The Budyko functions

Different expressions of the Budyko functions as a function of the
aridity index

The Budyko curves are analytical formulations of the functional
dependence of actual evaporation

The Turc–Mezentsev relationship Eq. (4) between the ratio

Potential evaporation establishes an upper limit to the evaporation process
in a given environment. It is generally given by a Penman-type equation
(Lhomme, 1997a), which is the sum of two terms – a first term depending on the
radiation load

In most of the Budyko type functions encountered in the literature, potential
evaporation

In the present paper, the behaviour of the drying power of the air

The paper is organised as follows. First, the basic equations used in the
development are detailed: the choice of a particular Budyko function is
discussed and the complementary evaporation relationship, implemented through
a generalised form of the advection–aridity model (Brutsaert and Stricker,
1979) is presented. Second, the feasible domain of the drying power of the
air

Among the Budyko functions given in Table 1, one particular form is retained
in our study: the one initially obtained by Turc (1954) and Mezentsev (1955)
through empirical considerations and then analytically derived by Yang et al.
(2008) through the resolution of a Pfaffian differential equation with
particular boundary conditions. Three reasons guided this choice: (i) the
function is one of the most commonly used; (ii) it involves a model parameter

Correspondence between the two forms of the Turc–Mezentsev
functions (

The complementary evaporation (CE) relationship expresses that actual
evaporation

At this stage of the development it is important to make clear that two
different Priestley–Taylor coefficients are defined in our analysis in
relation to the CE relationship: one (

As a consequence of land–atmosphere interactions expressed by the CE
relationship, the drying power of the air

It is interesting to note that the shape parameter

Using the CE relationship as a basis, this section examines the link existing
between the Priestley–Taylor coefficient

We have now two sets of Budyko functions:

Comparison between the Turc–Mezentsev function

Comparison of functions

Variation of the Priestley–Taylor coefficient

For every value of

The Budyko curves have two different and
equivalent dimensionless expressions:

The authors are very grateful to three anonymous reviewers and the handling editor for their constructive comments. They also gratefully acknowledge the UMR LISAH for its valuable scientific support and significant financial contribution, as well as A. Gaby for having inspired some of the main ideas of the paper. Edited by: F. Tian Reviewed by: three anonymous referees