Geoscience Reference
In-Depth Information
include the flux gradient relationships (i.e.
f
M
,
f
H
and
f
V
) which depend on (
z
-
d
)/
L
,
and which therefore depend on the ambient fluxes of sensible heat flux and
momentum. But these in turn are themselves dependent on the resistances that are
being calculated.
Important points in this chapter
Dimensionless prognostic equation for TKE
: in the constant flux layer above
a uniform horizontal surface the prognostic equation for turbulent kinetic
energy (TKE) in the ABL can be re-written in dimensionless form as Equation
(20.1).
●
Dimensionless gradients
: in the dimensionless prognostic equation for TKE
the fourth term can be used to define
f
M
, the dimensionless gradient
of
wind speed (wind speed gradient normalized to friction velocity and height
above zero plane displacement): similar dimensionless gradients of virtual
potential temperature,
f
H
, and specific humidity,
f
V
, can also be defined.
●
Application of
f
V
: in K Theory the reciprocals of the dimension-
less functions
f
M
,
f
H
and
f
V
act as multipliers to modify the mixing length
(and thus the efficiency of turbulent transfer) in the surface layer.
f
M
,
f
H
and
●
Dimensionless measure of stability
: in the dimensionless prognostic equa-
tion for TKE the second term can be used to define, (
z
-
d
)/
L
, a dimensionless
measure of atmospheric stability, in terms of which the dimensionless
functions
f
M
,
f
H
and
f
V
(and thus the efficiency of turbulent transfer) can be
parameterized.
●
Specification of
f
V
: the functional forms of
f
M
,
f
H
and
f
V
with
respect to (
z
-
d
)/
L
are assumed to be universally applicable and field
experiments were carried out to define them: the expressions in Table 20.1
are adopted in this text.
f
M
,
f
H
and
●
From kinematic to natural units
: before application equations for the
kinematic fluxes of sensible heat, latent heat and momentum derived from
K-Theory must be returned to natural units to give Equations (20.17),
(20.20), and (20.21).
●
Resistances
: integrating the relationships between fluxes and gradients of
atmospheric variables gives
resistances
(by analogy with Ohm's law) that
relate fluxes to the differences in variables between two heights.
●
Aerodynamic resistance
: total aerodynamic resistance to the turbulent
transfer between a level in the atmosphere and a 'source' level in a canopy
can be derived in terms of wind speed, zero plane displacement, and
aerodynamic roughness, e.g., Equations (20.34), (20.35), and (20.36).
●
