Adaptive-mesh Grid Techniques for Climate Modeling on Millennial Time Scales

	This visualization shows small-scale flow impinging a mountain using three levels of refinements on the cubed-sphere mesh. Operator integration factor splitting is employed for advancing the solution in time, enabling large time steps (360 seconds) even at a fine resolution of 70 km squared. This simulation approach has the potential to improve forecast accuracy and reduce model running time on current and upcoming supercomputer architectures. View animation (106 MB mpeg).
	Steady-state solution to the shallow water equations is compared in two different adaptive dynamical cores. Introducing a refinement into the balanced steady-state flow for the finite volume dynamical core (left) produces a counterintuitive result: the error grows! This does not occur with the spectral-element dynamical core (right, finer scale), which means this new core shows great promise as a replacement for the dynamical core used in the Community Climate Simulation Model (CCSM) and other atmospheric models currently in production.

Weather and climate simulation are extremely complex problems that require many long-duration computer simulations of the Earth's atmosphere. Recently, attempts have been made to improve the accuracy of long-duration models by simulating localized flow structures such as hurricanes. Simulating such details requires higher resolution and is required by applications in the atmospheric and air-quality communities, at operational centers attempting to forecast significant weather events, and for research endeavors that focus on the dynamics of severe storms and tornadoes.

Recent developments in computational mathematics techniques are being applied to existing models to help them simulate local structures such as storms and fronts. We are applying adaptive-mesh grid techniques to atmospheric models, and this promotes collaboration between the mathematicians who develop these methods and meteorologists who model and study such events. Weather modelers worldwide are striving to increase model resolution, but their methods have been limited to only reducing the spacing between grid points everywhere, which drastically increases computer time. U.S. modelers are currently trailing in this approach because it requires such close interaction between atmospheric modelers, computational scientists, and computer scientists. Our new method employs techniques designed to leapfrog that strategy: we are developing more efficient models that can automatically hone in on localized structures with high precision while simulating other areas with lower resolution. Further, this approach is tailored to operate efficiently on current and upcoming computer architectures.

This new methodology was compared with a low-order dynamical core for standard test cases, and the results were startling. Our new high-order approach is not only more efficient computationally, but for the same number of grid points, it was more precise and less diffusive. Less diffusivity allows simulations of thousands of years of atmospheric processes without degradation. Also, our tests of the time stepping showed greatly improved efficiency. Efforts are now being applied to a new adaptive global weather model that will run on petascale supercomputers.

This effort supports NCAR's strategic priorities of "Conducting research in computer science, applied mathematics, statistics, and numerical methods," "Developing community models," and "Improving prediction of weather, climate, and other atmospheric phenomena." It will yield more efficient and accurate models, help reinforce NCAR's image as a leader in cutting-edge numerical methods, and may set the standard for next-generation climate and weather models. By using the best applications available, NCAR's atmospheric modeling community can concentrate their efforts on improving our understanding of the planet.

This project exploring adaptive-mesh grid techniques in spectral-element dynamical cores is supported by the NSF with awards 0222282, 0530845, and Core funding.