Our understanding of tropical meteorology and its ability to influence the middle latitudes is the major stumbling block to increasing medium term (two week) weather prediction over the United States (midlatitudes). In this project, the PI proposes to study multiscale asymptotics for the PDEs which govern tropical atmospheric waves and their connection to midlatitude waves, extending the PI's previous work in the field. The three aspects of this project are: (1) A boundary layer asymptotic analysis connecting tropical waves in the weak temperature gradient approximation to quasi-geostrophic mid-latitude waves through a new subtropical matching layer; (2) The effect of the (large scale) climatological flow (the Hadley circulation) and the sub-grid circulation (moist convection) on the Intraseasonal Multiscale Moist Dynamics models of tropical waves and the Madden-Julian Oscillation (MJO). This involves the derivation of a closed planetary scale description of the MJO using the PI's stochastic sub-grid models and multi-scale asymptotic theory; (3) The analytic and numerical study of three non-linear PDEs - two of which are non-local - which arise from the analysis of tropical atmospheric waves.
The dynamics of the atmosphere in the middle latitudes has long been studied as a problem of both practical interest (for understanding weather patterns over North America and Europe) and of theoretical interest (since the equations which govern atmospheric dynamics displayed a rich set of behavior as soon as scientists began studying them). More recently, however, we have realized that the tropical atmosphere also provides an enormous set of unsolved problems both for practical purposes and for mathematical theory. Computer simulations have shown that a better understanding of tropical atmospheric dynamics will not only improve our understanding of tropical weather but it will greatly increase our understanding of weather patterns in the middle latitudes, thereby improving weather predictions over North America and Europe. This project focuses on two general phenomena: (1) how tropical weather is organized on very large scales and (2) how tropical weather patterns interact with midlatitude weather patterns and thereby modify midlatitude weather. In the process of studying these phenomena, the PI has found new simplifications to the complicated equations of atmospheric dynamics - these equations are approximations which elucidate the important aspects of tropical organization and tropical/midlatitude interactions. This work is an example of scientific problems creating new mathematics and careful mathematical analysis creating better scientific theories.
