Nonlinear Albedo-Temperature Coupling in Climate Models

An analytical study is made of the number, stability and bifurcations of solutions of time-dependent Budyko-type climate models with various nonlinear albedo parameterizations. With Budyko's (1969) albedo, a general stability criterion is derived and it is found that, for the present value of the solar constant, the present climate and ice-covered earth solutions are stable, a spurious solution is unstable and there is an ice-free solution which is stable. A Seller's (1969) type albedo leads to a stable present climate and an ice-covered earth solution as well as an unstable climate. Faegre's (1972) albedo produces a present climate which is unstable and has an incorrect behavior as the solar constant or the infrared flux is changed, as well as a stable warmer climate and an ice-covered earth solution. It is found that latidutinal variations in the albedo way have a profound effect on the number and stability of the solutions.