From reading questions and answers here, it seems most skeptics read actual climate literature with a critical mindset, thinking that whatever is discussed is untrue, or at least intentionally misleading. This attitude, I think, frees them from having to think about the material they are reading from the attitude of trying to understand why it is correct. In contrast, they read material from skeptics with a much less critical attitude, thinking the work from "professional" skeptics is correct without analyzing it critically to see if it is consistent with known physics. Do you think it would make a difference if skeptics went back to the basics and read the underlying science again with a less critical attitude, trying to understand it as being correct to see why so many climate scientists are convinced by the theory?
For example, rather than think that the NAS panel is lying about temperature reconstructions, go back and really read the document and try to understand the differences and distinctions between the Medieval Warm Period and what is going on today. Another good example is Trenberth's radiative balance paper. It's complicated, but taking the time to go through it really illustrates how radiative transfer works, and what radiative balance means. Radiative transfer through inhomogeneous atmospheres would be a good place to start too, but there isn't one seminal reference you could point to, since the theory was developed over many years.
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