This paper reports results from an investigation into possible total electron content (TEC) on ray paths between GPS satellites and satellites in geostationary orbit. The Sheffield University Plasmasphere Ionosphere Model (SUPIM) has been used to estimate the TEC for conditions appropriate to solar maximum as a first step to assessing possible errors in the potential use of the navigation satellites for station keeping in the geostationary orbit. It has been found that in general, for paths through the plasmasphere, where the satellite-to-satellite geometry is far removed from eclipse by the Earth's horizon, the TEC is usually less than 20 TECU (total electron content units, 1 TECU = 1016 el m−2) with resultant errors in single-frequency GPS positioning of a only a few meters. However, when the rays cross the equatorial F2 ionosphere at near-grazing incidence close to the layer peak, TEC of up to some 2000 TECU have been found, with consequent potential single-frequency GPS positioning uncertainties of hundreds of meters. The exact magnitudes of the TEC are very dependent on the precise geometry and vary significantly with time, so they would be difficult to simulate in any real-time, model-based mitigation system.
 While extensive studies have been carried out over several decades on a worldwide basis on the effects of the ionized atmosphere on satellite-to-ground propagation paths, very little work has been carried out on paths involving links between satellites. However, with the increasing use of radio systems for practical applications, in particular satellite-based navigation and positioning, interest is now turning to propagation effects on satellite-to-satellite paths. One specific aspect concerns possible future requirements for the station keeping of satellites in the commercially very important, but potentially congested, geostationary orbit. Geostationary satellites are tracked currently using a network of ground stations, though a possible development at some future stage could involve position location making use of a satellite navigation system like the Global Positioning System (GPS). GPS satellites have nadir-directed antennas, since the system is designed primarily for terrestrial users. In consequence, reception by satellites in geostationary or geosynchronous orbits would involve signals transmitted by GPS satellites essentially on the far side of the Earth. The propagation paths for such satellite-to-satellite links are very long, and they have the potential to pass tangentially through regions of the ionized atmosphere where the electron density is high, particularly when the GPS satellite is close to eclipse. It is thus of interest to investigate propagation effects on such links. Since the main propagation effects that cause degradation to practical systems and give rise to positioning errors are dependent on the path integral of the electron density, it is important that assessment is made of the possible magnitudes of the total electron content (TEC) likely to be encountered in GPS-to-geostationary satellite propagation.
2. Sheffield University Plasmasphere Ionosphere Model (SUPIM)
 The approach in the study has been to simulate conditions found along geostationary-to-GPS satellite paths using the Sheffield University Plasmasphere Ionosphere Model (SUPIM), a proven physical model of processes in the atmosphere within the plasmapause. SUPIM enables estimates to be obtained of electron densities in the ionosphere/plasmasphere system at low latitudes and midlatitudes on a global scale. It has already been used successfully in propagation studies to validate ground-based GPS measurements of TEC using the SCORE process and to estimate the contribution of the protonosphere to the GPS TEC, as witnessed by the four papers by Lunt et al. [1999a, 1999b, 1999c, 1999d].
 The SUPIM model has been described in a number of papers [e.g., Bailey and Sellek, 1990; Bailey et al., 1993; Bailey and Balan, 1996], so only an outline is given here. In SUPIM, coupled time-dependent equations of continuity, momentum, and energy balance are solved by an implicit finite difference scheme along closed magnetic field lines, between base altitudes of about 120 km in conjugate hemispheres, to give values for the concentrations, field-aligned fluxes, and temperatures of the O+, H+, He+, N2+, O2+, and NO+ ions and the electrons, at a discrete set of points along the field lines. For the present study, the geomagnetic field was represented by a tilted dipole that reproduced in a realistic way the displacement of the geomagnetic and geographic equators and the magnetic declination angle. The concentrations and temperatures of the neutral gases were obtained from the MSIS86 thermospheric model [Hedin, 1987], the neutral wind velocities from the HWM90 neutral wind model [Hedin et al., 1991], and the solar EUV fluxes from the EUVAC solar EUV flux model [Richards et al., 1994]. The remaining model inputs, for example, the photoionization and photoabsorption cross sections, chemical reaction rates, heating (including photoelectron heating) and cooling rates, and collision frequencies, are described by Bailey et al.  and Bailey and Balan .
 The SUPIM code has been used to estimate the TEC along GPS-to-geostationary satellite ray paths. The investigations have concentrated on trying to assess the magnitudes of the largest TEC likely to be encountered on the very long satellite-to-satellite paths and, in particular, identifying the geometrical and geophysical circumstances that give rise to the greatest TEC and hence the largest potential propagation errors. To fulfill these aims, the model simulations have been run for conditions appropriate to solar maximum, with the solar flux index chosen to be 150 units. In addition, the E × B drift input to the model was selected to correspond to a well-developed equatorial anomaly. The simulations have been concentrated in the main on ray path geometries transecting the equatorial ionosphere with the satellites close to eclipse by the Earth.
 Since the main concern of the study has been to estimate the possible extreme magnitudes of the TEC that might be found on such paths, no attempt has been made to simulate the exact geometrical changes characterized by particular GPS orbits. The approach has been to try to determine the TEC that might be encountered along ray paths between a satellite at GPS height of about 20,200 km and a synchronous satellite at some 36,600 km altitude in the equatorial plane stationed at different longitudes. It was found that the TEC values obtained were very sensitive to the detailed geometry of the tangential ray paths through the ionosphere close to the layer peak. In consequence, rather than replicating the precise orbits for the GPS constellation, it was decided to investigate the TEC encountered when a satellite at GPS altitude was moved such that the ray path geometry was close to eclipse, first in the equatorial plane and second in latitude. The intention was to acquire relevant information on approximate magnitudes of the TEC likely to be encountered rather than precise details corresponding to particular geometrical situations arising from the actual satellite orbits. A large number of simulations have been run to amass data for a wide range of circumstances. However, the presentation here is confined to a few representative examples that are illustrative of the results obtained. It can be noted that the assumption has been made in the simulations of a fixed plasmapause at L = 5, with zero electron density above that altitude. However, the resultant errors in the TEC arising from this disregard of any plasma beyond the plasmapause are negligible in comparison with the contributions from the ionospheric sections of the ray paths.
Figure 1 is representative of the situation as the ray path encounters the electrons in the ionospheric F2 layer near to the layer peak. Both satellites are in the geographic equatorial plane, with the ray path geometry close to eclipse. In the chosen example shown, the geostationary satellite is located at 0° longitude at various universal times, with the second satellite at GPS altitude and at a succession of longitudes, ranging from 153°E until the ray path eclipses below the Earth horizon when the satellite is at about 156.5°E longitude. The large magnitude of the TEC found, as the ray path passes tangentially through the equatorial ionosphere close to the F2 layer peak, can be appreciated from this example. It can be seen that between 0600 and 1200 UT, there is a band of ray path geometries for which the TEC exceeds 1000 TECU (total electron content units, 1 TECU = 1016 el m−2). It can be noted that these high values correspond to local times in the zone where the ray path is in the vicinity of the F2 layer peak that are approximately in the range from 1100 to 1700 LT. In addition, it can also be seen from Figure 1 that for a given ray path, like that with the GPS satellite at 155°E, for example, the TEC values can change by a factor of more than 5 throughout the course of a day. Correspondingly large values of TEC can be seen in Figure 2 for ray paths to the geostationary satellite at 0° longitude that intersect the ionosphere when the GPS satellite ranges from eclipse at about 203.5°E longitude to about 206°E in the Western Hemisphere. The times at which the greatest magnitudes are found are now in the 1500–2100 UT sector, again corresponding to local times when the ray path is close to the F2 layer peak of late morning to midafternoon. The plot of Figure 2 is continued on a different scale in Figure 3, with the GPS satellite still in the equatorial plane, but at longitudes from 207° to 215°. It can be seen that as the ray path moves away from intersection with the ionospheric F2 layer near the peak, then the TEC values at all universal times tend toward magnitudes of less than some 20 TECU. This result is typical of the TEC found in many simulations of situations where the geometry is such that the ray paths between the satellites are far removed from intersection with the ionospheric F2 layer. It can thus be concluded that for most ray paths that cross the plasmasphere between GPS and geostationary satellites, the TEC magnitudes are such that the resultant propagation errors are likely to be less than a few meters. However, the situation is very different when the ray path geometry is close to eclipse by the Earth horizon.
 Many simulations of satellite-to-satellite ray paths have been investigated here with the geometry no longer confined to the equatorial plane. Figure 4 has been chosen as a representative example of the spatial changes in TEC encountered. Here the geostationary satellite is again at 0° longitude with the second satellite at GPS altitude now at 155.81°E, a precise longitude chosen because it resulted in some of the highest TEC values found in this sector. Results are shown for a range of colatitudes of this second satellite between 70° and 110°, that is, spanning 20° on either side of the equatorial plane. TEC values corresponding to universal times from 0800 to 1500 UT are presented in the example. The plot shows two asymmetric and sharp maxima in TEC for ray paths on either side of the equator that are passing through the equatorial anomaly region and reaching altitudes close to the F2 layer peak. In the example presented, the TEC magnitudes can be seen to reach some 1800 TECU at the maximum to the south of the equator around 1000–1200 UT, with consequent potential errors in single-frequency GPS positioning of hundreds of meters. A further example is given in Figure 5, where the satellite at GPS altitude is now at 157°E longitude, though the geostationary satellite is still on the 0° meridian. It can be seen that for a band of geometries close to the equator, the two satellites are in eclipse with respect to each other, with the ray paths encountering the Earth. However, asymmetric maxima can be seen at greater separations where the TEC values along the ray paths are very large. It can be appreciated from these representative examples that the TEC is very dependent on the exact ray path geometry, with significant variations being found for relatively minor changes in the locations of the satellites. In addition, the results show that the regular temporal variations in the ionosphere can give rise to order of magnitude changes in TEC along a given path, which could correspond to propagation delay differences of hundreds of meters.
 The results presented to date have used examples where the geostationary satellite was at 0° longitude. However, since the equatorial anomaly is controlled by geomagnetic processes, the ionization maxima are found at different geographic latitudes in different longitude sectors. Many simulations have been carried out here to estimate the TEC over a wide range of global conditions. One example is shown in Figure 6 that is illustrative of the general findings but also contains an extreme TEC value. Here the different curves correspond to different longitudes for the geostationary satellite, while the satellite at GPS altitude is 155.71° farther to the east in each case, with the results being plotted for a range of colatitudes spanning 40° about the equator. The time chosen in the example is 0600 UT. The precise longitudinal difference between the two satellites and the universal time were selected because these yielded the highest TEC value found in the entire study. The complex nature of the large spatial variations in TEC in the central band about the equator can be appreciated from the example. An extreme value of some 2000 TECU can be seen, while the changes for different locations round the globe are very large. Indeed, taking into account both spatial and temporal variations, it can be concluded that for essentially similar geometries of the ray paths between the satellites at different longitudes and different times, the TEC could vary by approaching 2 orders of magnitude.
 The SUPIM model has been used to estimate the TEC on ray paths between satellites in geostationary and GPS altitude orbits under conditions appropriate to solar maximum. In general, for geometries where the ray path crosses the plasmasphere well away from eclipse by the Earth horizon, the TEC values are less than 20 TECU, so that positioning to meter accuracy is, in principle, possible using single-frequency GPS operation. However, the situation is very different when the ray paths are close to eclipse, passing through the ionospheric F2 layer at grazing incidence near to the peak where local daytime electron densities are high. The TEC values have been shown to be very sensitive to small changes in the detailed geometry. Magnitudes of up to some 2000 TECU have been found for a band of geometries close to the equator when the ray paths encounter ionization in the equatorial anomaly. Very large changes in TEC have been found for essentially similar satellite geometries at different longitudes and times. The results presented here have been intended to be representative in support of the following general conclusions from the study. The investigation has indicated that it would be very difficult, because of the high temporal/spatial variation of the extreme TEC values on ray paths close to eclipse, to use an ionospheric model in a reliable way in real time to mitigate against the potential positioning errors of hundreds of meters that could arise in the use of single-frequency GPS for the station keeping of synchronous satellites. However, if steps were taken to ensure that observations from ray paths close to eclipse were eliminated from the GPS navigation analysis, then positioning to meter accuracy should be possible.
 This study has been undertaken within the context of the COST 271 action of the European Community. Financial support for COST 271 activities at UWA from the UK Radiocommunications Agency, now part of Ofcom, is acknowledged with thanks.