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

用于缓解气候变化战略的政策建议的简单气候模型中海洋热吸收的表示通常基于潜在温度的某种平均形式的一维垂直平流/扩散方程 (VAD) 的变体。在此类模型中，通常调整有效平流和湍流扩散以模拟给定目标气候模型的行为。然而，由于这种“行为”校准的统计性质通常会掩盖有效扩散和平流对负责海洋热量吸收的实际物理过程的确切依赖性，因此很难理解其局限性以及如何改进 VAD。本文提出了 VAD 的物理校准，旨在为负责海洋热量吸收的过程提供有效扩散和平流的明确可追溯性。这种构造依赖于使用潜在温度坐标的潜在温度的完整三维平流扩散的粗粒化。这种公式的主要优点是参考温度剖面的时间演变完全是由于始终为正定的有效扩散率与发生在表面的水团转换之间的竞争，如经典水团分析文献中所述。这些量在当今气候和全球变暖实验的数值模拟中进行评估。在这个框架中，