Does the heat content of the upper oceans continue to rise steadily due to man made climate change?
No don’t think so and don’t think your graphs show it. They show increased warming but hardly steady. There are fluctuations as you would expect. Given that there are various mechanisms for transferring some of this heat to the deep oceans and also to atmosphere and thus land. Further there are issues of latent heat exchanges [melting ice, evaporation] which do not result in temperature changes but certainly involve energy transfers. So ‘continue to rise steadily’ is not really what I would expect, I would expect continuing long term increase, but with lots of variability along the way. As to one respondent’s comment that increased salinity would increase evaporation, sorry but that is simply wrong. Increased salinity reduces evaporation, and the amount of evaporation involved would in any case have far too small an effect to be measured, or to be of any consequence.
