https://www.nature.com/articles/s41586-018-0651-8
Yes indeed. James Annan uses those new values of OHC to calculate an implied probability distribution for ECS (climate sensitivity):
The median value for ECS from that is 2.57 C. So it fits nicely with this thread title.
http://julesandjames.blogspot.com/2018/11/blueskiesresearchorguk-that-new-ocean.html
First, per James Annan's article, Annan states that estimates of ECS based on standard energy balance calculations (which he presents in his plot that you show) is biased to result in low estimates of ECS due to the "pattern effect" discussed in the second linked reference by Andrews et al. (2018).
Second, per Annan's calculations only consider heat absorbed by the ocean for a relatively short period, while the oceans have been absorbing anthropogenic heat since around 1750.
Title: "That new ocean heat content estimate"
https://bskiesresearch.wordpress.com/2018/11/01/that-new-ocean-heat-content-estimate/Extract: "Plugging the numbers in to a standard energy balance approximation we get the following estimates for the equilibrium sensitivity:
…
This simple calculation has a (now) well-known flaw that tends to bias the results low, though how low is up for debate (it’s the so-called “pattern effect” or you might know it as the difference between effective and equilibrium sensitivity).
…
Another caveat in my calculation is that the new paper’s main result is based on a longer time interval going back to 1991, if the ocean heat uptake has been accelerating then that would imply a larger increment to the Johnson et al figure (which relates to a more recent period) and thus a larger effect."
Timothy Andrews et al. (30 July 2018), "Accounting for changing temperature patterns increases historical estimates of climate sensitivity; Geophysical Research Letters,
https://doi.org/10.1029/2018GL078887https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018GL078887Abstract
Eight Atmospheric General Circulation Models (AGCMs) are forced with observed historical (1871‐2010) monthly sea‐surface‐temperature (SST) and sea‐ice variations using the AMIP II dataset. The AGCMs therefore have a similar temperature pattern and trend to that of observed historical climate change. The AGCMs simulate a spread in climate feedback similar to that seen in coupled simulations of the response to CO2 quadrupling. However the feedbacks are robustly more stabilizing and the effective climate sensitivity (EffCS) smaller. This is due to a ‘pattern effect’ whereby the pattern of observed historical SST change gives rise to more negative cloud and LW clear‐sky feedbacks. Assuming the patterns of long‐term temperature change simulated by models, and the radiative response to them, are credible, this implies that existing constraints on EffCS from historical energy budget variations give values that are too low and overly constrained, particularly at the upper end. For example, the pattern effect increases the long‐term Otto et al. (2013) EffCS median and 5‐95% confidence interval from 1.9K (0.9‐5.0K) to 3.2K (1.5‐8.1K).
Third, Andrews et al (2018)'s findings taken together with Brown & Caldeira 2017
https://www.nature.com/articles/nature24672 and Caldwell 2018
https://journals.ametsoc.org/doi/10.1175/JCLI-D-17-0631.1 should firmly place ECS at 3.5 or greater.