Over 90 percent of the heat energy added to Earth’s climate system by human activities has gone into the ocean, in part because, well, it's awfully big.

That awful-bigness makes monitoring all that heat energy a real challenge. A new study led by Peter Gleckler and Paul Durack at Lawrence Livermore National Laboratory compiled as much data as possible and compared it to climate model simulations. The comparison not only shows that the ocean's warming can only be explained by human impacts (surprise!) but also highlights just how quickly global warming is occurring outside of our view.

Although a large number of automated floats have been measuring temperatures in the upper 2,000 meters of the ocean for over a decade now, ship-based measurements from the past are more sparse. And the deeper the water, the fewer the available measurements. Because of this, studies analyzing the cause of ocean temperature changes have mainly stuck to the upper 700 meters. For this study, the researchers pulled together some more data—including the Challenger Expedition from the 1870s—in order to make deep ocean comparisons more worthwhile.

The basic approach is to run climate models and compare their output to the limited data we have. That comparison is then used to produce estimates of what's going on at times and in locations where we don't have data.

The researchers broke the data into three layers: the upper 700 meters, an intermediate layer down to 2,000 meters, and the depths below. Then Gleckler et al calculated the simulated warming from each of those layers using the climate models that were run for the last IPCC report. They included both simulations of the past century (including anthropogenic greenhouse gas changes) and long baseline simulations with nothing but natural variability.

For each layer, the average warming trend of the model simulations including human activities fell right in with the observations for the period of 1971 to 2005. (Although the uncertainty on the deepest observations is so large that the researchers say that the particularly spot-on match there “may be fortuitous.”) The natural variability simulations, however, rarely saw 35-year warming trends as strong as the ones we've observed.

The next step is a little more interesting: since the average of the simulations fits the data well, they calculated the simulated ocean heat energy change going back to 1865. That allowed them to consider how that change has played out over time, despite the gaps in empirical estimates.

For example, the researchers point out the surprising fact that half the total accumulation of heat energy since 1865 occurred after 1996. That’s how quickly warming has taken off over the past few decades.

Additionally, we get a better estimate of how to apportion warming between those three layers of the ocean. Almost two-thirds of the heat energy added to the oceans has accumulated in the upper 700 meters, with another 15 percent below 2,000 meters, and 20 percent in between.

The total, by the way, is almost half of a yottajoule of heat energy added since 1865. (That's a 5 followed by twenty-three zeroes...) I won’t tell you how many Olympic-sized swimming pools full of dynamite sticks it takes to reach half a yottajoule.

Nature Climate Change, 2016. DOI: 10.1038/nclimate2915 (About DOIs).