Systematic Mathematical Strategies for Multi-Scale Stochastic Modeling and Uncertainty in Atmosphere/Ocean Science

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One of the grand challenges of contemporary science is a comprehensive predictive model for the atmosphere and coupled climate system. This is one of the most difficult multi-scale problems in science today because there is an incredible range of strongly interacting anisotropic nonlinear processes over many spatio-temporal scales; contemporary comprehensive computer models, GCM's, are currently incapable of adequately resolving or parametrizing many of these interactions on time scales appropriate for seasonal prediction as well as climate change projections. Thus, the multi-scale problems in atmosphere/ocean dynamics serve as important prototypes for developing new systematic multi-scale strategies which are valuable in other scientific disciplines ranging from nanotechnology to macro-molecular dynamics to protein folding, etc. The societal impacts for these efforts are also large; it has been estimated recently that a one-month increase in lead time for El Nino prediction would save $100 billion worldwide. Basic questions which drive climate research are the prediction of the weather from 1 to 14 days, the prediction of climate variations on seasonal to yearly time scales, and finally, climate-change projections on decadal and centennial time scales as well as quantifying the uncertainty associated with these predictions. One of the striking recent observational discoveries is the profound impact of tropical variations on all of these problems. The primary influence of the tropics occurs through the interaction and organization of clouds into clusters, super-clusters, and planetary-scale dynamics, an inherently fully nonlinear multi-scale process. For climate change, water vapor is the most important greenhouse gas and the microphysical processes in clouds are a key mechanism for radiative feedback. In fact, only a 4% change in average cloudiness would overwhelm the effects of CO2 in climate change. Current evidence suggests that a few global planetary teleconnection patterns, such as the Pacific North America Oscillation, often summarize the weather and climate impact of the tropics for the mid-latitude atmosphere. Since it will be impossible to run resolved coupled atmosphere/ocean comprehensive numerical models for climate change, reduced models involving these basic large scale patterns are of central importance. Majda proposes to continue work on some of the most important issues and stumbling blocks for medium-range climate forecasting through the tools of modern applied mathematics, centering around novel strategies for: 1) multi-scale interaction of clouds, convection, and planetary waves in the tropics; 2) stochastic modeling of unresolved features for both the atmosphere/ocean and for quantifying uncertainty and predictive capability in complex systems through information theory. This will lead to new strategies for deterministic and stochastic parametrization of unresolved scales for the atmosphere and ocean, potentially significant low-order dynamic stochastic models for these processes, and more rigorous quantification of uncertainty in weather and climate-change predictions. Such research often has additional potential benefit for other disciplines in science and engineering; also novel issues for applied PDE's and numerical analysis are expected to arise.