Transformations for temperature flux in multiscale models of the tropics

How much of the observed planetary-scale heating in the tropics is due to eddy flux convergence? A mathematical framework to address this important practical issue is developed here. We describe a pair of velocity transformations that remove components of the upscale temperature flux in the multiscale intraseasonal, planetary, equatorial synoptic-scale dynamics (IPESD) framework derived by Majda and Klein [J. Atmos. Sci. 60: 393-408, (2003)]. Using examples from the models of the Madden-Julian Oscillation of Biello and Majda [Proc. Natl. Acad. Sci. 101: 4736-4741, (2004); J. Atmos. Sci. 62: 1694-1721, (2005); Dyn. Oceans Atmos., in press] we demonstrate that the transformation for the meridional temperature flux convergence is possible with any restrictions on the heating profile, we show under which conditions the transformation for the vertical temperature flux convergence exists and, further, that the meridional transformation leads to a reinterpretation of lower troposphere Ekman dissipation as active heating plus zonal momentum drag. The meridional temperature flux transformation and induced meridional circulation is a new, tropical wave example of the transformed Eulerian mean theory in the case of strong vertical stratification of potential temperature. The asymptotic ordering of the flows means that the removal of the meridional temperature flux convergence has implications for how planetary-scale heating rates are inferred from velocity convergence measurements.