2005 Computerworld Honors Program

	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.