Vol50,6,2007 699 ANNALS OF GEOPHYSICS, VOL. 50, N. 6, December 2007 Key words ionospheric scintillation – GPS scintil- lation monitors – scintillation indices 1. Introduction The amount of scintillation activity present in radio waves propagating through the upper atmosphere is estimated by means of scintilla- tion indices which measure the stochastic fluc- tuating components of these electromagnetic radiations. The scintillation activity is assessed on both intensity and phase of radio signals re- ceived on the ground, after propagating through drifting irregularities of the electron density spatial distribution in the ionosphere. The scintillation index, used overall for esti- mating the fluctuations induced by drifting plasma density irregularities on the signals in- tensity, is the index S4 (Briggs and Parkin, 1963), i.e. the intensity standard deviation nor- malised to the average received intensity and is given by (1.1) where I is the received intensity and the 〈.〉 op- erator denotes an ensemble average. The phase scintillation index σφ is usually de- fined as the standard deviation of the received phase. Of course, these standard deviations are aimed to estimate the signal fluctuations induced by radio wave scintillations. Thus, the signal components subject to fluctuations due to ionos- S I I I 4 2 2 2 2 = − On the relationship between the geometrical control of scintillation indices and the data detrending problems observed at high latitudes Biagio Forte Centre for Atmospheric Research, University of Nova Gorica, Slovenia Abstract The experimental estimate of radio waves scintillation, caused by plasma density irregularities in the ionosphere, is usually attempted by means of scintillation indices which are essentially standard deviations of stochasticly fluctuating parts of the received radio wave intensity and phase. At high latitudes, provided that the propagation problem may be modelled by means of the weak scattering theory, the typical scintillation indices S4 and σφ de- pend on a geometrical factor which introduces some amplifications on their values. Scintillation indices S4 and σφ measured at auroral latitudes are estimated by means of different boundary detrending conditions and the geo- metrical effect on those detrending conditions is investigated. In the case of the polar Low Earth Orbiting (LEO) satellite links considered here, high phase with low intensity scintillation events do not seem to be related to geo- metrical effects only, but rather to misleading data detrending. Mailing address: Dr. Biagio Forte, Centre for Atmo- spheric Research, University of Nova Gorica, Vipavska 13, PO Box 301, SI-5001 Nova Gorica, Slovenia; e-mail: biagio.forte@p-ng.si 700 Biagio Forte pheric scintillation (i.e., caused by drifting elec- tron density irregularity structures in the iono- sphere) need to be identified and separated from other signal components. This is usually accom- plished by means of a detrending process applied to the intensity and phase of the received radio signal, filtering out those signal components not pertaining to the scintillation mechanism. The detrending process usually takes place in the fre- quency domain and is characterised by a low fre- quency edge below which signal fluctuations and trends are assumed to be not related to ionos- pheric scintillation. The choice of such a cut-off frequency depends on the geometry of the prop- agation problem considered. The key point is to choose the cut-off frequency low enough to catch the bulk of intensity scintillation, leaving S4 unmodified for all the experimental condi- tions, determined by the signal wavelength and by the ionospheric relative drift. The cut-off fre- quency choice clearly depends on the experi- mental features implying that a general value does not exist. For instance, in the case of the past Wideband experiment based on a polar low Earth orbiting satellite transmitting several radio beacon wavelengths, such a value was fixed to be 0.1 Hz (Fremouw et al., 1978). This has been the cut-off frequency value used overall, in both high and low latitude exper- iments dealing with generic beacon satellites, al- though not always LEO. In the last decade, the rising interest in assessing the impact of ionos- pheric scintillation on satellite based navigation systems has led to the development of GPS scin- tillation monitors allowing for the retrieval of the scintillation information from all the satellites on track (Van Dierendonck et al., 1993; Beach and Kintner, 1999). The detrending process used in these monitors relies on a fixed low frequency cut-off edge equal to 0.1 Hz, as in the case of beacon satellites based experiments. It has been a common and accepted picture that GPS scintillation monitors detect high phase scintillation in the presence of low inten- sity scintillation at high latitudes, implying that GPS equipment is subject to disturbances in the phase rather than on the intensity of the signals, irrespective of how this may impact the func- tioning of GPS receivers (Doherty et al., 2000; Pi et al., 2001; Aquino et al., 2007). A possible explanation of «phase without amplitude» scintillation events routinely ob- served by GPS scintillation monitors at high latitudes is based on erroneous data detrending, due to a fixed cut-off frequency (0.1 Hz) not ap- propriate to the propagation conditions which may occur at high latitudes for GPS signals (Forte and Radicella, 2002). Moreover, there seems to be no clear evidence for a geometrical control of the scintillation indices as measured on GPS links (Forte and Radicella, 2004), sim- ilar to what is observed with polar LEO beacon satellites which leads to enhancements of the phase scintillation index whenever the ray path lies within an L-shell (Fremouw, 1980). Here, some scintillation events measured by means of polar LEO beacon satellites are analysed to explain how the classical phase scin- tillation index σφ may introduce some troubles in the estimate of the phase scintillation activity on a given satellite link. This takes into account possible geometrical effects on σφ and an alter- nate index for the assessment of phase fluctua- tions induced by drifting electron density irreg- ularities at ionospheric heights (Forte, 2005). 2. Experimental data The experimental data used here are based on radio signals coherently transmitted from Tsykada beacon satellites at two frequencies: 150 MHz and 400 MHz. These radio signals are received at nearly aligned ground stations which are used overall for tomographic ionos- pheric reconstruction at European auroral lati- tudes (fig. 1). The intensity and phase of the re- ceived radio signals are sampled at a 50 Hz rate making it possible to estimate the scintillation activity experienced while traversing drifting electron density irregularities in the ionosphere. No elevation mask angle is applied to the data, so that border effects at the beginning and end of the time series shown hereafter are associat- ed mainly with low elevation angle phenomena. A detrending process is applied to the raw data to select only those stochastic fluctuations induced by drifting plasma density irregularities on both intensity and phase of the signals re- ceived on the ground. The detrending process is 701 Geometrical and detrending effects on scintillation indices essentially a high-pass filter designed in the fre- quency domain and characterised by a fixed cut- off low frequency edge. All the fluctuations cor- responding to frequencies below this cut-off are ruled out from the calculation of the scintillation indices, as they are considered not pertaining to ionospheric scintillation. The scintillation in- dices S4 and σφ are calculated for three different values of the cut-off low frequency edge: 0.1 Hz, 0.3 Hz, and 0.5 Hz. The values assumed for the low frequency limit in the detrending process are consistent with the typical values for the Fresnel fluctuation frequencies relative to the geometry of satellites links considered. The Fresnel frequency is given by (2.1) where VREL is the relative drift at ionospheric al- titudes composed of the satellite motion and the electron density irregularities drift, while dF is the Fresnel radius. Considering that at high lat- itudes plasma density irregularity structures may have drift speeds ranging from about 100 m/s to about 1 km/s (Aarons, 1982), the Fresnel frequencies for the Tsykada satellites links are expected to be around a few Hz. This is also confirmed by the experimental data. Figure 2a-d shows some scintillation events observed at Kiruna (Lat: 67.84°N, Long: 20.41°E, f d V REL F F = Fig. 1. The ground stations used for recording Tsy- kada signals: Tromso (TRO), Kiruna (KIR), Lulea (LUL), and Kokkola (KOK). Fig. 2a-d. Intensity power spectral densities normalised to the mean received intensity, as measured for differ- ent satellite links. This shows that a Fresnel frequency of a few Hz may normally occur at auroral latitudes. The measurements are taken during the night of 30 october 2003 from a) Kokkola, b) Kiruna, c) and d) Lulea. a b c d 702 Biagio Forte L: 5.6) during the night of 30 October 2003. The power spectral densities corresponding to 20 s time intervals show Fresnel frequencies of a few Hz as indicated, owing to real values for the rela- tive ionospheric drift, for the distance of the re- ceiver to the phase screen approximating the elec- tron density structures, and for the satellite zenith angle. The values chosen for the cut-off frequen- cy in the data detrending process are aimed to show how S4 and σφ estimates modify as the low frequency detrending limit is shifted towards higher fluctuation frequencies, owing to Fresnel frequencies of a few Hz for the links considered here. The key point is understanding whether large σφ values may always be explained in terms of geometrically induced enhancements or in terms of misleading data detrending conditions as well (Forte, 2005). 3. Discussion Figure 3 shows scintillation indices meas- ured for the 400 MHz radio signal during a satel- lite pass over the ground station located in Lulea (Lat: 65.58°N, Long: 22.17°E, L: 4.7) on the night of 30 October 2003 starting at 19:30:29 UT. The top left plot shows S4 values for the three different low frequency detrending limits: the solid line refers to a cut-off frequency of 0.1 Hz, the dashed line refers to a cut-off frequency of 0.3 Hz, while the dotted line refers to a cut-off frequency of 0.5 Hz. The top right plot shows σφ values in radians for the same cut-off frequency values. The bottom left plot shows a new param- eter proposed for the estimate of phase scintilla- tion, which is given by (Forte, 2005) (3.1) where the 〈.〉 operator denotes an ensemble av- erage and φ is the received and detrended phase. Sφ values are given in rad/s. The bottom right plot shows the geometrical factor G (in ar- bitrary units) responsible for amplifications of σφ values. For axially symmetric irregularity structures G achieves a maximum only at the magnetic zenith, while for sheetlike structures G maximises whenever the propagation vector lies within the plane of the sheet which is also L-shell aligned (Rino, 1979). The G factor S t 2 2 2φ =φ c m Fig. 3. Scintillation indices recorded during the night of 30 October 2003 from the ground station located in Lulea. The solid lines refer to a detrending cut-off frequency of 0.1 Hz, the dashed lines to 0.3 Hz, and the dot- ted lines to 0.5 Hz. Also shown the geometrical factor G for this satellite link. 703 Geometrical and detrending effects on scintillation indices shows a localised peak for a pierce point lati- tude between 60° and 70° which is associated with a local peak in both σφ and Sφ occurring slightly after 19:35:00 UT. No similar localised peaks appear in S4 which takes low values in the neighbourhood of the localised peak in G. This seems to be a typical situation where a radio wave with a ray path aligned with an L-shell is weakly scattering on an electron density irregu- larity structure. For all the events shown here the G factor has been calculated assuming sheetlike electron density irregularities struc- tures, which appear to be typical at auroral lati- tudes. The axial ratios which define G are those relative to sheetlike irregularities, i.e. 8:8:1 (Ri- no and Owen, 1980). The values of σφ indeed experience an en- hancement due to a pure geometrical factor which is perfectly described by means of the weak scattering theory (Rino, 1979). After this peak, an overall increase in the scintillation ac- tivity is recorded along the ray path which is not aligned with a magnetic field line anymore. The detrending effect is clearly visible on the scintil- lation indices: an evident rescaling of σφ occurs when increasing the value of the low cut-off fre- quency detrending limit, while such a rescaling is essentially negligible on both S4 and Sφ. In par- ticular, the rescaling observed on σφ shows how the detrending effect and the geometrical effect are separate and consistent with each other. The σφ enhancement caused by purely geometrical reasons is still evident on its rescaled values as well as on the Sφ index. Moreover, rescaled val- ues of σφ are still tracking the higher scintillation event starting after 19:38:00 UT, in accordance with S4 and Sφ behaviour. A slightly different situation is depicted in fig. 4, which shows scintillation indices meas- ured for the 400 MHz signal during a satellite pass over the ground station located in Kiruna on the night of 30 October 2003, beginning at 23:11:39 UT. High scintillation activity is pres- ent on this link as shown by all the three indices. There is a peak in G which appears to be soft, owing to a limited ray path alignement with L- shells. The geometrical effect on σφ is probably taking place, but very difficult to notice, due to the mixing with an overall high scintillation ac- tivity present throughout the entire satellite pass. Fig. 4. Scintillation indices recorded during the night of 30 October 2003 from the ground station located in Kiruna. The solid lines refer to a detrending cut-off frequency of 0.1 Hz, the dashed lines to 0.3 Hz, and the dot- ted lines to 0.5 Hz. Also shown the geometrical factor G for this satellite link. 704 Biagio Forte On the contrary, the detrending effect is clearly visible: again, an evident rescaling of σφ values occurs when the low frequency boundary of the detrending process is shifted towards higher fluctuation frequencies. Such a rescaling does not occur for both S4 and Sφ which show almost the same values in the three different detrending conditions. Nevertheless, the σφ values corre- sponding to cut-off frequencies of 0.3 Hz (dashed line) and 0.5 Hz (dotted line) are still tracking the high scintillation event present throughout the link as their behaviour is consis- tent with both S4 and Sφ trends. Although S4 and Sφ values remain unmodi- fied after changing the detrending cut-off fre- quency, the question is still whether the correct cut-off frequency for σφ is 0.3 Hz or 0.5 Hz. This clearly depends on the Fresnel frequency values corresponding to each link geometry. The Fresnel frequency may vary even during a single satellite pass owing to the changing satellite position, to the drift of the irregularity structures along the ray path, and to the dis- tance of the receiver from the phase screen as- sociated with those structures.The difficulties related to the choice of a unique detrending cut- off frequency, suitable for a proper estimate of phase scintillation, make the classical σφ a prob- lematic parameter (Forte, 2005; Beach, 2006). Although this has been already observed in the case of GPS satellites links at high latitudes and explained in terms of weak scattering results (Forte, 2005; Forte et al., 2004; Beach, 2006), the data presented here show that the detrend- ing problem may be a critical issue also in the case of different satellite links, unless a careful analysis of the propagation geometry and con- ditions is performed in order to establish the most appropriate cut-off frequency value. For instance, an example of such a careful analysis was provided in the Wideband experiment (Fre- mouw et al., 1978). Figure 5 provides the last case study to be considered. Scintillation indices observed on the 400 MHz link are plotted. These indices refer to the satellite pass started at 18:16:31 UT and re- ceived from the ground station located in Kiruna. Low scintillation activity is observed on this Fig. 5. Scintillation indices recorded during the night of 30 October 2003 from the ground station located in Kiruna (for a time interval different than in fig. 4). The solid lines refer to a detrending cut-off frequency of 0.1 Hz, the dashed lines to 0.3 Hz, and the dotted lines to 0.5 Hz. Also shown the geometrical factor G for this satel- lite link. 705 Geometrical and detrending effects on scintillation indices satellite pass. Neglecting the initial and final epochs which correspond to low satellite eleva- tion, S4 is around 0.3 first and mostly around 0.1 later. Sφ is also mostly around 2÷3 rad/s, which correspond to low scintillation values, as may be noticed by comparing the Sφ values appearing in fig. 5 and those in figs. 3 and 4 relative to high scintillation events. The classical phase scintilla- tion index σφ records values around and in excess of 1 rad for a typical cut-off frequency of 0.1 Hz, while for cut-off frequencies of 0.3 Hz and 0.5 Hz there is a significant drop to lower values, more appropriate to low scintillation conditions. Both S4 and Sφ maintain almost the same values for all the three different low frequency bound- ary conditions in the detrending process, as the difference between the corresponding values is negligible. The three case studies show how S4 and Sφ are not affected by misleading data detrending, as they maintain their values unmodified when shifting the detrending cut-off frequency to- wards even higher fluctuation frequencies. This confirms the intrinsic weakness of σφ for the es- timate of the phase scintillation activity, partic- ularly at high latitudes, and the evident capabil- ity of the new Sφ parameter to properly assess the impact of ionospheric scintillation on the phase of a radio wave. As may be noticed in fig. 5, a less pro- nounced peak is present in G which corresponds to a peak in σφ, still visible for the 0.3 Hz and 0.5 Hz lines. To some extent, such a peak is also re- flected in Sφ. This proves again that the geomet- rical effect and the detrending effect are separate and consistent with each other. The geometrical effect only cannot satisfactorily explain the oc- currence of high Sφ values with low S4 values, not only in the case of GPS satellites links but also in the case of Tsykada satellites links. Even in the case of polar LEO satellites links, it seems that a misleading data detrending may still be a critical issue in the estimate of the classical phase scin- tillation index Sφ. 4. Conclusions The analysis of the scintillation activity recorded on Tsykada satellites links through the estimate of the classical indices S4 and Sφ, cou- pled with the new parameter Sφ, clarifies the re- lationship between the geometrical effect which may control σφ in presence of weak scattering and the detrending effect which may introduce misleading large σφ values, particularly at high latitudes. The case studies considered indicate that the geometrical effect and the detrending effect are separate and consistent with each other. En- hancements in σφ owing to localised peaks in the geometrical factor G remain evident even after the rescaling produced by the increase in the low frequency boundary of the data de- trending process. Only the geometrical effect cannot explain the overall occurrence of high σφ values with low S4 values, as this effect is very localised and limited only to those satellite po- sitions making the ray path aligned with an L- shell. In case of satellite passes mostly domi- nated by high scintillation activity, the geomet- rical effect seems not to be very evident, while the detrending effect on σφ appears to be indeed very evident. The geometrical effect also seems to be present on the new parameter Sφ which does not depend on the low frequency boundary condi- tions, while S4 does not show any geometrical or detrending effects. The Sφ parameter appears to be a more ro- bust indicator for the estimate of radio waves ionospheric phase scintillation, not only in the case of GPS links but also for overall polar LEO satellites links, such as the Tsykada ones. It should be noticed that the Sφ index is not related to the existing theory on radio wave scintillations, but more tailored to the opera- tional aspects of satellite based navigation sys- tems. Such an index, indeed, is aimed to esti- mate the signal dynamics caused by ionospher- ic scintillations which may even lead to signal loss of lock. 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