A parametric sensitivity study of entropy production and kinetic energy dissipation using the FAMOUS AOGCM

The possibility of applying either the maximum entropy production conjecture of Paltridge (Q J R Meteorol Soc 101:475–484, 1975) or the conjecture of Lorenz (Generation of available potential energy and the intensity of the general circulation. Pergamon, Tarrytown, 1960) of maximum generation of available potential energy (APE) in FAMOUS, a complex but low-resolution AOGCM, is explored by varying some model parameters to which the simulated climate is highly sensitive, particularly the convective entrainment rate, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document}, and cloud droplet-to-rain-conversion rate, cT. The climate response is analysed in terms of its entropy production and the strength of the Lorenz energy cycle. If either conjecture is true, the parameter values which yield the most realistic climate will also maximise the relevant quantity. No maximum is found in the total material entropy production, which is dominated by the hydrological cycle and tends to increase monotonically with global-mean temperature, which is not constant because the parameter variations affect the net input of solar radiation at the top of the atmosphere (TOA). In contrast, there is a non-monotonic, peaked behaviour in the generation of APE and entropy production associated with kinetic energy dissipation, with the standard FAMOUS values for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document} and cT occurring nearly at the maximising ones. The maximum states are shown to be states of vigorous baroclinic activity. The peak in the generation of APE appears to be related to a trade-off between the mean vertical stability and horizontal stratification. Experiments are repeated for a simplified setup in which the net solar input at TOA is fixed. Again a peak in the generation of APE is found in association with the maximum baroclinic activity, but no trade-off of the kind shown by simple climate models is found between meridional heat transport and the meridional temperature gradient. We conclude that the maximum entropy production conjecture does not hold within the climate system when the effects of the hydrological cycle and radiative feedbacks are taken into account, but our experiments provide some evidence in support of the conjecture of maximum APE production (or equivalently maximum dissipation of kinetic energy).