Collaborative Research: CMG: Predictability and Dynamics of Models of Quasigeostrophic Turbulence and Their Low-Dimensional Truncations

点击翻译按钮获取中文摘要

This project will develop new mathematical strategies for quantifying the predictability of complex geosystems. One part of the project will quantify the predictability of deterministic truncations of the doubly-periodic, two-layer representations of oceanic and atmospheric flows, derived by Galerkin projections, and compare this to the rate of loss of information in the full two-layer model. Loss of information will be measured by using relative entropy. The behavior of the spectra of Lyapunov exponents of the models will also be compared. The study will examine whether signatures of low-dimensional chaotic structures can be found in solutions of the full two-layer problem. The direct calculation of relative entropy will be compared with estimates derived from moments. A second part of the project will extend this type of analysis to stochastic extensions of low-dimensional models with a view to searching for changes in predictability and in the nature of the low-dimensional chaotic structures. The project will conclude with further statistical tests to describe the behavior of climatological variables, e.g. to examine transition pathways between regimes. This research will advance knowledge and understanding of mid-latitude atmospheric processes. Fundamental questions such as the way in which low-dimensional phase space structures are affected by intrinsic stochastic noise and how to develop reduced models that represent low-frequency variability of the atmosphere will be addressed. In addition, novel numerical methods applicable to the simulation and predictability analysis of a wide range of models in atmosphere/ocean science will be developed.