Agriculture Reference
In-Depth Information
2.
T
HE STRUCTURE OF THE
L
AND
-A
IR
P
ARAMETERIZATION
S
CHEME
(LAPS)
2.1. The Governing Equations and Approaches
The net radiation absorbed by the canopy and soil is assumed to be partitioned into
sensible heat, latent heat, and storage terms, as
∂
T
f
(1)
R
=
λ
E
+
H
+
C
nf
f
f
f
∂
t
∂
T
R
=
λ
E
+
H
+
C
g
,
(2)
ng
g
g
g
∂
t
where
R
nf
,
R
ng
are net radiation fluxes (W m
-2
); λ is latent heat of vaporization (J kg
-1
);
λE
f
,
λE
g
are evapotranspiration fluxes (W m
-2
);
H
f
, H
g
are sensible heat fluxes (W m
-2
);
C
f
,
C
g
are
heat capacities (J K
-1
m
-2
); and
T
f
, T
g
are surface temperatures (K). The subscripts
f
and
g
refer
to the upper-level canopy and soil, respectively (Figure 2). The fluxes of sensible and latent
heat from the canopy and ground are represented by electrical analog models in which the
fluxes are proportional to potential differences (in temperature or vapor pressure) and
inversely proportional to resistances, which are equivalent to the inverse integrals of
conductances over a specified length scale. For example, an aerodynamic resistance is
calculated by integrating the inverse of a turbulent transfer coefficient between the reference
points. The LAPS schematic diagram in Figure 2 [21,22] shows that these heat fluxes may be
written as shown in Eqs. (3) through (6)
⎛
⎞
ρ
c
W
1
−
W
[
]
⎜
⎝
⎟
⎠
λ
E
=
p
e
(
T
)
−
e
f
+
f
,
(3)
f
*
f
a
γ
r
r
+
r
b
b
c
where
ρ
and
c
p
are the density and specific heat of air (kg m
-3
, J kg
-1
K
-1
);
γ
is the
psychrometric constant (mb K
-1
);
e
*
(
T
f
) is saturated vapor pressure at temp
er
ature
T
f
(mb);
e
a
is canopy air space vapor pressure (mb);
W
f
is canopy wetness fraction;
r
is bulk canopy
boundary layer resistance (s m
-1
); and
r
is bulk canopy stomatal resistance (s m
-1
).
ρ
c
α
e
(
T
)
−
e
p
s
*
g
a
,
(4)
λ
E
=
g
γ
r
+
r
surf
d
where α
s
is a factor to correct for soil dryness [23],
e
*
(
T
g
) is saturated vapor pressure at
temperature
T
g
(mb),
r
surf
is soil surface resistance (s m
-1
), and
r
d
is aerodynamic resistance
between soil surface and canopy air space (s m
-1
).
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