Scattering height estimation using scintillating Wide Area Augmentation System/Satellite Based Augmentation System and GPS satellite signals



[1] An experiment to measure equatorial amplitude scintillations on the geostationary Wide Area Augmentation System (WAAS) Satellite Based Augmentation System (SBAS) signal was conducted in Cachoeira Paulista (22.70°S, 45.01°W geographic coordinates; −17.74°N, 21.74°E geomagnetic coordinates), Brazil from December 2003 through February 2004. The purpose of this paper is to estimate the scattering height of the irregularities using the WAAS signal scintillations as compared to nearby Global Positioning System (GPS) signal scintillations. Estimating the scattering height is important because the calculated zonal drift velocity of the irregularities using the measured scintillation pattern velocity on the ground is height dependent. Accurate height estimation is also required if one wishes to develop phase screen scintillation models. The difference in the pattern velocities is due to the different signal puncture point velocities with respect to the ionospheric drift. Two east-west receivers are used to measure the scintillation pattern drift velocity and to compare the results of the geostationary WAAS satellite signal to that of a GPS satellite signal, which has a nonzero ionospheric signal puncture point velocity. By varying the assumed scattering height for the measurements from the nearby GPS signal, the zonal velocity measurements from the GPS scintillations can be matched to those of the WAAS scintillations, and a scattering height estimate can be made. When the puncture points have minimal separation, the inferred ionospheric irregularity zonal velocities should be equal. On the two nights for which data are available, scattering height estimates of 669 ± 209 km for the first night and 388 ± 139 km for the second night were obtained. On the second night, the reported mean hmF2 as calculated using a collocated Digisonde was 385 ± 17 km over the same period as the GPS/WAAS scattering height estimate. The geometry of this experiment was not optimal, but analysis demonstrates that future experiments could be substantially more accurate.

1. Introduction

[2] An inexpensive technique for estimating ionospheric zonal drifts in equatorial zones is to measure the east-west movement of scintillation patterns with spaced receivers [e.g., Vacchione et al., 1987; Spatz et al., 1988; Bhattacharyya et al., 2001]. This measurement contains information about the ionospheric irregularity's location and velocity. The GPS network of satellites is a source of signals for making scintillation measurements from multiple signals simultaneously. In the case of GPS, the signal puncture point velocity is frequently a substantial fraction of the equatorial zonal drift velocity [Kintner et al., 2001]. The contribution of the signal puncture point velocity is dependent on the scattering height estimate [Ledvina et al., 2004], which leads to uncertainty in the accuracy of zonal velocity estimates derived from GPS signal scintillations. Furthermore, accurately modeling scintillations requires good scattering height estimates. A technique that could be used to estimate the scattering height, and hence accurate zonal velocities, is presented.

[3] Early efforts to estimate zonal drifts with GPS signals near the equatorial anomalies led to results similar to those of accepted techniques such as using incoherent scatter radar at the magnetic equator but with some differences, suggesting the probability of vertical shears in the zonal drift [Kil et al., 2000, 2002]. Later, a more rigorous analysis showed that the effect of averaging over a range of signal elevation and azimuth angles reduced or eliminated the contamination of vertical drifts and variable scattering heights when estimating average zonal drifts using GPS signals [Ledvina et al., 2004].

[4] The Wide Area Augmentation System (WAAS) signal transmitted on the GPS L1 frequency (1.57542 GHz) is another radio source that can be used to estimate zonal drifts. Since the WAAS signal is transmitted from a geostationary satellite, velocity estimations from both moving and stationary ionospheric signal puncture points can be compared when the satellites' ionospheric puncture points are close. To make this comparison, an experiment using spaced GPS receivers was conducted from Cachoeira Paulista, Brazil. The receivers were modified to track the WAAS signal and to record its signal power at 50 samples per second. Two of these receivers were located with an east-west separation of 112 m. The experiment was conducted for 63 days from December 2003 to February 2004. During this period, there were two instances of a GPS signal puncture point passing near the WAAS signal puncture point while both signals were experiencing scintillations. Analysis of these two events is presented in this paper.

2. Technique

[5] The spaced-receiver technique is often used to estimate ionospheric drift velocities. This technique requires transmission of a transionospheric radio signal from one or more satellites. While passing through the ionosphere, the signal is diffracted by plasma density irregularities of the appropriate Fresnel scale size embedded within the surrounding plasma of the ionosphere. The diffraction of the signal produces a scintillation pattern on the ground that varies in both amplitude and phase [Yeh and Liu, 1982]. Receivers located well below the ionosphere are used to record the amplitude and/or phase variations. The recorded data are then postprocessed to obtain the ionospheric drift velocities using cross-correlation [Costa et al., 1988] or cross-spectral techniques [Costa and Fougere, 1988].

[6] The structure of the ionospheric irregularities associated with equatorial spread F drift zonally from west to east and are measured to be greatly elongated meridionally [Kintner et al., 2004] because of the parallel conductivity of the ionosphere at F region heights. The ratio of the zonal (perpendicular) conductivity to the meridional (parallel) conductivity is much less than one, so the irregularities are highly elongated along the field lines. Since the meridional irregularity scale length is large (much greater than 1 km) [Kintner et al., 2004], any drifts in the meridional direction will have little effect on the measurement of zonal drifts.

[7] In the case of a geostationary radio source propagating through the ionosphere, the scintillation pattern velocity is the projection of the irregularity velocity onto the Earth's surface. This projection causes the measured velocity on the ground to differ from the true ionospheric zonal velocity [Kintner et al., 2001]. For example, both vertical and zonal irregularity velocities map into a zonal scintillation pattern velocity. As shown in Figure 1, the projection of the scintillation pattern as observed is further complicated when a nongeostationary satellite is used for the measurement. In this case, the scintillation pattern twists, and the pattern velocity is dependent on the elevation and azimuth to the satellite, the direction of the magnetic field at the irregularity height, and both the zonal and vertical velocities [Ledvina et al., 2004]. There is an arrangement, however, in which the projected scintillation pattern velocity will not combine both the vertical and zonal irregularity velocities. For example, when the receiver, satellite signal, and irregularities all lie within a meridional plane, the scintillation pattern velocity as observed on the ground is solely produced by the irregularity zonal velocity.

Figure 1.

Scintillation pattern observed in the plane of the receivers (defined by the magnetic east-west and north lines) is the projection of the irregularity, which is aligned with the magnetic field vector, B, at the irregularity height. The observed pattern is also affected by the relative satellite position and motion with respect to the receiver. In the magnetic meridional plane, the observed fade pattern is not affected by the satellite-receiver geometry nor by the magnetic field vector at the ionospheric irregularity height (adapted from Kintner et al. [2004]).

[8] Measurements are made by at least two receivers placed magnetically east-west, and the drift velocity measurements are made in the local receiver coordinate system that is defined by the spatial orientation of the receivers. The relationship between the zonal scintillation pattern velocity measured in the receiver coordinate system, vgpsx, and the satellite and ionospheric velocities can be approximated by [Ledvina et al., 2004]

equation image

where zsat is the satellite height, zion is the mean scattering height of the diffraction-causing irregularities, vionx is the zonal irregularity velocity, viony is the meridional irregularity velocity, and vionz is the vertical irregularity velocity. Similarly, vsatx, vsaty, and vsatz are the zonal, meridional, and vertical satellite velocities, respectively, and will be collectively defined as vsat.

[9] In the case of GPS satellites, vsat is easily determined using the transmitted ephemerides, which are available to any user either from the broadcast navigation message or from online resources such as the National Geodetic Survey's Continuously Operating Reference Stations Web site.

[10] All vectors in equation (1) and all subsequent equations pertain to the coordinate frame of the receivers. Usually, the receivers are oriented in the local magnetic frame, so all vector quantities must be rotated into the local magnetic frame.

[11] The mapping factors qy/qx and qz/qx are defined as

equation image
equation image

where Bx, By, and Bz are the International Geomagnetic Reference Field (IGRF) components of the magnetic field vectors at the signal ionospheric puncture point, θ is the satellite azimuth angle from magnetic north, and ϕ is the satellite zenith angle. The modifications of viony and vionz by the mapping factors qy/qx and qz/qx represent the twisting of the scintillation pattern observed on the ground due to the different orientation of the magnetic field vectors at the ionospheric puncture point. Furthermore, the pattern velocity on the ground is modified both by the satellite signal ionospheric puncture point velocity, vsat, and the respective mapping factors qy/qx and qz/qx. At the magnetic meridional plane, the mapping factors qy/qx and qz/qx both become zero because θ and Bx are zero.

[12] In equation (1), the unknowns are the mean scattering height, zion, the zonal irregularity velocity, vionx, the meridional velocity, viony, and the vertical irregularity velocity, vionz. Note that these variables are defined in the local receiver reference frame where the meridional velocity is in the magnetic north-south direction. This coordinate frame differs from some satellite reference frames where meridional is defined as perpendicular to the zonal and magnetic field vectors.

[13] The goal is to estimate the scattering height, which generally requires making assumptions about these unknowns. The large parallel conductivity of the ionosphere in the F region causes the irregularities to be greatly elongated in the meridional direction; that is, the irregularities parallel to the magnetic field are generally much larger than the Fresnel scale and will not influence the amplitude scintillations. Hence there is no parallel irregularity velocity contribution to vionz and viony. The quantity vionz may be quite large during the growth phase of the irregularities. However, the growth generally is completed an hour or two after sunset. After this period, the vertical ionospheric velocity is known to be about −10 to −20 m/s [Fejer et al., 1991], which is typically an order of magnitude smaller than the zonal velocity. Further requiring the mapping factors qy/qx and qz/qx to have magnitude less than 0.05 ensures that vionz never contributes more than 1 m/s to zonal scintillation drift velocity measurements. This situation corresponds to satellite signal paths lying within the magnetic meridional plane.

[14] Under these assumptions, equation (1) simplifies to

equation image

[15] Note that in equation (4), even when the mapping factors qy/qx and qz/qx are small, the satellite meridional and zonal velocity may be quite large and will contribute significantly to the overall scintillation pattern velocity.

[16] In the case of a high-elevation geostationary satellite at the magnetic meridional plane, ∣vsat∣ = 0 and zsatzion, equation (4) simplifies to

equation image

so equation (5) yields a zonal irregularity velocity that is height insensitive.

[17] The overall goal of this method is to estimate the scattering height of the irregularities. Using the equations and assumptions presented above, this goal is attainable. The first step is to choose a location for logging scintillation data where the WAAS satellite signal (or equivalent geostationary satellite signal) resides near the magnetic meridional plane. As mentioned earlier, the position of the WAAS signal puncture point at 350 km must result in mapping factors qy/qx and qz/qx that have magnitude less than 0.05. Furthermore, choosing scintillation data that occur well after sunset will further minimize the meridional and vertical velocity contamination due to the rapidly growing irregularities.

[18] Next, concurrent scintillation data from spaced receivers for both the WAAS satellite and a GPS satellite must be available. The scintillations must be occurring on both the WAAS signal and the GPS signal while the GPS signal ionospheric puncture point is near both the magnetic meridian and the WAAS satellite signal ionospheric puncture point. In the text of this paper, the term ionospheric signal puncture point or ionospheric puncture point is used to indicate the position of the signal at a particular height and does not explicitly refer to the scattering height of the irregularity, the determination of which is the goal of this paper.

[19] For the GPS satellite, the idea of being near the magnetic meridian will have the same definition as the WAAS satellite; that is, qy/qx and qz/qx have magnitude less than 0.05. Furthermore, the GPS signal puncture point must be physically close to the WAAS signal puncture point. For this paper, close is defined as a radial distance of about 100 km from the WAAS signal ionospheric puncture point at an assumed altitude of 350 km. This definition of close, however, may not be optimal. It is generally known that the irregularities associated with spread F are greatly elongated along the field line. Along the field lines and within the magnetic meridional plane, the velocities may agree over a much longer distance. Perpendicular to the plane, it is unclear what the optimal distance may be as it likely depends on several factors, including the satellite velocity, ionospheric velocity, conductivity, and irregularity strength.

[20] The last step is to calculate the ionospheric zonal drift velocities, vionx, for the WAAS satellite (which is scattering height insensitive) using equation (5). The zonal drift velocities derived from the GPS signal are also calculated over a range of reasonable scattering heights, zion, using equation (4). The zonal drift velocities as obtained using the GPS measurements at several assumed scattering heights are then compared to the velocities obtained from the WAAS measurements to determine the best fit–estimated scattering height.

[21] Selecting a point on the Earth where the ionospheric puncture point of the WAAS satellite is near the magnetic meridional plane of the receiver is not trivial. Furthermore, the occurrence of an ionospheric puncture point from a GPS satellite signal that passes near to the geostationary satellite's ionospheric puncture point during a scintillating period is rare. Two cases are presented where the proper positioning of the receiver during scintillations resulted in such a case, and the technique is tested.

3. Observations

[22] The data set consists of GPS L1 and WAAS amplitude scintillation data collected in Cachoeira Paulista, Brazil (22.70°S, 45.01°W geographic coordinates; −13.48°N, 25.30°E geomagnetic coordinates) from December 2003 through February 2004. The WAAS amplitude data were collected from the INMARSAT AOR-W (54°W, pseudorandom noise (PRN) 122) satellite. The location of the receivers is such that the WAAS satellite's ionospheric puncture point is nearly in the magnetic meridional plane. As viewed from the receivers, the WAAS signal path lies only 5.5° away from the magnetic meridional plane, which is 33 km at 350 km altitude, giving respective values of the qy/qx and qz/qx mapping factors of −0.04 and 0.03. These mapping factors are within the constraints defined earlier.

[23] The data were collected using two zonally spaced GPS L1 scintillation receivers that were designed at Cornell University [Beach and Kintner, 2001] and were later modified to obtain WAAS signal power data. These receivers record wideband power on the GPS L1 and WAAS signals broadcast from the satellites at a data rate of 50 samples per second.

[24] Over the 63 day span, the WAAS signal and a GPS signal were both scintillating on only 17 nights. On two of these 17 nights, PRN 9's ionospheric signal puncture point came close to WAAS's ionospheric signal puncture point.

[25] The data for PRN 9 are processed by first selecting all scintillations with an S4 index greater than or equal to 0.20 and at a satellite elevation greater than 40°. All scintillations with an S4 index greater than or equal to 0.20 were considered for the geostationary WAAS satellite since its elevation remains fixed at 61.5°. The S4 index is computed as defined by Yeh and Liu [1982]. Over successive windows of 60 s, the cross-correlation functions between receivers are computed, and a minimum normalized correlation limit of 0.5 is enforced. The correlation limit has been chosen to eliminate weak correlations between receivers due to weak scintillations or rapid time-evolving scintillation patterns, which tend to bias scintillation pattern velocity estimates. For PRN 9, the zonal drift velocities were calculated over assumed scattering heights from 100 to 1000 km in 1 km steps. The limits on the scattering heights were chosen to extend well below and beyond the typical F region peak density heights where the irregularities are found. The 1 km step size was selected to provide sufficient resolution for the calculated zonal velocity which, as will be explained later, is highly sensitive to several factors.

[26] Figure 2 shows the polar elevation/azimuth plot for the trajectory of PRN 9 and the position of the WAAS satellite on 26 January 2004. The S4 index observed for both satellites is plotted in Figure 3 for the same day. Figure 4 shows the zonal velocity of the ionosphere for both PRN 9 and WAAS AOR-W assuming zion = 350 km.

Figure 2.

Elevation/azimuth plot for PRN 9 on 26 January 2004 (solid line). The dash-dotted line represents the magnetic meridional plane. The minimum distance between the signal puncture points of PRN 9 and the WAAS satellite is about 13 km at an assumed height of 350 km.

Figure 3.

S4 index plots for both (top) PRN 9 and (bottom) the WAAS satellite on 26 January 2004. The scintillations occur well after sunset, suggesting that the irregularities are not moving vertically. PRN 9 crossed the meridional plane of the receiver at 2350 LT.

Figure 4.

Zonal velocity estimated from PRN 9 (black squares) and WAAS (gray circles) amplitude measurements on the night of 26 January 2004. The velocities agree well, even though at 2248 LT the distance of PRN 9's ionospheric signal puncture point is at a perpendicular distance of over 200 km from the magnetic meridional plane.

[27] Figure 5 shows the zonal velocity obtained for both PRN 9 and WAAS AOR-W on 24 January 2004. On this particular evening, there was a reversal in the zonal velocity. Because of the nature of the GPS satellite orbits, PRN 9's trajectory on this day is nearly identical to that shown in Figure 2 for 26 January 2004. The S4 values for this day differed from those on 26 January 2004, but they are similar in magnitude and are not shown.

Figure 5.

Same as Figure 4 except for 24 January 2004. Note the reversal in the zonal velocity for the evening. The gap in the data at 2320 is a result of data processing. Since a 60 s correlation window with normalized correlation limits of 0.5 were used, a pattern velocity that takes more than 30 s to drift between the receivers will not meet the minimum correlation limits; hence a velocity cannot be calculated.

4. Discussion

[28] On 26 January 2004, PRN 9 crossed the magnetic meridional plane of the receiver at 2358 hours LT at a distance of approximately 36 km from the WAAS ionospheric signal puncture point. Similarly, on 24 January 2004, the closest distance along the meridian was also 36 km at 2406 hours LT.

[29] As the ionospheric puncture point of PRN 9 approaches the WAAS signal ionospheric puncture point, the velocities should agree more closely. As shown in Figure 6, the velocities are similar in magnitude; nevertheless, a consistent scattering height for the entire interval cannot be determined. In reality, the scattering height of the irregularities may actually be quite variable because the irregularities are known to extend in height from 350 to 2000 km [Kelley et al., 2006]. The scintillations may be caused by irregularities at any or a combination of these heights.

Figure 6.

Zonal velocities for 26 January 2004 from 2324 to 2354 LT. The error bars indicate the range of velocities at heights of 100 km (smallest velocity) to 1000 km (largest velocity). At 2324 LT, PRN 9's ionospheric signal puncture point lies about 50 km from the magnetic meridional plane. Over the entire interval shown, the ionospheric signal puncture point of PRN 9 was within 100 km of the WAAS ionospheric signal puncture point.

[30] At the very least, this method allows a bound for the entire interval to be set on the scattering height. In this particular case, the heights are constrained between 175 and 575 km for the period lasting from 2324 to 2354 hours LT. Over the interval shown, the radial distance from the WAAS signal puncture point to the GPS signal puncture point at 350 km altitude is less than 100 km.

[31] The scattering height estimates have been obtained in a least squares sense by finding the minimum sum of the squared differences between the WAAS zonal velocities and the zonal velocities for PRN 9 at each scattering height. The standard deviation of the scattering height estimate has been obtained by multiplying the computed change in height over change in velocity of equation (4) with the standard deviation of the velocities from the least squares analysis. This analysis yields a mean scattering height estimate over this time period of 388 km with a standard deviation of 139 km.

[32] Over the period from 2330 to 2412 LT on 24 January 2004, the ionospheric signal puncture point of PRN 9 also came within 100 km of the WAAS ionospheric signal puncture point. Again, using the same method as before, the scattering height estimates were obtained and are shown in Figure 7. On this particular night, the scattering height falls between 100 and 900 km. The mean scattering height on this night is 669 km with a standard deviation of 209 km.

Figure 7.

Zonal velocities for 24 January 2004 from 2330 to 2412 LT. The error bars indicate the range of velocities at heights of 100 km (smallest velocity) to 1000 km (largest velocity). Again, the ionospheric signal puncture point of PRN 9 was within 50 km of the magnetic meridional plane and within 100 km of the WAAS ionospheric signal puncture point.

[33] To gauge how well this technique determines the scattering heights, the result for 26 January 2004 is compared to collocated Digisonde data. The hmF2 heights obtained on this evening are shown in Figure 8. Over the interval from 2330 LT to 2400 LT, the mean hmF2 height as reported by the Digisonde is 385 km with a standard deviation of 17 km. The distance at 350 km altitude from the point directly above the Digisonde to the WAAS signal puncture point is approximately 150 km. This comparison to the Digisonde data must be made carefully because hmF2 represents the height of peak electron density and may not actually be indicative of the scintillation-causing irregularity height. However, the result does agree well with the height estimate obtained using this technique for the same period of 388 km. Digisonde data were not available for 24 January 2004.

Figure 8.

Plot showing hmF2 heights obtained from a collocated Digisonde for 26 January 2004. Over the period from 2330 to 2400 LT, the mean height was 385 km, which agrees well with the calculated height of 388 km using the method detailed in this paper.

[34] The height of the irregularities causing the scintillations may be quite variable; hence the large variability calculated above may be indicative of the true variations in the scattering height. Good estimates of the scattering height are hard to obtain and are often given only in an average sense. In the past, estimates of the scattering height have been made from estimates of the Fresnel minima, which, in turn, are inferred from nulls in the scintillation power spectrum [Bhattacharyya et al., 2001] and scintillation pattern zonal velocity estimates. Alternately, Ledvina et al. [2005] have suggested that relating the projection angle (Figure 1) to an IGRF magnetic field through a Kalman filter can be used to estimate the scattering height. In all cases, the scattering height estimate depends on the accuracy of the zonal velocity estimate.

[35] In the example analyzed here (Figure 6), a variation of 6 m/s in the scintillation pattern velocity is observed when the scattering height changes by 100 km. Hence the accuracy of the scintillation pattern velocity estimate is critical to estimating the scattering height. The resolution of velocity estimates for our experiment was 1 m/s. The estimated height step size was chosen with this resolution in mind. A floor on the cross-correlation normalized limit was set at 0.5 to yield accurate velocity estimates. Nonetheless, the measurement noise has never been quantified in a realistic environment, and the true errors are unknown. On the other hand, the weak dependence of the zonal drift velocity on the assumed scattering height allows the zonal irregularity drift velocity to be estimated accurately with scintillation drift velocities, even with moderate errors in estimating the scattering height; however, this is not always true.

[36] A different trajectory for the GPS satellite orbit can yield better scattering height estimates in spite of errors in measuring the scintillation pattern velocity. The velocity estimates obtained by equation (4) depend only on the satellite velocity and the assumed scattering height, zion. The terms in equation (4) can be rearranged to

equation image

which yields the dependence of the ionospheric zonal velocity on the scattering height estimate and the zonal velocity of the satellite. The larger the zonal velocity of the satellite, the more sensitive the estimated drift velocity is to the scattering height. On both of the nights presented, the zonal velocity (in the local receiver coordinate frame) of PRN 9 as it approached the magnetic meridian of the receiver was about 1360 m/s, which yielded the 6 m/s per 100 km sensitivity. However, when the entire satellite velocity of 3000 m/s is zonal, the sensitivity becomes 36 m/s per 100 km, greatly improving the resolution of the scattering height estimates. Future experiments in which the GPS satellite zonal velocities are much larger will yield a much better estimate of the scattering height.

5. Summary

[37] A spaced-receiver scintillation experiment was conducted in Cachoeira Paulista, Brazil, from December 2003 through February 2004 in an effort to determine the scattering height and hence to make better estimates of the zonal velocity. Scattering height estimates are also useful for modeling scintillation-causing irregularities. Analysis of the experiment geometry and GPS satellite velocity suggested that the technique is promising for higher satellite zonal velocities. A satellite orbit whose ionospheric puncture point zonal velocity is large yields a smaller bound on the scattering height estimate. In the examples presented herein, the data are adequate to demonstrate that the scattering height can be bounded and is in good agreement with the Digisonde hmF2 peak electron density height.


[38] Research at Cornell University was funded by the Office of Naval Research under grant N00014-04-1-0105. The authors thank INPE for their support and assistance, with special thanks to Eurico R. de Paula, Sinval Domingos, and Crisitano de Castilho for both the GPS installation and operation at Cachoeira Paulista and the Digisonde data.