Cumulus Convection and the Madden-Julian Oscillation of the Tropical Troposphere

Parameterizations of cumulus convection for use in large scale numerical models of the atmosphere are classified according to whether they are based on an energy equilibrium principle or on a balance between the supply of mass or moisture and its consumption by convection. Though some of the most popular cumulus parameterizations are based on mass or moisture balance, I argue that energy balance is a more appropriate governing principle. Physical consistency and the absence of spurious short wavelength instabilities are points in its favor. A simple energy equilibrium parameterization with a minimal representation of precipitation processes is then described, with the objective of reducing the convective parameterization problem to its essential elements. This model is first shown not to exhibit small scale instabilities. When wave-related variations in the surface entropy flux are included, it is then found (in agreement with other energy balance models) to support large scale waves similar to the observed Madden-Julian oscillation of the tropical troposphere. The characteristic period of the waves is related to the time needed