The earth’s ionosphere acts as a perturbing medium on satellite-based navigational systems like GPS. Two propagation effects are very prominent: 1) range error due to the group delay of the signal in travelling through the ionosphere, and 2) phase and amplitude scintillations caused by irregularities in electron density distribution. The group delay is directly proportional to the ionospheric Total Electron Content (TEC). One unit of TEC i.e. 1×10 16 el/m^2 introduces a range error of 0.16m at the L1 1.6GHz frequency of GPS. As far as the TEC is concerned, the region located about ±30 0 dip around the magnetic equator has two very pronounced features. Nearly one-third of the total global ionization is concentrated within this narrow belt around the magnetic equator. During daytime and early evening hours, there is a systematic variation of maximum ionization (N m F2) with latitude. This feature, known as the Equatorial Anomaly, is characterized by two crests around ±30 0 dip and a trough at the magnetic equator. The anomaly extends in the topside ionosphere also, the separation between the crests decreasing with altitude. As a result, the Total Electron Content which is the sum of the ionization along a path through the ionosphere exhibits features similar to that of the N m F2. Beyond the crests of the anomaly, there is a sharp transition from a very high value of electron density or TEC to a low value in the mid-latitudes [Klobuchar et al, 2001 and references therein]. The equatorial anomaly has been explained in terms of the “Fountain Effect” [Appleton, 1946; Hanson and Moffet, 1966] due to the electrodynamic ExB drift of ionization over the magnetic equator and its subsequent distribution along the magnetic field lines. The electrodynamic drift depends on many factors like the local time, season, solar and geomagnetic activities.
The Indian subcontinent essentially covers the equatorial zone in the South-Asian longitudes, with the magnetic equator touching the southern tip of the peninsula near Trivandrum. The equatorial anomaly crest roughly lies around the line joining Calcutta and Ahmedabad. Locations like Delhi are situated north of the above line in the equatorial-mid-latitude transition zone. An estimate of the range error introduced by the ionosphere in the equatorial zone is thus very difficult. The low-cost stand-alone single frequency standard precision GPS receivers normally employ the Klobuchar model of the ionosphere for correction of the ionospheric group delay. This and other models used so far are empirical in nature and are based on TEC data measured at several locations in the mid-latitudes, mostly in the American and European zones. Data from the equatorial stations are sparse and are mostly from the South American sector. The validity of these models in the equatorial region, particularly the Indian longitude sector, is yet to be tested. All the available TEC models are climatic in nature. For operation of navigational systems with accurate estimates of error, real-time data on TEC have to be provided.
The error due to the group delay is normally taken care of in differential GPS (DGPS) by measuring the difference between the observed pseudo range and the geometrical range from a reference location whose position is accurately known. The error data are transmitted to users in the neighborhood of the reference station. Because of the effects described above in the equatorial zone, the range over which the error data are valid from a reference station is limited. An extension of the DGPS is the Wide Area Augmented System (WAAS). In WAAS, a number of reference stations distributed over a large area like continental US (CONUS), Brazil, Chile, Argentina, European continent (EGNOS), Japan or India will monitor TEC data. A 5 0 x5 0 grid has been suggested for the separation between reference stations. In this case, TEC values along different paths of available GPS satellite links from reference stations are measured. From the measured Slant TEC, an estimate of TEC in the vertical direction over this 5 0 x5 0 grid has to be generated. An user like an aircraft gets the above information from reference stations via a geostationary satellite. The equivalent Vertical TEC data are then used by the GPS receiver in the aircraft to estimate the group delay errors in the slant paths from the aircraft to the GPS satellites. The problem thus essentially translates into conversion of the recorded Slant TEC data from reference stations to equivalent Vertical TEC values and the reverse process from the equivalent Vertical TEC to Slant TECs.
In the mid-latitudes, where the TEC normally shows a smooth spatial variation, this conversion can be performed in terms of geometrical (Secc, where c is the zenith angle) parameter. In the equatorial zone, in view of the large gradients of TEC and its variability with geophysical conditions, a simple geometrical conversion is not possible. This paper presents studies of some problems associated with conversion of Slant TEC into equivalent Vertical TEC and vice versa. TEC data measured by the Faraday Rotation technique from Calcutta, a station situated virtually under the northern crest of the equatorial anomaly in the Indian zone is compared with those derived from the widely used Parameterized Ionospheric Model (PIM1.6).
Ionospheric TEC has been measured by the Faraday Rotation technique at Calcutta (Lat: 22.58 0 N Long: 88.38°E; Dip: 32°N) during 1977-1990 by monitoring the plane polarized VHF signal at 136MHz from the Japanese geostationary ETS-II (130 0 E). The equivalent Vertical TEC have been calculated by using the formula
NT = W f2/kM
where W is the amount of Faraday Rotation suffered by a linearly polarized wave transmitted by the satellite in its traversal through the ionosphere,
f is the signal frequency,
M = òNHcosqsecc/òNdh is the weighted magnetic field factor,
N is the electron concentration,
H is the earth’s magnetic field,
q is the angle between the direction of ray and the magnetic field,
c is the ionospheric zenith angle,
k = 2.97×10-2 (in M.K.S. unit) is a constant.
The Slant TEC is obtained by multiplying the equivalent Vertical TEC by the geometrical factor Secc. With PIM, both the equivalent Vertical and Slant TEC along the path of ETS-II have been computed by integrating ionization in layers of 20km thickness.
Figure 1 shows the diurnal variation of the mean equivalent Vertical TEC in different seasons during the peak of the 21 st solar cycle in 1979. It is observed that the model consistently overestimates the TEC values, particularly during the autumnal equinox of 1979, when the sunspot number reached a peak value of 172. However, signatures of the persistence of high electron content in the post-sunset hours of equinoctial months present in the form of “humps” known as secondary maxima in the observed data are reproduced in the model plot. There is quite a good correspondence between the actually observed data and PIM values in the late night and early morning hours. In low sunspot number years, the absolute values of TEC are less and the match between the observed and model values are quite close, particularly during May-July months.
Figure 2 shows the variation of Slant TEC with time. The observed values are translated from equivalent Vertical to Slant TEC by simple multiplication with the geometrical factor Secc. For the model values, the ionization along the path of ETS-II are integrated in the altitude range 90-1600km for layers of thickness 20km and the result is referred to as the Path Integrated (PI) Slant TEC. It is observed that the difference between the actual observations and the model computations still persists, but to a smaller extent. The distinction between the simple Secc multiplied Slant values and the Path Integrated Slant values, both obtained from PIM, are well illustrated in Figure3. It is observed that although the basic nature of variation of electron content is the same in both the cases, the Path Integrated values offer a better alternative as they overestimate the actual observations to a less extent. Figure 4 shows the relation between the measured seasonal mean equivalent Vertical TEC averaged over the local time interval of 11-16hrs and the corresponding sunspot number during the period 1978-1985. The values in summer and winter follow a trend similar to the sunspot number. During the equinoxes the satellite was eclipsed and there were large data gaps. Although the minimum value of electron content remains almost the same irrespective of solar activity, the maximum ranges from 114 TEC units during 1979 to 29 TEC units in 1985.
A comparison of the electron content measured from the plane polarized beacon transmission from the Japanese geostationary satellite ETS-II with the values generated from the Parameterized Ionospheric Model (PIM1.6) do not yield satisfactory results for the equatorial region, particularly during the afternoon hours of equinoctial months in high solar activity years. PIM, which is a fast global ionospheric and plasmaspheric model, produces electron density profiles between 90 and 25000km altitude, corresponding critical frequencies and heights for the ionospheric E and F2 regions and TEC for specified geophysical conditions. This model which predominantly uses data from the American and European longitude sector as its data base exhibits significant deviations from the observed data even during the summer months of 1979, a high solar activity year. The presence of large spatial gradients of TEC in the equatorial region coupled with its variability under different geophysical conditions renders simple geometrical conversion of equivalent Vertical TEC to Slant values unreliable. Even with the Path Integrated Slant TEC values, there are wide differences between the actually observed electron content and the model computations. The result reflects the fact that climatic models like PIM are unable to properly represent the dynamic nature of the equatorial plasma transport processes and do not account for the variability of the sharp spatial gradients of ionization in this region. It is also observed from ground-based measurements that while the ratio of maximum TEC varies by a factor of 4 in the equatorial region, its variation in the mid-latitudes is greater. PIM uses some input parameters, like electrodynamic drift obtained from observations made in the western hemisphere. The validity of these parameters around the present location in the equatorial region, particularly the Indian longitude sector, is to be further examined.
- Appleton, E.V., Two anomalies in the ionosphere, Nature, 157, 691, 1946.
- Hanson, W.B. and Moffet, R.J., Ionization transport effects in the equatorial F-region, J. Geophys. Res., 71, 5559, 1966.
- Klobuchar, J.A., P.H. Doherty, A. DasGupta, M.A. Sivaraman and A.D. Sarma, Equatorial anomaly gradient effects on a space-based augmentation system, Proc. International Beacon Satellite Symposium, Boston (USA), 2001.