Plasmasphere effects on total electron content (TEC) measurements conducted using Global Positioning System (GPS) receivers are typically neglected for the North American region, because of the relatively high magnetic latitudes there, but model and measurement cases for this region are presented here to demonstrate the magnitude of the effects for GPS TEC measurements away from vertical and for the associated equivalent vertical TEC values. For high solar flux conditions, the effects of high, distant electron content can range up to 25 TEC units for equivalent vertical TEC, or up to 65 TEC units for slant TEC determinations derived from vertical TEC measurements. The effects of the plasmasphere for TEC calibrations conducted in North America include systematic overestimation of the equivalent vertical TEC and excessive latitudinal gradients, especially at night. These may not be readily evident in the calibration results, and some alternatives for addressing these circumstances are considered.
 The plasmasphere is a large toroidal domain of light ionized particles situated above the ionosphere and confined by the Earth's magnetic field. Although plasmaspheric charge densities are considerably less than those of the ionosphere, the large extent of the plasmasphere can produce significant total electron content (TEC) for lines of sight passing through the plasmasphere. In some circumstances (primarily nighttime and low solar flux periods), this plasmaspheric electron content (PEC) can be significant in comparison to the ionospheric electron content (IEC), affecting the processing of GPS ionospheric TEC measurements and the interpretation of these measurements.
 A previous study by Lunt et al. [1999a] provided a quantitative assessment of the PEC for GPS measurements in the European sector, noting that the effects would be smaller for North America because of the relative positions of the magnetic and geographic equators at those longitudes. Comparisons of the local vertical TEC, for 40° latitude in the two regions, were also presented, confirming this expectation, which corroborated previous frequency dispersion and Faraday rotation measurements conducted using the ATS-6 satellite [Kersley and Klobuchar, 1978], although the latter used a higher effective altitude (approximately 2500 km, versus the 1100 km value used by Lunt et al. [1999a]) for the boundary between the ionosphere and the plasmasphere.
 For equatorward off-vertical lines of sight, the PEC becomes greater, adversely affecting the standard conversion of off-vertical TEC (“slant TEC”) measurements to equivalent vertical TEC values. Comparisons performed using the Sheffield University Plasmasphere Ionosphere Model (SUPIM) [Bailey and Balan, 1996] are presented here to display the magnitude of the plasmasphere effect for this conversion for the North American region, as well as displaying intrinsic limitations for the conversion between slant and vertical TEC for just the ionosphere.
2. Geometrical Considerations
 For the discussion here and in subsequent sections, the boundary between the ionosphere and plasmasphere is considered to be at an altitude of 1000 km, independent of latitude. There is some arbitrariness to this designation, but it does correspond approximately to the altitude of the Transit (or Navy Ionospheric Monitoring System (NIMS)) satellites, allowing operational measurements of the separate ionospheric contribution to TEC [Ciraolo and Spalla, 1997; Lunt et al., 1999c], with the plasmaspheric contribution being derived as the difference between GPS and NIMS TEC measurements.
 For off-vertical lines of sight in the meridian plane, the intersection of the line of sight with this ionosphere-plasmasphere boundary can be considerably far removed from the observation station and even from the nominal ionospheric penetration point (IPP) in the ionospheric F layer, at about 350 km altitude. Figure 1 displays the latitude offsets from the observation station for these intersections, for the full range of elevations, assuming a line of sight in the meridian plane. For all but the lowest (below about 10° elevation) off-vertical lines of sight, the distance of the boundary penetration point (BPP) from the IPP is larger than the distance of the IPP from the observation station. This indicates that the plasmasphere characteristics for the line of sight can be significantly different from the local vertical plasmasphere characteristics above the IPP, especially for low-elevation lines of sight. A consequence of these latitude differences is that even for middle latitude regions near 45° magnetic latitude, the plasmasphere region above the equatorial anomaly crests, typically at about ±15° magnetic latitude, would be detectable, even though the F layer for the anomaly crests is below the horizon.
 The larger distances associated with the BPP also present some features not usually considered for the shorter distances associated with the IPP, because the curvature of the Earth becomes more significant. The ground trace of any line of sight is a segment of a great circle on the surface of the Earth. Thus, directly eastward or westward lines of sight eventually progress equatorward, sampling regions of the plasmasphere that are typically more extensive than near the observation station, except for stations close to the magnetic equator, which would tend to view poleward for most directions, and, consequently, sample less extensive regions of the plasmasphere. Away from the equator, even lines of sight slightly poleward of directly east or west progress equatorward, as indicated in Figure 2. The line of sight displayed in Figure 2 corresponds to the lowest azimuth case appearing in Figure 3, which displays the BPP latitude for various elevations, where the associated azimuths are chosen such that the IPP latitude is the same as the site latitude, for a site at 45° latitude. The general results are latitude-dependent, but in this case, the BPP latitude can be 3° equatorward of the site. The latitudes for a representative plasmasphere penetration point (PPP) altitude (1400 km) along the same lines of sight are also displayed, where this PPP altitude is approximately that for the TOPEX, Jason-1, or Jason-2 satellites, which could perform space-based vertical TEC measurements. These PPP latitudes can be as much as 4.75° equatorward of the site.
 For the same lines of sight, the local time offsets at each of the penetration point altitudes are displayed in Figure 4. These differences, which can be nearly 2 h for the IPP and can exceed 3 h for the PPP, for horizontal lines of sight, can have significant influences on the interpretation of ionospheric/plasmaspheric TEC measurements, by providing a TEC background associated with different regional conditions.
 The conversion between slant TEC and an equivalent vertical TEC is typically performed on a geometrical basis, representing the electron density distribution for the ionosphere by either a thick shell [e.g., Sardón et al., 1994] or a thin shell [e.g., Lunt et al., 1999b]. For the thin shell conversion (which is the same as the thick shell formula in the limit of zero thickness), the conversion formula from slant TEC (STEC) to equivalent vertical TEC (VTEC) is
where ɛ is the elevation angle of the line of sight, Re is the radius of the Earth, and HIPP is the effective altitude of the ionosphere (typically associated with the F layer).
 A variant of this formula provides some accommodation for the electron density distribution of the ionosphere and plasmasphere. This variant is
where ΔH is an effective thickness for the ionosphere and plasmasphere. While not strictly equivalent to the thick shell formula, this variant provides a very good approximation for the thick shell conversion for moderate effective thicknesses. With this formulation, the effective altitude HIPP can be retained for the geographical calculations of the IPP locations.
3. Electron Density Effects From the Plasmasphere
 The following discussions are more specific to a particular site, because of the varying distribution of plasmaspheric electron density with latitude and longitude. For these examples, an observing station location corresponding to the Hillsboro, Kansas (HBRK) Continuously Operating Reference Station (CORS) site was chosen, near the geographical center of the contiguous United States of America. The geographic coordinates of this site are 38.3°N, 97.3°W, and the magnetic latitude of this site is about 49°N. The cited electron density results are those derived from SUPIM, for times corresponding to a fully replenished plasmasphere (i.e., 20 days after a storm depletion event).
 The quantity displayed in Figure 5 is the cumulative integrated electron density along the line of sight, from the (ground) station location to various altitudes, encompassing the GPS satellite altitudes (20,200 km). Figure 5a displays the integrated electron density along lines of sight at 35° elevation for SUPIM calculations at low solar flux (F10.7 = 75), for noon local time, both northward (azimuth equal to 0°) and southward (azimuth equal to 180°) from the site. The northward line of sight exhibits an asymptotic value for the cumulative slant TEC, attained at an altitude just above 2000 km, primarily as a consequence of the line of sight crossing the plasmapause, beyond which no densities are computed. The PEC contribution is only about 1.4 TEC units for this line of sight, slightly less than 10% of the total. In contrast, the cumulative slant TEC for the southward line of sight continues to increase with altitude, although only very gradually near the GPS satellite altitudes, and the PEC contribution is about 7.8 TEC units, which is nearly one-third of the total. The median altitude for the PEC for this line of sight is about 3800 km, so half of the total PEC lies between 1000 km and 3800 km, while the remaining half lies above 3800 km.
Figure 5b displays similar results, but for SUPIM calculations at high solar flux (F10.7 = 250). Again, the northward line of sight exhibits an asymptotic value for the cumulative slant TEC, attained at about 2550 km altitude, with a PEC contribution of about 5.5 TEC units, slightly more than 7% of the total. The cumulative slant TEC for the southward line of sight continues to increase with altitude, and the PEC contribution is about 10.5 TEC units, which is only about 11% of the total. The median altitude for the PEC for this line of sight is about 1950 km.
 These results are qualitatively consistent with the results derived by Lunt et al. [1999a, Figures 3 and 4], for European longitudes and slightly higher geographic latitudes, but also using SUPIM. Although the absolute value for the PEC increases with increasing solar flux, the relative value for the PEC is higher at low solar flux, primarily because the IEC is considerably lower for low solar flux (solar minimum conditions). The lower median altitude for the plasmasphere at high solar flux is a consequence of the increased plasmasphere electron density at lower altitudes, near the ionosphere-plasmasphere boundary.
 The varying relative content of PEC against IEC with solar flux presents some challenges in selecting an appropriate effective thickness for the combined ionosphere and plasmasphere, but the situation is further complicated by the separate variation of the plasmasphere in response to storms, with a considerable depletion of the plasmasphere directly following the storm and a gradual replenishment (with a timescale of about 10 days) until the occurrence of a subsequent storm (usually before achieving complete replenishment) [Lunt et al., 1999c]. The diurnal variation of the plasmasphere presents an even more rapid variation in the PEC than the replenishment, although most of the diurnal relative variation of PEC to IEC is a consequence of the larger ionosphere variations [Lunt et al., 1999a].
 To evaluate these effects, with particular attention to the conversion between slant TEC and vertical TEC, several cases were examined, using SUPIM simulations for the HBRK CORS site and its vicinity. Slant TEC values were computed for an observation station at HBRK, with separate tabulations for the individual ionosphere and plasmasphere contributions. True vertical TEC values also were computed at latitudinal intervals along the meridian for that site. Comparisons of these slant and vertical TEC values permit a determination of the combined effective altitude and thickness, as well as allowing an assessment of the variation of the conversion between slant TEC and vertical TEC for a range of elevations (or, for a line of sight along the meridian, an equivalent range of IPP latitudes).
Figure 6a displays a noontime case for low solar flux, comparing the equivalent vertical TEC (converted from slant TEC) to the true vertical TEC, for the ionosphere alone (IVTEC) and for the composite ionosphere and plasmasphere (CVTEC). For the IVTEC (corresponding to a depleted plasmasphere condition), a good agreement (within one TEC unit) exists between the equivalent vertical TEC and the true vertical TEC for all elevations, using just the thin shell conversion with HIPP equal to 350 km. However, the presence of a replenished plasmasphere produces a considerable discrepancy between the equivalent vertical TEC and the true vertical TEC, with generally overestimated VTEC equatorward of the site and underestimated VTEC poleward of the site, a discrepancy arising from the considerable latitudinal offsets of the sampled plasmasphere regions from the local vertical regions, as noted previously. The latitudinal (or elevation) variation of this discrepancy is such that no single value for the thickness correction (ΔH) is sufficient to produce adequate agreement over any significant region in the vicinity of the observation station.
 Similar results are displayed in Figure 6b, for the same solar flux level, but for local midnight. For this case, a thickness correction ΔH = 65 km produces a better agreement for comparing the equivalent vertical TEC to the true vertical TEC, but the thin shell approximation (ΔH = 0 km) produces similar agreement for all elevations above 35°. The presence of a replenished plasmasphere produces discrepancies similar to that for the noontime case, and these also cannot be resolved by a single value for the thickness correction.
Figure 7a similarly displays a noontime case for high solar flux, but the value for the thickness correction (ΔH) has been increased to 65 km to produce good agreement for the comparison of equivalent vertical IVTEC to the true vertical IVTEC over a reasonable latitude range in the vicinity of the observation station. The equivalent vertical IVTEC diverges from the true vertical IVTEC below 25° elevation, although by a somewhat smaller amount poleward of the site than equatorward, where the discrepancy quickly exceeds 10 TEC units. Good agreement between the equivalent vertical TEC and true vertical TEC for the composite ionosphere and plasmasphere (CVTEC) occurs over a somewhat smaller range of latitudes (or elevations), but the onset of the discrepancy occurs sooner poleward of the site, with the onset of the equatorward discrepancy occurring at about the same latitude as for the IVTEC case. The thickness correction can be adjusted to produce better agreement for the CVTEC comparison, with a value ΔH = 225 km generating a minimal discrepancy above 35° elevation, but the onset of a large discrepancy occurs just below this elevation threshold equatorward of the site, with a much smaller discrepancy poleward of the site.
Figure 7b displays the corresponding midnight case for high solar flux, for a thin shell conversion with HIPP reduced to 250 km, although no single value for the effective ionospheric altitude (HIPP) is sufficient to produce adequate agreement over any significant region in the vicinity of the observation station. Because of the change for HIPP from the noontime case, the relationship between elevation and IPP latitude has also changed.
 The previous discussion addresses some of the plasmasphere TEC effects on the measurements and interpretation (as equivalent vertical TEC) of slant TEC, including the assessment of a value for the altitude to be used in converting slant TEC to equivalent vertical TEC. The plasmasphere TEC also affects the inverse determination of slant TEC from vertical TEC measurements, as would be available as interpolated values from a grid of reference tabulations (e.g., WAAS). The primary basis for this effect is that the background plasmasphere TEC (and, to some extent, the high-altitude background ionosphere TEC) is far removed from the vicinity of the local vertical, as noted in section 2.
Figure 8 displays the noontime (Figure 8a) and midnight (Figure 8b) differences between slant TEC derived from a local vertical TEC measurement (at the designated IPP latitude) and the true slant TEC measured at the reference observation station (HBRK), using the same SUPIM cases displayed previously as vertical TEC for low solar flux (Figure 6). Although reasonably good accuracy (within one TEC unit, except at the lowest elevations) is obtained for the ionosphere alone (as in the case of a depleted plasmasphere), the plasmasphere could contribute discrepancies in excess of 4 TEC units even above moderate elevation thresholds (35°), with significantly larger discrepancies at lower elevations. The maximum slant TEC, for the combined ionosphere and plasmasphere, is about 60 TEC units, occurring for the lowest elevation equatorward of the site.
 Similar results are displayed in Figure 9 for the high solar flux case, for which it is evident that the ionosphere, by itself, is potentially a significant contributor to the discrepancies in derived slant TEC values. The plasmasphere contribution to these discrepancies in slant TEC are relatively smaller but still significant in absolute terms. These evaluations also were conducted using the same SUPIM cases displayed previously for high solar flux (Figure 7), with a maximum slant TEC of about 370 TEC units at the lowest elevation (equatorward).
4. TEC Calibration Effects From the Plasmasphere
 Because the plasmasphere electron content can have significant effects on the determination of equivalent vertical TEC, it would be expected that these can appear in bias calibration methods that are based on the TEC measurements themselves [e.g., Lanyi and Roth, 1988; Sardón et al., 1994; Wilson and Mannucci, 1994; Bishop et al., 1994]. A demonstration of this was provided by Lunt et al. [1999b] for moderately high midlatitudes (about 50° geomagnetic latitude) and subsequently by Mazzella et al.  for equatorial and midlatitude cases (up to 45° geomagnetic latitude), with both investigations using variants of the SCORE method [Bishop et al., 1994]. The general tendency of the PEC is to produce an overestimation of bias values for the equatorial region, resulting in lower VTEC estimates (including negative nighttime TEC excursions), but to produce an underestimate of bias values at locations near the fringe of the plasmasphere, with overestimated VTEC values and significant VTEC gradients. (The latter effects were also noted for other calibration methods (P. Doherty, private communication, 2007), while the same regional variation for the plasmasphere effect on VTEC determinations was noted by Anghel et al. .)
 A case for actual GPS TEC data demonstrating plasmasphere effects is provided by the IGS station at Westford, MA (latitude 42.6°), on 14 February 2007 (P. Doherty, private communication, 2007). The derived VTEC, performed by a variant of SCORE in geomagnetic coordinates, is displayed in Figure 10a, exhibiting relatively high nighttime TEC levels and significant latitude gradients in VTEC. The latitude gradients of VTEC are evident from association of the VTEC variations (Figure 10a, middle) with the IPP latitudes for the GPS satellite tracks (Figure 10a, bottom). In contrast, a calibration performed by an extension of SCORE (denoted as SCORPION [Mazzella et al., 2007]) with provisions for determining the plasmasphere TEC is displayed in Figure 10b. The nighttime TEC levels and latitude gradients previously attributed to the ionosphere are substantially reduced, while the plasmasphere slant TEC values (Figure 10b, top) are shown as being at a significant level relative to the ionospheric TEC. The magnitude of these plasmasphere slant TEC values (0–8 TEC units) is comparable to the values (3–7 TEC units) determined by Law  from comparisons of GPS TEC values for sites (Pittsburgh, PA and Charleston, SC) at different latitudes, in somewhat similar conditions (equinox and summer solstice, 1997).
5. Further Discussion and Conclusions
 The SUPIM results displayed above indicate discrepancies in equivalent vertical TEC representations, derived from slant TEC measurements, ranging up to about 25 TEC units for high solar flux conditions, but only up to about 3 TEC units for low solar flux conditions. The inverse conversions, for equivalent slant TEC determinations derived from vertical TEC measurements, display discrepancies ranging up to about 65 TEC units for high solar flux conditions, but only up to about 7 TEC units for low solar flux conditions. Although the plasmasphere accounts for most of the discrepancy for the low solar flux conditions, the discrepancy for the high flux conditions is primarily attributable to the ionosphere itself, arising from high-altitude electron densities equatorward of the observation site, while the plasmasphere contribution is only comparable to that for low solar flux conditions. The ionospheric contribution to the conversion discrepancies between slant and vertical TEC can be expected to vary according to the conditions associated with the equatorial anomaly.
 The quantitative results described here depend both on the physical processes represented in SUPIM and on the specific geophysical parameters used for the model simulations, but the qualitative results are indicative of issues to be addressed. The shell conversion between slant TEC and vertical TEC has previously been demonstrated to have limitations in accuracy because of gradients in the ionosphere [Tsedilina et al., 1994] and effects of the altitude distribution for electron density [Smith et al., 2008], and similar limitations are evident in some of the ionospheric cases displayed here. The presence of the plasmasphere presents a further complication, especially at the lower solar flux levels and associated lower ionospheric electron densities, both through accentuated latitude gradients and a variable content, depending on the degree of replenishment of the plasmasphere. Thus, specification of a single effective altitude (or a combined reference altitude and effective thickness) becomes somewhat problematic. If the effective altitude for the shell conversion is allowed to have a latitudinal dependence, based on the IPP latitude for a specified reference altitude, the variable content of the plasmasphere and its typical remoteness from the vicinity of the local vertical still complicate this determination. The combined effects of the shell conversion and plasmasphere content can adversely affect representations of equivalent vertical TEC, or, for application to GPS navigation, the inverse conversion for use of reference vertical TEC values in determining slant TEC values as range corrections.
 Some caution must be exercised in attempting to determine the effective ionospheric altitude (HIPP) (or the combination HIPP + ΔH) by inverting the conversion formula for slant TEC to equivalent vertical TEC, using measurements (or even model calculations) for the respective STEC and VTEC values. The formal solution, arising from this inversion, is
but near the local zenith, as ɛ approaches 90° and VTEC/STEC approaches 1, the ratio cos(ɛ)/sin(arccos(VTEC/STEC)) approaches 0/0. Formally assessing the error in the determination of HIPP, based on this solution, emphasizes the dependence on 1/sin[arccos(VTEC/STEC)], which diverges as VTEC/STEC approaches 1, influencing a broad range of angles near the local zenith. This effect could account for some of the extreme HIPP values reported by Birch et al. , especially because their corresponding VTEC and STEC values were not associated with the same IPP coordinates, thus allowing some additional contributions to the VTEC/STEC ratio arising from latitude and local time variations of the ionosphere (and plasmasphere).
 The influence of the plasmasphere electron content on the slant TEC conversions can also produce indirect, and sometimes unidentifiable, effects on calibrations of GPS TEC measurements. (See, for example, the simulations conducted by Lunt et al. [1999b] or the comparative calibrations conducted by Carrano et al.  with and without incorporating a plasmasphere model.) Consequently, investigations to measure the plasmasphere content as the difference between GPS TEC and NIMS TEC (or ionospheric TEC estimates from ionosondes) can experience systematic errors for the GPS TEC, dependent on the plasmasphere content. Examination of the latitude gradients of the GPS VTEC, as displayed in Figure 10a, can possibly indicate the plasmasphere influence, but for investigations where only a local vertical GPS TEC is presented [e.g., Ciraolo and Spalla, 1997; Belehaki et al., 2003], the plasmasphere effect on the GPS TEC calibration may not be discernable. The comparable investigations by Lunt et al. [1999c] were accompanied by prior model validations [Lunt et al., 1999b] and equatorward latitudinal exclusions for the GPS TEC calibrations, to minimize the plasmasphere influence.
 The SCORPION technique, which arose from consideration of the validations conducted by Lunt et al. [1999b], still utilizes the thin shell conversion between slant TEC and vertical TEC for the ionospheric component, obtained by removing a parametric representation of the plasmaspheric TEC contribution from the composite slant TEC [Mazzella et al., 2002, 2007]. The parameters of this representation are themselves derived from the same GPS slant TEC measurements. As demonstrated by the model validations of Lunt et al. [1999b] and Mazzella et al. , an imposed removal of the plasmasphere can allow excellent determinations of the combined receiver and satellite biases as well as the derived ionospheric TEC. Consonant with the limitations noted by Tsedilina et al.  and from independent investigations conducted for the development of SCORE [Andreasen et al., 1998], an elevation threshold of 35° is also imposed for conversions between slant TEC and vertical TEC, reducing the effects of inaccuracies in the thin shell conversion associated with lower elevations.
 GPS TEC calibration methods that rely on tomographic inversions of the TEC measurements [e.g., Meggs et al., 2004] would also need to consider the representation of the plasmaspheric electron content in the functions that describe the spatial distribution of the electron densities. Because the median plasmasphere altitude can be as high as 3800 km, as noted for Figure 5, the regional coverage required by ground stations to adequately sample the plasmasphere electron densities would need to be large. (See also Figures 1 and 2.) However, the larger ground coverage will also encompass further plasmasphere regions around its borders, indicating that only a global coverage may be satisfactory.
 As demonstrated by Lunt et al. [1999b], model validations of a GPS TEC calibration technique can provide valuable information regarding the performance of the technique and possible insights for further developments. Development of databases for this purpose is discussed by Leitinger . The results presented by Lunt et al. [1999b] and here indicate that inclusion of the plasmasphere contributions is essential for the reliability of the validations, even at middle latitudes. Consideration of the plasmasphere contributions is especially significant for lower latitudes, where the plasmasphere typically has a greater extent across the sky and determination of its effects becomes more challenging [Mazzella et al., 2007; Anghel et al., 2009].
 The author is grateful to Graham J. Bailey for providing SUPIM and supporting its use, and to the reviewers for helpful comments. Development of SCORPION was conducted in collaboration with G. Susan Rao and supported by the Air Force Research Laboratory Space Vehicles Directorate under SBIR contracts FA8718-04-C-0009 and FA8718-05-C-0026. The figures were prepared using the Generic Mapping Tools (GMT) graphics [Wessel and Smith, 1998].