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Ionospheric total electron content and WAAS in the Indian zone  A. DasGupta, A. Paul & S. Ray Institute of Radio Physics and Electronics University of Calcutta Calcutta adg1bkpr@hotmail.com ashikp@cucc.ernet.in
Introduction
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. 1x10 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). Data 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 = 2.97x10-2 (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. Results 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 1
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