Geography Reference
In-Depth Information
D.2
PSEUDOADIABATIC LAPSE RATE
Section 9.5.2 showed that from the first law of thermodynamics the lapse rate
for a saturated parcel undergoing pseudoadiabatic ascent can be obtained from the
formula
∂q
s
∂T
ρg
∂q
s
∂p
dT
dz
+
g
c
p
=−
L
c
c
p
dT
dz
−
(D.10)
p
T
=
Noting that q
s
0.622 is the ratio of the molecular weight of
water to that of dry air and utilizing (D.4), we can express the partial derivatives
in (D.10) as
∂q
s
∂p
εe
s
/p, where ε
=
∂q
s
∂T
ε
2
L
c
e
s
pRT
2
q
s
p
ε
p
∂e
s
∂T
=
εL
c
q
s
RT
2
T
≈−
and
p
≈
=
Substitution into (D.10), and noting that g/c
p
=
d
, then yields the desired result:
dT
dz
=
[1
+
L
c
q
s
/ (RT )]
1
εL
c
q
s
/
c
p
RT
2
s
≡−
d
+
