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Apparently emissivity has several components which are likely to change in various situations. Thus using it as a constant is only an approximation. Any climate models which use it as a constant are technically imprecise, although the range of values for emissivity would have to be studied to consider how much error this adds.
On The Confusion Of Planck Feedback Parameters
Although the surface temperature change is 3.0 C with the Planck feedback parameter ( previous value ) for CO2 doubling when lapse rate ,water vapor, surface albedo and cloud feedbacks are included in the IPCC AR4, it is shown to be 0.5 – 0.75 C with ( Planck feedback parameter ) proven here. Since the IPCC overestimates the threat of carbon dioxide by 4 – 6 times, the revaluation will be needed for the CO2 reduction policies in terms of cost and potential hazards.
Blog comments :
Calculus is Calculus. A calculator will give an answer based upon its inputs. And Calculus will give a result based on the terms in your starting equation which are based on your assumptions of what it is that you are calculating.
The world is a ‘grey body’. Integration ( over atmospheric columns ) can be done numerically by stripped down climate models, or done algebraically by using constants that already embed the emissivity ‘integration’ over altitude.
The maths is OK, it’s the interpretation of it that is incorrect, and has, through simplification, in " summaries for policy makers " brought about " catastrophic global warming ".