The Madden-Julian Oscillation and Convective Aggregation

Abstract

The Madden-Julian oscillation (MJO) is a region of enhanced precipitation which forms every 30-60 days over the Indian Ocean and slowly propagates to the east over the Pacific. Despite being the dominant mode of intraseasonal variability in the tropical troposphere, most numerical models struggle to accurately predict the MJO, and this issue is compounded by a lack of theoretical understanding. In this thesis we will discuss progress towards a theoretical model of the MJO. Whilst there have been many proposed theoretical models in the 50 years since its discovery, none are universally accepted. We will even show that one recent model, which showed promising MJO-like behaviour in a two-dimensional model with minimal assumptions, relies on insufficient numerical resolution. In a separate phenomenon, known as convective aggregation, convection in `cloud-resolving' numerical models is sometimes observed to spontaneously transition from homogeneous conditions to a single persistent precipitating region balanced by dry descent in the remainder of the domain. Numerical models which allow convective self-aggregation tend to have a more robust representation of the MJO, so these phenomena may be linked. We will investigate a novel extension of a previous theoretical model of convective aggregation to include large-scale dynamics. The previous model is simply based on a diffusion equation for moisture with a source/sink term representing the combined effects of precipitation, evaporation and cloud physics. The new extended model adds advection to the moisture equation alongside linearised single-layer dynamics with a moisture dependent heating term. At small scales the new model is similar to the old and exhibits formation and growth of distinct moist regions. At larger scales the behaviour is modified by dynamics, allowing a theoretical description of the impact of rotation on convective aggregation. Uniform rotation and damping limit the scale of aggregated regions. On an equatorial beta-plane, the organisation into moist and dry regions is limited to a region localised near the equator, with possibility of longitudinal propagation do to the asymmetry of advection by the Matsuno-Gill response to the moist heating. In the simplest version of this model the equatorial behaviour is not convincingly MJO-like, with too slow propagation and an incorrect horizontal structure, however the inclusion of an additional physical effect, the moistening of the interior flow due to convergence in the boundary layer, gives behaviour that is more similar to the observed MJO in both spatial structure and propagation speed. The model derived and analysed in this thesis gives insight into the link between convective aggregation and the MJO and potentially provides a basis for quantitative interpretation for several aspects of tropical variability on intraseasonal time scales, both that observed in the real atmosphere and that observed in state-of-the-art numerical simulations.