Potential Vorticity of the Madden-Julian Oscillation

This study explores the extent to which the dynamical structure of the Madden Julian oscillation (MJO), its evolution, and its connection to diabatic heating can be described in terms of potential vorticity (PV). The signature PV structure of the MJO is an equatorial quadrupole of cyclonic and anticyclonic PV that tilts westward and poleward. This PV quadrupole is closely related to positive and negative anomalies in precipitation that are in a swallowtail pattern extending eastward along the equator and splitting into off-equatorial branches westward. Two processes dominate the generation of MJO PV. One is linear, involving MJO diabatic heating alone. The other is nonlinear, involving diabatic heating and relative vorticity of perturbations spectrally outside the MJO domain but spatially constrained to the MJO convective envelope. The MJO is thus partially a self-sustaining system and partially a consequence of scale interaction of MJO-constrained stochastic processes. Convective initiation of the MJO over the Indian Ocean features a swallowtail pattern of negative anomalous precipitation and associated anticyclonic PV anomalies at the early stage, and increasing cyclonic PV generation straddling the equator in the midtroposphere due to increasing positive anomalies in precipitation. These lead to the swallowtail pattern in positive anomalous precipitation and the associated PV quadrupole that signifies the fully developed MJO. The equatorial Kelvin and Rossby waves bear PV structures distinct from that of the MJO. They contribute insignificantly to the structure and generation of MJO PV. Solely based on the PV analysis, a hypothesis is proposed that the fundamental dynamics of the MJO depends on neither Kelvin nor Rossby waves.