67
Comparative Analysis of Surface Energy Balance Models
analysis of the correlations between T r and vegetation indices or surface albedo (e.g.,
Moran et al. 1994; Roerink et al. 2000).
In this chapter, the “single-source surface energy balance algorithm for land
(SEBAL)” (Bastiaanssen et al. 1998a,b), the “two-source energy balance (TSEB) modeling scheme” (Norman et al. 1995), and the “simplified-surface energy balance index
(S-SEBI)” (Roerink et al. 2000) were analyzed and compared with each other to model
surface energy fluxes in an agricultural area characterized by typical Mediterranean
crops. A reliable accounting of fragmentation of these landscapes usually requires the
processing of a high-spatial-resolution data sets, many being remotely sensed. The
impact of different spatial resolutions on model-derived fluxes was also investigated
to understand the main conceptual differences between the two models, which use a
“single-layer” (SEBAL) and a “two-layer” (TSEB) scheme, respectively.
4.2 MODEL DESCRIPTIONS
A detailed description of the SEBAL and TSEB models can be found, respectively, in the
work of Bastiaanssen et al. (1998a,b) and of Norman et al. (1995) and Kustas and Norman
(1999a,b). The first comparison between the two models in the same study area can be
found in the work of Ciraolo et al. (2006). In this section, we describe only the main differences of the models, with particular attention to the sensible heat flux computation.
In both models, R n can be estimated by computing the net available energy, thus
accounting for the rate lost by surface reflection in the shortwave (0.3–2.5 μm) and
emitted in the longwave (6–12 μm) parts of the spectrum:
R
R
T
T
n
swd
a
r
= −
+
−
′
(
)
(
),
1
0
4
4
α
ε ε σ
σ
(4.3)
where R swd is the global incoming solar radiation in the shortwave (in watts per
square meter), α is the surface albedo (dimensionless), ε′ is the atmospheric emissivity (dimensionless), ε 0 is the surface emissivity (dimensionless), and σ is the Stefan–
Boltzmann constant (in watts per square meter per Kelvin to the fourth power).
Moreover, the TSEB model splits R n between canopy (R n,c ) and the soil (R n,s ) by
means of an exponential extinction law, where the decay factor is computed as a
function of leaf area index (LAI; in square meters by square meters):
R
R
LAI
n s
n
z
, =
−
(
)
exp
.
/ cos( ) ,
0 45
2
θ
(4.4)
R n,c = R n – R n,s
(4.5)
where R n is computed using Equation 4.3, and θ z (rad) is the solar zenith angle.
The soil heat flux is commonly computed using empirical approaches: In SEBAL,
G 0 is expressed as a semiempirical fraction of R n , accounting for albedo, normalized
difference vegetation index (NDVI), and surface temperature:
G R
T
n
r
0
2
4
0 003
0 006
1 0 98
=
+
−
α
α
α
( .
.
)(
.
)
NDVI .
(4.6)
In TSEB, G 0 is expressed as a fraction c g (≈0.35) of R n at the soil surface R n,s .
Comparative Analysis of Surface Energy Balance Models
analysis of the correlations between T r and vegetation indices or surface albedo (e.g.,
Moran et al. 1994; Roerink et al. 2000).
In this chapter, the “single-source surface energy balance algorithm for land
(SEBAL)” (Bastiaanssen et al. 1998a,b), the “two-source energy balance (TSEB) modeling scheme” (Norman et al. 1995), and the “simplified-surface energy balance index
(S-SEBI)” (Roerink et al. 2000) were analyzed and compared with each other to model
surface energy fluxes in an agricultural area characterized by typical Mediterranean
crops. A reliable accounting of fragmentation of these landscapes usually requires the
processing of a high-spatial-resolution data sets, many being remotely sensed. The
impact of different spatial resolutions on model-derived fluxes was also investigated
to understand the main conceptual differences between the two models, which use a
“single-layer” (SEBAL) and a “two-layer” (TSEB) scheme, respectively.
4.2 MODEL DESCRIPTIONS
A detailed description of the SEBAL and TSEB models can be found, respectively, in the
work of Bastiaanssen et al. (1998a,b) and of Norman et al. (1995) and Kustas and Norman
(1999a,b). The first comparison between the two models in the same study area can be
found in the work of Ciraolo et al. (2006). In this section, we describe only the main differences of the models, with particular attention to the sensible heat flux computation.
In both models, R n can be estimated by computing the net available energy, thus
accounting for the rate lost by surface reflection in the shortwave (0.3–2.5 μm) and
emitted in the longwave (6–12 μm) parts of the spectrum:
R
R
T
T
n
swd
a
r
= −
+
−
′
(
)
(
),
1
0
4
4
α
ε ε σ
σ
(4.3)
where R swd is the global incoming solar radiation in the shortwave (in watts per
square meter), α is the surface albedo (dimensionless), ε′ is the atmospheric emissivity (dimensionless), ε 0 is the surface emissivity (dimensionless), and σ is the Stefan–
Boltzmann constant (in watts per square meter per Kelvin to the fourth power).
Moreover, the TSEB model splits R n between canopy (R n,c ) and the soil (R n,s ) by
means of an exponential extinction law, where the decay factor is computed as a
function of leaf area index (LAI; in square meters by square meters):
R
R
LAI
n s
n
z
, =
−
(
)
exp
.
/ cos( ) ,
0 45
2
θ
(4.4)
R n,c = R n – R n,s
(4.5)
where R n is computed using Equation 4.3, and θ z (rad) is the solar zenith angle.
The soil heat flux is commonly computed using empirical approaches: In SEBAL,
G 0 is expressed as a semiempirical fraction of R n , accounting for albedo, normalized
difference vegetation index (NDVI), and surface temperature:
G R
T
n
r
0
2
4
0 003
0 006
1 0 98
=
+
−
α
α
α
( .
.
)(
.
)
NDVI .
(4.6)
In TSEB, G 0 is expressed as a fraction c g (≈0.35) of R n at the soil surface R n,s .