Entropy production and coarse graining of the climate fields in a general circulation model

We extend the analysis of the thermodynamics of the climate system by investigating the role played by processes taking place at various spatial and temporal scales through a procedure of coarse graining. We show that the coarser is the graining of the climatic fields, the lower is the resulting estimate of the material entropy production. In other terms, all the spatial and temporal scales of variability of the thermodynamic fields provide a positive contribution to the material entropy production. This may be interpreted also as that, at all scales, the temperature fields and the heating fields resulting from the convergence of turbulent fluxes have a negative correlation, while the opposite holds between the temperature fields and the radiative heating fields. Moreover, we obtain that the latter correlations are stronger, which confirms that radiation acts as primary driver for the climatic processes, while the material fluxes dampen the resulting fluctuations through dissipative processes. We also show, using specific coarse-graining procedures, how one can separate the various contributions to the material entropy production coming from the dissipation of kinetic energy, the vertical sensible and latent heat fluxes, and the large scale horizontal fluxes, without resorting to the full three-dimensional time dependent fields. We find that most of the entropy production is associated to irreversible exchanges occurring along the vertical direction, and that neglecting the horizontal and time variability of the fields has a relatively small impact on the estimate of the material entropy production. The approach presented here seems promising for testing climate models, for assessing the impact of changing their parametrizations and their resolution, as well as for investigating the atmosphere of exoplanets, because it allows for evaluating the error in the estimate of their thermodynamical properties due to the lack of high-resolution data. The findings on the impact of coarse graining on the thermodynamic fields on the estimate of the material entropy production deserve to be explored in a more general context, because they provide a way for understanding the relationship between forced fluctuations and dissipative processes in continuum systems.