Mathematical models for the tropical troposphere

The Fluctuation-Dissipation Theorem (equivalently Linear Response Theory) predicts a relation between the natural quasi-random behaviour of a system and its response to external forcing. This project will examine the applicability of these ideas to the tropical
troposphere and the implications for important aspects of weather and climate prediction. The student will consider recently formulated mathematical models for the tropical troposphere that represent the key interactions between dynamics, radiation and moist processes. Many of these models have been derived in attempting to understand a particular aspect of tropical variability -- the Madden-Julian Oscillation -- the mechanism for which remains a subject of vigorous debate. The student will extend study of these models to examine the relation between forced response and variability, modifying and generalising them as appropriate.