Excerpt from Resplandy et al. (2018) discussing how Ocean Heat Content is related to climate sensitivity:

	Ocean heat uptake, sea level and climate sensitivity. Climate sensitivity has been estimated to fall within the range of +1.5 K to +4.5 K for a doubling of CO2 (ref. 1). The impact of an increase in the ocean heat uptake on the effective equilibrium climate sensitivity (the apparent equilibrium climate sensitivity diagnosed from nonequilibrium conditions) can be estimated using a cumulative approach on the Earth energy balance (see Fig. 2 in ref. 1):

	N=F−α∆T (3),

	where N is the global heat imbalance, which mostly consists of the ocean heat uptake; F is the radiative forcing (in W m^−2); ∆T is the increase in surface temperature (in K) above a natural steady state; and α is the climate feedback parameter (in W m^−2 K^−1), which is inversely proportional to the effective equilibrium climate sensitivity. All terms in equation (3) are time integrated over the period of interest.

	The IPCC Fifth Assessment Report gives a ∆OHC of 0.80 × 10^22 J/yr for 1993–2010, which is about 0.5 × 10^22 J/yr lower than the ∆OHC that is compatible with both APO and hydrographic constraints. By applying equation (3) to surface temperature data over the period 1991–2016 (HadCrut version 4.5, ref. 64, with a 1860–1879 preindustrial baseline), we found that the upward revision of the global heat imbalance, N, by +0.5 × 10^22 J/yr pushes up the lower bound of the equilibrium climate sensitivity from 1.5 K back to 2.0 K. An increase of the lower bound from 1.5 K to 2 K corresponds to a need to reducye maximum emissions by 25% to stay within the 2°C global warming target (because of the almost linear relationship between warming and cumulative emissions; see Fig. SPM.10 in ref. 1). This corresponds to a reduction in maximum allowable cumulative CO2 emissions from 4,760 Gt CO2 to 3,570 Gt CO2.