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Geomagnetic Field Modelling Efforts with SwarmPresent Possibilities and Future Opportunities
Nils Olsen, Lars Tøffner-Clausen, Christopher C FinlayDTU Space, Technical University of Denmark
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 1 / 23
Thanks to the Swarm DISC team
Outline
Swarm magnetic data have been successfully used to derivehigh-quality models of the core field ...
... but the present altitude of Swarm (450 km) seems to betoo high to improve on models of the lithospheric field derivedfrom low-altitude (< 350 km) CHAMP data
Can the unique East-West gradient information provided bySwarm (Alpha – Charlie) improve lithospheric field models,despite the high altitude?
What are the statistics of residuals (measurements andunmodelled external field sources), in particular regarding theirtemporal correlation?
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 2 / 23
Outline
Swarm magnetic data have been successfully used to derivehigh-quality models of the core field ...
... but the present altitude of Swarm (450 km) seems to betoo high to improve on models of the lithospheric field derivedfrom low-altitude (< 350 km) CHAMP data
Can the unique East-West gradient information provided bySwarm (Alpha – Charlie) improve lithospheric field models,despite the high altitude?
What are the statistics of residuals (measurements andunmodelled external field sources), in particular regarding theirtemporal correlation?
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 2 / 23
Outline
Swarm magnetic data have been successfully used to derivehigh-quality models of the core field ...
... but the present altitude of Swarm (450 km) seems to betoo high to improve on models of the lithospheric field derivedfrom low-altitude (< 350 km) CHAMP data
Can the unique East-West gradient information provided bySwarm (Alpha – Charlie) improve lithospheric field models,despite the high altitude?
What are the statistics of residuals (measurements andunmodelled external field sources), in particular regarding theirtemporal correlation?
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 2 / 23
Magnetic intensity residuals F obs − Fmod
Swarm Alpha, Apr 2014 to Dec 2016
CHAOS-6 model describing magnetic fieldfrom core, lithosphere and large-scalequiet magnetosphere subtracted
non-polar latitudes:2.14 nT rms
≈ 5× larger residuals at polar latitudesdue to unmodeled external contributions
mean ±1σ in 2◦ bins
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 3 / 23
East-West scalar gradient residuals ∆F obsEW −∆Fmod
EWDifference of instantaneous measurements between the two satellites Swarm Alpha and Swarm Charlie
CHAOS-6 model describing magnetic fieldfrom core, lithosphere and large-scalequiet magnetosphere subtracted
non-polar latitudes:0.38 nT rms
≈ 3× larger residuals at polar latitudesdue to unmodeled external contributions
mean ±1σ in 2◦ bins
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 4 / 23
Residual scatter vs. latitude: Field Data
-90 o -60 o -30 o 0o 30 o 60 o 90 o
QD latitude
0
1
2
3
4
5
6
7
8
9
stan
dard
dev
iatio
n [n
T]
Br
Bθ
Bφ
F
Enhanced scatter in auroral region
Br is least disturbed(in non-polar regions)
Smallest scatter in F at ±35◦
where magnetosphericring-current field is ⊥ to internaldipole field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 5 / 23
Residual scatter vs. latitude: Gradient Data
North-South (alongtrack) gradient
-90 o -60 o -30 o 0o 30 o 60 o 90 o
QD latitude
0
0.5
1
1.5
2
2.5
3
stan
dard
dev
iatio
n [n
T]
∆Br
∆Bθ
∆Bφ
∆F
0
5
10
15
20
25
[pT
/km
]
East-West gradient
-90 o -60 o -30 o 0o 30 o 60 o 90 o
QD latitude
0
0.5
1
1.5
2
2.5
3
stan
dard
dev
iatio
n [n
T]
∆Br
∆Bθ
∆Bφ
∆F
0
5
10
15
20
25
[pT
/km
]
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 6 / 23
Residual scatter vs. latitude: Gradient Data
North-South (alongtrack) gradient
-90 o -60 o -30 o 0o 30 o 60 o 90 o
QD latitude
0
0.5
1
1.5
2
2.5
3
stan
dard
dev
iatio
n [n
T]
∆Br
∆Bθ
∆Bφ
∆F
0
5
10
15
20
25
[pT
/km
]
East-West gradient
-90 o -60 o -30 o 0o 30 o 60 o 90 o
QD latitude
0
0.5
1
1.5
2
2.5
3
stan
dard
dev
iatio
n [n
T]
∆Br
∆Bθ
∆Bφ
∆F
0
5
10
15
20
25
[pT
/km
]
Estimate of data error, to be used for geomagnetic modeling
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 6 / 23
Temporal correlation of non-polar residualsField component Br
500 non-polar night-side satellite tracksduring geomagnetic quiet times
Values of Br separated by ≤ 2 minutesare highly correlatedProbably due to external field variationsthat are not properly described byCHAOS-6 (un-modelled sources)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 7 / 23
Temporal correlation of non-polar residualsNorth-South (alongtrack) gradient ∆Br,NS
500 non-polar night-side satellite tracksduring geomagnetic quiet times
North-South gradient ∆Br ,NS isuncorrelated after 15 sec
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 7 / 23
Temporal correlation of non-polar residualsEast-West gradient ∆Br,EW
500 non-polar night-side satellite tracksduring geomagnetic quiet times
East-West gradient ∆Br ,EW is slightlymore correlated (why? geophysical signalor data bias?) but uncorrelated after30 sec
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 7 / 23
Temporal correlation of non-polar residualsEast-West gradient ∆Br,EW
500 non-polar night-side satellite tracksduring geomagnetic quiet times
East-West gradient ∆Br ,EW is slightlymore correlated (why? geophysical signalor data bias?) but uncorrelated after30 sec
Large-scale external field variations areeffectively eliminated in gradient data
allows for higher sampling rate whenselecting gradient data ...
... and for selecting data duringgeomagnetic less quiet conditions
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 7 / 23
Is Swarm still too high for useful lithospheric studies?
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 8 / 23
Lithospheric signature at various altitudes
10 20 30 40 50 60 70 80 90 100 110 120
degree n
10-4
10-2
100
102
Pow
er [n
T2]
at ground
40000 4000 2000 1000 800 700 600 500 400 350 n [km]
10-2
10-1
100
101
Am
plitu
de [n
T]
Lithospheric signalfor n = 100 (λ = 400 km):
54 pT @ 300 km altitude25 pT @ 350 km altitude5.6 pT @ 450 km altitude
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 9 / 23
Lithospheric signature at various altitudes
10 20 30 40 50 60 70 80 90 100 110 120
degree n
10-4
10-2
100
102
Pow
er [n
T2]
h = 450 km
Swarm (presently)
at ground
40000 4000 2000 1000 800 700 600 500 400 350 n [km]
10-2
10-1
100
101
Am
plitu
de [n
T]
Lithospheric signalfor n = 100 (λ = 400 km):
54 pT @ 300 km altitude25 pT @ 350 km altitude5.6 pT @ 450 km altitude
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 9 / 23
Lithospheric signature at various altitudes
10 20 30 40 50 60 70 80 90 100 110 120
degree n
10-4
10-2
100
102
Pow
er [n
T2]
h = 450 km
Swarm (presently)
h = 300 km
h = 350 km
CHAMP in 2010
at ground
40000 4000 2000 1000 800 700 600 500 400 350 n [km]
10-2
10-1
100
101
Am
plitu
de [n
T]
Lithospheric signalfor n = 100 (λ = 400 km):
54 pT @ 300 km altitude25 pT @ 350 km altitude5.6 pT @ 450 km altitude
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 9 / 23
Lithospheric signature at various altitudes
10 20 30 40 50 60 70 80 90 100 110 120
degree n
10-4
10-2
100
102
Pow
er [n
T2]
h = 450 km
Swarm (presently)
h = 300 km
h = 350 km
CHAMP in 2010
at ground
40000 4000 2000 1000 800 700 600 500 400 350 n [km]
10-2
10-1
100
101
Am
plitu
de [n
T]
Lithospheric signalfor n = 100 (λ = 400 km):
54 pT @ 300 km altitude25 pT @ 350 km altitude5.6 pT @ 450 km altitude
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 9 / 23
What is the information content of
magnetic field data B, F
North-South magnetic gradient data ∆BNS , ∆FNS
East-West magnetic gradient data ∆BEW , ∆FEW
for modelling the lithospheric field?
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 10 / 23
Expansion Coefficients gmn , h
mn of the Internal Field
B = −grad V
V = a∑n,m
[gmn cosmφ+ hm
n sinmφ](ar
)n+1
Pmn (cos θ)
+ V ext
r , θ, φ are spherical coordinatesa is Earth’s radiusgmn and hm
n are the sphericalharmonic expansion coefficientsof the internal magnetic field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 11 / 23
Expansion Coefficients gmn , h
mn of the Internal Field
B = −grad V
V = a∑n,m
[gmn cosmφ+ hm
n sinmφ](ar
)n+1
Pmn (cos θ)
+ V ext
r , θ, φ are spherical coordinatesa is Earth’s radiusgmn and hm
n are the sphericalharmonic expansion coefficientsof the internal magnetic field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 11 / 23
Expansion Coefficients gmn , h
mn of the Internal Field
B = −grad V
V = a∑n,m
[gmn cosmφ+ hm
n sinmφ](ar
)n+1
Pmn (cos θ)
+ V ext
r , θ, φ are spherical coordinatesa is Earth’s radiusgmn and hm
n are the sphericalharmonic expansion coefficientsof the internal magnetic field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 11 / 23
Expansion Coefficients gmn , h
mn of the Internal Field
B = −grad V
V = a∑n,m
[gmn cosmφ+ hm
n sinmφ](ar
)n+1
Pmn (cos θ)
+ V ext
r , θ, φ are spherical coordinatesa is Earth’s radiusgmn and hm
n are the sphericalharmonic expansion coefficientsof the internal magnetic field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 11 / 23
Variances of Gauss Coefficients
a CHAMP field data (B,F ),∆t = 2 min sampling
b CHAMP NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
c Swarm EW gradient(∆BEW ,∆FEW ), ∆t = 30 sec
d Swarm NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
blue: well resolvedyellow: poorly resolved
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 12 / 23
Variances of Gauss Coefficients
a CHAMP field data (B,F ),∆t = 2 min sampling
b CHAMP NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
c Swarm EW gradient(∆BEW ,∆FEW ), ∆t = 30 sec
d Swarm NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
blue: well resolvedyellow: poorly resolved
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 12 / 23
Variances of Gauss Coefficients
a CHAMP field data (B,F ),∆t = 2 min sampling
b CHAMP NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
c Swarm EW gradient(∆BEW ,∆FEW ), ∆t = 30 sec
d Swarm NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
blue: well resolvedyellow: poorly resolved
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 12 / 23
Variances of Gauss Coefficients
a CHAMP field data (B,F ),∆t = 2 min sampling
b CHAMP NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
c Swarm EW gradient(∆BEW ,∆FEW ), ∆t = 30 sec
d Swarm NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
blue: well resolvedyellow: poorly resolved
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 12 / 23
Variances of Gauss Coefficients
a CHAMP field data (B,F ),∆t = 2 min sampling
b CHAMP NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
c Swarm EW gradient(∆BEW ,∆FEW ), ∆t = 30 sec
d Swarm NS gradient(∆BNS ,∆FNS), ∆t = 30 sec
CHAMP NS gradients contain mostinformation on lithospheric field
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 12 / 23
Ratio of Variances shows possible model improvement
CHAMP NS gradient data is baselineWhat is model improvement whenadding other data?
a adding Swarm NS gradient data
b adding CHAMP field data
c adding Swarm EW gradient data
d adding Swarm NS and EWgradient data
green: model improvementblack: no model improvement
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 13 / 23
Ratio of Variances shows possible model improvement
CHAMP NS gradient data is baselineWhat is model improvement whenadding other data?
a adding Swarm NS gradient data
b adding CHAMP field data
c adding Swarm EW gradient data
d adding Swarm NS and EWgradient data
green: model improvementblack: no model improvement
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 13 / 23
Ratio of Variances shows possible model improvement
CHAMP NS gradient data is baselineWhat is model improvement whenadding other data?
a adding Swarm NS gradient data
b adding CHAMP field data
c adding Swarm EW gradient data
d adding Swarm NS and EWgradient data
green: model improvementblack: no model improvement
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 13 / 23
Ratio of Variances shows possible model improvement
CHAMP NS gradient data is baselineWhat is model improvement whenadding other data?
a adding Swarm NS gradient data
b adding CHAMP field data
c adding Swarm EW gradient data
d adding Swarm NS and EWgradient data
green: model improvementblack: no model improvement
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 13 / 23
Ratio of Variances shows possible model improvement
CHAMP NS gradient data is baselineWhat is model improvement whenadding other data?
a adding Swarm NS gradient data
b adding CHAMP field data
c adding Swarm EW gradient data
d adding Swarm NS and EWgradient data
Swarm EW+NS gradient data addmore to model than CHAMP field data
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 13 / 23
LCS-1: A new Lithospheric Field Model
CHAMP NS gradient data
Swarm NS and EW gradient data
30 sec sampling, core + large-scale magnetospheric field removed
Model parametrized by 35,000 “point sources” (monopoles) located 100 km below surface
Data misfit: minimize robust (Tukey-weighted) data misfit
Model regularization: minimize ||Br ||1 (i.e. L1-norm) at surface (ellipsoid)
Final step: Representation by spherical harmonics up to n = 185 ensuring ∇ · B = 0
More on this lithospheric model on Thursday afternoonOlsen et al: “A New Lithospheric Field Model based on CHAMP and Swarm Magnetic Satellite Data”
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 14 / 23
LCS-1: A new Lithospheric Field Model
CHAMP NS gradient data
Swarm NS and EW gradient data
30 sec sampling, core + large-scale magnetospheric field removed
Model parametrized by 35,000 “point sources” (monopoles) located 100 km below surface
Data misfit: minimize robust (Tukey-weighted) data misfit
Model regularization: minimize ||Br ||1 (i.e. L1-norm) at surface (ellipsoid)
Final step: Representation by spherical harmonics up to n = 185 ensuring ∇ · B = 0
More on this lithospheric model on Thursday afternoonOlsen et al: “A New Lithospheric Field Model based on CHAMP and Swarm Magnetic Satellite Data”
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 14 / 23
LCS-1: A new Lithospheric Field Model
CHAMP NS gradient data
Swarm NS and EW gradient data
30 sec sampling, core + large-scale magnetospheric field removed
Model parametrized by 35,000 “point sources” (monopoles) located 100 km below surface
Data misfit: minimize robust (Tukey-weighted) data misfit
Model regularization: minimize ||Br ||1 (i.e. L1-norm) at surface (ellipsoid)
Final step: Representation by spherical harmonics up to n = 185 ensuring ∇ · B = 0
More on this lithospheric model on Thursday afternoonOlsen et al: “A New Lithospheric Field Model based on CHAMP and Swarm Magnetic Satellite Data”
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 14 / 23
Z at Earth’s surfaceLCS-1 model, n = 16 − 185
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 15 / 23
Z at Earth’s surfaceMF7 Lithospheric Model (Maus et al., 2010), n = 16 − 133
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 15 / 23
Bangui AnomalyMF7 Lithospheric Model (Maus et al., 2010)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 16 / 23
Bangui AnomalyLCS-1 Lithospheric Model
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 16 / 23
Conclusions, Recommendations, and Opportunities
Swarm data from first three years of mission provide, in combination with other data,high-resolution models of core field changes ...
... and unprecedented map of lithospheric field, despite the presently high altitude of 450 km
Unique East-West gradient information measured by Swarm
Is the present East-West separation of +1.4◦ between Swarm Alpha and Charlie optimal?
Proposed evolution of constellation: a slow (within 1 to 2 years) decrease of East-West separationfrom +1.4◦ to 0◦, followed by an increase to ≤ −1.4◦
This will allow to investigate the optimum separation for enhanced lithospheric field modelling,will improve knowledge on time-space correlation of external signals,and support in-flight inter-satellite calibration
... and looking forward to a long Swarm mission (10+ more years)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 17 / 23
Conclusions, Recommendations, and Opportunities
Swarm data from first three years of mission provide, in combination with other data,high-resolution models of core field changes ...
... and unprecedented map of lithospheric field, despite the presently high altitude of 450 km
Unique East-West gradient information measured by Swarm
Is the present East-West separation of +1.4◦ between Swarm Alpha and Charlie optimal?
Proposed evolution of constellation: a slow (within 1 to 2 years) decrease of East-West separationfrom +1.4◦ to 0◦, followed by an increase to ≤ −1.4◦
This will allow to investigate the optimum separation for enhanced lithospheric field modelling,will improve knowledge on time-space correlation of external signals,and support in-flight inter-satellite calibration
... and looking forward to a long Swarm mission (10+ more years)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 17 / 23
Conclusions, Recommendations, and Opportunities
Swarm data from first three years of mission provide, in combination with other data,high-resolution models of core field changes ...
... and unprecedented map of lithospheric field, despite the presently high altitude of 450 km
Unique East-West gradient information measured by Swarm
Is the present East-West separation of +1.4◦ between Swarm Alpha and Charlie optimal?
Proposed evolution of constellation: a slow (within 1 to 2 years) decrease of East-West separationfrom +1.4◦ to 0◦, followed by an increase to ≤ −1.4◦
This will allow to investigate the optimum separation for enhanced lithospheric field modelling,will improve knowledge on time-space correlation of external signals,and support in-flight inter-satellite calibration
... and looking forward to a long Swarm mission (10+ more years)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 17 / 23
Conclusions, Recommendations, and Opportunities
Swarm data from first three years of mission provide, in combination with other data,high-resolution models of core field changes ...
... and unprecedented map of lithospheric field, despite the presently high altitude of 450 km
Unique East-West gradient information measured by Swarm
Is the present East-West separation of +1.4◦ between Swarm Alpha and Charlie optimal?
Proposed evolution of constellation: a slow (within 1 to 2 years) decrease of East-West separationfrom +1.4◦ to 0◦, followed by an increase to ≤ −1.4◦
This will allow to investigate the optimum separation for enhanced lithospheric field modelling,will improve knowledge on time-space correlation of external signals,and support in-flight inter-satellite calibration
... and looking forward to a long Swarm mission (10+ more years)
Nils Olsen (DTU Space) Geomagnetic Field Modelling Efforts 17 / 23