Abstract
An ‘almost trivial’ climate system of geometrical dimension zero is analysed, the complexity of which has been reduced to a minimum. It can be simply described as the globally averaged energy flux balance between infrared emission and solar heat input, expanded by a linear albedo-temperature feedback. This nonlinear and time-dependent climate model is formulated as a gradient system of a potential and can be analysed without explicit time integration. It includes many of the results which are also exhibited by one-dimensional energy balance models. Two equilibrium solutions appear. The stable one is characterized by the interglacial, whereas the unstable equilibrium defines a lower bound for temperature (state variable) changes which the system can absorb. Beyond a threshold of an external parameter combination (fold catastrophe) no equilibria exist so that the system attains a ‘deep freeze’ climate situation. A −2 power law describes the linear response of the (internally stable) system to weather fluctuations.
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