Geoscience Reference
In-Depth Information
example of wind speed observations at two heights. For neutral conditions we can use
the logarithmic proile (see also Eq. (
3.23
)):
z
z
u
2
uz
() ()
− =
uz
*
ln
(3.39)
2
1
κ
1
When
u
(
1
,
u
(
2
,
z
1
and
z
2
are known,
u
*
can be determined for this set of observa-
tions. Next, with this
u
*
the roughness length can be determined from:
z
z
u
⇔
κ
u
()
z
2
uz
() () ()
− ≡
uz
uz
=
*
ln
z
=
z
exp
−
2
(3.40)
2
0
2
0
2
κ
u
0
*
A more direct way, without the intermediate calculation of
u
*
, would be to take the
ratio of Eqs. (
3.39
) and (
3.40
), and calculate
z
0
from that (see
Question 3.24
).
For scalars the extension of the proiles towards the surface is less straightforward.
First one needs a value of the concentration of that scalar at the surface. For tempera-
ture this is possible because one can estimate the surface temperature from the emit-
ted longwave radiation (provided that one knows the emissivity of the surface). Then
the roughness length for heat,
z
0h
, is found by extrapolating the proile to that level
where the temperature is equal to the observed surface temperature.
The roughness length for heat is by no means equal to that of momentum. This is
due to the fact that the exchange of momentum (i.e., friction) between the air and the
surface takes place mainly by pressure forces (form drag), whereas the heat transport
between the surface and the air directly adjacent to it occurs by molecular diffusion
only. The latter is far less eficient, leading to a relatively high surface temperature
for a given amount of heat transport. Hence the temperature proile has to be extrap-
olated much further down to ind the observed surface temperature. This is illustrated
in
Figure 3.18
. Often the roughness length of heat is considered relative to that of
−
≡
z
z
momentum, either as a simple ratio
z
0
/
z
0h
or as
κB
1
ln
0
.
0
h
Although the details of the relationship between the roughness length for momen-
tum and the roughness length for scalars is not yet fully clear, it is a necessary concept
to provide a link between the sensible heat lux and the surface temperature:
•
In atmospheric models the surface temperature is a variable that both enters into the cal-
culation of the sensible heat lux (see later) and in that of the emitted longwave radiation.
Besides, the calculation of the soil heat lux is affected indirectly (see
Section 2.3
). The
use of an incorrect value of the roughness length for heat may yield signiicant errors
in the surface temperature and hence in the predicted surface luxes (e.g., Beljaars and
Holtslag,
1991
).
Surface temperatures observed from satellite-borne sensors are often used to estimate the
•
surface energy balance (including the sensible heat lux). In those calculations the rough-
ness length for heat is a critical parameter.
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