“It came out of a computer, so it must be right.”
There is no possibility we know the temperature profile of the world’s oceans, particularly deeper than 300 meters prior to 1990 ALACE and deeper than 1000 meters prior to ARGO in 2004, to support the conclusions of this paper.
The Uncertainty Monster is alive and well, swimming just under the surface of this paper. 1×10^20 J (really J/m) translates to a temperature resolution of 0.07 dec C maximum scale for each meter in the OHC plots. (Rule of Thumb: 27.5 ZJ = 0.01 deg C for the 0-2000 meter water column).