Poleward energy transport: is the standard definition physically relevant at all time scales?

Poleward energy transport in the atmosphere and oceans constitutes an important branch of the global energy budget, and its role in the climate system has been the subject of many studies. In the atmosphere, the transport is affected by “eddies” and large scale meridional cells, both with zero net mass transport across latitude circles, but also partly by processes associated with a net transport of mass across latitude circles. The latter must cease to operate in steady state, but they may be significant when time variability of the heat budget is considered. Indeed, examination of reanalysis data on short (daily to monthly) timescales shows that mass variations on these timescales result in surprisingly large fluctuations (in excess of 1015\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{15}$$\end{document} W = 1 PW) in the poleward heat transport. These fluctuations are referred to as “extensive”, for they primarily alter the mass integrated energy of the region considered, but not its averaged value. It is suggested that extensive fluctuations mask more meaningful climate signals present in the heat transport variability ​on monthly and interannual timescales, and a new formulation is proposed to isolate the latter. This new formulation is applied successfully to reanalysis data and climate model simulations.