Energy Balance Climate Models

Chapter 6Time Dependence in the 1-D Models

In Chapter 5, we found that time-independent, zonally symmetric models can be cast into the form of a linear differential equation in the latitude variable with zero-flux boundary conditions at the poles. In the case of a latitude-independent thermal diffusion coefficient, the system can be solved with Legendre polynomials. In this chapter, we extend this procedure to the case of time dependence. Such an extension allows for idealized seasonal-cycle simulations for the zonally symmetric planet. Introducing time dependence necessarily requires some kind of effective heat capacity for the column of air–land or air–ocean medium. When we take the planet to have a homogeneous surface and constant diffusion ...