Super-resolution solar model achieves order out of chaos
Over the past few decades, computer models of the Sun's interior have matured, showing that turbulent flows of plasma create a chaotic magnetic tangle. And after observing the Sun's surface for hundreds of years, scientists know that order emerges from that tangle in the form of the solar cycle.
When run at relatively low resolution, three-dimensional models of the Sun have been able to capture the solar cycle, which includes a predictable flip-flopping of the Sun's magnetic field about every 11 years. But something puzzling would happen when researchers increased model resolution in an effort to explore smaller-scale magnetic processes: the large-scale patterns associated with the solar cycle could no longer be seen.
A new study published in the journal Science, shows that, for the first time, the Sun's large-scale patterns can re-emerge when a model's resolution is pushed even further, to a scale finer than any ever attempted. To perform the pioneering experiment, the research team—led by Hideyuki Hotta, of Chiba University in Japan, and including Matthias Rempel, of the National Center for Atmospheric Research (NCAR), and Takaaki Yokoyama, of the University of Tokyo—harnessed two of the world's most powerful supercomputers: NCAR's Yellowstone and the K computer at Japan's RIKEN Advanced Institute for Computational Science.
The experimental results give scientists important insight into how the Sun's magnetic fields, both tiny and massive, can co-exist and interact without destroying the solar cycle.
"It's like our model has to travel through this valley to get to the other side," said Rempel, a senior scientist at NCAR's High Altitude Observatory and a co-author of the paper. "Many other models of the same type are still on their way into the valley."
The existence of this conceptual valley is likely related to the fact that solar dynamos—the process by which the energy of turbulent flows of plasma is converted into magnetism—occur on both large and small scales inside the Sun. The large-scale solar dynamo is thought to be responsible for the solar cycle. But small-scale solar dynamos also exist, though their effects on the global scale are not well understood.
"There is a lot of small-scale turbulence on the Sun. The smallest eddies, or magnetic whirlpools, you find can be just meters, or even centimeters, in size," Rempel said. "The question is, when you have both large-scale and small-scale dynamos operating at the same time, how do they influence each other?"
Scientists have tried to answer this question by increasing the resolution of their solar models so that the large-scale and small-scale processes could be "seen" at the same time. But in these earlier simulations, the small-scale turbulence appeared to interfere with the large-scale dynamo, and the solar cycle pattern dissipated.
In the new study, the researchers attacked the problem by pushing the model resolution even further. The result was that the model established connections between the small and large magnetic fields, allowing the solar cycle pattern to re-emerge.
Essentially, the models used in previous attempts could see the small-scale phenomena, but it may be that they couldn't see them well enough.
"In the past, the resolution was not high enough to really grow the small-scale component and see its full impact," Rempel said.
Viscosity and computing power
Rempel thinks the key to building the large-scale patterns may be found in how models of differing resolution represent the apparent viscosity of the Sun's plasma. At low resolution, models assume that the plasma is more viscous—flowing more like honey than water—which allows order to emerge in the model system.
But as the resolution increases, the equations that govern the model actively lower the plasma's viscosity. This allows small-scale interactions to begin to play out, but makes it more difficult for large-scale patterns to form.
When the model was pushed to much higher resolution for the new study—about four times higher than previous attempts—the model's viscosity was dropped further still. But because the small-scale dynamos were able to fully evolve in the simulation, the model was able to let new magnetic fields form and grow, something that didn't happen before. The result was that the snarl of new magnetic fields created a level of magnetic stress that caused the plasma to act as if it was more viscous, even though it wasn't.
While some innovative modeling code allowed the scientists to go to a higher resolution using fewer computing resources than would normally be required, the effort still demanded a lot of computing power. The sheer amount of computing resources needed—and the scarcity and expense of those resources—mean that, practically speaking, many solar physicists may not be able to run their models at a resolution high enough to maintain the Sun's large-scale pattern.
Hotta first came to UCAR as a visiting researcher in 2010, returning in 2011 and 2012 to work with Rempel on thesis projects he was conducting at the University of Tokyo. UCAR scientists were impressed with Hotta's computer code early on, as he used a novel approach to increase computer model fidelity in examining solar dynamo and stellar convection problems.
"Whenever Hideyuki Hotta was running his simulations on Yellowstone, we'd see a significant jump in efficiency on the supercomputer," said Dave Hart, who manages the User Services Section of NCAR's Computational and Information Systems Laboratory (CISL), which is charged with operating NCAR's supercomputing resources for the scientific community. "We can’t say with absolute certainty that his code was responsible, but it seemed to happen too often to be a coincidence."
The results of Hotta's study offer at least a stop-gap solution for scientists trying to better understand the complicated interplay of the Sun's dynamos. The study suggests that researchers who can't go to an extremely high resolution may be able to get similar results by artificially increasing the model's viscosity.
More important, the new study offers a look at why increasing the viscosity would work.
"The Sun is magnetic on all scales," Rempel said. "We have shown that it's really important to understand this and account for how those magnetic fields interact."
Supercomputing for super resolution
To complete the study, Rempel and Hotta used 15 million core hours on the NCAR-Wyoming Supercomputing Center's Yellowstone system. Their system allocations were awarded through the competitive NCAR Strategic Capability program, which facilitates large-scale, shorter-term supercomputing projects.
"Yellowstone provided the resources required to carry out a large number of high-resolution calculations, which we used to determine the detailed setting of an ultra-high resolution calculation," Hotta said. "Since the data analysis system at NCAR's Computational and Information Systems Laboratory shares storage with Yellowstone (unlike Japanese supercomputers), we were able to see the detailed results of our calculations quickly, without transferring huge amounts of data."
H. Hotta, M. Rempel, and T. Yokoyama, Large-scale magnetic fields at high Reynolds numbers in magnetohydrodynamic simulations, Science, doi: 10.1126/science.aad1893
National Center for Atmospheric Research
University of Tokyo
Ministry of Education, Culture, Sports, Science and Technology (Japan)
Joint Institute for Computational Fundamental Science (Japan)
Project for Solar-Terrestrial Environment Prediction (Japan)