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Earth’s Dynamic Magnetic Field: The State of the Art Comprehensive Model

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.

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Earth’s Dynamic Magnetic Field: The State of the Art Comprehensive Model

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

  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 (Ynm ) n=6, m=0 n=6, m=3 n=6, m=6

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

  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 Rn at about n = 15 • Modelled as n = 15-65 • Considered static • Vector biases solved for at observatories

  20. Rn Spectrum of Internal Field

  21. Fluid Velocity at Core-Mantle Boundary

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

  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 • Field-aligned currents (FACs) connect ionosphere and magnetosphere in polar region • 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 Br at CMB at 2000

  38. CM Core Fat Surface at 1980

  39. CM Core DFat Surface from 1980 to 2000

  40. CM Lithospheric Br at 400 km

  41. CM Ionospheric Z at Surface

  42. CM Magnetospheric Z at Surface on 22 Aug 1998

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

  44. CM F-region Jfrom 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

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