Theory and evidence that the Madden-Julian Oscillation is a dispersive, convectively coupled moisture wave
Abstract:A linear wave theory for the Madden-Julian Oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. Using column-integrated moisture as a prognostic variable, a dispersion relation is derived that solely depends on the convective adjustment timescale, a parameter that indicates the amount of moisture available for propagation and the distance that free Kelvin waves are able to travel in the presence of dissipation.
The dispersion relation adequately describes the MJO's signal in the wavenumber-frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of the time varying field of outgoing longwave radiation, it is estimated that that the MJO's group velocity is 2/5 as large as its eastward phase speed. This dispersion is the result of the anomalous winds in the Kelvin and Rossby wave responses modulating the mean distribution of moisture such that the moisture anomaly propagates eastward while wave energy propagates westward.
Additionally, it is found that cloud-radiation feedbacks cause growth of the moist wave to be largest at the planetary scales. It is hypothesized that this scale selection mechanism is the result of upper-level cloudiness exhibiting a larger zonal extent than precipitation. The longwave radiative heating from these upper-level clouds causes an expansion of the region of ascent under weak-temperature gradient balance.