Estimating Satellite Orbital Drag During Historical Magnetic Superstorms
Denny M. Oliveira, Eftyhia Zesta, Hisashi Hayakawa, Ankush Bhaskar
EEstimating satellite orbital drag during historical magnetic superstorms ∗ Denny M. Oliveira † , Eftyhia Zesta , Hisashi Hayakawa , and Ankush Bhaskar
Goddard Planetary Heliophysics Institute, University of Maryland, Baltimore County, Baltimore, MD,United States NASA Goddard Space Flight Center, Greenbelt, MD, United States Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan Institute for Advanced Researches, Nagoya University, Nagoya, 4648601, Japan Rutherford Appleton Laboratory, Chilton, United Kingdom Catholic University of America, Washington D.C., United States
Abstract
Understanding extreme space weather events is of paramount importance in ef-forts to protect technological systems in space and on the ground. Particularly inthe thermosphere, the subsequent extreme magnetic storms can pose serious threatsto low-Earth orbit (LEO) spacecraft by intensifying errors in orbit predictions. Ex-treme magnetic storms (minimum Dst ≤ –250 nT) are extremely rare: only 7 eventsoccurred during the era of spacecraft with high-level accelerometers such as CHAMP(CHAllenge Mini-satellite Payload) and GRACE (Gravity Recovery And Climate ex-periment), and none with minimum Dst ≤ –500 nT, here termed magnetic superstorms.Therefore, current knowledge of thermospheric mass density response to superstormsis very limited. Thus, in order to advance this knowledge, four known magnetic su-perstorms in history, i.e., events occurring before CHAMPs and GRACEs commissiontimes, with complete datasets, are used to empirically estimate density enhancementsand subsequent orbital drag. The November 2003 magnetic storm (minimum Dst =–422 nT), the most extreme event observed by both satellites, is used as the bench-mark event. Results show that, as expected, orbital degradation is more severe forthe most intense storms. Additionally, results clearly point out that the time dura-tion of the storm is strongly associated with storm-time orbital drag effects, being asimportant as or even more important than storm intensity itself. The most extremestorm-time decays during CHAMP/GRACE-like sample satellite orbits estimated forthe March 1989 magnetic superstorm show that long-lasting superstorms can havehighly detrimental consequences for the orbital dynamics of satellites in LEO. Key Points: • Satellite orbital drag during magnetic superstorms (standard/equivalent Dst ≤ –500nT) has been quantitatively estimated • The November 2003 extreme magnetic storm is used as the benchmark event and formodel performance assessment when predicting drag effects • Interplay between storm-time duration and minimum Dst and Dst-like values deter-mine the severity of satellite drag effects in low-Earth orbit ∗ Paper published in
SpaceWeather , doi: hhttps://doi.org/10.1029/2020SW002472 † Electronic address: [email protected]; [email protected] a r X i v : . [ phy s i c s . s p ace - ph ] J u l lain Language Summary We investigate drag effects on satellites orbiting Earth in its upper atmosphere during mag-netic storms caused by the impacts of solar superstorms. During magnetic storms, the upperatmosphere is heated and expands upwards, resulting in increased drag forces on satellitesflying in those regions. Enhanced drag effects directly impact operations of such space-craft, for instance, orbital tracking and predictions, maneuvers, and lifetime maintenance.The U.S. Federal Government has recognized space weather phenomena as natural hazards,and the understanding of their consequences, particularly during extreme circumstances, isof paramount importance. The very extreme events, here termed magnetic superstorms,occurred before the space era when no in-situ observations of the atmospheric density areavailable. Therefore, we use an empirical model to estimate drag from these historical events.Results generally show that the most extreme events drive the most severe effects. Addi-tionally, we point out that another storm feature, its time duration, can play a significantrole in enhancing drag. Therefore, we argue that space weather forecasters should be awareof events with long duration, particularly the ones caused by sequential impacts of solardisturbances on the Earths magnetic field, when predicting and forecasting the subsequentdrag effects on satellites in the upper atmosphere.
Magnetic storms are global phenomena that occur due to the interaction of solar perturba-tions with the Earth’s magnetosphere (Gonzalez et al., 1994). The most intense and severemagnetic storms are commonly caused by coronal mass ejections (CMEs) (Balan et al., 2014;Daglis, Thorne, Baumjohann, & Orsini, 1999; Gonzalez et al., 1994). CMEs usually havea shock at their leading edge that is promptly followed by a sheath and a magnetic cloud(Balan et al., 2014; Gonzalez et al., 1994; Kilpua et al., 2019). Extreme magnetic storms arecaused by the impact of extremely fast CMEs on the Earth’s magnetosphere (Tsurutani &Lakhina, 2014), usually associated with highly depressed values of the southward componentof the interplanetary magnetic field (Balan et al., 2014; Daglis et al., 1999; Gonzalez et al.,1994; Kilpua et al., 2019; Tsurutani & Lakhina, 2014).Extreme space weather events like severe magnetic storms have been recognized by theU.S. Federal Government through the National Space Weather Strategy and Action Plan(National Science and Technology Council, 2015a, 2015b) as a natural hazard, and the needto establish benchmarks for extreme space weather events has also been recognized by thescientific community (e.g., Jonas, Murtagh, & Bonadonna, 2017; Lanzerotti, 2015; Riley etal., 2018). The intensity of magnetic storms is usually measured by depletions of the groundhorizontal magnetic field component recorded by magnetometers located at mid- and low-latitudes by means of the disturbance storm time (Dst) index (section 2.1). Extremely severeevents, here termed magnetic superstorms, with minimum Dst ≤ –500 nT, are notably rare(Chapman, Horne, & Watkins, 2020; Cliver & Dietrich, 2013; Hayakawa, Ebihara, Willis,et al., 2019; Riley et al., 2018; Vennerstrøm et al., 2016). For instance, the March 1989event, the only superstorm occurring during the space age (Meng, Tsurutani, & Mannucci,2019), is well-known for the occurrence of low-latitude aurorae (Allen, Sauer, Frank, & Reiff,1989; Pulkkinen, Bernabeu, Eichner, Beggan, & Thomson, 2012; Rich & Denig, 1992) andintense geomagnetically induced currents (GICs) which caused the blackout of the Hydro-Qu´ebec system in Canada for several hours, leading to serious economic losses (Bolduc, 2002;Kappenman, 2006; Pulkkinen et al., 2017). However, though arguably, the most extreme2round horizontal magnetic field perturbation ( ∼ –1600 nT) on record was recorded by theColaba station during the Carrington event of September 1859 (Hayakawa, Ebihara, Willis,et al., 2019; Siscoe, Crooker, & Clauer, 2006; Tsurutani, Gonzalez, Lakhina, & Alex, 2003).Since that is the only known low-latitude data set available to date, a global analysis ofthat storm cannot be performed (Blake et al., 2020; Cliver & Dietrich, 2013; Hayakawa,Ebihara, Willis, et al., 2019; Siscoe et al., 2006). For this reason, the Carrington event isnot addressed in this paper.During active times, large amounts of electromagnetic energy enter the ionosphere-thermosphere system causing the prompt thermosphere heating and upward extension dueto mechanical collisions between ions and neutrals (e.g., Emmert, 2015; Pr¨olss, 2011). Thisenergy has access to the thermosphere primarily through high latitudes (Connor et al., 2016;Fuller-Rowell, Codrescu, Moffett, & Quegan, 1994; Huang, Su, Sutton, Weimer, & David-son, 2014; Kalafatoglu Eyiguler, Kaymaz, Frissell, Ruohoniemi, & Rast¨atter, 2018; Liu &L¨uhr, 2005; Lu, Richmond, L¨uhr, & Paxton, 2016), and propagates equatorward due to theoccurrence of gravity waves and wind surges (Bruinsma & Forbes, 2007; Fuller-Rowell etal., 1994; Hocke & Schlegel, 1996; Sutton, Forbes, & Knipp, 2009). Therefore, the heatingand upwelling of the thermosphere are global phenomena (Liu, L¨uhr, Henize, & K¨ohler,2005; Richmond & Lu, 2000; Sutton et al., 2009). As a result, satellites that happen tofly in those regions experience increased effects of drag forces leading to stronger orbitaldegradations or altitude losses (Prieto, Graziano, & Roberts, 2014; Pr¨olss, 2011; Zesta &Huang, 2016). The understanding and control of orbital drag effects during active times canenhance predictability and forecasting of satellite tracking, reentry processes, and mainte-nance of satellite life times (Berger, Holzinger, Sutton, & Thayer, 2020; Pr¨olss, 2011; Zesta &Huang, 2016), particularly during extreme magnetic storms (Oliveira & Zesta, 2019). Mostof these studies have used data obtained from state-of-the-art accelerometers onboard twolow-Earth orbit (LEO) satellites, namely CHAMP (CHAllenge Minisatellite Payload; Reig-ber, L¨uhr, & Schwintzer, 2002) and GRACE (Gravity Recovery And Climate Experiment;Tapley, Bettadpur, Watkins, & Reigber, 2004). These spacecraft were launched after 2001(section 2.2).The most extreme magnetic storm experienced by CHAMP and GRACE took place inNovember 2003 with minimum Dst = –422 nT. Consequently, there are no assessments ofsatellite drag in LEO during magnetic superstorms inferred from high-accuracy accelerome-ter data. The orbital degradations of CHAMP and GRACE associated with the November2003 event 60 hrs through stormy times were, respectively, ∼ –160 m and ∼ –71 m (Krauss,Temmer, Veronig, Baur, & Lammer, 2015; Oliveira & Zesta, 2019), much more severe thanthe natural drag caused by the quiet-time backgorund density estimated by Oliveira andZesta (2019), namely –24.11 m and –6.86 m, respectively. Hence, these are the most extremestorm-time orbital decays measured with high-quality accelerometer data. In order to em-pirically estimate drag effects during magnetic superstorms, standard Dst data and groundmagnetometer data of historical superstorms reconstructed from historical archives are usedby a thermospheric empirical model (section 2.3) for density computations (section 2.4).These events occurred in March 1989 (Allen et al., 1989; Boteler, 2019), with the traditionalDst index available, September 1909 Hayakawa, Ebihara, Cliver, et al. (2019); Silverman(1995), May 1921 (Hapgood, 2019; Silverman & Cliver, 2001), and October/November 1903(Lockyer, 1903; Ribeiro, Vaquero, Gallego, & Trigo, 2016), with an alternative version to theDst index available. These four magnetic superstorms are here examined because they arethe only events with known and complete magnetograms that satisfy the threshold Dst/Dst-like ≤ –500 nT. The main characteristics of these storms’ effects will be presented in section3.1. Effects of storm time duration associated with minimum values of Dst and Dst-like data3ill be estimated and compared. As a result, this effort will improve our understanding ofsevere satellite orbital drag effects in LEO caused by magnetic superstorms. In this study, magnetic activity is represented by the Dst index provided by the WorldData Center for Geomagnetism, Kyoto, Nose, Iyemori, Sugiura, and Kamei (2015). This1-hr-resolution index was defined in 1957, the International Geophysical Year (IGY), as de-scribed by Sugiura (1964). Specifically, Dst is computed by averaging latitudinally weightedhorizontal magnetic field perturbations, with a background removal scheme, recorded bymid- and low-latitude stations with reasonably even longitudinal separation according tothe expression
Dst = 14 (cid:88) i =1 ∆ H i cos Λ i , i in [HON, SJG, HER, KAK] (1)where ∆ H i is the horizontal magnetic perturbation of the i-th station, and Λ i is the con-temporary magnetic latitude of the i-th station. The colored stars in Figure 1 show thestations, with their corresponding names, abbreviations, and geographic locations, used tocompute standard Dst after the IGY. Dst = 14 (cid:88) i =1 ∆ H i cos Λ i , i in [HON, SJG, HER, KAK] (2)where ∆ H i is the horizontal magnetic perturbation of the i-th station, and Λ i is the con-temporary magnetic latitude of the i-th station. The colored stars in Figure 1 show thestations, with their corresponding names, abbreviations, and geographic locations, used tocompute standard Dst after the IGY.Additionally, recent efforts have been undertaken to provide alternative (but similar)versions to the standard Dst index for historical magnetic superstorms with archival mate-rial. The events took place in October/November 1903 (Hayakawa, Ribeiro, et al., 2020),September 1909 (Love et al., 2019b), and May 1921 (Love et al., 2019a). This alternativeindex, also with resolution of 1 hr, was reconstructed with data obtained from four low/mid-latitude stations, with the best possible longitudinal separation, and is represented here byDst † (Dst “dagger”). The corresponding contemporary magnetic latitudes were computedby the authors. A background removal scheme similar to the one used to calculate Dst isused in the source papers as well. The stations used to compute Dst † used in this study areshown by the colored crosses in Figure 1. Therefore, the Dst † index is given by Dst † = 14 (cid:88) j =1 ∆ H j cos Λ j , j in [CLA, COI, CUA, ZKW] for Oct/Nov 1903[API, MRI, SFS, VQS] for Sep 1909[API, SFS, VSS, WAT] for May 1921 (3)The Dst † data for the magnetic superstorms used here are available as supporting in-formation provided by the respective references (Hayakawa, Ribeiro, et al., 2020; Love et4 − − − − −
30 0 30 60 90 120 150 180 geographic longitude [deg] − − − − g e og r a ph i c l a t i t ud e [ d e g ] -45 ◦ -30 ◦ -15 ◦ ◦ ◦ ◦ ◦ Standard (Dst) and alternative (Dst † ) disturbance storm time stations Standard Dst stations .Honolulu [HON], United StatesSan Juan [SJG], Puerto RicoHermanus [HER], South AfricaKakioka, [KAK], Japan.
Magnetic coordinates for 1957 .Magnetic latitudesMagnetic equator
Alternative Dst † stations Apia [API], Western Samoa (1909, 1921)Coimbra [COI], Portugal (1903)Colaba [CLA], India (1903)Cuajimalpa [CUA], Mexico (1903)Mauritius [MRI], Mauritius (1909)San Fernando [SFS], Spain (1909, 1921)Vassouras [VSS], Brazil (1921)Vieques [VQS], Puerto Rico (1909)Watheroo [WAT], Australia (1921)Zi-Ka-Wei [ZKW], China (1903)
Figure 1: Geographic locations of the ground magnetometer stations that compose thestandard Dst network that has been used by the World Data Center for Geomagnetism,Kyoto et al. (2015) since 1957 (colored stars), and the alternative Dst † network used byHayakawa, Ribeiro, et al. (2020), Love et al. (2019b), and Love et al. (2019a) for the his-torical events of October/November 1903, September 1909 and May 1921 (colored crosses),respectively. Magnetic latitudes (solid cyan lines) and the magnetic equator (solid orangeline) were computed by the Altitude-Adjusted Corrected Geomagnetic Coordinates ModelLaundal and Richmond (2017); Shepherd (2014) for 1957. Note that SJG is very close toVQS and therefore not clearly shown in this figure.al., 2019a, 2019b). Details of individual stations and magnetograms for each correspondingDst † network are provided in the source articles. CHAMP and GRACE neutral mass density ( ρ ) data obtained from their respective high-accuracy accelerometers are used in this work. CHAMP was launched in 2001 at the initialaltitude 456 km and orbital inclination 87.25 ◦ . It covered each 1 hr local time in 5.5 dayswith orbital period 90 min. The GRACE-A and -B spacecraft were launched in 2002 atthe initial altitude 500 km and orbital inclination 89.5 ◦ . The GRACE constellation coveredeach 1 hr local time in 6.7 days with orbital period 95 min. GRACE-A flew ∼
220 kmahead of GRACE-B. As discussed in Oliveira and Zesta (2019), only GRACE-A data areused, henceforth GRACE data, because GRACE-A data show higher quality than GRACE-B data. CHAMP re-entered in 2010, while GRACE re-entered in 2018. Uncertainties and5alibration techniques of both missions have been discussed by many papers (e.g., Bruinsma,Tamagnan, & Biancale, 2004; Doornbos & Klinkrad, 2006; Flury, Bettadpur, & Tapley,2008).The density data used in this study are normalized and intercalibrated as described inOliveira, Zesta, Schuck, and Sutton (2017) and Zesta and Oliveira (2019). Basically, theJacchia-Bowman 2008 (hereafter JB2008, Bowman et al., 2008, see below) empirical modelcomputes quiet-time densities ( ρ ) in order to obtain the background state for the quietthermosphere. This approach ensures that the ratio and the difference between the storm-time and quiet-time densities are as close to one ( ρ/ρ ≈
1) and zero ( ρ – ρ ≈
0) as possible,respectively. As a result, storm-time density enhancements can be extracted more effectively(Oliveira & Zesta, 2019; Oliveira et al., 2017; Zesta & Oliveira, 2019).
The first clear link between magnetic activity and satellite orbital drag effects was estab-lished by Jacchia (1959), who used Sputnik 1958 δ > –75 nT. Dst and Dst † data of the historical magnetic superstormsrecorded by the stations shown in Figure 1 will be used along with LEO satellite orbitaldata during the event of November 2003 to estimate the subsequent drag effects. Neutral mass densities are derived by high-accuracy accelerometers according to the dragequation (Prieto et al., 2014): a d = − ρC D Sm V V = | (cid:126)V s/c − (cid:126)V wind | , (4)where a d is the spacecraft acceleration caused by drag forces; ρ is the local thermosphericneutral mass density; C D is the drag coefficient; S/m is the area-to-mass ratio; and V is therelative velocity between the spacecraft velocity ( (cid:126)V s/c ) and the ambient neutral wind velocity( (cid:126)V wind ). In this equation, all quantities are presumably known, and therefore it is solvedfor ρ in order to yield density. However, these parameters (particularly C D ) can introduce6ignificant errors in density computations (Moe & Moe, 2005; Prieto et al., 2014; Zesta &Huang, 2016). In this study, drag coefficients computed with error mitigation methods bySutton (2009) were used.Chen, Xu, Wang, Lei, and Burns (2012) provide the following expression for the compu-tation of storm-time orbital decay rate:d a d t = − C D Sm (cid:112) GM (cid:104) a (cid:105) ∆ ρ , (5)with a being the semi-major axis of the satellite orbit here replaced by the temporalEarth’s radius plus satellite altitude (Oliveira & Zesta, 2019), G = 6.67 × − m · kg − · s − the gravitational constant, M = 5.972 × kg the Earth’s mass, and ∆ ρ the differencebetween the modeled storm-time and quiet-time densities. As outlined by Oliveira andZesta (2019), the daily average of the semi-major axis a is represented by (cid:104) a (cid:105) . A compar-ison between the use of both (cid:104) a (cid:105) computation methods for a magnetically quiet day (notshown) reviewed a very minimal difference in d a/ d t . In addition, Krauss et al. (2015) andOliveira and Zesta (2019) found the same results for the orbital decay of GRACE duringthe November 2003 storm.Finally, the storm-time orbital decay ( d ( t )) is computed by the sum over all d a/ d t valuesalong the satellite’s path for any ( t , t ) interval: d ( t ) = t (cid:90) t a (cid:48) ( t )d t , (6)where a (cid:48) ( t ) = d a ( t ) / d t . The benchmark event for the current study occurred in November 2003. That storm hadminimum Dst = –422 nT, the most intense magnetic storm event with both CHAMP andGRACE neutral mass density data available. Ground magnetometer data and neutral massdensity data for the GRACE satellite are shown in Figure 1 of Zesta and Oliveira (2019).The solar flux F10.7 index increased from 151 sfu (solar flux units) on 19 November to 175sfu on 23 November. The Dst and F10.7 indices for that storm are shown in Figure 2.Figure 3 documents the orbits of CHAMP and GRACE in the time interval from 19 to 23November 2003. The dial plots show orbits as a function of magnetic latitudes (MLATs) andmagnetic local times (MLTs). The magnetic coordinate system used is the Altitude-AdjustedCorrected Geomagnetic Model (Laundal & Richmond, 2017; Shepherd, 2014, AACGM,).The left column shows altitudes for CHAMP, while the right column shows altitudes forGRACE. The top row indicates data for the northern hemisphere, while the bottom row in-dicates data for the southern hemisphere. The colorbars indicate altitudes for both satellitesin the same periods.CHAMP is in a near noon-midnight orbit. The orbit altitudes of CHAMP increasedat high latitudes and at the magnetic poles of both hemispheres and decreased at mid-and low-latitudes. Similar behavior is shown by GRACE whose orbits were confined withinthe mid-noon/dusk and mid-midnight/dawn sectors. Therefore, both spacecraft providereasonable coverage between the day and night sectors. The altitude variations shown in7 − − − − − − D s t [ n T ] Dst and F10.7 indices for the November 2003 extreme magnetic storm F . [ s f u ] DstF10.7
Figure 2: Dst data (blue solid line) and F10.7 data (solid orange line) for the extrememagnetic storm of November 2003. The two dashed green vertical lines indicate the 13-hrtime interval between CME impact and minimum Dst value occurrence.Figure 3 caused by density variations at different MLATs and MLTs are mitigated by thedensity intercalibration method introduced by Oliveira et al. (2017).CME leading edges are usually associated with the occurrence of positive jumps in theDst index, while its sudden depression is associated with the arrival of CME magneticmaterial or sheaths (e.g., Gonzalez et al., 1994; Kilpua et al., 2019). The first perturba-tion, termed storm sudden commencement (SSC), is caused by the shock compression (e.g.,Oliveira et al., 2018; Shi et al., 2019), while the second event, termed storm main phase, isassociated with strong driving of the magnetosphere via magnetic reconnection (e.g., Dagliset al., 1999; Gonzalez et al., 1994; Kilpua et al., 2019). Examples of SSCs and storm mainphases represented by the Dst and Dst † indices during magnetic superstorms caused by fastCMEs are illustrated in Figure 4.Figure 4 shows ground magnetometer time series for the magnetic superstorms of (a) Oc-tober/November 1903 (Dst † ); (b) May 1921 (Dst † ); (c) March 1989 (Dst); and (d) September1909 (Dst † ). Data are plotted 12 hr and 72 hr around each respective SSC (dashed verticalblack lines). Times are shown as Greenwich Mean Time (GMT) for all events, except as Uni-versal Time (UT) for the 1989 event because UTs were introduced only in 1928 (Hapgood,2019). Given the similarities of UTs and GMTs, here they will be used interchangeably(Hapgood, 2019). The highlighted areas of each panel correspond to the time interval be-tween SSC and minimum Dst/Dst † occurrences, which also mark the beginning of the stormrecovery phase. This time interval will henceforth be referred to as the storm developmentduration time in this paper.Panels (a) and (b) show that the 1903 event is the weakest (minimum Dst † = –531 nT),whilst the 1921 event is the strongest (minimum Dst † = –907 nT) amongst all events. Incontrast, the development duration times of both events are almost the same, ∼
14 hr and ∼
12 hr, respectively. Storm strengths can be estimated by computing how fast Dst (orDst † ) is depressed during storm development. The average slope of Dst/Dst † during thedevelopment phase is quantified by the difference of Dst/Dst † minimum minus Dst/Dst † ◦ ◦ ◦ ◦ ◦ CHAMPNorthern Hemisphere
00 03 060912 MLT1518 21 − ◦ − ◦ − ◦ − ◦ − ◦ Southern Hemisphere
390 395 400 405 410 415
CHAMP altitude [km]
00 03 060912 MLT1518 21 ◦ ◦ ◦ ◦ ◦ GRACENorthern Hemisphere
00 03 060912 MLT1518 21 − ◦ − ◦ − ◦ − ◦ − ◦ Southern Hemisphere
480 490 500 510 520
GRACE altitude [km]
Figure 3: CHAMP (left-hand-side column) and GRACE (right-hand-side column) orbits, inmagnetic coordinates (Altitude-Adjusted Corrected Geomagnetic Model coordinate system),for the northern hemisphere (top row) and southern hemisphere (bottom row). The colorbarsrepresent the corresponding altitudes during the time interval 19-23 November 2003, thebenchmark event chosen for this study. The grey arrows in all panels indicate CHAMP’sand GRACE’s trajectories in both hemispheres.peak at SSC compression by the development time. This provides a quantifiable measureof the impactfulness of the storm, meaning that storms with very low amplitude rates arecommonly associated with high geomagnetic activity (e.g., Gonzalez et al., 1994). The es-timated amplitude rates are –46.4 nT/hr and –80.0 nT/hr for the October/November 1903and May 1921 events, respectively. These numbers explain why the effects of the 1921 event,such as equatorial extent of low-latitude aurorae (Chree, 1921; Silverman & Cliver, 2001),and GIC impacts on contemporary telegraph systems (Hapgood, 2019; Kappenman, 2006)were more severe than the effects of the 1903 event, mostly represented by mid-latitude au-rorae (Hayakawa, Ribeiro, et al., 2020; Page, 1903), and local GIC impacts on contemporarytelegraph systems in the United States and in the Iberian Peninsula (Hayakawa, Ribeiro, etal., 2020; Ribeiro et al., 2016).On the other hand, the superstorms of March 1989 and September 1909 (panels c andd) had very similar minimum values for Dst and Dst † , around –590 nT. However, the storm9 Greenwich Mean Time/Date − − − − − D s t † [ n T ] d September 1909
Love et al. (2019a)SSC + main phase: 8 hr
Greenwich Mean Time/Date − − − − − D s t † [ n T ] b May 1921
Love et al. (2019b)SSC + main phase: 12 hr
Universal Time/Date − − − − − D s t [ n T ] c March 1989
WDC for GeomagnetismSSC + main phase: 24 hr
Greenwich Mean Time/Date − − − − − D s t † [ n T ] a October/November 1903
Hayakawa et al. (2020)SSC + main phase: 14 hr
Dst (standard) and Dst † (alternative) indices for the selected magnetic superstorms Figure 4: Ground magnetometer Dst and Dst † time series, with resolution of 1 hr, for thestorms of (a) October/November 1903 (Hayakawa, Ribeiro, et al., 2020, Dst † ,); (b) May 1921(Love et al., 2019a, Dst † ,); (c) March 1989 (World Data Center for Geomagnetism, Kyotoet al., 2015, Dst); and (d) September 1909 (Love et al., 2019b, Dst † ,). The highlightedregions correspond to the time span between storm sudden commencement (SSC, verticaldashed lines) and the beginning of the storm recovery phases (minimum Dst or Dst † ), ortime duration of storm development.development duration of the 1989 event (24 hr) was 3 times longer than that of the 1909event (8 hr). Consequently, the development amplitude rates of both superstorms were–23.8 nT/hr and –75.0 nT/hr, respectively. With respect to the aurorae of these events,Hayakawa, Ebihara, Cliver, et al. (2019) estimated, based on contemporary observations,that their equatorward extent reached ∼ ◦ MLAT during the 1909 superstorm, as op-posed to 40 ◦ MLAT estimated from particle precipitation measurements by satellites duringthe 1989 superstorm (Pulkkinen et al., 2012; Rich & Denig, 1992). Intense GICs occurredduring both events, with several reports of geophysical disturbances on telegraph systemsin 1909 (Hapgood, 2019; Hayakawa, Ebihara, Cliver, et al., 2019; Love et al., 2019b; Sil-verman, 1995), and on power transmission lines in 1989, particularly the power blackout inQu´ebec, Canada (Allen et al., 1989; Boteler, 2019; Kappenman, 2006; Oliveira & Ngwira,2017). During the 1989 event, the only event with satellite-based data amongst the foursuperstorms, the number of space objects “lost” in LEO increased dramatically around pe-riods of maximum intensity due to errors introduced by storm heating effects into trackingsystems (Allen et al., 1989; Burke, 2018; Joselyn, 1990). The left (not highlighted) part ofTable 1 summarizes these storm properties.A comprehensive comparison of GIC effects caused by the superstorms on the contem-porary ground infrastructure, i.e., telegraph systems and power grids, is a difficult task to10 ρ [ k g/ m ] × − CHAMP observationmodelquiet
Universal Time/Date − − R e l a t i v ee rr o r [ % ] obs − modobs × − GRACE observationmodelquiet
Universal Time/Date − − obs − modobs CHAMP and GRACE data/model error for the November 2003 magnetic storm
Figure 5: Top row: Observed densities by CHAMP (left) and GRACE (right) and quiet- andstorm-time densities predicted by JB2008 for the November 2003 benchmark event. Bot-tom row: CHAMP (left) and GRACE (right) relative error between observed and modeledthermospheric densities for the same event. The grey highlighted area corresponds to thestorm development time (time interval between SSC occurrence and minimum Dst value),which is 13 hrs in this case.be accomplished. However, the comparisons above show that the latitudinal extent of theauroral oval was more equatorward for the events with lower amplitude rates (May 1921 andSeptember 1909 events). Next, the effects of these amplitude rates on storm-time orbitaldrag will be evaluated and compared for the four historical magnetic superstorms studiedin this paper.
Since the November 2003 magnetic storm is chosen in this work as the benchmark event,CHAMP and GRACE thermospheric neutral mass density response and the subsequentorbital drag effects for that storm are shown here, and an effort to compute errors associatewith drag effects is performed. The orbital drag framework of Oliveira and Zesta (2019)summarized in section 2.4 is used for the drag computations. The Dst and F10.7 indices forthe benchmark event are shown in Figure 2.Figure 5 documents density observed by CHAMP (upper left) and GRACE (upper right)along with JB2008 quiet- and storm-time density predictions for the benchmark storm. Thedynamics of that storm orbital effects were discussed in detail by Oliveira and Zesta (2019)particularly for GRACE’s case. In general, the predicted density dynamics follows CHAMPand GRACE observations quite well, but there are remarkable differences with respect todensity values. Firstly, density for both satellites was highly underestimated during heatingand cooling of the thermosphere, being more severe in CHAMP’s case. Secondly, overestima-tions of JB2008 results for GRACE’s orbit are higher than CHAMP’s during thermospheric11ecovery times (Oliveira & Zesta, 2019; Zesta & Oliveira, 2019). This density dynamics isreflected on the observed/predicted density relative errors shown by the solid purple linesof Figure 5 in the lower left panel for CHAMP and in the lower right panel for GRACE.Figure 6 shows drag results for CHAMP’s and GRACE’s orbits, respectively. The greyhighlighted areas in all panels indicate the storm development time (13 hrs) similarly tothe ones shown in Figure 4. The odd rows of these figures show storm-time orbital decayrates (d a/ d t , equation 4), while the even rows show storm-time orbital decay ( d , equation5). The left column shows observation results, while the right column shows JB2008 results.In the even rows, the magenta lines indicate the “natural” orbital decay caused by thebackground density if there was no storm activity. The background density for storm-timedrag computations was obtained by the method developed by Oliveira et al. (2017).As a result of the density dynamics shown in Figure 5, at t = 72 hrs, the storm-timeorbital decays estimated for CHAMP and GRACE shown in Figure 6 are underestimated by13.57% and overestimated by 16.32%, respectively. However, the uncertainties associatedwith the magnetic superstorms here investigated should differ from these uncertainties fortwo reasons: (i) the superstorms are more intense, and (ii) the superstorms had differentdevelopment times and therefore different magnetic activity during different times. Theseuncertainties are obtained for the most extreme magnetic storm during both CHAMP andGRACE commission times, and therefore may represent an upper limit of JB2008 uncer-tainties for extreme magnetic storms with high-level thermosphere neutral mass densityavailable. Figure 7 shows results of storm-time satellite orbital drag effects estimated according to theframework presented in section 2.4 but for the magnetic superstorms. The computations areperformed for the orbits of CHAMP and GRACE (Figure 3), with the orbital parametersthe satellites had during the November 2003 storm. The sample CHAMP- and GRACE-like satellites are flown through an upper atmosphere produced by the JB2008 model forDst/Dst † of the superstorms of Figure 4. All solar indices are kept the same, as those ofthe benchmark storm. For the sake of comparisons, results are plotted as a function ofarbitrary times (GMT/UT) 12 hr before and 72 hr after the SSC onset as seen in Figure4. The dashed vertical black lines (t = 0) indicate the times of SSC occurrence, while thehighlighted areas correspond to the storm development duration as shown in Figure 4 foreach corresponding storm.The top 4 panels of Figure 7 (a1-d1) show results for CHAMP’s orbit, while the bottom4 panels (a2-d2) show results for GRACE’s orbit. Panels a1 and a2 show storm-time orbitaldecay rates (equation 5) computed for the October/November 1903 superstorm (yellowline) and May 1921 superstorm (green line) for CHAMP and GRACE, respectively. Bothevents had approximately the same development times and very different intensities (Table1). The same is shown in panels c1 (CHAMP) and c2 (GRACE) for the superstorms ofMarch 1989 (red line) and September 1909 (blue line). In this case, the storms had verysimilar intensities, but different development durations (Table 1). The storm-time orbitaldegradation (equation 6), is shown for CHAMP (panels b1 and d1) and GRACE (panels b2and d2). The same colors used to represent d a/ d t results in panels a1/c1 and a2/c2 aboveare used to represent d results in panels b1/d1 and b2/d2.Figure 7a1 shows that d a/ d t values during October/November 1903 for CHAMP werevery close to zero before CME impact. On the other hand, d a/ d t values preceding the stormyperiod of May 1921 show some variations (meaning ∆ ρ is not necessarily close to zero),12 − − − − d a / d t [ m / d a y ] Observed and JB2008 drag effects for CHAMP’s orbit during the Nov 2003 extreme storm − − − − − − − − − − − d [ m ] Observed [ − − − − − − − − JB2008 [ − − − − − − − d a / d t [ m / d a y ] Observed and JB2008 drag effects for GRACE’s orbit during the Nov 2003 extreme storm − − − − − − − − − − d [ m ] Observed [ − − − − − − − JB2008 [ − − Figure 6: Top four panels: Orbital drag effects measured by CHAMP (left column) andestimated for the same orbit by JB2008 (right column) during the November 2003 extrememagnetic storm. The framework presented in section 2.4 and introduced by Oliveira andZesta (2019) were used for the computations. The four lower panels show similar results forGRACE. 13able 1: Summary of the properties of the magnetic superstorms (non-highlighted area) andsubsequent orbital drag results (highlighted area) shown in Figures 4 and 7, respectively.The same is shown for the benchmark event (bottom rows).
Magnetic superstorm properties Orbital drag effectsStorm SSC Min Development Amplitude Satellite Min MinMonth GMT/UT Dst/Dst † duration b Rate c Name d a/ d t d and year (Day) a [nT] [hr] [nT/hr] [m/day] [m]Oct/Nov 1903 0100(31) –531 14 –46.4 CHAMP –272.23 –91.23GRACE –178.83 –60.40May 1921 2300(14) –907 12 –80.0 CHAMP –432.98 –196.24GRACE –319.43 –142.09Mar 1989 0200(13) –589 24 –23.8 CHAMP –621.29 –388.59GRACE –469.95 –305.58Sep 1909 1200(25) –595 8 –75.0 CHAMP –285.14 –96.61GRACE –191.25 –62.14Benchmark storm properties Orbital drag effectsNov 2003 0900(20) –422 13 –33.8 CHAMP d –752.43 –171.22GRACE e –233.75 –89.35 a Greenwich Mean Time or Universal Time and Day of Storm Sudden Commencement (SSC). b Time between SSC and minimum Dst/Dst † occurrence. c d(Dst/Dst † )/dt d Mean altitude of CHAMP: 399.30 km e Mean altitude of GRACE: 490.10 km presumably linked to high magnetic activity shown by ground magnetometer data duringthe same pre-storm period (Hapgood, 2019; Love et al., 2019b). CHAMP d a/ d t valuesfor the 1921 event decreased faster in comparison to minimum d a/ d t values for the 1903event. Similar orbital drag dynamics is observed for GRACE (a2), but the absolute valuesof the drag response are smaller (Table 1) because GRACE operated at higher altitudes incomparison to CHAMP (Krauss, Temmer, & Vennerstrom, 2018; Oliveira & Zesta, 2019).The d a/ d t results for CHAMP and GRACE are summarized in Table 1.For the same pair of storms, the storm-time orbital degradations of CHAMP (panel b1) atthe end of 72 hr after CME impact were –91.23 m and –196.24 m for both events, respectively.The same estimated results for GRACE (b2) are –60.40 m (1903) and –142.09 m (1921).Comparatively, the percentual difference between drag effects during both superstorms forCHAMP (115.10%) are higher than the percentual difference of the superstorm intensites(70.81%) most likely because the magnetosphere was hit by another CME on 16 May 1921(Love et al., 2019a, Figure 4;), leading to an additional magnetosphere energization during itsrecovery, which in turn impacted drag effects. Similarly, the orbital drag relative differenceis higher in the case of GRACE (135.25%), when compared with the case of CHAMP. Assuggested by (Oliveira & Zesta, 2019, Figure 10), this is presumably due to the interplaybetween heating propagation from auroral-to-equatorial latitudes and (possibly) the directuplift of neutrals at low and equatorial latitudes more evident at altitudes higher than 400km Tsurutani et al. (2007).In summary, the main features that arise from the comparison between these events are:(i) CHAMP and GRACE decayed faster during the most intense event (1921) due to itssharper negative excursion of the Dst † index and lower amplitude rate (Figure 4a and b;Table 1); and (ii) the relative differences between d for both events do not closely followthe relative differences between minimum Dst † values. This is likely the case because themagnetosphere was struck by another CME during its recovery, increasing the magneto-spheric activity which in turn affected the subsequent orbital drag effects. Tables 1 and 214 − − − − d a / d t [ m / d a y ] a1 Storm-time orbital drag effects for CHAMP’s orbit
Orbital decay rate
Oct/Nov 1903May 1921 − − − − − c1 Orbital decay rate
Mar 1989Sep 1909 − − arbitrary time [hours] − − − − d [ m ] b1 Orbital decay − − − − arbitrary time [hours] − − − − − d1 Orbital decay − − − − − − − d a / d t [ m / d a y ] a2 Storm-time orbital drag effects for GRACE’s orbit
Orbital decay rate
Oct/Nov 1903May 1921 − − − − − c2 Orbital decay rate
Mar 1989Sep 1909 − − arbitrary time [hours] − − − − d [ m ] b2 Orbital decay − − − − arbitrary time [hours] − − − − − d2 Orbital decay − − Figure 7: Satellite orbital drag predicted by JB2008 for the selected events for CHAMP’sorbit (a1-d1) and GRACE’s orbit (a2-d2) during the November 2003 event, but with hy-pothetical Dst/Dst † values. Panels a1/b1 and a2/b2: d a/ d t and d for the events in Oc-tober/November 1903 (yellow lines) and May 1921 (green lines). Panels c1/d1 and c2/d2indicate the same, but for the events in March 1989 (red lines) and September 1909 (bluelines). The highlighted areas correspond to the storm development duration, or the time in-terval between SSC occurrence and the end of the storm main phase (minimum Dst or Dst † occurrence). These results give a sense of possible orbital decay effects during the super-storms because there are no CHAMP and/or GRACE data available during the superstormsevaluated in this paper. 15able 2: Comparisons between magnetic superstorm intensity and satellite orbital dragseverity for the magnetic superstorms predicted by JB2008 in this study. Magnetic Comparisons between Relative differences of drag effects [%]Superstorm Superstorm CHAMP GRACEMonth/Year intensities and durations d a/ d t d d a/ d t dOct/Nov 1903 May 1921 is 70.81% stronger 59.05 115.10 78.62 135.25May 1921 Nearly the same durationsSep 1909 March 1989 is 3 times longer 117.30 302.22 145.73 391.76Mar 1989 Nearly the same intensitiesMay 1921 March 1989 is 2 times longer 43.49 a a Percentual differences between more severe (March 1989) with respect to less severe(May 1921) drag effects summarize these results.The comparisons between estimated drag effects for the March 1989 and September1909 superstorms are remarkably different. These events had very similar strengths (similarminimum Dst and Dst † values), but their development times were quite distinct. Figure 7c1shows that 1909 CHAMP d a/ d t values could have shown a very sharp negative excursionafter CME impact, which follows very closely the same feature in the Dst † index (Figure4d). The minimum d a/ d t value (–285.14 m/day) for the September 1909 superstorm wasreached shortly before minimum Dst † . On the other hand, the March 1989 drag effects arequite different, since d a/ d t decreased more slowly in comparison to the former case due tothe differences in storm development amplitude rates. This is explained by the fact thatthe magnetosphere was most likely struck by multiple CMEs while the storm main phasewas developing (Boteler, 2019; Fujii et al., 1992; Lakhina & Tsurutani, 2016). Similarly tothe 1909 case, the minimum d a/ d t value (–621.29 m/day) occurred shortly before minimumDst occurrence. The thermosphere recovery of the 1989 superstorm took longer than thethermosphere recovery of the 1909 superstorm, most likely because the magnetosphere washit yet by more CMEs shortly after the beginning of the magnetosphere recovery (Figure4c). A similar behavior is shown by the GRACE results, panel c2, but with smaller absolutevalues due to higher GRACE altitudes. The relative differences between d a/ d t peak valuesof CHAMP and GRACE for both superstorms are 117.30% and 145.73%, even though bothevents had approximately the same minimum Dst and Dst † values and very different stormdevelopment durations and amplitude rates.Now the storm-time orbital degradations in both cases are evaluated. Figure 7d1 showsthat CHAMP d decreased faster during the main phase of the 1909 event, reaching valuesnear its minimum value around the beginning of storm recovery. This is a typical featureof drag effects triggered by a storm caused by an isolated CME (Krauss et al., 2018, 2015;Oliveira & Zesta, 2019). Conversely, CHAMP’s orbital degradation decreased more dramat-ically during the recovery of the 1989 superstorm. These drag effects correlate well with avery sharp negative excursion presented by the Dst index, which is also directly related withthe occurrence of low-latitude aurorae and very intense GICs around the world (Allen et al.,1989; Hayakawa, Ebihara, Cliver, et al., 2019; Kappenman, 2006). This time also coincideswith the loss of orbital control of several objects in LEO as shown by satellite-based data(Allen et al., 1989; Burke, 2018; Joselyn, 1990). The storm-time orbital decays for the 1909and 1989 events are –96.61 m and –388.59 m for CHAMP and –62.14 m and –305.58 m forGRACE. Their relative differences are 302.22% and 391.76%, closely following the propor-tion of storm time developments in the case of CHAMP. Taking into consideration that bothsuperstorms were almost equally intense, these results show that the storm time duration16able 3: Storm-time orbital decay for the magnetic superstorms corrected against theNovember 2003 benchmark event.Satellite orbital Superstorm month/yearname decay Oct/Nov 1903 Sep 1909 May 1921 Mar 1989CHAMP a d [m] (model) –91.23 —96.61 –196.24 –388.59 d [m] (corrected) –103.61 –109.72 –222.87 –441.32GRACE b d [m] (model) –60.40 –62.14 –142.09 –305.58 d [m] (corrected) –50.54 –52.00 –118.90 –255.71 a Underestimation of 13.57%. b Overestimation of 16.32%. can play a major role in driving orbital drag effects. Note also that relative differences arehigher in the case of GRACE, most likely explained by the reasons suggested by Oliveiraand Zesta (2019) as mentioned before.Another striking difference concerning minimum Dst and Dst † values, storm developmentduration and subsequent amplitude rate impacts arises from the comparison between theMay 1921 and March 1989 superstorms. The 1921 event was more than 50% stronger thanthe 1989 event, but active times during the latter lasted twice longer. The storm-time orbitaldecay for the March 1989 event was nearly twice more severe than the May 1921 event inboth CHAMP’s and GRACE’s cases (Figure 7 and Tables 1 and 2). These results clearlyreveal that a long-lasting magnetic superstorm can drive much more severe drag effects incomparison to a short-lasting, even stronger, superstorm. Tables 1 and 2 summarize themain results discussed in sections 3.1 and 3.2.The results presented so far correspond to the storm-time orbital decay values estimatedby JB2008. Furthermore, the uncertainties computed for CHAMP’s and GRACE’s orbitaldrag effects during November 2003 (section 3.2.1) can be used to obtain more realistic dragresults. Results are shown in Table 3, where white cells show model results, whereas greycells show corrected results. In these new computations, only assumptions on overall errorlevels (at t = 72 hrs) were used since realistic errors cannot be obtained for the differentsuperstorms because there are neither CHAMP nor GRACE density data available duringthese superstorm times.There are no solar wind nor interplanetary magnetic field data available for the magneticsuperstorms discussed in this paper. Furthermore, it is important to emphasize that ourstatements concerning CME impacts are supported by our current knowledge of the under-lying science: intense magnetic storms, particularly extreme events, are usually caused byCMEs (Balan et al., 2014; Daglis et al., 1999; Gonzalez et al., 1994; Kilpua et al., 2019;Lakhina & Tsurutani, 2016; Tsurutani & Lakhina, 2014). Extreme magnetic storms (minimum Dst ≤ –250 nT) are very rare. Only 39 extreme eventshave taken place since the beginning of the space era (Meng et al., 2019), while only 7extreme events were observed by CHAMP and GRACE (Oliveira & Zesta, 2019; Zesta &Oliveira, 2019). Additionally, only one magnetic superstorm (minimum Dst ≤ –500 nT)occurred since 1957, while none were ever observed by either CHAMP or GRACE. There-fore, current knowledge of thermospheric mass density response to magnetic supersotormsand the subsequent storm-time drag effects are very limited. Then, in order to estimate17hese effects, 4 historical magnetic superstorms with complete magnetograms were selected:one with standard Dst data (March 1989), and 3 with Dst † (Dst-like) data occurring onOctober/November 1903 (Hayakawa, Ribeiro, et al., 2020), September 1909 (Love et al.,2019b), and May 1921 (Love et al., 2019a). These Dst and Dst † data were used as inputdata for the JB2008 thermosphric empirical model for density computations. The extrememagnetic storm of November 2003 (minimum Dst = –422 nT), the most extreme event dur-ing CHAMP’s and GRACE’s commission times, at the altitudes ∼
400 km and ∼
490 km,respectively, was used as the benchmark event. The orbital drag framework provided byOliveira and Zesta (2019) was used for drag estimations.First, two events with different intensities but with approximately the same storm de-velopment times were compared (October/November 1903 and May 1921). Although the1921 superstorm was ∼
70% stronger than the 1903 superstorm, the drag effects in theformer were up to 135% more severe than the effects in the latter (GRACE’s case). Thisis attributed to the likely impact of another CME during the recovery phase of the 1921superstorm. Second, the other pair of superstorms, with very similar strengths, but with theSeptember 1909 storm development being 3 times shorter than the March 1989 storm devel-opment, were compared. Results show that the relative difference of the storm-time orbitaldegradation for the 1989 event was about 400% higher than the 1909 event (GRACE’s case).This is explained by the likely impacts of several CMEs on the magnetosphere during themain and recovery phases of the March 1989 superstorm (Boteler, 2019; Fujii et al., 1992;Lakhina & Tsurutani, 2016). Therefore, as opposed to latitudinal extent of aurorae, a su-perstorm with a smaller amplitude rate (absolute value) can cause more detrimental effectson orbital drag in comparison to an even stronger superstorm that develops faster (largerabsolute value of amplitude rate). The CHAMP and GRACE storm-time orbital decaysas predicted by JB2008 and corrected by errors obtained during the November 2003 event(Table 3) are much more severe than the orbital degradation due to the background densi-ties during the benchmark storm shown in Figure 6 for CHAMP (–28.68 m) and GRACE(–9.59 m). For example, results for the March 1989 event show that the CHAMP storm-timeorbital decay was estimated to be ∼ –441.32 m: such value has never been measured by aLEO spacecraft with high-level accelerometers. Therefore, these results set a new basis forthese effects. Despite the fact that these effects can have significant error levels particularlyduring the storm recovery phases due to the lack of nitric oxide cooling effects in the model(Bowman et al., 2008; Knipp et al., 2017; Mlynczak et al., 2003; Oliveira & Zesta, 2019;Zesta & Oliveira, 2019), these results reveal the comparative roles of time durations andstrengths of magnetic superstorms in controlling drag effects.The results of this work clearly show that multiple CME impacts on the Earth’s mag-netosphere (as in the March 1989 superstorm), particularly occurring during active times,can largely enhance satellite orbital drag due to long and sustained storm times. Thesedrag effects can be more severe when compared to drag effects during storms caused by asingle CME leading to even more intense storms, but lasting shorter. Therefore, orbital dragforecasters should be aware of potential impacts of several CMEs on the terrestrial magne-tosphere during ongoing magnetic storms (e.g., Zhao & Dryer, 2014, and many referencestherein). Additionally, different thermospheric empirical models should produce differentresults, with JB2008 outperforming NRLMSISE-00 and HASDM outperforming JB2008Bowman et al. (2008), but with DTM2013 outperforming JB2008 (Bruinsma, 2015). In afuture work, simulation results using different models of tens of historical severe and ex-treme magnetic storms, with minimum Dst ≤ –250 nT (Chapman et al., 2020; Hayakawa,Ebihara, et al., 2020; Meng et al., 2019; Oliveira & Zesta, 2019; Zesta & Oliveira, 2019), willbe statistically studied. 18 cknowledgments D.M.O. acknowledges the financial support provided by NASA through the grant HISFM18-HIF (Heliophysics Innovation Fund). E.Z. was supported by the NASA Heliophysics In-ternal Scientist Funding Model through the grants HISFM18-0009, HISFM18-0006 andHISFM18-HIF. H.H. has been supported by the JSPS grant-in-aids JP15H05816 (PI: S.Yoden), JP17J06954 (PI: H. Hayakawa). HH was also partly funded by the Institute forAdvanced Researches of Nagoya University and the research grant for Exploratory Re-search on Sustainable Humanosphere Science from Research Institute for Sustainable Hu-manosphere (RISH) of Kyoto University. A.B is supported by the Van Allen RadiationBelt Probes mission. The Information System and Data Center in Postdam, Germanycan provide access to CHAMP data through https://isdc.gfzpotsdam.de/champisdc/accesstothechampdata/ , and to GRACE data through https://isdc.gfzpotsdam.de/graceisdc/gracegravitydataanddocumentation/ . The JB2008 code along with solar andmagnetic activity data is available at http://sol.spacenvironment.net/jb2008/ . References
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