That is a good question! Willis Eschenbach raised it at WUWT recently: HERE A convincing answer would be invaluable. For years a lot of opinions swirl around. Prof. R. Pielke Sr (2008) regards „monitoring of global average ocean heat content as the appropriate metric to assess global warming.” HERE The IPCC-2007 assumes a warming of the upper sea level 0 to 700 meters, HERE, claiming that “Approximately 7.9 million temperature profiles were used”. Is that a lot? Definitely not, as only three cubic-meters of water have the same heat capacity as an air-column of 1x1x10’000meter. The number of data required would go into billions. The Ocean is huge, deep and cold.

 

An image from the Atlantic may serve as illustration. It seems Willis Eschenbach recognizes rightly when he concludes his essay:

“we can say nothing about whether the ocean
might be warming, cooling, or standing still.”

Links provided above:

http://wattsupwiththat.com/2015/06/06/can-we-tell-if-the-oceans-are-warming/

https://pielkeclimatesci.wordpress.com/2010/09/12/a-short-explanantion-of-why-the-monitoring-of-global-average-ocean-heat-content-is-the-appropriate-metric-to-assess-global-warming-2/


https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch5s5-2-2.html