Ionospheric effects on differential GPS applications during auroral substorm activity

Transcription

1 Ž. ISPRS Journal of Photogrammetry & Remote Sensing Ionospheric effects on differential GPS applications during auroral substorm activity S. Skone ), M.E. Cannon Department of Geomatics Engineering, The UniÕersity of Calgary, 500 UniÕersity Dr. NW, Calgary, AB, Canada TN 1N4 Accepted 9 April 1999 Abstract The use of the Global Positioning System Ž GPS. technology has become increasingly incorporated into airborne remote sensing applications over the past decade. While GPS positioning results may prove adequate for several applications at present, users should expect to experience degraded positioning accuracies over the next few years due to auroral substorm activity. Such degraded accuracies will arise from increased spatial decorrelation of ionosphere range delay errors in differential GPS applications, as the ionospheric activity increases during solar maximum. In this paper, the spatial decorrelation of ionospheric range delay is estimated during a substorm event and compared with quiet time values. Positional errors Ž in both vertical and horizontal measurements. in the range cm RMSE were observed during a 1997 substorm event that is representative of the activity anticipated at solar maximum around the year 000. q 1999 Elsevier Science B.V. All rights reserved. Keywords: differential GPS; ionospheric effects; airborne remote sensing; auroral region; substorm activity 1. Introduction Global Positioning System Ž GPS. is a satellite navigation system which allows the position of a receiver on the earth to be computed using range information contained in the satellites RF signals. Twenty-four satellites currently provide worldwide coverage and GPS positioning capability. Errors in the satellite range estimates can degrade positioning accuracies. These errors may be mitigated through the use of differential GPS Ž DGPS. positioning algorithms, where range errors are calculated at reference stations and transmitted to remote users. ) Corresponding author. Tel.: q ; Fax: q ; sskone@ensu.ucalgary.ca Differential GPS has been used in support of georeferencing airborne remote sensing applications for a number of years ŽAnderson, 1989; Baustert et al., 1989; Schwarz et al., Positioning accuracy requirements vary according to the application, and some typical cases are listed in Table 1 ŽSchwarz et al., Required accuracy, ranging from less than 10 cm for engineering and cadastral applications to 5 m for resource applications, can be achieved through proper GPS receiver selection, limitations on the reference-user receiver distance and the use of proper data processing algorithms Ži.e., carrier vs. code phase approaches.. Under normal operating conditions, the errors remaining after differential processing are due to atmospheric effects Žboth tropospheric and ionospheric errors., multipath and, to r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 80 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing Table 1 Airborne remote sensing positioning requirements Application area Position RMS accuracy Ž m. Engineering, Cadastral Forestry Ž detailed Cartographic mapping 1: Resource applications 5 a lesser extent, orbital errors. Multipath, or the reflection of signals off nearby objects, can be mitigated through proper antenna selection and placement. Atmospheric errors, on the other hand, can be rather large depending on the weather conditions Žin the case of the troposphere. and the activity of the ionosphere. Ionospheric error and its contribution to the overall aircraft positioning error budget is a particularly important topic given that the next solar maximum is in the year f000. At that time, the ionospheric error will increase in magnitude and the occurrence of geomagnetic storms will be more frequent, particularly for users in northern and equatorial latitudes. This may result in poor GPS tracking capabilities due to scintillation effects, as well as poorer differential positioning accuracies due to decreased spatial correlation of the ionospheric effect. This paper focuses on describing the ionospheric effects on GPS measurements and provides an estimate of the errors that can be expected at solar maximum, through analysis of a geomagnetic substorm event which occurred in April This analysis also includes a discussion of the spatial decorrelation of ionosphere range delays and the propagation of these errors into expected DGPS position accuracies.. Ionospheric effects on GPS A GPS receiver measures two types of observables: carrier phase in number of cycles, and code group delay in seconds. These measurements are converted to carrier phase range and pseudorange measurements, respectively, through multiplication by the speed of light in a vacuum. Implicit in GPS range measurements, therefore, are the assumptions that the GPS signal travels at the speed of light and the wavelength of the signal is equal to its wavelength in a vacuum along its entire path length. This is equivalent to assuming that the phase and group indices of refraction, np and n g, are equal to one throughout the propagation medium, where the carrier phase range Ž F. and pseudorange Ž PR. are calculated as follows: l 0 l 0 ct Fs ld Ns d Ns d n n l H H H ž / path path p path p 0 c sh dt Ž 1. n path p c PRsH ÕgdtsH dt Ž. n path path g where Õg is the group velocity, c is the speed of light in a vacuum, l is the true wavelength, l0 is the wavelength in a vacuum, d N denotes the differential number of cycles and d t denotes the differential element of time. F and PR are both measured in units of length Ž nominally meters.. The assumption ngs nps 1 is incorrect in re- gions such as the troposphere and ionosphere, where the index of refraction may differ significantly from one. In the dispersive ionosphere, the phase index of refraction depends on several factors: Ne Ž p. 1 v 1 ž m / p 0 np s1y s1y v Ž p. f N s1y40.3 Ž 3. f where N s electron density; e s electron charge s 1.60=10 y19 C; mselectron masss9.1095= 10 y31 kg; 0 spermittivity of free spaces8.854= 10 y1 C rnm ; fsfrequency of the carrier signal. The phase index of refraction therefore depends only on the electron density N. A corresponding expression for the group index of refraction can be derived as follows: dnp N N ngsnpqf s1y40.3 q d f f f N s1q40.3 Ž 4. f The second term in Eqs. Ž. 3 and Ž. 4 causes the signal velocity to differ from c, giving rise to abso-

3 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing Fig. 1. The slant TEC, as measured along the satellite receiver line-of-sight. The majority of TEC is concentrated in the ionosphere shell, near altitudes of 350 km. lute range errors associated with GPS signal propagation through the ionosphere Žas integrated along the path length.: Nd ss TEC Ž 5 H. f f path where TEC represents the total electron content along a1m column along the signal path. The majority of TEC is concentrated near altitudes of 350 km, where the largest electron densities are found Ž Fig. 1.. The dispersive nature of the ionosphere Ž dnrd f/0. allows direct calculation of the absolute TEC, if range measurements are available on two separate frequencies: TECs y Ž PR ypr. Ž f f ž / 1 for the case of a dual-frequency GPS receiver, where f s MHz Ž herein referred to as L1. 1 and f s MHz Ž herein referred to as L.. The corresponding absolute ionosphere range delay can be derived from Eq. Ž. 5. Such range delays, along the slant line-of-sight through the ionosphere shell, are referred to as slant range delays. For differential GPS applications, the decorrelation of slant ionosphere range delay depends directly on the distribution of spatial irregularities in electron density. Such irregularities can be significant in the auroral region. 3. Auroral region and substorm effects The auroral oval is located at northern latitudes and is characterized by enhanced conductivity and energetic electron precipitation ŽFig. ; Feldstein and Starkov, This region is limited in latitudinal extent, located between approximately 558 and 658 N geographic latitude Žnightside North American sector., with an average width of 5 78 ŽRostoker and Skone, Dayside oval boundaries are f 108 higher; the oval being partially fixed with respect to both the Sun and the geomagnetic pole ŽAkasofu, Auroral regions include much of Canada and Alaska, in addition to parts of Russia and Northern Europe. Under active conditions, energy from the solar wind is released into the auroral ionosphere via large-scale electric currents carried primarily by electrons along terrestrial magnetic field lines. The precipitating electrons collide with neutral atmospheric constituents, resulting in emissions of visible and ultraviolet radiation. Localised intensifications of electrons result in the visible aurora Ž Northern Lights. and variable TEC. Structured irregularities in TEC can be extremely localised, with horizontal scale sizes ranging from 0 to 400 km ŽCoker et al., Significant decorrelation of TEC, and equivalently, ionosphere range delay, can occur over short distances. Such irregularities are characteristic of magnetospheric substorms, which generally occur in the local time sector magnetic local time Ž MLT.. The most volatile phase of substorm development is the expansiõe phase, which can last min Ž Hargreaves, During the substorm, auroral oval boundaries may expand southwards. Northern Lights have been observed as far south as

4 8 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing Fig.. Series of ultraviolet images from the POLAR satellite, depicting auroral intensifications during the April 11, 1997 substorm Žcourtesy of G. Parks, The University of Washington.. the southern United States during intense substorm events. Sunspot activity is directly correlated with the emission of solar electromagnetic radiation and the creation of solar flares, two phenomena that control the level of auroral activity. The solar activity undergoes periodic variations over several time scales, the principal cycle having an 11-year period. A solar maximum was last observed in 1989, with the next solar maximum being predicted for the year 000 Ž. Kunches, At this time, an increase in the frequency and magnitude of magnetospheric substorms will accompany the enhanced solar flare activity. 4. Sample substorm event April 11, 1997 A substorm event took place over North America on April 11, The evolution of auroral intensifi-

5 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing cations during the substorm expansive phase was observed in a series of ultraviolet images from the POLAR satellite. This satellite was located at approximately 6 R E altitude, over the North American sector. The POLAR imager was developed so as to be sensitive to vacuum UV wavelengths exclusively, such that the ultraviolet images essentially depict intensities of electron precipitation. In Fig., the darker regions correspond to the most intense electron precipitation and variable TEC. The image at 045 UT in Fig. shows a continuous auroral oval Ž the lighter region. at geographic latitudes of 508, and possibly less Žimage resolution is limited by field of view., over Canada. These latitudes are approximately 58 south of typical oval boundaries, which is consistent with southward expansion of the oval during initial phases of substorm development. At 0301 UT, a bright intensification is observed near the equatorward oval boundary, initiating the substorm onset and expansive phase. Intensifications are later observed at higher latitudes, pro- gressively moving westward and poleward Ž03 UT image.. These intensifications gradually dissipate until 0347 UT, when a second intensification occurs. During this expansive phase, aurora were reported as far south as New Hampshire and Boston. It is evident, from the series of images, that auroral intensifications are present in a region covering approximately 608 of longitude and 108 of latitude. For airborne remote sensing operations in such regions, significant decorrelation of TEC Žionosphere range delay. would be observed. Spatial characteristics of TEC are discussed in Section Characteristics of ionosphere range delay During the period of substorm development, dual frequency GPS observations were available from 10 reference stations in the Natural Resources Canada Ž NRCan. wide area network at 30 s intervals ŽFig. 3; Caissy et al., Using these observations, mea- Fig. 3. GPS reference stations in the Natural Resources Canada wide area network.

6 84 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing surements of slant ionosphere range delay ŽL1 frequency. were calculated for each given satellite receiver pair using Eqs. Ž. 5 and Ž. 6. In this way, a time series of ionosphere range delays were derived for each satellite receiver pair in the network, and information concerning variations in ionosphere range delay during substorm activity can be derived. Fig. 4 shows sample time series of slant ionosphere range delay for satellite SV 6, as observed from four stations in the NRCan network. Fig. 5 shows corresponding tracks of the satellite receiver lines-of-sight, in the ionosphere shell where the majority of TEC contributing to the range delay is concentrated. The rotational period of the GPS satellites is approximately 1 h, such that the satellite receiver line-of-sight moves through various regions of the ionosphere over time. The time series of TEC variations, therefore, actually represents combined effects of both temporal variations and spatial gradients in TEC, as described by the convective derivative: drdtseretq Ž ÕP=. Ž 7. where ErEt denotes the partial derivative with respect to time, Õ is the satellite receiver line-of-sight velocity in the ionosphere shell and = is the spatial gradient. As an example, the abscissa in Fig. 4 has been labeled to reflect relative changes in space for SV tracks observed from Fort Churchill. Note that distances depend on the line-of-sight velocity in the ionosphere shell, which is a function of satellite Ž. Fig. 4. Ionosphere slant range delays L1, as calculated for four stations in the NRCan network on April 11, Series are offset for comparison purposes. Distances are labeled for SV tracks observed from Churchill.

7 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing Fig. 5. Line-of-sight ionospheric pierce points in the ionosphere shell, corresponding to Fig. 4. elevation angle and depends on the location of the reference station. Line-of-sight velocities range from f0 mrs at elevation angles greater than 808, to 150 mrs at 08 elevation Variations in ionosphere range delay during substorm actiõity From Figs. 4 and 5, information can be derived concerning the amplitude and regional dependence of variations in ionosphere range delay associated with auroral disturbances. In Fig. 4, prior to 0300 UT Ž substorm onset., small variations in range delay are observed from Flin Flon and Fort Churchill. These variations are associated with smaller intensifications in the auroral oval, which are often observed as precursors to the more intense expansive phase activity Ž Murphree et al., Prior to 0300 UT, observations from Algonquin are smoothly varying, as the satellite receiver line-of-sight travels though a region south of the auroral oval, where no disturbances are present. At 0300 UT, significant variations in TEC are observed at Algonquin, which arise from the equatorward intensification observed at 0301 UT in Fig.. As this intensification moves poleward Ž Fig.., increasingly large variations are observed at Flin Flon and Fort Churchill. When the second intensification occurs further westward, at 0345 UT, larger variations are observed at Whitehorse. It is evident that the larger TEC variations are correlated with auroral disturbances, resulting in temporal and spatial features with amplitudes in the range 30 to 75 cm. These features cause significant spatial decorrelations in GPS ionosphere range delay errors, degrading DGPS positioning accuracies. An estimate of the spatial decorrelation associated with these features is presented in Section Spectral analysis of ionosphere range delay Ž. Variations in time series of TEC Fig. 4 arise from both temporal changes in the number of ionospheric electrons, and the spatial distribution of ir-

8 86 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing The quiet time statistics were derived as a baseline for comparison with the statistics derived during auroral disturbances. Typical quiet time variations in ionosphere range delay are similar to those observed from Algonquin prior to the substorm onset Ž see Fig. 4.. Fig. 6. Power spectral density for the substorm data set. regularities in electron density. While it is difficult to separate these effects, it is useful to determine approximate estimates of the scale sizes and amplitudes associated with auroral disturbances from such discrete time series through spectral analysis. This is done by deriving power spectral density profiles in the wave number domain for individual time series of range delay values Method The spectral properties were computed for all available series of ionosphere range delay Ži.e., Fig. 4., as defined in the spatial domain. A typical technique for computing these properties is the Fast Fourier Transform. The sampling interval as defined in the spatial domain, however, is uneven. This results from the varying satellite receiver line-ofsight velocities in the plane of the ionospheric shell, which depend on the changing satellite elevation angle. For such unevenly sampled data, alternative techniques to the Fast Fourier Transform must be used to map data into the wave number domain. An algorithm for spectral analysis of unevenly sampled data, herein referred to as the Lomb method ŽPress et al., 1997., is implemented here. This algorithm essentially computes least squares best fits to a linear combination of sines and cosines at each resolved wave number. In this analysis, a discrete series of 18 sampled data points were analysed successively. In order to calculate statistics for entire data sets, the power spectral densities were binned in wave number increments of km y1 and averaged. Spectral characteristics were derived for both the substorm event on April 11, 1997, and a series of quiet periods from 5... Results Figs. 6 and 7 show the one-sided power spectral densities, as derived for the substorm and quiet data sets. It is clear that the majority of power for the ionosphere range delays during storm conditions is concentrated in wave numbers ranging from 0.0 to 0.04 km y1. In contrast, the majority of power for the quiet ionosphere range delays is concentrated at lower wave numbers and higher wavelengths. This implies that the variations in Fig. 4 have wavelengths on the order of 5 50 km. Such fine-scale irregularities are a concern for differential GPS systems operating over short baselines. It is useful to calculate variances of harmonic components within a limited wave number range, in order to estimate amplitudes associated with finescale auroral disturbances. This may be done by isolating spectral components in the desired wave number range, transforming them back into the spatial domain and calculating the variance of the transformed series. Fig. 8 summarizes the variance values calculated for both the substorm and quiet data sets, in various wave number ranges. The variance of those harmonic components in the range Fig. 7. Power spectral density for the quiet data set.

9 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing Fig. 8. Variances of ionosphere range delay, in various wave number ranges, for the substorm and quiet data sets. km y1 is on the order of 0.1 m. This corresponds to an ionospheric delay of 35 cm Ž L1., with scale sizes in the range 5 50 km. These results suggest that fine-scale ionospheric features with amplitudes on the order of cm may exist in regions of auroral disturbances during substorm events. It has been demonstrated that significant variations in TEC and, equivalently, ionospheric range delay, are observed during auroral substorm events. The spatial characteristics of such disturbances suggest scale sizes less than 50 km, with amplitudes approximately three times larger than typical quiet times values. The presence of these features will result in degraded differential positioning accuracies over short baselines. Uncorrelated ionospheric range errors from each satellite will propagate into position accuracies via a dilution of precision factor, based on satellite geometry. These factors are of similar magnitude in both the vertical direction and the horizontal plane. For a typical dilution of precision factor of.0, differential ionosphere range residuals may translate into Ž vertical and horizontal. position errors of cm or more during periods of substorm activity. This calculation is based on the estimated amplitudes of auroral disturbances, as derived in Section 5... These degraded accuracies are of concern for airborne remote sensing applications operating in, or near, auroral regions. In particular, precise engineering and cadastral applications may be affected by active ionospheric conditions. During the next solar maximum predicted around the year 000, moderate major substorm events similar to the one studied in this paper are expected to occur up to 10% of the time. 6. Discussion and conclusions Acknowledgements The authors thank Natural Resources Canada and The University of Washington for providing data. S. Skone acknowledges financial support from the Amelia Earhart International Fellowships and the Killam Memorial Fund. References Akasofu, S.I., Polar and Magnetospheric Substorms. Dordrecht Reidel Pub., Dordrecht, Holland. Anderson, O., Experience with kinematic GPS during aerial photography in Norway. Proceedings of the 4nd Photogrammetric Week. Stuttgart Univ., Stuttgart, Germany, pp Baustert, G., Cannon, M.E., Dorrer, E., Hein, G., Krauss, H., Landau, H., Schwarz, K.P., Schwiertz, C., German Canadian experiment in airborne INS GPS integration for photogrammetric applications. Proceedings of the IAG Geodesy Symposia 10. Springer, Verlag, New York, pp Caissy, M., Heroux, P., Lahaye, F., MacLeod, K., Popelar, J., Blore, J., Decker, D., Fong, R., Real-time GPS corrections service of the Canadian Active Control System. Proceedings of the ION GPS-96, Kansas City, MO, pp Coker, C., Hunsucker, R., Lott, G., Detection of auroral

10 88 ( ) S. Skone, M.E. CannonrISPRS Journal of Photogrammetry & Remote Sensing activity using GPS satellites. Geophys. Res. Lett., Feldstein, Y.I., Starkov, G.V., Dynamics of auroral belt and polar geomagnetic disturbances. Planet. Space Sci. 15, Hargreaves, J.K., 199. The Solar Terrestrial Environment. Cambridge Univ. Press, Cambridge. Kunches, J.M., Now it gets interesting: GPS and the onset of solar cycle 3. Proceedings of the ION GPS-97, Kansas City, MO, pp Murphree, J.S., Elphinstone, R.D., Cogger, L.L., Hearn, D., Viking optical substorm signatures. In: Kan, J.R., Potemra, T.A., Kokubun, S., Iijima, T. Ž Eds.., Magnetospheric Substorms, Geophysical Monograph 64, AGU, Washington, DC. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., Numerical Recipes in C. Cambridge Univ. Press, Cambridge. Rostoker, G., Skone, S., Magnetic flux mapping considerations in the auroral oval and the Earth s magnetotail. J. Geophys. Res. 98, Schwarz, K.P., Chapman, M.A., Cannon, M.E., Gong, P., An integrated INSrGPS approach to the georeferencing of remotely sensed data. Photogramm. Eng. Remote Sens. 59 Ž 11., Schwarz, K.P., Chapman, M.A., Cannon, M.E., Gong, P., Cosandier, D., A precise positioningrattitude system in support of airborne remote sensing. Proceedings of ISPRS Commission II, Ottawa. In: IAPRS 30 Ž. :