Geoscience Reference
In-Depth Information
If we could use this equation to determine a turbulent lux, just in terms of the vertical
gradient of the transported quantity and a diffusivity, life would be very easy. But note
that Eq. (
3.1
) is really only a
deinition
of
K
h
: we only say that there is a parameter
(
K
h
) that links the lux to a local gradient, but we do not make any statement about the
magnitude or variation of this proportionality factor, not even about its sign (although
one would hope that a diffusion coeficient is positive). Also note that the temperature
in Eq. (
3.1
) carries an overbar, denoting that this is an average temperature (an instan-
taneous proile would show too much variation, as can be seen in
Figure 3.2
).
Equation (
3.1
) can also be used in a reverse sense: using observations of the lux
and the gradient, the turbulent diffusivity can be deduced. To this end, we use data
gathered on a sunny day in June, at the Cabauw tower (operated by Royal Nether-
lands Meteorological Institute [KNMI]) in the centre of the Netherlands.
Although observations of temperature are available up to 200 m height, we restrict
ourselves to the lowest 20 m, as in this lower layer we can assume the sensible heat
lux to be rather constant with height (within 10%, to be discussed later,
Section
3.4.2
) so that we can use the
surface
sensible heat lux to represent the lux at a given
height.
Figure 3.3b
shows the temperature proile at two instances: at night time and
during mid-day. Temperatures are much lower at night than during the day. The gradi-
ent is positive at night and negative at day. Finally, the gradients are larger (in absolute
sense) close to the surface than at higher levels. From these temperature proiles we
can directly infer the behaviour of the turbulent diffusivity (
Figure 3.3d
):
•
The values of the diffusivities (order of 1 m
2
s
-1
) are much larger than the molecular ther-
mal diffusivity (roughly 2·10
-5
m
2
s
-1
).
The combination of a positive temperature gradient with a negative sensible heat lux
•
gives a positive diffusivity at night. The same result is obtained for daytime with a nega-
tive gradient and a positive heat lux.
From Eq. (
•
3.1
) it is clear that the large temperature gradients close to the surface are
connected to small values for the diffusivity. One
could
interpret this as: to transport the
same amount of energy (we assumed the lux to be constant with height) a smaller dif-
fusivity is needed when the gradient is larger. But nature has a different causality chain:
because the diffusivity is smaller close to the surface, a larger gradient is needed to trans-
port the same amount of energy.
The diffusivities are much higher during daytime than during night time (by one to two
•
orders of magnitude).
To conclude,
Figure 3.3c
shows the entire diurnal cycle of the diffusivities at three
heights. The variation between day and night and the variation with height are clearly
visible here as well. There are some undeined points around sunrise and sunset,
which are due to the fact that when gradients and luxes become small, they may
change sign at different moments, yielding negative values for the diffusivity.
Essentially, the rest of this chapter is devoted to the variation of the turbulent diffu-
sivities with height and time and how we can understand and describe that variation.
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