Derivation of zero-dimensional from one-dimensional climate models

A one-dimensional energy-balance equation involving diffusive energy transport and taking into account the ice-albedo feedback is considered. A systematic elimination of the spatial degrees of freedom is performed. This gives rise to a zero-dimensional climate model displaying the explicit dependence of planetary albedo on planetary temperature and on some model parameters. In the general case, the zero-dimensional model involves memory effects as well as two characteristic relaxation rates.