Potential for issuing ionospheric warnings to Canadian users of marine DGPS

Transcription

1 SPACE WEATHER, VOL. 6,, doi: /2007sw000336, 2008 Potential for issuing ionospheric warnings to Canadian users of marine DGPS S. Skone 1 and A. Coster 2 Received 11 May 2007; revised 19 November 2007; accepted 11 December 2007; published 11 April [1] Under normal operating conditions marine DGPS horizontal positioning accuracies on the order of several meters are achieved in North America. Degradations in positioning accuracy can occur during enhanced ionospheric activity. An ionospheric phenomenon known as storm enhanced density (SED) is observed to develop in the middle to high latitudes during ionospheric storm events. Very large gradients in total electron content are observed in the vicinity of this feature with DGPS positioning errors increased by a factor of versus quiet conditions. The specific evolution of a given SED event and the magnitude of expected impact are not generally predictable. A method to monitor development of SED is to compute ionospheric maps in real time. Local gradients can then be computed for various geographic regions from North American maps of ionospheric delay. Sources of real-time ionospheric information include the Wide Area Augmentation System (WAAS) and the Canadian GPS.C service. These are wide area differential GPS systems. In this paper, a real-time ionospheric warning system is investigated for North American (primarily Canadian) DGPS users based on available real-time data. The WAAS and GPS.C ionospheric models are inadequate to resolve ionospheric gradients for km scale sizes. Raw GPS data from GPS.C reference sites can be used, however, to observe large ionospheric gradients and interpret the expected impact on DGPS users. Potential exists to issue marine user warnings based on this method. Results of this work can readily be extended to land DGPS applications, such as the NDGPS service in the United States. Citation: Skone, S., and A. Coster (2008), Potential for issuing ionospheric warnings to Canadian users of marine DGPS, Space Weather, 6,, doi: /2007sw Introduction [2] Differential GPS (DGPS) involves calculating range errors at a reference station and relaying the error information to remote users within the region of coverage. At the user location orbital and atmospheric/ionospheric errors are reduced, satellite clock error is eliminated, but receiver noise and multipath still remain. Typical differential errors are 1--2 ppm. During high levels of ionospheric disturbance, however, differential errors can be increased significantly. The ionospheric range error is a function of the signal frequency and the electron density along the signal path: I ¼40:3 TEC f 2 ðin metersþ ð1þ 1 Department of Geomatics Engineering, University of Calgary, Calgary, Alberta, Canada. 2 Haystack Observatory, Massachusetts Institute of Technology, Westford, Massachusetts, USA. where TEC denotes the total electron content integrated along the signal path (in el/m 2 ), f is the signal frequency (in Hz), and + ( ) denotes the group delay (phase advance). Large gradients in TEC are associated with a phenomenon known as storm enhanced density (SED) in the middle to high latitudes. This effect is a concern for DGPS users in North America. [3] Marine users rely on DGPS services for hydrographic surveying applications, exploration/exploitation of marine resources, assistance to vessel traffic management services, search and rescue operations, and environmental assessment and cleanup. Marine horizontal positioning accuracy requirements are m (95%) and m (95%) for safety of navigation in inland waterways and harbor entrances/approaches, respectively [U.S. Department of Defense/Department of Transportation, 2001]. Marine DGPS accuracies of better than 20 m (95%) are required for several hydrographic surveying applications [International Hydrographic Organization, 1998]. During severe ionospheric activity, such accuracies cannot be achieved Copyright 2008 by the American Geophysical Union 1of22

2 Figure 1. Example of storm enhanced density over North America on 20 November reliably using available Canadian or United States Coast Guard DGPS services. If a real-time ionospheric warning system could be developed for marine users, however, NOTSHIP (Notices to Shipping, warnings issued by Canadian Coast Guard about hazards to navigations) action could be taken to provide timely updates about degraded positioning accuracies. The development of such a real-time warning capability is the focus of this paper. [4] The SED feature is illustrated in Figure 1 as the plume of high density TEC shown in red. Electric fields associated with a mechanism known as the subauroral polarization stream (SAPS) [Foster and Burke, 2002] are the driving mechanism for SED [Foster et al., 2007; Coster and Foster, 2007]. SAPS is characterized by a strong sunward flow channel which covers a latitudinally broad region (3-- 5 degrees) and is observed during geomagnetically active times in the dusk-to-dawn sector a few degrees below the auroral oval [Foster and Vo, 2002]. The SAPS fields can extend from the auroral boundary to below 45 degrees latitude and can last several hours. The SED plume is produced when some fraction of plasma from an enhanced TEC region beneath the plume is stripped away and moved sunward under the E B force generated by the Earth s magnetic field and the equatorward edge of the strong poleward SAPS field [Foster et al., 2005]. [5] SED can be described as a longitudinally narrow, high total electron content (TEC) plume that is observed in the premidnight and afternoon sectors in North America during geomagnetically disturbed conditions. The SED feature has been observed in North and South America [Coster et al., 2001; Foster et al., 2002; Coster et al., 2003], Europe [Yizengaw et al., 2006], and Japan [Maruyama, 2006]. The SED feature forms over Europe around local noon [Colerico et al., 2007]. Associated with SED are sharp temporal and spatial TEC gradients which can cause large differential ionospheric range errors. An example of such DGPS positioning errors is given in Figure 2. [6] The first identification of a repeatable and spatially distributed SED feature was by Foster [1993] who used data from the Millstone incoherent scatter (IS) radar [Vo and Foster, 2001]. Since that time, the SED feature has been studied in detail with satellite data from the DMSP and IMAGE satellites, and with TEC data collected from multiple GPS receivers located across the United States and Canada [Coster et al., 2003]. During ionospheric storms in May and October 2003, marine DGPS horizontal position accuracies have been degraded by factors of Position errors of 20 m or more have persisted for hours and are well beyond system tolerance specified for marine DGPS users. Such ionospheric activity is not unusual during the years following solar maximum. The last solar maximum was in We are currently in solar minimum conditions. The solar activity is expected to increase over the next few years as the next solar cycle begins. [7] In the United States the SED phenomenon typically develops in the eastern United States, with the plume of ionization extending northwest into Canada. The specific evolution of a given event and the magnitude of expected impact are not generally predictable, although there is some evidence of a consistent pattern [Colerico et al., 2007]. One problem with prediction of SED is the lack of available real-time parameters. For example, geomagnetic indices are often used to quantify space weather events. These are generally three-hourly values and do not pro- 2of22

3 Figure 2. The 95th percentile DGPS horizontal positioning errors UT on 20 November Position solutions were computed using all km baselines within the CORS network, with errors averaged in 5-degree latitude/longitude bins. vide sufficient information about local effects in North America at a given time. The only method to monitor the development of SED, and associated severe gradients of interest for DGPS users, is to compute ionospheric maps in real time or near real time. Local gradients can then be computed for various geographic regions from these North American maps of ionospheric delay. In regions where large gradients are identified, warning messages quantifying the expected level of positioning error can then be issued to marine users. 2. Real-Time Ionospheric Information [8] Ionospheric information is available in real time through the Wide Area Augmentation System (WAAS) and the Canadian GPS.C service. These systems, and available data, are described in this section. It is noted that the NOAA Space Environment Center also provides near real-time TEC maps and slant TEC values within North America [Fuller-Rowell, 2005]. The NOAA SEC products at Canadian latitudes are based on a subset of Canadian stations included in the GPS.C service, however, and only the GPS.C service is directly investigated here The WAAS [9] The WAAS provides satellite clock, satellite orbit, and ionospheric corrections for wide area differential GPS positioning (WADGPS). The WAAS uses a sparse network of 25 dual frequency reference stations in the United States (Figure 3) to derive the WADGPS corrections. The current lack of WAAS reference stations in Canada is a limitation for accurate modeling of the ionosphere at Canadian latitudes. [10] For the WAAS ionosphere model, a grid of ionospheric corrections is defined at regular spacings in latitude and longitude [Altshuler et al., 2002]. The grid spacing is 5 for geographic latitudes of 55 or less, 10 for geographic latitudes in the range , and 10 in latitude and 90 in longitude for the geographic latitude 85 [U.S. Department of Transportation, 1999]. This grid is transmitted to single frequency users in RTCA format via geostationary downlink. The ionospheric vertical TEC value at each grid point is derived in near real time updated at least every 5 min. The ionospheric information can be derived using a WAAS-capable receiver to log the appropriate RTCA messages, and these data could be used in a real-time ionospheric warning system Canadian GPS.C Service [11] An alternative to the WAAS is the Canadian GPS.C service. The GPS.C operates in a manner very similar to the WAAS, with satellite clock, orbit, and ionospheric corrections derived using a network of GPS reference stations. These corrections are then transmitted to users in Canada for wide area differential GPS positioning. [12] The Canada-wide DGPS service (CDGPS) project is a Canadian Federal/Provincial/Nunavut Government partnership to deliver GPS corrections to all Canadians 3of22

4 Figure 3. WAAS reference stations ( via the MSAT communication satellite [Kassam et al., 2002]. These corrections are freely accessible and are derived from the GPS.C real-time wide area differential GPS (WADGPS) correction information. The Geodetic Survey Division at Natural Resources Canada is responsible for delivering the GPS.C using a network of real-time GPS reference stations. The WADGPS corrections are generated using a system of Real Time Active Control Points (RTACP) across Canada (Figure 4), where each station has a UNIX server and console, a high-quality dual frequency GPS receiver, an external frequency reference (rubidium, cesium, or hydrogen maser), a meteorological station, and a communications router. Data are acquired, validated, stored, and forwarded to the Real Time Master Active Control Station (RTMACS). [13] The RTMACS processes the GPS and meteorological data from the RTACPs to produce three products: satellite orbit corrections, satellite clock corrections, and an ionospheric vertical delay grid. These data are then transmitted back to the RTACPs through the wide area network, as well as being uploaded to, and broadcast by, the MSAT satellite. These corrections are formatted using a modification of the RTCA-SC-159 format, and are broadcast via geostationary downlink in real time. Users with CDGPS-compliant receivers are able to receive such corrections throughout Canada, and achieve real-time wide area DGPS positioning (with typical three-dimensional (3-D) accuracies of 1--3 m). [14] A byproduct of this service is the availability of ionospheric maps across Canada and the northern United States in real time, updated at 5-min intervals. The ionosphere model is based on the two-dimensional thin-shell approximation, where a 17-coefficient polynomial describes TEC variations in latitude and local time. Ionospheric L1 delay corrections are then extracted from this ionosphere model at grid points spaced 5 by 5 in latitude and longitude. In parameterizing the ionospheric information in a 5 5 grid, high-resolution features may be lost. If sufficient information is available to identify the presence of large ionospheric gradients, however, an ionospheric warning service may be based on this real-time freely available information. Figure 4 shows the GPS.C ionosphere grid points, and the locations of 13 real-time GPS reference stations used to derive the ionosphere model. Raw dual frequency GPS observations are also available for each RTACP from NRCan via ftp. 3. Ionosphere Truth Data [15] In order to evaluate the resolution of real-time ionospheric information (as described in the previous section), truth ionosphere observations are required for comparison. High-resolution ionosphere maps are therefore produced in postmission by combining dualfrequency data from more than 400 ground-based GPS receivers around the United States and Canada. These ionosphere maps are herein referred to as truth maps. SED was observed in such ionosphere maps derived for North America for two case study events: October 2003 and 20 November [16] The data used to produce these ionosphere TEC maps include observations from both the International GPS Service (IGS) ( and the 4of22

5 Figure 4. Real-time Active Control Points used to derive GPS.C ionospheric corrections (red triangles) and the ionosphere grid points (blue points). Continuously Operating Reference Stations (CORS). The CORS network is coordinated by the U.S. National Geodetic Survey ( The data were accessed via publicly available data archives on the World Wide Web ftp://cddisa.gsfc.nasa.gov/gps/ and A map of all GPS stations used in generating the ionosphere maps is shown in Figure 5. [17] The line-of-sight TEC values from these sites were converted to vertical TEC values using a simple mapping function, and associated to an ionospheric pierce point latitude and longitude, assuming a peak ionospheric height of 350 km. GPS satellite and receiver interfrequency biases were estimated and removed from the data. To minimize mapping function errors in modeling the vertical TEC, the elevation angle was restricted to be greater than 30 degrees. The satellite or SV biases used were determined by the JPL modeling efforts. The receiver biases were determined by an in-house process using the algorithms described by Rideout and Coster [2006]. The TEC processing is strictly data driven and uses no outside modeling to compute TEC values other than a simplified mapping function to compute slant TEC to vertical. Spatial maps of TEC were prepared in 30-min batch intervals. This batch interval was chosen in order to be consistent with the 30-min 95th -percentile DGPS positioning statistics derived in a later section; 30 min is a reasonable interval length in terms of evolution of SED events (typically lasting min) and the amount of data required to reliably compute 95th -percentile values. The vertical TEC has been binned in latitude/ longitude bins. No smoothing is used; the high level of detail is due primarily to the persistence of a wellorganized connected structure and to the large quantity of data processed. [18] Examples of such truth maps are shown in Figure 6. Large gradients in the TEC distribution are observed over the continental United States into Canada during the October 2003 event. A plume of TEC associated with SED is apparent during the period UT on both 29 and 30 October. The plume of SED has moved north and westward over a period of several hours, leading to the increased TEC values and gradients in the western region pictured in Figure 6. While observations are sparse at the high latitudes, it appears that the SED feature may extend over the polar region into Europe. [19] Similar to the October event, the presence of SED is clearly observed over North America on 20 November Figure 7 shows the distribution of TEC over North America during UT and UT. The plume of SED has moved westward during the 2-h period, with a narrow region of enhanced electron content through the eastern United States into western Canada. The evolution of this feature in global maps of TEC demonstrates that the electrons observed UT flow over the pole, from North America into Europe. [20] It is possible to derive ionospheric gradient information from the truth ionosphere maps. By differencing the TEC values in adjacent bins (either in the north--south or west-- east directions) values for both the latitude and longitude gradients can be derived across Canada and the United States. Latitude gradients are positive northwards and longitude gradients are positive eastward. Both latitude 5of22

6 Figure 5. GPS reference stations used to generate high-resolution ionosphere TEC maps from GPS observations ( and longitude gradients are derived from 30-min truth TEC maps and are defined in units of TECU (10 16 el/m 2 )per degree. [21] Temporal development of both latitude and longitude gradients is shown for the October storm event in Figure 8 for a location in western Canada. Large positive gradients are followed by negative gradients as the peak of the SED plume travels over the location of interest on both 29 October and 30 October. Figure 9 shows gradients for a location in central Canada during the November 2003 event. Large gradients are associated with the SED plume traveling over central Canada during the late hours UT on 20 November. Note the significantly smaller gradients on days with only average ionospheric activity: 28 October (in Figure 8) and 21 November (Figure 9). 4. Assessment of WAAS Ionospheric Corrections [22] In order to evaluate the feasibility of using WAAS ionospheric corrections to detect severe ionospheric activity, the archived WAAS RTCA messages were retrieved from the U.S. Federal Aviation Administration and decoded for the October and November 2003 ionospheric storm events. The WAAS ionosphere maps are then compared with the high-resolution truth maps. Note that these truth maps are derived using observations from approximately 30 Canadian stations, versus no Canadian stations being used to generate the WAAS ionospheric grids. [23] In this section, a qualitative analysis of the WAAS ionosphere maps is conducted. Figures 10 and 11 show the WAAS ionosphere maps during periods of SED on 29 and 30 October 2003, respectively. These can be compared with the high-resolution truth maps in Figure 6. The WAAS ionosphere grid captures the presence of the SED feature in western Canada, but the northern extent of the narrow plume of enhanced ionosphere (and the associated gradients) is underestimated. The local enhancement over western Canada in the truth maps is not evident in the WAAS maps. This is due to the lack of WAAS GPS reference stations in Canada, such that there are no available GPS observations to define the WAAS model at Canadian latitudes. Steep gradients at the western and eastern edges of the SED plume are also smoothed in the WAAS representation. The highest peak TEC values and large localized gradients near the SED plume are not fully resolved in the WAAS maps. [24] Similarly, Figure 12 shows the WAAS ionosphere map for the 20 November 2003 storm event. This can be compared with the high-resolution truth map in Figure 7. 6of22

7 Figure 6. GPS TEC map derived from 400+ reference stations for (top) UT on 29 October and (bottom) UT on 30 October The WAAS ionosphere map shows a general enhancement of TEC in the central United States consistent with the SED plume, but the feature is smoothed and does not extend into Canada. Again, the lack of WAAS GPS reference stations in Canada limits WAAS model capabilities for resolving local features at Canadian latitudes. [25] Temporal development of both latitude and longitude gradients is shown for the October storm event in Figure 13 for a location near the centre of the SED plume in western Canada. These gradients are derived from the WAAS ionosphere maps. While there are some larger gradients during the peaks of the storm activity on both 7of22

8 Figure 7. GPS TEC maps derived from 400+ reference stations for (top) UT and (bottom) UT on 20 November and 30 October, the magnitudes of these gradients are not sufficiently enhanced to use these values as unambiguous identifiers of SED events. The gradients at Canadian latitudes (e.g., red points) are also significantly less than those in the United States. Deficiencies in the WAAS ionosphere model exist at Canadian latitudes and, as a result, gradients derived from this model do not accurately reflect local ionospheric phenomena. Gradients during the SED event are greater than 10 TECU/deg for the truth data 8of22

9 Figure 8. Longitude and latitude gradients derived in western Canada (48.5 N, W) on October (see Figure 8) but are only 2 TECU/deg for the WAAS ionosphere maps. [26] Figure 14 similarly shows gradients derived from the WAAS maps for a location in central Canada during the November 2003 event. Again, only minimal increases in the latitude and longitude gradients are observed during the periods of SED development (late hours UT on 20 November). Overall, the real-time WAAS ionosphere maps do not have sufficiently high resolution and Figure 9. Longitude and latitude gradients derived in central Canada (48 N, 85 W), November of22

10 Figure 10. GPS TEC map derived from the WAAS ionosphere grid for the periods UT on 29 October Figure 11. GPS TEC map derived from the WAAS ionosphere grid for the period UT on 30 October of 22

11 Figure 12. GPS TEC map derived from the WAAS ionosphere grid for the period UT on 20 November Figure 13. Longitude and latitude gradients derived in western Canada (red points, location 48.5 N, W) from WAAS TEC maps, October Gradients derived for all of North America from the WAAS maps are also plotted for comparison (black points). 11 of 22

12 Figure 14. Longitude and latitude gradients derived in central Canada (red points, location 48 N, 85 W) from WAAS TEC maps, November Gradients derived for all of North America from the WAAS maps are also plotted for comparison (black points). accuracy at Canadian latitudes for use in real-time ionospheric warnings. 5. Assessment of GPS.C Ionospheric Corrections [27] This analysis is identical to that conducted in for the WAAS ionosphere maps. In order to evaluate the feasibility of using GPS.C ionospheric corrections to detect severe ionospheric activity, the archived GPS.C real-time ionosphere grids were retrieved from Natural Resources Canada and decoded for the October and November 2003 ionospheric storm events. The GPS.C ionosphere maps are then compared with the high-resolution truth maps. Note that the truth maps are derived using observations from approximately 30 Canadian stations, versus the 13 stations used to generate the GPS.C ionosphere grids. [28] Figures 15 and 16 show the GPS.C ionosphere maps during periods of SED on 29 and 30 October These can be compared with the high-resolution truth maps in Figure 6. The GPS.C ionosphere grid captures the presence of the SED feature, but the steep gradients at the western and eastern edges of the SED plume are smoothed in the GPS.C representation. The highest peak TEC values and large localized gradients near the SED plume are not resolved in the GPS.C maps. [29] Similarly, Figure 17 shows the GPS.C ionosphere grid for the 20 November 2003 storm event. This can be compared with the high-resolution truth map in Figure 7. Again, the ionosphere map derived using the 5 5 GPS.C ionosphere grid shows an enhancement of TEC in central western Canada consistent with the SED plume, but the feature is smoothed and peak values for the GPS.C grid are significantly lower than the truth values. [30] Temporal development of both latitude and longitude gradients is shown for the October storm event in Figure 18 for a location near the centre of the SED plume in western Canada. Gradients are derived from the GPS.C ionosphere maps. While there are some larger negative latitude gradients during the peaks of the storm activity on both 29 and 30 October, the magnitudes of the gradients are not sufficiently enhanced to use these values as unambiguous identifiers of SED events. Gradients derived from GPS.C ionosphere maps are well below the range of 10 to 10 TECU/deg (and more) observed for the truth data (see Figure 8). [31] Figure 19 similarly shows gradients for a location in central Canada during the November 2003 event. Only minimal increases in the latitude and longitude gradients are observed during the periods of SED development (late hours UT on 20 November). Overall, the real-time GPS.C ionosphere maps do not have sufficiently high resolution and accuracy to use for real-time ionospheric warnings. 6. Assessment of Real-Time Canadian GPS Data [32] The GPS.C ionosphere grid is derived from raw line-of-sight ionospheric observations at 13 real-time GPS reference stations in Canada. These raw observations may be made available in real-time by Natural Resources 12 of 22

13 Figure 15. GPS TEC map derived from the GPS.C ionosphere grid for the period UT on 29 October Canada (NRCan), with a few modifications to their current processing schemes. While such information is not as readily available (and as easy to access) as the GPS.C products, these raw data are an alternative for deriving information about the state of the ionosphere in real-time. The potential of exploiting such raw data for ionospheric warning purposes is investigated in this section. Figure 16. GPS TEC map derived from the GPS.C ionosphere grid for the period UT on 30 October of 22

14 Figure 17. GPS TEC map derived from the GPS.C ionosphere grid for the period UT on 20 November [33] The raw satellite-receiver line-of-sight ionospheric observations are derived every second for all satellites in view at each of the 13 real-time GPS stations (see station locations in Figure 4). Figure 20 shows the satellite-receiver line-of-sight ionospheric pierce points for each real-time GPS reference station over a 24-h period. The pierce point is defined as the point where the satellite-receiver line-of-sight intersects with the ionospheric shell at Figure 18. Longitude and latitude gradients derived in western Canada (48.5 N, W) from GPS.C TEC maps, on October of 22

15 Figure 19. Longitude and latitude gradients derived in central Canada (48 N, 85 W) from GPS.C TEC maps, November km altitude. Over 24 hours, the full ionosphere over Canada is observed. At any given time, a subset of these observations would be available. By considering these raw ionospheric observations, more information about the state of the ionosphere may be derived than through analyzing the GPS.C ionosphere grid product. [34] Figures 21 and 22 show the spatial distribution of TEC derived from the raw real-time GPS observations for the 29 and 30 October 2003 periods of SED. These plots Figure 20. Satellite-receiver line-of-sight ionospheric pierce points for all real-time NRCan GPS reference stations over a 24-h period. 15 of 22

16 Figure 21. GPS TEC map derived from the raw NRCan ionospheric observations for the period UT on 29 October can be compared with the high-resolution truth maps in Figure 6. For both cases, the raw ionospheric observations (binned into 5 5 pixels for plotting purposes) show the SED feature in western Canada. The degree of resolution is not as high as for the truth data (in which observations from 30 Canadian GPS reference stations are used to derive the ionosphere map), but the SED feature is clearly identified in the raw observation plots. Figure 22. GPS TEC map derived from the raw NRCan ionospheric observations for the period UT on 30 October of 22

17 Figure 23. GPS TEC map derived from the raw NRCan ionospheric observations for the period UT on 20 November [35] Similarly, Figure 23 shows the spatial distribution of TEC derived from the raw real-time GPS observations for the 20 November 2003 period of SED. This plot can be compared with high-resolution truth values in Figure 7. Again, the raw observations resolve the SED feature, consistent with the truth ionosphere map. There is potential to make use of such raw GPS.C observations to identify the presence of increased ionospheric activity. Figure 24. Longitude and latitude gradients for all locations in Canada (black points) and for a single location in western Canada (48.5 N, W) (red points), as derived from raw NRCan ionospheric observations, October of 22

18 Figure 25. Longitude and latitude gradients for all locations in Canada (black points) and for a single location in central Canada (48 N, 85 W) (red points), as derived from raw NRCan ionospheric observations, November [36] The temporal development of both latitude and longitude gradients is shown for the October storm event in Figure 24 for a location near the SED plume in western Canada. Gradients are computed from the ionosphere maps derived from the raw NRCan observations. Larger negative latitude gradients are observed during the peak storm activity on both 29 and 30 October, with magnitudes many times larger than normal. Similarly, increased longitude gradients are observed during the late hours UT on both 29 and 30 October, consistent with development of the ionospheric storm event. Magnitudes of gradients derived from raw NRCan ionospheric observations are sufficiently enhanced to identify the SED events. Results in Figure 24 are comparable to gradients derived from truth data (Figure 8). [37] Figure 25 similarly shows gradients for a location in central Canada during the November 2003 event. Increases in the latitude and longitude gradients are observed during the periods of SED development (late hours UT on 20 November). Results in Figure 25 are comparable to gradients derived from truth data (Figure 9). Overall, the raw NRCan observations have sufficient information for potential use in real-time ionospheric warnings. 7. Correlation of Gradients With DGPS Errors [38] In order to confirm that the ionospheric gradients derived from the raw NRCan GPS observations (in the previous section) are valid indicators of degraded DGPS positioning accuracy, direct correlations of positioning errors and ionospheric gradients are computed. [39] The direct correlation of ionospheric gradients (derived from real-time raw NRCan ionospheric observations) and DGPS positioning errors is demonstrated here as follows: [40] 1. Latitude and longitude gradients are computed throughout Canada using the raw NRCan ionospheric observations on a 5 5 grid at 30-min intervals (e.g., Figures 21, 22, and 23). The latitude and longitude gradients are combined in a single total gradient estimate for each grid cell. [41] 2. Thirty-minute 95th -percentile DGPS position errors are computed using GPS data from IGS reference stations. Four km baselines centered on reference station NANO and four km baselines centered on reference station WSLR are analyzed for western Canada during October One 198 km baseline (ALGO- NRC1) is analyzed for the 20 November Results are matched with the local gradients computed in step 1 for the appropriate time and location. Figure 26 shows the reference stations used in this DGPS analysis. [42] Figure 27 shows the 95th-percentile DGPS horizontal positioning errors as a function of ionospheric gradient for the three baseline scenarios. Note that each point plotted represents a 30-min statistic for the given location and storm event. Both quiet ionospheric conditions and severe storm effects are represented in these multiple-day data sets. A general positive correlation is observed, with an increase in position errors for the larger ionospheric 18 of 22

19 Figure 26. GPS reference stations used in the DGPS position computations. gradients. There are some cases of lower position errors for larger gradients, however. Note that the position errors for WSLR are larger in general, as these results were derived for the longest baselines ( km). [43] The cumulative probabilities of DGPS horizontal positioning errors were also derived for various ranges of ionospheric gradients: ppm, ppm, and ppm, where ppm represents mm of L1 range delay per kilometer. These results were derived for the combined Figure 27. Horizontal DGPS positioning errors as a function of ionospheric gradient, for km baselines (reference NANO) and km baselines (reference WSLR) for October 2003 and a 200 km baseline (reference NRC1) for 20 November of 22

20 Figure 28. Distribution of DGPS horizontal position errors as a function of ionospheric gradient, for the km baselines (users NANO and NRC1). Cumulative probabilities are also shown, with the dashed line indicating the 95th percentile. data set of reference stations NANO (October storm event) and NRC1 (November storm event). These data sets were chosen because the processing was conducted for km baselines more representative of marine users. The longer baselines for user WSLR represent an extreme case. Consistent with the correlations in Figure 27, increased 95th -percentile DGPS positioning errors are observed in Figure 28 for the larger ionospheric gradients. Such statistics could be used to predict position errors for a given level of ionospheric gradient in a real-time ionospheric warning system. [44] Note that almost all position errors for the smallest gradients ( ppm) in Figure 28 are below 2 m. In contrast, only 30 percent of the position errors for the largest gradients ( ppm) are below 2 m. For the larger gradients, there is a high probability that a given user would experience position errors exceeding normal error bounds. A warning could be sent to marine users when gradients exceed 20 ppm. [45] The 95th-percentile position errors in Figure 28 are (1) 1.85 m for ionospheric gradients of ppm, (2) 7.50 m for ionospheric gradients of ppm, (3) 11.0 m for ionospheric gradients of ppm. These values are consistent with those predicted using the ruleof-thumb formula that follows from the least-squares position estimation: 2DRMS ¼ 2 s HDOP ð2þ where s is the differential range error. If it is assumed that 2DRMS is approximately equivalent to the 95thpercentile horizontal position error and that s consists primarily of the ionospheric differential range error, equation (2) can be rewritten in terms of the ionospheric gradient (ppm) and baseline length (b): 2DRMS ¼ 2 ppm b HDOP [46] If a baseline length of 150 km is assumed, to be consistent with the km baselines used to derive results in Figure 28, and an average HDOP of 1.4 is used, the 2DRMS values can be predicted theoretically for various ionospheric gradients. These 2DRMS values are given in Table 1. The last column in this table includes the empirically derived results (from Figure 28) for comparison. The predicted 2DRMS and observed 95th -percentile DGPS horizontal positioning errors are consistent. [47] Measured ionospheric gradients, as derived from the NRCan raw GPS observations, could therefore be used directly to predict the magnitude of DGPS horizontal Table 1. DGPS Horizontal Positioning Errors as a Function of Ionosphere Gradient Gradient, ppm Baseline Length, km HDOP 2DRMS, m ð3þ 95th Percentile, m of 22

21 positioning errors for ionosphere storm events. An ionospheric warning system based on measured ionospheric gradients could be used to predict DGPS errors in a given region. 8. Summary [48] The following sources of information were evaluated for potential use in an ionospheric warning system for GPS users: WAAS ionospheric corrections, GPS.C ionospheric corrections, and raw NRCan reference station (RTACP) observations. The following conclusions are made. [49] The WAAS ionosphere model underestimates the magnitude and extent of ionospheric effects at Canadian latitudes. The WAAS model is computed from 25 GPS reference stations in the United States with no observations from Canadian stations contributing to the model. This limitation leads to poor resolution of ionosphere features for Canadian users during periods of increased ionospheric activity. The WAAS ionosphere estimates are not adequate for detecting storm-enhanced density at Canadian latitudes and should not be used in an ionospheric warning system for marine users. [50] The GPS.C ionosphere grid does not have sufficiently high accuracy and resolution to detect the localized ionospheric features and severe ionospheric gradients associated with DGPS position errors. For example, the magnitudes of ionospheric gradients derived from these GPS.C ionosphere maps are a factor of five too low (based on comparisons with high-resolution truth ionosphere data). [51] The raw ionospheric observations derived from 13 real-time NRCan GPS reference stations may be used to derive realistic ionospheric gradient estimates and detect localized ionospheric features. In particular, the plume of enhanced ionospheric electrons (called storm enhanced density) which leads to large DGPS position errors can be detected in ionosphere maps derived from these real-time NRCan observations. [52] DGPS horizontal positioning errors are generally well-correlated with ionospheric gradients estimated from the real-time NRCan raw observations. For gradients in the range ppm, 95th -percentile horizontal DGPS positioning errors of 2.1 m are predicted. The 95th - percentile horizontal DGPS positioning errors are increased to 7.5 and 11 m, respectively, for gradients in the range ppm and ppm. These values are for DGPS baselines of km, and are consistent with the simple theoretical formula for computing DGPS position errors: 2DRMS = 2 s HDOP, where the differential range s is assumed to depend on the ionospheric gradient and baseline length. [53] It is determined that the proposed warning system accurately predicts DGPS errors in a given region, based on the gradients derived from real-time ionosphere maps. Potential exists to issue marine user warnings based on this method. A near real-time warning system is envisioned which is based on 30-min estimates of ionospheric gradients. 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22 Rideout, W., and A. Coster (2006), Automated GPS processing for global total electron content data, GPS Solutions, 10, , doi: /s U.S. Department of Defense/Department of Transportation (2001), 2001 Federal radionavigation plan, Rep. DOD-VNTSC-RSPA-01-3/ DOD , Washington, D. C. U.S. Department of Transportation (1999), FAA specification: Wide Area Augmentation System (WAAS), Rep. FAA-E-2892B, Washington, D. C. Vo, H. B., and J. C. Foster (2001), A quantitative study of ionospheric density gradients at midlatitudes, J. Geophys. Res., 106(A10), 21,555. Yizengaw, E., M. B. Moldwin, and D. A. Galvan (2006), Ionospheric signatures of a plasmaspheric plume over Europe, Geophys. Res. Lett., 33, L17103, doi: /2006gl A. Coster, Haystack Observatory, Massachusetts Institute of Technology, Westford, MA , USA. S. Skone, Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4. (sskone@geomatics.ucalgary.ca) 22 of 22