The Effects of Convective Parameterization on Simple Linear Models of the Madden-Julian Oscillation

Abstract

Simple linear models of the Madden-Julian Oscillation (MJO) attempt to explain the MJO’s planetary scale and slow eastward propagation using linearized equations of motion with key physical processes represented by parameterizations. Of particular interest is the parameterization used in many recent models to represent the coupling between dry dynamics and moist convection. Key questions remain concerning the functional form of the parameterization as well as the parameter values estimated previously. In this work, a systematic comparison of two convective parameterizations common in MJO models is performed. It is found that the sensitivity of convection to temperature anomalies is a strong control on both the propagation and growth of MJO-like model solutions. A small but non-zero temperature sensitivity results in an increase in the phase speed of the wave at all scales, while removing temperature sensitivity entirely results in a reduction in phase speed for scales smaller than $k=2$. Temperature sensitivity also acts as a scale selection mechanism; reduced temperature sensitivity results in stronger growth of the $k=1$ solution and strong damping of smaller waves. Additionally, changes in temperature sensitivity result in changes to the horizontal structures of the wave, and changes to the phase relationships between the moisture, temperature, and horizontal wind fields.