Geoscience Reference
In-Depth Information
Integrating this equation over the height range
z
1
to
z
2
assuming there is no
significant loss of sensible heat flux (i.e. no flux divergence) between these two
levels, gives:
( )
()
z
z
1
H
∂
q
2
2
(20.26)
v
.
dz
=
.
dz
∫
∫
K
z
∂
−
ρ
c
z
H
z
ap
1
1
which can be re-written as:
(
)
z
=
1
z
=
2
q
−
q
v
v
(20.27)
H
a
p
=
r
2
(
1
r
H
where
v
q
are the virtual potential temperatures at
z
1
and
z
2
(with
z
1
being closer to the surface), and
( )
q
z
=
1
and
z
= 2
v
z
1
2
()
2
(20.28)
r
=
∫
.
dz
H
1
K
z
H
1
There is analogy between Equation (20.27) and Ohm's Law, which describes flow
of electrical current through a resistance in response to a voltage difference
between the ends of the resistance, i.e.
Voltage
(20.29)
Current
=
Resistance
The flow of sensible heat is analogous to the 'current,' and the difference in virtual
potential temperature analogous to the voltage difference that is driving the flow
of current. This analogy identifies
r
as a 'resistance' in Equation (20.27) that is
acting to moderate the flow of sensible heat between the two levels driven by
the difference in the virtual potential temperature between
z
1
and
z
2
. Similar
integrated diffusion equations can be written to describe the flow of momentum
and latent heat in terms of the 'resistances, thus:
()
2
1
ρ
c
(
e
z
=
1
−
e
z
=
2
)
(20.30)
ap
l
E
=
2
1
γ
()
r
V
and
(
u
z
=
2
−
u
z
=
1
)
(20.31)
tr
=
a
2
1
()
r
M
The three resistances
r
are in fact the
aerodynamic resistances
between the levels
z
1
to
z
2
for sensible heat, latent heat, and momentum transfer,
()
r
2
1
,
()
r
2
1
and
()
2
1
