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

摘要

The Budyko functions iB/isub1/sub(Φsubp/sub) are dimensionless relationships relating the ratio iE/i / iP/i (actual evaporation over precipitation) to the aridity index Φsubp/sub?=?iE/isubp/sub / iP/i (potential evaporation over precipitation). They are valid at catchment scale with iE/isubp/sub 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 iλ/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 (iE/isub0/sub) with a varying coefficient iα/isub0/sub. Matching the CE relationship with the Budyko function leads to a new transcendental form of the Budyko function iB/isub1/sub′(Φsub0/sub) linking iE/i / iP/i to Φsub0/sub?=?iE/isub0/sub / iP/i. For the two functions iB/isub1/sub(Φsubp/sub) and iB/isub1/sub′(Φsub0/sub) to be equivalent, the Priestley–Taylor coefficient iα/isub0/sub 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.