Mid-latitude Ionospheric Scintillations

Background

The research field of mid-latitude ionospheric scintillations involves the examination of transionospheric radio signals and a specific class of changes to the signals that take place. The occurrence of ionospheric scintillations may be disruptive to signals passed between ground stations and orbiting man-made satellites and so is of concern in the field of satellite communications and satellite control. As a pure research tool, it is instructive in revealing the small scale structure of the ionosphere which in turn aids research efforts aimed at mapping the space weather conditions at any given time. By looking at the small scale structure of the ionosphere and the changes that may take place, changes in the solar-terrestrial environment can be studied and their effects on the Earth's atmosphere understood. A case exists for more concerted study of the mid-latitude region in particular, as efforts to date have displayed a selective bias towards equatorial and auroral regions of the ionosphere. One area where an understanding of mid-latitude ionospheric scintillations may be crucial in the future is the use of Global Positioning Satellite (GPS) systems for commercial purposes. Without a proper understanding of propagation conditions for GPS signals, proposed uses for GPS, such as automated navigation could place lives at risk.

Introduction

Mid-latitude ionospheric scintillations are known to have an effect on transionospheric radio signals. Specifically, a radio signal is emitted from a source above the Earth's atmosphere (be it a satellite or radio star), travels through space to the ionosphere, interacts with the ionosphere and proceeds to some receiving point, usually in the form of a receiving station on the ground. The received signal, usually above 40 MHz in frequency, displays rapid fluctuations in phase and amplitude that are not consistent with changes in the source strength and modulation. The analogy used to describe the phenomenon is the 'twinkling' of a star as observed by the naked eye. In ideal viewing conditions, a star would appear to have a constant brightness. However what is often seen is a situation in which the brightness of the star fluctuates rapidly. In radio frequency scintillations, records measuring the amplitude and phase of the radio wave show rapid changes in a like manner . It has been established, that, at the frequencies necessary for transionospheric radio propagation, absorption in the signal is negligible. Consequently, it is known that fluctuations in signal strength are not caused by absorption. The actual modification of the signal is due to changes in the phase of the waveform as it propagates through the ionosphere. Amplitude scintillations are actually caused by interference between different components of the wavefront, emergent from the ionosphere, as it travels to the ground. Amplitude scintillations are the more widely studied form of scintillations and are the concern of the remainder of this document.

Theory

Analysis of electromagnetic propagation within ionised media such as the ionosphere reveals that modification of the phase is caused by changes in the path length traversed by the wave. As occurs at optical frequencies, deviation of the ray path results as the wave passes through media with different refractive indices. In the ionosphere, the refractive index n is found as a function of several parameters, the most important being the 'free' electron density. The function describing the refractive index within the ionosphere is known as the Appleton-Hartree equation, a complicated expression in its full form. It is possible however to use a reduced form of the equation by specifying two approximations: When these approximations are taken into account, the Appleton-Hartree equation reduces to the formulae specified below in equation 1.
Equation 1
where is the angular wave frequency, and is the angular plasma frequency. can be further specified by the relation
Equation 2
where N is the electron density, e is the electronic charge, is the permittivity of free space and m is the mass of an electron. The dependence of the the refractive index on the electron density becomes obvious from this relation. The other variables involved in the calculation of n are fixed for a given wave.

The point that emerges from the theory of ray propagation in the ionosphere is that changes in the phase of the wavefront and therefore the occurrence of scintillations is due to a degree of non-uniformity within the ionosphere. Typically, it is said that 'irregularities' exist within the ionosphere consisting of anisotropic electron density distributions. In an isotropic medium, an electromagnetic wave is expected to move through the medium with all points on the wavefront being in phase. In an anisotropic medium, Hyugen's principle states that irregularities within the medium will act as radiators for the wave, with each point on the wavefront projecting waves of different phase. Simple wave theory indicates that, if a wave that is uniform in amplitude enters the region, the amplitude of the resultant wave will be non-uniform. This is the cause of the scintillation pattern produced.

Of the many attempts to explain the scintillation process, the diffraction and scattering models have enjoyed more popularity than any others. Comparitive studies of the two techniques have shown the results of the two models to be similar in situations where the scattering is weak and the level of scintillation is moderate. Of the two, the diffraction model has displayed a wider set of applicable conditions and is more widely used. The diffraction interactions may be more readily comprehended by students with backgrounds in physical optics, relieving the beginner of the need to develop an intuition for processes described by the mathematics. The details of the diffraction model will be described below, using the approach described by Briggs and Parkin (1963) in their much quoted paper. As per the discussions focussed on in their article, the examination of the theory will focus on the two scenarios of an extended isotropic irregularity, in the form of a thin diffracting screen, and an irregularity elongated along the Earth's magnetic field that shows a high level of anisotropy. For more information on the scattering model, the reader is referred to Rino (1979).

Isotropic Irregularities and Thin Diffracting Screens

Figure 1
Figure 1 displays the most succesful of the theories describing the process leading to ionospheric scintillations, that of a thin diffracting screen of ionospheric irregularities. A ray from the source travels a distance z2 to be incident on the ionosphere at an angle i. The ionospheric region inducing scintillation is modelled to be a screen of thickness h at a distance h above the ground that acts to change the phase of the wave passing through it. The wave then propagates a further distance z1 through the atmosphere to arrive at the receiving point on the ground at a zenith angle . The observed scintillation pattern is then recorded.

Whilst figure 1 depicts a satellite as being the source, work using radio stars as sources, was successfully conducted for many years before the advent of artificial satellites. The theory applicable to the two cases is very similar, the discrepancy lying with the distance between the source and the ground. This distance H, which is assumed to be constant for values of <70°, goes to infinity in the case of a radio star, whereas it retains a finite value for the satellite case. Examining the variation of the given parameters with zenith angle produces the set of equations displayed.

Equation 3
Equation 4
Equation 5
where is the radius of the Earth. Comparing the satellite and radio star source cases, equation 3 and equation 4 are the same but z2 goes to infinity as seen from equation 5.

In modelling the thin screen, diffraction is said to be caused by electron density irregularities, embedded within the layer, changing the phase of the wave. It is traditional, in describing the extent of the irregularity, to utilise the three-dimensional correlation function of the electron density to model its spatial distribution. The specific surfaces of equal correlation, that fit observations and produce the simplest mathematical form, are those of an ellipsoid of revolution with the major axis centered along the magnetic field. The variation in the correlation function along any radius being Guassian. The coordinate system most suited to such a description is cylindrical in nature with one axis s aligned with the magnetic field and another r perpendicular to the field. Transposing this coordinate system onto a Cartesian one, and suggesting that s is contained within the yz plane, it may be viewed in figure 2 below that the magnetic field direction makes an angle with the Oz axis. (This axis is typically used as the direction of the wave propagation vector.)

Figure 2
As seen from the diagram, the electron density cloud is elongated in the direction of the Earth's magnetic field. The length of this elongation is reported in the literature as the ratio of the elongation to the lateral extent of the irregularity (ie. in the direction perpendicular to the Earth's magnetic field), via the axial ratio . This lateral extent is defined to be the radius, r0, at which the three dimensional correlation function of the electron density falls to a value of 1/e, hence giving an effective length to the irregularity of r0. Whilst the values and r0 are used in the reporting of experimental results, according to theory, it is the collection of 'blobs' that makes up the nature of the screen. Accordingly, when examining the propagation of a wave through the medium, this must be taken into account when including the term associated with the electron density correlation function. Fortunately, it occurs that the form for the electron density distribution of a random superposition of such 'blobs' is also Guassian, differing from that of a singular blob by only a multiplicative constant. (This was first established by Ratcliffe in 1956 and since then has been accepted to the point where the term, of magnitude , has been dropped in quoting the characteristics of the electron clouds forming the phase diffracting screen, a practice that has been adopted in this discussion.)

The presence of an electron density irregularity is mathematically represented by an excess electron density N. Utilising a short wavelength approximation, (valid for scintillation), the deviation in the refractive index of the medium due to the excess electron density is
Equation 6
where is the wavelength and re is the classical radius of the electron. In travelling a distance l though the medium, a phase change in the wave would be given by
Equation 7
showing explicitly the effect of the irregularity on the phase of a wave passing through it. At the frequencies involved in scintillation studies and in the realm of possible electron densities fluctuations, (determined by experimental measurements), deviation of the ray through refraction is quite small, allowing line of sight propagation to be used. In the specific case of the thin diffracting screen geometry, the distance traversed through the irregular medium has a value L. Referring to figure 1, this can be calculated via

Equation 8

Actually conducting ray tracing through the screen and analysing the specific phase changes this induces is a difficult procedure. In order to obtain a more readily applied measure of the effect of the electron density irregularities, useful for instance in looking at predicted behaviour under a variety of conditions, workers in the field tend to favour using the root mean square deviation of the phase, . Bringing together the results of previous equations, and using the mean excess electron density, , the root mean square phase deviation is
Equation 9
According to this representation, the level of scintillation activity, which depends on , varies due to changes in the zenith angle i and the angle between the ray and the Earth's magnetic field , sometimes called the aspect angle or in honour of its proponents the Briggs-Parkin angle. It is assumed that the values for , h, and r0 are uniform at all points in the screen. Values quoted for these parameters of the model are for those of the screen acting as one isolated irregularity and should not be taken to mean that the electron blobs all have these values. The relation in equation 9 carries a dependence that is frequently isolated from consideration in studies of scintillation geometry by only making observations of the conditions on one wavelength.

Anisotropic Irregularity and Grazing Incidence Reflection

The case for an anisotropic irregularity is not disimilar to that for an isotropic diffracting screen as outlined above. Of special consideration in the anisotropic case though is the specific propagation geometry that must account for variation in the level of scintillation as a function of the azimuth as well as the zenith angle.

As per figure 2, the irregularity is thought to lie along the direction of the Earth's magnetic field, and have some extention perpendicular to this direction. As opposed to the diffraction screen model, where screens of several hundred kilometers in extent are considered, the approximate radius for the anisotropic isolated irregularity case is known to be around the kilometer scale. It becomes clear then that scintillation enhancement is expected only for very small angles between the magnetic field direction and the direction of propagation. In considering the signals from the Explorer VII satellite at the Brisbane station, Briggs and Parkin (1963) were able to simplify their examination of the situation by removing the azimuthal variation. (This was done by considering only passes that lay in the magnetic meridion plane, an approach that has been successfully used over time.) Using the diffraction theory, they were able to conclusively demonstrate that scintillation enhancement followed as the ray path came to coincide with the direction of the magnetic field, demonstrating that this was where the irregularities lay and that the diffraction theory was able to supply an adequate description of this behaviour.

Prior to this paper, and indeed after it, a common practice existed for researchers to model this situation by using reflection models. In the course of a variety of investigations looking at the existence of field-aligned irregularities, such as Singleton and Lynch (1962), Parkin (1968) and Jones (1969), it became evident that such a procedure could be used only if reflection occurred at grazing incidence. Early interpretations of the model (using reflection) tended to indictate that the maximum occurrence of scintillation activity took place for incidence at angles normal to the Earth's magnetic field. Such predictions included the necessary assumption that the irregularities were described by a spatial distribution that included a sharp transition between the diffuse ionosphere and the concentrated electron density distribution of the anisotropic irregularity.

Briggs and Parkin (1963) seemed to explicitly refute this theory of sharp boundaries for the anisotropic irregularities on the basis of the experiments they conducted and the more standard expectation that the electron density fell off gradually as one moved outwards from the center of the irregularity. However, if the hypothesis of Jones (1969) and others is used, that weak field-aligned irregularities are always present in the mid-latitude ionosphere, a possibility exists that sharp boundary reflection could be possible. In the placid mid-latitude ionosphere, it could be possible for very high electron densities to be present along magnetic field lines atop a much lower background level for the majority of the ionosphere in quiet conditions. The actual process involved in the grazing incidence phenomena is one of refraction at small angles leading to total internal reflection. As such, the weak field-aligned irregularity scenario could fulfil the conditions necessary for grazing incidence reflection and so the theory may indeed be valid. The relative simplicity of the theory and its ready qualitative results make it an attractive alternative in some forms of analysis. The diffraction theory however is often more useful in situations requiring predictions for the likely occurrence of scintillation activity in the use of models.
Figure 3
Figure 3 displays the general principle involved in applying the grazing incidence concept to the problem of scintillation studies. As was the case in the diffraction screen model, the irregularity is aligned along the magnetic field line and has correlation surfaces of an ellipsoid of revolution. (The case may be easily extended to more general geometries such as the case of TID wavefronts.) A planar wave propagating from above the ionospheric region passes through the layer under consideration, and in instances where the aspect angle is very small (assuming the problem is fixed to one degree of freedom ie. fixed azimuth or fixed zenith angle), some component of the wavefront may experience total internal reflection within the irregularity. The resulting change to the direction of propagation and the difference between the path lengths traversed by the affected and unaffected segments of the wave make it possible for wavefronts originating from the same source to interfere at a receiving location. As for a diffracted wave, amplitude scintillation records are observed on the ground.

Analysis of Scintillation Records

The amount of ray deviation associated with the diffraction process and the grazing incidence model is small. (The angles in figure 3 have been exaggerated.) In the atmosphere, it is necessary for the rays to be projected distances in excess of 100 km before appreciable interference takes place. To illustrate this point, the case is considered for scintillation observations at the Brisbane station. The approximate radius for the scintillation causing irregularities has been determined to be about the kilometer mark. If we suggest that the observations are conducted using a frequency of 150 MHz, then the necessary propagation distance would be revealed from the following equation.
Equation 10
The necessary distance between the ionospheric point at which the irregularity sits and the receiving point is then shown to be in excess of 250 km.

The simple relationship of equation 10 is widely used in the course of scintillation investigations, although not quite in the manner suggested above. The wavelength at which observations are made is known in all cases as the receiver frequency is a fixed parameter of the receiving apparatus. However, the size of the irregularities causing the scintillation is usually the object of scrutiny. By examining information gained from other sources, such as ionosonde records, the height of the ionospheric region in which the irregularities are embedded can be gleaned. By observing on a number of frequencies simultaneously, bounds can be placed on the irregularity size and the information used in similar propagating conditions. (The kilometer irregularity size for the Brisbane station is consistent with observations over a thirty year time span.)

The most widely used relationship in scintillation observations is that for measuring the severity of amplitude scintillations, quoted as the S4 index. The index, found below in equation 11
Equation 11
measures the time averaged change in the amplitude of the wave detected by the receiver equipment. In general, recorded data is processed by computer equipment to find the S4 index value for a specific time block. The temporal averaging process requires the analyst to find the index value for a segment of the record, typically around ten seconds in length, before searching for trends in the S4 index that can be explained in terms of propagation models.

In the initial stages of scintillation research, when the use of chart recording systems was common, other scintillation indices were used. The highly subjective nature of the classification systems such as the so called S.I. value made comparisons between data sets obtained by different research efforts very difficult. Following a series of different indices being suggested, workers in the field settled on the S4 index to be the standard as it provides an unambiguous definition and is easily computed using modern techniques.

The index is used in several different contexts in the scintillation research field. Its use to grade the severity of measured scintillation has already been mentioned. When used in this manner, investigators have determined that there are a couple of levels of scintillation. Briefly they might be described by

  • weak scintillation for S4 < 0.6
  • strong scintillation for S4 > 0.6
  • saturation for S4 > 1.0
The importance of the three cases lies in the analysis of the scintillation behaviour and the level of disruption to communications. Obviously, when the signal reaches saturation, information content is usually lost (a very rare occurrence in mid-latitudes). The weak and strong case distinction is tied to the applicability of the propagation models used in analysing the effect of the electron density irregularities on the transionspheric signal.

The most important use of the index is in providing reasonable estimates of signal disruption for a specific position on the Earth. Propagation models such as the thin diffraction screen, tend to provide the effects of an electron density level and geometric alignment in terms of the r.m.s phase deviation of equation 9. The r.m.s. phase deviation can be converted to an S4 value that is more valuable when trying to mate experimental data sets to predictions based on models. When this is done, communications engineers and their ilk are able to work out the probability of disruption to ground linked signals as a function of the S4 index. The succesful integration of mid-latitude scintillation morphologies into the models currently being used, which tend to concentrate only on the equatorial and auroral regions, will be critical in the commercial success of proposed micro-satellite clusters for use in the television and satellite phone industries. Such low orbit satellites, operating at VHF or possibly UHF frequencies, will experience the majority of their traffic within mid-latitude regions. Mid-latitude scintillation behaviour, which signals are sensitive to at such frequencies, will be of more interest in the future in constructing models using the S4 scintillation index.

Cross-correlational analysis forms the basis for many of the investigations conducted by observers with access to more than one recording station. The cross-correlation coefficient is used to examine whether or not events recorded at seperated sites are caused by the same irregularities. For values of the coefficient exceeding 0.7, it is assumed that the pattern projected onto the ground originates from the same irregularity and on this basis, several analytical techniques can be employed. The use of computers to analyse digitally recorded data has been particularly useful in this context.

An instructive technique conducted using correlational analysis is the so called full correlation analysis (FCA) technique which is able to obtain the exact dimensions irregularities and therefore the all important axial ratios used to describe the rod-like electron density inhomogeneities. MacDougall (1990) in particular has employed this method with great success to obtain results which have vindicated the belief that these irregularities are highly elongated with axial ratios up to 60 expected from theory. The apparent similarity of the patterns found at the ground is also of use in determining the speed that the irregularities travel at, if one does not have access to phased-array backscatter radar facilties. The scintillation drift measurement technique relies on the establishment of minute differences in the arrival time of the signal received by three or more stations, preferrably arranged into a closely spaced right-angled triangle, found by using cross-correlational analysis to measure the lead or lag time of a feature in the record at two stations. A clear illustration of this technique is presented by Hargreaves in a recently published text (The solar-terrestrial environment 1992). Hargreaves not only presents the fundamentals of the process clearly, he also points out the shortcomings of the technique while assuring the reader that
`` The method is beyond reproach if applied to a single irregularity and the measurements are accurate. ''
As with the S4 scintillation index, cross-correlation analysis can be performed using computer systems that allow for new techniques to be developed and processes, that were formerly tedious error prone tasks, to be carried out in a minimum amount of time with increased accuracy. The FCA technique and the scintillation drift measurements conducted during modern campaigns using computer systems have been able to validate measurements using other technology or theoretical results, that were not being supported by the accumulated body of evidence from experimental campaigns. Digitally recorded data can be analysed more accurately and in most cases is more sensitive than analog chart records where a finite pen size may obliterate information that can be revealed using correlational techniques. Its widespread use is producing new results and further techniques such as ionospheric tomography which will no doubt enhance the understanding level that has been currently attained.

The examination of amplitude scintillation records using Fourier analysis has revealed that the power spectrum can be regarded as a measure of the degree of anisotropy of the irregularities responsible. Studies by Kerlsey and Chandra, Wernik et. al. and others have shown that the power spectra of amplitude scintillations is related to the in-situ spatial spectrum of the electron density inhomogeneities causing the interference mechanism. Using the power-law model, it has been revelead that the temporal power spectrum is directionally proportional to the three-dimensional exponent used to construct the model, the value of which has a mean value of approximately -4. The value obtained for the spectral index of the scintillations is expected to have a value 1 greater than that for the irregularity spatial power spectra. The phase spectral index q is expected to be dependent on the anisotropy of the irregularities, which is itself a measure of the degree of field alignment of the irregularities and the axial ratios that describe its extent. Investigations that consider the spectral index as a function of time during a pass would expect to see the aspect angle decrease and the ray path become coincident with the alignment of any rod-like irregularities. A study in 1995 conducted by the author found that this expectation was born out in the results obtained. Examinations of the spectral index as scintillation increased showed an almost symmetrical increase and then decrease in the value of q as the ray path of the signal from the Transit satellites passes through the field point. The large values for the slope obtained, which were in the order of -6 to -8, are reminiscent of the broken slopes found by Kersley and Chandra which they attributed to the position of the irregularites as being in the F-region where it is known such irregularities have a highly elongated structure. The general conclusion obtained from irregularity spectra studies is that the spectral index q is a function of the degree of anisotropy of the irregularities, which is itself a representation of the size of the irregularities and the degree to which they are aligned with the magnetic field. Studies concerned with the effect of FAIs should therefore necessarily include the use of power spectral information in the analysis of their character.

The analysis of amplitude scintillation records is conducted by different techniques based on the manner in which the information is recorded and the desired outcome from an investigative campaign. As a general rule, modern observation techniques involve the measurement of scintillation activity by using multiple spaced receiver systems connected to digitising systems. The storage of information in digital format has the advantage of easy transmission and copying of records for use in co-operative investigations. Analysis of the amplitude scintillations using computer software and signals processing techniques is also possible, speeding up the findings of investigations and allowing the employment of techniques that are difficult if not impossible without the iterative abilities of computers. While old fashioned chart recording systems can be used, indeed they may be preferrable for the recording of geosynchronous satellite systems because of the volume of information produced, the ability to automate analysis techniques through computer systems is infinitely preferrable because of its speed and the removal of human error from the analysis procedures.

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Last updated 28/12/1997 by Mark Keir