Geoscience Reference
In-Depth Information
Figure 19.2
Schematic
diagram of a slab model with
fixed profiles of virtual
potential temperature and
humidity, the mean values of
which change in response to
inputs from the surface and
through the entrainment
layer.
Entrainment layer
H
e
E
e
Fixed virtual
temperature
profile
Fixed
humidity
profile
H
s
E
s
Surface layer
q
v
t
q
t
∝
H
e
+
H
s
∝
E
e
+
E
s
Whole boundary layer
Whole boundary laye
r
Equations (18.1) and (18.2). In practice, slab models can provide a reasonable
approximate description of the actual behavior of the ABL in daytime conditions.
Local, first order closure
The most popular closure scheme adopted in the ABL over flat homogenous
surfaces is framed by analogy with Newton's law for molecular viscosity and
Fourier's and Fick's laws for molecular diffusion of heat and mass. It involves
assuming linear relationships between turbulent fluxes and the local mean gradient
of the relevant atmospheric variable driving these fluxes. For example, in the case
of kinematic momentum flux,
t
k
, sensible heat,
H
k
, and vapor flux,
E
k
, in the vertical
direction, the relevant local mean gradients are those of wind speed, potential
temperature, and specific humidity, respectively, and the associated general
equations describing their interrelationship are:
∂
u
−τ
=
(
uw
¢¢
)
= −
K
.
(19.4)
k
M
∂
z
∂
q
v
H
=
θ
¢¢
w
= −
K
.
(19.5)
v
∂
k
H
q
Eqw K
z
∂
=
¢¢
= −
.
(19.6)
V
∂
k
where
K
M
, K
H
, and
K
V
are the (at this stage undefined)
eddy diffusivities
for the
turbulent fluxes of momentum, sensible heat, and water vapor.
