An Analytical Upper Bound on Transient Ocean Heat-Uptake Efficiency from Energy Conservation
The ocean heat-uptake efficiency controls how much of the radiative forcing from rising greenhouse gases warms the surface versus the deep ocean on transient timescales, and it is a leading source of spread in near-term projections. We derive an analytical upper bound on the transient heat-uptake efficiency from a two-layer energy-balance model plus the constraint that the deep-ocean warming cannot exceed the integrated surface flux divided by the deep heat capacity. The bound depends only on observable quantities: the surface warming trend, top-of-atmosphere imbalance, and an estimate of the deep-ocean heat capacity, all available from public datasets. We propagate observational uncertainty through the bound and identify which observation most tightly constrains it. No model is run; the result is a closed-form inequality.