The MJO on the Equatorial Beta Plane: An Eastward-Propagating Rossby Wave Induced by Meridional Moisture Advection

Linearized wave solutions on the equatorial beta plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward-propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers (less than or similar to 6). The mode dispersion curve appears as an eastward extension of the westward-propagating equatorial Rossby wave solution. This mode is therefore termed the eastward-propagating equatorial Rossby wave (ERW). The zonal wavenumber-2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading-order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability-like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward-propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite-time-scale convective adjustment and less effective zonal wind-induced moistening at smaller scales. Similarities in the phase speed, preferred scale, and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.

Automated summary

This study examined linearized wave solutions on the equatorial beta plane in the presence of a background meridional moisture gradient, focusing on the eastward-propagating equatorial Rossby wave (ERW) that is unstable at planetary scales. Analysis revealed that the presence of the ERW is influenced by moisture advection, with moistening from low-level easterlies leading to instability. The study also found that the scale selection of the ERW is partly due to convective adjustments over finite time scales and less effective zonal wind-induced moistening at smaller scales.