The atmospheric circulation and states of maximum entropy production

Authors:

Axel Kleidon, Klaus Fraedrich, Torben Kunz and Frank Lunkeit

Abstract:

Energy balance models suggest that the atmospheric circulation operates close to a state of maximum entropy production. Here we support this hypothesis with sensitivity simulations of an atmospheric general circulation model. A state of maximum entropy production is obtained by (i) adjusting boundary layer turbulence and (ii) using a sufficiently high model resolution which allows sufficient degrees of freedom for the atmospheric flow. The state of maximum entropy production is associated with the largest conversion of available potential energy into kinetic energy which is subsequently dissipated by boundary layer turbulence. It exhibits the largest eddy activity in the mid latitudes, resulting in the most effective transport of heat towards the poles and the least equator-pole temperature difference. These results suggest that GCMs have a fundamental tendency to underestimate the magnitude of atmospheric heat transport and, therefore, overestimate the equator-pole temperature gradient for the present-day climate, for the response to global climatic change, and for atmospheres of other planetary bodies.

Reference:

• Geophysical Research Letters, 30 (23), 2223, doi:10.1029/2003GL018363.
• Weblink to publisher's web page.
• Postprint of this manuscript (accepted version of the paper formatted by author).
• BibTex entry.

Figure 1: Entropy production by atmospheric heat transport as a function of (a) the spatial resolution, expressed by the model’s spectral triangular truncation number; and (b) the intensity of boundary layer turbulence, determined by a friction time constant, with larger values representing less friction. For (a), the simulations at each resolution were used with the value of τFRIC for which entropy production was at a maximum. For (b), the simulations conducted at T42 resolution were used.

Figure 2: Latitudinal variation of net entropy fluxes for different model resolutions and boundary layer turbulence. (a) Model simulations using different resolution with optimum values for τFRIC, for T10 resolution (dotted), T21 resolution (dashed), T31 resolution (dash-dotted) and T42 resolution (solid). (b) Model simulations using different intensities of boundary layer turbulence at T42 resolution for the following values of τFRIC: 0.1 days (dotted), 1 day (short dashes), 3 days (solid), 10 days (long dashes), and 100 days (dash-dotted). The simulations are conducted under prescribed northern hemisphere summer conditions.

Figure 3: Latitudinal variation of poleward atmospheric heat transport for different model resolutions and boundary layer turbulence, with notations as in Figure 2. Negative values of heat transport correspond to southward transport of heat.

Figure 4: Differences in the latitudinal variation of temperatures for the lowest atmospheric model layer in comparison to the simulated climate of maximum entropy production. (a) effects of different model resolutions between T10 and T42 resolution (dotted), same for T21 (dashed), and T31 (dash-dotted) resolution, each with optimum values of τFRIC. (b) effects of different intensities of boundary layer turbulence between τFRIC = 0.1 day and τFRIC = 3 days (dotted), same for τFRIC = 1 day (short dashes), same for τFRIC = 10 days (long dashes), same for τFRIC = 100 days (dash-dotted), each at T42 resolution.