SATELLITE BEACON EXPERIMENTS FOR IONOSPHERIC STUDIES. 3.1 Introduction. Chapter -3

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1 Chapter -3 SATELLITE BEACON EXPERIMENTS FOR IONOSPHERIC STUDIES This chapter gives an introduction to Earth s ionosphere, stating the importance of ionospheric studies using satellite beacon systems. Various methods of TEC measurement are also explained in detail here. 3.1 Introduction The earth s atmosphere is stratified into several distinct altitude regions that are defined by their vertical neutral temperature gradients. The lowest region is called the troposphere and it extends from the surface to about 10 km in mid-latitudes and upto km over equatorial and low-latitudes, and weighs about 75% of the total mass of the atmosphere. The ionosphere and the upper atmosphere are important for the existence of life on the earth since they absorb much of the dangerous solar radiation before it reaches the surface. Extending roughly from 60 to 1000 km, the ionosphere is the region of the atmosphere where sufficient number of ions and free electrons exist to affect the propagation of radio waves. Created by photo-ionization due to solar radiation, these charged particles influence radio propagation through the ionosphere by reflection, scattering, absorption and refraction. So even though the ionosphere weighs only ~1% of the total atmospheric mass, it has a significant impact on our health and life. The ionosphere is often illustrated as a smooth homogenous layer of the atmosphere, but it is far from being uniform in shape and composition. The ever changing ionosphere possesses many three dimensional (horizontal as well as vertical) structural features whose spatial and temporal scales vary widely. This is so because the ionosphere is heavily dependent upon solar radiation and therefore varies with time of day and solar activity over any region. 19

2 3.1.1 General characteristics of ionosphere: Electron density profiles Distinct layers develop within the ionosphere because the solar energy absorption characteristics of the ionosphere vary as the atmospheric composition changes with altitude. This produces a large variation of the electron density in the vertical direction. Thus, the vertical electron density profile, or the electron density changes as a function of height, is a fundamental aspect of describing the ionosphere. Figure 3.1 shows the differing night time and daytime electron density profiles, for midlatitude regions. Figure 3.1 Typical vertical profiles of electron density in the mid-latitude ionosphere (Source: Hargreaves, 1995) From the figure, it can be seen that during daytime, the solar spectrum is incident on a neutral atmosphere that is increasing exponentially in density with decreasing altitude. Since the photons are absorbed in the process of photoionization, the beam itself decreases in intensity as it penetrates. The combination of decreasing solar flux, increasing neutral density, and diffusion provides a simple explanation for the 20

3 basic large scale vertical layer of ionization shown in Fig The peak plasma density occurs in the F layer and attains values as high as 10 6 cm 3 near noontime. The factor that limits the peak density value is the recombination rate, the rate at which ions and electrons combine to form a neutral molecule or atom. This in turn very much depends on the type of ion that exists in the plasma and its corresponding interaction with the neutral gas. Thus it can be seen that the electron density at any location is dictated by the production, loss and transport mechanisms, which continuously happen in the medium. Periodic variations of the ionosphere are due to the rotation of the Earth (diurnal variations), sunspot cycle, the Earth s orbit around the sun, and the rotation of the sun itself. Since the ionosphere is formed by photo-ionization by solar radiation, it varies over the 24-hour daytime/ nighttime period and over the 11/22 year solar/ solar magnetic cycles. Thus the ionosphere is constantly changing due to fluctuations in solar activity and geomagnetic activity as indicated by Klobuchar [1983]. So, in addition to periodic variations, the ionospheric structure also displays random and chaotic characteristics. In order to study the ionosphere with its complex spatial and temporal behavior, the current theories and understanding of the ionosphere have been incorporated into various computer models. Though these models are fairly accurate in the midlatitudes, due to the equatorial anomalies, (Also known as Appleton Anomaly, this forms the electron density enhancements at about ± 15 magnetic latitude as mentioned by Dunford [1967]), these are not as accurate in the low - latitude regions, which explains the need to conduct detailed and continuous studies of the equatorial ionosphere, by the various methods. India being near the equator comes under this latter category and so research works are carried out for this. 3.2 Radio wave propagation in the ionosphere The lower, un-ionized part of the atmosphere includes both the troposphere and the stratosphere. However, about 80% of refraction effects on the radio wave travelling through the atmosphere is produced by the troposphere. The index of refraction of un-ionized air is independent of frequency in this region, at least below 15 GHz as 21

4 specified by Ya Al pert [1973]. Hence the errors due to contributions from the troposphere are much less compared to the ionospheric contributions and it is imperative to study the ionospheric contributions first to understand communication and propagation better. Since the Earth s ionosphere is embedded in the magnetic field of the Earth, the charged particles that constitute the ionosphere experience the effect of this geomagnetic field due to the significantly less ion-neutral collisions. Hence understanding the propagation of electromagnetic waves through such a medium requires solving Maxwell s equations for that medium. In this case, the plasma in the presence of a magnetic field will have a variety of effects on the radio signals passing through it such as refraction, signal delay, polarization rotation, fading and fluctuations as mentioned in the handbook by Louis J. Ippolito [1999] These effects cause scintillation, absorption, variation in the direction of arrival, propagation delay, dispersion, frequency change and polarization rotation of the radio waves as detailed in ITU recommendations [1997]. The following definitions as described by Ippolito [1986] help us to understand these effects. Ionospheric Scintillation refers to the rapid fluctuation of the amplitude, phase, polarization, and angle-of-arrival caused when radio waves pass through electron density irregularities in the ionosphere. Absorption is a reduction in the amplitude (field strength) of a radio wave caused by an irreversible conversion of energy from the radio wave to matter in the propagation path. Absorption due to the ionosphere is dependent on geographic location and time of day. Angle of Arrival Variations are changes in the direction of propagation of radio waves caused by refractive index changes in the transmission path. Propagation Delay also called group delay is a reduction in the propagation velocity of a radio wave, caused by the presence of free electrons in the propagation path. The group velocity of the radio wave is retarded, thereby increasing the travel time over that expected for a free space path. 22

5 The dispersive properties of the atmosphere define an upper limit on the information bandwidth or channel capacity that can be supported by a radio wave, termed as coherence bandwidth. When a transmitted radio wave reaches the receiving antenna by two or more propagation paths, there occurs a frequency change at the receiver. This phenomenon is termed as multipath propagation. This can result from refractive index irregularities in the ionosphere. The rotation of the polarization sense of a radio wave popularly known as Faraday rotation is caused by the interaction of the radio wave with electrons in the ionosphere in the presence of the Earth s magnetic field. This rotation of the plane of polarization occurs because the two rotating components of the wave progress through the ionosphere with different velocities of propagation. The refractive index is often introduced as a parameter to describe the ionospheric medium and is seen to characterize the amount of bending that occurs. Similarly, observations of the bending of radio signal or the delay of the signal provide information about the index of refraction. Therefore, a quantitative description of radio wave propagation through the ionosphere can be examined through the index of refraction and its dependence on the fundamental properties of the plasma. According to the frequency of the propagating wave, it can be seen that the wavelength plays an important role in RF signal propagation and reflection characteristics, according to George Kennedy and Bernard Davis [1993]. Radio signals having frequencies above 30 MHz usually penetrate the ionosphere and therefore, are useful for ground-to-space communications. The ionosphere occasionally becomes disturbed as it reacts to certain types of solar activity. Frequencies between 2 MHz and 30 MHz are adversely affected by increased absorption, whereas on higher frequencies (e.g., 30 MHz to 100 MHz) unexpected radio reflections can result in radio interference. Very high frequencies (VHF) ranging from about 30 MHz to 300 MHz propagates primarily by line of sight. For most applications this limits reliable propagations to about km. For ultra high frequencies (UHF from 300 MHz up to about 3 GHz, line-of-sight is the 23

6 primary mode of propagation. This frequency range is the primary segment used for satellite communications and navigation systems including TRANSIT and GPS. Scattering of radio power by ionospheric irregularities produces fluctuating signals (scintillation), and propagation may take unexpected paths. Some satellite systems, which employ linear polarization on frequencies up to 1 GHz, are affected by Faraday rotation of the plane of polarization. Figure 3.2 illustrates these various ways in which ionosphere affects a radio signal propagation. Figure 3.2 Ionospheric radio wave propagation effects (Source : NiCT) 3.3 Methods for ionospheric measurements From the above discussion on the propagation characteristics of ionosphere, it can be understood that a detailed study of ionospheric properties is required in order to understand any sort of electromagnetic propagation through it, which then renders its results to radio communication. Also, since most of the characteristics are dependent on the complex refractive index, methods to measure and study this provides a handle to understand the medium better. There are various ground based 24

7 systems like ionosonde, atmospheric radar systems like HF radar, VHF backscatter radar, meteor wind radar etc which give the fluctuations in the lower regions of the ionosphere as mentioned in Davies [1989], Titheridge [1988] and Attila Komjathy [1997] among various others. Other in-situ measurement techniques like rocket borne payloads include various probes such as Langmuir probe, electric field probe etc which give the instantaneous measurement of the electron density along the trajectory of the rocket. These two have one main disadvantage of being location dependent. Satellite based systems for ionospheric studies can provide a global variation, which can be generated as electron density maps. The most popular satellite based system for ionospheric studies is a coherent beacon, wherein a minimum of two coherent signals are transmitted from the satellite and are received simultaneously at various locations directly. The data from these are used to generate integrated electron density profiles along the ray paths from the satellite to the ground station, which is the Total Electron Content (TEC). This forms an important tool for characterising the ionosphere. 3.4 Satellite based systems for ionospheric studies Depending upon the basic functionalities for which they have been launched, satellites fall under the category of military/ defense, communication and navigation. For the ionospheric propagation studies conducted so far, major contribution comes from data collected with navigation satellites as said by Hunsucker [1991], Maini and Agarwal [2007] and Ilyushin [2008]. These satellites were launched initially to aid the navigation by determining their position location and as such involved direct reception at the location/ ship. This direct reception of the transmitted radio signals from the satellites effectively pointed to propagation studies of the ionospheric medium. Satellite-Based Systems have the following advantages over ground system for ionospheric studies. They transmit signals that can be "seen" over a far larger area than groundbased systems. 25

8 With the appropriate technology they can transmit signals through cloud and rain, and can be used day or night. They recognise no national boundaries, and hence can be used globally wherever they are visible, on the ground, in the air and at sea. Satellites are tamperproof. For most national authorities, there is no investment in the necessary space hardware. Remote sensing gives variety of possibilities for imaging. Usage of satellites for observing propagation parameters of radio waves helps to make measurement from sources beyond the ionosphere. Signals can be observed over far larger area than ground based systems, simultaneous observation from different ground stations are, possible which improves the validity of results. Depending on their altitude and elevation above the Earth s surface, satellites are classified into three as per Maral et al [2009]: LEO, MEO and GEO satellites. LEO satellites orbit the Earth between km altitudes and will be visible for minutes only above any particular location on Earth. They have a typical orbital time of about 90 to 120 minutes. In order to provide global coverage for navigation, a large number of satellites are required. The advantages of LEOs are lower launch costs and less propagation delay and less free-space losses when compared to other satellite configurations. The disadvantages are orbital perturbations due to atmosphere drag and hence low predicted life time and high Doppler rates due to their motion. LEO satellite systems find major application in providing real time voice and data communications globally. These satellites were also the ones primarily used for navigation around twenty years before and which are now the chief contributors to the ionospheric studies. These also include military intelligence and weather satellites. 26

9 Satellites in the LEOs are further classified into Polar orbiting satellites, if their orbital inclination is near 90 Equatorial satellites, with inclination less than 20 Sun-synchronous satellites, having fixed equatorial crossing time every day MEO satellites orbit the Earth between km with 2-4 revolutions round the earth per day. They are more stable though the launch costs are higher than LEOs. As they travel slowly, they are visible for approximately 2 to 6 hours in each pass. These satellites can be arranged in constellation so that at least four are visible from any point on the Earth s surface at any time. Present GPS satellites fall under this category. They are primarily used for obtaining precise location measurements anywhere on Earth and thus provide more accurate information for navigation. The data from these satellites is also useful for ionospheric studies, through the measurement of TEC. GEO satellites orbit the Earth at a fixed distance of km and cover 1/3 rd of the earth s surface at a time. Thus three satellites positioned approximately 120 apart can cover the entire globe. These systems are used for two-way voice, data and video services as well as to provide fixed services to particular region. Their major disadvantage is the higher launch costs. They cannot provide line-of-sight communication in urban areas and mobile applications. These satellites include commercial and military communications satellites and satellites providing early warning of ballistic missile launch. Satellites in geostationary orbit appear stationary from a fixed location on Earth since their period of revolution is the same as that of Earth. Hence a coherent beacon transmission from such a system will be able to yield short term variations of the Earth s ionosphere over that region. A configuration of these orbits above Earth is shown together in figure

10 Figure 3.3 Pictorial representation of Satellite orbits (Source: Satellite system elements Satellites function as "orbiting control stations. In order to track a satellite transmitter, the ground receiver must be equipped with the basic details of the satellite motion, like its time of arrival and exit over the horizon, its elevation and azimuth location above the ground location etc, so that pass schedules can be computed. The most important component useful for this is the satellite ephemeris. Satellite ephemeris gives a position of astronomical objects in the sky and can be considered as a chronologically arranged collection of state vectors indicating their position with respect to a reference co-ordinate system. This ephemeris is used as observations to fit a Two Line Element (TLE) set using standard computer programs. The TLE is a data format used to convey sets of orbital elements that describe the orbits of Earth-orbiting satellites. From this, there is executable software available for computing the satellite pass schedules above any location on Earth. 28

11 The *.TLE files are structured with data consisting of a satellite name (24 characters long) and a standard NORAD two-line element set. The TLE data for each satellite consists of three lines in the following format: A sample TLE set for satellite Oscar 23 is shown below. Line 0 is a twenty-four character name. Lines 1 and 2 are the standard Two-Line Orbital Element Set Format consisting of two 69-character lines of data which can be used together with NORAD's SGP4/SDP4 orbital model to determine the position and velocity of the associated satellite. The only valid characters in a two-line element set are the numbers 0-9, the capital letters A-Z, the period, the space, and the plus and minus signs. A description of the two-line element format as explained in the website of Prof. T S Kelso, is given in Table 3.1. Table 3.1 Two-Line Element set format definition Field Column Description Line Line Number of Element Data Satellite Number Classification International Designator (Last two digits of launch year) International Designator (Launch number of the year) International Designator (Place of the launch) Epoch Year (Last two digits of year) Epoch (Day of the year and fractional portion of the day) First Time Derivative of the Mean Motion Second Time Derivative of Mean Motion (decimal point assumed) BSTAR drag term (decimal point assumed) Ephemeris type Element number Checksum (Modulo 10) (Letters, blanks, periods, plus signs = 0; minus signs = 1) 29

12 Line Line Number of Element Data Satellite Number Inclination [Degrees] Right Ascension of the Ascending Node [Degrees] Eccentricity (decimal point assumed) Argument of Perigee [Degrees] Mean Anomaly [Degrees] Mean Motion [Revs per day] Revolution number at epoch [Revs] Checksum (Modulo 10) The elements in the two-line element sets are mean elements calculated to fit a set of observations using a specific model the SGP4/SDP4 orbital model and is not a single method of conversion. Accuracy of the TLE sets is dependent upon a number of factors like the sensors used onboard, amount of data collected and type of orbit and condition of the space environment. 3.6 Ionospheric parameters from satellite based observations As mentioned above, one of the major ionospheric parameter that can be studied with a satellite based transmitter is the TEC as reported by several works including Kane [1975] and Kersley et al [2004]. This is a derived parameter indicative of the electron density or number of electrons along the ray path from the satellite to the ground, in a cross- sectional area of 1 m 3. This parameter is also dependent on the incident solar radiation, so that over any location on earth, the night-time TEC is lower than the day-time values. Thus, the TEC above a particular spot on the Earth has a strong diurnal variation as reported by Jakowski et al [2011] among various others. The changes in TEC can also occur on much shorter time scales. There are also seasonal variations in the TEC and the variations that follow the Sun s 27- day rotational period and 11 year solar activity cycle. Hence a continuous study of TEC is an absolute must in order to develop a better universal ionospheric model. 30

13 Yet another major parameter is the scintillation index, which is also derived from the fluctuations observed in the amplitude of the radio wave passing through the ionosphere. The same receiver system can be made use of to study both the TEC and scintillation index, this provides an added advantage Genesis of satellite based systems for ionospheric studies On 1 January 1997, the Navy Ionospheric Monitoring System (NIMS) took birth as the first proper satellite system which can be used globally to study ionosphere. The NIMS had its origin as the Transit satellite, which were actually launched for navigational purposes. The satellites in the Transit series are being used as dualfrequency beacons by ground collection sites to determine the free electron profile of the ionosphere as detailed by William H. Guier [1998]. The current Transit constellation consists of six Oscar satellites located in three planes, with two satellites per plane. Each satellite can transmit signals at 150 and 400 MHz at either -80 ppm (operational) oscillator offset or -145 ppm (maintenance) oscillator offset. The first Transit satellites transmitted signals at four frequencies: 54, 162, 216, and 324 MHz. Simultaneous measurements of all four signals provided experimental data to evaluate ionospheric effects as a function of frequency. These data were limited in duration and global location. To further observe ionospheric effects throughout a solar cycle and at selected global locations near the magnetic equator, two NASA beacon exploration satellites collected additional data in the mid-1960s. Those measurements supplied experimental data that were used to verify assumptions about ionospheric effects and characterize the magnitude of the residual ionospheric effect for the navigational and geodetic positioning error budget as explained by Robert J Danchik [1998]. The final design of Transit was based on a two frequency method for correcting ionospheric error; at 150 and 400 MHz, where the first-order ionospheric effect dominated, and all higher-order effects were negligible. These latter effects are caused by the bending of the signal path of each signal and the difference in phase velocity between each path. The dual-frequency signals from the Transit satellite yield real-time measurements of the changes in total electron content (TEC) between the satellite and receiver. 31

14 With simultaneous data from various ground stations, computerized tomography was proposed as a method of imaging the ionosphere in In the early 1990s, this new technique began being used in experiments to provide a more complete mapping of the ionosphere. It means by using an array of receivers and collecting data over a large angular aperture, the number density can be reconstructed from the data. Called computerized ionospheric tomography (CIT), it applies medical tomographic methods to the study of the ionosphere. CIT provides a powerful tool to address the spatial variability of the ionosphere. The advantage of tomography technique is that it can give a snapshot picture of the latitude-altitude variation of the ionosphere, using data from a chain of ground receivers, by recording the coherent beacon signals from a low-earth orbiting satellite. This technique has been widely used to study the large-scale structures of the ionosphere. This is an area where extensive research is still carried out. Some of the studies reported include Andreeva et al [1992], Andreeva [2000], Kersley and Pryse [1996], Raymund et al [1994], Kunitsyn and Treshchenko [1994], Yeh and Raymund [1991] and Materassi et al [2003]. The primary data for the tomographic inversion is the line of sight TECs estimated along a number of ray paths from a chain of ground receivers aligned along the same longitude. These TECs are then inverted to obtain the electron density distribution as a function of latitude and altitude over a given longitude. The schematic geometry of the CIT for data collected over minutes with the receivers spaced ~1000 km apart is shown in figure 3.4. Figure 3.4 Pictorial representation of the satellite-receiver geometry for CIT 32

15 With the development of CIT techniques, the satellite portion of Transit continues to serve as an instructional tool for a more complete understanding of the processes that exist in the ionosphere TEC studies with satellite systems Since the advent of artificial satellites in 1957, at least five different techniques have been exploited to provide a measure of the integrated electron concentration or the total electron content. They are Faraday rotation, Doppler shift, group delay, dispersive phase, and elevation angle of arrival. Early comparison of these various techniques, especially the first two or three, can be found in the works by Garriott and de Mendonca [1963] and Rao and Yeh [1968], while the last technique is discussed by Garriott et al [1970], Bramley [1974] and later on by Davies [1980, 1989]. All these experimental techniques can be used to measure the total electron content from the ground observer to the satellite along an oblique straight-line path. The number of free electrons in a column (defined as of unit cross-sectional area) from the satellite (S) to the receiver (R) is the slant TEC along the path. This TEC can be determined from the differential phase of dual-frequency satellite transmissions as explained by Davies, [1989], but in that case it contains an unknown constant, c, because of the unknown number of differential phase cycles at the start of the measurement. This measured TEC is related to the true slant TEC by (3.1) where y s is the measured TEC along the path, N is the electron density, ds is the differential distance along the path between the satellite and receiver and c is an unknown constant. Simultaneous TEC data from polar-orbiting satellites recorded by multiple groundbased receivers were first used for developing tomography algorithms. A comparison of different methods in this regard has been reported by Raymund [1995]. The satellites are of LEO type, in either the Russian Cicada system or the Navy Navigation Satellite System (NNSS) that later became known as the Navy 33

16 Ionosphere Monitoring System (NIMS). They transmit two coherent frequencies at nominal values of 150 and 400 MHz. Owing to their LEO orbit the ionosphere can often (but not always) be considered temporally static during a satellite pass. The tomographic method used above is called ray tomography, which addresses the evolution of large scale ionospheric structures. GEO satellite based beacon systems, which came next, used amplitude modulated 150 and 400 MHz and a new tomographic technique called diffraction tomography evolved, with triangulation mode of simultaneous data collection. This technique aimed to address the continuous evolution and properties of small scale structures, assuming the ionosphere variations are static over the stations located at < 100 km apart. Later, the development of global, three-dimensional, time-varying tomographic algorithms made use of the GPS constellation of satellites as data sources according to Kintner and Ledvina [2005] and Gary Bust and Cathryn Mitchell [2008]. The GPS satellites are at an altitude of ~20,000 km and transmit at frequencies of ~1.2 and ~1.6 GHz. With GPS, true 3-D time-evolving tomographic imaging becomes possible. Thus this can be attributed to the spread spectrum modulation technique that is prevalent in the GPS systems. Ionospheric imaging of the electron density provides snapshots of the global plasma structure and its temporal evolution, since electron density is considered the most important parameter from the applications perspective as it governs all of the effects on radio signals. Measuring changes in the ionosphere through changes in the electron density is central to understanding the solar-terrestrial environment impact on communication, surveillance, and navigation systems here on Earth. Ionospheric imaging involves using integrated measurements of electron density or TEC to produce two-, three-, and maybe future four-dimensional maps of electron density. 3.7 Methods of TEC measurement It is to be understood that any electromagnetic wave from a satellite passing through the Earth s atmosphere undergoes two significant refraction effects, caused by the ionized and un-ionized portions of the Earth s atmosphere. The ionospheric 34

17 refraction effects on the Doppler signal, caused by the ionized part of the upper atmosphere, are a function of the transmitted frequency. For large (>100 MHz) transmitted frequencies f, William Guier [1998] showed that the Doppler shift D f as measured at the ground site can be written as Δ.. (3.2) where dρ/dt is the geometric range rate; c is the velocity of light; a 1 is proportional to the time derivative of the total electron content along the geometric slant-range vector from station to satellite; a 2 depends on signal polarization and on the magnetic field component in the direction of travel of the signal and is typically 1% of a 1 and a 3 has several components and involves, among other effects, the difference between the signal path and the slant-range vector. Here, the first-order effect is the largest. By transmitting two phase-coherent signals at different frequencies, this first-order term can be eliminated by combining the signals. The various common methods used for TEC measurement has been reported in detail by Davies et al [1976, 1977]. The ones referred to in this work include Differential Doppler method, Faraday Rotation method and Group Delay method. The following section details the mathematical derivation of TEC from each of these methods Differential Doppler method In the ionosphere, the phase velocity of propagation of an electromagnetic wave is more than the free space velocity of light. This is essentially due to the wavelength in the ionosphere being larger than in free space, with the frequency remaining the same (in the absence of Doppler shift). This results in the phase path between the satellite and the ground receiver to be less than free space value. Consider a ground- based receiver, monitoring a satellite radio-wave transmission at frequency f from satellite. The wave passes through the medium of propagation, i.e., ionosphere of relative index μ, where 1 (3.3) 35

18 in which N is the electron density and K is a constant equal to / 4, where e is the charge on an electron, the permittivity of free space and m e the electron mass. The total phase path, P from the satellite S, to receiver, R is (3.4) in which s represents the path from satellite to receiver. The differential of P with respect to time is (3.5) The frequency monitored at the ground, f r is different from that transmitted at the satellite because of a Doppler shift. This frequency shift, as given by Vorob ev and Krasil nikova [1994] is f r -f, where f 1 P (3.6) and λ is the wavelength of the transmitted signal in free space. Substituting for dp/dt gives f 1 2 (3.7) which separates out the two components of frequency shift, the first due to the motion of the satellite relative to the receiver and the second due to the ionospheric refraction effect. Suppose a satellite transmits two frequencies designated as f 1 and f 2 respectively. For the NIMS satellites these are approximately 400 MHz and 150 MHz, the second frequency being precisely 3/8 of the higher one. The frequencies observed at the receiver, f 1r and f 2r, would then be. (3.8) 36

19 . (3.9) where λ 1 and λ 2 are the free space wavelengths of the two transmitted radio waves. Subtracting one frequency from the other and integrating with respect to time now gives the differential phase, (3.10) Substituting yields (3.11) From this integral, it is understood that the term due to satellite motion gets cancelled as the frequencies are coherent and the effective change in frequency is dependent on the number of free electrons in a column (defined as of unit crosssectional area) from the satellite to the receiver. As 3f 1 = 8f 2 and 8λ 1 =3λ 2, the above equation becomes.. (3.12) Now, substituting for f 2 = (3/8) f 1 in equation (3.12),. (3.13) Substituting for the slant total electron content (TEC) defined by. (3.14) in equation (3.15) gives, (3.15) 37

20 where c is the constant of integration. Therefore (3.16) in which ψ 0 = -C and Faraday Rotation method Under quasi longitudinal condition and under the assumption that there is no coupling between the two characteristic modes and that there is no absorption, the total angle of polarization as seen from the figure 3.5 reproduced from Ramarao [2004], can be given by the following equation. Ω Ω Ω (3.17) where is the angle of rotation of the ordinary wave vector, and is the angle of rotation of the extra ordinary wave vector. Figure 3.5 Rotation resultant of two oppositely rotating vectors of equal amplitude and different velocities about the direction of propagation For a distance of one wavelength λ, the rotation of a component vector is 2π. Hence the rotation in radians for unit distance is and therefore, Ω (3.18) 38

21 Ω (3.19) where S is the distance from transmitter (in the satellite) to the receiver (at the ground) and λ + is the wavelength of ordinary wave, λ - is the wavelength of extraordinary wave. Substituting equations (3.18) and (3.19) in (3.17), we get Ω (3.20) i.e., Ω 0 (3.21) where and μ + and μ - are the refractive indices of the ordinary and extra- ordinary waves respectively and λ 0 is the free space wavelength. In order to get the value of (μ + - μ - ) i.e., to get the value of Ω, we have to consider the Appleton- Hartree equation for the complex refractive index of an ionized medium with the external magnetic field present. The Appleton- Hartree formula for the complex refractive index, as detailed in Davies [1989], is given by 1 (3.22) where X, Y and Z are the magnetic parameters (reduced frequencies) defined as, and where is the square of the angular plasma frequency and is given by 2 (3.23) is the gyro magnetic angular frequency and is given by 2 (3.24) 39

22 The components of are and where and (3.25) (3.26), and, n is the complex refractive index (µ - iχ) is the absorption index is the angular frequency of the propagating wave is the frequency of collision of electrons with heavy particles N is the number density of electrons B 0 is the flux density μ 0 is the magnetic permeability of free space is the electric permittivity of free space and θ is the angle between wave normal and the direction of the magnetic field. All the parameters are in rationalized MKS units. For the propagation of high frequency radio waves through the E and F- regions of the ionosphere, collision frequency is usually very small and therefore, and can be neglected. Then 1 (3.27) Multiplying and dividing the second term of RHS of the above equation with 2(1-X), the expression reduces to 1 (3.28) Therefore, the two refractive indices for the ordinary and extra-ordinary waves as 40

23 1 1 (3.29) (3.30) (3.31) i.e. (3.32) For frequencies much higher than the plasma frequency, the refractive indices are very close to unity. So (μ + +μ _ ) can be approximately taken as 3. Hence the above equation becomes (3.33) If the wave normal lies in the magnetic field (θ = 0), then Y L = Y and Y T = 0 and the equation (3.33) will be considerably simplified. Even if θ 0, a good approximation to μ + may be obtained by taking Y T = 0, this is known as the Quasi- Longitudinal approximation, and it generally holds for high frequency waves in the ionosphere, provided is not around unity and θ is not around 90. The actual condition for the validity of quasi- longitudinal approximation is 1 Applying the quasi- longitudinal approximation to equation (3.33) we get (3.34) Substituting this value in equation (3.21) for Ω, we get Ω (3.35) But, 41

24 Ω (3.36) Since the frequency (HF and VHF) is much higher than the gyro- frequency, f H i.e. f >> f H, equation (3.36) can be written as Ω cos (3.37) where and is a constant. Thus the relation of the plane of polarization is proportional to the path length (S) the electron density(n) the strength of the imposed magnetic field (H 0 ) the inverse square of the wave frequency (1/f 2 ) In the above derivation for Ω, it is assumed that the electron density and the magnetic field (strength and direction) are constant over the integrated path. When these parameters vary along the path, the equation for Ω must be replaced by their integral form. Ω. (3.38) Ω.. (3.39) 42

25 In the above equation, the assumption of QL condition contributes to the factor cosθ. If Ψ is the angle made by the radio beam with the zenith, then from figure 3.6, the element of the path length ds, is Ψ Ω.. Ψ. (3.40) where h is the height of the satellite. Figure 3.6 Diagram showing the relation between dh and ds. Ψ is a geometrical factor involving the earth s magnetic field and is known as the magnetic field factor (M). Since M varies slowly with height as referred by Ramarao [2004], Rao and Yeh [1968], it is possible to assign a weighted mean value to it, and can be expressed as Ω. (3.41) In the above equation, is the total electron content (TEC) of the ionosphere in a vertical column of unit cross-section. or.. Ω

26 where is given by It was shown by earlier works like Garriot et al [1970] and Davies et al [1976] that for VHF propagation and for high elevation angles, the refraction is negligible. Thus the electron content N T can be computed by measuring the Faraday rotation angle Ω by using the relation. Ω (3.44) where f is in Hertz, Ω is in degrees, is in Tesla. According to Royden et al [1980, 1984], this method was the first one used to calculate interplanetary distances as well as for calibration of TEC calculated with other methods Modulation Phase Delay (group delay) method In the absence of any ionization in the intervening medium an electromagnetic wave travels with the velocity of light between the satellite and ground. The presence of ionization decreases the group velocity of propagation, with the result that a modulated wave from a satellite takes longer time to reach the ground if the medium in between is ionized. This increase in travel time t, over the free space travel time can be written as 1 (3.45) where μ is the group refractive index in an elemental ray path ds and C the velocity light in free space. Substituting for μ as (3.46) where N is the electron density (m -3 ) in the elemental ray path ds and f is the frequency transmission(hz). An idea of the magnitude involved can be obtained from the following considerations. The slant range of ATS-6 satellite at 35 E longitude from 44

27 Trivandrum was km. A radio wave, takes about 123 milliseconds to travel this distance in free space. Assuming a value of Nds = 5.0 x el m -2, which is about the minimum value that will be encountered at any time, t can be calculated to be μsec and 0.85 μsec for 140MHz and 40 MHz frequencies respectively. Assuming Nds= 5.0 x el m -2 which is about the largest value that was observed, over the equator, during sunspot maximum period, t becomes13.76 μsec for 140 MHz transmissions and 169 μsec for 40 MHz. The corresponding apparent range increase are 4 km for 140MHz signal and 50.7 km for 40 MHz. Incidentally it may be noted that the range accuracies considered necessary for navigational purposes, using beacon transmission in the VHF band is about 150 meters. This calls for a correction of the range due to ionospheric electron content along the ray path. This time delay if measured accurately gives directly the TEC. This time delay can be measured by modulating the carrier with an accurately known frequency. An amplitude modulated wave modulated by a carrier angular frequency ω c and modulating angular frequency ω m and radiated from a satellite, can be written as (3.47) where A c and A m are the carrier and modulation amplitudes respectively and θ c and θ m are the initial arbitrary phases of the carrier and the modulation respectively. Equation (3.47) can be written in terms of the spectral decomposed form as cos 2 2 (3.48) These three components as received on ground have their general phase relation as (3.49) where μ is the phase refractive index at a point along the ray path element, λ the free space wavelength corresponding to angular frequency ω and θ the initial arbitrary phase. The integration is carried out along the ray path. From magneto- ionic theory, 1 (3.50) 45

28 where K = 80.6 in MKS UNITS N = Electron density in electrons per m 3 f = operating frequencies Hz Substituting equation (3.50) in the general phase relation of equation (3.49), (3.51) where R is the slant range of the satellite from the receiver and c the velocity of the light. The phase relations for the carrier and the upper side band can be written as (3.52) (3.53) The modulation phase (3.54) If we have two frequencies, f and f R, which are far apart like 150 MHz and 400MHz, both amplitude modulated by the same modulating frequency f m (say 1 MHz) with the same initial phase θ m, we can use Φ R m the phase of the modulation on 400MHz as the reference, with respect to which the modulation phase φ f m of 150MHz can be measured. Thus (3.55) where is a constant for given f, f R and f m and is given by (3.56) 46

29 Taking the example of f = 150 MHz, f R = 400 MHz and f m = 1MHz, change of of 360 degrees implies the additional group delay of 2μsec introduced by the ionosphere on 150 MHz compared to the delay on 400MHz. 3.8 Comparison of earlier and existing satellite systems for TEC measurement There are various methods of measuring the TEC of ionosphere using satellites, as has been briefed in the previous section. The most popular and the earliest of these techniques is the use of Low Earth Orbiting satellites. These satellites were conceived and launched as navigation satellites to aid primarily ship-based navigation. Later on, it was understood that these signals themselves can be made use of for ionospheric studies, as mentioned in the series of reports from APL, who were the pioneers in navigation systems as explained by Robert J Danchik [1998]. All these satellites had a pair of coherent radio frequencies, one at VHF and other at UHF, which were received by the ground stations. Although Faraday rotation measurements was the first mode of receiving signals from outer space and even stars, the differential doppler method of TEC measurement became the popular one. Data received from a LEO satellite would include both the satellite Doppler and the ionospheric changes, recorded in the receiver as a phase change. Knowing the satellite Doppler, it is possible to remove this so that the ionospheric contribution can be segregated. A network of stations operated for such simultaneous measurement from these satellites use first order approximation to calculate ionospheric electron density. For a geostationary satellite, the differential Doppler signals depend upon the time rate of change of TEC and there will be a large ambiguity in the total number of cycles of phase difference along the path. In this case, it is preferable to measure the group delay or differential phase P between identically modulated signals. All ambiguity is currently resolved by using two widely spaced carriers. Also since long and continuous data can be obtained in such cases, this can throw light on various other ionospheric phenomena also. Hence both the differential doppler measurements and modulation phase delay measurements are useful from a 47

30 geostationary satellite beacon. The CRABEX (Coherent Radio Beacon experiment) payload flown onboard GSAT-2 of ISRO was developed for this and it also included Faraday rotation measurements. Observations with geostationary satellites are on the basis of the absence of any appreciable motion of the sub ionospheric point. Using a network of stations spread over a limited a geographic area, it is possible to reconstruct the large scale horizontal variation in the ionosphere structure. This has been attempted by Mendillo and Klobuchar [1975] with observations from ATS-6 satellites. Thus it is seen that the data from geostationary beacon satellites allow the monitoring of time changes in the ionospheric TEC under nearly constant geometrical conditions whereas with the data from LEO beacon satellites, spatial changes of TEC can be got, though the period/timescale of observation is short compared with timescales for ionospheric processes. A newer approach to measurement of TEC comes with the use of GPS systems. In 1973 the US Department of Defense decided to establish, develop, test, acquire and deploy a space borne Global Positioning System (GPS). The result of this decision is the present NAVSTAR GPS (Navigation Satellite Timing And Ranging Global Positioning System) as reported by Hoffman [1992]. The GPS is proved to be allweather, space- based navigation system. The primary goal for developing the GPS was of military nature. The multipurpose usage of NAVSTAR GPS has developed enormously within the last three decades. GPS is aimed to have a universally accessible air navigation safety communications, which is also immune to harmful interferences. These satellites are positioned at Medium Earth orbit i.e., at a height of ~20000 km and transmit dual frequency signals which are spread spectrum modulated. In order to overcome the ambiguity associated with LEO system measurements, the dual frequency carrier phase and code delay observations are combined to obtain ionospheric observables related to the slant TEC along line of sight. The GPS receiver processes the L- band signals transmitted from the satellites to determine user, position, velocity and time (PVT). The user equipment generates the pseudo range measurement by tracking the satellite navigation signal by generating identical code of the transmitted signal. The measured transit-time includes the 48

31 travel time between the satellite vehicle and receiver and the clock bias. The GPS satellites being in Medium Earth Orbit also require tracking through ephemeris. The satellite ephemeris is sent along with the navigation message and is available to all the users. The GPS receivers are built to receive more than one satellite at any given time, since the coding scheme used is spread spectrum. Also, as the duration of visibility of each satellite is ~2 hours, it can be considered that there is continuous data available as there are a large number of satellites. But there are clock errors which play an important role in the measurements. A tomographic inversion problem with simultaneous data from different stations also needs to address the second-order and higher order approximations of the ionospheric variability in order to yield better results. The various satellite configurations useful for ionospheric measurements are brought out in Table 3.2 below. 49

32 Table 3.2 Comparison of satellite configurations useful for ionospheric studies Type of satellite GSAT (CRABEX LEO (OSCAR, payload onboard COSMOS, RaBIT) GSTA-2) MEO (GPS) Transmitter Two spread Two coherent Two coherent carriers spectrum modulated carriers modulated as SSBSC signals Polarisation of transmitted signals LHCP mostly Linear RHCP Frequency of operation VHF,UHF (150, 400 MHz) VHF, UHF (149, 150, 399, 400 MHz) L-band (1575 and 1227 MHz) Receiving antenna Crossed dipole Yagi/parabolic dish Patch Differential Doppler, Methods of TEC measurement Ionospheric parameters derived Disadvantage Requirement for tomographic studies Type of tomography Data availability at ground station Differential Modulation phase Doppler delay, Faraday Differential Doppler rotation Relative TEC Absolute TEC, PEC Absolute TEC 2nπ ambiguity Huge launch and maintenance costs Clock errors Receiver stations Receiver stations Three receiver placed along the networked close together to longitudinal track longitudinally and form a triangle of satellite, latitudinally, (Spaced receiver separated at ~ 200- separated at ~500 technique) at <50 km 500 km km Ray Diffraction Ray Duration of the satellite pass, i.e., Almost continuous minutes Continuously with large number of per pass with 3-4 satellites good passes per day 50

33 3.9 Summary Satellite beacon experiments have been used for ionospheric studies since the early eighties. Though most of these satellite payloads were launched initially for navigation purposes, they proved to give useful data for understanding the medium through which they traverse. The TEC measured along the ray path from the satellite vehicle to the ground receiver thus attained importance as the chief parameter that can give a good handle on the ionospheric structure and variations. Three different techniques of TEC measurement are detailed here Differential Doppler, Faraday rotation and Modulation Phase Delay (group delay). The method of Differential Doppler for TEC measurement still remains the popular technique and is used with LEO, MEO and GEO satellite beacon systems. The other two techniques have been used in geostationary beacon systems only. 51