Nonlinear Dynamics and Regional Variations in the MJO Skeleton

A minimial, nonlinear oscillator model is analyzed for the Madden--Julian Oscillation (MJO) "skeleton,'' i.e., its fundamental features on intraseasonal/planetary scales: (i) slow eastward phase speed of roughly 5 m/s, (ii) peculiar dispersion relation with group velocity of roughly 0, and (iii) horizontal quadrupole vortex structure. Originally proposed in recent work by the authors, the fundamental mechanism involves neutrally stable interactions between (i) planetary-scale, lower-tropospheric moisture anomalies, and (ii) the envelope of sub-planetary-scale, convection/wave activity. Here, the model's nonlinear dynamics are analyzed in a series of numerical experments, using either a uniform sea surface temperature (SST) or a warm-pool SST. With a uniform SST, the results show significant variations in the number, strength, and/or locations of MJO events, including, for example, cases of a strong MJO event followed by a weaker MJO event, similar to TOGA-COARE. With a warm-pool SST, MJO events often begin as standing oscillations and then propagate slowly eastward across the warm pool, a behavior imitating MJOs in nature. While displaying the fundamental features of the MJO skeleton, these MJO events had significant variations in their lifetimes and regional extents, and they displayed intense, irregular fluctuations in their amplitudes. The model reproduces all of these features of the MJO skeleton without including mechanisms for the MJO's "muscle,'' such as refined vertical structure and upscale convective momentum transport from sub-planetary-scale convection/waves. Besides these numerical experiments, it is also shown that the nonlinear model conserves a total energy that includes a contribution from the convective activity.