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Anomaly-diffusing energy balance models (AD-EBM) are routinely employed toanalyze and emulate the warming response of both observed and simulated Earthsystems. We demonstrate a deficiency in common multi-layer as well ascontinuous-diffusion AD-EBM variants: They are unable to, simultaneously,properly represent surface warming and the vertical distribution of heatuptake. We show that this inability is due to the diffusion approximation. Onthe other hand, it is well understood that transport of water from the surfacemixed layer into the ocean interior is achieved, in large part, by the processof ventilation---a process associated with outcropping isopycnals. We,therefore, start from a configuration of outcropping isopycnals and demonstratehow an AD-EBM can be modified to include the effect of ventilation on oceanuptake of anomalous radiative forcing. The resulting EBM is able tosuccessfully represent both surface warming and the vertical distribution ofheat uptake, and indeed, a simple four layer model suffices. The simplicity ofthe models notwithstanding, the analysis presented and the necessity of themodification highlight the role played by processes related to the down-wellingbranch of global ocean circulation in shaping the vertical distribution ofocean heat uptake.

Improved Representation of Ocean Heat Content in Energy Balance Models