Geography Reference
In-Depth Information
9.5.4
Convective Available Potential Energy (CAPE)
Development of convective storms depends on the presence of environmental con-
ditions favorable for the occurrence of deep convection. Several indices have been
developed to measure the susceptibility of a given temperature and moisture pro-
file to the occurrence of deep convection. A particularly useful measure is the
convective available potential energy
. CAPE provides a measure of the maximum
possible kinetic energy that a statically unstable parcel can acquire (neglecting
effects of water vapor and condensed water on the buoyancy), assuming that the
parcel ascends without mixing with the environment and adjusts instantaneously
to the local environmental pressure.
The momentum equation for such a parcel is (2.51), which can be rewritten
following the vertical motion of the parcel as
Dw
Dt
=
Dz
Dt
Dw
Dz
=
w
Dw
b
Dz
=
(9.45)
where b
(z) is again the buoyancy given by
g
ρ
env
−
ρ
parcel
ρ
parcel
g
T
parcel
−
T
env
b
=
=
(9.46)
T
env
and T
env
designates the temperature of the environment. If (9.45) is integrated
vertically from the level of free convection, z
LF C
, to the level of neutral buoyancy,
z
LN B
, following the motion of the parcel the result is
z
LN B
g
T
parcel
−
dz
w
max
2
T
env
=
≡
B
(9.47)
T
env
z
LF C
Here, B is the maximum kinetic energy per unit mass that a buoyant parcel could
obtain by ascending from a state of rest at the level of free convection to the level
of neutral buoyancy near the tropopause (see Fig. 9.10). This is an overestimate
of the actual kinetic energy realized by a nonentraining parcel, as the negative
buoyancy contribution of liquid water reduces the effective buoyancy, especially
in the tropics.
In a typical tropical oceanic sounding, parcel temperature excesses of 1-2 K
may occur over a depth of 10-12 km. A typical value of CAPE is then B
≈
500 m
2
s
−
2
. In severe storm conditions in the Midwest of North America, how-
ever, parcel temperature excesses can be 7-10 K (see Fig. 9.10) and B
2000-
3000 m
2
s
−
2
. Observed updrafts in the latter case (up to 50 m s
−
1
) are much
stronger than in the former case (5-10 m s
−
1
). The small value of CAPE in the
mean tropical environment is the major reason that updraft velocities in tropical
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