The Effective Vertical Advection-Diffusion Balance

Abstract:

The capacity of the world ocean to transfer heat to deeper levels is a crucial factor in setting the magnitude and temporal evolution of the global temperature response under transient climate change. A traditional framework to discuss the vertical ocean heat balance is the classic upwelling-diffusive model of Munk [1966] between upwelling of cold abyssal waters and downward diffusion of warm waters. This simple framework is also often used to interpret (and predict) transient heat uptake under climate change. However, this is done in an ad-hoc manner, with little acknowledgment of the complex physics hidden behind the vertical velocity w and diffusivity k_ν of the classic model (advection of heat by the mean and eddy circulation, diffusion along and across surfaces of constant density, deep convection). Here, we derive an effective vertical velocity and an effective diffusivity for each advective and diffusive process from the steady-state temperature tendencies of two models, an eddy-parameterizing (HadCM3) and an eddy-permitting climate model (HiGEM). For both models, we find that both the effective vertical velocity and diffusivity change sign in mid-depth, highlighting the two physical regimes in which the residual advection is balanced by diapycnal diffusion (deep ocean) and isopycnal diffusion (upper to mid-depths). These findings are at odds with common practices which assume that w and k_ν are positive constants (in space and time), but is consistent with previous studies of the modeled heat balance. We further present the time-evolution of the effective quantities under an idealized transient climate change simulation. We demonstrate that these spatial and time variations are key to evaluate the transient heat uptake. Implications for the use of simple upwelling-diffusive models to interpret transient heat uptake will be discussed.