Roy Spencer posted the following comparison between the 20th Century runs from most (15) of the IPCC AR4 climate models, and Levitus observations of ocean warming during 1955-1999. Here are the best 4 models:
The accuracy of the other models is far worse.
In Roy’s assessment:
Previous investigators (as well as the IPCC AR4 report) have claimed that warming of the oceans is “consistent with” anthropogenic forcing of the climate system.
The actual rate of accumulated heat — the area between the green dots and the vertical line — much smaller than any of the models.
As Roy notes, it is generally believed that all of the increase in ocean heat is from increasing GHGs.
It should be mentioned the above analysis assumes that there has been no significant natural source of warming during 1955-1999. If there has, then the diagnosed climate sensitivity would be even lower still.
As I show here, the observations are consistent with the accumulation of heat from an excess of 0.2W/m^2 forcing by the Sun over the period of the Grand Solar Maximum. In other words, the increase caused by GHGs may not even be detectable.
An increase of 0.1W/m2 for one year would move 3.1×10^6 Joules of heat (31×10^6 sec in a Yr) to the ocean, heating the mixed zone to 150m by 0.006K (at 4.2 J/gK), producing a rate of global temperature increase of 0.06K per decade.