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Earth System Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

ESD Reviews 15 Feb 2019

ESD Reviews | 15 Feb 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth System Dynamics (ESD).

ESD Reviews: Thermodynamic optimality in Earth sciences. The missing constraints in modeling Earth system dynamics?

Martijn Westhoff1, Axel Kleidon2, Stan Schymanski3, Benjamin Dewals4, Femke Nijsse5, Maik Renner2, Henk Dijkstra6, Hisashi Ozawa7, Hubert Savenije8, Han Dolman1, Antoon Meesters1, and Erwin Zehe9 Martijn Westhoff et al.
  • 1Vrije Universiteit, Amsterdam, The Netherlands
  • 2Max-Planck-Institut für Biogeochemie, Jena, Germany
  • 3Luxembourg Institute of Science and Technology, Esch-sur-Alzette, Luxembourg
  • 4University of Liege, Liege, Belgium
  • 5University of Exeter, Exeter, UK
  • 6Center for Complex Systems Studies, Department of Physics, Utrecht University, Utrecht, The Netherlands
  • 7Hiroshima University, Hiroshima, Japan
  • 8Delft University of Technology, Delft, The Netherlands
  • 9Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

Abstract. Thermodynamic optimality principles have been often used in Earth sciences to estimate model parameters or fluxes. Applications range from optimizing atmospheric meridional heat fluxes to sediment transport and from optimizing spatial flow patterns to dispersion coefficients for fresh and salt water mixing. However, it is not always clear what has to be optimized and how. In this paper we aimed to clarify terminology used in the literature and to infer how these principles have been used and when they give proper predictions of observed fluxes and states.

We distinguish roughly four classes of applications: predictions using a flux-gradient feedback, predictions using a constant thermodynamic potential boundary conditions, predictions based on information theoretical approaches and comparative studies quantifying entropy production rates from observations at different sites. Here we mainly focus on the flux-gradient feedback, since it results in clear physical limits of energy conversion rates occurring in the Earth system and its subsystems. We show that within the flux-gradient feedback application, maximum entropy production is in many cases equivalent to maximum power and maximum energy dissipation. We advocate the maximum power principle above the more widely used maximum entropy production principle because entropy can be produced by all kinds of fluxes, but only optimized fluxes performing work coincided with observations. Furthermore, the maximum power principle links to the maximum amount of free energy that can be converted into another form of energy. This clearly separates the well defined physical conversion limit from the hypothesis that a system evolves to that limit of maximum power. Although attempts have been made to fundamentally explain why a system would evolve to such a maximum in power, there is still no consensus. Nevertheless, we think that when the maximum power approach is correctly and consistently used, the positive (or negative) results will speak for themselves.

We end this review with some open research questions that may guide further research in this area.

Martijn Westhoff et al.
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Martijn Westhoff et al.
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Publications Copernicus
Short summary
Even models relying on physical laws have parameters that need to be measured or estimated. Thermodynamic optimality principles potentially offer a way to reduce the number of estimated parameters by stating that a system evolves to an optimum state. These principles have been applied successfully within the Earth system, but it is often unclear what to optimize and how. In this review paper we identify commonalities between different successful applications as well as some doubtful applications.
Even models relying on physical laws have parameters that need to be measured or estimated....