Sample substorm event — April 11, 1997 Characteristics of ionosphere range delay

Ž Fig. 2. Series of ultraviolet images from the POLAR satellite, depicting auroral intensifications during the April 11, 1997 substorm courtesy . 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 under- goes 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 2000 Ž . Kunches, 1997 . At this time, an increase in the frequency and magnitude of magnetospheric sub- storms will accompany the enhanced solar flare ac- tivity.

4. Sample substorm event — April 11, 1997

A substorm event took place over North America on April 11, 1997. The evolution of auroral intensifi- cations during the substorm expansive phase was observed in a series of ultraviolet images from the POLAR satellite. This satellite was located at ap- proximately 6 R altitude, over the North American E 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. 2, the darker regions correspond to the most intense elec- tron precipitation and variable TEC. The image at 0245 UT in Fig. 2 shows a continu- Ž . ous auroral oval the lighter region at geographic Ž latitudes of 508, and possibly less image resolution . is limited by field of view , over Canada. These latitudes are approximately 58 south of typical oval boundaries, which is consistent with southward ex- pansion of the oval during initial phases of substorm development. At 0301 UT, a bright intensification is observed near the equatorward oval boundary, initiat- ing the substorm onset and expansive phase. Intensi- fications are later observed at higher latitudes, pro- Ž gressively moving westward and poleward 0322 UT . image . These intensifications gradually dissipate un- til 0347 UT, when a second intensification occurs. During this expansive phase, aurora were reported as far south as New Hampshire and Boston. It is evi- dent, from the series of images, that auroral intensifi- cations are present in a region covering approxi- mately 608 of longitude and 108 of latitude. For airborne remote sensing operations in such regions, Ž significant decorrelation of TEC ionosphere range . delay would be observed. Spatial characteristics of TEC are discussed in Section 5.

5. 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 . Ž NRCan wide area network at 30 s intervals Fig. 3; . Caissy et al., 1996 . Using these observations, mea- Fig. 3. GPS reference stations in the Natural Resources Canada wide area network. Ž surements of slant ionosphere range delay L1 fre- . quency were calculated for each given satellite–re- Ž . Ž . ceiver pair using Eqs. 5 and 6 . In this way, a time series of ionosphere range delays were derived for each satellite–receiver pair in the network, and infor- mation concerning variations in ionosphere range delay during substorm activity can be derived. Fig. 4 shows sample time series of slant iono- sphere range delay for satellite SV 26, 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 ma- jority of TEC contributing to the range delay is concentrated. The rotational period of the GPS satel- lites is approximately 12 h, such that the satellite–re- ceiver 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 gradi- ents in TEC, as described by the convective deriva- tive: drd t s ErEt q Õ P = 7 Ž . Ž . where ErEt denotes the partial derivative with re- spect 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 dis- tances 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, 1997. Series are offset for comparison purposes. Distances are labeled for SV tracks observed from Churchill. 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 f 20 mrs at elevation angles greater than 808, to 150 mrs at 208 elevation. 5.1. 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 Ž . UT substorm onset , small variations in range delay are observed from Flin Flon and Fort Churchill. These variations are associated with smaller intensi- fications in the auroral oval, which are often ob- served as precursors to the more intense expansive Ž . phase activity Murphree et al., 1991 . Prior to 0300 UT, observations from Algonquin are smoothly vary- ing, 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 equa- torward intensification observed at 0301 UT in Fig. Ž . 2. As this intensification moves poleward Fig. 2 , increasingly large variations are observed at Flin Flon and Fort Churchill. When the second intensifi- cation 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 spa- tial features with amplitudes in the range 30 to 75 cm. These features cause significant spatial decorre- lations in GPS ionosphere range delay errors, degrad- ing DGPS positioning accuracies. An estimate of the spatial decorrelation associated with these features is presented in Section 5.2. 5.2. Spectral analysis of ionosphere range delay Ž . Variations in time series of TEC Fig. 4 arise from both temporal changes in the number of iono- spheric electrons, and the spatial distribution of ir- 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 ap- proximate estimates of the scale sizes and amplitudes associated with auroral disturbances from such dis- crete 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. 5.2.1. Method The spectral properties were computed for all Ž available series of ionosphere range delay i.e., Fig. . 4 , as defined in the spatial domain. A typical tech- nique 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-of- sight 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 Ž data, herein referred to as the Lomb method Press et . al., 1997 , is implemented here. This algorithm es- sentially 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 128 sampled data points were analysed successively. In order to calculate statistics for entire data sets, the power spectral densities were binned in wave number incre- ments of 0.001 km y1 and averaged. Spectral charac- teristics were derived for both the substorm event on April 11, 1997, and a series of ‘‘quiet’’ periods from 1996. 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 Ž . onset see Fig. 4 . 5.2.2. 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 0.02 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 25–50 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 fine- scale auroral disturbances. This may be done by isolating spectral components in the desired wave number range, transforming them back into the spa- tial domain and calculating the variance of the trans- formed 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 0.02–0.04 Fig. 7. Power spectral density for the quiet data set. 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 0.12 m 2 . This corresponds to Ž . an ionospheric delay of 35 cm L1 , with scale sizes in the range 25–50 km. These results suggest that fine-scale ionospheric features with amplitudes on the order of 30–40 cm may exist in regions of auroral disturbances during substorm events.

6. Discussion and conclusions