346 Weather Systems

Solution: Substituting values into (8.4), we obtain

For reference, values of CAPE ranging from 0 to1000 J kg�1 are considered marginal for deep con-vection, 1000–2500 adequate to support moderateconvection, 2500–4000 adequate to support strongconvection, and in excess of 4000 indicative of thepotential for extreme convection.12 �

If it were a common occurrence for air parcelsin ordinary cumulus clouds to reach their level offree convection, the CAPE would never build up tovalues high enough to support vigorous deep con-vection. Hence, the degree to which convection isinhibited by the presence of a stable layer or inver-sion at the top of the planetary boundary layer alsoplays a role in setting the stage for convectivestorms. A measure of this so-called convective inhi-bition (CIN or CINH) is the energy, in units of

� 3978 J kg�1 CAPE � 287 � 10 �C � ln(700�175)

J kg�1, required to lift the reference air parcel to itsLFC. So defined, CIN may be viewed as negativeCAPE and can be represented as an area on askew-T ln p plot, as shown in Fig. 8.42. To set thestage for vigorous deep convection it is essentialthat the CIN be non-zero, but not so large that itprecludes the possibility of deep convection alto-gether. For CIN � 100 J kg�1, deep convection isunlikely to occur in the absence of external forcing,such as might be provided by the approach of astrong front. A return of several thousand units ofCAPE on an investment of perhaps several tens ofunits of “startup costs” required to overcome theCIN rivals the performance of the most successfulnew enterprises in the world of business!

The geographical distribution of the frequency oflightning flashes shown in Fig. 6.56 provides a meas-ure of the degree to which the vertical stratificationof temperature and moisture over various regions ofthe world is conducive to deep convection. Many ofthe features in this pattern mirror the distribution ofrainfall shown in Fig. 1.25. However, relative to therainfall, lightning flashes are relatively more frequentover the continents than over the oceans because theheating of the land surface greatly enhances theCAPE during the afternoon hours, giving rise tomore vigorous convection.

For the CAPE inherent in the temperature andmoisture sounding to be realized, two things need tohappen: the environmental air needs to be destabi-lized (i.e., the CIN needs to be reduced) by liftingand, within this destabilized air mass, air parcels needto be lifted up to their LFC. Lifting destabilizes theenvironmental sounding by weakening the inversionthat caps the mixed layer so that buoyant air parcelsfrom below can break through it. This process is illus-trated schematically in Fig. 8.43.

The lifting and associated low level convergencethat is responsible for lifting the inversion layer andthereby destabilizing the environmental sounding isusually associated with some large-scale forcingmechanism such as the approach of an extratropicalcyclone, which can be anticipated a day or more inadvance on the basis of numerical weather prediction.In contrast, the lifting of the air parcel that initiates

12 Another widely used indicator of the potential for deep convection is the so-called lifted index (LI), defined as the temperaturedeficit (relative to the environment) of an air parcel originating at the earth’s surface that is lifted dry adiabatically up to its lifting conden-sation level and then moist adiabatically up to the 500-hPa level. Negative lifted indices are indicative of a potential for deep convection;values below �9 indicate the potential for severe convection. Variants of the lifted index based on air parcels originating at various heightswithin the planetary boundary layer are also sometimes used.

100-

200-

300-

400-

500-

600-

700-

800-

900-1000-

–20 –15 –10 –5 0 5 10 15 20 25 30 35 40

Td T

LFC

EL

LCL

CAPE

CIN

Fig. 8.42 A hypothetical sounding illustrating the conceptsof convective available potential energy (CAPE) and convec-tive inhibition (CIN). The CAPE and CIN in this sounding areindicated by shading.

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Courtesy of Brian Morganti

A B

352 Weather Systems

lower, darker cloud base, followed by an abrupt windshift and temperature drop that marks the arrival ofthe gust front. Heavy precipitation would not beginuntil a few minutes after the passage of the gust frontand might include hail. The shallow pool of cool,moistened downdraft air left behind by the stormmay persist for hours, inhibiting the development offurther convection.

c. Supercell storms

The distinguishing characteristic of the supercellstorm is its rotating updraft that is clearly evident inFig. 8.50, and even more so in time-lapse photo-graphs and in dual-Doppler radar imagery. Rotationrenders the supercell storm more robust by inducingthe formation of a mesolow (i.e., a pressure mini-mum) within the updraft, which is superimposedupon the hydrostatically balanced pressure field thatexists by virtue of the density gradients. The mesolowforms as the rotating air is pulled outward from thecenter of the updraft by the centrifugal force.Pressure at the center of the updraft drops until theinward-directed pressure gradient force and the out-ward-directed centrifugal force come into in a state

of cyclostrophic balance, as illustrated schematicallyin Fig. 8.51. Under these conditions,

(8.5)

where V is the speed of the air circulating around theupdraft at radius r.16

V2

r�

1� �p�r

Fig. 8.49 Schematic of an idealized multicell storm developing in an environment with strong vertical shear in the direction ofthe vertically averaged wind. The vertical profile of equivalent potential temperature �e in the environment is shown at the left,together with the wind profile. Arrows in the right panel denote motion relative to the moving storm.

0 20 40320 340e(K) u(m s–1)

(a) (b)

Rain shaft Gust front

Moist layerInversion

New cells

Mamma

Anvil

Tropopause

"Overshooting"cloud top

0C0C

Storm motion 125

250

500

1000

15

10

5

0

Hei

ght (

km)

Pre

ssur

e (h

Pa)

(c)Direction of motion

16 Geostrophic balance and cyclostrophic balance are special cases of the more general, three-way gradient wind balance discussed inSection 7.2.6. In the case of geostrophic balance, the centrifugal force is neglected, while in the case of cyclostrophic balance the Coriolisforce is neglected. Which forces need to be retained and which ones can be neglected depend on whether the vorticity of the system underconsideration is much smaller than, comparable to, or much larger than the planetary vorticity; for the specific case of circular vortices, itdepends on the rotation rate, as shown in Exercise 8.9. In contrast to flow that is in geostrophic balance, cyclostrophic flow can circulate ineither direction around a mesolow and, indeed, both clockwise and counterclockwise circulations have been observed.

Fig. 8.50 Supercell thunderstorm over north-central Kansason May 8, 2001, with a rotating updraft and a shaft of heavyrain and hail. [Courtesy of Chris Kridler.]

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358 Weather Systems

Fig. 8.59 Looking north toward the approaching forwardflank of a strong gust front marked by a distinctive arcus cloudwith strong counterclockwise rotation about a horizontal axispointing into the page. [Courtesy of Kathryn Piotrowski.]

Fig. 8.60 Thunderstorms over the midwestern United States,just before sunset July 10, 1994, as revealed in satellite imagery.The low sun angle accentuates the overshooting cloud tops.[NASA-GSFC GOES Project.]

Fig. 8.58 Shelf cloud at the base of the updraft of a supercellstorm looking southward along the forward flank of the gustfront in the direction of the mesocyclone. The gust front isadvancing rapidly toward the left (E), propelled by rain-cooled downdraft air. When viewed from a distance lookingfrom left to right, rising cloud motion often can be seen in theleading (outer) part of the shelf cloud, while the undersideoften appears turbulent, and wind-torn, as in this image.[Courtesy of Brian Morganti.]

Substituting v0 � 100 m s�1, � � 1.25 kg m�3, then�p � 1.25 � 104 Pa � 125 h Pa. This estimated valueis consistent with the observation that funnel cloudsoften extend all the way down to the ground.Pressure deficits in excess of 40 hPa have been docu-mented at the Earth’s surface, and it is conceivablethat even larger ones would be observed if it were

possible to obtain measurements in the middle oftornadoes. The lifting of dense objects by tornadoesis suggestive of the existence of upward pressuregradient forces many times the gravitational acceler-ation � (i.e., pressure decreasing with height at a ratefar in excess of the hydrostatic value of �1 hPa per8 meters). �

Fig. 8.57 Wall cloud developing along the base of a bell-shapedrotating updraft at the center of the mesocyclone of a supercellstorm. The view is looking SW. Observers located to the southof the storm at this time observed a tornado that rapidlybecame enshrouded in rain. [Courtesy of Brian Morganti.]

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A, Courtesy of Kathryn Piotrowski. B-E, Courtesy of Eric Nguyen.

A B C

D E

8.62 Tornado & Wall Cloud

©1988 David Blanchard.