Geometrical control of the effective outer scale imposed by detrend filtering, in the presence of highly anisotropic irregularities, explains differences between scintillation indices ratio at different locations. On the basis of weak scatter theory results, the behavior of the geometrical factor G, responsible for static effect of diffraction, is investigated in the case of GPS satellites. A simple comparison is made between GPS satellites and polar orbiting satellites used in the past for scintillation experiments to understand such differences in the behavior of scintillation indices measured by means of GPS scintillation monitors.
 The effect of ionospheric scintillation on satellite based navigation systems is potentially very important. For this purpose, special equipments have been designed in order to evaluate scintillation indices by using GPS transionospheric radio signals. This is possible by means of “GPS scintillation monitors”, that are commercial GPS receivers modified in order to measure scintillation indices [Van Dierendonck et al., 1993; Beach and Kintner, 1999]. Several studies using GPS derived scintillation data have been conducted revealing different scintillation indices behaviors at low and high latitudes. At high latitudes high phase scintillation indices are often found in presence of low intensity scintillation indices [Doherty et al., 2000; Pi et al., 2001].
 Two decades ago, a similar variation of scintillation indices ratios with geomagnetic latitude was found by means of Wideband data mainly. The Wideband experiment was based on a multifrequency (ten spectral lines between VHF and S band) coherent radio beacon transmitting continuously from a 1000 km, high inclination orbit. Its purpose was to extensively characterize the perturbations (mainly scintillations) imposed on transionospheric radio waves by ionospheric plasma density irregularities, as those found at auroral and equatorial latitudes [Fremouw et al., 1978].
 In general, it was suspected that data detrending, coupled with irregularities anisotropy and line-of-sight scanning, may play a role in the differences observed in the scintillation index ratios at different stations [Fremouw, 1980].
 On the basis of weak scatter theory, possible factors responsible for such feature in scintillation indices behavior have been analyzed. By means of a polar orbiting satellite, as in the Wideband experiment, it was found that the average nighttime auroral zone scintillation activity can be characterized by a localized enhancement at the point at which the propagation vector lies within an L shell [Rino and Matthews, 1980; Rino and Owen, 1980].
 The problem of GPS scintillation data detrending has been already pointed out and analyzed as a possible explanation of high phase scintillation indices against low intensity scintillation indices measured at high latitudes by means of a GPS scintillation monitor [Forte and Radicella, 2002] of the type described by Van Dierendonck et al. .
 Here the attention is focused on another possible mechanism that could explain high latitudes enhancements of phase scintillation indices, as derived from GPS data. This analysis is based on the geometrical factor G, one of the factors controlling the phase scintillation index, under weak scatter assumption. The localized enhancement found in the nighttime auroral scintillation activity was explained in the case of Wideband observations by means of a localized peak in G at the point at which the ray path lies within an L shell, for field aligned sheet-like irregularities [Rino and Owen, 1980]. The same geometrical factor G is now computed for GPS satellites, having in principle different geometry with respect to polar orbiting satellites.
2. Geometrical Factor G
 Data detrending introduces an artificial outer scale relative to the temporal cutoff frequency adopted by the detrending process. As shown by Rino [1979a], the variance of phase so detrended can be expressed as:
where p is the power law index of phase spectrum, τc is the detrending period. T is given by:
where re is the classical electron radius, λ is the radio wavelength, L is the thickness of the scattering layer and θ is the incidence angle. The gamma functions stem from normalizing the 3-D ionospheric spatial spectrum to the variance of electron density, 〈ΔNe2〉. Moreover, ν ≈ p/2. The main geometrical factor is:
where a and b are irregularity axial ratios along and across the geomagnetic field, respectively, and A, B and C are geometrical parameters, depending on the direction of the ray path with regard to the geomagnetic field [Rino and Fremouw, 1977]. The strength of irregularities is given by:
where q0 is the spatial outer scale.
 Finally, the last parameter of (2) is the effective velocity Ve, which is the relative velocity between irregularity motion and ionospheric penetration point motion, usually computed at 350 km of altitude. Before characterizing scintillation indices for GPS data by means of weak scatter theory results [Rino, 1979a], the validity of such a theory for GPS satellites should be checked. This is accomplished by evaluating the randomization factor U, given by [Rino, 1979a; Fremouw, 1980]:
with z the effective “reduced height” of the irregularities. When U ≪ 1, the weak scatter theory can be applied [Rino, 1979b].
 In the case of Wideband satellite experiment, it was found [Fremouw, 1980]:
allowing for the use of the weak scatter results to study the behavior of scintillation indices.
 In the case of GPS satellites, for a same incidence angle θ as for Wideband satellite, it can be shown that:
allowing for the use of the weak scatter theory to characterize scintillation mechanisms for GPS satellites.
3. G Factor for GPS Satellites
 For axially symmetric irregularities, G achieves a maximum only at the magnetic zenith, while for sheet-like structures G maximizes whenever the propagation vector lies within the plane of the sheet. In the case of Wideband satellite the enhancement for L shell aligned sheets occurs at a fixed magnetic latitude, irrespective of elevation of the pass. The propagation angle relative to the local magnetic field direction varies with altitude. The actual geomagnetic latitude assigned to the enhancement varies slightly with the altitude assigned to the structured region [Rino and Owen, 1980]. Such a geometrical enhancement has a signature on Wideband TEC data also. This was explained by vertical F region slabs about 100 km thick with steep gradients on their equatorward edge [Rino and Owen, 1980].
 To check the possible geometry influence on GPS observations, the geometrical factor G is computed for a set of representative GPS satellites, by using WBMOD model [Secan et al., 1995]. The geometrical factor G has been computed for a set of 14 GPS satellites with different link geometry, as observed from two typical auroral sites as Anchorage and Poker Flat (Alaska).
Figure 1 shows the typical localized peak in G resulting in a localized enhancement in the scintillation activity measured from a polar orbiting satellite at 1000 km of altitude, at a typical auroral ground station [Rino and Owen, 1980]. Figure 2 shows the situation corresponding to the SVN 15 of the GPS constellation, as observed from Poker Flat. The top plot shows G computed for SVN 15, under given orbital conditions. The middle plot shows the elevation angle for SVN 15, observed from Poker Flat. The bottom plot shows isolines of equal dip-latitude, indicating particular L shells, while the dots represent the ionospheric penetration point trajectory at the F peak (i.e., 350 km of altitude). Figures 3, 4 and 5 show the same arguments for SVN 26, 21 and 36, respectively, when observed from Poker Flat.
Figures 6, 7, 8, and 9 show geometrical factors, elevation angles and ionospheric penetration point trajectories with respect to Anchorage observing site. These four SVNs have been chosen as representative cases among all of the analyzed cases.
 In general, the factor G shows a flat behavior for GPS satellites. There can be particular cases, as showed in Figure 5, with relatively small and wide peaks in G. In this case, the peak amplitude is less than the peak amplitude for a polar orbiting satellite (as it can be deduced comparing Figures 1 and 5), while the peak observed for GPS satellites can be wider than the peak observed for polar orbiting satellites, due to different effective velocities.
 Comparing Figures 5 and 9, it can be observed that the G peak at Poker Flat is delayed in time with respect to Anchorage, because of different link geometry. These particular cases show that GPS ray path is close to the condition of lying within an L shell. Field lines elongated irregularities can enhance phase scintillation indices under such a condition, since phase scintillation index is more sensitive than intensity scintillation index to the geometrical factor G, as it is pointed out from (1). If this happens, scintillation activity should be correctly interpreted, because such an enhancement is not produced by particular geophysical conditions, but it is just due to purely geometrical reasons.
 The behavior of the geometrical factor G appears to be different for GPS and polar orbiting satellites. In the latter case G shows a sharp and pronounced peak whenever the ray path lies within an L shell, while for GPS satellites G appears constant and eventually with smoothed peaks. For GPS satellites, those smoothed and wide peaks have an amplitude definitely smaller than in the case of polar orbiting satellites. A geometrical enhancement in scintillation activity measured from GPS satellites at auroral sites cannot be assumed as a general rule. A small enhancement in phase scintillation index could take place if the GPS ray path lie within an L shell. This condition is rarely and not completely encountered for GPS satellites: even if encountered, to a certain extent, the peak amplitude is reduced with respect to polar orbiting satellites. The most plausible explanation of high phase scintillation indices against low intensity scintillation indices measured by means of GPS scintillation monitors at high latitudes remains that based on erroneous data detrending [Forte and Radicella, 2002]. This because no global enhancements in GPS derived phase scintillation indices can be explained by means of geometrical factors like G.
 According to Forte and Radicella , data detrending algorithms, with a cutoff frequency not appropriate to current geophysical conditions coupled to GPS satellites geometry, can be responsible for distortions of amplitude and phase scintillation information, including the possibility of obtaining “phase without amplitude scintillation” at high latitudes.
 When measuring scintillation activity through satellite data, the separation of scintillation from other effects (e.g., multipath, satellite motion) is needed and this is usually done by data detrending. Data detrending is accomplished by digital filters characterized by a fixed low cutoff frequency, allowing the extraction of high frequency component of received transionospheric data. The major contribution to amplitude fluctuations spectra is at the Fresnel frequency. This parameter allows to locate the spectral window pertaining to ionospheric scintillation fluctuations, both in amplitude and in phase. The Fresnel frequency depends on relative drift and distance between observer and irregularity, for fixed transmission wavelength. Thus it varies with geomagnetic latitudes and activity because irregularity characteristics vary with them. If the cutoff frequency is not appropriate to current geophysical conditions and GPS satellites geometry, a low frequency contribution can erroneously be taken into account in the evaluation of scintillation indices. Such a contribution is heavier in phase fluctuations than for amplitude fluctuations, since at low fluctuations frequencies the phase power spectrum has still a power law behavior, while the amplitude power spectrum is constant [Forte and Radicella, 2002].
 The geometrical factor G has been investigated for GPS satellites observed from auroral locations. The phase scintillation index, derived from GPS data, can be described by means of weak scatter theory [Rino, 1979a]. One parameter responsible, among others, of enhancements in phase scintillation indices is the geometrical factor G. Such enhancements take place when the ray path lies within an L shell: these enhancements are highly localized for polar orbiting satellites observed from auroral sites [Rino and Owen, 1980]. In these cases, sheet-like irregularities aligned with geomagnetic field lines come into play [Rino and Matthews, 1980]. The behavior of the geometrical factor G is investigated for GPS satellites observed from two auroral sites as Anchorage and Poker Flat (Alaska). In general, G shows a flat behavior for GPS satellites, but in particular cases relatively small and wide peaks appear, indicating the alignment of the ray path with L shells embedded irregularities. Such a geometrical situation seems to be not easily encountered by GPS satellites, while it always occurs for polar orbiting satellites [Rino and Owen, 1980].
 The behavior of the geometrical factor G cannot explain global high phase scintillation indices against low intensity scintillation indices measured by means of GPS scintillation monitor at high latitudes. Even if the phase scintillation index described in (1) depends on several factors, an erroneous data detrending remains the main explanation of high phase scintillation against low intensity scintillation measured by means of GPS data at high latitudes [Forte and Radicella, 2002].