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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?

Outline

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

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

Residual scatter vs. latitude: Field Data

-90 o -60 o -30 o 0o 30 o 60 o 90 o

QD latitude

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

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

∆Bθ

∆Bφ

East-West gradient

-90 o -60 o -30 o 0o 30 o 60 o 90 o

QD latitude

∆Bθ

∆Bφ

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

∆Bθ

∆Bφ

East-West gradient

-90 o -60 o -30 o 0o 30 o 60 o 90 o

QD latitude

∆Bθ

∆Bφ

Estimate of data error, to be used for geomagnetic modeling

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)

Temporal correlation of non-polar residualsNorth-South (alongtrack) gradient ∆Br,NS

North-South gradient ∆Br ,NS isuncorrelated after 15 sec

Temporal correlation of non-polar residualsEast-West gradient ∆Br,EW

East-West gradient ∆Br ,EW is slightlymore correlated (why? geophysical signalor data bias?) but uncorrelated after30 sec

Temporal correlation of non-polar residualsEast-West gradient ∆Br,EW

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

Is Swarm still too high for useful lithospheric studies?

Lithospheric signature at various altitudes

10 20 30 40 50 60 70 80 90 100 110 120

degree n

at ground

40000 4000 2000 1000 800 700 600 500 400 350 n [km]

Lithospheric signalfor n = 100 (λ = 400 km):

54 pT @ 300 km altitude25 pT @ 350 km altitude5.6 pT @ 450 km altitude

10 20 30 40 50 60 70 80 90 100 110 120

degree n

h = 450 km

Swarm (presently)

at ground

40000 4000 2000 1000 800 700 600 500 400 350 n [km]

10 20 30 40 50 60 70 80 90 100 110 120

degree n

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 20 30 40 50 60 70 80 90 100 110 120

degree n

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]

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?

Expansion Coefficients gmn , h

mn of the Internal Field

B = −grad V

V = a∑n,m

[gmn cosmφ+ hm

n sinmφ](ar

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

B = −grad V

V = a∑n,m

[gmn cosmφ+ hm

n sinmφ](ar

Pmn (cos θ)

+ V ext

B = −grad V

V = a∑n,m

[gmn cosmφ+ hm

n sinmφ](ar

Pmn (cos θ)

+ V ext

B = −grad V

V = a∑n,m

[gmn cosmφ+ hm

n sinmφ](ar

Pmn (cos θ)

+ V ext

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

CHAMP NS gradients contain mostinformation on lithospheric field

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

Swarm EW+NS gradient data addmore to model than CHAMP field data

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”

Z at Earth’s surfaceLCS-1 model, n = 16 − 185

Z at Earth’s surfaceMF7 Lithospheric Model (Maus et al., 2010), n = 16 − 133

Bangui AnomalyMF7 Lithospheric Model (Maus et al., 2010)

Bangui AnomalyLCS-1 Lithospheric Model

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)

geomagnetic field modelling efforts with swarm â•fi ... · dtu space, technical university ......

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