  The MaddenJulian 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, multi-scale features, and
quadrupole structures, remains elusive. In this study, we use a shallow water
model to simulate the MJO. In our 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. Slowly eastward propagating (MJO-like) signals and red noise spectra
are observed in our simulations. In the time-longitude domain, MJO-like signals
with multi-scale structures are observed. In the Fourier domain, spectral peaks
associated with the MJO-like signals are observed. In the longitude-latitude
map view, quadrupole vortex structures associated with the MJO-like signals are
observed. We propose that the simulated MJO signal is an interference pattern
of westward and eastward inertia-gravity(WIG and EIG) waves. Its propagation
speed is one 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 number density of
convection events. Our results suggest that the MJO perhaps is not a
large-scale low-frequency wave, in which convection acts as quasi-equilibrium
adjustment. Small-scale high-frequency waves might be important.
