Apparently, the deep ocean in the Pacific is still cooling (slightly), while the Atlantic depths have been heating, and at a much faster comparative rate. The reason is quite surprising - it takes a long, long time for top water to circulate to the bottom in the Pacific, and so cooling from centuries ago is still affecting its depths:
At depths below 2000 m, the Atlantic warms at an average rate of 0.1°C over the past century, whereas the deep Pacific cools by 0.02°C over the past century....
Deep Atlantic waters are directly replenished by their formation in the North Atlantic, but deep Pacific waters must propagate from the Atlantic and Southern oceans. Radiocarbon observations (11) indicate that most waters in the deep Atlantic were last at the surface 1 to 4 centuries ago, whereas most deep Pacific waters have longer memory due to isolation from the atmosphere for 8 to 14 centuries (6). As a result of differing response times, Atlantic temperature trends reflect warming over recent centuries, including that associated with anthropogenic influences, whereas the Pacific is still cooling as a consequence of ongoing replacement of Medieval Warm Period waters by Little Ice Age waters.The paper indicates that their modelling and re-examination of some records indicate that surface cooling from the Little Ice Age is a good explanation of the deep Pacific cooling.
I gather, from looking at the diagram in the paper, that the total increase in heat in the Atlantic depths means that, on average, the global total ocean depths are still heating. But it certainly appears that (like sea level rise), deep ocean heating is much "lumpier" when you look at the regions than I would have guessed.
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