The subject of this post isn’t the only new research on how ocean heat content has changed. Zanna et al. have taken a new approach to estimating it based on sea surface temperature history.
Of course knowing sea surface temperature at some point in time, doesn’t tell you the ocean heat content profile throughout the depths of the ocean at that time. But if you know the sea surface temperature history, and the heat-content-at-depth history, you can (at least theoretically) find a “transfer function” which tells you how the heat content profile depends on the time history of surface temperature. After all, the waters at depth were near the surface some time in the past and that’s where and when they got their heat.
Those familiar with heavy math (like diff.eq) may recognize the “transfer function” as something by the name (among others) “Green’s function.” Zanna et al. use historical data for both surface temperature and heat content to estimate this Green’s function, which is essentially a “fingerprint” of how heat moves from the surface through the depths of the ocean. With Green’s function in hand, they could compare the result from that model (which they call “GF” for short) to observations, and found that the match was surprisingly good. It appears that the Green’s-function approach was, at the very least, one of those models which is useful.
The real utility is that they extend the calculation further back in time, to the past when ocean heat observations are not available. They were, thereby, able to estimate ocean heat content back to 1875. They display their results for the usual ranges from 0 to 700m depth and from 0 to 2000m depth, but they also estimate values below 2000m. It would appear that all depths of the ocean have been getting hotter.
They call their estimate the “historical passive OHC reconstruction” because it assumes that the transfer function is static, i.e. that the way heat propogates through the ocean hasn’t changed much. Detailed comparison of the best-observed region (the Atlantic basin) suggests, as they say,
The agreement of our results with observations suggests that most of the basin-integrated heat storage in the Atlantic is passive, meaning that it is explained almost entirely by the propagation of SST anomalies via the time–mean transport into the ocean interior and consistent with our use of a constant GF. We estimate that only about up to 5% of the Atlantic OHC change over the last 45 y may be due to unaccounted changing ocean processes or errors in methods.
While basin-wide heat content observations match the GF estimate well, there are suggestive differences on smaller scales within the best-observed area, the Atlantic. In particular, comparison of the rates of increase of OHC (Ocean Heat Content) since 1955 by latitude show signs of change:
Our results suggest that, if the heat storage was entirely determined by the climatological transports, its magnitude over the last 40 y would be less pronounced in low latitudes and more pronounced north of the Gulf Stream than observed, despite the large uncertainty in all estimates in these regions. We attribute 1.3 ZJ per degree latitude per decade of the heat storage between 20° N and 50° N in the North Atlantic to redistribution by changes in ocean transport. We infer that, during 1955–2017, one-third to one-half of the warming in the Atlantic basin between 20° S and 50° N was due to heat convergence from ocean circulation changes.
Ocean heat content is going up, at all depths including below 2000m. Ocean circulation is changing. The imlications are, I suppose I should at least say, worrisome. And of course, as the authors say,
Monitoring and understanding OHC change and the role of circulation in shaping the patterns of warming remain key to predicting global and regional climate change and sea-level rise.
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Open Mind 
The ocean is heated from the top–sunlight being absorbed by water with a very low albedo (~2%). Transferring heat into the ocean depths is done by stirring by surface winds and tides. It is not thermodynamic.
Finding indications of increases in heat transport to the ocean interior is worrying. It means that the earth is warming faster although it also means that it is helping to minimize global rise of surface temperature.
Mitch, my understanding is that heat is transfered to the depths by THC, thermohaline circulation, not “surface winds and tides”
In order for new water to go down, the old water has to be pumped back up through buoyancy added by mixing with waters in layers above the bottom. This mixing is driven by tides in the deep ocean and winds near the surface. The densest waters are formed from cold saline waters near the poles and form the replacement for water pumped up.
Yes, the surface wind effect is called Eckman transport. I forgot about that.
The whole shebang, including that in your last sentence, is called THC.
I have never seen anything written about “tides in the deep ocean”. Have you a link?
I did not know this, but you asked an interesting question, David. So I was lucky to find this nice backgrounder:
http://oceanmotion.org/html/background/tides-ocean.htm
Doc Snow, thank you.
By the way, for anyone interested: “Sea level hotspots from Florida to Maine: Drivers, impacts, and adaptation“, a conference, 23-25 April 2019, with Abstract submission and application window now closing on 25th January 2019 (postponed):