Geoscience Reference
In-Depth Information
20
Surface Layer
Scaling and
Aerodynamic
Resistance
Introduction
In the previous chapter, first order closure equations were defined by analogy with
molecular transfer processes. These equations related the kinematic turbulent
fluxes of momentum, sensible heat and latent heat to the mean profiles of wind
speed, virtual potential temperature and specific humidity through the (initially
unspecified) eddy diffusivities
K
M
, K
H
, and
K
V
, respectively. Observationally-
guided mixing length theory was then introduced to argue that in neutral
conditions
K
M
, K
H
, and
K
V
are all equal and can be expressed in terms of the von
Kármán constant, the height above the zero plane displacement, and either
u
*
as in
Equation (19.23) or the mean wind speed and aerodynamic roughness length as
in Equation (19.24).
Here, we go further than this and seek first order closure in unstable and stable
conditions. Providing the aerodynamics of the surface exchange is expressed in
dimensionless form, the influence of stability can be accounted for using
hypothetically universal, empirical correction functions. Such functions, which
are often called
stability corrections
, are necessarily also parameterized in terms
of an appropriately defined dimensionless measure of atmospheric stability.
The mathematical procedure used to define this dimensionless representation of
aerodynamic transfer and dimensionless stability corrections is called
surface
layer scaling
.
Once first order closure based on mixing length theory has been generalized
to apply in all stability conditions, the resulting equations can be re-expressed in
an alternative form that considers the rates of surface exchange by turbulent
transfer as being controlled by a resistance to flow called
aerodynamic resistance
.
The representation of inhibition to surface transfers in terms of resistances is now
widely accepted and almost universally adopted in models.
