This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The vast range of scales occurring in the Earth's climate system cannot be explicitly captured in global climate models, even on emerging petascale computers. This project will further understanding of the effects of physics at a scale that is too small to be resolved by models on the larger climate system by: 1) exploring potentially novel asymptotic expansions that provide reduced single-scale equations for each of the three important small-scale processes: convection, mesoscale eddies, and submesoscale eddies; 2) extending the asymptotic expansion technique to explicitly derive the coupling between small-scale regimes and large-scale flows; 3) developing state-of-the-art high-performance parallel codes to simulate the reduced single-scale and multiscale equations; 4) performing high-resolution simulations on high-performance computers; 5) analyzing the simulations to extend understanding of the behavior of each small-scale process, including flow dynamics, energetics, and transport properties; and 6) testing a range of existing parameterizations and superparameterizations of unresolved physics using eddy-resolving models to understand the scope and impact of our multiscale approach.
The development of coupled asymptotic expansions to study multiscale phenomena has potential applications across many fields of science and engineering, in addition to the geosciences. This research is intended to demonstrate and apply the advantages of this approach to improve mathematical and computational study of the climate system. In geosciences, the asymptotic mathematical approach has long been used to improve computation--the first numerical weather forecasts were only possible because of the quasigeostrophic asymptotic expansion. The geosciences have long led asymptotic analysis as well; among the earliest examples of matched asymptotic expansions are studies of oceanic western boundary currents, such as the Gulf Stream and Kuroshio. Finally, the research is intended to directly improve climate models' representation of small-scale physics, which will aid our goals in improved forecasting and understanding of climate and mankind's influence on it.
