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Volume 9, issue 3 | Copyright

Special issue: Thermodynamics and optimality in the Earth system and its...

Earth Syst. Dynam., 9, 1127-1140, 2018
https://doi.org/10.5194/esd-9-1127-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 21 Sep 2018

Research article | 21 Sep 2018

Diurnal land surface energy balance partitioning estimated from the thermodynamic limit of a cold heat engine

Axel Kleidon and Maik Renner Axel Kleidon and Maik Renner
  • Biospheric Theory and Modelling Group, Max-Planck-Institut für Biogeochemie, Jena, Germany

Abstract. Turbulent fluxes strongly shape the conditions at the land surface, yet they are typically formulated in terms of semiempirical parameterizations that make it difficult to derive theoretical estimates of how global change impacts land surface functioning. Here, we describe these turbulent fluxes as the result of a thermodynamic process that generates work to sustain convective motion and thus maintains the turbulent exchange between the land surface and the atmosphere. We first derive a limit from the second law of thermodynamics that is equivalent to the Carnot limit but which explicitly accounts for diurnal heat storage changes in the lower atmosphere. We call this the limit of a cold heat engine and use it together with the surface energy balance to infer the maximum power that can be derived from the turbulent fluxes for a given solar radiative forcing. The surface energy balance partitioning estimated from this thermodynamic limit requires no empirical parameters and compares very well with the observed partitioning of absorbed solar radiation into radiative and turbulent heat fluxes across a range of climates, with correlation coefficients r2 ≥ 95% and slopes near 1. These results suggest that turbulent heat fluxes on land operate near their thermodynamic limit on how much convection can be generated from the local radiative forcing. It implies that this type of approach can be used to derive general estimates of global change that are solely based on physical principles.

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Turbulent fluxes represent an efficient way to transport heat and moisture from the surface into the atmosphere. Due to their inherently highly complex nature, they are commonly described by semiempirical relationships. What we show here is that these fluxes can also be predicted by viewing them as the outcome of a heat engine that operates between the warm surface and the cooler atmosphere and that works at its limit.
Turbulent fluxes represent an efficient way to transport heat and moisture from the surface into...
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