Earth’s Dynamic Magnetic Field: The State of the Art Comprehensive Model Terence J. Sabaka Geodynamics Branch NASA/GSFC with special thanks to Nils Olsen Danish Space Research Institute

Outline  Introduction  Data  Parameterization  Estimation  Results  Conclusions

Electromagnetic Basics: The Biot-Savart Law

Major near-Earth Current Systems

Nature of near-Earth Magnetic Fields  Core  Motion of conductive outer core fluid  30,000-50,000 nT  Changes on order of centuries  Ionosphere  Dynamo layer between km altitude in the E-region  nT at surface  EEJ is from enhanced eastward current at dip equator

Nature of near-Earth Magnetic Fields  Magnetosphere  Magnetopause, tail and ring currents  nT at surface  Broad scale, but rapidly changing  FACs  Connect ionosphere with magnetosphere at high latitudes in the F-region  nT during quiet times

Nature of near-Earth Magnetic Fields  Lithosphere  Rigid portion of crust above Curie temperature  Induced and remanent  Up to 20 nT at satellite altitude  Induced fields  Time varying external fields influencing conductive material in Earth skin layer  Magnitude depends upon inducing period

Time Scales of Magnetic Fields from Various Sources

Terrestrial Magnetic Field Applications  Orientation/Reckoning  Used by satellites including GPS  Navigation systems  Geophysical prospecting  Aeromagnetic surveys  Towed by ships  Military targets  Deep Earth probing  Space weather

Comprehensive Approach to Modelling Terrestrial Fields  Method  Parameterize fields from all major near- Earth sources  Coestimate these parameters by solving an inverse problem  Use satellite vector/scalar and ground- based observatory hourly-means data  Advantages  Optimal for frequency overlap  More feasible than treating fields as noise

Data Used for Modelling  Satellites  POGO – , scalar only, elliptic  Magsat – 1980, vector, six months duration, only dawn and dusk, 450 km  Oersted – 1999-present, vector, 750 km  CHAMP – 2001-present, vector, 400 km  Observatories  Several hundred, continuous, but poorly distributed  Vector hourly-mean values

Recent Satellite Magnetic Mapping Missions Oersted – vector and scalar at ~ 750 km CHAMP – vector and scalar at ~ 400 km

Permanent Magnetic Observatory Stations

Maxwell’s Equations Ampere’s Law Absence of magnetic monopoles Faraday’s Law Gauss’ Law

(Laplace Eqn) (Internal) (External) Potential Fields (zero J)

Absence of Monopoles Internal: n = 0 term violates Maxwell’s monopole equation at origin O External: n = 0 term is constant, doesn’t contribute

Spherical Harmonic Functions (Y n m ) n=6, m=0 n=6, m=3 n=6, m=6

Toroidal Fields (non-zero J in thin shells) Vector potential Toroidal scalar Toroidal only

Parameterizing Core and Lithospheric Fields  Core  Broad scale, dominates n = 1-14  Secular variation (SV) represented by cubic B-spline functions  Lithosphere  All spatial scales, but breaks from core R n at about n = 15  Modelled as n =  Considered static  Vector biases solved for at observatories

R n Spectrum of Internal Field

Fluid Velocity at Core- Mantle Boundary

magnetospheric ring-current ionospheric current systems External Field Current Systems

Ionospheric Daytime Electron Density

Parameterizing Ionospheric E-region Field  Primary  Assume currents flow in sheet at 110 km  Use potential functions conforming to quasi-dipole (QD) coordinates defined by DGRF1980  Diurnal and seasonal variation  Solar activity via scaling by F10.7 cm flux  Induced  A priori 1-D conductivity model (4-layer)  Infinite conductor at 1000 km depth

Continuity Across E-region Sheet Current

E-region Breathes with F10.7 cm Solar Flux

Quasi-Dipole Chart at Surface from DGRF1980

Parameterizing Magnetospheric Field  Primary  Distant currents not differentiated  Potential functions in dipole coordinates  Diurnal and seasonal variation  Ring current activity via linear dependence of external dipole on Dst index  Induced  Same as for E-region  Internal dipole also linear in Dst

Dst Behavior Around Storm Main Phase on 18 Aug 1998

Parameterizing Ionospheric F-region Field  Magsat (vector only)  Modelled separately for dawn and dusk  Assume QD meridional currents  Use toroidal functions conforming to QD coordinates  Seasonal variation  Oersted (vector only)  Same as above, but single model with diurnal variation

Ionospheric F-region Currents 1.Field-aligned currents (FACs) connect ionosphere and magnetosphere in polar region 2.Meridional currents associated with the equatorial electrojet (EEJ)

Ionospheric F-region Currents

The Principle of Least- Squares Estimation

Estimation of CM Parameters via Iterative Gauss Method  Solves non-linear LS problems  Fast convergence  Cheaper than Newton method  Allows for A priori information  Smooth core SV  Eliminate nightside E-region current  Damp excursions from LT external dipole  Smooth F-region current

CM Fits to Observatory Hourly-Means

CM Fits to Satellite Data

CM Core B r at CMB at 2000

CM Core F at Surface at 1980

CM Core  F at Surface from 1980 to 2000

CM Lithospheric B r at 400 km

CM Ionospheric Z at Surface

CM Magnetospheric Z at Surface on 22 Aug 1998

CM F-region J r from Magsat at Dawn and Dusk

CM F-region J from Oersted at Noon

Conclusions  Present  CMs are only models accounting for all these field sources  CMs are separating fields in a consistent and plausible manner  Future  More realistic conductivity models  Better treatment of magnetospheric fields  Increased use of CMs for applications