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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 12
Hydrol. Earth Syst. Sci., 20, 4857–4865, 2016
https://doi.org/10.5194/hess-20-4857-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 20, 4857–4865, 2016
https://doi.org/10.5194/hess-20-4857-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 09 Dec 2016

Research article | 09 Dec 2016

Matching the Budyko functions with the complementary evaporation relationship: consequences for the drying power of the air and the Priestley–Taylor coefficient

Jean-Paul Lhomme1 and Roger Moussa2 Jean-Paul Lhomme and Roger Moussa
  • 1IRD, UMR LISAH, 2 Place Viala, 34060 Montpellier, France
  • 2INRA, UMR LISAH, 2 Place Viala, 34060 Montpellier, France

Abstract. The Budyko functions B1p) are dimensionless relationships relating the ratio E / P (actual evaporation over precipitation) to the aridity index Φp = Ep / P (potential evaporation over precipitation). They are valid at catchment scale with Ep generally defined by Penman's equation. The complementary evaporation (CE) relationship stipulates that a decreasing actual evaporation enhances potential evaporation through the drying power of the air which becomes higher. The Turc–Mezentsev function with its shape parameter λ, chosen as example among various Budyko functions, is matched with the CE relationship, implemented through a generalised form of the advection–aridity model. First, we show that there is a functional dependence between the Budyko curve and the drying power of the air. Then, we examine the case where potential evaporation is calculated by means of a Priestley–Taylor type equation (E0) with a varying coefficient α0. Matching the CE relationship with the Budyko function leads to a new transcendental form of the Budyko function B1′(Φ0) linking E / P to Φ0 = E0 / P. For the two functions B1p) and B1′(Φ0) to be equivalent, the Priestley–Taylor coefficient α0 should have a specified value as a function of the Turc–Mezentsev shape parameter and the aridity index. This functional relationship is specified and analysed.

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The Budyko functions are matched with the complementary evaporation relationship. We show that there is a functional dependence between the Budyko functions and the drying power of the air. Examining the case where potential evaporation is calculated by means of a Priestley–Taylor type equation with a varying coefficient, we show that this coefficient should have a specified value as a function of the Budyko shape parameter and the aridity index.
The Budyko functions are matched with the complementary evaporation relationship. We show that...
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