Geoscience Reference
In-Depth Information
4
Z
o
Z
o
H
In
(5)
(3)
Figure 22.5
Observed values of
ln(
z
0
/
z
H
) as a function of the
roughness Reynolds number
Re*
= (
u
*
z
o
)/ν for surface types
(1) vineyard, (2) short grass,
(3) medium grass, (4) bean crop,
(5) savanna scrub, and (6) and
(7) pine forest. (Redrawn from
Garratt, 1992, published with
permission.)
(2)
2
(4)
(6)
(1)
(7)
0
10
100
1000
10000
100000
Re*
−
2
The value of
r
e
has been measured in field studies for a wide range of natural,
permeable, fibrous surfaces. Figure 22.5 shows measured values of ln(
z
0
/
z
H
) as a
function of the roughness Reynolds number (defined by
Re*
) for a wide
range of surface types. Thus, the observed magnitude of ln(
z
0
/
z
H
) for the fibrous
vegetation surfaces is of order two which, given the very substantial observational
variability in these measurements, roughly corresponds to
z
0
P
≈ (
z
0
/ 10).
Substituting
z
0
P
≈ (
z
0
/ 10) into Equations (20.35) while allowing the possibility
that the measurement height for temperature,
z
m
′
=
(
u
*
z
o
)/
ν
, might differ from that for wind
speed,
z
m
, gives:
⎛
⎞
⎛
zd
zd
−
⎞
¢
−
1
(22.8)
r
H
==
ln
m
ln
m
⎜
⎟
⎜
⎟
a
ku
2
z
z
10
⎝
⎠
⎝
⎠
m
0
0
Commonly the whole canopy aerodynamic resistance,
r
a
, is assumed to be the
same for sensible and latent heat transfer and given by:
⎛
⎞
⎛
zd
zd
−
⎞
¢
−
1
(22.9)
rr r
===
V
H
ln
m
ln
m
⎜
⎟
⎜
⎟
a
a
a
ku
2
z
z
10
⎝
⎠
⎝
⎠
m
0
0
Roughness sublayer
The turbulent interaction of the atmosphere can be parameterized in one dimen-
sion through the aerodynamic parameters
z
0
and
d
, and similarity theory is
assumed to be independent of the nature of the underlying surface. However, field
observations over tall vegetation suggest that very close to the surface (typically for
heights up to 50
z
0
) this is not true and that surface-related features (such as the
'wakes' generated by individual plants) can alter the local efficiency of turbulent
