Geoscience Reference
In-Depth Information
Complementary fluxes with advection-aridity
This concept was first proposed by Bouchet (1963), who postulated, almost indiametrical
opposition to Equation (4.33), a certain complementary relation between the actual
evaporation
E
, and what we now recognize as the apparent potential evaporation
E
pa
.
The underlying argument may be developed as follows. If for one or other reason,
independent of the available energy, the actual evaporation
E
decreases below its true
potential value
E
po
, a certain amount of energy not used up in evaporation becomes
available. This manifests itself as an increase in the sensible heat flux
H
,or
E
po
−
E
=
H
(4.43)
At the regional scale this decrease of
E
, relative to
E
po
, affects primarily the temperature,
humidity and turbulence of the air near the ground, but it probably has a smaller effect
on the net radiation. This increased sensible heat flux
H
, causes an increase in the
apparent potential evaporation
E
pa
inferred for these drier and warmer conditions. In
general, to a first approximation this increase can be assumed to be proportional to
H
,
so that one has
E
pa
=
E
po
+
ε
a
H
(4.44)
ε
a
is an effectiveness parameter, which may depend on the adopted defi-
nition of
E
pa
. Combination of Equations (4.43) and (4.44) yields then
E
pa
+
ε
a
E
inwhich
=
(1
+
ε
a
)
E
po
. In the original derivation, Bouchet (1963) assumed that in(4.44)
E
pa
is
increased by exactly
H
; inthis case, combination of (4.43) and (4.44) yields immedi-
ately the simple complementary relationship
E
+
E
pa
=
2
E
po
(4.45)
This result can be rearranged to yield the actual evaporation indimensionless form
E
E
po
=
2
E
/
E
pa
(4.46)
1
+
E
/
E
pa
and similarly the apparent potential evaporation
E
pa
E
po
=
2
(4.47)
1
+
E
/
E
pa
/
In Equations (4.46) and (4.47) the ratio(
E
E
pa
) may be considered as a moisture or
humidity index, which depends on such factors as soilmoisture and vegetation density;
both relationships are illustrated inFigure 4.8. It can be seen that the dependence
of (
E
E
po
), as given by Equation (4.46) and shown inFigure 4.8, has a similar trend as
those shown inFigures 4.4 and 4.5.
Applications of Equation (4.45) have been made over different time scales, namely
monthly (Morton, 1976; 1983), daily (Brutsaert and Stricker, 1979) and hourly (Parlange
and Katul, 1992). In the application of Equation (4.45) by Brutsaert and Stricker
(1979),
E
pa
can be estimated by means of (4.23), and
E
po
can be taken as
E
pe
and esti-
mated by (4.31). Thus it was assumed that the effect of the aridity on the performance
of (4.23) under non-potential conditions would mainly show up in the second term, and
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