Geoscience Reference
In-Depth Information
Figure 3.17.
Effect of errors in surface luxes on the derivation of lux-gradient rela-
tionships for (
a
) momentum and (
b
) heat. The solid line depicts the reference lux-
gradient relationship, whereas the symbols show the effect of an error of 20% in
either the surface stress or surface heat lux. If similarity relationship and errors are
aligned, the experimentally determined relationship will be partly based on spurious
self-correlation.
Zero-Plane Displacement
The similarity relationships have been derived under the assumption that the height
above the surface
z
is a relevant height. However, the effect of roughness obstacles is
that they force the low upward. Hence the height relative to the ground surface under-
lying the roughness obstacles is not necessarily the most relevant height to describe
the height variation of the low properties. In terms of the plants in
Figure 3.13
: the
low does not 'know' how long the stems of those plants are, and hence the exact
location of the surface on which the plants stand is irrelevant. Therefore, in the rela-
tionships derived in this section (and that are used in later sections and chapters) this
has to be taken into account by always interpreting the height
z
as (
Z - d
) where
d
is
the zero-plane displacement height (or displacement height in short): the height of the
surface as the low experiences it. Then
Z
is the height above the substrate (Garratt,
1992
). For example, Eq. (
3.23
) should be interpreted as:
u
Zd
Zd
−
−
u
Z
u
Z
u
2
(
)
−
()
=
*
ln
(3.38)
κ
u
2
u
1
u
1
Physical interpretations of
d
are that it is either the height where the drag acts on
the canopy elements (Thom,
1971
; Jackson,
1981
), or it is the equivalent of the
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