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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 2
Hydrol. Earth Syst. Sci., 20, 589–603, 2016
https://doi.org/10.5194/hess-20-589-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

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

Hydrol. Earth Syst. Sci., 20, 589–603, 2016
https://doi.org/10.5194/hess-20-589-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 03 Feb 2016

Research article | 03 Feb 2016

A scaling approach to Budyko's framework and the complementary relationship of evapotranspiration in humid environments: case study of the Amazon River basin

A. M. Carmona1, G. Poveda1, M. Sivapalan2,3, S. M. Vallejo-Bernal1, and E. Bustamante4 A. M. Carmona et al.
  • 1Department of Geosciences and Environment, Universidad Nacional de Colombia, Sede Medellín, Medellín, Colombia
  • 2Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
  • 3Department of Geography and Geographic Information Science, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
  • 4Department of Mathematics, Universidad Nacional de Colombia, Sede Medellín, Medellín, Colombia

Abstract. This paper studies a 3-D state space representation of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (Ep) and precipitation (P). For this purpose we use three dimensionless and dependent quantities: Ψ  =  EP, Φ  =  EpP and Ω  =  EEp. This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between Ω and Φ in humid environments, owing to the unfeasibility of EpP  =  0 when EEp  →  1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: Ψ  =  kΦe, with k  =  0.66, and e  =  0.83 (R2  =  0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of Ω. This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the inter-annual variability of individual catchments is studied. Evidence of space–time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.

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We study a 3-D generalization of Budyko's framework that captures the interdependence among actual and potential evapotranspiration and precipitation. We demonstrate that Budyko-type equations present an inconsistency in humid environments, which we overcome by proposing a physically consistent power law that incorporates the complementary relationship of evapotranspiration into the Budyko curve. Evidence of space-time symmetry and signs of co-evolution of catchments are also found in Amazonia.
We study a 3-D generalization of Budyko's framework that captures the interdependence among...
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