Asymptotic Models for Tropical Intraseasonal Oscillations and Geostrophic Balance

Abstract

AbstractIn the tropics, rainfall is coupled with waves in the form of, for example, convectively coupled equatorial waves (CCEWs) and the Madden–Julian oscillation (MJO). In perhaps the simplest viewpoint of CCEWs, the effects of moisture and convective adjustment can predict the basic aspects of their propagation and structure: reduced propagation speeds and reduced meridional length scales. Here, a similar simple viewpoint is investigated for the MJO’s propagation and structure. To do this investigation, budget analyses of a model MJO are first presented to illustrate and motivate the asymptotic scaling assumptions. Asymptotic models are then derived for the MJO. In brief, the structure of the asymptotic MJO is described by a tropical geostrophic balance, and the slow propagation arises from the dynamics of moist static energy. To be specific, if the moist static energy has a background vertical gradient that is asymptotically weak (i.e., a moist stability that is nearly neutral), then it supports a slowly propagating wave. Beyond these main aspects, other processes also have an influence, such as eddy diffusion of moisture. In comparing the simple viewpoints of CCEWs and the MJO, one main difference is in the propagation speeds: relative to a dry wave speed of 50 m s−1, the MJO has a speed of 5 m s−1, resulting from a reduction factor of 0.1 related to moist stability, whereas the basic CCEW speed is 15 m s−1, resulting from a reduction factor of the square root of 0.1, related to the square root of the moist stability.