0.71 ± 0.10 W/m2.
Globally that works out to 360 trillion Watts, or 50,000 Watts per human!
They broke this down as follows:
0.61 ± 0.09 W/m2 taken up by the ocean from 0–1,800 m
0.07 ± 0.04 W/m2 by the deeper ocean, and
0.03 ± 0.01 W/m2 by melting ice, warming land, and an increasingly warmer and moister atmosphere.
So 86% of the extra AGW heat went into the top 1800 meters of the ocean. Plus or minus.
(Note: The global energy imbalance is not global radiative forcing. RFs are calculated and measured at the tropopause; global energy imbalance is with respect to the top of the atmosphere. And there are warming and cooling factors besides radiative forcings from greenhouse gases, like changes in solar irradiance, manmade and volcanic aerosol emissions, brown carbon, etc., and maybe even waste heat.)
You can easily get a good estimate of this energy imbalance number by using NOAA's data on ocean heat content from the Argo buoy network. The 0-2000 meter ocean heat content data the is here -- I find its linear trend to be, from 1Q2005 to 4Q2015,
0.66 ± 0.04 W/m2.
Pretty close for blog work -- within 10%. A little higher then their value for the ocean -- perhaps since I included an extra 200 meters -- and a little lower than the total value including everything.
- I used the data for the top 0-2000 meters of the global ocean. Not sure why they only used 0-1800 meters. (Incidently, the average depth of the ocean (= volume/area) is 3,682 meters, so you can say they measured the top half of the ocean.)
- I ignored (obviously) heat going into the ocean below 2000 meters, or into melting ice and the other small contributions. (I'm surprised that the deep ocean's energy gain is over 10% of the 0-2000 m region.)
- I divided the 0-2000 ocean heat gain by the Earth's entire surface area, since the vast majority of the heat goes into the ocean.
- My uncertainty was just the simple standard error from linear regression, i.e. no autocorrelation or anything fancy.
In 2012 Loeb, Johnson and others published a global energy imbalance of 0.50 ± 0.43 W/m2 for the period Jan 2001 to Dec 2010. (Note the first half of this period was before the 0-2000 m Argo data became available in 1Q2005; I guess that's why the uncertainty has dropped so much.) For a reason that escapes me, the latest paper says their previous estimate was 0.58 ± 0.38 W/m2.
Using their former number, that gives a change in global energy imbalance of 0.71-0.50 = 0.21 W/m2 in five years, or an acceleration of about 0.04 W/m2 per year. A 40% increase in just 5 years.
That's about half my number (not sure why). But as an acceleration, neither number can be dismissed as insignificant.
Added: ATTP has some thoughts on the implication for climate sensitivity and Lewis & Curry preprint.