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

Abstract

The Budyko functions B1(Φp) are dimensionless relationships relating the ratio E/P (actual evaporation over precipitation) to the aridity index Φp Combining double low line 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 Combining double low line E0/P. For the two functions B1(Φp) 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.