Geoscience Reference
In-Depth Information
Resistance
Figure 22.4
The concept of
excess resistance for the case of
sensible heat in which it is
assumed the additional
resistance for heat transfer above
that for momentum can be
parameterized in a single source
model by defining it to have a
lower source/sink height, at
which height the temperature
difference with respect to the
reference level is greater.
r
a
M
r
a
H
Effective sink
for momentum
r
e
Effective sink
for heat
T
o
'
T
o
Wind Speed or Temperature
derived from the above canopy wind speed profile in neutral conditions, the level
of the effective sink for momentum appears to be at (
d
z
o
), see Equation (19.22).
But the source/sink level for sensible heat and water vapor can be different, as
acknowledged in Equations (20.35) and (20.36). If the concept of excess resistance
is adopted, it is assumed that the effective source/sink level for sensible heat, for
example, is deeper in the canopy, see Fig. 22.4.
It is still assumed that the
eddy diffusivities
for the turbulent fluxes of momen-
tum, sensible heat, and water vapor (
K
M
, K
H
and
K
V
) are the same and given
by Equation (19.25) in neutral conditions. But the source/sink height for heat and
vapor in Equations (20.35) and (20.36) are at heights
z
0
H
and
z
0
V
above the zero
plane displacement,
d
, which are assumed to be less than
z
0
, the aerodynamic
roughness length for momentum. It is also usually assumed that the excess
resistance is the same for all properties and, therefore, that other properties have
a common source sink height
z
0
P
(
+
z
0
V
). Consequently, in neutral conditions,
the aerodynamic resistance for sensible heat, for example, is:
=
z
0
H
=
⎡
⎤
⎡
⎛
⎞
⎤
zd
⎛
zd
⎞
z
1
-
1
-
(22.5)
r
=
ln
=
ln
o
H
⎢
⎥
⎢
⎥
⎜
⎟
⎜
⎟
a
P
2
P
ku
.
z
k u
.
⎝
z
⎠
⎝
z
⎠
⎢
⎥
⎣
⎦
⎣
⎦
*
o
o
m
o
which equation can be re-written as:
ku
⎡⎤
⎡
zd
⎤
z
1
-
1
(22.6)
r
=
ln
+
ln
o
H
⎢
⎥
⎢⎥
a
2
2
P
ku
.
z
.
⎣
⎦
⎣⎦
o
m
m
o
Hence,
r
a
H
=
r
a
M
+
r
e
, where
⎡⎤
1
z
(22.7)
o
r
=
ln
⎢⎥
⎣⎦
e
2
P
ku z
.
m
o
