Bifurcation of the Greenhouse effect

The Greenhouse effect results from a balance between the solar incoming radiation and the outgoing planet emission. 

We solve for the full radiation field in the atmosphere including the visible (which is optically think) and the infra-red (which is partly optically think and partly thin) and equate the bolometric radiation falling onto the Earth with that emitted by the Earth.

 

We find several solutions, some are stable and some are unstable. We show that always there exists at least one solution> Under the temperature range in Earth-like planets there are more solutions which differ from one another by a finite ground temperature. 

 

We discuss when the solutions are stable/unstable and the implication of such solutions. We discuss the possibility of transition from a high energy solution to a low energy one and the meaning of it.