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[1] Ionospheric scintillation data detrending is reviewed in this paper. The attention is focused on satellite to ground links (mainly GPS) data. The problem of a fixed (“frozen”) cutoff frequency is pointed out. A possible explanation of the presence of “phase without amplitude” scintillations is given as a result of erroneous data detrending.

[2] The most used parameter to measure ionospheric amplitude scintillation activity is the S_{4} index, that is the standard deviation of received power divided by its mean value and defined as [Briggs and Parkin, 1963]

where I is the field intensity.

[3] Phase scintillation is measured by means of the standard deviation of the signal phase, σ_{ϕ}. These indices are usually computed from raw data over a one minute period.

[4]S_{4} index for ionospheric amplitude scintillation saturates theoretically at unity while σ_{ϕ} can increase indefinetely because it has no upper limit. The usual approach to describe strong scintillations is to make a statistics of the events with saturation and then compute percentages of occurrences of such events.

[5]Fremouw et al. [1978] chose a detrend filter with a fixed cutoff frequency of 0.1 Hz in their experiment with the orbiting Wideband satellite. This was a correct choice for the case of an orbiting satellite that had a scan velocity of about 3 km/sec in the F layer. In the case of scintillation experiments with GPS satellites, the use [Van Dierendonck et al., 1993] of the same 0.1 Hz detrend filter is not appropriate. We show that it can lead to distortions of amplitude and phase scintillation data. The distortions include the possibility of obtaining “phase without amplitude scintillation” as reported by Doherty et al. [2000].

2. Data Treatment Problems

[6] The major contribution to amplitude fluctuations spectra is at the Fresnel frequency ν_{F} [Rino, 1979]. This parameter allows us to locate the spectral window pertaining to “ionospheric scintillation” fluctuations, both in amplitude and in phase. The Fresnel frequency ν_{F} depends on relative drift and distance between observer and irregularity, for fixed transmission wavelength. Thus, ν_{F} varies with geomagnetic latitudes and activity because irregularity characteristics vary with them.

[7] It is

where V^{REL} is the relative drift (composed by the satellite motion V^{SAT} and the irregularity drift V^{IONO}); where z is the distance from the phase changing screen. In this paper we will focus our attention on GPS derived ionospheric scintillations data only. Typically, for GPS L1 and for a phase changing screen at 350 km, it is d_{F} = 360 m. Typical relative velocity values at low and high latitudes, on the basis of experimental values, are estimated.

2.1. Low Latitudes

[8] Considering, for instance, a GPS station at Ancon, Peru, (geogr. lat. = −11.5° and geogr. long. = −77°), typical values of GPS satellite velocity V^{SAT} at 350 km, with respect to this observation point, and at an elevation angle ≈ 40°, are

where y indicates the east-west direction. Since at low latitudes the irreguarities move along the magnetic east-west direction, only the satellite motion along such direction will be considered here. Typical values of ionospheric irregularity drift at these latitudes are V^{IONO} ≈ 100 ÷ 200m/sec along the east-west direction during premidnight hours [Aarons, 1982; Basu et al., 1999].

[9] Combining such values, different relative velocities can be obtained and, using (2), also different Fresnel frequencies can be calculated:

[10]Figure 1 is an illustrative representation in double logarithmic scales of the expected amplitude and phase power spectral densities, referring to a 3-D spatial power law irregularity spectrum ^{Φ}ΔN_{e} ∼ k_{⟂}^{−p}, with an outer scale much greater than the Fresnel scale: only asymptotical slopes are taken into account. Here k_{⟂} is the spatial frequency normal to the propagation direction and p is called “spectral index” [Yeh and Liu, 1982].

2.2. High Latitudes

[11] Considering, for instance, a GPS station at Fairbanks, Alaska, (geogr. lat. = +64.8° and geogr. long. = −147.5°) typical values of GPS satellite velocity V^{SAT} at 350 km, with respect to this observation point and at an elevation angle ≈ 50° ÷ 60°, are

Typical values of ionospheric irregularity drift values at these latitudes are V^{IONO }≈ 300 ÷ 500 m/sec along the east-west direction [Aarons, 1982]; it can also be V^{IONO} ≈ 1000 m/sec during active conditions [Basu et al., 1999].

[12] Under these conditions, assuming a relative drift along the y direction only, different relative velocities and Fresnel frequencies can be calculated:

Assuming now V^{IONO} ≈ 1000 m/sec, one obtains

[13] At high latitudes usually it is ν_{F }> ν_{c}, but ν_{F} could also be one order of magnitude greater than ν_{F} at low latitudes (compare (8)–(11) with (4)–(5)). At high latitudes the major contribution to amplitude scintillation spectrum is pushed toward higher frequencies with respect to the frequency range valid at low latitudes. If the cutoff frequency ν_{c} used at high latitudes is the same of that used at low latitudes, the fluctuations spectra observed at high latitudes are both pushed toward higher frequencies, with respect to the fluctuations spectra observed at low latitudes (Figure 2).

[14] The resulting effect is an increase in σ_{ϕ} and S_{4} (i.e., the area under these curves). The increase in σ_{ϕ} is, however, more evident than the increase in S_{4} because the phase spectral density function behavior at low temporal frequencies is Φ_{ϕ} ∝ ν^{1−p}, where p is the spectral index, while the amplitude spectral density function at low temporal frequencies is Φχ ∝ constant [Yeh and Liu, 1982]. Under these circumstances, both amplitude and phase scintillation information is distorted: particularly, the phase scintillation is overestimated more than the amplitude scintillation, because fluctuations at frequencies not pertaining properly to “scintillations” have been taken into account in the phase spectrum.

[15] The scintillation spectral window pertaining to a particular set of data can be identified by evaluating the Fresnel filtering effects on the amplitude spectral density function: an accurate estimate of ν_{F} is then needed.

[16] To identify in a right way the Fresnel frequency, one should not use the approach by Fremouw et al. [1978] and Van Dierendonck et al. [1993] adopted to detrend intensity data in order to isolate the scintillation component. For them, if I_{k} is the received intensity sample at time t_{k} and I_{k}^{L} is the low-pass (with ν_{c} = 0.1 Hz) filtered values of I_{k}, the information on intensity scintillation lies on

This relation alters the actual spectral peaks and some error can be made in locating the Fresnel frequency ν_{F}.

[17] A more correct relation to consider intensity detrending and then to careful identify the Fresnel frequency is

as used by Beach and Kintner [1999]. This operation should take place because a given signal is the sum of its low and high frequency parts, not the product.

[18] The problem is the choice of a particular cutoff frequency that is fixed in order to attempt automated processing operations. In the case of Fremouw et al. [1978], a cutoff frequency ν_{c} = 0.1 Hz was carefully chosen for the particular system used in the Wideband experiment. The problem comes out when GPS scintillation monitor users and designers use the same cutoff frequency value as in Fremouw et al. [1978]: while ν_{c} = 0.1 Hz was a reasonable choice for Fremouw et al. [1978] and their system, in the case of GPS scintillation monitors the relative velocity values are very different from those of the Wideband experiment. At low latitudes the problem can be not so critical (as showed before), but at high latitudes the choice of a cutoff frequency appropriate to the system used can be crucial.

2.3. Geomagnetic Storm Effects at High Latitudes

[19] Recent experimental scintillation data have been presented for both high and low latitudes [Doherty et al., 2000; Pi et al., 2001]. The data taken at high latitudes correspond to periods affected by geomagnetic storms. For these data, examples of “phase without amplitude” scintillations were presented. These phenomena have not a straightforward explanation on theoretical basis for the given link geometry.

[20] In the work of Doherty et al. [2000], experimental rate of change of TEC (in m/min) were also presented. During the April 2000 storm, peak values of rate of change of TEC equal to ≈ 3 m/min were detected and correlated to “apparent” phase scintillations. The advance on L1 carrier phase corresponding to 3 m/min in is

It implies that during geomagnetic storms at high latitudes there can be greater and faster fluctuations in TEC than during quiet conditions.

[21] Since at high latitudes amplitude and phase spectra can be pushed toward higher frequencies with respect to low latitudes spectra (ν_{F}^{HIGH} values can be up to one order of magnitude greater than ν_{F}^{LOW} values), in general the same cutoff frequency value used both at high and low latitudes could be not appropriate for data detrending. According to the situation depicted in Figure 2, the phase standard deviation (i.e., the phase scintillation index σ_{ϕ}) measured at high latitudes could contain not only phase scintillations but also TEC fluctuations (i.e., low frequency phase fluctuations) erroneously taken into account. In such cases, when the situation depicted in Figure 2 does occur, data detrending is not able to eliminate completely TEC fluctuations. This fact is produced by a cutoff frequency value too low with respect to the Fresnel frequency. Thus, in general, the phase scintillation indices σ_{ϕ} measured at high latitudes would be higher than those measured at low latitudes - under the same geophysical conditions - simply because Fresnel frequencies can be different at high and low latitudes while the cutoff frequency remains always the same (ν_{c} = 0.1 Hz is a widely used value for data detrending).

[22] Such a mechanism becomes critical in evaluating phase scintillation activity at high latitudes during geomagnetic storms. In Figure 3 an illustrative situation that could provide a possible explanation of high phase scintillations against low amplitude scintillations is represented. The theoretical behavior for amplitude and phase spectra is sketched in double logarithmic scales, taking into account asymptotical slopes only (a 3-D spatial power law irregularity spectrum is assumed) [Yeh and Liu, 1982], for quiet and disturbed geomagnetic conditions at high latitudes. The amplitude spectrum at high latitudes would not be substantially modified in presence of geomagnetic storm because the measured amplitude scintillation is low, assuming that the measurements of Doherty et al. [2000] are correct from the point of view of detrending equations (12)–(13). The geomagnetic storm effect should be more evident in the phase spectrum: the phase spectrum slope at low frequencies (i.e., ν < ν_{F}) should be increased, as experimental rates of change of TEC indicate [Doherty et al., 2000; Pi et al., 2001]. The high frequency phase spectrum slope would be nearly equal to the amplitude spectrum, according to the two-slope mechanism for the phase spectrum observed by Basu et al. [1991]. If the phase spectrum slope increasing that occurs during geomagnetic storms is not eliminated by proper data detrending, high phase scintillations for low amplitude scintilations could be measured. This can happen when the cutoff frequency value used in data detrending is not appropriate to the actual value of the Fresnel frequency. As observed by Basu et al. [1991], the low frequency part of the phase power spectrum is responsible for 70% of the measured σ_{ϕ}. The contribution to S_{4} in the same low frequency part of the intensity power spectrum is limited to 10%. The most important part of the intensity power spectrum is around the Fresnel frequency. The low frequency part of the power spectra, well below the Fresnel frequency, can significantly increase the σ_{ϕ} values, but not the S_{4} values.

[23] Thus, since during geomagnetic storms TEC fluctuations are dominant in the computation of phase standard deviations because of the low frequency phase spectrum increase, unappropriate data detrending could give rise to more evident cases of high phase scintillation against low amplitude scintillation. In such situations the data interpretation is confusing and erroneous: faster TEC fluctuations are not recognized and phase scintillation is overestimated.

[24] While the amplitude scintillations are those fluctuations originated from irregularity scales smaller than the first Fresnel radius (Fresnel scale), the phase fluctuations can be originated from irregularity scales both smaller and greater than the Fresnel scale. The phase scintillations are those fluctuations originated from irregularity scales smaller than the Fresnel scale. This mechanism could explain the high σ_{ϕ} values with low S_{4} indices measured at Fairbanks, Alaska, during a geomagnetic storm and presented by Doherty et al. [2000].

3. Conclusions

[25] The major contribution to amplitude fluctuations spectra is at the Fresnel frequency ν_{F} that is not fixed, but it depends on the relative ionospheric drift, the wavelength used by the sampling signal and the distance between the observation point and the irregularity causing scintillation. The Fresnel frequency variations are more pronounced in the case of an highly variable links geometry, as for GPS.

[26] Data detrending, when the separation of deterministic and stochastic components is done using a fixed cutoff frequency and not appropriate to the actual geophysical conditions during measurements, can lead to a misleading data interpretation (for instance an overestimate of phase scintillation).

[27] During geomagnetic storms at high latitudes, the problem introduced by frozen filtering is amplified, because TEC fluctuations are greater and faster than during quiet conditions causing a phase spectrum slope increase at low frequencies. If the phase and amplitude spectra are computed by means of a data detrending not able to eliminate the phase slope increase at low frequencies (i.e., choosing the spectral window pertaining to scintillations in particular geophysical conditions), situations of “phase without amplitude” scintillation could arise.

[28] Moreover, experimental scintillation data collected by measuring signals of different sources (GPS, GEO, NNSS, Wideband satellites) are not comparable among themselves when treated with the same detrending conditions (i.e., equal cutoff frequency), because of the changing geometry and different signal characteristics.

[29] The importance of a correct treatment and interpretation of experimental raw data lies in (1) the validation of theoretical ionospheric scintillation models by means of experimental data and in (2) a proper assessment of the impact of ionospheric scintillations on satellite communications and navigation.