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). The investigator studies multiscale asymptotics for the partial differential equations that govern tropical atmosphere atmospheric waves and their connection to midlatitude waves, extending his previous work in the field. The three aspects of this project are: (1) The effect of the climatological flow (the Hadley circulation) on the Intraseasonal Multiscale Moist Dynamics models of the Madden-Julian Oscillation (MJO); (2) The effect of mean shear on the non-linear interaction of equatorial Rossby or Kelvin waves with midlatitude Rossby waves; (3) The coupling of tropical waves to a stochastic model of moist convection and the derivation of a closed, single scale, stochastic model of the Madden-Julian Oscillation. This last project could yield a transformative development because it would be the first MJO model whose structure is systematically derived from multiscale asymptotics (Biello and Majda) and whose convective forcing arises from a tested model of cloud dynamics (Khouider, Biello and Majda).
The effect of small and fast phenomena on large and slower phenomena is a ubiquitous question in modern science and policy-making. In economics, for example, the question may be phrased, "How do individual actions organize to yield steady economic conditions or unstable economic conditions?" In atmospheric science, this question is manifested as "How do small scale events such as storms and storm systems organize themselves to affect the mean climate in which they sit?" While large modern computational simulations have yielded many insights into this multi-scale organization, they are limited in that the smallest structures they can resolve are still large; for example, most climate computations cannot see structures smaller than 60 miles across. So, the equations that these computers solve must resort to a model (whether empirically determined, or ad hoc) in order to describe these unresolved structures. A more systematic approach is to use techniques of modern applied mathematics in order to isolate the phenomena at each scale that are the essential elements of this multi-scale coupling. The investigator's work focuses on using these modern applied math techniques to understand the multi-scale coupling of the tropical atmosphere. Specifically, he seeks to understand how storm systems, which live for several days, organize to affect planetary scale wind patterns, which modulate over the course of several months. Furthermore, these wind patterns generate weather waves that propagate away from the tropics over the continental U.S. The investigator uses similar mathematical techniques to understand this wave generation. Improving our understanding of these phenomena will increase the accuracy of US weather forecasts.
