Geoscience Reference
In-Depth Information
interference is that the effective value of the area-average boundary-layer resistance
is higher than would be calculated by a parallel summation of the values for indi-
vidual leaves. One way to approximately describe the effect of mutual interference
is to assume the increase in the effective area-average boundary-layer resistance can
be allowed for by including a simple multiplicative factor called a
shelter factor
.
The contribution to a canopy flux at a particular level in a canopy might be
assumed proportional to the difference between the mean value of an atmospheric
variable in the canopy air stream and the mean value of that same variable at the
surface of the vegetation elements (leaves) at that level. The equations describing
the contributions to the sensible heat flux, latent heat flux, and momentum flux
generated or lost at level
z
are then respectively given by:
(
TT
−
)
(21.12)
()
d
=
r
c
s
z
Hz ap
()
R
Hz
r
c
ee
R
(
−
)
ap
s
(21.13)
()
d
=
z
λ
Ez
g
()
V z
(0
−
u
)
(21.14)
()
d
=
r
z
t
z
a
R
()
M z
where
T
z
, e
z
, and
u
z
are the temperature, vapor pressure, and wind speed of the
mean canopy air stream at level
z
, respectively, and
T
s
and
e
s
are the mean values of
the temperature and vapor pressure at the surface of the leaves at level
z
,. In
Equations (21.12) to (21.14), the mean boundary-layer resistances for heat, water
vapor, and momentum for the
N
leaves in a small height range
dz
around the level
z
are respectively defined by:
−
1
⎡
⎤
N
A
∑
(21.15)
()
R
=
P
i
⎢
⎥
Hz H
R
i
⎢
⎥
⎣
⎦
i
=
1
H
−
1
⎡
N
A
⎤
∑
()
R
=
P
i
(21.16)
⎢
⎥
Vz V
R
i
⎣
⎦
i
=
1
V
−
1
⎡
⎤
N
A
∑
(21.17)
()
R
=
P
i
⎢
⎥
Mz M
R
i
⎢
⎥
⎣
⎦
i
=
1
M
where
A
i
is the area and
R
H
i
, R
V
i
, and
R
M
i
are the boundary-layer resistances
per
unit area
of the
i
th leaf, and
P
H
, P
V
, and
P
M
are shelter factors for heat, water vapor
and momentum, respectively. Because it is the reciprocal of the boundary-layer
