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evapotranspiration is often fairly similar to the evaporation from open water under the
same conditions. As mentioned above, a possible explanation for this is that the stomatal
impedance to water vapor diffusion may be compensated by the larger roughness values,
resulting in larger transfer coefficients, of the vegetational surface.
Another point of ambiguity is that potential evaporation is often estimated by means
of meteorological data observed under nonpotential conditions. Because the air interacts
with the underlying surface, this is not the same rate as that which would be calculated
or observed, if the surface had been moist or adequately supplied with water. There-
fore, potential evaporation estimated on the basis of measurements carried out under
nonpotential conditions should be called “apparent” to reflect this fact. Examples of
apparent potential evaporation are the estimates made by means of an evaporation pan or
by means of the Penman equation (4.23), on the basis of measurements in the actual, i.e.
non-potential or arid, environment. Another example of apparent potential evaporation
would be that obtained by means of Equation (4.3), inwhich q s at the dry surface is
assumed to be given by q ( T s ), i.e. the saturation specific humidity at the temperature
of that surface. In what follows the “true” potential evaporation will be denoted by E po ,
and the apparent potential evaporation by E pa .
4.3.3
Operational methods for landsurfaces
Many operational procedures used in applied hydrology to predict evaporation involve
some type of potential evaporation, used in conjunction with a procedure to derive the
actual evaporation from it for the prevailing non-potential conditions.
Proportional fluxes with surface moisture “bucket”
Probably the oldest method, which follows work by Budyko (1955; 1974) and Thornth-
waite and Mather (1955), is based on the following proportionality
E
= β e E p
(4.33)
where E p is a potential evaporation rate, and
β e a reduction factor reflecting the mois-
ture availability. As mentioned above, potential evaporation is a somewhat ambiguous
concept; not surprisingly, therefore, in practice Equation (4.33) has been applied with
two different classes of E p , such as E pa , the apparent potential evaporation as defined in
the previous section, and E pe , the Priestley-Taylor equation given in(4.31).
The reduction factor
β e is often assumed to be a function of soil water content. In
the application of (4.33) with such expressions for apparent potential evaporation E pa as
(4.3) and (4.23), a common assumption has been
β e =
1
for
w>w 0
(4.34)
β e =
(
w w c )
/
(
w 0 w c )
for
w w 0
where
w c isalower
cut-off value below which E is zero. This is illustrated inFigure 4.4. The value of
w 0 isacritical soil water content above which E equals E p , and
w
can be determined on the basisofasoil water budget (see Thornthwaite and Mather,
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