Arthur Smith's response to Gerlich and Tscheuschner

http://arxiv.org/abs/0802.4324

"Proof of the Atmospheric Greenhouse Effect".

Contrary to the claims of G&T, I show here that:
1. An average surface temperature for a planet is perfectly well defined with or without rotation, and with or without infrared absorbing gases.

2. This average temperature is mathematically constrained to be less than the fourth root of the average fourth power of the temperature, and can in some circumstances (a planet with no or very slow rotation, and low surface thermal inertia) be much less.

3. For a planet with no infrared absorbing or reflecting layer above the surface (and no significant flux of internal energy), the fourth power of the surface temperature always eventually averages to a value determined by the incoming stellar energy flux and relevant reflectivity and emissivity parameters.

4. The only way the fourth power of the surface temperature can exceed this limit is to be covered by an atmosphere that is at least partially opaque to infrared radiation. This is the atmospheric greenhouse effect.

5. The measured average temperature of Earth’s surface is 33 degrees C higher than the limit determined by items (2) and (3). Therefore, Earth is proved to have a greenhouse effect of at least 33K.