The greenhouse effects of H2O and CO2 are well known to be critical aspects of Earth's climate, and can be simulated with great accuracy by computer models. Such models are quite complicated, however, and so a satisfactory intuition for these effects is often lacking, and it can be difficult to quantitatively reason about them from first principles.
In this talk I will present a set of closely related simple models for aspects of the H2O and CO2 greenhouse effects, derived from the principles of radiative transfer. These models allow for pencil-and-paper estimates of basic features of the greenhouse effect, such as the radiative forcing from CO2 and the rate at which H2O cools the atmosphere by infrared emission. There is also a surprising connection between the greenhouse effect and precipitation, allowing our simple models to explain why total precipitation increases by roughly 2% per degree of surface warming.