Geography Reference
In-Depth Information
Thus, as is shown in detail in Appendix D, following the ascending saturated
parcel
1
L
c
q
s
(RT )
+
dT
dz
=
1
εL
c
q
s
c
p
RT
2
s
≡−
d
(9.42)
+
where ε
=
0.622 is the ratio of the molecular weight of water to that of dry air,
d
g/c
p
is the dry adiabatic lapse rate, and
s
is the
pseudoadiabatic lapse
rate,
which is always less than
d
. Observed values of
s
range from
≡
4Kkm
−
1
∼
6-7 K km
−
1
in warm humid air masses in the lower troposphere to
∼
in the
midtroposphere.
9.5.3
Conditional Instability
Section 2.7.3 showed that for dry adiabatic motions the atmosphere is statically
stable provided that the lapse rate is less than the dry adiabatic lapse rate (i.e.,
the potential temperature increases with height). If the lapse rate lies between
dry adiabatic and pseudoadiabatic values (
s
< <
d
), the atmosphere is stably
stratified with respect to dry adiabatic displacements but unstable with respect
to pseudoadiabatic displacements. Such a situation is referred to as
conditional
instability
(i.e., the instability is conditional to saturation of the air parcel).
The conditional stability criterion can also be expressed in terms of the gra-
dient of a field variable θ
e
, defined as the equivalent potential temperature of a
hypothetically saturated atmosphere that has the thermal structure of the actual
atmosphere.
2
Thus,
d
L
c
q
s
c
p
T
d ln θ
e
=
d ln θ
+
(9.43)
where T is the actual temperature, not the temperature after adiabatic expansion
to saturation as in (9.40). To derive an expression for conditional instability we
consider the motion of a saturated parcel in an environment in which the potential
temperature is θ
0
at the level z
0
. At the level z
0
−
δz the undisturbed environmental
air thus has potential temperature
θ
0
−
∂θ
∂z
δz
Suppose a saturated parcel that has the environmental potential temperature at
z
0
−
δz is raised to the level z
0
. When it arrives at z
0
the parcel will have the
potential temperature
θ
0
−
∂z
δz
∂θ
θ
1
=
+
δθ
2
Note that θ
e
is
not
the same as θ
e
except in a saturated atmosphere.
