospheric irregularities BOWMAN G. G., HAINSWORTH D. W. and DUNNEG. S. BUDDENK. G.

1986

Radio Sci. 21, 291.

1961

Radiowaves in the Zonosphere. Cambridge University

DYSONP. L. and BENNETT J. A. DYSON P. L., MCCLUREJ. P. and HANSONW. B. ROBINSON I. and DYSONP. L. ROBINSON I. and DYSONP. L.

1987

J. J. J. J.

Press. 1974

1977a 1977b

atmos. terr. Phys. geophys. Res. 79, atmos. terr. Phys. atmos. terr. Phys.

49, 565. 1497. 39,263. 39, 709.