Geoscience Reference
In-Depth Information
where
g
is the acceleration due to gravity and
θ
0
is the reference-level potential
temperature at the cloud-base level.
By substituting for
W
and taking
θ
∗
as the production of temperature perturbation
at the cloud-base level by MFC, we arrive at the following expression since there is
a linear relationship between the vertical velocity perturbation
W
and temperature
perturbation
θ
(from Eqs. 1.4 and 1.6):
θ
*
(2.1)
θ
=
ln
z
=
θ
fz
.
*
k
Thus, the in-cloud vertical velocity and temperature perturbation follow the
fz
dis-
tribution (Fig. 1.5).
2.1.4
In-Cloud Temperature Lapse Rate Profile
The saturated adiabatic lapse rate
Γ
sat
is expressed as
=−
L
Cz
d
d
χ
,
ΓΓ
sat
p
where
Γ
is the dry adiabatic lapse rate,
C
p
is the specific heat of air at constant pres-
sure, and d
χ
/d
z
is the liquid water condensed during parcel ascent along a saturated
adiabat
Γ
sat
in a height interval d
z
.
In the case of cloud growth with vertical mixing, the in-cloud lapse rate
Γ
s
can
be written as
=−
L
C
d
d
q
z
,
ΓΓ
s
p
where d
q
, which is less than dχ, is the liquid water condensed during a parcel ascent
d
z
and
q
is less than the adiabatic LWC
q
a
. From Eq. (2.1),
(2.2)
θ
fz
d
d
θ
θ
*
ΓΓ Γ
=−=−=−
Γ
,
s
z
r
r
where d
θ
is the temperature perturbation
θ
during parcel ascent d
z
. By concept, d
z
is the dominant turbulent eddy radius
r
(Fig. 1.2).
2.1.5
Total Cloud LWC Profile
The total cloud LWC
q
t
at any level is directly proportional to
θ
as given by the fol-
lowing expression:
Search WWH ::
Custom Search