Numerical Modelling of the Earth's magnetic field induced by ocean tides
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1 Numerical Modelling of the Earth's magnetic field induced by ocean tides Jan Dostal1, Zdeněk Martinec2, Maik Thomas1 (1) Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences (2) Dublin Institute for Advanced Studies, Dublin 2, Ireland
2 Geopotential satellite missions CHAMP accuracy ~1 nt SWARM November 2013 accuracy ~0.1 nt Magnetic field Motional induction GRACE Gravity field Earth system dynamics Ocean tides Observed M2-tide signal in nt (Tyler et al. 2003) GOCE Mass redistribution
3 Electromagnetic induction in the ocean atmosphere BE ocean u sediment Main magnetic Field BE x ocean velocity u
4 Electromagnetic induction in the ocean atmosphere BE ocean u - sediment Main magnetic Field BE x ocean velocity u Lorentz force: el. charge deflection el. field
5 Electromagnetic induction in the ocean atmosphere BE ocean horizontal j u + - Main magnetic Field BE x ocean velocity u Lorentz force: el. charge deflection el. field electric current density j vertical j sediment
6 Electromagnetic induction in the ocean poloidal mag. Field B atmosphere BE ocean horizontal j u + - toroidal mag. Field B Main magnetic Field BE x ocean velocity u Lorentz force: el. charge deflection el. field electric current density j vertical j sediment ocean-induced magnetic field B
7 Ocean-induced magnetic field constituents poloidal magnetic field due to conductivity contrast atmosphere poloidal magnetic field due to ocean flow variability continent ocean sediment, crust toroidal magnetic field el. currents upper mantle lower mantle
8 Symmetrically layered model For the ocean (source layer) - inhomogeneous differential equation Electric conductive layers (sediment, mantle) - homogeneous differential equation u BE
9 Solution and parmetrization The induction equation has the form of the Helmholtz equation analytical solution in frequency domain possible Parametrization in lateral direction - vector spherical harmonics Description of the source term in vector spherical harmonics Prarmatrization in radial direction: Numerical solution Analytical solution Matrix-propagator technique Spherical Bessel functions (Dostal et al. 2012) validation Weak formulation Finite elements (time domain solution)
10 Background magnetic field POMME 6 (Maus et al. 2010) toroidal field cut-off degre jmax= 6 poloidal field dipol term only in 10 4 nt
11 Water transport of M2-tide Ocean velocities: OMCT model tidal dynamic M2-tide (T=12h 42min ) ocean flow with well known period allows solution in frequency domain average velocities weighted by bathymetry (transport) cut-off degree jmax = 48 only horizontal flow barotropic flow
12 Water transport of M2-tide components imag. part (sin-part) real part (cos-part) in cm/s
13 Radial profile of electrical conductivity beneath the ocean in the ocean layer: σ = S/m for uniform ocean: σ = 3.5 S/m ocean layer depth h = 4 km in S/m
14 Ocean-induced magnetic field constituents poloidal magnetic field due to conductivity contrast atmosphere poloidal magnetic field due to ocean flow variability continent ocean sediment, crust toroidal magnetic field el. currents upper mantle lower mantle
15 Verification of the amplitude of primary poloidal magnetic field induction thin sheet approach (verticaly integrated values) finite layer approach (continent not considerd) OMCT in nt Dostal (2009)
16 Profile of the poloidal magnetic field mantle atmosphere in nt
17 Ocean-induced magnetic field constituents poloidal magnetic field due to conductivity contrast atmosphere poloidal magnetic field due to ocean flow variability continent ocean sediment, crust toroidal magnetic field el. currents upper mantle lower mantle
18 Amplitude of the toroidal magnetic field at ocean bottom in 10-3 nt
19 Radial profile of the toroidal magnetic field beneath the ocean in 10-3 nt detail ocean
20 Amplitude of the secondary poloidal magnetic field ocean layer: σ = 3.5 S/m continent σ = 10-3 S/m in nt
21 Summary finite layer model for ocean-induced magnetic field considering real radial conductivity profile identical source term (M2-tide): primary poloidal magnetic component ~ 4-6 nt secondary poloidal magnetic component ~ 4-5 nt (coastal effect) toroidal magnetic field ~ 10-3 nt (barotropic flow)
22 Summary finite layer model for ocean-induced magnetic field considering real radial conductivity profile identical source term (M2-tide): primary poloidal magnetic component ~ 4-6 nt secondary poloidal magnetic component ~ 4-5 nt (coastal effect) toroidal magnetic field ~ 10-3 nt (barotropic flow) => The secondary poloidal magnetic field achieves the same magnitudes like the primary poloidal part
23 Summary finite layer model for ocean-induced magnetic field considering real radial conductivity profile identical source term (M2-tide): primary poloidal magnetic component ~ 4-6 nt secondary poloidal magnetic component ~ 4-5 nt (coastal effect) toroidal magnetic field (barotropic flow) ~ 10-3 nt => The secondary poloidal magnetic field achieves the same magnitudes like the primary poloidal part => The thin layer approximation is not sufficient for sophisticated prediction of the ocean- induced magnetic field
24 Thank you for your attention.
25 Governing Equations
26 Ansatz for poloidal magnetic field Arbitrary vector field decomposition in spheroidal and toroidal part Poloidal field is divergence free spheroidal field in general not Condition for magnetic field Solution Induction equation for the poloidal mode
27 Toroidal magnetic field real part (cos part) imag part (sin part) in 10-3 nt
28 Radial profile of the toroidal magnetic field beneath the ocean in 10-3 nt detail ocean
29 Poloidal magnetic field in nt
30 Magnetic field decomposition Primary induced poloidal magnetic field horizontal electric currents (vertical integrated value -plane) Toroidal mag. field vertical electric currents ocean layer with finite thickness (calculation with radial integrated values not possible) Secondary induced poloidal magnetic field horizontal electric currents
31 Motivation global model for ocean-induced magnetic field constituent (SWARM) motionally induced magnetic field as additional indicator for observation the ocean dynamic single layer modelling prediction of the magnetic signal (Tyler et. al.,2003, Kuvshinov & Olsen, 2005) CHAMP observation (Tyler et. al.,2003) 3D model surrounding electric conductive space secondary effect of poloidal magnetic field Predicted and observed M2-tide signal in nt (Tyler et al. 2003)
32 Average velocities in shalow regions ocean volume transport by 4km ocean depth layer (max 3 cm/s) average velocities by 1km ocean depth layer; high velocities in coastal region (max. 6 cm/s) in 10-3 nt
33 Ocean flow with radial decay Study case 1km ocean depth layer average velocities Considering the derivative term 100% linear decay of the ocean Only nonderivative term velocities between ocean surface Tidal dynamic and bottom Barotropic velocities dpt in nt in 10-3 nt Non barotropic ocean flow Derivative term dominant factor for toroidal magnetic field
34 Numerical Modelling of the Earth's magnetic field induced by ocean tides Jan Dostal1, Zdeněk Martinec2,3, Maik Thomas1,4 (1) Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Section 1.3: Earth System Modelling, Telegrafenberg, D-14473, Potsdam, Germany (2) Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2, Ireland (3) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, V Holesovickach 2, Prague 8, Czech Republic (4) Institut fuer Meteorologie, Freie Universitaet Berlin, D-12165, Germany
35 Electromagnetic induction in the ocean poloidal mag. Field B atmosphere BE ocean horizontal j u + - toroidal mag. Field B Main magnetic Field BE x ocean velocity u Lorentz force: el. charge deflection el. field electric current density j vertical j sediment ocean-induced magnetic field B
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