Global Heat Balance and Heat Uptake in Potential Temperature Coordinates

Abstract

The representation of ocean heat uptake in Simple Climate Models 7 used for policy advice on climate change mitigation strategies is often based on 8 variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for 9 some averaged form of potential temperature. In such models, the effective ad10 vection and turbulent diffusion are usually tuned to emulate the behaviour of 11 a given target climate model. However, because the statistical nature of such a 12 “behavioural” calibration usually obscures the exact dependence of the effective 13 diffusion and advection on the actual physical processes responsible for ocean heat 14 uptake, it is difficult to understand its limitations and how to go about improving 15 VADs. This paper proposes a physical calibration of the VAD that aims to provide 16 explicit traceability of effective diffusion and advection to the processes responsi17 ble for ocean heat uptake. This construction relies on the coarse-graining of the 18 full three-dimensional advection diffusion for potential temperature using poten19 tial temperature coordinates. The main advantage of this formulation is that the 20 temporal evolution of the reference temperature profile is entirely due to the com21 petition between effective diffusivity that is always positive definite, and the water 22 mass transformation taking place at the surface, as in classical water mass analy23 ses literature. These quantities are evaluated in numerical simulations of present 24 day climate and global warming experiments. In this framework, the heat uptake 25 in the global warming experiment is attributed to the increase of surface heat flux 26 at low latitudes, its decrease at high latitudes and to the redistribution of heat 27 toward cold temperatures made by diffusive flux. 28