Orsted Initial Field Model

5 Pages·2000·0.4 MB·English

by  Olsen, N.

Oersted Initial Field Model
A popular summary of "Orsted Initial Field Model" submitted to Geophysical Research
Letters by N. Olsen and 26 international co-authors including C. V. Voorhies (Code 921,
NASA's Goddard Space Flight Center, Greenbelt, MD 20771). July, 2000.
As a secondary payload poised atop a Delta rocket, the Danish geomagnetic research
satellite Oersted was launched February 23, 1999 from Vandenberg AFB in California.
The principle aim of the Oersted mission is to accurately map Earth's global magnetic
field, a field which has changed significantly in the twenty years since NASA's
enormously successful Magsat mission. After attaining a near polar orbit with altitudes
ranging from 638 to 849 km, the mini-sat class Oersted spacecraft extended an 8 meter
long gossamer mast carrying both vector and scalar magnetometers. These instruments
measure both the direction and strength of the ambient magnetic field. The orientation of
the measured field relative to the fixed stars is determined using an effectively non-
magnetic Star Imager bonded to the vector magnetometer. The Oersted Initial Field
Model is derived from both scalar and calibrated, oriented vector magnetic data using the
time-tested technique of spherical harmonic analysis. The thousands of measured data
fitted by this main field model were carefully selected to reduce contributions from
electric currents flowing in Earth's partially ionized upper atmosphere and from magnetic
storms caused by the fluctuating solar wind. Moreover, the weighted least squares fit to
these select data reflects the anisotropic residual covariance needed to account for small
errors in the observations, notably in the angle of rotation about the bore-sight of the
single Star Imager. As expected, the model fits the measured field to about one part in
ten thousand. Although the Oersted Initial Field Model includes Gauss coefficients
through degree and order 19, we only recommend use of coefficients from this initial
field model up to degree 14 at most.
Orsted Initial Field Model
N. Olsen 1, R. Holme 2, G. Hulot z, T. Sabaka 4, T. Neubert 5, L. T0ffner-Clausen 5,
E Primdahl 1,8, J. JCrgensen _, J.-M. l.,tger r, D. Barraclough 8,J. Bloxham 9,
J. Cain 1°, C. Constable _I, V. Golovkov 12,A. Jackson 13,P. Kotz614, B. Langlais 3,
S. Macmillan 8, M. Mandea 3, J. Merayo 6, L. Newitt xS,MI Purucker 4, T. Risbo 16,
M. Stampe 1, A. Thomson 8, C. Voorhies 4
Abstract. Magnetic measurements taken by the Orsted satellite during geomag-
netic quiet conditions around January 1, 2000 have been used to derive a spherical
harmonic model of the Earth's magnetic field for epoch 2000.0. The maximum
degree and order of the model is 19 for internal, and 2 for external, source fields;
however, coefficients above degree 14 may not be robust. Such detailed models
exist for only one previous epoch, 1980. Achieved rms misfit is 2 nT for the scalar'
intensity and 4 nT for the vector components perpendicular to the magnetic field.
This model is of higher detail than the IGRF 2000, which for scientific purposes
related to the Orsted mission it supersedes.
introduction
ever, the satellite was still inthe commissioning phasebefore
september 1999, and the measurements used for the present
Twenty years after the Magsat mission, the Orsted satel-
study are more accurate.
lite was launched on February 23, 1999 in a near polar or-
bit with an inclination of 96.5°, a perigee at 638 km and
Data selection and pre-processing
an apogee at 849 km. The principal aim of the Orsted mis-
sion [Neubert etal., in preparation] istoaccurately map the
Data from geomagnetic quiet conditions between Decem-
Earth's magnetic field.
ber 18, 1999 and January 21, 2000 were selected according
The goal ofthis paper istopresent anaccurate "snapshot" to the following criteria: Kp < 1+ for the time of obser-
of the geomagnetic field at epoch 2000.0 based ongeomag- vation, Kp < 20 for the previous three hour interval, IDstl
netic quiet days around January 1, 2000. To reduce contam- < 10nT and Id(Dst)/dt[ < 3 nT/hr. To reduce contribu-
ination of the lower degree expansion coefficients by spatial tions from ionospheric currents at middle and low latitudes,
aliasing, the analysis was performed through degree and or- only night-side data (local time about 22:00) were selected.
der 19for the internal fieldand 2 for the external field. How-
Vector data were used fordipole latitudes iAaip[ < 50°, and
ever, we only recommend use ofcoefficients uptodegree 14 scalar data for 50° or if attitude data were not
])kdipl ___
at most.
available. To further reduce contributions from polar cap
Orsted data from May to September 1999 were used to ionospheric currents, only data for which the dawn-dusk in-
derive the IGRF 2000 [Olsen and Sabaka, 2000]. How- terplanetary magnetic field component was weak ([ByI <
3 nT) were used. An equal area distribution was approxi-
1Danish Space Research Institute, Copenhagen, Denmark mated bydecimating the data tomeasurement times at least
2GeoForschungsZentrnm, Potsdam, Germany 30s/sin 0apart, where 0isgeocentric co-latitude. All orbits
sIPGP, Paris, France
were visually inspected and those suspected of contamina-
4NASAJGSFC, Greenbelt/MD, USA
5Danish Meteorological Institute, Copenhagen, Denmark tion by external currents were removed. Attitude informa-
81nstitute for Automation, DTU, Lyngby, Denmark tion over the South Atlantic Anomaly (SAA) was sparse due
rCEA-Direction des Technologies Avanc_s, France
toradiation effects onthe star imager, resulting in a paucity
8British Geological Survey, Edinburgh, UK
9Harvard University, Cambridge MA, USA of vector data there. Since this region is close to the dip-
l°Florida State University, Tallahassee, FL, USA equator (the thin line in Figure 1) where vector data are
11University of California, San Diego, CA, USA mandatory toavoid the Backus effect [Stern and Bredekamp,
12IZMIRAN, Troitsk, Russia
1975], 66 data points during four orbits on the geomagnetic
1aUniversity of Leeds, UK
14Hermanus Magnetic Observatory, S. Africa quiet days October 9 and November 26, 1999were added to
15Natural Resources Canada constrain field direction in this region. Figure 1shows the
16Copenhagen University, Denmark distribution of the 2148 scalar data points and 3957 vector
N. Olsen et al.: _rsted Initial Field Model
.'.-.'..",,..,..,..._:._,t.,-.. _v. I.',, ...,- ,q..• /:._." ,-•.,."....._..",";,_::.". ,.,_.,_ ,:'.,.; ,_ _'_, . ...'_,.,_.t,.,"_. ..,',.. " ............'.1.............................
30"
-50 _I I I I /
30 60 90 120 150 1BO
O"
[
-30"
-60"
30 60 gO 120 150 180
-90' -.....
180" 240" 300" O" 60" 120" 180"
m
Figure 1. Data distribution. Scalar measurements are shown
by small and vector measurements by larger symbols. Open
30 6O 90 120 1.SO 180
circles present additional vector data to fill the gap in the
SAA.
=-°
-5O
triplets used for the model. 5OC 30 60 90 120 150 180
The attitude accuracy of the 0rsted star imager (SIM) is
anisotropic: determination of the SIM bore-sight direction "-_o
("pointing") is more accurate than determination of the ro-
-.,.'50
tation around the bore-sight ("rotation"). This results in rel- 30 60 90 120 150 160
50
atively more noise in the rotation angle, which is also more
sensitive to distorting effects like instrument blinding (for
instance by the moon). This attitude anisotropy results in
correlated errors between the magnetic components, which -rio i 1 i e
0
should be taken into account when deriving field models erl
[Holme and Bloxham, 1996; Holme, 2000].
Figure 2. Residuals (observations minus values predicted by
Let fi be the unit vector of the SIM bore-sight, and let
the model of Table 2) as a function of co-latitude O for the
B be the observed magnetic field vector. B and fi define
nightside part of orbit # 4343, December 22, 1999, 01:21 -
o a new coordinate system (provided they are not parallel),
02:11 LIT. Kp = 0o and Dst = +9 nT.
and the magnetic residual vector SB = (_BB, _Bt, _B3)
can be transformed such that the first component, dBB, is in
the direction of B, the second component, _B.l., is aligned (_Br, 8Bo, 8B,) system, but is concentrated in 8Bx in the
with (fix B), and the third component, _Bz, is aligned with (SBe, _B±, _B3) system. _5B3remains slightly more noisy
B x (fi.xB). The last two components are perpendicular to than 8Be due to pointing uncertainty and field-aligned cur-
the magnetic field. In this coordinate system, the errors on rents. In particular, _Bs signatures at 8 m 25° and 170°
the different field components are uncorrelated. are caused by auroral field-aligned currents. The gap in the
Let _ be the attitude error of the bore-sight (pointing er- vector components between/9 = 100° and 135° is due to
ror), X that around bore-sight (rotation error) and let _rbe moon-blinding of the star imager.
the (attitude independent) error of the scalar intensity. Con- Most all data selected span 35 days during which the field
sidering only linear terms in _band X, the component _BB changes by up to 20 nT due to secular variation (SV). It has
is independent of attitude errors. $B3 is affected only by been decided to account for this change by propagating all
pointing errors, whereas dB± is influenced by both pointing observations to epoch 2000.0 since this a) reduces the model
errors and rotation errors [Holme, 2000]. Since the rotation misfit of *Bo and _Bz by 10% and 6%, respectively (that
uncertainty is believed to be the main error source, the com- of _B± is not changed); and b) reduces the magnetic power
ponent B± is more contaminated than the two other compo- Rn for all degrees above n = 12 (mean reduction: 17%).
nents and should be down-weighted. The latter indicates that SV between neighboring measure-
As an example, Figure 2 shows the residuals of the ments taken at different epochs will, if not corrected for, pro-
nightside part of orbit # 4343. The upper panels present duce spurious high degree signals. Two different SV models
residuals (_SBr, 6Be, 6B¢_) as a function of colatitude 8; the were used: an updated version of the IGRF 2000 SV model
lower panels present the residuals as (6BB, 6B±, 6B3) •The [Macmillan and Quinn, 2000] and a model generated from
noise is clearly spread over all three components in the Orsted data spanning over 9 months. Negligible difference
N. Olsen et al.: Orsted Initial Field Model
was found, so it was decided to use the Orsted SV model for gtot IN out mean rms
internal consistency. This model is still in development, and t_,_polar 1322 13 -0.16 2.77
will be the subject of a future publication. t_Fnon-polar + 5BB 4783 49 0.04 1.87
5B± 3957 49 1.12 8.38
Model parameterization and estimation 5Ba 3957 49 -0.04 2.62
5B_ 3957 i 49 0.63 4.79
I
The magnetic field B = -grad V can be derived from a 5Bo 3957 49 -0.20 5.58
magnetic scalar potential V which is expanded into terms of 5B_, 3957 49 -0.36 5.21
spherical harmonics:
Table 1. Number Ntot of data points, number Nout of re-
moved outliers, means, and rms misfits (in nT) for the dif-
v = + i,7) P2 O)
ferent components. "Polar" denotes data with IAdip[ > 50°.
_.n.._ l rn-_O
+ E (q_cosmq_+ s_sinmrb) P_(cos0)
in spherical components. Figure 3 shows the data residu-
n_l rrl-----0
als as a function of dipole co-latitude. The largest residuals
i •
in 5BB are found in the southern polar cap (0dlp > 170o)
and are attributed to ionospheric currents in the summer po-
[_P°(cos O)+ (_ cos0 + s'isin0) P_(cos 0)] }. lar cap. Electrical conductivity is smaller in the northern
(winter) polar cap ionosphere due to absence of solar irradi-
a = 6371.2 km is the mean radius of the Earth, (r, O,_b)
ation, and therefore the 6BB residuals in the northern polar
r_ are geocentric coordinates, Pnm (cos0) are the associated
cap (0dip < 10°) exhibit a smaller scatter than their counter-
Schmidt-normalized Legendre functions and (gnm, hnm) and
parts in the southern polar cap. However, contributions from
(qnrr_, Srnn.) are the Gauss coefficients describing internal and
ionospheric polar electrojets are present even in the northern
external source fields, respectively. The coefficients _,
auroral zone (0dip _ 23°).
and _ account for the Dst-dependent part of the external
The large rms and mean values for 5B.L (present even
dipole. Its internal, induced, counterpart is represented via
when the data are weighted isotropically) confirm the neces-
the factor QI = 0.27, a value found from Magsat data by
sity to downweight this component using the covarianee ma-
Langel and Estes [1985]. The model has 410 parameters
I (399 static internal, 8 static external, and 3 coefficients of trix Cd. A resolution analysis shows that B.L resolves only
6% of the model parameters if the data are treated in this
i Dst-dependency).
way, but 24% if data errors are assumed to be isotropic. The
The coefficients are estimated by an iterative least-
corresponding values for BB (Ba) are 38% (27%) and 27%
squares fit, minimizing eTC_le where the residuals e =
(23%), whereas the resolving power of F is 30% and 27%,
dobs- dmod are the differences between observations and
respectively. The model fits the data with a(normalized) chi-
values predicted by the model, and Ca is the a-priori covari-
squared misfit of 1.01 which isclose tounity, consistent with
ante of residuals due to data errors and fields left unmodeled.
To account for the anisotropic attitude accuracy, C_ was as-
signed the form of Eq. 18 of Holme and BIoxham [1996],
1o................ :....., .......... i................ L............... !................................
with _r = 2.25 nT, _b= 10" and X = 60" (these values are
i -::.',.,.i . ...'_ :._.:. _., :..
justified by the a-posteriori model misfit, pre-flight instru- o
ment error estimates are 3" and 20" for SIM and 0.2 nT for
the vector magnetometer). -I0
When solving the least-squares problem, three iterations I0
were found to be sufficient. Outliers were removed after the
second iteration; as outlier selection criterion we have used
15 nT for 5BB and 5B3 but 30 nT for 5B±. If one of the _-1o
component residuals was above its threshold value, all three _ ....
components were removed.
1
Results and Discussion -,o_ a_ _':" .................... :--:;::....... j
Number of data points fitted, residual means and rms mis- o 30 6o o_ _o _so _ao
fits of the model are given in Table 1.The anisotropy of rms
misfit in (rBn, 6B±, 5Ba) components is much larger than
Figure 3. Residuals as a function of dipole co-latitude.
# f •
N. Olsen et al.: _rsted Initial Field Model
J
the weighting (a-priori data errors a, _b, X) being correct. n m g_ h_ n I m g_ h_
I 0 -296 i7.37 11 ' 0 2.54
The model coefficients are given in Table 2. Only internal
1 -1729.24 5185.6.d II I -1.58 0.36
coefficients up to n = 14 are listed; the complete model is 2 0 -2268.46 il 2 -I.83 i.29
available at www.dsri.dk/Oersted/Field_models/OIFM/. 2 3068.92 -2481.7'; I1 3 1.47 -0.85
2 2 1670.76 -457.6_ 11 4 -0.08 -2.59
Experiments with various truncation levels of the spher-
3 0 1340.16 11 5 0.18 0.90
ical harmonic expansion gave the largest changes in the 3 1 -2288.34 -227.87 1I 6 -0.74 -0.65
southern polar cap (0di p _> 175°), centered around the mag- 3 2 1252.09 293.2_ 11 7 0.78 -2.82
netic pole. This indicates that contributions from iono- 3 3 714.08 -49!.32 I1 8 1.85 -0.89
4 0 932.11 I1 9 0.01 -!.08
spheric current systems in the summer hemisphere are prob- 4 I 786.66 273.2 ! 11 10 1.05 -1.98
ably present in the data and model in spite of our attempt to 4 2 249.82 -231.7C 1i 1i 4.07 -0.44
minimize external current contributions by careful data se- 4 3 -403.30 119.53 12 0 -2.53
lection according to geomagnetic indices and IMF By. 4 4 11i.25 -303.65 12 I -0.51 -0.40
5 0 -217.06 12 2 0.19 0.25
To address these contributions will likely require inclu- 5 1 351.98 42.76 12 3 0.86 2.38
sion of more satellite data, ground data, and perhaps co- 5 2 222.06 171.19 12 4 -0.22 -2.66
estimation of ionospheric field parameters. Doing so is be- 5 3 -130.52 -132.88 12 5 0.85 0.54
5 4 -168.40 -39.42 12 6 -0.60 0.29
yond the scope of our model. 5 5 -12.92 106.44 12 7 0.30 0.02
The model presented here provides a firm basis for stud- 6 0 71.40 12 8 -0.34 -0.03
ies of the ionospheric, magnetospheric, lithospheric and core 6 1 67.40 -16.86 12 9 -0.50 0.21
6 2 74.17 64.34 12 10 -0.26 -1.00
fields. The initial model from Orsted, the first magnetic 6 3 -160.81 65.34 12 I1 -0.16 -0.48
mapping mission of the "International Decade of Geopo- 6 4 -5.77 -61.03 12 12 0.30 0.54
tential Research", will also aid interpretation of the addi- 6 5 17.00 0.80 13 0 -0.24
tional, continuous, high precision measurements of Earth's 6 6 -90.38 43.96 13 1 -0.81 -0.81
7 0 79.07 13 2 0.44 0.23
time-varying geomagnetic and gravitational fields acquired 7 1 -73.59 -65.03 13 3 0.07 1.79
by forthcoming missions like Champ and SAC-C. 7 2 -0.04 -24.69 13 4 -0.39 -0.49
7 3 33.10 6.17 13 5 1.31 -0.95
7 4 9.11 24.03 13 6 -0.46 -0.03
Acknowledgments. The Orsted Project was made possible 7 5 7.03 14.87 13 7 O.74 O.63
by extensive support from the Ministry of Trade and Industry, the 7 6 7.08 -25.34 13 8 -0.30 0.21
Ministry of Research and Information Technology and the Ministry 7 7 -1.31 -5.71 13 9 0.32 0.62
of Transport in Denmark. Additional international and crucial sup- 8 0 23.92 13 10 -0.14 0.29
port was provided from NASA, ESA, CNES and DARA. 8 I 5.99 12.18 13 11 0.26 -0.23
8 2 -9.20 -21.05 13 12 0.24 -0.24
8 3 -7.74 8.63 13 13 -0.08 -i.03
References
8 4 -16.54 -21.39 14 0 -0.57
8 5 8.95 15.30 14 I -0.06 0.12
Holme, R., Modelling of attitude error in vector magnetic data: ap- 8 6 7.03 8.76 14 2 -0.20 -0.74
plication to Orsted data, Earth, Planets and Space, submitted, 8 7 -7.97 -14.92 14 3 -0.13 0.19
2000. 8 8 -7.01 -2.46 14 4 -0.18 0.40
Holme, R., and J. Bloxham, The treatment of attitude errors in 9 0 5.30 14 _ 5 0.18 -0.11
9 1 9.63 -19.91 14 i 6 -0.06 0.42
satellite geomagnetic data, Phys. Earth Planet. Int., 98, 221-
233, 1996. 9 2 2.93 13.07 14 7 0.05 0.20
9 3 -8.58 12.50 14 8 0.26 0.26
Langel, R. A., and R. H. Estes, Large-scale, Near-Earth magnetic 9 4 6.32 -6.23 14 9 0.03 0.30
fields from external sources and the corresponding induced in- 9 5 -8.76 -8.31 14 10 0.59 0.03
temal field, J. Geophys. Res., 90, 2487-2494, 1985. 9 6 -1.53 8.46 14 11 -0.41 -0.03
Macmillan, S., and J. M. Quirm, The 2000 revision of the joint 9 7 9.13 3.88 14 I 12 0.04 0.05
UK/US geomagnetic field models and an IGRF 2000 candidate 9 8 -4.24 -8.29 14 13 0.38 0.04
model, Earth, Planets and Space, submitted, 2000. 9 9 -8.09 4.88 14 14 0.44 0.21
10 0 -3.03
Olsen, N., and T. J. Sabaka, Determination of the IGRF 2000
model, Earth, Planets and Space, submitted, 2000. 1I00 21 -61..4566 01..3847 n1 m0 ' ._2q._4m3 I srnrl
Stem, D. P., and J. H. Bredekamp, Error enhancement in geomag- tO 3 -2.95 4.12 i I 0.84 -3.73
netic models derived from scalar data, J. Geophys. Res., 80, 10 4 -0.32 4.94
1776-1782, 1975. 10 5 3.67 -5.86 2 1 0.29 -0.32
10 6 1.11 -1.18 2 -0.52 -0.04
N. Olsen, Danish Space Research Institute, J'uliane Maries I0 7 2.09 -2.84
Vej 30, DK - 2100 Copenhagen O, Denmark. (e-mail: i0 8 4.41 0.24 --"m _ra
n qn an
[email protected]) I0 9 0.42 -1.98 1 -0.59
I0 tO -0.94 -7.67 I 0.04 0.10
Table 2. Expansion coefficients of internal (g_, hnm) and
external (qm, Snm) contributions, in nT. q-nm and 8-rnn present
the Dst-dependent part of the external coefficients.