An Idealized Semi-Empirical Framework for Modeling the Madden–Julian Oscillation

Abstract

Abstract The authors present a simple semi-empirical model to explore the hypothesis that the Madden–Julian oscillation can be represented as a moisture mode destabilized by surface flux and cloud–radiative feedbacks. The model is one-dimensional in longitude; the vertical and meridional structure is entirely implicit. The only prognostic variable is column water vapor W. The zonal wind field is an instantaneous diagnostic function of the precipitation field. The linearized version of the model has only westward-propagating (relative to the mean flow) unstable modes because wind-induced surface latent heat flux anomalies occur to the west of precipitation anomalies. The maximum growth rate occurs at the wavelength at which the correlation between precipitation and surface latent heat flux is maximized. This wavelength lies in the synoptic- to planetary-scale range and is proportional to the horizontal scale associated with the assumed diagnostic wind response to precipitation anomalies. The nonlinear version of the model has behavior that can be qualitatively different from the linear modes and is strongly influenced by horizontal advection of moisture. The nonlinear solutions are very sensitive to small shifts in the phasing of wind and precipitation. Under some circumstances nonlinear eastward-propagating disturbances emerge on a state of mean background westerlies. These disturbances have a shocklike discontinuous jump in humidity and rainfall at the leading edge; humidity decreases linearly and precipitation decreases exponentially to the west.