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The Budyko functions B-1(Phi(p))are dimensionless relationships relating the ratio E/P (actual evaporation over precipitation) to the aridity index Phi(p) = E-p/P (potential evaporation over precipitation). They are valid at catchment scale with E-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 lambda, 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 (E-0) with a varying coefficient alpha(0). Matching the CE relationship with the Budyko function leads to a new transcendental form of the Budyko function B-1'(Phi(0)) linking E/P to Phi(0) = E-0/P. For the two functions B-1(Phi(p)) and B-1'(Phi(0) ) to be equivalent, the Priestley-Taylor coefficient alpha(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

hydrology and earth system sciences

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