Mathematical Modeling with Multidisciplinary Applications

CHAPTER 19

MARKOV-JUMP STOCHASTIC MODELS FOR TROPICAL CONVECTION

BOUALEM KHOUIDER

Mathematics and Statistics, University of Victoria, Canada

19.1 INTRODUCTION

Atmospheric convection is the process through which warm and moist air parcels rise from the surface, condense liquid water and form cumulus clouds. This results in precipitation and heavy storms. The process of condensation is accompanied by the release of latent heat, which is associated with the phase change of water from vapor to liquid and/or ice. In the tropics, moist convection constitutes a major source of energy for both local and large-scale circulations. Precipitation patterns in the tropics are organized into cloud clusters and superclusters on a wide range of scales; they range from the convective cell (the cumulus cloud) of 1 to 10 km, to planetary scale waves with oscillation periods of 40 to 60 days. Due to the complex interactions between the local processes of convection and the large-scale waves, climate models fail to properly capture tropical circulation patterns and their effect on the global circulation. In a climate model, the governing equations are discretized on a coarse mesh of roughly 100 km to 200 km and the effects of processes that are not resolved on such grids are represented by a parameterization also called a subgrid model. According to the last report of the United Nations’ Intergovernmental Panel on Climate Change (IPCC), the interactions of clouds and the climate system is one of the ...