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3D Numerical Simulation of a Geomagnetic Field Reversal
Los Alamos National Laboratory / Pittsburgh Supercomputing Center
Los Alamos, NM
USA

Year: 1996
Status: Finalist
Category: Science
Nominating Company: Cray Research, Inc.

Three-dimensional supercomputer simulation of the earth's magnetic field, using 5,000 hours of computer time to simulate 80,000 years of history provides new insights into the way the earth works.
Man has been aware of the Earth's magnetic field for thousands of years
and has used it for navigation for hundreds of years. The field has
protected life on Earth by providing a magnetic shield against solar
cosmic rays. Palaeomagnetic records show that it has existed for more
than a billion years; and it probably has existed since the Earth's
beginning. Yet, based on the Earth's dimensions and electrical
conductivity, the free decay time for the Earth's field is only about
13,000 years; so scientists have long postulated that there must be some
mechanism that continually regenerates the field. Understanding the
Earth's magnetic field requires a model that reproduces its salient
features: a field that is maintained for many magnetic decay times, is
dominantly dipolar at the surface with a dipole axis that on the average
lies close to the geographic axis of rotation, exhibits secular
variation of the non-dipolar structure on time scales of ten to a
hundred years, and has occasional reversals of the dipole polarity that
take a few thousand years to complete and occur a few hundred thousand
years apart. According to Merrill & McElhinny (in "The Earth's Magnetic
Field", Academic Press, 1983), Albert Einstein considered understanding
the origin of the Earth's magnetic field as being one of the five most
important unsolved problems in physics.

Gary A. Glatzmaier (Los Alamos) and Paul H. Roberts (UCLA) have recently
developed the first fully self-consistent three-dimensional (3D)
numerical model of the "geodynamo", the mechanism in the Earth's core
that generates and maintains the geomagnetic field. With this model,
running on computers at the Pittsburgh Supercomputing Center, they have
produced a successful simulation of the Earth's field that is providing
answers to many fundamental questions about the field's structure and
evolution.

The computer model solves the nonlinear magnetohydrodynamic (MHD)
equations that govern the 3D structure and evolution of an
electrically-conducting fluid undergoing convection in a
rapidly-rotating spherical shell, their model of the Earth's outer
liquid core. Convection is driven by both thermal and compositional
buoyancy sources which develop at the boundary between the solid inner
core and the outer liquid core (the inner-core boundary, ICB). As the
core slowly cools, iron in the liquid iron alloy freezes onto the solid
inner core, precipitating the lighter constituent (e.g., silicon), which
is compositionally buoyant. Latent heat is also given off in this
process, providing a source of thermal buoyancy. In the model, the local
fluxes of light constituent and latent heat at the ICB are both
proportional to the local, time-dependent cooling rate at the ICB. Heat
is transferred out of the core at the boundary between the outer liquid
core and the solid mantle above (the core-mantle boundary, CMB)
according to the Earth-like heat flux pattern they specify at the CMB.
The resulting convection in the outer liquid core, influenced by the
Earth's rotation, twists and shears magnetic field, generating new
magnetic field to replace that which diffuses away. The generated
magnetic field diffuses into the solid, electrically-conducting, inner
core providing magnetic torque between the inner and outer cores.
Magnetic torque also exists between the outer liquid core and a solid
mantle above via a thin conducting layer just above the CMB. The rest of
the mantle is assumed an insulator since its conductivity is so small
compared to the conductivity of the core; so the external magnetic field
above this layer at the CMB is a source-free potential field.
Time-dependent rotation rates of the solid inner core and solid mantle
are determined by the net torques at the ICB and CMB, respectively.

The model prescriptions (mass, dimensions, rotation rate, material
properties, specified heat flux at the CMB) are, as much as possible,
Earth-like. The resulting simulated magnetic field has so far been
maintained for more than 80,000 years (six magnetic decay times), with
no indication that it will decay away. The strength and dipole-dominated
structure of the magnetic field at the surface of the modeled Earth is
very similar to that measured on the Earth; and the secular variation of
the non-dipolar structures of the field is characterized by a westward
drift, similar to that seen in the Earth's field. However, besides
demonstrating for the first time that the Earth's magnetic field could
be generated by a convective dynamo mechanism, the really exciting
feature of the simulation is a reversal of the dipole polarity that
occurs about 36,000 years into the simulation and takes a little more
than a thousand years to complete, after which the field does not
reverse again during the remaining 44,000 years of the simulation. This
first 3D simulation of a magnetic field reversal has several properties
(like a significant decrease in the magnetic field strength during the
reversal and recovery after the reversal) similar to those seen in the
Earth's palaeomagnetic reversal record captured in rocks and sediments.

Slides 1-3 show snapshots of the structure of the simulated 3D magnetic
field, which is portrayed via lines of force that are drawn out to two
Earth radii and colored gold where the radial component of the field is
directed outward and blue where it is inward. The striking transition
from the relatively smooth structure of the potential field outside the
core to the much more complicated and intense field structure inside the
core occurs at the CMB. The field outside the core usually has a
dominantly dipolar structure as seen before (Slide 1) and after (Slide
3) the reversal with the dipole axis nearly aligned with the rotation
axis, which is vertical in these figures. This simulation provides, for
the first time, answers to the long-standing questions of why the
Earth's magnetic field is so strongly dipolar and why the dipole axis is
closely aligned with the rotation axis of the Earth. To understand this,
consider the snapshot of one component of the simulated fluid flow that
is illustrated in Slide 4 in which regions of strong eastward flow are
colored gold and regions of strong westward flow are blue. There is an
imaginary cylinder within the liquid core (tangent to the inner core and
parallel to the rotation axis, see Slide 4) on which large shears in the
east-west flow develop due to the effects of rotation, the spherical
geometry, and the solid inner core. These shears generate strong
magnetic field by stretching it out in an east-west orientation (see
Slide 3). The tangent cylinder intersects the CMB in the polar regions
and so provides a large supply of outward directed field at one pole and
inward directed field at the other pole to maintain the external dipolar
structure that has its axis nearly aligned with the rotation axis.

The reversal of the dipole polarity is illustrated in Slides 1-3. Notice
how, at the top of the figure, the field is directed outward before the
reversal (Slide 1) and inward after the reversal (Slide 3). During the
middle of the polarity transition (Slide 2) the field structure at the
surface is much more complicated and its dipolar part, which no longer
dominates at this time, has an axis that passes through the equatorial
plane. A movie of this simulation shows how the field in the outer
liquid core is continually attempting to reverse its axial dipole
polarity on a short time scale (roughly 100 years) corresponding to
convective overturning but usually fails because the field in the solid
inner core, which can only change on a longer diffusive time scale
(about 2000 years), usually does not have enough time to completely
diffuse away before it is re-generated at the ICB. Once in many attempts
the 3D configurations of the buoyancy, flow, and magnetic field in the
outer core are right for a long enough period of time for the inner core
axial dipole field to diffuse away, thus allowing the reversed axial
dipole field in the outer core to diffuse into the inner core and
establish the new reversed polarity. This simulation suggests that the
strong nonlinear feedback in three dimensions and the different time
scales of the liquid and solid cores are responsible for the Earth's
stochastic reversal record.
The Glatzmaier-Roberts simulation of the geodynamo has provided answers
to several long-standing questions (as discussed in the previous
section) about the Earth's magnetic field that have arisen from both
palaeomagnetic and more contemporary geomagnetic measurements. As a
result of this one simulation, palaeomagnetic and geomagnetic
observational researchers have this year, for the first time, actively
sought to collaborate with the geodynamo modeling community. Previous
models of the geodynamo were always too unrealistic and non-unique
because the full set of equations was never self-consistently solved;
they typically were only two-dimensional and employed ad hoc, prescribed
flows instead of solving for 3D fluid flow with the magnetic field. As a
result these previous models never demonstrated that the Earth's field
could be generated by a convective dynamo and never produced a field
like the Earth's field. The collaboration that has begun will provide
feedback between those who have been measuring the Earth's field and
those who have been modeling it, which will benefit both communities.
Already the simulation has provided support for the traditional
palaeomagnetic assumption that the Earth's field is usually dipole
dominated. However, the simulation has also provided reason to suspect
that the assumption the Earth's field is dipole dominated during its
reversals, which palaeomagnetic reversal studies have long relied on,
may not be a valid one. Palaeomagnetic reversal studies are now
beginning to account for the quadrupole part of the field in addition to
the dipole part.

This year the Glatzmaier-Roberts geodynamo simulation has created new
excitement not only for scientists who measure and model the Earth's
field, but for many scientists outside geophysics and laymen who have a
strong curiosity about the Earth's magnetic field and wish to improve
their understanding of the environment they live in. This has become
evident by the publicity these results have received this year in the
press (as discussed in the next section).

The simulation has also provided a basis for understanding, and maybe
someday predicting, the secular variation in the Earth's field as seen
at the surface. Small changes in the local direction of the field occur
continually; this is one reason why regional charts and maps (Slide 5)
that show magnetic North relative to geographic North are typically
updated every ten years.

The axial dipolar structure of the Earth's magnetic field, through its
interaction with the solar wind, creates a magnetosphere around the
Earth that shields life from harmful solar cosmic radiation. However,
the simulation indicates that during a magnetic reversal the field
strength above the surface is much weaker; so the magnetosphere would be
smaller, which could affect the structure and size of the Earth's
ionosphere, stratosphere, and protective ozone layer. In addition, the
equatorial directed magnetic dipole during a reversal (Slide 2) rotates
with the diurnal rotation of the Earth, probably resulting in a very
different type of magnetosphere that may not provide an effective shield
against cosmic radiation. This modified magnetic and radiation
environment during a magnetic reversal, besides no longer providing a
reliable means of navigation for birds, could affect the survival and
evolution of many species.

Much research needs to be done to improve our understanding of magnetic
reversals and their environmental consequences. Fortunately, there is
plenty of time to conduct these studies before the next one occurs since
magnetic reversals take a few thousand years from start to end. However,
the last magnetic reversal occurred about 780,000 years ago; so we may
be overdue. The Earth's magnetic field strength has been decreasing
since scientists began monitoring it 150 years ago, which according to
the reversal simulation could be an indication that a magnetic reversal
may be about to begin. On the other hand, the present decline in the
field strength may just be a fluctuation. More collaborative research by
observational and computational scientists should uncover more
definitive precursors of a reversal.
Information technology has played an important role in this project at
several levels, from the methods for computing the numerical solution to
the methods of communicating the results to others. The numerical model
grew out of models that had originally been developed by Glatzmaier over
a decade ago to simulate convection and magnetic field generation in the
sun's interior. However, as discussed in the last section, the physical
conditions in the liquid core of the Earth (e.g., the large Coriolis and
magnetic Lorentz forces compared to the small viscous and inertial
forces) required the development of a new, more sophisticated numerical
method that is more accurate and stable. The code, which is highly
vectorized, is also parallelized for parallel processing on today's
supercomputers.

Glatzmaier developed, tested, and debugged the computer code at the Los
Alamos National Laboratory, but did the production runs on the Cray C-90
computer at the NSF Pittsburgh Supercomputing Center, which at the time
was the best computer for this problem. Roberts, at UCLA, provided
strong theoretical guidance in the development of the model and in the
analysis and physical interpretation of the solution. The 80,000-year
simulation required more than 5000 hours of cpu time and took over two
years to accomplish. The simulation was broken into many individual
runs, each typically spanning 500 years. The jobs were submitted
remotely from Los Alamos over the Internet and the progress was checked
daily. Data files produced by each job were routinely transmitted over
the Internet back to Los Alamos for analysis. This daily reliance on the
Internet to remotely run a large problem over a period of two years
demonstrated that computational scientists no longer need to work where
the supercomputers are located. It also allows scientists to easily run
their computer codes on new computers that become available in other
places. Soon the Glatzmaier-Roberts code may be running on massively
parallel computers at Los Alamos and at various other centers around the
Country.

Analyzing the 3D, time-dependent, multi-variable solution required new
visualization tools. For example, Glatzmaier developed the program that
generates the 3D graphical data from a snapshot of his solution that he
then inputs to the commercial software, AVS (Advanced Visual Systems),
that produces the images of the 3D vector field in terms of lines of
force (Slides 1-3). He also developed programs that he used to make
several graphical movies of the simulated magnetic reversal. These
images and movies proved to be extremely valuable for analyzing and
understanding the 3D structure and evolution of the field. They were
also valuable for describing the solution and explaining the dynamo
mechanism to others both in written publications and oral presentations.

The results were initially communicated in two refereed papers by
Glatzmaier and Roberts ("A three-dimensional convective dynamo solution
with rotating and finitely conducting inner core and mantle" Physics of
the Earth and Planetary Interiors, vol. 91, 63-75, 1995; and "A three
dimensional self-consistent computer simulation of a geomagnetic field
reversal" Nature, vol. 377, 203-209, 1995). The second article was
featured on the cover of Nature on September 21, 1995. Since then there
has been an explosion of publicity regarding this simulated geomagnetic
field reversal. Several newspapers in at least five countries covered
the story (e.g., the Washington Post, on September 25, 1995). Several
scientific magazines also wrote follow-up articles. Articles appeared in
EOS (American Geophysical Union), the American Institute of Physics
Bulletin, Geotimes (American Geological Institute), PSC News, Scientific
Computing World magazine (England), GEO magazine (Germany), FACTS
magazine (Switzerland), and in the January 1996 issue of Physics Today
which also featured it on the cover. Articles are also about to appear
in Eureka magazine (France) and Science et Vie magazine (France). For
several of these articles, color figures (similar the those in Slides
1-4) were sent over the Internet to the magazines for their use. The
popularity of these results has apparently been due to the familiarity
most people have with the concept of the Earth's field and the easy way
of relating a magnetic field reversal to a compass needle pointing south
instead of north (Slide 5). Even though the details of the physics and
the computations are complicated, the basic concepts are familiar.

So far Glatzmaier and Roberts have given about 15 invited talks on their
results at universities and other scientific institutions in the USA and
5 invited talks in Europe. In these talks, the computer graphical slides
and movies of their simulated magnetic field reversal were always very
helpful for describing the 3D structure and time dependence of the
field. Copies of their video movies were also given, upon request, to
universities in the USA, the UK, Australia, Bulgaria, and Japan; and
they are now part of the "Time Capsule" for the Smithsonian collection.
This is the first 3D self-consistent numerical simulation of the
geodynamo and of a geomagnetic field reversal. The only other effort to
develop a geodynamo model in the USA is at Harvard University. Efforts
are also underway in the UK, Australia, Japan, Germany, and France.

The Glatzmaier-Roberts geodynamo model was the 40th version of a model
that originally was developed by Glatzmaier to simulate the solar dynamo
(Glatzmaier "Numerical simulations of stellar convective dynamos. I. The
model and method" Journal of Computational Physics, vol. 55, 461-484,
1984). Each version tested a different numerical method, attempting to
overcome numerical difficulties (described ahead). Finally, after
several years of development and testing, the 40th version proved robust
enough to accurately and efficiently solve the full set of nonlinear
equations and produce the first geodynamo simulation.
The original goal of this project was to test if a convective dynamo
within the parameter regime appropriate for the Earth could generate and
maintain a magnetic field without decaying away. This has been
postulated for about 40 years but, until now, never demonstrated. The
Glatzmaier-Roberts geodynamo simulation has now clearly demonstrated
that it is possible and has shown how the geodynamo mechanism works. In
addition, it has provided answers to long-standing questions like why
the Earth's field is dominantly dipolar with a magnetic axis nearly
aligned with the Earth's rotation axis and how the secular variation of
the non-dipolar part of the field occurs. Finally, the simulation
unexpectedly demonstrated how a magnetic field reversal can occur and
why the times between reversals are long and differ so greatly.

Future plans for this project call for improved representations of the
physics. In particular, more studies will be done to better understand
what forces at the CMB may trigger a field reversal. For example, the
effects of torques between the liquid core and the solid mantle
resulting from topography at the CMB will be investigated; and the
effects the precession of the mantle due to the gravitational forces of
the sun and moon may prove to be important to the dynamics of the liquid
core. In addition, there are plans to use the simulated 3D
time-dependent magnetic field as input for a different model that
computes the magnetosphere resulting from the interaction of the Earth's
field and the solar wind in order to study the structure and evolution
of the magnetosphere during a magnetic reversal.
The magnetohydrodynamic equations describe how the fluid temperature,
density, pressure, gravitational potential, light constituent
concentration, flow velocity, and magnetic field all vary in three
dimensions and time and how they all provide nonlinear feedback on the
others. Every time the computer solves this large set of coupled
equations the solution is advanced 30 days everywhere in the Earth's
core and, for the external magnetic field, well beyond the core. The
numerical difficulty is that the viscous forces in the modeled core are
typically five orders of magnitude smaller than the Coriolis forces (due
to rotation) and the Lorentz forces (due to electric currents flowing
across magnetic field). Consequently, to have a stable and accurate code
for the parameter regime appropriate for the Earth, the Lorentz forces
were treated explicitly (i.e., using present and past information to
advance the solution) while the Coriolis forces were treated implicitly
(i.e., using future information). The resulting coupling between
spherical harmonic coefficients of the solution required a new method
(version 40) that involved the construction of large block-banded matrix
equations that are solved each 30-day timestep.

After several years of development, this robust code then required over
5000 cpu hours of supercomputer time to simulate the 80,000 years. This
was accomplished remotely over the Internet between Los Alamos and the
Pittsburgh Supercomputing Center. This large computing resource was
obtained by writing proposals that successfully competed nationwide for
NSF computing resources over a period of two years.

Besides the technical difficulties involved in the development and
computation of this numerical study, there were psychological
difficulties. Glatzmaier and Roberts set out to develop a computer model
that would solve a complex problem that many other very capable
scientists failed to solve. The many years of hard work and frustration
when methods would not work required perseverance, especially when there
seemed to be so little chance for success. However, the challenge and
hope for success was addicting; and the investment eventually paid off
beautifully. The excitement felt by Glatzmaier and Roberts is now shared
by many.