Space–Time Spectral Analysis of the Moist Static Energy Budget Equation

Abstract

Abstract The budget of column-integrated moist static energy (MSE) is examined in wavenumber–frequency transforms of longitude–time sections over the tropical belt. Cross-spectra with satellite-derived precipitation (TRMM-3B42) are used to emphasize precipitation-coherent signals in reanalysis [ERA-Interim (ERAI)] estimates of each term in the budget equation. Results reveal different budget balances in convectively coupled equatorial waves (CCEWs) as well as in the Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances. The real component (expressing amplification or damping of amplitude) for horizontal advection is modest for most wave types but substantially damps the MJO. Its imaginary component is hugely positive (it acts to advance phase) in TD-type disturbances and is positive for MJO and equatorial Rossby (ERn1) wave disturbances (almost negligible for the other CCEWs). The real component of vertical advection is negatively correlated (damping effect) with precipitation with a magnitude of approximately 10% of total latent heat release for all disturbances except for TD-type disturbance. This effect is overestimated by a factor of 2 or more if advection is computed using the time–zonal mean MSE, suggesting that nonlinear correlations between ascent and humidity would be positive (amplification effect). ERAI-estimated radiative heating has a positive real part, reinforcing precipitation-correlated MSE excursions. The magnitude is up to 14% of latent heating for the MJO and much less for other waves. ERAI-estimated surface flux has a small effect but acts to amplify MJO and ERn1 waves. The imaginary component of budget residuals is large and systematically positive, suggesting that the reanalysis model’s physical MSE sources would not act to propagate the precipitation-associated MSE anomalies properly.