Geoscience Reference
In-Depth Information
with total leaf area. At a value of
LAI
which varies with (
z
M
/
h
), normalized
aerodynamic roughness then decreases with LAI as meanwhile (
d
/
h
) continues
to rise.
When the height of maximum leaf area is about halfway up the canopy, i.e.,
(
z
M
/
h
)
0.5, the variation of normalized displacement height with leaf area index
is approximately described by:
∼
⎡
0.25
⎤
LAI
⎛
⎞
(22.2)
d
≈
1.1 ln 1
h
+
⎢
⎥
⎜
⎟
⎝
⎠
5
⎢
⎥
⎣
⎦
Similarly, for (
z
m
/
h
)
0.5 the variation of normalized aerodynamic roughness
with leaf area index is approximately described by:
∼
0.5
LAI
zz h
⎛
⎞
(22.3)
≈+
¢
0.29
for
I
≤
1
⎜
⎟
o
o
⎝
⎠
5
⎛
d
⎞
(22.4)
z
≈
0.3
h
1
−
for
LAI
>
1
⎜
⎟
o
⎝
⎠
h
where
z
o
' is the aerodynamic roughness of the underlying (soil) surface.
Excess resistance
One significant general result found in the wind tunnel studies described in
Chapter 21 is that the leaf boundary-layer resistance for the transfer of
momentum is typically about an order of magnitude less than that for other
exchanged entities, because momentum transfer can be by the efficient
bluff
body
process in addition to the
skin friction
process. This general difference
between the boundary-layer resistance for momentum and other exchanged
entities is not likely to be greatly altered by the mutual sheltering of clumped
leaves. This raises the question, how can this known difference in boundary-
layer resistances best be simply acknowledged in formulae describing the total
resistance between the surface of the leaf and the above-canopy reference level
when a big leaf representation is used?
The approach that has now almost universally been adopted for allowing for
the difference in boundary-layer resistances is to add an '
excess resistance
' to the
aerodynamic resistance for momentum transfer when the effective aerodynamic
resistance for other exchanges is calculated. The excess resistance approach not
unrealistically assumes that the effective source/sink level for other exchanged
entities is lower in the canopy than the sink of momentum, because the rate of
divergence of downward momentum flux in the canopy is enhanced by bluff body
processes. The momentum flux therefore dissipates more quickly than it would
were only skin friction processes available. As discussed in Chapter 19, when
