Geoscience Reference
In-Depth Information
6. After leaving the loop, compute the momentum lux, sensible heat lux and latent heat
lux from
u
*
,
θ
*
and
q
*
.
Note that once the above iteration (including the
active
scalar
θ
or
θ
v
) has produced
values for
u
*
and
θ
*
, the luxes of
passive
scalars can be computed explicitly (without
iteration) using expressions similar to Eq. (
3.29
), but now with a known
z/L
.
Recall that all heights used in these calculations should be taken relative to the
displacement height (i.e., any occurrence of
z
in fact should be read as (
Z - d
); see
Section 3.5.6
).
Question 3.23:
Given are the following observations at 2 and 10 meter height: potential
temperatures are 281.52 and 280.41 K, and wind speeds are 1.7 and 2.9 m s
-1
, respec-
tively.
a) Using a spreadsheet program, determine iteratively
u
*
and
θ
*
for this situation (sim-
ply use
θ
*
in the deinition of the Obukhov length, rather than
θ
v*
).
b) Determine the sensible heat lux (assume
ρ
=1.15 kg m
-3
and
c
p
= 1015 J kg
-1
K
-1
).
3.6.2 Fluxes from Observations at a Single Level in the Air
and One at the Surface
In many practical applications it is useful or necessary to take the lower level of
the equations that describe vertical differences (Eq. (
3.29
)) at the surface. But this
directly poses a problem because taking
z
u
1
or
z
t
1
equal to zero would imply a division
by zero. Furthermore, the surface is located within the roughness sublayer in which
the similarity relationships are even not valid. To overcome this problem, the concept
of the roughness length
z
0
is introduced: the surface value of the variable under con-
sideration is supposed to occur at height
z
0
above the surface. Then, if the roughness
lengths for momentum and the scalars (see later) are known, as well as the surface
values of wind speed and the scalars under consideration, the luxes can be deter-
mined. But the 'if' in the previous sentence is a big 'if'.
Roughness Length: Concept
For the wind speed proile this concept is straightforward: the wind speed should be
zero at the surface,
18
that is, the wind does not slip. Then the roughness length
z
0
is
determined in such a way that the wind speed proile described by Eq. (
3.29
) becomes
zero at
z = z
0
. The roughness length for momentum is also called the
aerodynamic
roughness length. For the determination of the roughness length for momentum one
either needs wind speed measurements at two heights or observations at one height,
but then including the momentum lux momentum lux. In addition, information on
stability in the form of
z/L
is needed. For neutral conditions (
z/L
= 0) this proce-
dure is simpliied because of the absence of buoyancy effects, and we elaborate the
18
This is valid for a solid surface. For low over water the speed at the surface will be equal to the low speed of the
water.
Search WWH ::
Custom Search