Equation (4.24) introduces the concepts of equilibrium evapotranspiration LE eq ,
imposed evapotranspiration LE i , and decoupling coefficient X. Equilibrium
evapotranspiration, LE eq , is defined as
LE eq ¼
D
D þ c
ðR n À GÞ
ð 4:25Þ
The potential evapotranspiration condition LE pot , relates to the maximum
evaporation, in the extreme case of a uniformly humid surface, which may be free
water or vegetation with high water availability. With the gradual saturation of the
atmosphere adjacent to the surface vapor pressure deficit and evaporation will
decrease reaching the equilibrium evaporation. The equilibrium evaporation is,
therefore, an extreme situation corresponding to the rate of free evaporation on a
surface, after saturation of the adjacent atmosphere (Cunha 1977).
Equation (4.25) corresponds to the first term of the right side of Eq. (4.24) when
X = 1. The term XLE eq is the evapotranspiration rate that would occur if the energy
balance of a surface was determined by the diabatic radiative term of the Penman–
Monteith equation , in the absence of any relationship to the atmospheric conditions. However, the D parameter in the equation, related to air temperature, imparts
some dependency of LE eq on the atmosphere.
The Priestley–Taylor equation relates to the potential and equilibrium evaporations as follows (Vogt and Jaeger 1990)
LE pot ¼ 1:26LE eq
ð4:26Þ
showing that the evaporation potential is greater than the equilibrium evaporation.
The proportionality constant in Eq. (4.26) depends on how the boundary layer
height evolves throughout the day (Chap. 1), and how to air dry is transported in
this layer by downward movements of air masses, trapped by the top inversion
layer.
The vertical flux of water vapor is about 24–36% of LE eq (Balddochi et al. 1997)
for forest canopy under dry conditions. Homogeneous forest canopies, with closed
covers and large water availability, can transpire at a rate of 1.26 times the equilibrium evapotranspiration .
A further quantity (1 − X)LE i , the imposed evaporation, representing the second
term on the right side of Eq. (4.24), relates to the evaporation rate that would occur
if the energy budget of a surface was dominated by an adiabatic term. This term
increases with the value of qc p (e s (T(z)-e(z))/r a , integrating the right-side numerator
of Eq. (4.24), when the value of r a is very low in strong winds and rough forest
canopies.
An electrical analogy can be applied to the second term on the right side of
Eq. (4.24), where the vapor pressure deficit is the potential difference, and the
electrical resistance is the sum of the different resistances to vapor diffusion.
The decoupling factor X, which is the separating factor in Eq. (4.24) between
the balance and imposed evaporation, is defined as
4.5 Evaluation of Evapotranspiration and Energy Coupling …
119
imposed evapotranspiration LE i , and decoupling coefficient X. Equilibrium
evapotranspiration, LE eq , is defined as
LE eq ¼
D
D þ c
ðR n À GÞ
ð 4:25Þ
The potential evapotranspiration condition LE pot , relates to the maximum
evaporation, in the extreme case of a uniformly humid surface, which may be free
water or vegetation with high water availability. With the gradual saturation of the
atmosphere adjacent to the surface vapor pressure deficit and evaporation will
decrease reaching the equilibrium evaporation. The equilibrium evaporation is,
therefore, an extreme situation corresponding to the rate of free evaporation on a
surface, after saturation of the adjacent atmosphere (Cunha 1977).
Equation (4.25) corresponds to the first term of the right side of Eq. (4.24) when
X = 1. The term XLE eq is the evapotranspiration rate that would occur if the energy
balance of a surface was determined by the diabatic radiative term of the Penman–
Monteith equation , in the absence of any relationship to the atmospheric conditions. However, the D parameter in the equation, related to air temperature, imparts
some dependency of LE eq on the atmosphere.
The Priestley–Taylor equation relates to the potential and equilibrium evaporations as follows (Vogt and Jaeger 1990)
LE pot ¼ 1:26LE eq
ð4:26Þ
showing that the evaporation potential is greater than the equilibrium evaporation.
The proportionality constant in Eq. (4.26) depends on how the boundary layer
height evolves throughout the day (Chap. 1), and how to air dry is transported in
this layer by downward movements of air masses, trapped by the top inversion
layer.
The vertical flux of water vapor is about 24–36% of LE eq (Balddochi et al. 1997)
for forest canopy under dry conditions. Homogeneous forest canopies, with closed
covers and large water availability, can transpire at a rate of 1.26 times the equilibrium evapotranspiration .
A further quantity (1 − X)LE i , the imposed evaporation, representing the second
term on the right side of Eq. (4.24), relates to the evaporation rate that would occur
if the energy budget of a surface was dominated by an adiabatic term. This term
increases with the value of qc p (e s (T(z)-e(z))/r a , integrating the right-side numerator
of Eq. (4.24), when the value of r a is very low in strong winds and rough forest
canopies.
An electrical analogy can be applied to the second term on the right side of
Eq. (4.24), where the vapor pressure deficit is the potential difference, and the
electrical resistance is the sum of the different resistances to vapor diffusion.
The decoupling factor X, which is the separating factor in Eq. (4.24) between
the balance and imposed evaporation, is defined as
4.5 Evaluation of Evapotranspiration and Energy Coupling …
119