All these things are estimates based on the other values. If you actually look at the heat emitted by the earth (as measured by satellite) and the heat arriving from the sun (as measured by satellite), you end up with errors that are much much larger than the quoted heat gain.
You only get the quoted heat gain (so many atom bombs) if you assume that the measurements of the heat gain of the oceans are correct. Unfortunately, the error bars on the ocean heat measurements are also huge. This happens because the temperature changes in the ocean are exceedingly small. Here is a recent Nature Climate Change article showing the details:
Deep-ocean contribution to sea level and energy budget not detectable over the past decade
Llovel, Willis, Landerer & Fukumori
Nature Climate Change 4, 1031-1035 (2014)
...
Finally, we combine our estimate of upper-ocean warming (above 2,000 m) with the ocean heat content change in the lower layer (below 2,000 m) to estimate the heat uptake by the entire ocean. We find a net ocean warming equivalent to a radiative imbalance of 0.64 ± 0.44 W m−2 since 2005. Here we have included the potential systematic uncertainties and assume that errors are uncorrelated between estimates of warming above and below 2,000 m depth. Our estimate of full-depth ocean warming is in good agreement with a recent estimate of Earth’s net energy imbalance of 0.50 ± 0.43 W m−2 for the period from 2001 through 2010 28. Nevertheless, our full-depth ocean heat content change and its contribution to global mean sea level relies on a strong hypothesis. We have assumed that each observing system is independent and that errors are uncorrelated over timescales longer than one month. If this assumption is invalid then the error bounds quoted in our analysis might be underestimated.
...
http://www.nature.com/nclimate/journal/v4/n11/full/nclimate2387.html
Now the figure "0.64 ± 0.44" shows that they can't distinguish between oceans absorbing 0.64-0.44 = 0.20 and 0.64+0.44 = 1.08 W/m^2. This is more than a factor of five between the top end of their estimate and the bottom end. But it gets worse. They made their error estimates assuming that the various measurements are independent. The universe is almost never that kind.
The more mature branches of physics have learned that signals need to be ignored until they reach about 5 or 6 sigma. For example, the elementary particle physicists didn't announce the Higgs boson until they were 5-sigma sure that their figures were correct. The reason they wait this long is because they have a long and embarrassing history of announcing incorrect results at the 2 or 3 sigma level.
The climate scientists haven't gone through that long history of bad results yet. Instead, they're in the midst of their first big screw-up, the "pause". The reason they were so sure there would be no pause is that they had hundreds of simulations by dozens of different groups and 99% of them showed strongly rising temperatures. They didn't realize that these estimates were not, in fact, independent. And so they concluded that there was going to be a huge temperature rise. When temperatures didn't rise for the first 5 years they ignored it, then they denied it for another 5 years, and now they're trying to wish it away and no two groups seem to agree on the same excuse, LOL.
If you come back and look at how climate science does business 20 years from now they'll undoubtedly be a mature science and will keep quiet until they are 99% sure of their results *and* are sure that they are independent (and so that their statistics are real). Right now they repeatedly make statistical errors in the direction of more certainty than actually exists.
Here are some links on the 5-sigma "gold standard" that is used in elementary particle physics, and why it's used:
5 Sigma What's That?
Evelyn Lamb, Scientific American Blog, July 17, 2012
Chances are, you heard this month about the discovery of a tiny fundamental physics particle that may be the long-sought Higgs boson. The phrase five-sigma was tossed about by scientists to describe the strength of the discovery. So, what does five-sigma mean?
In short, five-sigma corresponds to a p-value, or probability, of 3x10-7, or about 1 in 3.5 million. This is not the probability that the Higgs boson does or doesn't exist; rather, it is the probability that if the particle does not exist, the data that CERN scientists collected in Geneva, Switzerland, would be at least as extreme as what they observed.
High-energy physics requires even lower p-values to announce evidence or discoveries. The threshold for "evidence of a particle," corresponds to p=0.003, and the standard for "discovery" is p=0.0000003.
The reason for such stringent standards is that several three-sigma events have later turned out to be statistical anomalies, and physicists are loath to declare discovery and later find out that the result was just a blip.
...
http://blogs.scientificamerican.com/observations/five-sigmawhats-that/
Shifting Standards Experiments in Particle Physics in the Twentieth Century
Allan Franklin, University of Pittsburgh Press (2013)
(Prologue pp xiv-xv)
According to the story, which received wide circulation within the high-energy physics community, Rosenfeld pointed out that given the large number of graphs that were plotted each year by experimenters, one would expect to see a significant number of three standard-deviation effects even if the data were distributed randomly and no particles or resonances were present. Rosenfeld (1975) discussed the issue in print. In discussing the existence of the kappa(725), a K Pi resonance that had been reported five times, but subsequently disappeared, Rosenfeld stated the following: "We compiled and histogrammed (by computer) 60,000 new K Pi events, and found no substantial further evidence and went on to ask how frequently such striking statistical fluctuations should be expected at some given mass in the K Pi system. (At the time about 2 million bubble chamber events were being measured annually, and about a thousand physicists were hunting through 10,000 to 20,000 mass histograms each year, in search of striking features, real or imagined,) We concluded that the five kappa claims were just about what we should expect" (564-65).
http://www.amazon.com/Shifting-Standards-Experiments-Particle-Twentieth/dp/0822944308/
