The Earth's Real Inside Story: Modulating the Geodynamo

Paul H. Roberts
UCLA

hen we use a compass to find our way, we take advantage of the fact that our planet has a magnetic field with two poles, north and south. Magnetism was the first physical property to be attributed to the body of the Earth as a whole, by William Gilbert in his 1600 work De Magnete; even gravitation had to wait until 1687 to be discovered by Isaac Newton. As a dynamic property, magnetism depends on the creation and maintenance of an electric current. Earth's "generator" or geodynamo lies deep within the planet, a continuously flowing shell of liquid iron surrounding an inner core of solid iron at the very center.

Over geological time, Earth's magnetic field has varied in strength, and the location of its poles has shifted. From time to time, the poles have even changed places, in what are called magnetic reversals. Now a group of geophysicists led by Gary Glatzmaier of UC Santa Cruz is using high-performance computation to penetrate the mechanism of the geodynamo and discover the details of such changes.

At the February 2000 annual meeting of the American Association for the Advancement of Science, Glatzmaier reported on the group's most recent simulations, published last fall in Nature. Their results suggest that temperature structure in the lower mantle (just above the core) plays a large role in controlling the frequency of magnetic reversals.

THE EARTH'S MAGNETIC FIELD

A COMPUTATIONAL BEHEMOTH

DETAILED RESULTS

REFERENCE

Glatzmaier, G.A., R.S. Coe, L. Hongre, and P.R. Roberts. 1999. The role of the Earth's mantle in controlling the frequency of geomagnetic reversals. Nature, 401 (28 October), 885–890.

Results from a simulation by Gary Glatzmaier, Paul Roberts, and colleagues show the Earth's outer core region (yellow) where the fluid flow is the greatest, the core-mantle boundary (blue mesh), and the inner core boundary (red mesh).

THE EARTH'S MAGNETIC FIELD

Paleomagnetic records indicate that Earth has had a geomagnetic field for at least 3 billion years. The inner structure of the planet--from crust through upper and lower mantle to liquid and solid cores--has been deduced from seismic measurements over the past century. Only recently, though, have attempts been made to simulate the complex thermodynamics and magnetohydrodynamics within the Earth's core that account for the paleomagnetic record. The detailed studies of plate tectonics driven by mantle convection have depended upon large-scale computing, and now it is clear that details of the dynamics of Earth's magnetic field will also be arrived at by computation.

The rocks show that the north and south magnetic poles of Earth have traded places perhaps several hundred times during the past 160 million years. The duration of the reversing episodes is relatively short (1,000–6,000 years), compared with the long intervals between reversals. The average period between reversals is about 200,000 years, but there have also been very long periods of 30 million to 40 million years without any such activity.

"Our model is the first three-dimensional, dynamically self-consistent computer simulation of the evolving planetary magnetic field--the first to yield quickly occurring reversals, with long periods in between, as appears to be the case for Earth," Glatzmaier said. "We also observed in these simulations that the solid inner core persistently rotates faster than the mantle. This was the basis for our prediction of the super-rotation of Earth's inner core. Several seismic analyses have since found evidence of super-rotation, although the more recent analyses suggest that the inner core is rotating less rapidly than we originally predicted."

Glatzmaier, a professor of Earth Sciences, worked with a team including Robert S. Coe, professor of Earth Sciences at UC Santa Cruz; Lionel Hongre, a postdoctoral researcher at UC Santa Cruz; and Paul H. Roberts, a distinguished geophysicist from the Institute for Geophysics and Planetary Physics of UCLA. (IGPP is a UC multicampus research organization including UCLA, UC San Diego, UC Riverside, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and, recently, UC Santa Cruz.)

"It took several years for Paul and me to construct the geodynamo model, and in 1995 we published the results of our first simulation, which included a magnetic dipole reversal," Glatzmaier said. "The model solves the three-dimensional, time-dependent thermodynamic, velocity, and magnetic field equations simultaneously, each constantly feeding back to the others."

"An important point to make about our model," Roberts said, "is that it is very closely tied to the known geophysics. For example, we include no arbitrary heat sources in the core."

The Glatzmaier-Roberts geodynamo model simulated the 3-D magnetic field structure of the Earth. Blue field lines are directed inward and orange field lines are directed outward. The rotation axis of the Earth is vertical through the center; the field lines are drawn out to two Earth radii.

A COMPUTATIONAL BEHEMOTH

The group's latest simulations have taken nearly five years to accomplish, using the Cray T3E and Cray T90 at SDSC as well as computers at Los Alamos National Laboratory, NCSA, the Pittsburgh Supercomputing Center, the Texas Advanced Computing Center, and two NASA computer centers (Goddard and Marshall).

The average numerical time step in the Glatzmaier-Roberts model is about 15 days, but they need to simulate the activity of the geodynamo over hundreds of thousands of years. The model solves the equations throughout the core, using a spectral method based on spherical harmonics and Chebyshev polynomials. They are now working on algorithmic improvements to prepare for runs on the teraflops-class machines. Ultimately, Glatzmaier hopes to simulate a much longer portion of the history of geomagnetism.

"We recently achieved a speed of 630 gigaflops on a short run with very high spatial resolution using 1,500 T3E processors at one of the NASA centers," Glatzmaier said. A single, 100,000-year, low-resolution run may take three or four months to complete, he said, depending on queue availabilities. "We've run five or six jobs almost daily on machines all over the country for the past four years, and we are really looking forward to the improvements in the computing environment that will allow us to do less job-sitting and a lot more work."

DETAILED RESULTS

The 1999 Nature paper presents scenarios in which eight different patterns of heat flux from the core to the mantle were imposed over the core-mantle boundary. The temperature of the fluid outer core is relatively constant. It runs from 5,300 K at the inner core boundary to about 4,000 K at the core-mantle boundary--temperatures similar to those found on the surface of the Sun. So it is the temperature of the lower mantle material at the core-mantle boundary that actually determines the overall flux--the rate at which heat leaves the core. The mantle material, although cooler overall, may vary in temperature along the core-mantle boundary. Where the material is coolest, heat is transferred from core to mantle fastest. The simulations kept the total heat flow across the core-mantle boundary constant but varied the local heat flux across the core-mantle boundary in various ways.

It is the motion of the fluid outer core that continuously generates Earth's magnetic field. Without the dynamo motion, the field would, once created, decay in about 20,000 years. Convection in the outer core is driven by both thermal and compositional buoyancy sources at the inner core boundary, produced as the planet slowly cools and iron in the fluid alloy solidifies onto the inner core. These buoyancy forces, together with the Coriolis forces due to Earth's rotation, orient the fluid flow in a cylindrical fashion (Figure 1), causing the complex fluid dynamics that result in Earth's large-scale, slowly changing magnetic field (Figure 2).

"Of our eight cases, we ran four for 100,000 years and four more for more than 300,000 years each," Glatzmaier said. "All the cases but one exhibited magnetic field reversals. The most Earth-like case as far as reversals go was one in which the heat flux was uniform across the boundary. We also tried what we thought would be a more geophysically realistic case, in which the heat flux traced the Pacific 'Ring of Fire,' but this produced less Earth-like reversals. This suggests that the variations in heat flux over the Earth's core-mantle boundary may be less than geophysicists have imagined. Further simulations at much higher resolution are needed."

For that, the extraordinary computational power now coming on line will certainly be required. "We will also need the transparency and persistence that a national computational infrastructure can supply," Glatzmaier said. "This will give us greater confidence in our simulations of the dynamics deep within the Earth." --MM *