# Presentation: 481020

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

## 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

## 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 – 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

## 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

## Potential Fields (zero J)

- (Laplace Eqn)

- (Internal)

- (External)

## 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 (Ynm )

- Spherical Harmonic Functions (Ynm )

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

- Rn 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

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

- CM Core F at Surface at 1980

- CM Core F at Surface from 1980 to 2000

- CM Lithospheric Br at 400 km

## CM Ionospheric Z at Surface

## CM Magnetospheric Z at Surface on 22 Aug 1998

## CM F-region Jr from Magsat at Dawn and Dusk

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

## CM F-region J from Oersted at Noon

- 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