Geoscience Reference
In-Depth Information
Figure 3.18
Relationship between roughness lengths, surface values and proiles:
for momentum (left) and temperature (right). The solid lines are the proiles accord-
ing to Eq. (
3.29
). In the region where they are valid the lines are solid. The dashed
lines indicate that the proiles are extrapolated downward into the roughness sublayer
where the surface layer proiles are not valid.
Question 3.24:
Given the observations of
Question 3.19
, determine the roughness
length for momentum for the surface under consideration.
Question 3.25:
Given the following wind speed observations: 10 m s
-1
at 10 m height
and 7 m s
-1
at 2 m. Assume neutral conditions.
a) Compute the friction velocity
u
*
, and the roughness length
z
0
.
b) Compute the aerodynamic resistance
r
a
for
z
= 2 m (i.e., the resistance between the
surface and 2 m).
Observations above the same terrain at another moment show the same wind speeds.
Now the potential temperature appears to be 20 °C at 10 m height and 21.5 °C at 2 m.
c) Is the surface layer neutrally, stably or unstably stratiied?
d) Note for each of the following variables if they will be larger than, smaller than, or
equal to the values determined in the questions (a) and (b):
u
*
,
z
0
and
r
a
(for
z
= 2m).
Explain your answers.
Question 3.26:
A correct value for the roughness length for heat is important to obtain
the correct link between surface temperature and sensible heat lux.
Given are a sensible heat lux of 200 W m
-2
, an air temperature at 2 m height of
20 ºC, a friction velocity of 0.4 m s
-1
and a roughness length for momentum of 5 cm
(ignore the effect of stability). Then, using an expression similar to Eq. (
3.40
) (but
then for temperature: in fact Eq. (
3.42
) ignoring the stability correction), the sur-
face temperature can be determined, provided that we know the roughness length
for heat.
Compute the surface temperature for the following values of the ratio
z
0
/z
0h
: 10, 100
and 1000.
Search WWH ::
Custom Search