Session 3 : Estimation of real evapotranspiration
322
momentum and the reference height. T a (°C) is the air temperature at a reference height (z) above
the surface, and T o (°C) is the aerodynamic surface temperature defined above.
Since aerodynamic temperature cannot be directly measured, it is often replaced by radiative
temperature (T r ) in the formulation of sensible heat flux. The problem is that the derivation of
exchange coefficient from Monin-Obukhov similarity theory does not apply when the surface
radiative temperature is used instead of aerodynamic temperature in the surface heat flux
formulation. Under dense canopy, the difference between aerodynamic and radiative surface
temperatures is very small, which leads to small errors in heat flux prediction. Over sparsely
vegetated surfaces, however, the difference can exceed 10 °C, as a result the sensible heat flux
can be largely overestimated.
The approach suggested by Chehbouni et al. (1996a-b) consists of formulating a relationship
between aerodynamic and radiative surface temperature, and they then defined the coefficient β
as:
β =
−
−
T T
T T
o
a
r
a
Numerical simulations (Chehbouni et al., 1996a) have shown that the multitemporal
behaviour of the coefficient β through the growing season is compared to the variation of Leaf
Area Index, which leads to a parameterization of the coefficient β with respect to LAI as:
β =
−
−
1
1
exp( / (
))
L L LAI
where L is an empirical factor that was set by least squares regression to a value of 1.5
(Chehbouni et al., 1996a). Previous studies have indicated that a modified Beer’s law expression
can accurately describe the general relationship between vegetation index and LAI (Asrar et al.,
1984). In this analysis, an exponential type relationship was used to obtain LAI from remotely
sensed MSAVI as:
MSAVI
LAI
=
−
−
0 88 0 78
0 6
.
. exp( .
)
By combining the last three equations, sensible heat flux can be expressed in terms of one
remotely sensed surface temperature, MSAVI , and air temperature.
Finally latent heat flux can be formulated as the residual term of the energy balance equation
as:
LE Rn G H
=
− −
For the remaining of the paper surface fluxes estimated as described above will be called
remotely sensed surface fluxes.
322
momentum and the reference height. T a (°C) is the air temperature at a reference height (z) above
the surface, and T o (°C) is the aerodynamic surface temperature defined above.
Since aerodynamic temperature cannot be directly measured, it is often replaced by radiative
temperature (T r ) in the formulation of sensible heat flux. The problem is that the derivation of
exchange coefficient from Monin-Obukhov similarity theory does not apply when the surface
radiative temperature is used instead of aerodynamic temperature in the surface heat flux
formulation. Under dense canopy, the difference between aerodynamic and radiative surface
temperatures is very small, which leads to small errors in heat flux prediction. Over sparsely
vegetated surfaces, however, the difference can exceed 10 °C, as a result the sensible heat flux
can be largely overestimated.
The approach suggested by Chehbouni et al. (1996a-b) consists of formulating a relationship
between aerodynamic and radiative surface temperature, and they then defined the coefficient β
as:
β =
−
−
T T
T T
o
a
r
a
Numerical simulations (Chehbouni et al., 1996a) have shown that the multitemporal
behaviour of the coefficient β through the growing season is compared to the variation of Leaf
Area Index, which leads to a parameterization of the coefficient β with respect to LAI as:
β =
−
−
1
1
exp( / (
))
L L LAI
where L is an empirical factor that was set by least squares regression to a value of 1.5
(Chehbouni et al., 1996a). Previous studies have indicated that a modified Beer’s law expression
can accurately describe the general relationship between vegetation index and LAI (Asrar et al.,
1984). In this analysis, an exponential type relationship was used to obtain LAI from remotely
sensed MSAVI as:
MSAVI
LAI
=
−
−
0 88 0 78
0 6
.
. exp( .
)
By combining the last three equations, sensible heat flux can be expressed in terms of one
remotely sensed surface temperature, MSAVI , and air temperature.
Finally latent heat flux can be formulated as the residual term of the energy balance equation
as:
LE Rn G H
=
− −
For the remaining of the paper surface fluxes estimated as described above will be called
remotely sensed surface fluxes.