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

• Main Authors: J.-P. Lhomme, R. Moussa
• Format: Article
• Language: English
• Published: Copernicus Publications 2016-12-01
• Series: Hydrology and Earth System Sciences
• Online Access: http://www.hydrol-earth-syst-sci.net/20/4857/2016/hess-20-4857-2016.pdf

The Budyko functions <i>B</i>₁(Φ_p) are dimensionless relationships relating the ratio <i>E</i>&thinsp;/&thinsp;<i>P</i> (actual evaporation over precipitation) to the aridity index Φ_p = <i>E</i>_p&thinsp;/&thinsp;<i>P</i> (potential evaporation over precipitation). They are valid at catchment scale with <i>E</i>_p 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 <i>λ</i>, 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 (<i>E</i>₀) with a varying coefficient <i>α</i>₀. Matching the CE relationship with the Budyko function leads to a new transcendental form of the Budyko function <i>B</i>₁′(Φ₀) linking <i>E</i>&thinsp;/&thinsp;<i>P</i> to Φ₀ = <i>E</i>₀&thinsp;/&thinsp;<i>P</i>. For the two functions <i>B</i>₁(Φ_p) and <i>B</i>₁′(Φ₀) to be equivalent, the Priestley–Taylor coefficient <i>α</i>₀ 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.