Abstract
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.
Highlights
In different climates, partitioning of rainwater into evaporation and run-off is different as well
As hydrological processes are essentially dissipative, we suggest that thermodynamic-optimality principles are deemed to be very interesting candidates
The most popular among these are the closely related principles of maximum entropy production (Kleidon and Schymanski, 2008; Kleidon, 2009; Porada et al, 2011; Wang and Bras, 2011; del Jesus et al, 2012; Westhoff and Zehe, 2013) and maximum power (Kleidon and Renner, 2013; Kleidon et al, 2013; Westhoff et al, 2014) on the one hand – both defining the optimum configuration between competing fluxes across the system boundary – and, on the other hand, minimum energy dissipation (Rinaldo et al, 1992; Rodriguez-Iturbe et al, 1992; Hergarten et al, 2014) or maximum free-energy dissipation (Zehe et al, 2010, 2013), focusing on free-energy dissipation associated with changes
Summary
In different climates, partitioning of rainwater into evaporation and run-off is different as well. The resulting modelled fluxes were plotted in the Budyko diagram and followed the curve with a similar scatter as real-world catchments Another very interesting approach was presented by Kleidon and Renner (2013) and Kleidon et al (2014), using the perspective of the atmosphere. Evaporation at the surface and condensation in the atmosphere deplete this gradient even further at the expense of more vertical moisture transport and more convective motion Their approach showed some more spreading around the Budyko curve for the same 35 catchments as used in Porada et al (2011), but they used a simpler model that has to be forced with far fewer observations, namely solar radiation, precipitation, and surface temperature.
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