An idealized semi - empirical framework for modeling the 1 Madden - Julian oscillation

5 We present a simple semi-empirical model to explore the hypothesis that the Madden-Julian 6 oscillation can be represented as a moisture mode destabilized by surface flux and cloud7 radiative feedbacks. The model is one-dimensional in longitude; vertical and meridional 8 structure are entirely implicit. The only prognostic variable is column water vapor, W. The 9 zonal wind field is an instantaneous, diagnostic function of the precipitation field. 10 The linearized version of the model has only westward-propagating (relative to the mean 11 flow) unstable modes, because wind-induced surface latent heat flux anomalies occur to the 12 west of precipitation anomalies. The maximum growth rate occurs at the wavelength at 13 which the correlation between precipitation and surface latent heat flux is maximized. This 14 wavelength lies in the synopticto planetary-scale range and is proportional to the horizontal 15 scale associated with the assumed diagnostic wind response to precipitation anomalies. 16 The nonlinear version of the model has behavior that can be qualitatively different from 17 the linear modes, and is strongly influenced by horizontal advection of moisture. The non18 linear solutions are very sensitive to small shifts in the phasing of wind and precipitation. 19 Under some circumstances nonlinear eastward-propagating disturbances emerge on a state 20 of mean background westerlies. These disturbances have a shock-like discontinuous jump 21 in humidity and rainfall at the leading edge; humidity decreases linearly and precipitation 22 decreases exponentially to the west. 23