This article is the first in a series on the nine NASA HPCC Earth and Space Sciences (ESS) Project Science Team II Grand Challenge Investigations. See story 4 for more information on the ESS project.

The sun, while a star, has distinct weather patterns that affect not only itself but the Earth as well.

"There are a number of phenomena like solar flares and eruptions on the sun, which create a very large number of very energetic charged particles that come out from the sun in the solar wind," said ESS Project Grand Challenge Investigator John Gardner of the Naval Research Laboratory (NRL), Washington, D.C. "When they reach the earth's ionosphere, they can create very large magnetic storms, which can interfere with satellites and communication systems."

With long-term investments in such resources, the world's military and space agencies wish to learn the causes of - and eventually predict - solar weather. Theory supported by observations points to magnetic energy buildup and release in the sun's corona (outer atmosphere) as the basic source, but only computation can replicate the full, 3-D dynamics. Modeling the internal dynamics and comparing them with observations has been the aim of Gardner's team of NRL, NASA Goddard Space Flight Center (GSFC) and Stanford University scientists.

A Wide Range of Scales

The sun is primarily very hot gas, or plasma, and magnetic field. The Gardner group studies the corona, which begins shortly beyond the visible surface (photosphere) and extends out to at least two solar radii before turning into the solar wind. In the corona, magnetic field dominates and heats the gas to 20 million degress Celsius, compared to 5,600 degrees at the photosphere. "The fundamental question is how the magnetic field energizes the gas" to produce observed solar activity, said NRL co-investigator Spiro Antiochos.

"One of the things that makes it a mystery is that the corona is very hot and conducts electricity very well, which makes it very difficult to dissipate the energy required to maintain the corona," explained group member Richard De Vore of NRL. "These are countervailing tendencies."

Underlying this paradox is the interaction of structures on a wide range of spatial scales - the greatest obstacle to accurate modeling of the sun. Antiochos said that structures span from 1 million kilometers down to a few meters (see illustration). All scales must ultimately be included, but "in numerical simulation, your problem is that you are limited by your grid size," Gardner said. "The challenging part is to be able to get enough resolution so you can get a physical understanding of what's happening."
An additional complication is that "there are two classes of evolution that magnetic field and plasma can undergo," Antiochos said. At global scales, one generally finds ideal evolution which is very fast and maintains the identity if every magnetic field line. At the much smaller, dissipative scales, there is resistive evolution, which is slow and allows field lines to diffuse. "If you can't get grids that are large enough, then the spacial scales on which diffusion is occurring are so close to the energy containing spatial scales that energy diffusion overwhelms the system," said NRL team member Russell Dahlburg. STUFF MISSING

Before ESS Project Science Team I funding in 1992, the group was using 64³ grids. Now, they are regularly doing 128³ simulations and a few at 256³. "As a result of [the HPCC] program, we have gotten to the point where we are actually being able to separate the ideal scale from the dissipative scale," Gardner said.

Magnetic Fluxtube Tunneling

This advance has enabled discovery of magnetic fluxtube tunneling, a new type of magnetic reconnection. Studies show that reconnect ion can generate and dissipate enough magnetic energy to fuel observable activity. Fluxtubes are bundles of magnetic field, which "will come together and exchange sections" in reconnection, Antiochos said. "Fluxtubes are like nicely stretched rubber bands. After reconnecting, fluxtubes will accelerate away from each other ... and release energy," which Dahlburg said can equal up to 1,000 atomic bombs.

"People have looked at this process analytically in 2-D and have done some work computationally, but you can get wrong impressions in 2-D," Antiochos explained. "In 3-D, you get completely different results."

Employing a 128³ spectral code on NRL's 256-node CM-5 supercomputer, Gardner's team simulated moving two fluxtubes together. "When fluxtubes are parallel, you get what you expect in 2-D physics; either the fluxtubes come together and reconnect or they bounce off each other," Antiochos said. The process becomes 3-D in the fluxtubes interact at and angle. "In 3-D, fluxtubes also can go right through each other [and] exchange those portions that are intersecting. That was a complete surprise!" Antiochos exclaimed.

These findings have implications for other coronal phenomena. "There is a class of very large flares know as two-ribbon flares," Dahlburg said. "If you look at them in hard X-rays, they are bursty. The bursts are short, lasting only one-third of a second. It is hypothesized, in the two-ribbon flare, that instead of having two large planes of magnetic field reconnect there are thousands of fluxtubes reconnecting."

In addition, reconnection plays a role in chromospheric eruptions, which occur in the narrow region between the photosphere and the corona. It also plays a role in the solar prominences, which involve cold, dense material being suspended within the hot corona, and resulting cornal mass ejections — the most spectacular of all solar activity.

Computational Techniques

In modeling these structures, spectral and finite-volume codes have proven to be effective, complementary approaches.

The high-order spectral method is useful for studying processes that require accurate resolution over a broad range of spatial scales (e.g., magnetic reconnection). Gardner's Science Team I investigation brought the CRUNCH3D Fourier collocation code from 64³ to 256³ grid points. Because of its ability to represent the dissipative physics with the greatest fidelity, CRUNCH3D was instrumental in the magnetic fluxtube tunneling discovery.

The finite-volume approach is optimal for modeling systems with flow properties that undergo large changes over short distances (e.g., shocks). Efforts have centered on 2-D and 2.5-D flux-corrected transport (FCT) codes with increased computing power doubling resolution Asymmeetric 2.5-D calculations of chromospheric eruptions showed for the first time moving magnetic islands that produce dense plasma jets resembling observed structures.

A goal of the Science Team II work is to reach 1024³ resolution in order to capture more spatial scales. Simulating the full range on near-term supercomputers, however, will require the more radical adaptive mesh refinement (AMR).

"If there are one million kilometers on each side, even 1024³ won't let you resolve the structures that form," Antiochos stressed. "Energy is put in at the global scale, but you need magnetic reconnection in a few selective, small regions." In AMR, smaller grids within the overall grid follow specific structures. "The mesh adapts to the problem being solved," DeVore said. "One of the big issues is what are the criteria you use to decide to refine here or de-refine there."

Another key problem in doing AMR efficiently is load balancing, distributing the work among hundreds of processors so they are "all busy all the time," DeVore said. The Gardner group previously focused on NRL's 256-node CM-5. They are now adapting their codes to the HPCC CRAY T3D (512 processors) and later the CRAY T3E (up to 1,024 processors).

Structures in the usn range in size from 1 million kilometers down to a few meters. Gardner's team today regularly uses simulations with 128³ grids, which allow interaction of at best three scales. One goal of their research is to reach 1024³ resolution, but encompassing all the scales on near-term supercomputers will require adaptive mesh refinement codes.

While programming scalable parallel machines is rigorous, the advantages they provide in speed and memory, and thus resolution, make them the platform of choice for solar modeling. Gardner pointed to a factor of 10 improvement from a CRAY C90 to the CM-5. Both CRUNCH3D and FCT perform at 4 gigaflops on 256 nodes and would scale to 15 gigaflops on 1,024-nodes. The CRAY T3E will allow performance of over 100 gigaflops.

The benefits of these techniques have extended to the wider super computing community with several hundred researchers having downloaded the FCT code from the HPCC Project Software Exchange and CRUNCH3D being used to study photospheric fluxtubes at the University of California, Berkeley. De Vore said that new code versions will be made as portable as possible by using MPI (Message Passing Interface) to handle communications.

Solar Weather Prediction

In tandem with computational innovation, "NRL has one of the largest solar groups in the country," Antiochos said. Members are or will be involved in analyzing data from the Yohkoh, SOHO, and TRACE satellite missions. "We can couple theory with the observations," he said, and then "isolate the essential physics with fixed-grid codes. To do the actual, detailed comparisons with observations — the true validation of the theory — you need the AMR code for quite a few of them."

"And ultimately, I think what we want is a numerical weather predictor for the sun," Gardner said, "and from that point you would be able to make predictions from observations of what is going to happen three, five, seven days down the road. We are still a ways away from that. The goal now at this stage is to understand enough about the mechanisms so that when you take observational data and you look at it, you can make some intelligent predictions about what will evolve next."

Other co-investigators on the "Understanding Solar Activity and Heliospheric Dynamics" Grand Challenge team include Judith Karpen, James Klimchuk, and Lee Phillips of NRL, Joseph Davila and Leon Ofman of GSFC, and George Roumeliotis of Stanford University.