1. 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

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

3. Electromagnetic Basics: The Biot-Savart Law

4. Major near-Earth Current Systems

5. 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 100-140 km altitude in the E-region  10-50 nT at surface  EEJ is from enhanced eastward current at dip equator

6. Nature of near-Earth Magnetic Fields  Magnetosphere  Magnetopause, tail and ring currents  20-30 nT at surface  Broad scale, but rapidly changing  FACs  Connect ionosphere with magnetosphere at high latitudes in the F-region  30-100 nT during quiet times

7. 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

8. Time Scales of Magnetic Fields from Various Sources

9. 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

10. 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

11. Data Used for Modelling  Satellites  POGO – 1965-1971, 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

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

13. Permanent Magnetic Observatory Stations

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

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

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

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

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

19. 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 = 15-65  Considered static  Vector biases solved for at observatories

20. R n Spectrum of Internal Field

21. Fluid Velocity at Core- Mantle Boundary

22. magnetospheric ring-current ionospheric current systems External Field Current Systems

23. Ionospheric Daytime Electron Density

24. 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

25. Continuity Across E-region Sheet Current

26. E-region Breathes with F10.7 cm Solar Flux

27. Quasi-Dipole Chart at Surface from DGRF1980

28. 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

29. Dst Behavior Around Storm Main Phase on 18 Aug 1998

30. 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

31. 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)

32. Ionospheric F-region Currents

33. The Principle of Least- Squares Estimation

34. 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

35. CM Fits to Observatory Hourly-Means

36. CM Fits to Satellite Data

37. CM Core B r at CMB at 2000

38. CM Core F at Surface at 1980

39. CM Core  F at Surface from 1980 to 2000

40. CM Lithospheric B r at 400 km

41. CM Ionospheric Z at Surface

42. CM Magnetospheric Z at Surface on 22 Aug 1998

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

44. CM F-region J from Oersted at Noon

45. 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