#### Proof of the Atmospheric Greenhouse Effect

**Arthur P. Smith**

*American Physical Society, 1 Research Road, Ridge NY, 11961*

A recently advanced argument against the atmospheric greenhouse effect is refuted. A planet without an infrared absorbing atmosphere is mathematically constrained to have an average temperature less than or equal to the effective radiating temperature. Observed parameters for Earth prove that without infrared absorption by the atmosphere, the average temperature of Earth’s surface would be at least 33 K lower than what is observed.

PACS numbers: 92.60.Vb,05.90.+m

##### I. INTRODUCTION

The results presented here are not new. However the form of presentation is designed to clearly and accurately respond to recent claims^{1} that a physics-based analysis can “falsify” the atmospheric greenhouse effect. In fact, the standard presentation in climatology textbooks^{2} is accurate in all material respects. The following explores in more detail certain points that seem to have been cause for confusion.

First presented are the definitions of basic terms and the relevant equations for the flow of energy. The situation for a planet with no infrared-absorbing atmosphere is then examined, and a constraint on average temperature is proved. Several specific models of planets with no infrared-absorbing atmosphere are then solved, including one presented by Gerlich and Tscheuschner^{1}, and it is verified that all satisfy this constraint.

A simple infrared-absorbing atmospheric layer is added to these models, and it is proved that the temperature constraint is easily violated, as is shown by the observational data for Earth.