MAGNETIC SIGNALS GENERATED BY OCEAN FLOW IN THE SWARMSATELLITE DATA: PREDICTION AND OBSERVATION

Jakub Velı́mský1, Zdeněk Martinec1,2, David Einšpigel1,2, and Libor Šachl1,21Charles University in Prague, Faculty of Mathematics and Physics, Department of Geophysics

2Dublin Institute for Advanced Studies, School of Cosmic Physics, Geophysics Section

ABSTRACTMotion of sea water in the Earth’s main magnetic field generates the secondary induced field whichcan be decomposed into its poloidal and toroidal components. While the toroidal component is notdirectly observable outside the oceans, the poloidal magnetic field have been already validated byCHAMP satellite magnetic observations, land-based magnetic measurements and sea surfacemagnetic field measurements, despite the poloidal field being rather weak, reaching an intensity of upto a few nT. New possibilities of observations of the ocean-induced magnetic field came with thelaunching of ESA’s Swarm mission satellites which have provided a valuable amount of high-precisionand high-resolution measurements of the Earth’s magnetic field. For a detection of weakocean-induced signals and their interpretation, numerical modelling is crucial. We present results ofmodelling of the secondary magnetic field generated by ocean flow. Two ocean flow models areincorporated: 1) DEBOT, a barotropic (BT) model of ocean tide flow, and 2) LSOMG, a baroclinic (BC)model of global ocean currents. The secondary magnetic field is modelled using a three-dimensionaltime-domain approach. A preliminary comparison of predicted signals and observed signals extractedfrom Swarm satellite data will be shown. The future aim is to assimilate magnetic data provided bySwarm mission into the models.

1. DEBOT — A BAROTROPIC MODEL OF OCEAN TIDE FLOWModel descriptionI Barotropic model, based on

the shallow water equations(Einšpigel and Martinec, inpress)

I Full lunisolar tidal forcingI Discretization in space:

finite differences on theArakawa C-grid

I Discretization in time:a generalizedforward-backwardtime-stepping scheme,stable and second-orderaccurate

Key parametersI Internal wave drag: Conversion of BT tides into BC waves,τ int =

πL ĥ

2 Nb v, ĥ2 is bottom roughness, Nb is buoyancy frequency, L isscaling factor

I Bathymetric dataset: ETOPO1 or GEBCOI Self-attraction and loading of the seawater: Change of the gravitational

potentional due to change in mass distribution of the seawater;reduced gravity gε = g (1− ε)

I Eddy viscosity: Turbulences on very short scales cause energy lossesin the large-scale motions, ~σ = AH∇ · E, AH is eddy viscosity, E isstrain rate tensor

I Bottom friction, s = r v|v|

2. LSOMG — A BAROCLINIC MODEL OF GLOBAL OCEAN CURRENTS

I z-coordinate baroclinic ocean model in hydrostatic and Boussinesq approximationsI Discretization in space: finite differences on the Arakawa C-gridI Discretization in time: staggered time-stepping of BT and BC subsystems with different time steps;

BT system uses the predictor-corrector schemeI Bathymetry: GEBCO or ETOPO1I Temperature and salinity distributions: World Ocean Atlas 2013I Wind speed: NCEP/NCAR

3. ELMGIV — TIME-DOMAIN EM INDUCTION MODEL

I Spatial discretization by spherical harmonics and1-D finite elements (Velı́mský and Martinec, 2005)

I Crank-Nicolson time integration schemeI Excitation by a complete Lorentz force vectorI 1-D mantle conductivity profile

2 3 4

log (τ in S)

4000

5000

6000

r (k

m)

0.001 0.01 0.1 1 10

σ (S/m)

I barotropic flows: 2-D near-surface conductance map based on bathymetry and sediment thicknessesI baroclinic flows: 3-D near-surface conductivity model based on bathymetry and sediment thicknesses

4. PREDICTION OF MAGNETIC SIGNATURES OF TIDAL FLOWSSnapshot of horizontal velocitiesof tidal flow at t = 2014.20964422AH = 104 m

2/s, r = 3, ε = 0.08,L = 10000, 30′ × 30′ resolution

−0.04 −0.02 0.00 0.02 0.04

vϑ (m/s)

−0.04 −0.02 0.00 0.02 0.04

vϕ (m/s)

Induced magnetic field along selected Swarm tracks

−6 −4 −2 0 2 4 6

X (nT)

A orbit 001755 ↑, 2014−03−17 13:42:38 − 2014−03−17 14:14:01

−6 −4 −2 0 2 4 6

Y (nT)

B orbit 001751 ↓, 2014−03−17 13:32:06 − 2014−03−17 14:03:47

−6 −4 −2 0 2 4 6

Z (nT)

C orbit 001752 ↑, 2014−03−17 13:50:04 − 2014−03−17 14:21:32

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5−60 −40 −20 0 20 40 60

ϑ

Snapshot of induced magnetic field at 480 km altitude

REFERENCESEinšpigel, D. and Martinec, Z. A new derivation of the shallow water equations in geographical coordinates and theirapplication to the global barotropic ocean model (the debot model). Ocean Modelling, in press. doi:10.1016/j.ocemod.2015.05.006.

Velı́mský, J. and Martinec, Z. Time-domain, spherical harmonic-finite element approach to transient three-dimensionalgeomagnetic induction in a spherical heterogeneous earth. Geophys. J. Int., 160:81–101, 2005.

5. SENSITIVITY OF MAGNETIC SIGNATURES TO MODEL SETTINGSEffect of resolution, eddy viscosity, self-attraction and loading, and internal wave drag

Run spatial resolution AH ε LA 20′ × 20′ 1 104 m2/s 0.08 0B 30′ × 30′ 1 104 m2/s 0.08 0C 30′ × 30′ 1 104 m2/s 0.10 0D 30′ × 30′ 1 104 m2/s 0.12 0E 30′ × 30′ 1 105 m2/s 0.08 0F 30′ × 30′ 5 104 m2/s 0.08 0G 30′ × 30′ 1 104 m2/s 0.08 8000H 30′ × 30′ 1 104 m2/s 0.08 10000I 30′ × 30′ 1 104 m2/s 0.08 12000

Induced magnetic field along the track A001755.5

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−50 0 50

ϑ

X (nT)

A

B

C

D

E

F

G

H

I

−50 0 50

ϑ

Y (nT)

A

B

C

D

E

F

G

H

I

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−50 0 50

ϑ

Z (nT)

A

B

C

D

E

F

G

H

I

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

−50 0 50

ϑ

Z (nT)

6. PREDICTION OF MAGNETIC SIGNATURES OF GLOBAL CURRENTSSnapshot of velocities of wind-forced flow at t = 2014.20964422 in the uppermost ocean layerModel settings: horizontal resolution: 1◦, vertical resolution: 11 layers, BC time step 1800 s, BT timestep 30 s

−0.0002 −0.0001 0.0000 0.0001 0.0002

vr (m/s)

r=6370.994 km

−0.4 −0.2 0.0 0.2 0.4

vϑ (m/s)

−0.4 −0.2 0.0 0.2 0.4

vϕ (m/s)

Induced magnetic field along selected Swarm tracks

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

X (nT)

A orbit 001755 ↑, 2014−03−17 13:42:38 − 2014−03−17 14:14:01

−1.0 −0.5 0.0 0.5 1.0

Y (nT)

B orbit 001751 ↓, 2014−03−17 13:32:06 − 2014−03−17 14:03:47

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

Z (nT)

C orbit 001752 ↑, 2014−03−17 13:50:04 − 2014−03−17 14:21:32

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−60 −40 −20 0 20 40 60

ϑ

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6−60 −40 −20 0 20 40 60

ϑ

Snapshot of induced magnetic field at 480 km altitude

7. PRELIMINARY ANALYSIS OF SWARM DATATrack-by-track analysisI Swarm Level 1b data in NEC frame,

1 s sampling, version 0404I Removal of CHAOS-5 main field modelI Night-time (22:00–06:00 LT), magnetically quiet,

mid-latitude data (−60◦,+60◦)I Degree 25 Legendre polynomial fit (smoothing)I Degree 5 Legendre polynomial fit and

extrapolation to polar areasI Analysis of the expansion coefficients

determines whether a source of the field is theonly one and whether the source is purelyinternal or external or a combination of both

I Desired ocean-induced signals have only oneinternal source, otherwise the data are biased bysignals from the magnetosphere or ionosphere

I The signals of the 1st and 2nd order have oftenan external source in the magnetosphere,hence, only the 3rd–5th order signals are used

Figure descriptionI Top: Position and time of the trackI Middle top: Residua after removal of the main

field (thin lines) and a fitted expansion intoLegendre polynomials to the 5th degree (thicklines)

I Middle bottom: Amplitudes of the signal. Asource of the magnetic field is the only one if thelight blue and red dots overlap, and the source isinternal if the purple dots lie on the x axis

I Bottom: The 3rd–5th order signals and residuaof the fitted data

Track No. A07312day=199.601local time (h)=5.23 data missing = 0longitude = −137.799983dB=Swarm−main

−20

−10

0

10

20

X, Z

(nT

)

0 20 40 60 80 100 120 140 160 180Colatitude

0riginal data (red, blue), dPn and Pn fit (thick)

0.01

0.1

1

10

100

Am

pli

tude

0 2 4 6 8Degree j

red = X comp.

blue = Z comp.

−2

−1

0

1

2

X, Z

(nT

)

40 60 80 100 120 140Colatitude

geo.mff.cuni.cz/SwarmOceans/ velimsky@karel.troja.mff.cuni.cz