An Air–Sea Coupled Skeleton Model for the Madden–Julian Oscillation

Abstract

his work is an extension and improvement of the minimal Madden?Julian oscillation (MJO) ?skeleton? model developed by Majda and Stechmann, which can capture some important features of the MJO?slow eastward propagation, quadrupole-vortex structure, and independence of frequency on wavelength?but is unable to produce unstable growth and selection of eastward-propagating planetary waves. With the addition of planetary boundary layer frictional moisture convergence, these deficiencies can be remedied. The frictional boundary layer ?selects? the planetary-scale eastward propagation as the most unstable mode, but the dynamics remains confined to atmospheric processes only. Here the authors study the role of air?sea interaction by implementing an oceanic mixed-layer (ML) model of Wang and Xie into the MJO skeleton model. In this new air?sea coupled skeleton model, the features of the original skeleton model remain; additionally, the air?sea interaction under mean westerly winds is shown to produce a strong instability that selectively destabilizes the eastward-propagating planetary-scale waves. Although the cloud?shortwave radiation?sea surface temperature (CRS) feedback destabilizes both eastward and westward modes, the air?sea feedback associated with the evaporation and oceanic entrainment favors planetary-scale eastward modes. Over the Western Hemisphere where easterly background winds prevail, the evaporation and entrainment feedbacks yield damped modes, indicating that longitudinal variation of the mean surface winds plays an important role in regulation of the MJO intensity in addition to the longitudinal variation of the mean sea surface temperature or mean moist static stability. This theoretical analysis suggests that accurate simulation of the climatological mean state is critical for capturing the realistic air?sea interaction and thus the MJO.