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We investigated the applicability of the maximum entropy production hypothesis to time-varying problems, in particular, the seasonal cycle using a conceptual model. Contrarily to existing models, only the advective part of the energy fluxes is optimized, while conductive energy fluxes that store energy in the ground are represented by a diffusive law. We observed that this distinction between energy fluxes allows for a more realistic response of the system. In particular, a lag is naturally observed for the ground temperature. This study therefore shows that not all energy fluxes should be optimized in energy balance models using the maximum entropy production hypothesis, but only the fast convective (turbulent) part.

A Maximum Entropy Production Hypothesis for Time Varying Climate Problems: Illustration on a Conceptual Model for the Seasonal Cycle