Progress in the development, testing, and evaluation of kinematic geomagnetic forecast models and their utility in magnetic prediction of the core-mantle boundary of the Earth and in determination of the core radius is reported. The GFSC 9/80 model, which uses MAGSAT data, was determined to be of high quality

Benton, E. R.

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Quarterly Status and Technical Progress Report #10
(Covering the Period 1 April 1982 to 30 June 1982)
NASA Contract NAS5-25957 (MAGSAT)
Investigation of Geomagnetic Field Forecasting
and Fluid Dynamics of the Core
Principal Investigator: Edward R. Benton
Department of Astro-Geophysics, University of Colorado
Boulder, Colorado 80309
1 July 1982
RECEIVED
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1. Problems: None
2. Approach
a. Conventional Kinematic Geomagnetic Forecast Models for Epoch 1980
Task a of this contract calls for the construction of two conven-
tional kinematic geomagnetic forecast models for epoch 1980, based on
pre-MAGSAT data. The two models selected for this purpose are the
definitive model of Barraclough, Harwood, Leaton and Malin (1978), desig-
nated herein as IGS 65, and the model of Cain, Hendricks, Langel, and
Hudson (1967), designated as GSFC 12/66. The first of these draws on data
from the period 1955 to 1973 and gives main field and secular variation
coefficients for epoch 1965 to ore er and degree N - 8. The second model
is based on data from the period 1j00 to 1966 and includes Gauss coeff-
icients of the main field, secular variation and secular acceleration
for epoch 1960, to order and degree N - 10. These two models were
selected as among the best pre-MAGSAT models, based in part on their
successfully tested ability to predict the radius of earth's core-mantle
boundary magnetically, when compared with appropriate models of MAGSAT
data (Voorhies & Benton, 1982).
We have used all of the available coefficients for the main field
and time variations in these models to forecast the main field coeffici-
ents furward in time to epoch 1980 by straightforward expansion in Taylor
series. We intend to include the resulting tables of these kinematic
forecast coefficients in the final report.
It is known that, generally, magnetic models tend to deteriorate
in accuracy rather rapidly when they are extrapolated outside the time
interval during which the model is constrained by observations. For
IGS 65 there was a 7 year extrapolation (from 1973 to 1980) but for
GSFC 12/66 the extrapolation is over the 14 year interval from 1966
to 1980. It must be expected then that the IGS 65 model would give
the better kinematic forecast at 1980. The following approach to test
this supposition has been developed and implemented. MAGSAT data for
epoch 1980 (more accurately 1979.85) were re-fit to the same fitting
levels as in IGS 65 and GSFC 12/66 (Benton, Estes, Langel, and Muth,
1982). Then the difference between these re-fitted MAGSAT models
(designated MGSTRF) and the pre-MAGSAT models was formed and contoured
at earth's surface to reveal the locations and magnitudes of the
discrepancies. The main results are described under Accomplishments.
We regard Task a as essentially complete.
b. Evaluatiott of Magnetic Model GSFC 9/80
An approach has been developed and partially implemented for
evaluating one aspect of the quality of the new geomagnetic model
designated GSFC 9/80 (Langel, Estes, and Mead, 1981). This sort of
work was not explicitly contemplated at the time this MAGSAT investi-
gation was planned, but it is, nonetheless, thought to be worth doing
as part of this project.
1
The work described by Voorhies and Benton (1982) strengthens
our belief that, in the short run (i.e. on the time scale of decades),
earth's core moves like a perfect conductor while the mantle can
simultaneously be treated as a perfect insulator. That physics implies
that the magnetic flux crossing each patch of area on the core-mantle
boundary bounded by a zero contour of vertical magnetic field should
be a constant of motion. By simple addition, so is the total unsigned
magnetic flux crossing the entire core-mantle boundary. This provides	 4
a criterion against which to test geomagnetic main field and secular
variation models. As elaborated below under Accomplishments, we have
completed a set of computations of flux through patches for both the
IGS 65 model and the GSFC 9/80 model; we find that the GSFC 9/80 model
conserves flux both patchwise and in toto, substantially better than
does IGS 65.
Another basis for evaluating a model is to ask how accurately
it locates, magnetically, the core-mantle boundary, whose radius is,
of course, very well-known from seismology. In Voorhies and Benton,
1982 this question was answered for GSFC 12/66 and IGS 65 by comparing
each of them with an appropriate (i.e. consistent) MAGSAT model. We
have now used the main field, secular variation, and secular acceler-
ation of GSFC 9/80 alone and found the core radius magnetically to
an accuracy better than that obtained by Voorhies and Benton (see
elaboration below).
3. Accomplishments
a. Conventional Kinematic Geomagnetic Forecast Models
Six important contour maps have been produced to help determine just
how inadequate is our ability to forecast geomagnetic time evolution
a decade or so into the future. The first set of three maps plots
contours (for a truncation level N T = 10) of ABre AB69 AB  at earth's
surface where, for example,
AB 
	 Br1MGSTRF	 Br I GSFC 12/66
and the re-fit to MAGSAT data is for a fitting level NF=10, so as to
be consistent with GSFC 12/66. The epoch of MGSTRF is 1979.85 and that of
GSFC 12/66 has been brought forward to 1980. Maximum differences are
two negative cells, located beneath the Indian Ocean and of magnitude
2396 and 2144 nT. Thus, although GSFC 12/66 does a good job over
the 30 year interval 1930-1960 of determining the radius of earth's
core-mantle boundary when compared to MAGSAT models for 1980, it makes
errors of over 2,000 nT, compared to MAGSAT, when extrapolated 14 years
beyond the end of the interval constrained by data. Maximum values of
JAB E1 1, JAB I are comparable but somewhat smaller, 1510 nT and 1499 nT,
respectiveiv.
2
The other three contour maps are for the differences ABr , AB a, ABA
where now
AB  a Br I MGSTRF - Br I IGS 65.
Fitting and truncation levels are N =NT
 8 and the epoch of MGSTRF is
1979.85, while IGS 65 has been brouNht forward to 1980. Maximum
values of JAB i, JAB6 J ,IAB,4 1	 are, as expected, substanti&V y
smaller over Ehe 7 year exttapolation frodr 1973 to 1980, namely, 661 nT,
420 nT, and 346 nT, respectively.
b. Evaluation of Maeetic Model GSFC 9/80
The results summarized in Figure 1 of the last Progress Report (#9)
have also been obtained for the model IGS 65. Although not yet drafted
into final form, it is apparent from the rough figure that total flux
crossing the core-mantle boundary is not nearly so well conserved by
this model as for GSFC 9/80.
Calculations of the magnetic flux through individual patches on the
seismic core-mantle boundary bounded by null-flux curves have been
completed for a truncation level of N=8. At that truncation level there
are five magnetic equators (North polar, Pacific, Main, South American,
African) so there are five independent flux conserving constraints
that ought to be satisfied.F :o r model IGS 65, for the five epochs
1955, 1960, 1965, 1970, 1975 we find deviation from constancy expressed
as an overall percentage variation for the various patches as follows:
North Polar (131%); Pacific (91%) ; Northern Magnetic Hemisphere
(0.53%); South American (8.7%);African (9.6X). In contrast, for the
model GSFC 9/80 for the five epochs 1960, 1965, 1970, 1975, 1980, we
find: North Polar (86X); Pacific (15.7X); Northern Magnetic Hemisphere
(0.35%); South American (2.5%); African (7.9X). In each case, GSFC 9/80
satisfies these frozen-flux constraints substantially better than does
IGS 65.
To check on how well GSFC 9/80 determines the core radius, magnetically,
a rather complete set of calculations ha s been made. The total absolute
magnetic fluxes crossing the spheres of radius ratio r/a = 1, 0.9, 0.8, 0.7,
0.6, 0.58, 0.56, 0.54, 0.52, 0.50 have been calculated at epochs 1960,
1970, 1980 for the complete range of truncation levels from N = 1 through
N	 13. The best value for core radius is achieved for N T =T8 by
finding the value of r at which the unsigned flux in 1980 was the same as
at 1960. That value is 3463 km, only 22 km (or 0.63%) below the accurate
seismic radius of 3485 km. Comparisons at shorter time separations (1960
to 1970, 1970 to 1980) give substantially poorer results (3215 km and
3670 km, respectively). We attribute this to dominance of round-off
error from subtracting two large numbers which are not sufficiently
different when the time interval is only 10 year:.
4. Signific:nt Results
A basis for evaluating geomagnetic models of the main field and its
secular variation (plus U gher time derivatives if they are part of the
model) has been developed. One asks (a) how well does the complete
model locate the core-mantle boundary magnetically, using Lite technique
3
of Hide (1978), and (b) how well does the model conserve magnetic flux
crossing patches of area on the core-mantle boundary bounded by
null-flux curves (Backus, :.968)? Calculations in progress strongly
suggest that the recent geomagnetic model GSFC 9/80 for the 20 year
period 1960-1980 is an extremeii nigh quality model from this viewpoint.
For example, when truncated to N-8, then back at the two extremes of its
data interval (1960 and 1980), it conserves total absolute magnetic
flux across the sphere of radius r-3463 km, which is only 22 km (or 0.63%)
below the seismic core radius of 3485 km.
5. Publications: None
6. Recommendations: None
"^. Data Utility: The modelling effort at GSFC is indispensable to
this project and the data products received to date have been out-
standing. The high quality found in the model GSFC 9/80 is, no doubt,
due in part to the treatment of observatory anomalies, but also to
the insertion of highly accurate MAGSAT data.
4


Investigation of geomagnetic field forecasting and fluid dynamics of the core

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