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complementary approach shows specific promise as a practical tool, itstill awaits a
definitive physical analysistomakeit fully effective.
A unified parametric formulation
As reviewed here, several of the procedures in current practice, can be cast inasingle form
as follows
E = β e a
Ce u 1 ρ ( q 2 q 2 )
+ γ
γ
+ γ
Q ne + b
(4.50)
inwhich a and b are weighting constants for the first and second terms, respectively, which
together with the remaining parameters
γ depend on the chosen model. As before,
β e is used if actual evaporation is obtained by reduction of potential evaporation E pe or E pa ;
in the potential evaporation given by Penman's equation (4.23), the remaining parameters
are a = b = 1, and γ = γ , whereas in that givenbyPriestley and Taylor's equation (4.31)
they are a = α e , b = 0, and γ = γ . In the Penma n- Monteith equation (4.39), for actual
evaporation, β e = a = b = 1 and γ = γ (1 + r s Ce u 1 ). In the advection-aridity version of
Brutsaert and Stricker (4.49) they are β e = 1, a = 2 α e 1, b =− 1 and γ = γ . Equation
(4.50) indicates that the different formulations are related, but the parameters can vary
considerably.
β e and
4.3.4 Diurnal cycle over land: the self-preservation approximation
It is well known that under certain favorable conditions, when horizontal advection is not too
strong, the daytime variations of the major energy fluxes at land surfaces are quite similar.
Thissimilarity in the diurnal cycle of the different energy flux components over land is
illustrated inFigures 2.19 and 2.20, and inFigure 4.9. This means that during any given
day the ratios of these fluxes remain approximately constant, which may be considered a
manifestation of some kind of “self-preservation.” Because evaporation is usually relatively
small during the night, this self-preservation can sometimes be useful to relate daily averages
with instantaneous or hourly values. This idea was made use of by Jackson et al . (1983) by
means of ( L e E / R s ), in order to estimate the total daily latent heat flux on the basisofa
one-time-of-day value. The idea was also used for the same purpose by Shuttleworth et al .
(1989), Sugita and Brutsaert (1991), and Nichols and Cuenca (1993) by means of the
evaporative fraction EF = L e E / ( R n G )orEF = L e E / ( L e E + H ). Crago (1996) applied
the idea with still another dimensionless evaporation rate, namely α e = E / E e , where E e is
the equilibrium evaporation defined in Equation (4.30).
In more general terms (Brutsaert and Sugita, 1992), the assumption of self-preservation
requires that the evaporative flux ratio,
ER = L e E / F
(4.51)
be taken as a constant during the daytime hours. In (4.51) F is some other flux term
(beside L e E ) in the surface energy budget, which exhibits a similar diurnal cycle as L e E ,
so that it can serve as a reference. The assumption of similarity can be assessed for differ-
ent flux terms inFigures 4.10 (mainly the curves with the open symbols) and 4.11, with
data measured during FIFE, the First ISLSCP Field Experiment conducted inhilly tallgrass
terrain in eastern Kansas; it appears to work well when F is taken as the available energy
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