Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 102

The φ -functions are generally called lux-gradient (or lux-proile) relationships
because they describe how the lux of a quantity (contained in u * , θ * , q * or q x* ) are related
to their respective gradients. Physically, the dimensionless gradients can be interpreted
as the inverse of transport eficiency as it is the gradient needed to produce a certain
lux. If turbulence is intense, only a small gradient is needed to produce a given trans-
port and hence the eficiency is large relative to neutral conditions (small dimensionless
gradient and hence a small value for the φ -function). This is consistent with the example
shown in Figure 3.14 , where the unstable part of the function is below the neutral value.
The reverse argument holds for the stable side: suppressed turbulence leads to a smaller
transport eficiency and hence to a larger dimensionless gradient.
The dimensionless gradients also show that - for a given stability and hence trans-
port eficiency - the magnitude of the vertical gradient of a quantity scales linearly
with the surface lux: if the surface lux doubles, the gradient will double as well.
Once the φ -functions are known they can be used inversely, for example, to deter-
mine the sensible heat from the vertical temperature gradient. This is discussed in
Section 3.6 .
In the 1960s a number of ield experiments were conducted to determine the shape
and coeficients of those universal functions (see Dyer, 1974 ). It happened only then
because the instrumentation needed was not available earlier. One of the key experi-

z
L



  

ments was the Kansas experiment (1968). The result for φ m

  , from that experi-
ment, is shown in Figure 3.14 as an illustration. The functions used in this topic are
given in Section 3.5.3 and are shown in Figure 3.17 .
In fact, MOST is more general. According to MOST any mean turbulence quantity
(not only vertical gradients, but also variances, etc.) is a universal function of z

L when
the quantity is made dimensionless with a combination of the relevant scale(s) (from
the list in Eq. ( 3.17 )), and height z .

Question 3.13: To apply MOST to other mean turbulent quantities, those need to be
non-dimensionalized with a combination of relevant scales.
a) How can the standard deviation of temperature ( σ T ) be made dimensionless?
b) How can the structure parameter of temperature, C T 2 (which has units of K 2 m -2/3 ) be
made dimensionless?

3.5.2 Physical Interpretation of z/L and Its Relationship
to the Richardson Number

The dimensionless group z

L was formed, because we supposed that it would give
information on the intensity of turbulence, based on the TKE budget equation. In
that sense it should contain the same information as the Richardson number derived