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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 20, issue 1 | Copyright

Special issue: Catchment co-evolution: space–time patterns and functional...

Hydrol. Earth Syst. Sci., 20, 479-486, 2016
https://doi.org/10.5194/hess-20-479-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 28 Jan 2016

Research article | 28 Jan 2016

Does the Budyko curve reflect a maximum-power state of hydrological systems? A backward analysis

M. Westhoff1, E. Zehe2, P. Archambeau1, and B. Dewals1 M. Westhoff et al.
  • 1Department of Hydraulics in Environmental and Civil Engineering (HECE), University of Liege (ULg), Liege, Belgium
  • 2Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

Abstract. Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle.

In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving run-off and evaporation for a simple one-box model. We did this in an inverse manner such that, when the conductances are optimized with the maximum-power principle, the steady-state behaviour of the model leads exactly to a point on the asymptotes of the Budyko curve. Subsequently, we added dynamics in forcing and actual evaporation, causing the Budyko curve to deviate from the asymptotes. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves subject to observed dynamics in rainfall and actual evaporation. Thus by constraining the model that has been optimized with the maximum-power principle with the asymptotes of the Budyko curve, we were able to derive more realistic values of the aridity and evaporation index without any parameter calibration.

Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

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Short summary
We derived mathematical formulations of relations between relative wetness and gradients driving run-off and evaporation for a one-box model such that, when conductances are optimized with the maximum power principle, the model leads exactly to a point on the Budyko curve. With dry spells and dynamics in actual evaporation added, the model compared well with catchment observations without calibrating any parameter. The maximum-power principle may thus be used to derive the Budyko curve.
We derived mathematical formulations of relations between relative wetness and gradients driving...
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