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x
=
ρ
′′
and the surface luxes that are the subject of this topic.
Figure 3.8
shows this link for
the sensible heat lux and water vapour lux: heat and water vapour are exchanged
between the surface and the atmosphere by nonturbulent transport (
H
and
E
). In the
atmosphere above the surface the transport takes place by turbulence and is expressed
by the covariance of the vertical wind speed and the transported quantity. If turbulent
luxes are considered suficiently close to the surface, the surface lux and the turbu-
lent lux are very similar because what goes into the atmosphere at the surface has
to pass at a few metres above the ground as well (for a more precise discussion, see
Section 3.4.3
). In the context of this topic, this leads to the following link between
surface luxes and turbulent luxes:
Now the question arises as to what is the link between the turbulent lux
F
wX
•
Transport of heat: The energy lux is
p
′′
(in W m
-2
), where it should be noted
that both the dry air component and the water vapour carry sensible heat:
c
p
is the speciic
heat of moist air.
8
Transport of water vapour: The mass lux is
Hc
w
=
ρ
θ
=
ρ
′′ (in kg s
-1
m
-2
); the energy lux is
•
E
wq
=
ρ
′′
(in W m
-2
).
Transport of an arbitrary gas, for example, the mass lux of CO
LL
wq
E
v
v
=
ρ
′′ (in kg
•
2
:
F
wq
c
c
s
-1
m
-2
).
Transport of momentum:
=
−
w
′′ (in N m
-2
) (the covariance is usually negative
(downward momentum transport), but as the surface stress
τ
is taken positive, a minus
sign is included).
τ
ρ
•
Apart from the energy luxes (sensible and latent heat lux) and mass luxes (e.g.,
water vapour and CO
2
), another form of the luxes is often used in the context of
turbulence research: the so-called kinematic lux. This is the mass lux divided
by density (comparable to the relationship between dynamic and kinematic vis-
cosity) and in the case of the heat lux the sensible heat lux divided by
ρc
p
. The
relationship between the three representations is shown in
Table 3.2
. It is impor-
tant to realize that if one of the three representations is known, the others can be
determined.
8
In fact the transported quantity is enthalpy
c
p
θ
and thus:
Hwc
(
p
. As the speciic heat
c
p
depends
on speciic humidity (see
Appendix B
), this would lead to extra terms in the Reynolds decomposition:
Hc
w
=
ρ
′ ′
=
. .
. . However, the last term in the Reynolds
decomposition is erroneous (it suggests that all water vapour transported upward has been heated at the surface
from 0 K to the ambient temperature). The error is related to the fact that enthalpy is like potential energy: it can
be known only up to an unknown reference value: only differences in enthalpy can be studied, no absolute values.
In the context of this topic the relevant locations would be the surface and observation height. Assuming the turbu-
lent luxes to be constant with height (equal to the nonturbulent surface luxes), the expression for
H
(at a certain
observation level) could be written as:
Hcwc
=
ρ
θ
θ
ρθρ
cw
′′
+
c
084
wq
′′
θ
′′
+
084
wq
′′
θ
+
0 84
wq
′′
pd
p
pd
−
( )
084. : if the temperature at measurement
level is lower than the surface temperature, the water vapour has lost some of its sensible heat (for more details, see
van Dijk et al.,
2004
).
=
ρθρ
′′
+
wq
′′
θ θ
p
pd
s
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