They also made two other big mistakes.
- SB & LC both used a simplified description of the climate system that likely violates conservation of energy. It involves how they treat the ocean, but it's as if if one assumed that the Sun not only heats the Earth, but also that the Earth significantly heats the Sun.
- Later in their analysis they make a different assumption: that the ocean exchanges no heat.
- The most important issue, though, involves the relative role of clouds. SB simply assume a value for the importance of clouds relative to the ocean: that they have 2.3 times the forcing. (LC assumes this number is 0.5.) Dessler calculates the value from actual data and finds the value is 0.05.
By the way, these are very, very simple climate models SB and LC are using. It's essentially just air on top of water, warmed by the Sun. All the things we hear about: carbon dioxide, other GHGs, land use changes, are shoved in one term with a given climate sensitivity. All the "radiative forcings," like changes in clouds, are shoved into another term, and all the other "nonradiative forcings," like heat exchange between the air and oceans, are shoved into another term. The air changes temperature just liked you learned in 8th grade science: according to its specific heat value. That's it.
Dessler uses the same model only by way of comparison and rebuttal.
This is, of course, a simplification of their scientific arguments, but I think it boils down to these items (and essentially to #3). I haven't interviewed anyone or confirmed the above, I'm just a journalist so I could well be wrong. In any case, people will no doubt fight over them for a good while longer.