Suppose that most of the global mean surface warming in the past half century was due to internal variability rather than external forcing, contrary to one of the central conclusions in the IPCC/AR4/WG1 Summary for Policymakers. Let’s think about the implications for ocean heat uptake. Considering the past half century in this context is convenient because we have direct, albeit imprecise, estimates of ocean heat uptake over this period.
Set the temperature change in question, , equal to the sum of a forced part and an internal variability part: , with , so is the fraction of the temperature change that is forced. The assumption is that this is a linear superposition of two independent pieces, so I’ll write the heat uptake as .
When the surface of the Earth warms due to external forcing, we expect the Earth to take up heat. But what do we expect when the surface warms due to internal variability? Can we use observations of heat uptake to constrain ?