MODELING OF THE EARTH’S MAGNETIC FIELD AND ITS VARIATIONSWITH ØRSTED, CHAMP, AND ØRSTED-2/SAC-C: CURRENT STATUS AND

FUTURE PROSPECTS

Organized by N. Olsen 1Report by M. Purucker 2

With contributions from J. Bloxham, C. Constable, H. Kim, S. Maus, M. Mandea, N. Olsen, M.Purucker, M. Rother, T. Sabaka, L. Toffner-Clausen, S. Vennerstrøm, and R. von Frese

1 Danish Space Research Institute, Copenhagen, Denmark, Email: nio@dsri.

2 Raytheon ITSS at Geodynamics Branch, Goddard Space Flight Center, Greenbelt, MD 20771 USA, Email:purucker@geomag.gsfc.nasa.gov.

ABSTRACT

A two-day workshop, held September 26-27, 2002in Copenhagen following the OIST-4 meeting,focused on modeling of the Earth’s magnetic fieldand its variations. Several major themes werecovered: 1) Extraction of the Lithospheric Signal,2) Ionospheric Contributions, 3) Ørsted andCHAMP data center activities 4) Calibration andalignment of magnetic satellite data, 5) Core fieldand secular variation, 6) the utility and availabilityof the Comprehensive Magnetic Field Model, and7) new analysis of old satellite data. Shortpresentations and discussion followed tutorials.More than 30 scientists and students attended andparticipated in this very successful workshop,

INTRODUCTION

Focusing on the modeling of high-precision, multi-spacecraft data, this workshop reported on advancesin modeling, and separating, the multitude ofmagnetic fields encountered in near-earth space.

EXTRACTION OF THE LITHOSPHERIC SIGNAL

Modeling of lithospheric fields (M.Purucker/NASA)

The recent book by Langel and Hinze (1998)provides a summary of modeling methods and isrecommended reading. The most used techniquestoday are spherical harmonic analysis andequivalent source dipoles.

Both techniques need regularization; the process ofgenerating models that puts the least amount ofspurious detail into the field. Tables 1 and 2 heregive some further details of these techniques.

Several outstanding problems present opportunitiesfor students. First, the amount of new high-qualitydata generated by the three satellites quickly

overwhelms most modeling techniques. Data byparameter methods are less susceptible to thisproblem than data by data methods.

You probably want to consider some simple stepsto minimize the data you use, while maximizing theinformation in that data. For example, don’t ask aglobal basis to do a local job. Use something likecollocation with suitably chosen covariances first toreduce the data to a manageable amount, then usespherical harmonics or the equivalent sourcetechnique with a global basis.

Isolating crustal anomalies and othersmaller scale features from satellitemagnetic data: advantages anddrawbacks of along-track filtering,cross-correlation, and line-levelingtechniques (S. Maus/GFZ)

This talk focused on the development of physicallymotivated filters. It began by illustrating, with anexample from the CHAMP data, the external fields,which remain even after a field model with internaland external components has been removed fromthe observations.

How should the remaining external field signal(Figure 1) in these passes over Bangui, the largestcrustal anomaly on the Earth, be removed? Thefollowing approaches have been tried:

This was followed by the definition of a suitable,physically motivated polynomial. It was shownthat the removal of such a polynomial removedlittle crustal anomaly or small-scale signal.

The discussion by R. Haagmans (ESA) raised thepossibility of using spherical harmonic filters(Haagmans, 2000; Jakob-Chien and Alpert, 1997).

Satellite magnetic anomalies forlithospheric exploration (R. von Freseand H. Kim/OSU)The magnetic workshop considered two contrastingperspectives for processing satellite magneticobservations for lithospheric anomalies. The typicalglobal geophysics approach represents and analyzessatellite magnetic data by spherical harmonics thatemphasize the more regional anomaly attributes forlithospheric analysis. However, a fuller exploitationof the local anomaly details in the track coverage ispossible from the exploration geophysics approachthat uses spherical coordinate distributions ofequivalent point sources (EPS) to model andanalyze the satellite magnetic observations. Indeed,any local-through-global distribution of satellitemagnetic data may be related to the effects of pointdipole arrays by EPS inversion (Figure 2) forestimating spherical coordinate anomalycontinuations, interpolations, differentialreductions-to-pole, gradients, correlations, etc.

Furthermore, adapting equivalent point sources forGauss-Legendre quadrature integration (Figure 2) isvery effective for relating satellite magneticanomalies to arbitrary spherical coordinatedistributions of lithospheric magnetizations.These two perspectives, in principle, shouldproduce complimentary results atBoth local and global scales. In practice, however,lithospheric studies tend to focus on more local (i.e.spherical patch) distributions of satellite magneticobservations where the exploration geophysicsapproach clearly offers significant advantages. Thispresentation is fully developed in these proceedingsin a paper by von Frese and Kim entitled “Satel

Ite magnetic anomalies for lithosphericexploration”.

IONOSPHERIC CONTRIBUTIONS

Ionospheric contributions to satellitebased internal field modeling: Newselection criteria? (S. Vennerstrøm,DSRI)

Contamination of internal field models by high-latitude ionospheric currents was discussed. Atpresent, this contamination is being minimized inthe global modeling by data selection, using onlyquiet intervals in the modeling. The data-selectionis based mainly on the low-latitude indices Kp andDst, which have the advantage of being availablewith a very short time-delay. It was howeverdemonstrated that intervals that meet the currentlyused selection criteria can be very disturbed in thepolar regions as measured by the mean averagedeviation from the internal field model of theabsolute magnitude of the field Babs(MAD)measured by CHAMP or Ørsted. The question ofwhether the satellite data could be used as analternative in the data selection process was thenexamined. The basic idea was that the presence ofionospheric currents could be detected in themagnetic field component perpendicular to theinternal field. This component does not enter mostof the present models, which over the polar regionsonly uses the absolute measurements. Due to therelative size of the internal and external magneticfields the perpendicular component has nomeasurable effect on the absolute value of themeasured field. Using the average size of theperpendicular component over the polar regions toselect the quiet intervals would therefore be aselection procedure based on the part of the satellitedata, which do not otherwise enter the modeling.The relationship between the average perpendicularcomponent and Babs(MAD) was investigatedstatistically, and these were shown to be highlyrelated. It was shown that a selection procedurebased on the average perpendicular component wassuperior to the current methods in terms of

minimizing Babs(MAD).

Figure caption: Histograms of Babs(MAD)measured by CHAMP for a selection of quietintervals based on current methods (Kp, Dst, IMFBy) compared to a selection based on the averageperpendicular component over the polar regions.Both selections where made for the same time-interval: autumn 2001. The threshold value of theaverage perpendicular component was adjusted sothat the same percentage of data was selected in thetwo cases.

CALIBRATION AND ALIGNMENT OFMAGNETIC SATELLITE DATA

Intercalibration of the scalar and vectormagnetometers on SAC-C with thoseon CHAMP and Ørsted (M.Purucker/NASA)

The scalar (SHM) and vector (CSC) magnetometerson SAC-C are undergoing calibration. As part ofthis process, the SAC-C magnetometer outputswere compared to their counterparts on CHAMPand Ørsted during close encounters of the satellites.The premise is that during close encounters, theionospheric and magnetospheric fields seen by thespacecraft will be similar. Three close encounterswere selected: 21 May 2001, 29 December 2001,and 15 June 2002. The December and June closeencounters were co-rotating encounters; during theMay encounter the satellites were counter-rotating.The May and June close encounters occurred onmagnetically quiet days while the Decemberencounter occurred in the midst of an activegeomagnetic period, with an SSC occurring in themiddle of the encounter. The analysis was precededby the removal of a main field model (internalcomponents only). For the May and Juneencounters the IDEMM model (Olsen et al, 2002)was removed through degree 46 while for theDecember encounter the 10b/01 field model wasremoved through degree 13.

The figure above shows both the time and spacedifferences associated with the nightside closeencounters of the Ørsted and SAC-C in lateDecember 2001. The time difference, in seconds, ismeasured as the time between identical latitudecrossings.

One component of the space difference, thealtitude, is also shown. This is also measured at thesame latitude. The longitude differences are shownon the global map, and vary from no separation at60 degrees South to about five degrees separation at60 North latitude.

After removal of the main field model throughdegree 13, the SAC-C data was resampled at theØrsted latitude locations. The difference betweenthe Ørsted and SAC-C residuals is a measure of thechanges necessary to bring the SAC-C vector andscalar magnetometers into agreement with theabsolute Ørsted Overhauser (OVH) magnetometer.

This approach fails in situations where the internalmagnetic field from the lithosphere or ionospherevaries significantly on spatial scales comparable tothe longitudinal separation of the two spacecraft.This failure has a diagnostic signature. Bothresiduals will co-vary and form a high-low or low-high pair that extends typically across 20 degrees oflatitude. Typical examples can be seen on Pass ‘G’near the equator and Pass ‘H’ at about 20 degreesSouth latitude. Two approaches to dealing with thisproblem are to remove a high degree static modelfrom the original data or to discard the data in theaffected regions (adopted in this presentation).

Note the sudden storm commencement (SSC)evident on Pass ‘K’ in simultaneous observations

from SAC-C and Ørsted. The SSC is also evident inthe simultaneous CHAMP observations. The SSCoccurs on 29 Dec 2001 at 05:20 UT.

The corrections necessary to bring themagnetometers into agreement are shown above,based on segments of the residuals from theprevious plot. Best fits to the residuals are shownwith the dark line. These corrections, at least for thescalar helium magnetometer (SHM), have beenconfirmed by comparison with a CHAMP closeencounter and an encounter where the SAC-Cspacecraft is traveling in the opposite direction.

Further details on this close encounter, and otherclose encounters, can be found atwww.dsri.dk/multimagsatellites/types/calibration.html.

ØRSTED AND CHAMP DATA CENTERS

Current status of Ørsted and Ørsted-2Data Processing (L. Toffner-Clausen/DMI)

Ørsted data – Outstanding issues

The Ørsted data are now being processed to a level(2.4) of accuracy, which is believed to be very closeto the final level. Small adjustments to the appliedcalibrations and corrections may still be made, e.g.to the corrections of the ACS magnetorquer-coilsdisturbances. These disturbances are however verysmall-less than 1.3 nT for more than 99% of themission, and the remaining error after the currentcorrection is expected to be less than 0.5 nT for alltimes

The method to smooth and interpolate attitude data(SIM data) produce one-second attitude informationis still being investigated. We hope to have asolution soon. We also need to finalize theprocessing of the two indicators of the magneticvector measurements: BAC (5-30 Hz fluctuations)and Bσ (error estimates). And we plan to produce aboom oscillation indicator indicating the amplitudeof boom oscillations in the range around 0.3 to 0.5Hz. When this is ready, MAG-L data files will beproduced in this form.

Ørsted-2 Data – Current StatusSHM-Scalar Helium Magnetometer. NASA/GSFCis investigating.CSC-Vector magnetometer. In-flight calibrationshave not yet proven satisfactory. DSRI isinvestigating.IST-Italian Star Tracker- We have received attitudedata from this body-mounted star tracker-imager.

DSRI is investigating the possibilities of usingthese data.

Current status of CHAMP DataProcessing (M. Rother/GFZ)Currently the only available CHAMP magneticfield data are corrected and in-flight calibrated fielddata at Level-2. Both vectors from the fluxgatemagnetometer and scalar data from the Overhausermagnetometer are available. The correctionsapplied to the data are based on ground calibrationefforts, sensor sensitivities, misalignments, offsets,static time adjustments, and satellite fields. Thescalar calibration using the absolute Overhauserobservations is run on a daily basis and the inputparameter set for the fluxgate processing is updatedevery two weeks. Therefore, the amplitude of thescalar residuals between the fluxgate andOverhauser magnetometers will depend on thenumber of days since the last parameter set update.

Unexplained differences of between 0.11 and 1 nTstill remain between the fluxgate and Overhausermagnetometers after all of these standardcorrections have been applied. Furthermore, wefound that there are two additional parameters tofit: two time shifts seem to be a function of time1) a phase shift between the OVM and FGM

sensors, currently between 10 and 20 ms.2) A phase shift of the CSC temperature sensor.

We have found on ground calibration a valueof about 8 minutes, but this seems to have awide variability till changing the sign. Butmost probably we are fitting another, unknowninfluence with this free parameter.

Helper script for handling CHAMP-ISDC dataTo help people who are downloading magneticfield data from the CHAMP-ISDC there is a simpleperl script available which can be run on Linuxboxes. This script can initiate the batch-modewithout using a browser, and will try to downloadthe requested files from the ISDC download areaand clean the download area for the next try. Avalid password for public access to the ISDC is stillrequired, but the script can simplify the process.For more information use the help text of the scriptitself. It is called getisdc.pl and can be found at:www.gfz-potsdam.de/pb2/pb23/SatMag/suppl.html

CORE FIELD AND SECULAR VARIATION

Geodynamo Modelling andGeomagnetic Field Modelling: A two-way street (J. Bloxham/Harvard)

At present, most of the ‘traffic’ is fromgeomagnetic field modeling to geodynamomodeling. In other words, data and field models arefar more important for geodynamo modeling thangeodynamo modeling is for geomagnetic fieldmodeling. What is needed is an entirely newapproach. Current methods are based on theextrapolation of observations. What is needed is touse techniques of data assimilation, as in weatherforecasting.

As part of this shift, two presently separate fields,field modeling and dynamo modeling, need tomerge. Data assimilation is highly developed in themeteorological and oceanographic community. Theobservations for such assimilation don’t need to beof the variables computed in the model. They onlyneed to be linear functions of the variables.

A compilation of existing geomagneticfield models, external field models, anda bibliography (M. Mandea/IPGP)Attached to the back of this workshop report is anup-to-date compilation of existing field models,courtesy of M. Mandea and her students.

THE UTILITY AND AVAILABILITY OFTHE COMPREHENSIVE MAGNETICFIELD MODEL (CM): THE CM USERGROUP

An introduction by D. Ravat was followed by apresentation from T. Sabaka. Participants suggestedenhancements to the CM, which would make itmore valuable to them. The followingenhancements have now been added by Sabaka andOlsen: 1) output is now available either in the spaceor frequency domain (as spherical harmoniccoefficients), 2) External fields can now be outputas a current (J), 3) magnetic indices (Dst, F10.7)can be automatically selected, 4) availability ofobservatory biases, which are now appended to thespherical harmonic model coefficient file, and 5)development of an official Web page fordissemination of information and communicationwith the user community.

Comprehensive magnetic fieldmodeling: Two applications (C.Constable, Scripps)C. Constable discussed the application of theComprehensive field model (Sabaka et al, 2002) to1) isolating the crustal contribution to the field andusing this to find the Lowes-Mauersbergerspectrum (Korte et al., 2002), and 2) isolating thelarge-scale magnetospheric contributions for Earthinduction studies.

NEW ANALYSIS OF OLD SATELLITE DATA(A.Jackson/Leeds)

A tutorial by A. Jackson followed by a discussion.This presentation appears as a short paper in theseproceedings by Jackson and Olsen entitled‘Possibilities for Re-analysis of Old Satellite Data’.

SUMMARYThe informal talks discussed here resulted in afruitful exchange of ideas. We hope it wasespecially helpful for students.

ACKNOWLEDGMENTS

We want to thank the Ørsted, Ørsted-2/SAC-C, andCHAMP projects for their support.

SUGGESTIONS FOR FURTHER READING ANDREFERENCES

Korte. M., C. Constable, and R. Parker (2002),Revised magnetic power spectrum of the oceaniccrust, J Geophys. Res., 107(B9), 2205,doi:10.1029/2001JB001389.

Haagmans, R., (2000), A synthetic earth for use ingeodesy, J. of Geodesy, v. 74, pp. 503-511.

Jakob-Chien, R., and B. Alpert, (1997), A fastspherical filter with uniform resolution, J. ofComputational Physics, v. 136, pp. 580-584.

Langel, R.A. and W. J. Hinze, (1998), Themagnetic field of the Earth’s lithosphere: Thesatellite perspective, Cambridge, 429 pp.

Olsen, N. (2002), A model of the geomagnetic fieldand its secular variation for epoch 2000 estimatedfrom Ørsted data, Geophys. J. Int, v. 149, pp. 454-462.

Olsen, N., R. Holme, and H. Lühr, (2002), Amagnetic field model derived from Ørsted,CHAMP, and Ørsted-2/SAC-C observations, Eos.Trans. AGU, 83(19), Spring meet. Suppl., AbstractGP21A-01. Available online atwww.dsri.dk/multimagsatellites

Sabaka, T., N. Olsen., and R. Langel, (2002):A comprehensive model of the quiet-time,near-Earth, magnetic field: Phase 3,Geophys. J. Int., Vol. 151, pp. 32-68.

Geom

agnetic field models

Model

Period – dataM

F, SVdegree /order

Tim

e (LT

)K

pD

stA

nother index / criteriaG

eomagnetic

latitudeU

niformity

Observations

CO

2: Holm

e,O

lsen, Rother,

Lühr

● Cham

p, Ørsted,

Ørsted-2/SA

C-C

● obs.

MF: 29

SV: 13

EXT: 2

18:00-06:00 LTK

p ≤ 1 (data)K

p ≤ 2o (3 hr*)| D

st | ≤ 10 nT| d(D

st)/dt | < 3 nT/hr|B

y| > 3 nT (too strong dawn-

dusk IMF com

ponentelim

inated)

● vector : lat. ≤50°● scalar : lat. > 50°or if attitude datanot available

Non-G

aussian distribution:IR

LS (iteratively reweighted

least squares), Huber w

eights

CH

AM

P: lower altitude =

better sensitivity to highdegree n coefficients

CM

3: Sabaka,O

lsen, Langel(G

eophys. J. Int.)

● Magsat

● obs.: O

HM

-1am (4 hr*)

OH

M-M

UL

(1 quiet day/month)

MF: 65

SV: 13

Non-LT term

sK

p ≤ 1- (data)K

p ≤ 2o (3 hr*)(M

agsat)

-20 ≤ Dst ≤ 50 nT

(Magsat)

F10.7: solar radiation flux index;1 value / yr, corrected for :● uncertainty of the antennagains● Earth reflected w

aves

● vector : lat. ≤ 50°● scalar : all lat.

● time: M

agsat data nov-dec1979, jan-feb 1980, m

ar-apr1980● space: satellite passes addedfor sparse regions

Weighting hypothesis:

● lat ≤ 50°: OH

M-1H

&O

HM

-MU

L & M

agsatdaw

n and dusk are isotropicprocesses● lat > 50°: O

HM

-MU

L &M

agsat dawn and dusk

processes are isotropic inthe X

Y plane

IGR

F 2000O

lsen, Sabaka,Tøffner-C

lausen(EPS, 2000)

● Ørsted:

a - may 1999

b - sep 1999c - m

ar-sep 99 (scalar) - m

ay-sep 99 (vect.)

MF: 12

night sideK

p ≤ 1+ (3 hr)K

p ≤ 2o (3 hr*)D

st ignored (± 20nT)

external field contributions:selection according to K

pvector: lat. < 50°

● decimation for scalar and

vector data: times of

measurem

ent > 30 sec apart● w

eighting: equal areasim

ulation

● noise reduction in therotation angle of the starim

ager

IGR

F 2000M

acmillan, Q

uinn(EPS, 2000)

● Ørsted

● obs.: 190● repeat stations

MF: 12

SV: 8

EXT: 5

0 - 2 am LT

Kp ≤ 2+

| Dst | ≤ 30 nT

● residuals < 1000 nT with

respect to 1995.0● lat.: 5°● long.: 5° (eq.) - 120° (poles)● 10°x10°: only sat. data● decim

ation: every 20th

sample chosen = every 20

th sec

● weighted outliers

IGR

F 2000Langlais, M

andea(EPS, 2000)

● main field:

- sat., obs. (vector) - m

arine (scalar)● SV

: monthly m

eans

MF: 10

SV: 8

● local night time

(MF)

Kp ≤ 2o

(MF, scalar

marine)

● MF: residuals < 500 nT w

ithrespect to 1997.5 m

odel● 145 obs.● 93 observations: 1980-1998● 67 repeat stations

● extrapolation of some

monthly m

eans● geographical w

eights

Olsen

(Geophys. J. Int.,

2002)

● Ørsted

● obs.m

ar 1999 - sep 2001

MF: 29

SV: 13

● local night time (sat.

& obs.)

Kp ≤ 1+ (data)

Kp ≤ 2o (3 hr*)

| Dst | ≤ 10 nT

| d(Dst)/dt | ≤ 3 nT/hr

● RC

: hourly means -> linear

slope -> subtraction from each

component at each observatory.

● Each hr: dP1 0/dθ

dip = - sinθdip is

fitted to ∆Xdip (residual in the

direction of N m

ag. pole).● R

C = am

plitude of this term● polar caps: data rejected if|B

y| > 3 nT

lat. ≤ 60° (for RC

criterion)

vector : lat. ≤ 50°scalar : lat. > 50°

● north going orbits chosen● equal-area sim

ulation(see decim

ation)● w

eighting: w

= 1 (0:00 MLT)

w ~ m

ax (cos(T/2), 0) Τ

= local time (rad)

Σw = 13 (U

T = 8:00) Σw

= 48.7 (UT = 20:00)

● correction for the localtim

e drift of the Ørsted

orbit plane● decim

ation: at least 60 sec / sinθ θ = geogr. colatitude● recalibration &

correctionfor stellar aberration

Olsen

(2002,nio_RC

.html)

● 1 sep - 31 dec 2001(C

hamp, Ø

rsted,Ø

rsted-2/SAC

-C)

● 1998 - 2000 (obs.)

18:00-06:00 MLT

(model subtracted

from the data)

● RC

from obs. &

sat. scalarresiduals● 5 day running m

ean RC

= - q1 0

lat. ≤ 60°(sat. &

obs.)● w

eighting: w

= 1 = max (obs., 0 M

LT) w

= min (daw

n, dusk)● w

decreases cf. m

ax (cos(T/2), 0) T = LT (radians)

● 8 Gauss coefficients

estimated w

ith IRLS &

Huber w

eights● R

C: better for the quiet-

time contribution than

the (previsional) Dst index

Langlais, Mandea,

Ultré-G

uérard(PEPI, 2002)

● Magsat:

1979-1980, 7 months

● Ørsted:

mar. 1999 - apr. 2000

MF: 29

EXT: 2

SV: 13

● Magsat: daw

n-side● Ø

rsted: night-time

(equator: 3 - 8 pm LT)

Kp ≤ 1+ (data)

Kp ≤ 2- (3 hr*)

| Dst | ≤ 5 nT

| d(Dst)/dt | ≤ 3 nT/hr

scalar: lat. > 50°● Ø

rsted: anisotropic weights:

- uncertainty in the attitude - rotation of the cam

era● M

AG

SAT: isotropic w

eights

● comparison w

ithpredicted values● outliers rem

oved

Comparison between IG

RF 2000 models

Mandea, Langlais

(EPS, 2000)Ø

rstednight side3 hr intervals

Kp = 0o or

Kp = 0+

2 sets: 10 points / (5°x5°) 10 points / (10°x10°)

● inflight calibrationcorrection

Abbreviations: obs. = observatories, sat. = observatories, LT = local tim

e, hr* = hours before the measurem

ent mom

ent, MF = m

ain field, SV = secular variation, EX

T = external component

Bibliography

Holm

e, R., N

. Olsen, M

. Rother, H

. Lühr, CO

2: A C

HA

MP m

agnetic model.

Sabaka, T.J., N. O

lsen, R.A

. Langel, A C

omprehensive M

odel of the Quiet-Tim

e, Near-Earth M

agnetic Field: Phase 3. Geophys. J. Int.

Olsen, N

., A m

odel of the geomagnetic field and its secular variation for epoch 2000 estim

ated for Ørsted data. G

eophys. J. Int., 149, pp. 454-462, 2002.Langlais, B

., M. M

andea, An IG

RF candidate m

ain geomagnetic field m

odel for epoch 2000 and a secular variation model for 2000-2005. Earth Planets Space, 52, pp. 1137-1148, 2000.

Mandea, M

., B. Langlais, Use of Ø

rsted scalar data in evaluating the pre-Ørsted m

ain field candidate models for the IG

RF 2000. Earth Planets Space, 52, pp. 1167-1170, 2000.

Macm

illan, S., J.M. Q

uinn, The 2000 revision of the joint UK

/US geom

agnetic field models and an IG

RF 2000 candidate m

odel. Earth Planets Space, 52, pp. 1149-1162, 2000.O

lsen, N., T.J. Sabaka, L. Tøffner-C

lausen, Determ

ination of the IGR

F 2000 model. Earth Planets Space, 52, pp. 1175-1182, 2000.

Olsen, N

, Com

parison between D

st and RC

. Monitoring M

agnetospheric Contributions using D

ata from O

rsted, Cham

p and Ørsted-2/SA

C-C

, 2002. http://ww

w.dsri.dk/m

ultimagsatellites/virtual_talks/olsen/noi_R

C.htm

l.Langlais, B

., M. M

andea, P. Ultré-G

uérard, High-resolution m

agnetic field modeling: application to M

AG

SAT and Ø

rsted data. P.E.P.I., accepted, 2002.

External field models

Model

Period – dataM

F, SVdegree /order

Tim

e (LT

)K

pD

stA

nother index / criteriaG

eomagnetic

latitudeU

niformity

Observations

Tsyganenkoexternal fieldm

odel(1996)

-100 ≤ Dst ≤ 20 nT

Does not include A

E as inputparam

eter0.5 ≤ P

sw ≤ 10 nPa (solar w

ind pressure)-10 ≤ B

y IMF , B

z IMF ≤ 10 nT

External field models and their param

eters

Description

Field model

Default value

Minim

um value

Maxim

um value

Kp

Mead-Fairfield, Tsy87s, Tsy87l, Tsy89, O

stapenko-Maltsev

00

9D

st (nT)O

lson-Pfitzer dynamic, Tsy96, O

stapenko-Maltsev

-30-600

50Solar w

ind pressure (nP)Tsy96, O

stapenko-Maltsev

30.5

10Solar w

ind density (cm-3)

Olson-Pfitzer dynam

ic25

1100

Solar wind velocity (km

s -1)O

lson-Pfitzer dynamic

300100

1200B

IMF,Y (nT)

Tsy960

-5050

BIM

F,Z (nT)Tsy96, O

stapenko-Maltsev

0-50

50

Bibliography

Bartels, J., The eccentric dipole approxim

ating the Earth's magnetic field, J. G

eophys. Res., 41, pp. 225-250, 1936.

Cain, J.C

., S.J. Hendricks, R

.A. Langel, W

.V. H

udson, A proposed m

odel for the international geomagnetic reference field-1965, J. G

eomag. G

eoelectr., 19 , pp. 335-355, 1967.Fraser-Sm

ith, A.C

., Centered and Eccentric G

eomagnetic D

ipoles and Their Poles, 1600-1985, Rev. G

eophys., 25, 1, pp. 1-16, 1987.Jensen, D

.C., J.C

. Cain, A

n interim geom

agnetic field, J. Geophys. R

es., 67, pp. 3568, 1962.O

lson, W.P., A

model of the distributed m

agnetospheric currents, J. Geophys. R

es., 79, pp. 3731-3738, 1974.O

lson, W.P., K

.A. Pfitzer, M

agnetospheric magnetic field m

odeling, Annual Scientific R

eport, AFO

SR C

ontract No. F44620-75-C

-0033, 1977.O

stapenko, A.A

., Y.P. M

altsev, Relation of the m

agnetic field in the magnetosphere to the geom

agnetic and solar wind activity, J. G

eophys. Res., 102, pp. 17467-17473, 1997.

Peddie, N.W

., International Geom

agnetic Reference Field: The Third G

eneration, J. Geom

ag. Geoelectr., 34, pp. 309-326, 1985.

Pfitzer, K.A

., W.P. O

lson, T. Mogstad, A

time dependent source driven m

agnetospheric magnetic field m

odel, EOS, 69, pp. 426, 1988.

Tsyganenko, N. A

., Global quantitative m

odels of the geomagnetic field in the cislunar m

agnetosphere for different disturbance levels, Planet. Space Sci., 35, pp. 1347-1358, 1987.

Tsyganenko, N.A

., A m

agnetospheric magnetic field m

odel with a w

rapped tail current sheet, Planet. Space Sci., 37, pp. 5-20, 1989.Tsyganenko, N

.A., and D

.P. Stern, Modeling the global m

agnetic field the large-scale Birkeland current system

s, J. Geophys. R

es., 101, pp. 27187-27198, 1996.http://w

ww

.spenvis.oma.be/spenvis/help/m

odels/blxtra/blxtrapar.html#TA

BLE.