First storm-time plasma velocity estimates from high-resolution ionospheric data assimilation

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, , doi: /2013ja019153, 2013 First storm-time plasma velocity estimates from high-resolution ionospheric data assimilation Seebany Datta-Barua, 1 Gary S. Bust, 2 and Geoff Crowley 3 Received 4 July 2013; revised 15 October 2013; accepted 5 November 2013; published 26 November [1] This paper uses data assimilation to estimate ionospheric state during storm time at subdegree resolution. We use Ionospheric Data Assimilation Four-Dimensional (IDA4D) to resolve the three-dimensional time-varying electron density gradients of the storm-enhanced density poleward plume. By Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE), we infer the three-dimensional plasma velocity from the densities. EMPIRE estimates of ExB drift are made by correcting the Weimer 2000 electric potential model. This is the first time electron densities derived from GPS total electron content (TEC) data are being used to estimate field-aligned and field-perpendicular drifts at such high resolution, without reference to direct drift measurements. The time-varying estimated electron densities are used to construct the ionospheric spatial decorrelation in vertical total electron content (TEC) on horizontal scales of less than 100 km. We compare slant TEC (STEC) estimates to actual STEC GPS observations, including independent unassimilated data. The IDA4D density model of the extreme ionospheric storm on 20 November 2003 shows STEC delays of up to 210 TEC units, comparable to the STEC of the GPS ground stations. Horizontal drifts from EMPIRE are predicted to be northwestward within the storm-enhanced density plume and its boundary, turning northeast at high latitudes. These estimates compare favorably to independent Assimilative Mapping of Ionospheric Electrodynamics-assimilated high-latitude ExB drift estimates. Estimated and measured Defense Meteorological Satellite Program in situ drifts differ by a factor of 2 3 and in some cases have incorrect direction. This indicates that significant density rates of change and more accurate accounting for production and loss may be needed when other processes are not dominant. Citation: Datta-Barua, S., G. S. Bust, and G. Crowley (2013), First storm time plasma velocity estimates from high-resolution ionospheric data assimilation, J. Geophys. Res. Space Physics, 118, , doi: /2013ja Introduction [2] The storm-enhanced density (SED) is a midlatitude continent-sized area of anomalously high electron content in the ionosphere that develops during severe geomagnetic storms. In some cases the SED has an associated plume of plasma that extends poleward. Studies by Foster et al. [2005] show sunward convection toward the plasmasphere as well and refer to the cause of the plume phenomenon as a subauroral polarization stream. The plume and SED can have a clearly defined boundary relative to the background 1 Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, USA. 2 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 3 Atmospheric and Space Technology Research Associates, LLC, Boulder, Colorado, USA. Corresponding author: S. Datta-Barua, Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA. (sdattaba@iit.edu) American Geophysical Union. All Rights Reserved /13/ /2013JA ionosphere. Figure 1 shows a map of the vertical total electron content (VTEC) above the eastern half of the United States during a storm that occurred on 20 November Each VTEC measurement is plotted at an assumed ionospheric height of 350 km, which does not capture the altitudinal variation of plasma density, leading to the mottled appearance of the map. Nevertheless, the large red area is the SED plume. Black dashed lines identify what we refer to here as the transition regions" between the disturbed ionosphere due to the SED and the nominal ionosphere. [3] A storm like the one shown in Figure 1 is particularly challenging to model because the transition region at each dashed line is very narrow. Yet it has significant operational impact. A high-density network of dual-frequency GPS receivers sited under the SED in Ohio measured the slant total electron content (STEC) as they tracked GPS satellite (SVN) 38 on this day and estimated that the slant differential ranging error between certain pairs of stations was as much as about 400 mm of delay at L1 frequency (or 2.4 TECU) per kilometer of separation between two stations that straddled the transition region [Datta-Barua et al., 2010a]. The difference in TEC (i.e., GPS ranging

2 Latitude [deg] /20/2003, 19:30 UT Longitude [deg] Figure 1. Map of equivalent vertical total electron content over the eastern U.S. during 20 November 2003, ionospheric storm at 19:30 UT. Transition regions are marked with dashed lines. error) can be 100 times larger than the nominal 4 mm/km during nonstormy periods, over horizontal distances of only 50 km [Ene et al., 2005; Lee et al., 2007]. Such large horizontal spatial variation poses a challenge to differential- GPS-based aircraft navigation systems [Pullen et al., 2009]. [4] Knowing the SED plasma gradients and motion in the transition region is not only useful for operational systems but is also important scientifically for understanding the midlatitude physical processes occurring during major magnetic storms. The plasma motion along magnetic field lines relates to the rate of diffusion, itself a function of temperature- and density-dependent particle collisions, as well as on plasma pressure gradients and neutral wind forcing [Schunk, 1996]. Understanding the plasma density s motion perpendicular to magnetic field lines yields knowledge of the local electric fields. Physics-based modeling of the positive ionospheric storm has been conducted [Lin and Yeh, 2005; Lekshmi et al., 2008; Lu et al., 2012, 2013]. Balan et al. [2009, 2010, 2011, 2013] have shown that storm time electric fields alone cannot produce SEDs but that storm time neutral winds alone or in combination with electric fields can do so. The physics of the SED remains an active area of scientific study. In order to understand what is happening dynamically at the boundary, we need to be able to resolve plasma distribution at high resolution. In addition, we would like to have some knowledge of the drifts both inside and outside the SED plume. [5] Here we (1) develop a high-resolution threedimensional time-varying estimate of the electron content in the ionosphere during this storm, (2) integrate through the estimated electron content to compute the magnitudes of differential VTEC and STEC that could have been experienced between pairs of stations on the ground, and (3) investigate the physical processes that drive the variation in electron content over space and time, comparing to Defense Meteorological Satellite Program (DMSP) satellite drift measurements and Assimilative Mapping of Ionospheric Electrodynamics (AMIE) independently derived ExB drifts. This paper presents the first efforts to image variations Vertical Total Electron Content [TECU] in storm time plasma density from assimilative imaging at 100 km scales and smaller and to use high-resolution density imaging to indirectly infer the ionospheric state via drift motion. [6] The paper is organized as follows. In section 2 we describe the method of analysis and software tools used. The plasma variation analysis and results are discussed in section 3. We compare the estimated drifts to in situ satellite data in section 4. Estimated ExB drifts specifically are compared to AMIE and with respect to the literature in 5. Our concluding remarks are in section 6. Technical derivations are available in the Appendices. 2. Method [7] Global Navigation Satellite System signals have enabled remote sensing of the ionosphere with higher spatial distribution and temporal resolution than instruments in the past. The density of the ground reference stations, sometimes separated by only 100 km or less, enables the datadriven high-resolution analysis conducted here. The overall processing is summarized in the flowchart in Figure 2. [8] Beginning from the top left of Figure 2, the International Reference Ionosphere (IRI) [Bilitza et al., 2003] is used as a background model and GPS data are used as measurements to be assimilated by Ionospheric Data Assimilation Four-Dimensional (IDA4D). IDA4D, described in 2.1, uses three-dimensional variational data assimilation to routinely produce mappings of the ionospheric densities globally [Bust et al., 2007]. In this work IDA4D is used to investigate spatial and temporal variations in ionospheric electron content. First, we run IDA4D at low resolution globally, with a 3 ı 3 ı grid horizontally over the U.S., to obtain global electron density distributions. We then rerun IDA4D in a high-resolution regional mode in the spatial regions where the SED is observed, using the 3 ı 3 ı densities as the background model, thus assuring that the high-resolution processing only adds finer scale structures to the already estimated ionospheric density. There are two high-resolution regional runs shown: (a) 1 ı 1 ı grid Figure 2. Data and modeling process flowchart. 7459

3 Latitude [deg N] Longitude [deg E] Figure 3. CORS station locations in Ohio and southern Michigan (blue diamonds). Stations whose data are not assimilated are marked (red cross). IDA4D/EMPIRE grid point nearest to GARF and neighboring points in magnetic cardinal and intercardinal directions are marked with blue stars. and (b) 0.5 ı 0.5 ı grid. These high-resolution regional images resolve plasma structuring on horizontal scales of km and vertical scales of 50 km. With the 3-D spatial electron density specification from IDA4D, TEC estimates can be generated by integrating through the estimated densities along a slant or vertical raypath. This computation is detailed in Appendix A. The 0.5 ı results are compared to GPS data that were assimilated and to data that were not, as indicated on the bottom left of the flowchart, and are discussed in section 3. [9] To understand the physical dynamics of the ionosphere, techniques have been developed that use electron density specification. Estimating Model Parameters from Ionospheric Reverse Engineering (EMPIRE) deduces drivers of ionospheric dynamics from time-evolving threedimensional images of ionospheric density. As shown in the flowchart of Figure 2, the 0.5 ı resolution plasma densities form the input data to the drift estimation tool EMPIRE. The Weimer 2000 high-latitude electrodynamic potential model provides the a priori model of the electric field producing ExB drift and is itself driven by solar wind data. EMPIRE produces localized estimates of the electric potential producing ExB plasma drifts and of the field-aligned ion velocities in the regions of the SED and its boundaries. The EMPIREestimated drifts are compared to DMSP-measured drifts (section 4) and AMIE-estimated ExB drifts, which are based on assimilation of independent high-latitude electrodynamic data (section 5). [10] We have selected the 20 November 2003 extreme storm for high-resolution analysis of transition effects. The presence of the SED and plume has been well documented for this storm; it had significant space weather effects on navigation systems. At that time the Continuously Operating Reference Stations (CORS) network of U.S. GPS stations had pockets of high-density ionospheric sampling. The Ohio/Michigan region of the United States, shown in Figure 3, was one such region. The CORS Ohio/Michigan data that are the source for our assimilative estimation are identified with diamonds and their four-character station ID. The sites marked with an x have data that are deliberately excluded from the assimilation to be used as comparison TEC data in section 3. The stars show select half-degree grid points that will be examined in that section as well. The center point labeled C is closest to the CORS station GARF and surrounding half-degree grid points labeled with their corresponding directions, e.g., N for the point immediately north in magnetic coordinates. The southwestern grid point is nearest to the excluded station WOOS (Wooster, Ohio). The CORS stations whose data are input to IDA4D to estimate electron densities have baseline separation distances comparable to that of the half-degree grid Ionospheric Data Assimilation Four-Dimensional [11] Ionospheric Data Assimilation Four-Dimensional (IDA4D) [Bust et al., 2000] is a continuous-time, threedimensional imaging algorithm [Bust et al., 2004] routinely used to produce 4-D (time and space) ionospheric electron density specifications for various science investigations [Bust and Crowley, 2007; Bust et al., 2007; Yin et al., 2006; Crowley et al., 2006]. In particular, IDA4D has been used to investigate the ionospheric response to major geomagnetic storms [Bust and Mitchell, 2008; Bust and Crowley, 2008], including the formation and evolution of SED. A complete Figure 4. IDA4D vertically integrated TEC over the midwestern U.S. at 19:30 UT at (a) 3 ı horizontal resolution, (b) 1 ı resolution, (c) 0.5 ı resolution. 7460

4 GPS upward looking TEC, LEO in situ observations of electron density, and satellite observations of 1356 Angstrom radiances. These were the sources used in this analysis, although GPS TEC form the vast majority. [13] The IDA4D data are provided on a global irregular grid. For large-scale global runs, the standard configuration is to have horizontal grid spacing of 2 ı 3 ı in latitude and 5 10 great circle degrees in longitude. In the region of interest for the transition region analysis, a higher-resolution horizontal grid at the EMPIRE target grid points is embedded in the global grid. Over the American sector, 3 ı spacing in both latitude and longitude is used for the low-resolution run. For the 1 ı and 0.5 ı resolution runs, the regional grid embedded in the IDA4D global run spans the midwestern U.S. only, running 45 ı to 60 ı north magnetic latitude and 24 ı to 10 ı west magnetic longitude. [14] The vertical grid has a 10 km resolution from 82.5 to km, 25 km resolution from to 825 km, 50 km up to km height, and 100 km resolution out to the top (a) GARF Measured Estimated (b) WOOS Measured Estimated Slant TEC [TECU] Slant TEC [TECU] Figure 5. (a) Vertical TEC from IDA4D densities at grid point labeled C nearest GARF and the nearest grid points east (E), northeast (NE), north (N), northwest (NW), west (W), southwest (SW), south (S), and southeast (SE). Thin lines show VTEC for 19 November Thick lines are for 20 November (b) 20 November 2003 differential VTEC north-south and east-west. (c) 20 November 2003 differential VTEC across the plume and along the plume. mathematical derivation of the IDA4D algorithm can be found in Bust et al. [2000, 2004] and Bust and Datta-Barua [2012a]. One of the powerful features of IDA4D is that the inversion grid is user selectable and need not be regular. This means that with IDA4D it is easy to embed a high-resolution local horizontal grid in the regions we want to investigate for sharp gradients. [12] IDA4D accepts any empirical or first principle model of the ionosphere as its background model. IDA4D is able to ingest a large number of diverse data sets including ground GPS TEC, low-earth-orbiting (LEO) TEC observations from Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) ground transmitters, virtual heights versus frequency from digisondes, incoherent scatter radar electron density profiles, bistatic high-frequency time delays versus frequency, LEO GPS occultation TEC, LEO Decorrelation rate [TECU/km] 0 18:00 21:00 11/20/03 UT Hour (c) 0 18:00 21:00 11/20/03 UT Hour GARF WOOS STEC Decorrelation to PRN 8 Dual frequency GPS Measured STEC IDA integrated Estimate of STEC 18:00 19:00 20:00 21:00 22:00 23:00 11/20/03 UT Hour Figure 6. Measured (solid line) and IDA4D-estimated (dashed) slant TEC in TECU over time at (a) GARF and (b) WOOS. (c) Difference in STEC between GARF and WOOS divided by the distance between the stations. 7461

5 with the Weimer 2000 electric potential. The motivation for doing this is to improve the accuracy of results, particularly at the high-latitude boundary of the region being investigated [Datta-Barua and Bust, 2011]. These are detailed in Appendix B. [17] To run EMPIRE, we use the high-resolution 0.5 ı 0.5 ı IDA4D density data set from the 20 November 2003, extreme ionospheric storm (Figure 4c). EMPIRE estimates of drifts are computed from 15:00 to 23:55 UT every 10 min based on motion from time t to time t +10min. Finite differencing is used in computing density rates and gradients in the preceding equations. [18] The EMPIRE grid focuses on the F2 region, using heights from 350 km to 700 km in 50 km intervals. The regular horizontal grid is identical to that of IDA4D within the Ohio/Michigan region. The power series for the electric potential is of order 3 in equatorial radius and order 4 in longitude. The power series for the field-aligned drift speed is of order 3 in each of radius, latitude, and longitude. 3. TEC Comparison [19] An example of the results of running IDA4D to generate low-, medium-, and high-resolution plasma density Figure 7. (a) IDA4D-estimated VTEC and DMSP 13 horizontal drifts; (b) EMPIRE-estimated drifts at DMSP 13 locations for 23:25 UT. of the grid at 2000 km. For this study the temporal resolution was 5 min due to the dynamical nature of super storms. The high-resolution run is initiated from 15:00 to 24:00 UT, spanning the period when the SED plume passes over the region. All data whose raypaths extend through the 3-D regional grid at a given time are used to produce an improved high-resolution result Estimating Model Parameters from Ionospheric Reverse Engineering [15] In the EMPIRE algorithm, the ion continuity equation is discretized in space-time and formulated as a linear system. The system is solved to estimate one or more of the drivers (production, loss, neutral winds, electric fields) that produced a time variation of the density over a region. [16] Previous efforts either modeled a driver as completely known or as an unknown to be solved. For this effort we will, for the first time, treat one of the ionospheric drivers as being partially known but then also estimate a correction to it. Specifically, the electric field is modeled a priori Figure 8. Comparison of DMSP 13 drift components to EMPIRE-estimated drift components (m/s) versus latitude. (a) DMSP in-track, (b) cross-track, (c) vertical, (d) magnetic field perpendicular, and (e) field aligned. 7462

6 Figure 9. Comparison of (a) Weimer model electric potential V 0 contours to (b) total EMPIRE-corrected potential V 0 + ıv at 23:25 UT. estimates is shown in Figure 4 with VTEC maps for 19:30 UT. The IDA4D densities over the grid are summed over all heights according to equation (A1) to produce the vertical total electron content VTEC. The color contours are planarly interpolated between each set of nearest three grid points. The result of the low-resolution IDA4D run in the midwest region of the U.S. is illustrated in Figure 4a. The vertically integrated IDA4D densities resulting from the 1 ı and 0.5 ı runs are shown in Figures 4b and 4c. [20] The TEC maps in Figure 4 with progressively higher resolution show the importance of resolving the transition region at high resolution. At low resolution, the SED saturates red at only a few points in the interior-most area of the plume. The perpendicular distance between the reddest grid point and the bluest runs northeast-southwest and spans the diagonal of more than one horizontal pixel, a distance of more than 3 ı.the1 ı resolution map does saturate red inside the SED plume, and the width of the yellow border (60 TECU) measured across a gradient northeast-to-southwest of the color contours is narrower than in the 3 ı map. The yellow transition is spanned by 1 ı pixels at certain points, e.g., 40 ı N, 85 ı W. The half-degree resolution map does not appear to narrow the transition region noticeably, but it does show finer structure and curvature of the transition regions, particularly on the northern section of the SED plume. [21] The VTEC for the grid point C nearest to GARF is shown in Figure 5a in blue dashed line from 15:00 to 22:00 UT. The vertically integrated densities at the neighboring grid points E, NE, N, NW, W, SW, S, and SE are also shown. All of these curves show the same general pattern over time. The IDA4D estimated densities indicate an interesting shoulder effect on the leading transition region at 18:30 UT, with a local maximum. The densities also imply a wide variation in VTEC within the bulk of the SED plume, from 19:00 to 20:30 UT. [22] For contrast, the VTECs for the previous day are shown with thin lines in Figure 5a. The VTEC for 19 November 2003 shows that (1) the TEC values are significantly lower on a quiet day, (2) the variation between neighboring grid points is much lower on a quiet day, and (3) the TEC variations shown for 20 November are unlikely to be due to IDA processing, since the same processing is applied to give the 19 November results. [23] To quantify the spatial variations in VTEC across these grid points on the storm day, we difference the VTEC computed between the center grid point C and the other grid points. The differences in VTEC running east to west (E-C and C-W) and north to south (N-C and C-S) are shown in Figure 5b. The differences in VTEC running approximately across the plume in the northeast-southwest direction (NE-C and C-SW) and the differences along the plume in the northwest-southeast (NW-C and C-SE) direction are plotted in Figure 5c. [24] In the cardinal directions (Figure 5b), there is relatively little difference in the east-west direction, reaching no more than TECU difference. Moreover, the (E-C) curve and the (C-W) curve track each other very closely. In contrast, there is a notable north-south differential VTEC, reaching at times 20 TECU. In addition, the southern differential (C-S) is generally more positive than the northern differential (N-C). [25] The differential VTEC is more revealing in the crossplume and along-plume directions, as seen in Figure 5c. The timing of the spatial variations is the same as in the cardinal directions. The differentials are no more than 10 TECU in the northwest-southeast (along-plume) direction. However, the magnitude of differential VTEC exceeds 30 TECU in the cross-plume direction around 20:00 UT. The southwest differential is generally more positive than the northeast. The northeast grid point has less TEC than the other points, as can be seen in Figure 5a. This means that around 20:00 UT, there is a steeper spatial gradient to the northeast corresponding to the trailing edge transition region. [26] There are no observational data in this vicinity with purely vertical lines of sight with which to compare the IDA4D VTEC results. For this reason it is helpful to compute slant TEC along signal raypaths between the known CORS station locations and the GPS satellites. These can then be compared to the observational data from the CORS sites. We focus on two neighboring CORS sites: GARF, whose data were ingested into the IDA4D estimation, and WOOS, whose data were not. These sites are nearest to the grid points C and SW, respectively. 7463

7 Figure 10. (a) IDA4D-estimated VTEC and DMSP 15 horizontal drifts; (b) EMPIRE-estimated drifts at DMSP 15 locations for 15:55 UT. [27] The upper plots in Figure 6 show the dual-frequency CORS observations of slant TEC over time for (a) GARF and (b) WOOS with a blue solid line. These dual-frequency data were processed to level satellite and receiver interfrequency biases by Jet Propulsion Lab Global Ionospheric Mapping (GIM) tool [Komjathy et al., 2005]. The GIM tool has been used routinely and robustly for many scientific campaigns and was used to produce the TEC map in Figure 1. In the data shown in Figure 6, thresholds for data quality control eliminated some dual-frequency measurements just before 21:00 UT. For this reason both curves have data gaps. However, the dual-frequency data shown here for GARF have been confirmed and validated with raw dual-frequency and L1-only data, and the data for WOOS have been investigated in depth for other lines of sight [Datta-Barua et al., 2010a]. [28] The results of slant TEC integration for lines of sight from stations GARF and WOOS to GPS satellite PRN 8 (SVN 38) are plotted with a dashed line in Figure 6a and 6b, respectively. Compared with the measurements, several observations can be made about the estimates. Before entering the plume, both estimates are higher than the observational data by TECU. The timing, rate, and magnitude of rise in TEC are comparable to the data. The internal structure of the plume s STEC is more accurate for GARF than for WOOS. In particular, the timing of the drops in TEC is accurate. This is to be expected, since GARF data were ingested but WOOS data were not. Neither of the estimates is accurate on the magnitude of the last part of the peak. Observations are in excess of 180 TECU at 21:00 UT, but the estimates are only 140 TECU. This means that while the timing of the decline in TEC is correct, the rate of decline is estimated to be lower. After 21:00 UT, the GARF estimate follows the measurement more closely than the WOOS estimate does. Neither of the estimates picks up any of the smaller high-frequency structure visible on the rising edge at 18:30 UT or after the plume passage at 21:30 UT. [29] We are interested not just between the absolute delays experienced by two different receivers but also by the spatial rate of change in TEC over horizontal distance that they imply. For GPS-based local differential navigation, this quantity is often referred to as the slope or gradient, measured in mm of delay at L1 frequency (which is proportional to TEC) per km of separation between two stations [Pullen et al., 2009]. In the case of GARF and WOOS, the station separation is about 70 km. Differencing the TEC between the two stations and dividing by their separation distance, we compute the slope in STEC over time. This is plotted in Figure 6c for the observed dual-frequency data (solid line) and the IDA4D estimates (dashed line). The two curves are leveled so that the bias in their initial measurements is 0, following the practice in the literature [Ene et al., 2005; Lee et al., 2007] to eliminate possible residual GPS interfrequency biases affecting estimated slope values. [30] For the observed data (solid line), the decorrelation in STEC between the stations begins at a minimum magnitude, even as the raypaths enter the plume at 18:20 UT. Shortly after the data dropout (due to processing), when data from both stations are simultaneously available, the slopes reach as large as 1.5 TECU/km in magnitude at 21:00 UT. [31] The IDA4D-based slopes change more smoothly, not exhibiting high-frequency variations that the observational data show. It does reach slopes of 0.3 TECU/km, which are large gradients in the threat model, but is only 20% as large as the largest magnitude slopes from this pair of observational sites data. The primary reason for the less steep decorrelation rates is that the WOOS data were excluded from the sample. However, TEC structure within the plume differs between GARF and WOOS observations more significantly than for the estimation. In particular, the STEC measurements showed different structure in the plume for GARF compared to WOOS (compare solid lines in Figure 6a and 6b). [32] In summary, the half-degree resolution provides additional and significant structuring information on the plume horizontally. However, underestimates of horizontal spatial rates of change can occur, particularly for data that are excluded from ingestion. This will lead to underprediction of TEC spatial rates of change. Since TEC rates of change are related to density rates of change spatially, these also imply lower spatial decorrelation in density will on 7464

8 Figure 11. Comparison of Weimer model electric potential V 0 contours to total EMPIRE-corrected potential V 0 + ıv at 15:55 UT. average occur through estimation with data exclusion. This leads to smaller computed values of ErN used in the drift estimation process using the ion continuity equation (B1) and so contributes to errors in the drift velocity estimation resulting from EMPIRE. 4. Comparison of Drifts to DMSP Data [33] In this section Defense Meteorological Satellite Program (DMSP)-measured ion drift data are compared to the EMPIRE estimates at the DMSP locations for this storm. The DMSP satellite constellation orbits at 840 km in sun-synchronous orbits. Each is equipped with the Special Sensors-Ions, Electrons, and Scintillation (SSIES) suite, which includes a retarding potential analyzer (RPA) to measure in-track ram direction speeds, and an ion drift meter (IDM) to measure the two components of the drift velocities perpendicular to the satellite motion, cross-track to the left when facing in the direction of motion, and vertically upward. The DMSP data are provided with quality flags from each of the instruments [34] Of the DMSP constellation, none passed directly over the plume while it was over the high-density GPS network in Ohio/Michigan during this time period. However, DMSP F13 passed through the Ohio/Michigan region 23:20 23:25 UT, as the plume was in the southwest part of the gridded region. In addition, DMSP F15 passed through the region before the plume passage, at 15:50 15:55 UT. We compare DMSP-measured drifts to the EMPIRE estimates for these times. [35] The DMSP orbit altitude is above the EMPIRE fitting region (maximum altitude of 700 km). For the ExB drift components, for which potential is constant along a magnetic field line, this is an acceptable comparison. Every point on the DMSP orbit maps along a field line to within our region. However, the field-aligned drifts, due to neutral winds and collisional effects, would have to be extrapolated beyond our region to reach DMSP altitudes. For this reason, we compute and show EMPIRE estimates for the DMSP geographic locations, but at 700 km altitude. [36] In Figures 7 9, we compare DMSP 13 drifts at 23:25 UT to EMPIRE indirect estimates. Figure 7 shows two color maps of VTEC as estimated by IDA4D over the region. Figure 7a overplots the DMSP measurements of the horizontal component of drift. Each arrow begins at the DMSP ground track location. For those same locations, the estimated drifts are shown in Figure 7b. A 500 m/s arrow length is shown for reference. [37] In these figures, the plume is in the south and west of the fitting region, containing about 40 TECU (light greenblue). DMSP traverses from the southeast corner, northwestward. Only the measurements flagged as having good quality from both the RPA and IDM are used, so the arrows appear at irregular intervals. The measured drifts in Figure 7a are southwestward around 600 m/s. Above 45 ı N the horizontal speeds exceed 1000 m/s. The estimated drifts in Figure 7b are almost all southwestward as well, but the magnitudes are about a factor of 2 3 low in the middle latitudes. The drift direction above 45 ı N points eastward, which is opposite the DMSP 13 measurements. [38] In Figure 8, individual components of the measured and estimated drift are compared as a function of geographic latitude. The components compared are in the satellite body coordinates Figures 8a 8c and in magnetic field-referenced components in Figures 8d 8e. [39] The RPA instrument measures the in-track speeds, but due to uncertainties in calibrating out the satellite motion, the resulting data are often noisy, as reflected in Figure 8a. South of 38 ı N, the measurements are around 500 m/s. The EMPIRE estimates do not capture this, showing almost 0 speed. North of there, though, the speeds are about 200 m/s but noisy enough that the EMPIRE estimates fall within their range. [40] The cross-track estimated speeds in Figure 8b trend with the measured speeds to within about 300 m/s, with the correct direction, until 45 ı N where they diverge. The vertical speeds are within 200 m/s, but because they are relatively low measured speeds, the estimates predict 100 m/s upward when the measurements show 100 m/s downward. [41] Meridional estimates shown in red in Figure 8d are biased by about 500 m/s but converge at higher latitudes. In contrast, the zonal estimates (blue) are within 100 m/s but diverge at higher latitudes. Finally, the field-

9 Figure 12. (left) Ionospheric plasma density maps at 450 km altitude from IDA4D and EMPIREestimated horizontal component of ExB drift at 450 km altitude at half-degree resolution. (right) Ionospheric VTEC maps from IDA4D and AMIE-estimated ExB drifts. (a,b) 18:05 UT, (c,d) 19:05 UT, (e,f) 20:05 UT. 7466

10 aligned estimates in Figure 8e are within about 100 m/s smoothly varying within the range spanned by the noisy measurements. [42] The field-perpendicular drifts (Figure 8d) are due to ExB drift, so we next examine the potential V 0 and estimated potential V = V 0 + ıv in the contour maps of Figure 9a and 9b, respectively. The upper plot shows isopotentials at 10 kv intervals over the region, as modeled by the Weimer high-latitude model. The equatorward boundary condition of the Weimer model is specified to be 0 V; north of there the potentials are negative, running east-west. This indicates a northward electric field. [43] The correction potential (not shown) largely cancels the Weimer model, such that the net potential spans 0 to 10 kv, as indicated with the color map in Figure 9b. The net potential yields relatively low speeds on the order of 100 m/s. The horizontal velocities are overplotted on this contour map, showing a clockwise circulation pattern centered about 47 ı N, 88 ı W. [44] In Figures 10 11, we compare results from the EMPIRE drift estimation process to data collected from DMSP F15 when it passes over the region at 15:55 UT. This is a contrasting period in which the estimated velocities are not as accurate. The local time is morning, so the overall VTEC is low and the SED plume has not yet reached this region, as seen in Figure 10. The DMSP satellite traverses from north to south. In Figure 10a, at each location on its ground track, the measured DMSP horizontal velocity is shown. These are primarily northeastward drifts, with magnitude increasing with latitude. At the north most points on the ground track, the winds are northward. The DMSP satellite seems to have one measured velocity southsoutheastward at 43 ı N, 90 ı W, but this has been confirmed to be a data point corrupted by noise [Hairston, 2013]. [45] The EMPIRE estimates of the DMSP drifts at the same ground track locations at this time are plotted over the same VTEC color map in Figure 10b. These speeds are almost due northward, with magnitudes exceeding 1000 m/s. The velocities turn slightly eastward with increasing latitude. In this comparison of results to separate data, the magnitudes estimated are too large and the direction disagrees with DMSP by about 90 ı azimuthal angle. [46] Consideration of the individual velocity components estimated versus measured (not shown) shows that the magnitudes estimated are well beyond the noise range of the RPA and IDM instruments. While the trend generally matches for the field-aligned and fieldperpendicular drifts, the field-perpendicular meridional drift is biased by 1000 m/s, and the zonal is biased by about 500 m/s, except at the highest latitudes. This implicates the electric potential estimate, which gives rise to ExB drift. [47] Figure 11a plots contour maps of the Weimer potential V 0 in units of kv at 15:55 UT over this region. The isopotentials run primarily north-south. Figure 11b shows the corrected potential resulting from EMPIRE, V 0 + ıv. The isocontours are not significantly different from the Weimer potentials, curving slightly northeast-southwest at higher latitudes. The electric field points east, perpendicular to the potential curves. The ExB drift points parallel to the isopotentials. The magnetic field-perpendicular velocities are dominated by the Weimer estimate of the potential In this case, EMPIRE has not made a significant correction to the potential. [48] To understand why this is the case, we can consider the continuity equation (B1), on which the EMPIRE estimation is based. At this time, the variation of density is low, so the left-hand side dn/dt 0. Our assumption of production and loss being in equilibrium makes those terms 0. The divergence of the flux has a term proportional to spatial gradient of N, which is very low. It also has a term proportional to divergence of v. The divergence of the velocity, based on the Weimer potential, is very nearly 0 as can be seen from Figure 11. In the end, the array that the inversion matrix multiplies is nearly 0. Thus, the resulting estimate is nearly 0. To obtain a nontrivial result in this situation, there must be a nonzero quantity. In this case, it is likely that relaxing our assumption of production and loss equilibrium will be needed to produce better results. [49] In summary, if there is adequate spatial and temporal variation in density, and other effects dominate production and loss, the indirect ion velocity estimation agrees reasonably well with the measured DMSP drifts in the middle of the fitting region in direction with about half the magnitude predicted. This is done without direct ingestion of any drift, electrodynamic, or neutral wind information. The advantage of such a method is that estimates of drift vectors can be made in the absence of direct in situ measurement. 5. Comparison of ExB Drifts to AMIE [50] Here we examine the drifts estimated by EMPIRE over the region, focusing on ExB drift at a single altitude. We compare these drifts to the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) high-latitude ExB estimates. AMIE assimilates high-latitude electrodynamic measurements to estimate the high-latitude electric potential. It does not use the same data sources that IDA4D and EMPIRE do. [51] The estimated horizontal drifts at 450 km altitude for 18:05, 19:05, and 20:05 UT are plotted at each highresolution grid point over a map of plasma density in Figures 12a, 12c, and 12e. Regions where arrows are not plotted are outside the half-degree resolution grid area. [52] For comparison, the AMIE-estimated drifts are plotted for 18:05, 19:05, and 20:05 UT in Figures 12b, 12d, and 12f. They are plotted on top of the IDA4D vertically integrated TEC. The color mapped quantities in the left plots (Figures 12a, 12c, and 12e) are densities at 450 km, and the right plots (Figures 12b, 12d, and 12f) are VTEC, so the color maps differ. [53] At 18:05 UT in Figure 12a, the plume is to the east of the Ohio/Michigan region. At 450 km, the edge of it is visible along the 82 ı W longitude. In this local morning time, the drifts are predicted to be primarily westward. Speeds are about 500 m/s at low latitudes, decreasing to about 300 m/s at high latitudes. [54] Figure 12c shows the EMPIRE-estimated drifts at 19:05 UT. By this time, the width of the plume is located over the region. In the blue low-density region outside the SED plume, the drift speed is very low. Across the edge of the SED at 36 ı N, 87 ı W, the flow is southeastward at less than 200 m/s. Within the plume, flow is northwestward, e.g., at 40 ı N, 85 ı W. The shift in direction from southeastward

11 to northwestward implies a slight shear, and this coincides with the plume seeming to be eroded from west to east (see the C shape of the color contour at 37 ı N, 85 ı W). [55] There are no abrupt changes in drift speed or direction indicated at the ionospheric transition region of the plume. However, it is notable that the drift direction is aligned with the wall of the ionospheric front (pictured as yellow). If drifts were moving southwestward, we might expect to see the wall widen over time. The fact that the drifts keep moving northwestward may help keep the plasma contained inside the plume. At higher latitudes, the flow is still northeastward, with speeds increasing with latitude. [56] At 20:05 UT, the EMPIRE-estimated drifts are as shown in Figure 12e. Flow is still slow and southeastward at low latitudes, where now there is no longer any plasma of the main SED. The shear still seems to appear to the west of the leading edge of the plume, such that the flow on the leading edge transition region is aligned with it, northwestward. Within the plume and on the trailing edge transition region, the flow is also northwestward. At high latitudes, the flow is northeastward, and this includes the region near 48 ı N, 82 ı W outside of the plume. This may imply an erosion effect of the ExB drift. [57] The AMIE velocities estimated for the same times are shown in Figures 12b, 12d, and 12f. It is notable that both EMPIRE and AMIE predict a northeastward flow at the northern section of the plume. AMIE does not predict southeastward flows at low latitudes, and at this resolution the relationship between drift directions and plume boundaries is not as clear as it is with EMPIRE. [58] It is worth placing these plots in context with the investigations in the literature. In the paper by Foster et al. [2005], the polar electric potentials two-cell patterns are plotted for these times. Since the electric field is perpendicular to isopotentials, and the drift is perpendicular to the field, the ExB velocity is generally parallel to the isopotential lines. In Figure 5 of [Foster et al., 2005], isopotentials centered around the + cell correspond to a counterclockwise flow. Just past noon, the Great Lakes can be seen at the lower latitudes. They fall between two isopotential curves. The looping of the lowest latitude curve shows a case where the drifts are moving eastward and south slowly and then switching around to mostly northward at higher latitudes. In other words, the EMPIRE estimate of low-speed southeastward flow at low latitudes may be reasonable and is consistent with the literature. 6. Conclusion [59] We have systematically investigated the ionospheric storm transition region (the boundary between the SED plume and surrounding ionosphere) at half-degree resolution, and the dynamics that cause it, with a focus on indirect estimation of electrodynamic effects. The density and drift estimates were compared against independent TEC data and against independent plasma drift data. The results presented here favorably indicate that data assimilation can reconstruct slant delays during extreme storms and can be used for investigating spatial variation in TEC. Drift measurement comparison indicates that adequate density rate and accurate accounting for production and loss is likely needed at times when other processes are not dominant [60] We have also used high-resolution four-dimensional electron density imaging to estimate plasma drift speeds and directions. We show a northwestward flow along the boundaries of the SED plume, one that possibly helps keep the boundary between the SED and the background ionosphere sharp. At low latitudes, a slight southeastward flow due to ExB drift and at high latitudes a higher speed northeastward flow are estimated, both of which are comparable to the literature. These are estimated using a background model (Weimer 2000) for electric potential and data assimilation to correct the model based on plasma densities, not on any electrodynamic measurement information. The results shown here are evidence that ionospheric drifts can be indirectly inferred from primarily TEC-based densities, which are generally more plentiful than drift data. [61] Efforts to improve the EMPIRE driver estimation process by implementing a full Kalman filter are ongoing. We plan to model all of the drivers including production, loss, and drifts. With the Kalman filter, we will update previous results at each in time, treating the state of the ionosphere as a Gauss-Markov process. We expect this will help improve some of the boundary inaccuracies and will improve the overall accuracy and robustness of the EMPIRE estimation process, since during times of low-density rate, the estimation can then revert to background model values. Appendix A: Integration of IDA4D Densities for TEC [62] Once the IDA4D plasma densities N(,, h) are estimated at half-degree latitude and longitude resolution over Ohio/Michigan at heights h, we investigate the ionospheric variations in TEC, considering both vertical raypaths and slant raypaths. To estimate vertical total electron content VTEC, in total electron content units (TECU), we compute VTEC(, ) = X i N(,, h i ) h i TECU (A1) where the summation occurs over all i heights of the IDA4D grid. The scale factor converts electrons per square meter to TECU. This method was used to produce the vertical TEC maps shown in Figures 4, 7, 10, 12b, 12d, and 12f. Using the half-degree electron density estimates, we also examine the VTEC variation at individual grid points over time (Figure 5). [63] The slant TEC, or STEC, computation must take into account the geometric angle that the raypath slices through each IDA4D voxel, which means that the STEC computation is slightly more complex than the VTEC expression of equation (A1). The slant raypath from a reference station on the surface of the Earth to a GPS satellite slices through the IDA4D grid at each altitude h i. For each latitude and longitude ( l,i, l,i ) at which a line of sight intersects an IDA4D grid height, we find the nearest IDA4D grid point ( g, g, h i ), by computing the Euclidean distance in the WGS-84 coordinate frame. We select that nearest grid point s density as the density to integrate at that point on the raypath. [64] The density N is multiplied by the height interval h i between that point and the next lower height. To scale the distance of the raypath accounting for its slant length, we multiply by an elevation el-dependent geometric factor

12 known as an obliquity factor OF, computed at each grid height h i for each intersection point. This way of computing slant TEC in TECU is summarized as STEC = X i OF(,, h i )= N( g, g, h i ) h i OF( l, l, h i ) (A2) cos arcsin 1 (A3) RE cos(el(,,hi)) R E+h i where N( g, g, h i ) is the IDA4D density of the grid point nearest to the raypath point ( l, l, h i ) at height h i, h i = h i h i 1, the obliquity factor is computed at the raypath point ( l, l, h i ) based on the GPS satellite elevation el as viewed from the ground station, and R E is the radius of the Earth. Appendix B: EMPIRE Algorithm [65] For the EMPIRE algorithm, we form the mass continuity equation as a linear system [Datta-Barua et al., 2009]. dn = a prod + a loss Er (N Ev ) Er (N Ev? ) (B1) dt ƒ ƒ a a exb [66] At a single grid point, the time rate of change of density N in a given volume element is due to the rate of production of ions a prod, the loss rate of ions a loss,andany plasma flow in or out of the volume. The velocity is decomposed into magnetic field-aligned v and field-perpendicular v? components. The drift directions and speeds are determined by the local electric fields (giving rise to v? )and neutral winds (contributing to v ). Any driver in the equation (production, loss, electrodynamics, neutral winds) may be treated as a known by using an external model beforehand, an unknown to be solved, or a combination of the two. [67] The continuity equation for each grid point is discretized and stacked into a system of linear equations of the form: y = Mx + a 0 + h y = N 1 N 2 t t ::: Nimax t a 0 = a 01 a 02 ::: a 0imax T i T (B2) (B3) (B4) where y i is the electron density rate of change observed from ionospheric imaging at the ith grid point, a 0 is the a priori model of any drivers being treated as known quantities through the use of some other model or outside information, x contains the coefficients of functions describing the remaining drivers to be estimated algebraically, and represents noise. The solution is given by weighted least squares pseudo-inverse, with weighting and regularization as described in Datta-Barua et al. [2010b]. [68] In this paper each a 0i in equation (B4) consists of those terms which are modeled a priori, i.e., production, loss, and ExB drift. We model production and loss as being negligible in comparison to the other dynamics a prod + a loss =0. This simplifies the problem because we are not required to add in constraints forcing nonnegativity of the production rate and nonpositivity of the loss rate. Thus, a 0 = a 0,exb. [69] The quantity a 0,exb is modeled with the Weimer 2000 electric potential. For the first time with EMPIRE, we will also estimate additive corrections for this parameter being modeled a priori. For this effort, we are interested in understanding the dynamics due to electric fields in the region, so we estimate corrections x?. We will not estimate a correction to production and loss. We will estimate the field-aligned drift v without a prior model. The x states associated with the field-aligned drift are defined by Datta-Barua et al. [2011], and the full array of unknowns in this effort is h T x = x T?i xt (B5) [70] To derive the expression for x? and a 0,exb, we assume the perpendicular velocity is attributed to an electric potential of a background model V 0 plus correction potential ıv based on the data: Ev? = E 0 EB B 2 Ev?,0 + ıe EB B 2 = ErV 0 EB + ErıV EB ƒ B 2 ƒ B 2 ıev? (B6) (B7) The field-perpendicular velocity can be inserted into the expression for the term a exb in the continuity equation (B1): a exb = Ev? ErN (Er Ev? )N = Ev?,0 ErN (Er Ev?,0 )N ƒ a 0,exb ıev? ErN (Er ıev? )N ƒ ıa exb (B8) (B9) The term a 0,exb is computed from the Weimer 2000 potential V 0 for all grid points and arrayed to form a 0. The additive correction term ıa exb is related to the unknowns x? and the columns of the matrix M multiplying them. [71] The model electric field term is defined to be a 0,exb = Ev?,0 ErN (Er Ev?,0 )N (B10) In the magnetic coordinate system used in EMPIRE, the velocity components are then h Ev?,0 = E0, B B 2 E 0, B r B 2 E 0,rB E 0, B r B 2 i T (B11) [72] We specify the electric field components E 0 = [E r, E, E ] T in magnetic spherical coordinates using a background electric potential model V 0. [73] The Weimer model has been developed as a high-latitude ionospheric electrodynamic model [Weimer, 2005] of the polar cap potential, producing a two-cell pattern. For this effort, the version used to generate values of V 0 in equation (B7) is the 2000 release [Weimer, 2001]. The inputs are solar wind parameters as measured from the ACE satellite and averaged over the previous 20 min. These data are available at the data repository of the Space Research Lab of Caltech ( The output is the electric potential for a user-defined point, specified in altitude-adjusted corrected geomagnetic coordinates (AACGM) for R =1, giving magnetic latitude and 7469