Premium
Structural and stochastic analysis of a zero‐dimensional climate system
Author(s) -
Fraedrich Klaus
Publication year - 1978
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710444017
Subject(s) - energy balance , nonlinear system , thermodynamic equilibrium , dimension (graph theory) , balance (ability) , statistical physics , environmental science , meteorology , mathematics , physics , thermodynamics , medicine , quantum mechanics , pure mathematics , physical medicine and rehabilitation
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.