Self-Scaling of the Statistical Properties of a Minimal Model of the Atmospheric Circulation

is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference TE. As TE increases, a transition takes place from a stationary regime - Hadley equilibrium - to a periodic regime, and eventually to a chaotic regime, where evolution takes place on a strange attractor. The dependence of the attractor dimension, metric entropy, and bounding box volume in phase space is studied by varying TE. It is found that this dependence is smooth and has the form of a power-law scaling. The observed smooth dependence of the system’s statistical properties on the external parameter TE is coherent with the chaotic hypothesis proposed by Gallavotti and Cohen, which entails an effective structural stability for the attractor of the system. Power-law scalings with respect to TE are also detected for global observables responding to global physical balances, like the total energy of the system and the averaged zonal wind. The scaling laws are conjectured to be associated with the statistical process of baroclinic adjustment, decreasing the equator-to-pole temperature difference. The observed self-similarity could be helpful in setting up a theory for the overall statistical properties of the general circulation of the atmosphere and in guiding - also on a heuristic basis - both data analysis and realistic simulations, going beyond the unsatisfactory mean field theories and brute force approaches.