Document [original]

Stolleetal. Earth, Planets and Space (2021) 73:51

https://doi.org/10.1186/s40623-021-01364-w

FULL PAPER

Observing Earth’s magnetic environment

withtheGRACE-FO mission

C. Stolle1,2* , I. Michaelis1, C. Xiong1, M. Rother1, Th. Usbeck3, Y. Yamazaki1, J. Rauberg1 and K. Styp‑Rekowski1,4

Abstract

The Gravity Recovery and Climate Experiment Follow‑On (GRACE‑FO) mission carries magnetometers that are dedi‑

cated to enhance the satellite’s navigation. After appropriate calibration and characterisation of artificial magnetic

disturbances, these observations are valuable assets to characterise the natural variability of Earth’s magnetic field. We

describe the data pre‑processing, the calibration, and characterisation strategy against a high‑precision magnetic field

model applied to the GRACE‑FO magnetic data. During times of geomagnetic quiet conditions, the mean residual to

the magnetic model is around 1 nT with standard deviations below 10 nT. The mean difference to data of ESA’s Swarm

mission, which is dedicated to monitor the Earth’s magnetic field, is mainly within ± 10 nT during conjunctions. The

performance of GRACE‑FO magnetic data is further discussed on selected scientific examples. During a magnetic

storm event in August 2018, GRACE‑FO reveals the local time dependence of the magnetospheric ring current

signature, which is in good agreement with results from a network of ground magnetic observations. Also, derived

field‑aligned currents (FACs) are applied to monitor auroral FACs that compare well in amplitude and statistical behav‑

iour for local time, hemisphere, and solar wind conditions to approved earlier findings from other missions including

Swarm. On a case event, it is demonstrated that the dual‑satellite constellation of GRACE‑FO is most suitable to derive

the persistence of auroral FACs with scale lengths of 180 km or longer. Due to a relatively larger noise level compared

to dedicated magnetic missions, GRACE‑FO is especially suitable for high‑amplitude event studies. However, GRACE‑

FO is also sensitive to ionospheric signatures even below the noise level within statistical approaches. The combina‑

tion with data of dedicated magnetic field missions and other missions carrying non‑dedicated magnetometers

greatly enhances related scientific perspectives.

Keywords: Earth’s magnetic field, Geomagnetism, Ionospheric currents, Magnetospheric ring current, Satellite‑based

magnetometers, Platform magnetometers, GRACE‑FO

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Introduction

Low Earth orbiting (LEO) satellite missions dedicated

to accurately measure the geomagnetic field have revo-

lutionised the capability of monitoring Earth’s magnetic

field. The first of these missions was MAGSAT, followed

by Ørsted, SAC-C, CHAMP, and recently Swarm. These

missions enabled studies of the recent evolution of the

core field (e.g., Hulot etal. 2002; Livermore etal. 2017),

global lithospheric field mapping on scales between 200

and 3000km (e.g., Maus etal. 2007; Olsen etal. 2017),

and the altitude-dependent description of the Earth’s

mantle conductivity (e.g., Grayver etal. 2016) to what

concerns geomagnetic sources located at Earth’s interior.

Concerning the exploration of the geospace environment,

geomagnetic LEO missions have especially contributed

by first possible observations of currents flowing in the

ionosphere that are only detectable by insitu measure-

ments. These include polar cusp, auroral, and inter-hem-

ispheric field-aligned currents (e.g., Olsen 1997; Lühr

etal. 2017; McGranaghan etal. 2017), vertical currents

at the magnetic equator (e.g., Park etal. 2010), Fregion

gravity-driven and plasma-pressure-driven currents

(e.g., Alken 2016; Laundal etal. 2019), or diamagnetic

Open Access

*Correspondence: cstolle@gfz‑potsdam.de

1 Helmholtz Centre Potsdam, GFZ German Research Centre

for Geosciences, Telegrafenberg, 14473 Potsdam, Germany

Full list of author information is available at the end of the article

Page 2 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

and field-aligned currents connected to irregularities at

equatorial or mid-latitudes (e.g., Rodríguez-Zuluaga and

Stolle 2019; Park etal. 2010; Stolle etal. 2006). A compre-

hensive review on achievements by high-precision geo-

magnetic data from space and their applications is given,

e.g., by Olsen and Stolle (2012).

In addition, high-amplitude signatures of electric cur-

rents in the ionosphere and magnetosphere have been

detected by observations from magnetometers at LEO

altitude that do not meet the accuracy of the above-men-

tioned dedicated geomagnetic missions. These are either

non-high-precision magnetic observations, e.g., the mis-

sion did not measure the magnitude of the total field

together with the variations of the magnetic components,

or it did not carry an optical bench on the magnetometer

boom (e.g., CSES, C/NOFS, DMSP, and e-POP, in the fol-

lowing examples). Another category are so-called plat-

form magnetometers which are mounted at the satellite

body and are primarily used for attitude determination

(e.g., AMPERE, CryoSat-2, GRACE, and GRACE-FO,

in the following examples). With its constellation of 66

satellites, maps of auroral field-aligned currents derived

from magnetometer data of the AMPERE project have

had large impact on the investigations of the polar ion-

osphere (e.g., Anderson et al. 2000; Korth et al. 2010;

Carter etal. 2016). The magnetometers on the DMSP sat-

ellites were used, e.g., to derive Poynting Flux at auroral

latitudes (Knipp etal. 2011) or to describe the relation of

the location between auroral FACs and particle energy

flux (Xiong et al. 2020). CASSIOPE e-POP data were

used to derive fine structures of auroral arcs (Miles etal.

2018), and observations from the low-inclination satellite

C/NOFS added in describing the local time dependence

of the geomagnetic signal due to the magnetospheric

ring currents during geomagnetic active times (Le etal.

2011). However, recently, Park etal. (2020) demonstrated

that statistical analyses of multiple years of field-aligned

current data derived from magnetometer observations

of the CryoSat-2 and GRACE-FO missions successfully

revealed mid-latitude inter-hemispheric currents. This

finding is especially interesting, because it proves the

capability of data from non-dedicated magnetometers to

be sensitive to small amplitude currents, as well.

Also core field structures have successfully been

derived from these types of data. Magnetometer data

from DMSP were applied for geomagnetic field mod-

elling in a spherical harmonic expansion up to degree

15 (Alken etal. 2014). A special consideration of data

from DMSP and ESA’s CryoSat-2 was taken to enhance

the data availability between the re-entry of CHAMP in

2010 and the launch of the Swarm mission in 2013 (e.g.,

Alken et al. 2020a; Finlay et al. 2020). Data from the

recently launched CSES mission of the China Earthquake

Administration have provided a candidate model for the

International Geomagnetic Reference Field (IGRF-13)

(Alken etal. 2020b; Yang etal. 2020).

Different characterisation and calibration strategies for

non-high-precision magnetometers in space have been

applied, e.g., on data of the AMPERE, DMSP, CryoSat-2,

or GRACE missions [e.g., Anderson etal. 2000; Alken

etal. 2014, 2020a; Olsen etal. 2020, Olsen (submitted

to Earth, Planets, and Space)]. This article introduces a

calibrated magnetometer data set for the Gravity Recov-

ery and Climate Experiment Follow-On (GRACE-FO)

mission.

The GRACE-FO mission is operated under a partner-

ship between NASA and the German Research Cen-

tre for Geosciences (GFZ). The primary objective of

GRACE-FO (Landerer etal. 2020) is to obtain precise

global and high-resolution models for both the static and

the time variable components of the Earth’s gravity field.

It is a successor to the original GRACE mission (Tapley

etal. 2004), which orbited Earth from March 2002 until

October 2017.

GRACE-FO was successfully launched on 22 May

2018. It is a constellation mission and the two identical

satellites, named GF1 and GF2 in the following, fly at the

same orbit but with GF1 leading GF2 by a distance of

approximately 220km. They fly on a near-circular polar

orbit with an inclination of

89◦

and at an altitude of 490

(± 10)km. A sketch of its formation is illustrated in Fig.1

and a summary on ‘quick facts’ on satellite orbits and

bodies is available at https ://grace fo.jpl.nasa.gov/overl ay-

quick -facts /.

As part of their attitude orbit control system (AOCS),

the GRACE-FO satellites carry magnetometers and this

article introduces a calibrated magnetometer data set

of GF1 and GF2. We first describe the original data and

the data pre-processing which we applied, followed by

describing the applied calibration and characterisation

techniques. The final data set is assessed, and it is com-

pared against Swarm observations during conjunction

events between the two missions. Finally, we discuss the

performance of the prepared data set for scientific appli-

cations on selected example areas. The processed mag-

netometer data published by this article are available at

ftp://isdcf tp.gfz-pot sd am.de/grace -fo/MAGNE TIC_

FIELD /, currently for 29months between June01,2018

and October31,2020. The data set is extended with con-

tinuing mission operation. The data published with this

article are version 0201.

Data sets anddata pre‑processing

As part of the attitude orbit control system (AOCS), each

GRACE-FO satellite carries two fluxgate magnetom-

eters (FGM), an active one, FGM A, and a redundant

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Stolleetal. Earth, Planets and Space (2021) 73:51

one, FGM B. So far, the redundant magnetometers were

not switched on for GF1 and only on few days for GF2

in February 2019. The left panel in Fig.2 shows the loca-

tion of the magnetometers on board the satellite. The

magnetometers are manufactured by Billingsley Aero-

space & Defence and are of type TFM100SH (Billingsley

2020). The measurement range is ± 65,000nT and the

root-mean-square noise level is

∼

60pT/

√Hz

. The data

are sampled at 1Hz as spot values with no on-board fil-

tering from higher frequency data.

Magnetometer calibration further relies on attitude

data derived from the three star cameras (STR) that

are mounted at the top and at each side of the satellite

(indicated by squared black open cylinders in Fig.1).

Fig. 1 Schematic view of the GRACE‑FO constellation mission (credits: NASA/JPL‑Caltech)

Fig. 2 (Left) location of FGMs at the satellite body. Flight direction (red arrow) is indicated for GF1. GF2 has opposite flight direction. (Right) location

of the magnetorquers at the bottom side of the satellite. Black arrows in both panels indicate the normal vector to the satellite bottom. In the left

panel, the magnetorquers are hidden by the front plate (credits: AIRBUS)

Page 4 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Among others, magnetic perturbation is often expected

from magnetorquers (MTQ) that are mounted to steer

pitch, yaw, and roll, respectively. At the GRACE-FO sat-

ellites, they are located at the opposite side of the satel-

lite body than the magnetometers do and their location

is indicated in the right panel of Fig. 2. GRACE-FO

magnetometer, magnetorquer currents, and attitude

data are part of the mission’s L1b data sets and are

available at ftp://isdcf tp.gfz-potsd am.de/grace -fo/. To

characterise the magnetic data, we also used informa-

tion on magnetometer temperature, battery currents,

and solar array currents. These data can be accessed on

request from the Information System and Data Centre

(ISDC) at GFZ Potsdam. An overview of used input

data is given in Table1. GRACE-FO L1b data are pro-

vided in zip files that contain ASCII files for each L1b

product listed in Table1. Each file consists of a header

and a data part, and time values are always handled as

GPS time. Most of L1b data are provided in 1Hz reso-

lution. However, magnetorquer currents comes in 2Hz.

The sampling rate of the magnetometers is 1Hz, but

they have been simulated in the L1b files being 2Hz by

doubling each 1Hz sample to technically be in concert

with MTQ sampling rates. Therefore, we ignore each

second record from MAG1B. Additionally, we found

that the magnetorquer currents saturate at ± 110mA.

Due to this limitation, we de-selected all values that

coincide with the saturated values to later avoid possi-

ble misinterpretation during characterisation.

Since data time stamps are not all given on the full sec-

ond, they are interpolated to a common time grid. We

use the time stamps of the star camera data as the ref-

erence for the grid. All other products have been inter-

polated to these reference time stamps using linear

interpolation. At these times and respective satellite loca-

tions, we further generated predictions of the core, the

crustal, and the large-scale magnetospheric field by the

CHAOS-7 model (Finlay etal. 2019, 2020). The mod-

elled values will later be the reference during calibra-

tions of GRACE-FO magnetic data. We also generated

quasi-dipole latitude (QDLAT) and magnetic local time

(MLT) (Richmond 1995; Emmert et al. 2010) for each

GRACE-FO record, that will help in data selection for

calibration and finally during the assessment of the cali-

bration results. We are later interested to assess magnetic

data in the Earth-fixed North-East-Centre (NEC) refer-

ence frame; also, CHAOS-7 predicts field data in NEC,

further used as

Bmodel,NEC

. However, since the estimated

calibration parameters are instrument intrinsic and cali-

bration is performed in this instrument frame of the

magnetometers (called FGM frame in the following),

appropriate rotations need to be applied. Earth’s nutation

and precession rotation matrix needed to rotate between

the International Terrestrial Reference Frame (ITRF) and

the International Celestial Reference Frame (ICRF) are

Table 1 Input data used forcalibration andcharacterisation, includingproduct name (if applicable), variable name, unit,

andtemporal resolution

Description Product Variable Unit Resolution

Magnetic field MAG1B MfvX_RAW nT 1 s

MfvY_RAW

MfvZ_RAW

AMTQ

Magnetorquer currents MAG1B torque1A, torque1B mA 0.5 s

Positive X, negative X torque2A, torque2B

Positive Y, negative Y torque3A, torque3B

Positive Z, negative Z

POS

Satellite position in ITRF GNV1B xpos, ypos, zpos m 1 s

STR

Rotation from ICRF to FGM in quaternion

representation SCA1B quaticoeff 1 s

quatjcoeff

quatkcoeff

quatangle

TFGM

Magnetometer temperature THT10060

◦C

32 s

ABAT

Battery current PHT10016 A 1 s

PHT10017

PHT10018

ASA

Solar array current PHT10030 A 1 s

PHT10036

PHT10041

Page 5 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

obtained by applying (IAU SOFA Board 2019, SOFAli-

baryfunctioniauC2t06a), where Earth rotation param-

eters are derived from the International Earth Rotation

and Reference Systems service (IERS 2020). The rotation

matrix between the ITRF and the ICRF frame,

RITRF2NEC

is then determined for respective time and Earth rota-

tion parameters. The rotation matrix between ITRF and

NEC depends on geocentric location (latitude and longi-

tude). The equation is based on Seeber (2003,p. 23) for

a North-East-Zenith frame but changing the sign of the

z-direction (3rd row) to get a right-handed North-East-

Center frame (NEC). The rotation matrix is described as:

with latitude



and longitude



In the case of the GRACE-FO L1b data, both mag-

netometer and star camera data are provided in the same

frame, the Science Reference Frame (SRF) (Note that this

might not be the case for other missions). SRF is a space-

craft frame and it has its origin at the center of mass of

the accelerometer proof mass, the x-axis is aligned with

the roll axis, the y-axis is aligned with the pitch axis,

and the z-axis is aligned with the yaw axis of the satel-

lite. Remaining misalignment between the orientation of

the FGM instrument and the SRF frame is later reflected

within the Euler angles during calibration.

The satellite attitude data provided by the star cameras

are given in a combined product for all 3 star cameras

and are in quaternion representation, which led us to

perform all rotations by quaternion notation. The rota-

tion from the SRF to the ICRF frame is directly given by

the star camera data. Since both the FGM and star cam-

era data are given in SRF, their rotation to ICRF is iden-

tical to

qFGM2ICRF

. Conversion of the direction cosine

matrices,

RITRF2NEC

and

RNEC2ITRF

, to quaternion repre-

sentations is realised by a function,

F

, following Wertz

(1978, p. 415) and

NEC2ITRF

F(RR

ITRF2NEC

−1)

and

qITRF2ICRF =F



(RITRF2NEC)

. In summary, the complete

rotation from the NEC to the FGM frame is given as:

CHAOS-7 predictions are finally rotated from NEC to

the FGM frame applying the rotation quaternion in Eq.2

following Wertz (1978,p. 759):

(1)

ITRF2NEC =



−

sin(�)

cos(�)

−

sin(�)

sin(�) cos(�)

−sin(�) cos(�) 0

−cos(�) ·cos(�) −cos(�) ·sin(�) −sin(�)



(2)

qNEC2FGM =

NEC2ITRF ·

ITRF2ICRF ·

−1

FGM2ICRF

(3)

BNEC

qNEC2ITRF

−−−−−−→ BITRF

qITRF2ICRF

−− − − − −→ BICRF

−1

FGM2ICRF

−− − − − −→ BFGM.

(4)

Bmodel,FGM =

−1

NEC2FGM ·

model,NEC ·

NEC2FGM.

Calibration and characterisation described in the next

section are performed in the instrument FGM frame. For

later interpretation of the data in the geophysical NEC

frame, the calibrated data are rotated back applying the

inverse of Eq.3.

Calibration andcharacterisation

The magnetometer data of GRACE-FO are pre-calibrated

on board to satisfy attitude and orbiting control via

AOCS. These magnetometer data are provided in the L1b

data. However, the characterisation of the data for artifi-

cial disturbances and further calibration are needed for

application in scientific studies. The applied calibration

and characterisation approach is similar to that applied

by Olsen etal. (2020), but a somewhat higher time vari-

ability was allowed for the estimated parameters applied.

Calibration and characterisation have been performed on

subsets of monthly data and for a subsample within each

month satisfying

|QDLAT|<50◦

Kp ≤2

|Dst|≤30 nT

and

B_Flag =0

. The flag

B_Flag

differs from zero if one

of the magnetorquers is saturated. Selecting monthly sets

is a compromise between high fluctuations of calibration

and characterisation parameters that would occur for

daily processing, but still capturing possible long-term

trends of the parameters.

An ordinary least-squares linear regression was applied

to these subsets:

where

Bcal

is the calibrated magnetic field vector after

calibration parameters

cal

=(b,s,u,e,ξ,ν)

have

been applied on the raw magnetic field vector

(see

also Eq. 9).

Bchar

is the estimated vector describing

the artificial magnetic field from the satellite derived

by the application of the characterisation parameters

mchar =(M, bat, sa, bt, st)

on the so-called housekeep-

ing data

dHK =(AMTQ,ABAT,ASA,TFGM,Est)

(see also

Eq. 13).

Bmodel,FGM

includes the CHAOS-7 magnetic

field estimations for both the core, crustal, and large-

scale magnetospheric field rotated into the instrument

FGM frame as described in Eq.4. The parameters

mcal

and

mchar

are optimized to reduce the defined squared

error S.

Additionally, the calibration has been applied with

different time-shifts of the magnetometer data set to

account for possible time stamp errors. Within an inter-

val of ± 2s, the data set was shifted in steps of 0.1s and

again in steps of 0.01s around the most probable target.

This investigation was applied on the most quiet data

set which was in January 2019. Best calibration results

(minimum of the absolute values of residual to CHAOS-

7) have been determined for GF1 with 0.95s for FGM

(5)

S=|(Bcal(mcal,E)+Bchar(mchar,dHK)) −Bmodel,FGM|2,

Page 6 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

data and for GF2 with 0.73s for FGM data. For GF2, the

residual was even smaller after time-shifts have also been

applied to housekeeping data, − 10s for solar array cur-

rents, 2s for battery currents, and 0.3s for magnetorquer

currents. For GF1, additional time-shifts on housekeep-

ing data did not reduce the residual and zero time-shift

was kept for housekeeping data. These time-shifts have

been applied to the magnetometer and/or housekeeping

data, respectively, before the final calibration and char-

acterisation was performed. Applying these time-shifts

gave evenly large or reduced residuals for each months in

the calibrated period.

Parameters forcalibration

The raw magnetic field vector provided by the L1b data is

represented in the three directional components within

the instrument FGM frame as

E=(E1,E2,E3)T

(see

Table 1 for corresponding field names) given in units

ofnT. The calibration approach estimates nine intrinsic

and three external parameters. Six of the intrinsic param-

eters are included in an offset vector

b=(b1,b2,b3)T

and a scale vector

s=(s1,s2,s3)T

. Ideally, the coils of

the FGMs are perfectly perpendicular to each other. To

account for an inexactness, a misalignment angle vec-

tor

u=(u1,u2,u3)T

includes the other three intrin-

sic parameters. The orientation of the instrument with

respect to the SRF is given in the specification of the

satellite, or in the case of the AOCS magnetometer of

GRACE-FO, these frames are identical in the L1b data.

In practice, also this orientation is not perfectly constant.

Misalignment of it is given in a vector of Euler (1–2–3)

angle representation

e=(e1,e2,e3)T

, following Wertz

(1978,p. 764), or in a direction cosine rotation matrix,

, which includes the three external parameters. Euler

(1–2–3) represents three rotations about the first, sec-

ond, and third axis, in this order. The parameters are used

to describe:

where

is the direction cosine matrix representation of

the Euler (1–2–3) angles

P−1

is the misalignment angle

lower triangular matrix with:

and

S−1

is the diagonal matrix including the inverse of

the scale factor:

(6)

Bcal =

−1

−

A(E

−

(7)

P−1=



1 00

sin(u1)

cos(u1)

cos(u1)0

−sin(u1)sin(u3)+cos(u1)sin(u2)

wcos(u1)−sin(u3)

wcos(u1)1/w



with:

=

−

sin2(u2)

−

sin2(u3),

Equation6 is valid, if, in first order, fluxgate magnetom-

eters are treated as linear instruments. If the condition

of linearity is not given (Brauer etal. 1997), a linearised

equation is applied by extending Eq. 6 for non-linear

effects of second (

) and third (

) order parameters

applied on second- (

Eξ

) and third-order (

Eν

) d ata:

with non-linearity parameters of second order:

non-linearity parameters of third order:

and modulated data vectors of second and third order:

Parameters forcharacterisation

Characterisation consists of the identification and, if

possible, correction of artificial magnetic perturba-

tions contained in the raw magnetic data. We identified

the magnetorquer currents,

AMTQ

, the magnetometer

temperature,

TFGM

, the battery currents,

ABAT

, and the

solar array panel currents,

ASA

, to affect the GRACE-

FO magnetometer data. We also consider an effect from

the correlation between the magnetometer temperature

and magnetic field residuals,

Est =E·(TFGM −T0)

where

is the monthly median of

TFGM

The characterisation equation is a combination of all

identified disturbances:

For both Eqs.9 and 13, input variables and parameters to

be estimated are summarised in Tables1 and 2, respec-

tively. Both the estimated parameters and the calibrated

magnetic observation products are provided on the ISDC

ftp site.

(8)

−1



1/s1

01/s20

0 01/s3



(9)

cal

=AE−b

(10)



11 ξ

22 ξ

33 ξ

12 ξ

13 ξ

ξ2

11 ξ2

22 ξ2

33 ξ2

12 ξ2

13 ξ2

ξ3



(11)



111 ν

222 ν

333 ν

112 ν

113 ν

223 ν

122 ν

133 ν

233 ν

123

ν2

111 ν2

222 ν2

333 ν2

112 ν2

113 ν2

223 ν2

122 ν2

133 ν2

233 ν2

123

ν3

111

ν3

222

ν3

333

ν3

112

ν3

113

ν3

223

ν3

122

ν3

133

ν3

233

ν3

123



(12)

ξ=(E

1,E

2,E

3,E1E2,E1E3,E2E3)

ν=(E3

1,E3

2,E3

3,E2

1E2,E2

1E3,

(13)

char =

MTQ +

bat

BAT +

ASA

+bt ·

(TFGM

−T

+st ·

Est

Page 7 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Results anddiscussion

This section discusses the final GRACE-FO data set and

its application. We assess the residuals to CHAOS-7

predictions of all vector components and perform an

independent validation by comparison to high-preci-

sion observations from the simultaneous Swarm mis-

sion, e.g., during orbit conjunctions or close flybys. By

discussing selected scientific applications on auroral

field-aligned currents and signatures of the magneto-

spheric ring current, this section aims at further out-

lining opportunities and limitations of the GRACE-FO

data set.

Assessment offinal data set

Table3 provides the mean and the standard deviations

of the residuals of the final magnetic field vector of GF1

and GF2 to CHAOS-7 predictions for

|QDLAT|<50◦

Kp ≤2

, and

|Dst|≤30 nT

. Averaged over the entire

period of GRACE-FO, the mean is zero, which is not

surprising, since the data have been calibrated against

CHAOS-7. The standard deviation is few nanotesla and

is in general a bit higher for GF2 than for GF1. For a sin-

gle day, the standard deviations do not differ significantly

from the one of the entire period, but the mean is slightly

biased. For comparison, the lower rows in Table3 pro-

vide the values for the raw magnetic data provided in

L1b. Both mean and standard deviation have dramati-

cally been reduced after calibration and characterisation.

The amplitudes in standard deviation of few nanote-

slas are similar to those of the root mean scatter of the

CryoSat-2 residuals discussed in Olsen et al. (2020),

which varied between 4 and 15nT depending on local

time and geomagnetic activity. This agreement is espe-

cially remarkable, because CryoSat-2 carries three iden-

tical magnetometers, and Olsen etal. (2020) compares

the mean of their calibrated times series, which further

reduces the effect of the intrinsic noise from the single

instruments.

To estimate the impact of the different parameters on

the final results, Eq.5 was applied but omitting single

parameters in Table2 in each application. The standard

deviation of the residuals to CHAOS-7 for each of these

applications is given in Table4 for both GF1 and GF2.

The minimum and maximum values of the residuals of

each respective result are also provided. Largest standard

deviation is observed when solar array and battery cur-

rents are not considered in the characterisation. Large

spikes or jumps can be corrected with knowledge of the

magnetorquer currents. For GF2, battery currents and

solar arrays have larger impact than for GF1. Also, on

GF2, the temperature dependence of the scale factor is an

important parameter.

Table 2 Estimated calibration and characterisation

parameters includingunits anddimensionality

Parameter Description Unit Dimension

Scale factors

Offsets nT 3

Misalignment angles rad 3

Euler (123) angles rad 3

2nd order non‑linearity

23 × 6

3rd order non‑linearity

33 × 10

Temperature dependency of offsets b

◦C

3 × 3

Temperature dependency of scale

factors s

◦

3 × 3

bat

Battery current scale factor

3 × 3

Solar array current scale factor

3 × 3

Magnetorquer current scale factor

3 × 3

Table 3 Mean andstandard deviation ofresiduals toCHAOS‑7 forGF1 andGF2 forgeomagnetic quiet timesandfor

asingle quiet day, 30 January 2019

BNEC

represents residuals for calibrated data and

BRAW

for data before calibration

Parameter Whole period Single day

Mean (nT) Std (nT) Mean (nT) Std (nT)

x y z x y z x y z x y z

GF1

BNEC

0.0 0.0 0.0 7.8 7.9 9.5 − 0.2 − 0.6 − 0.6 4.3 5.2 2.9

BRAW

− 323.1 − 551.5 78.3 95.7 323.1 131.8 − 302.4 − 561.5 85.1 97.3 321.5 130.5

GF2

BNEC

0.0 0.0 0.0 7.1 8.4 7.7 0.4 − 2.0 1.2 3.9 8.0 3.6

BRAW

1357.3 351.7 − 145.9 285.6 204.5 116.5 1331.5 380.1 − 173.1 295.3 206.8 116.6

Page 8 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Figure3 provides residuals between the processed data

and CHAOS-7 predictions for January 2019, e.g., their

mean of all residuals within each bin of a grid with bin

size of

5◦

geocentric latitude and

5◦

geocentric longi-

tude. The four columns are for the

, and

com-

ponent of the NEC frame, respectively, and for the total

field F. The first row displays residuals to the core, the

crustal and the large-scale magnetospheric field predic-

tions of CHAOS-7 for GF1, and the second row shows

the same for GF2. The grey lines indicate the

0◦

and

±70◦

magnetic latitude (QDLAT). The third row shows

the difference between GF1 and GF2 residuals. The last

row gives geomagnetic and solar indices and magnetic

local time of the data set of this month. Hence, the mis-

sion flew in a 07/19MLT orbit and the month was geo-

magnetically very quiet. In both GF1 and GF2, largest

deviations occur at auroral regions which result from

the auroral electrojet and field-aligned currents. Since

the data are collected at 07/19MLT, no significant low-

and mid-latitude ionospheric disturbances are expected,

neither significant effects from magnetospheric currents

during the quiet times. However, some systematic devia-

tions occur, such as above the northern Atlantic in the

BE

and

BC

components of GF1 and the ribbon at low

latitudes in

BC

of GF2. These could not be accounted

for through correlation with any known satellite charac-

teristic. However, residuals of 10nT or less can be seen

as an acceptable result for data from a non-dedicated

magnetometer where magnetic cleanliness of the sat-

ellite has not explicitly been taken care of. The differ-

ences between the GF1 and GF2 residuals show similar

amplitudes in mid and low latitudes, which indicates that

artificial disturbances from the satellite are not identical

between the two spacecraft. It is interesting to note that

the statistics for calibrated CryoSat-2 magnetic data pro-

vided by Olsen etal. (2020) (not shown) reveal a similar

behaviour. CryoSat-2 satellite carries three active mag-

netometers from the same type of Billingsley (Billingsley

2020) as does GRACE-FO, and, e.g., only

from one

magnetometer (magnetometer 2) show a disturbance at

the magnetic equator with similar amplitude than for

of GF2, but this effect is reduced or absent for the other

two data sets of

of CryoSat-2. In contrast, high ampli-

tudes due to auroral electric currents are largely reduced

in the third row of Fig.3, but did not vanish as could be

expected from a natural signal. This fact hints to small-

scale structures in the magnetic field at high latitudes that

have shorter wavelengths than 20s (Gjerloev etal. 2011),

being the mean separation time between GF1 and GF2.

These observations need detailed investigations, e.g.,

sorted for MLT or geomagnetic activity, to allow discrim-

ination between natural and satellite intrinsic variability,

which is currently beyond the scope of this paper. A first

analysis, however, revealed that the positive differences

Table 4 Magnetic impact of calibration and characterisation, respectively, for each parameter given in Eq. 13

andthenon‑linear parameters inEq.9

Results are given in the FGM (SRF) reference frame for GF1 and GF2

Parameter Std (nT) Min (nT) Max (nT)

x y z x y z x y z

GF1

�Bξ

5.2 6.9 3.8 − 28.1 − 67.9 − 38.6 21.5 25.8 20.3

�Bν

7.6 9.6 5.4 − 46.0 − 45.8 − 37.5 47.2 75.1 66.3

BMTQ

8.6 6.2 6.8 − 230.5 − 209.5 − 578.7 242.5 206.4 263.0

BBAT

17.0 29.5 18.4 − 309.4 − 343.1 − 354.2 196.5 536.8 225.6

BSA

66.3 112.0 74.4 − 503.4 − 174.3 − 554.2 106.6 863.8 262.1

BBT

1.9 3.2 1.6 − 16.2 − 17.8 − 18.2 16.9 28.6 10.4

BST

5.5 2.2 8.1 − 175.8 − 16.0 − 204.1 167.3 20.0 217.5

Bcal,NEC

7.8 7.9 9.5 − 220.6 − 112.2 − 287.7 217.9 161.8 329.0

GF2

�Bξ

5.1 7.8 4.2 − 17.7 − 28.6 − 19.6 28.7 28.7 34.1

�Bν

10.1 9.1 5.6 − 100.7 − 49.1 − 48.5 74.0 43.9 35.9

BMTQ

10.2 6.6 6.9 − 222.8 − 235.3 − 178.4 226.9 190.7 258.2

BBAT

21.1 21.4 18.6 − 131.1 − 87.8 − 100.6 66.8 87.5 136.9

BSA

19.2 35.1 29.0 − 60.0 − 184.2 − 230.4 85.0 166.1 117.1

BBT

4.1 6.9 4.5 − 44.5 − 26.4 − 11.9 30.1 114.5 81.6

BST

9.3 3.2 14.6 − 273.3 − 26.0 − 390.6 244.0 29.2 317.8

Bcal,NEC

7.1 8.4 7.7 − 6364.5 − 121.8 − 277.8 180.9 1013.9 7208.9

Page 9 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

at around

30◦E

at the daylight Southern polar region

accumulates around magnetic noon, which is the typical

region of the polar cusp and known for small-scale struc-

tures. As the reader shall note, Fig.3 represents one of

the geomagnetic quietest months of the processed period

of GRACE-FO data. The pattern changes from month to

month and mean residuals up to 15nT also at mid and

low latitudes occur at other months.

Figure 4 provides orbit-wise residual vectors in the

NEC frame for a period in September 2019 for ascend-

ing (

∼

 12 MLT) and descending (

∼

 00 MLT) orbits

around noon and midnight, respectively. Top panel red

lines show GF1 results and bottom panel blue lines GF2

results. Black lines provide mean values at each QDLAT.

The geomagnetic activity was low with Kp

≤

4 (median

Kp=1.3) and Dst>− 30nT (mean Dst=− 5.5nT). The

significant variability of the single orbits indicates the

day-to-day variability of ionospheric currents, and the

statistical mean hints to typical ionospheric features. As

expected, largest deviations occur at auroral latitudes.

The negative excursion of

and the flip of sign towards

negative towards North in

reflect signatures of the

eastward equatorial electrojet. The amplitudes in both

components of about 10nT are consistent with signa-

tures detected earlier in CHAMP (Lühr and Maus 2006).

The flip of sign towards positive towards north in

with

a few nanotesla amplitude during noon is also consistent

with the earlier CHAMP results and reflects inter-hemi-

spheric field-aligned currents. These signatures relate to

a statistical analysis for inter-hemispheric field-aligned

currents and F-region dynamo currents conducted by

Park etal. (2020) based on GRACE-FO data. GF2 obser-

vations are less clear for these low-latitude ionospheric

signatures, a fact which is also supported by Park etal.

(2020). On the night side, the GF1 residuals are very low

which is expected due to the absence of strong iono-

spheric currents. However, an inconsistency is visible

in GF2

at the magnetic equator, as already noted in

Fig.3. This disturbance seems being artificial and is in

opposite direction to the equatorial electrojet signatures

on the dayside. Assuming that this artificial disturbance

is not only confined to the night side, it might be the

reason why the dayside equatorial GF2

shows lower

amplitudes than the expected 10nT from the natural sig-

nal. Similar consideration seems true for all three com-

ponents, which are in general more disturbed during

nighttime at GF2 than at GF1 and appear artificial.

Fig. 3 Magnetic residuals to CHAOS‑7 (core, crustal, and large‑scale magnetospheric field) in the three NEC (left) components and the field

magnitude, F, (right) for GF1 and GF2, respectively. The panels in the third row show the difference between GF1 and GF2 residuals. The fourth panel

shows the distribution of geomagnetic and solar activity indices and magnetic local time

Page 10 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Fig. 4 Orbit‑wise magnetic residual to CHAOS‑7 (core, crustal and large‑scale magnetospheric field) in NEC frame for September 2019 for

ascending (12 MLT, left) and descending (00 MLT, right) orbits. The red lines correspond to GF1 and blue lines to GF2. Black lines provide mean

values at each QDLAT

Fig. 5 Magnetic local times (top) and orbit altitude (bottom) at equator crossings of the GRACE‑FO, Swarm, and CryoSat‑2 missions, as well as the

daily (grey) and monthly averaged (black) F10.7 index

Page 11 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Comparison tomagnetic data ofSwarm

Figure5 shows the MLT and altitude evolution of the

GRACE-FO, Swarm, and CryoSat-2 missions, as well as

the daily (grey) and monthly averaged (black) solar flux

index F10.7. GRACE-FO and SwarmB fly at similar alti-

tudes and a conjunction in MLT between GRACE-FO

and Swarm B occurred early November 2019. At this

time, the solar flux index has been low with approxi-

mately

F10.7 =70 sfu (1 sfu =1022 Wm

−2Hz−1)

Figure 6 compares the magnetic data between the

two missions during their conjunction interval between

November 2 and November 14. Geomagnetic activity

Fig. 6 GF1 (top) or GF2 (bottom) conjunctions with Swarm B. Panel 1: Kp and Dst indices, panel 2: magnetic local time of conjunction, panel 3:

intra‑satellite distance, panel 4: quasi‑dipole latitude of conjunction, and panels 5–7: difference between magnetic residuals of GF1 or GF2 and

Swarm B

Page 12 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

was low with Kp

≤2+

and Dst

≥

− 20nT. The two mis-

sions were counter-rotating, e.g., the MLT at their

respective equator crossings was

∼

10 MLT for the

ascending node of GRACE-FO and for the descending

node of SwarmB, and it was

∼

22MLT for the descend-

ing/ascending nodes, respectively. We define a ’conjunc-

tion’ when the distance between the GF1 or GF2 satellites

and SwarmB were less than 400km. Since the conjunc-

tions occurred during counter-rotating orbital segments,

they only lasted few seconds each. Panels 3 give the

intra-satellite distance for each conjunction and panels

4 provide the mean QDLAT at which the conjunction

happened. Panels 5–7 plot the differences between the

residuals of the calibrated magnetic data to the respective

CHAOS-7 predictions for GF1 or GF2 and SwarmB for

each conjunction and for each magnetic component. The

majority (> 80%) of the differences of the single conjunc-

tions are within ± 10nT for all 3 components. The small-

est scatter occurs for

, followed by that of

and then

. This can have several reasons, such that different

ionospheric currents affect different components at dif-

ferent latitudes. Another aspect is that

|BC|

includes the

widest range of values with up to 65,000nT, followed by

|BN|

up to 30,000nT, and

|BE|

up to 15,000nT. Variables

with wider ranges can be estimated with lower uncer-

tainty. The mean difference to SwarmB over all conjunc-

tions is slightly larger for day time than for night time

orbits, e.g., GF1 day time

�(BN,BE,BC)

= (−1.02, −2.56,

0.73) nT, GF1 night time

�(BN,BE,BC)

= (0.12, −0.41,

0.95) nT, GF2 day time

�(BN,BE,BC)

= (−0.20, −3.72,

1.44) nT, and GF2 night time

�(BN,BE,BC)

= (−1.18,

−0.07, 1.47)nT. The less good agreement during day may

result from dayside ionospheric currents which introduce

stronger spatial and temporal variability of the magnetic

field. The overall small differences between the GRACE-

FO and the Swarm observations further support the high

quality of the calibrated magnetic data set of the GRACE-

FO mission.

The magnetic effect ofthemagnetospheric ring current

duringtheAugust 26, 2018 storm

A geomagnetic storm with values of Dst < −150 nT

occurred on August 26, 2018. During this time, all Swarm

spacecraft, CryoSat-2, and GF1 were in orbit, and cali-

brated magnetic data are available for each of these mis-

sions. Unfortunately, GF2 does not provide magnetic

data for August 2018. Figure7 shows the evolution of the

magnetic effects of the magnetospheric ring current, as

well as the Dst index. The squares, triangles, and circles

represent medians of residuals of the horizontal compo-

nent of the magnetic field (



E ) within

±20◦

QDLAT and projected to

0◦

QDLAT for each low-lati-

tude orbital segment of the respective satellite. The resid-

uals are with respect to the CHAOS-7 core and crustal

field predictions. The large-scale magnetospheric field

was not subtracted, and signatures from magnetospheric

Fig. 7 Time‑series of residuals of calibrated Swarm, CryoSat‑2, and GF1 magnetic data to the core and crustal field of CHAOS‑7 around the

magnetic storm in August 2018. Ascending (asc) and descending (dsc) nodes are shown separately. The Dst index is also plotted. See text for details

Page 13 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

currents (including its induced counterpart in Earth)

remain included in the data. The point populations of all

missions follow in generally well each other and the Dst

index, despite the different retrieval technique for mag-

netospheric signatures in ground and satellite data. It is

known from earlier studies that ground-based derived

ring current signatures (such as for deriving the Dst

index) show systematic differences to those derived in

space (Maus and Lühr 2005; Olsen etal. 2005; Lühr etal.

2017), e.g., the ring current signal at LEO is generally

more negative than at ground, which is also here reflected

in an offset between the Dst index and the satellite-

derived residuals. In addition, different groups of mis-

sions categorised in ascending and descending nodes

appear to cluster and show an apparent offset to each

other. This apparent offset between the categories repre-

sent local time differences of the magnetospheric ring

current signature. Figure8 shows the SuperMAG Mag-

netospheric Ring current indices (SMR, Newell and Gjer-

loev 2012) for the four local time sectors at midnight,

dawn, noon, and dusk (00MLT, 06MLT, 12MLT, and

18MLT) together with the Dst index. Also here, a few

differences between the two index groups may occur due

to different retrieval techniques, such as in baseline

determination or selection of observatories (e.g., Love

and Gannon 2009; Gjerloev 2012; Newell and Gjerloev

2012). While the values for the four MLT sectors of the

SMR are close to each other before the storm onset

around 18 UTC on August 25, as well as during the

recovery phase after about 18UTC on August 27, they

significantly deviate during the main phase of the storm,

with highest values at 06MLT and lowest at 18MLT. The

values at 12MLT and 00MLT are similar to each other

and in-between the values at dawn and dusk.

Figure9a–d shows four snapshots of magnetic residu-

als equatorward of

±20◦

QDLAT and collected within

2 h time windows from each of the satellite missions,

before the storm onset (16UTC, August 25), shortly after

the storm onset (23UTC, August 25), during the main

phase of the storm (06UTC, August 26), and during the

recovery phase (04 UTC, August 27). After the storm

onset, a clear expansion of the magnetospheric field

develops at the dusk side and the signal is least at dawn.

This is in agreement with the SuperMAG indices, and

the values are comparable with about − 25nT/− 75nT

and − 100nT/− 200nT in panelsb andc at dawn/dusk,

respectively. The selected constellation of satellite mis-

sions did not cover midnight and noon, and less informa-

tion is available from these MLT sectors. The described

scenario is a typical storm behaviour and has been iden-

tified and discussed by statistical studies from LEO sat-

ellite observations or extended ground-based magnetic

networks (e.g., Le etal. 2011; Pick etal. 2019). It has been

attributed to either an asymmetric ring current compo-

nent, to addition ionospheric currents, or to effects of

Fig. 8 SMR indices at 1 min resolution for local time sectors at 00 LT, 06 LT, 12 LT, and 18 LT. The Dst index is also plotted

Page 14 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

enhanced high-latitude R2 field-aligned currents during

geomagnetic storms.

Auroral field‑aligned currents

The calibrated magnetometer data from GF1 and GF2

were used to derive magnetic field-aligned currents.

Therefore, we applied the processing algorithm, which

is based on Ampères law and is similar to that used

to derive Swarm single satellite field-aligned current

(FAC) products available as the Swarm Level-2 product

FACxTMS_2F (with x = A, B, C) from ESA and described

in Ritter etal. (2013) and Kervalishvili (2017). We refer

the reader to these documents for a detailed descrip-

tion of the algorithm. The method has also successfully

been applied to magnetic observations from earlier mis-

sions, like CHAMP (e.g., Wang etal. 2005) and to DMSP

(Xiong etal. 2020).

Figure 10 shows FACs derived from GF1 and GF2

data for an event on 31 October 2019 when they crossed

the northern auroral latitudes. At this time, Kp=

4−

AE

∼

100nT (Auroral Electrojet index), and Dst

∼

− 7nT.

The event was chosen due to co-located data by SwarmB,

which will be discussed in the next paragraph. The data

of the two GRACE-FO satellites show similar FAC vari-

ations along their orbits, but with a time delay of about

24s, the time difference when GF1 and GF2 reached the

highest magnetic latitude of their orbits (upper panel).

The middle panel shows the time-series plotted along

Apex latitude (MLAT, Richmond 1995; Emmert et al.

2010). FAC signatures derived from the two satellites

compare well to each other in location of occurrence

and in amplitude. Enhanced FAC events are observed

between

65◦

and

72◦

and

70◦

and

83◦

MLAT on the dusk

and dawn sides, respectively. At other latitudes, GRACE-

FO FACs show a noise level less than 0.5

µA/m2

. After

applying a low-pass filter with cut-off frequency of 20 s,

the FAC profiles from the two satellites are nearly iden-

tical. This cut-off frequency ensures a cut-off for kinetic

Alfvén waves that is observed to be at periods between

Fig. 9 MLT distribution of satellite magnetic field residuals, SMR, and Dst index for different UT. The integration time is 2 h and is provided in the

title of each panel and indicated by vertical grey lines in Figs. 7 and 8. The black circles give reference to the magnitude of the satellite data and the

indices

Page 15 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

4and 10s depending on ionospheric conductivity (Ishii

etal. 1992). The cross-correlation between the two time-

series over MLAT maximises with

Rmax

=0.86/0.73 for

the 1s-series and with

Rmax

=0.98/0.93 when the 20s

filter was applied. This maximum correlation was found

for zero time-shift for both the 1s and 20s-filtered FAC

series. This result indicates that large-scale structures in

the FAC event dominated and are persistent and almost

stationary within 24s, the time both satellites crossed the

same area. This result is in agreement with Gjerloev etal.

(2011) who applied magnetic data of the ST5 constel-

lation mission of 3spacecraft following each other with

varying separation between few seconds and 10min. The

mission was operational for 3months within May and

June2006 and was launched in dawn–dusk orbit. They

correlated the magnetic signatures of field-aligned cur-

rents of different scale sizes and concluded that FAC sys-

tems with scale sizes larger than 200km (corresponding

to 26s for an average satellite velocity of 7.5km/s) appear

to be stable on time scales of about 1 min. When several

years of GRACE-FO data will be available in future, sim-

ilar studies can be conducted across all local times and

seasons, with the only caveat of a fixed inter-spacecraft

separation.

Figure 11 shows the same event, but comparing

GF1 (black line) with SwarmB data (red line) during

a conjunction event. GF1 and SwarmB were counter-

rotating at similar magnetic local times (top panel),

Fig. 10 FACs derived from GF1 and GF2 for an event at the Northern hemisphere on October 31, 2019. The data are shown in 1 s samplings (top,

middle) and filtered by 20 s (bottom)

Page 16 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

Fig. 11 Location of GF1 and Swarm B orbits as well as FACs derived from GF1 and Swarm B plotted over MLAT for the same event as in Fig. 10. The

data are shown in 1 s samplings (middle) and filtered by 20 s (bottom)

Page 17 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

and the UTC difference was about 14 min at the

highest magnetic latitude of

88.8◦

and

85.8◦

of their

respective orbits. Enhanced FAC signatures display at

similar magnetic latitudes. The 1Hz FAC time-series

of SwarmB shows larger amplitudes than for GF1 at

some locations (middle panel) which may hint to a

possibly higher sensitivity of the Swarm science mag-

netometers, but may also represent differences in FAC

structures at the slightly different locations and times.

Away from the FAC event, Swarm shows a significantly

lower noise level than GRACE-FO. After applying a

low-pass filter with a cut-off frequency of 20s to the

1Hz data (lower panel) for both satellites, the large-

scale structures show consistent features with similar

amplitudes between the two missions. This example

shows that large-scale FACs derived from GF1 and

GF2 compare well with observations from high-pre-

cision magnetic data, e.g., from the Swarm mission,

and thus can be considered reliable. However, due the

enhanced noise level of nearly 0.5

µA/m2

, only case

studies with event magnitudes well above this noise

level can be investigated.

While the GRACE-FO magnetometers sample at a

rate of 1s without on-board filtering of higher sam-

pled data, the Swarm 1Hz observations are the result

of a filtering based on 50Hz samples. The comparison

above shows that spot sampling at 1Hz (such as for

GRACE-FO) does not seem to significantly affect the

results for FACs and especially is suitable to reliably

derive signatures of FAC structures with scale lengths

of 180km or longer (corresponds to 24s inter-space-

craft separation).

Figure12 shows a statistical view of the MLAT ver-

sus MLT distributions of FACs derived from GF1.

The data from the full data set available have been

sorted into MLAT (

1◦

) and MLT (1 h) for northward

(IMF

Bz>

0) and southward (IMF

Bz<

0) interplan-

etary magnetic field (IMF) conditions, as well as

separately for the two hemispheres. The FAC show

clear Region 1 (R1) and Region 2 (R2) patterns, with

higher intensity and expanding to lower latitudes for

southward IMF

. For northward IMF

(NBZ), the

known current pair NBZ appears poleward of the R1

sheet around local noon. The IMF

dependence of

FAC derived from GF1 compares well to those of pre-

vious publications (e.g., Wang etal. 2008; Korth etal.

2010; Milan et al. 2017). Furthermore, the intensity

of the FACs in the northern hemisphere is slightly

higher than that in the southern hemisphere, which

is consistent with the finding of Coxon etal. (2016)

derived from AMPERE data, Laundal etal. (2018) and

Workayehu etal. (2019) derived from Swarm obser-

vations, and with Xiong et al. (2020) derived from

DMSP observations. These plots show that also small

amplitudes near the noise level of GRACE-FO data

are well accessible when they are applied in a statisti-

cal approach. This capability was also demonstrated by

Park etal. (2020) who used CryoSat-2 and GRACE-FO

data and successfully characterised interhemispheric

field-aligned currents which have statistical ampli-

tudes of as low as few

nA/m2

Conclusions

The GRACE-FO mission carries vector magnetometers

as part of its AOCS. After careful calibration and char-

acterisation of artificial disturbances from the satellite,

the magnetic data are applicable for scientific monitor-

ing of the Earth’s space environment. The mean residuals

of the magnetic components to high-precision magnetic

field models, such as CHAOS-7, are small with around

a nanotesla for geomagnetic quiet periods and standard

deviations are low with <10nT. These results are similar,

e.g., to those of CryoSat-2 calibrated magnetometer data

(Olsen etal. 2020). Strong support is provided by agree-

ments between the magnetic residuals of the high-preci-

sion magnetic field Swarm mission within ± 10nT during

most of their conjunctions.

The calibrated GRACE-FO data can successfully be

applied to case studies to high-amplitude events, such as

signatures of the magnetospheric ring current of few tens

to hundreds of nanotesla during geomagnetic storms.

Especially in constellation with other LEO satellite mis-

sions flying at different orbits, this combination enables

to describe the local time behaviour of the ring current

signal. Auroral field-aligned currents are also reliably

and well detectable, and those have signatures in the

horizontal magnetic field components of several tens to

hundreds of nanotesla. It was shown that for large-scale

currents of scale lengths of 180km or more compare

well in amplitude with those derived from Swarm obser-

vations. Another opportunity is provided by the two-

satellite constellation of GRACE-FO to investigate scale

sizes of ionospheric structures. Only applied for a single

auroral FAC event here, the soon multi-year mission will

allow statistical approaches to characterise different local

times and seasons. In addition, the constellation may

be suitable to derive an enhanced algorithm to estimate

large-scale FAC structures, where local stationarity of

the FAC structures between the satellites is assumed, but

Page 18 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

the ambiguity resulting from temporal variations which

is included in a single satellite approach can be dropped.

An exciting venue from the GRACE-FO constellation

mission is its potential application of an improved char-

acterisation of artificial spacecraft fields. The knowledge

that the magnetometers on both spacecraft are identical,

but flying with opposite direction through the ionosphere

and magnetic field may further add in identifying suit-

able or improved characterisation parameters. Also, the

GRACE-FO satellites can potentially be operated with

both magnetometers (an active and a redundant one)

switched on at each satellites. The mean of calibrated

data of both instruments on one satellite is likely to fur-

ther reduce the noise level.

Calibrated data from non-dedicated magnetometers

in LEO have demonstrated high potential in extending

the duration, the local time, and spatial distribution of

available observations of Earth’s space environment and

Fig. 12 MLAT vs MLT distribution of FACs derived from GF1 magnetic data for the Northern (top) and Southern (bottom) hemisphere and for IMF

Bz>

0 (left) and IMF

Bz<

0 (right)

Page 19 of 21

Stolleetal. Earth, Planets and Space (2021) 73:51

magnetic sources of the Earth’s interior; especially, the

combination with dedicated magnetic field missions and

other missions carrying non-dedicated magnetometers,

greatly enhance the scientific perspectives. Neverthe-

less, successful calibration relies on the availability of a

high-precision magnetic field model that relies on high-

precision data such as from the Swarm mission. Data

from non-dedicated magnetometers at LEO can cur-

rently not replace the need for magnetic missions, but

strongly enhance the monitoring of the geomagnetic field

variability.

Abbreviations

AMPERE: Active Magnetometer and Planetary Electrodynamic Response

Experiments; AOCS: Attitude and Orbit Control System; CASSIOPE: CAScade,

Smallsat, and IOnospheric Polar Explorer; CHAMP: CHAllenging Minisatel‑

lite Payload; C/NOFS: Communications/Navigation Outage Forecasting

System; CHAOS: CHAmp Ørsted SAC‑C magnetic field model; CDF: Common

Data Format; CSES: China Seismo‑Electromagnetic Satellite; DMSP: Defense

Meteorological Satellite Program; Dst: Geomagnetic Equatorial Disturbance

Storm Time Index; ESA: European Space Agency; FAC: Field‑Aligned Currents;

FGM: Fluxgate Magnetometer; GFZ: Helmholtz Centre Potsdam, GFZ German

Research Centre for Geosciences; GRACE‑FO/GF: Gravity Recovery and Climate

Experiment Follow‑On; HK: Housekeeping; ICRF: International Celestial Refer‑

ence Frame; IGRF: International Geomagnetic Reference Field IGRF‑13; ISDC:

Information System and Data Center at GFZ; ITRF: International Terrestrial

Reference Frame; JPL: Jet Propulsion Laboratory; Kp: Geomagnetic index

(Planetare Kennziffer); L1b: GRACE‑FO Level 1b data; LEO: Low Earth Orbit;

MLAT: Modified Apex Latitude; MLT: Magnetic Local Time; MTQ: Magnetorquer;

NASA: National Aeronautics and Space Administration; NBZ: Northward

; NEC: North, East, Center coordinate system; QDLAT: Quasi‑dipole latitude;

SAC‑C: Satellite de Aplicaciones Cientifico‑B; SRF: Science Reference Frame;

STR: Star cameras (Star TRackers).

Acknowledgements

We thank Jaeheung Park and Alexander Grayver for fruitful discussions. We

acknowledge Krzysztof Snopek for GRACE‑FO mission operations and Chris‑

toph Dahle for assistance at ISDC. GRACE‑FO is operated under a partnership

between NASA and the Helmholtz Centre Potsdam, GFZ, German Research

Centre for Geosciences. The European Space Agency (ESA) is gratefully

acknowledged for providing the Swarm data. Kp is provided by GFZ, the Dst

and AE indices by the Geomagnetic World Data Centre Kyoto, and F10.7 by

the Dominion Radio Astrophysical Observatory and Natural Resources Canada.

Authors’ contributions

CS defined the study. IM pre‑processed and calibrated the data. TU provided

data and advised on satellite operations. JR derived FACs. CS, CX, IM, MR, and

KSR analysed the data. CS, CX, and YY interpreted the results. CS, IM, and CX

wrote the manuscript. All authors read and approved the final manuscript.

Funding

Open Access funding enabled and organized by Projekt DEAL. This study has

been partly supported by Swarm DISC activities funded by ESA under contract

no. 4000109587/13/I‑NB. KSR is supported through HEIBRIDS—Helmholtz

Einstein International Berlin Research School in Data Science under contract

no. HIDSS‑0001.

Availability of data and materials

The data generated and analysed in this paper are available at ftp://isdcf tp.gfz‑

potsd am.de/grace ‑fo/MAGNE TIC_FIELD (Michaelis et al. 2021).

Competing interests

The authors declare that they have no competing interests.

Author details

1 Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences,

Telegrafenberg, 14473 Potsdam, Germany. 2 Faculty of Science, University

of Potsdam, Karl‑Liebknecht‑Str. 24‑25, 14476 Potsdam, Germany. 3 Airbus

Defence and Space GmbH, Claude‑Dornier‑Straße, 88090 Immenstaad am

Bodensee, Germany. 4 Electrical Engineering and Computer Science, Technical

University of Berlin, Ernst‑Reuter‑Platz 7, 10587 Berlin, Germany.

Received: 15 September 2020 Accepted: 18 January 2021

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