Triggered Convection, Gravity Waves, and the MJO: A Shallow-Water Model

The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection.