The IPCC, in the AR4 working group one, stated what could be called the central claim of global warming, the estimate of the net radiative forcing.
“The understanding of anthropogenic warming and cooling influences on climate has improved since the TAR, leading to very high confidence that the effect of human activities since 1750 has been a net positive forcing of +1.6 [+0.6 to +2.4] W m–2.”
Remember a forcing is an imbalance that causes heating, like a hot plate heating a saucepan of water. While the forcing continues, the temperature of the water will continue to rise. Global warming is the theory that increases in CO2 in the atmosphere are causing the earth to warm dangerously.
The IPCC level of forcing equates to the stated estimates for doubling of CO2 from around 1.5 to 6C per doubling, and the central estimates of warming to the end of the century from increasing CO2 of about 3C.
The paper by Levitus et al. uses the array of ARGO floats, and other historic ocean measurements, to determine the change in the heat content of the ocean from 0 to 2000m, and so derive the actual net radiative forcing that has caused it to warm over the last 50 years.
“The heat content of the world ocean for the 0-2000 m layer increased by 24.0×1022 J corresponding to a rate of 0.39 Wm-2 (per unit area of the world ocean) and a volume mean warming of 0.09ºC. This warming rate corresponds to a rate of 0.27 Wm-2 per unit area of earth’s surface.”
Thus the best, recent measurements of the forcing 0f 0.3Wm-2 are below the lowest limits of the IPCC estimate from 0.6Wm-2 to 2.4Wm-2. The anthropogenic component of the forcing is even less, as a large part of the 0.3Wm-2 is due to increased solar insolation during the Grand Solar Maximum.
This mild forcing is right in the ballpark that skeptic scientists such as Lindzen, Spencer, Loehle and Idso (and myself) have been consistently saying is all that is justified by the evidence. It appears that Levitus et al. confirms the skeptics, and the IPCC has been falsified.

Go to link for remainder of post, including the laughable attempt by Skeptical Science to spin the Levitus paper.