Zonal Momentum Budget of the Madden–Julian Oscillation: The Source and Strength of Equivalent Linear Damping

Abstract

Abstract Linear, dissipative models with resting base states are sometimes used in theoretical studies of the Madden–Julian oscillation (MJO). Linear mechanical damping in such models ranges from nonexistent to strong, since an observational basis for its source and strength has been lacking. This study examines the zonal momentum budget of a composite MJO over the equatorial western Pacific region, constructed using filtering and regression techniques from 15 yr (1979–93) of daily global reanalysis data. Two different reanalyses (NCEP–NCAR and ERA-15) give qualitatively similar results for all major terms, including the budget residual, whose structure is consistent with its interpretation as eddy momentum flux convergence (EMFC) in convection. The results show that the MJO is a highly viscous oscillation, with a 3–5-day equivalent linear damping time scale, in the upper as well as lower troposphere. Upper-level damping is mainly in the form of large-scale advection terms, which are linear in MJO amplitude but involve horizontal and vertical background flow. Specifically, the leading terms are the advection of time-mean zonal shear by MJO vertical motion anomalies and advection of MJO wind anomalies by time-mean ascent. This upper-level damping in the western Pacific is mostly confined between 10°N and 10°S. In contrast, zonal wind damping in the lower troposphere involves EMFC (budget residual) and zonal mean linear meridional advection. Stated another way, the strong upper-level damping necessitates upper-level geopotential height gradients to maintain the observed zonal wind anomalies over the time scales implied by the MJO’s low frequency. The existence of the background flow thus tends to shift MJO temperature perturbations westward so that the warm anomaly ahead (east) of the convective center is shifted back into the convection. This shifting effect is fully realized only for anomalies with a period much longer than the 3–5-day damping time.