The interpretation of upscale temperature flux in multiscale models of the equatorial troposphere

An interesting question for both observations and theory is how much of an upscale eddy temperature flux convergence is actually mean heating on the planetary scales. It has been recognized (Neelin 1989) that momentum flux convergence driving a Gill model can be interpreted as direct heating driving the Gill model, in addition to a vertical/meridional balanced flow. In this paper, we elaborate on this observation in the context of the IPESD multiscale models for the tropical atmosphere (Majda & Klein 2003), and apply these ideas to recent multiscale models of the MJO \cite{mb,biel,biel1}. In particular, reversing Neelin's argument in order to remove components of an upscale temperature flux convergence, we show that the meridional temperature flux convergence can always be removed in favor of a momentum flux convergence. This transformation is made at the expense of introducing a vertical/meridional, Hadley-like flow localized to the region containing synoptic scale heating fluctuations, which is weaker than the balanced synoptic scale fluctuating flow which already persists there.

In cases where there is some zonal symmetry in the synoptic scale heating fluctuations, the vertical component of the temperature flux convergence can also be removed in favor of a momentum forcing and at the expense of introducing a vertical/zonal, Walker-like flow localized to the heating region. Unlike the case of the meridional component of the temperature flux convergence, the vertical/zonal flow induced by removing the vertical component of the temperature flux convergence is of the same order of magnitude as the synoptic scale fluctuations. The symmetry required of the heating is not so stringent as to be unrealistic, and, in fact, the MJO models of \cite{mb,biel} contain exactly these symmetries. Furthermore, the solvability condition for such solutions to exist requires that convective envelopes not move westward. In the case where the zonal symmetries are not exact, we show that a portion of the heating can, nonetheless, be transformed into momentum forcing.

Examples of the induced momentum flux convergence for the MJO models of Majda & Biello (2004) and Biello & Majda (2005) are considered.