66
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
quantitative soil and canopy parameters such as temporally and spatially distributed
ET (Menenti 2000). Some reviews of relevant algorithms that were proposed to estimate surface energy fluxes and ET based on remotely sensed images can be found in
the literature (Kustas and Norman 1996; Kalma et al. 2008; Schumugge et al. 2002).
A common way of estimating ET is to rearrange the energy balance equation and
solve it for latent heat flux, λET (in watts per square meter), as a residual term:
λET = R n – G 0 – H,
(4.1)
where λ is the latent heat of vaporization (in joules per kilogram), R n is the net radiation (in watts per square meter), G 0 is the soil heat flux (in watts per square meter),
and H is the sensible heat flux entailing the heat exchange between the surface and
the atmosphere due to the temperature gradient (in watts per square meter).
Typically, with reliable estimates of solar radiation, differences between remote
sensing estimates and observed values of available radiation (R n – G 0 ) are within
10%; as a consequence, the largest uncertainty in estimating λET comes from computing H. Following a classical approach of micrometeorology (Brutsaert 1982), sensible heat flux in the atmospheric boundary layer close to the surface where energy
exchange occurs because of the potential temperature gradient can be expressed as
H
c T
r
c T
T
r
p
ah
p
h
a
ah
=
=
−
ρ δ
ρ (
)
0
,
(4.2)
where ρ (in kilograms per cubic meter) is the air density, c p is the specific heat of
air (in joules per kilogram per kelvin), T 0h is the so-called “aerodynamic surface
temperature” (in Kelvin), T a is the air temperature at some reference height above the
canopy (in Kelvin), and r ah is the aerodynamic resistance to heat transfer between the
nominal source height corresponding to T 0h and the reference height (in seconds per
meter). If the radiometric temperature, T r (in Kelvin), obtainable from thermal remote
sensing is used as T 0h , empirical corrections to Equation 4.2 should be applied.
Numerous methods have been proposed over the years to solve this problem; a
common approach was to introduce an additional resistance, the so-called “excess
resistance,” to be added to r ah to account for differences between T 0h and T r (Kustas
et al. 1994). Another approach, generally suitable for homogeneous land cover, is to
assume an empirical relationship between T r and δT = (T 0h – T a ) to be calibrated on
the basis of boundary conditions. These are derivable through theoretical hypotheses
or directly from information within images. These approaches, known in the literature as a “single source,” treat the unique soil–canopy layer as semitransparent to
radiation. Theoretically, it works well only under restricted surface conditions, and it
does not work where T r depends on vegetation/soil interactions.
On the other hand, the more physically based “two-source” approach, namely,
vegetation and soil layers, takes into account this heterogeneity and explicitly provides the factors mainly influencing T r and T 0h . This approach uses two sets of soil
and canopy aerodynamic resistances connected in series or parallel, accounting for
the interactions between vegetation and soil energy fluxes. Another class of remote
sensing–based models to retrieve the actual ET is based on the simple empirical
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
quantitative soil and canopy parameters such as temporally and spatially distributed
ET (Menenti 2000). Some reviews of relevant algorithms that were proposed to estimate surface energy fluxes and ET based on remotely sensed images can be found in
the literature (Kustas and Norman 1996; Kalma et al. 2008; Schumugge et al. 2002).
A common way of estimating ET is to rearrange the energy balance equation and
solve it for latent heat flux, λET (in watts per square meter), as a residual term:
λET = R n – G 0 – H,
(4.1)
where λ is the latent heat of vaporization (in joules per kilogram), R n is the net radiation (in watts per square meter), G 0 is the soil heat flux (in watts per square meter),
and H is the sensible heat flux entailing the heat exchange between the surface and
the atmosphere due to the temperature gradient (in watts per square meter).
Typically, with reliable estimates of solar radiation, differences between remote
sensing estimates and observed values of available radiation (R n – G 0 ) are within
10%; as a consequence, the largest uncertainty in estimating λET comes from computing H. Following a classical approach of micrometeorology (Brutsaert 1982), sensible heat flux in the atmospheric boundary layer close to the surface where energy
exchange occurs because of the potential temperature gradient can be expressed as
H
c T
r
c T
T
r
p
ah
p
h
a
ah
=
=
−
ρ δ
ρ (
)
0
,
(4.2)
where ρ (in kilograms per cubic meter) is the air density, c p is the specific heat of
air (in joules per kilogram per kelvin), T 0h is the so-called “aerodynamic surface
temperature” (in Kelvin), T a is the air temperature at some reference height above the
canopy (in Kelvin), and r ah is the aerodynamic resistance to heat transfer between the
nominal source height corresponding to T 0h and the reference height (in seconds per
meter). If the radiometric temperature, T r (in Kelvin), obtainable from thermal remote
sensing is used as T 0h , empirical corrections to Equation 4.2 should be applied.
Numerous methods have been proposed over the years to solve this problem; a
common approach was to introduce an additional resistance, the so-called “excess
resistance,” to be added to r ah to account for differences between T 0h and T r (Kustas
et al. 1994). Another approach, generally suitable for homogeneous land cover, is to
assume an empirical relationship between T r and δT = (T 0h – T a ) to be calibrated on
the basis of boundary conditions. These are derivable through theoretical hypotheses
or directly from information within images. These approaches, known in the literature as a “single source,” treat the unique soil–canopy layer as semitransparent to
radiation. Theoretically, it works well only under restricted surface conditions, and it
does not work where T r depends on vegetation/soil interactions.
On the other hand, the more physically based “two-source” approach, namely,
vegetation and soil layers, takes into account this heterogeneity and explicitly provides the factors mainly influencing T r and T 0h . This approach uses two sets of soil
and canopy aerodynamic resistances connected in series or parallel, accounting for
the interactions between vegetation and soil energy fluxes. Another class of remote
sensing–based models to retrieve the actual ET is based on the simple empirical