Geoscience Reference
In-Depth Information
Figure 19.3
Typical daytime
profiles of potential
temperature through
vegetation and the overlying
ABL, and typical height
dependent profile of the
vertical sensible heat flux
showing regions where K
Theory does not apply
because flow is not linearly
related to the local gradients.
Zero gradient flow
K Theory applicable
Counter gradient flow
0
q
0
H
The signs in Equations (19.4), (19.5), a
nd (
19.6) may be confusing and merit
explanation. The fluxes
is away from
the surface, in the direction of the Z axis. But all fluxes are from higher concentra-
tions toward lower concentrations. Consequently, if the gradients of wind speed,
virtual potential temperature, and specific humidity are all positive (i.e., increase
with height), the equivalent turbulent fluxes will all be
towards
the surface and
their values therefore negative. The minus sign on the right hand side of Equations
(19.4), (19.5), and (19.6) is required for this reason. The (in this case kinematic)
fluxes of sensible heat and moisture (and other turbulent fluxes) are d
efined
to be
posit
ive in the direction of the Z axis, i.e., in the same direction as
uw
¢¢
q¢ ¢
v
w
, and
qw
¢¢
are positive when
w
′
,
, and
q¢¢
w
qw
¢¢
, see Chapter 4. However in Equation (19.4), the momentum flux, in this case
kinematic momentum,
t
k
, is by convention
uni
quely defined to be positive when
toward the surface, with opposite sign to
uw
. This convention is helpful later
when defining friction velocity (see Equation (19.19)) and it reflects the fact that
momentum transfer is always towards the ground whereas
H
k
and
E
k
are often
away from the ground in daytime conditions.
The parameterization of turbulent fluxes in terms of mean gradients given in
Equations (19.4), (19.5), and (19.6) (and similar equations that could be written for
the turbulent fluxes of other atmospheric entities) is referred to as
K Theory
. It is the
simplest and most commonly used first-order closure parameterization, and it is
found from experiment to work quite well in the surface layer. However, it is known
to fail frequently if applied to describe vertical transfer within a stand of vegetation or
in the mixed layer, as illustrated in Fig. 19.3 for sensible heat. Within vegetation there
is often a positive sensible heat flux away from the ground in the lower portions of the
canopy, over a height range where the virtual potential temperature profile would sug-
gest flow toward the surface. Higher in the ABL, in the mixed layer in daytime condi-
tions, the gradient of the profile of virtual potential temperature is very small when the
sensible heat flux is perhaps large, and is initially positive near the ground and then
negative in the upper ABL. This phenomenon is known as
counter gradient flow
.
¢¢
