Houze Robert A., Jr. Cloud Dynamics

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9.2 The Squall Line with Trailing Stratiform Precipitation 389

9.2.3.7 Vertical Vorticity in the Stratiform Region

The vertical vorticity

[defined in (2.56)] exhibits interesting behavior in the

stratiform region. Often a

center

of cyclonic vorticity forms in association with the

stratiform precipitation zone. Two observed examples are shown in Fig. 9.49 and

Fig. 9.50. A simulation with a mesoscale model of the type described in Sec.

9.2.3.6 shows a similar behavior (Fig. 9.51). The cyclonic vorticity maximum is

often observed to be

near

the back edge of the stratiform precipitation rather than

in the center

the stratiform region. However, this is not true for the model

example in Fig. 9.51, and the exact location of the vorticity center and other

details of the vorticity pattern vary from case to case.

262

Observations indicate that the development of the vorticity center in the trail-

ing stratiform region is especially strong and deep in the asymmetric type of

squall-line structure illustrated in Figs. 9.9b and 9.14b. The asymmetric structure

of the precipitation pattern is evidently in part a consequence of the vorticity

maximum. The results of one study of this type of vorticity center are indicated

schematically in Fig. 9.52. Analysis of the observed wind field shows that the

vertical vorticity

was intense at midstorm levels where strong rear inflow and

convergence existed; thus, stretching appears to have been the dominant mecha-

nism for intensifying the vorticity. A vorticity center of the observed strength

could have been produced from the planetary vorticity alone in

-1.5

h. Pre-

existing relative vorticity in the inflow current, such as might be associated with a

short-wave trough in the westerlies, would accelerate the process. The short spin-

up time helps explain why these mesoscale vortices are common features of the

midlevel convergent layer in the trailing stratiform regions of squall lines. The

strong

rear

inflow observed in the case shown in Fig. 9.52 was quite dry and

characterized by low

(Je, and the strong midlevel vorticity in that case was associ-

ated with convergence into the mesoscale downdraft. The downdraft region was

indeed dominated by cyclonic vorticity. The rear inflow air appears to have ob-

262 For a concise review of mesoscale vortex development in squall lines with trailing stratiform

regions, see Sec. I of Brandes (1990). Zhang and Fritsch (1987, 1988a,b) and Chen and Frank

(1992)

discuss the vortex development in model simulations of mesoscale convective systems.

Figure 9.47 Rear inflow in the tropical squall line shown in Figs. 9.7, 9.8, and 9.20. (a) Low-level

radar reflectivity pattern. Superimposed circles denote locations of wind profiles shown in (b). Profiles

show horizontal wind component normal to the leading convective line seen as the zone of intense

echoes in (a). Positive values denote flow from rear to front of the storm. (From Chong et al.,

1987.

Reprinted with permission from the American Meteorological Society.)

Figure 9.48 Mesoscale model simulation of the squall line with trailing stratiform region illustrated

in Figs. 9.15, 9.18, 9.31, 9.34, 9.40, 9.41, 9.43, 9.44, 9.45, 9.48, 9.53, and 9.54. Vertical cross section

normal to the squall line. Leading edge of the squall line at the ground is indicated by SL. Horizontal

flow perpendicular and relative to the squall line is indicated in m

S-I.

Positive values are directed from

rear to front (left to right). In (b) a model result with no diabatic heating has been subtracted from the

total result shown in (a). (From Zhang and Gao, 1989. Reprinted with permission from the American

Meteorological Society.)

Figure 9.49

storm

motion>

Figure 9.51

20ms·

100 Ion

20ms·\

9.2 The Squall Line with Trailing Stratiform Precipitation

391

tained horizontal vorticity by baroclinic generation [B

and B\' in (2.57) and (2.58)]

upstream to the south and west of the vorticity center where warm air lay to the

right facing downwind. As the inflow was tilted by the downdraft while it pene-

trated toward the

center

the stratiform region, its horizontal vorticity was tilted

into the vertical [second term on the right in (2.59)] and concentrated by conver-

gence [first term on the right in (2.59)].

The vorticity pattern associated with the symmetric type of squall-line struc-

ture (Fig. 9.9a) has been documented in detail for one case. The horizontal pattern

of vertical vorticity at midlevels was one of alternating bands: cyclonic in the

convective region, anticyclonic in a zone

just

behind the convective region, and

cyclonic at the back edge of the stratiform region (Fig. 9.53). A conceptual model

illustrating how this structure developed is shown in Fig. 9.54. The vortex tubes

shown were initially horizontal. The storm was located in a sheared environment

characterized by along-line wind that increased (in the into-the-page sense in Fig.

9.54) with height.

The

banded vorticity pattern is accounted for by the tilting and

stretching

the environmental vorticity. The tilting by the main up- and down-

drafts of the storm bent the vortex tubes upward and downward. Selected trajec-

tories (computed from Doppler

radar-observed

winds) are indicated. Where

stretching favored concentration of vertical vorticity the trajectories are solid, and

where concentration was disfavored they are dashed. The cyclonic vorticity in the

convective region was produced by the tilting on the forward side of the main

convective updraft.

The

anticyclonic vorticity zone immediately behind the con-

vective line was produced by tilting on the trailing side of the main convective

updraft and by tilting on the forward sides of the transition zone and mesoscale

downdrafts. The cyclonic vorticity maximum at the back edge of the stratiform

Figure 9.49 Analysis of the flow shown by a composite of rawinsonde data obtained in the vicinity

of a squall line with a trailing stratiform region in west Texas. Streamlines are superimposed on

features of the low-level radar reflectivity field. The convective echo cores in the squall line are

shaded. The curved lines trace the positions of lines of more intense echo embedded in the stratiform

precipitation region. The C marks the

"center

of curvature" of the echo bands. (From Leary and

Rappaport, 1987. Reprinted with permission from the American Meteorological Society.)

Figure 9.50 Composite analysis of the mesoscale component of the wind at the 650-mb level of a

tropical squall-line system. The smaller rectangle is the region within which the leading convective line

was found on radar. The larger rectangle is the region in which trailing stratiform precipitation was

found. Winds from soundings and aircraft were analyzed objectively and the mesoscale component of

the flow shown here was deduced by applying a mesoscale bandpass filter to the data to suppress

larger- and smaller-scale wavelengths. A full wind barb represents 5 m

S-I.

A vortex is evident toward

the rear of the stratiform region. Other aspects of this storm are represented in Figs. 9.42 and 9.59.

(From Gamache and Houze, 1985. Reproduced with permission from the American Meteorological

Society.)

Figure 9.51 Mesoscale model result showing vortex formation in the trailing stratiform region of a

midlatitude squall line. Relative wind vectors in a coordinate system moving at the speed of the vortex.

Shading shows areas of stratiform (i.e., model-resolved) precipitation. Contours enclose regions of

convective (parameterized) precipitation. (a) 500 mb and (b) 200 mb. (From Chen, 1990.)

392

9 Mesoscale Convective Systems

STRATIFORM

RAIN

REAR INFLOW JET

UPDRAFT

- LOWER TROPOSPHERIC FLOW

- MIDDLE TROPOSPHERIC FLOW

Figure 9.52 Schematic of the flow associated with an asymmetric type of squall-line system (as

described in Sec. 9.2.1 and Fig. 9.9) observed in Oklahoma. Scalloped areas represent precipitation.

(From Brandes, 1990. Reprinted with permission from the American Meteorological Society.)

300

240

E 180

120

motio

...J

-60

I -120

-180

-240

Figure 9.53 The pattern of vertical vorticity at the 675-mb level in a midlatitude squall-line

system. Vorticity is contoured every I x 10-

S-I

with negative values dashed. Background shading

indicates the low-level radar echo (i.e., rainfall) pattern. Dark shading shows the convective rain area,

the light shading the stratiform area, and the intermediate shading the region of heavier stratiform rain.

The storm in which the data were taken is the same as that represented in Figs. 9.15, 9.18, 9.31, 9.34,

9.40, 9.41, 9.43, 9.44, 9.45, 9.48, and 9.54. (From Biggerstaff and Houze, 1991a. Reproduced with

permission from the American Meteorological Society.)

region

Convective

,..r-----.~

,-----

....

'f----- -

_-l.

, /

" /

vorticity

midlevels

Re ionof antic clonic

Re ion of c clonic

---.J

Region

heaviest

stratiform

precipitationf

vorticity

midlevels

----------------------

r "

---

'-,

'~",,-

" "-

------~-

.'",

---

Figure 9.54 Conceptual model of the distribution and development of vertical vorticity in a

midlatitude squall line with a symmetric distribution of convective and trailing stratiform precipitation.

(a) Distribution of relative vertical vorticity in a cross section taken normal to the convective line with

solid (dashed) lines indicating positive (negative) relative vorticity

Wand

contours in the convective

region at twice the interval used in the stratiform region.

P and N indicate centers of positive and

negative

(b) Tilting and stretching involved in producing the observed vertical-vorticity pattern

shown in (a). CT (AT) indicates where bending of initially horizontal vortex tubes upward and

downward by the main up- and downdrafts of the storm produces centers of cyclonic (anticyclonic)

vorticity. Air trajectories computed from Doppler radar-observed winds are indicated. Where

stretching favored (disfavored) concentration of vertical vorticity, the trajectories are solid (dashed).

The storm represented is the same as that in Figs. 9.15, 9.18, 9.31, 9.34, 9.40, 9.41, 9.43, 9.44, 9.45,

9.48, and 9.53. (From Biggerstaff and Houze, 1991b. Reproduced with permission from the American

Meteorological Society.)

394 9 Mesoscale Convective Systems

precipitation region was formed by tilting and stretching in the downward rear

inflow at the back edge of the stratiform precipitation.

9.3 General Kinematic Characteristics of Mesoscale

Convective Systems

In Sec. 9.1 we saw that the mesoscale convective system exhibits a variety of

structures, as indicated by its pattern of precipitation. Although the pattern and

organization of the precipitation vary from case to case (e.g., Fig. 9.10), the large

area of rainfall of a mesoscale convective system is nearly always subdivided into

clearly identifiable convective and stratiform regions. In Sec. 9.2 we examined the

type of system in which the precipitation consists of a sharply defined leading line

of convective precipitation trailed by a region of stratiform precipitation (e.g., Fig.

9. lOa). We now consider the broader spectrum of mesoscale convective cloud

systems, including ones in which the precipitation exhibits other types of meso-

scale organizations (e.g., Fig. 9. lOb and c). In the remainder of this chapter, we

will examine the divergence and vorticity of the wind fields in and around meso-

scale convective systems of various types. Despite their diversity of structure,

these cloud systems exhibit rather similar gross patterns of divergence and vortic-

ity. These characteristics are important because they reflect how the mesoscale

convective systems are interacting with the larger-scale atmospheric circulation.

9.3.1 Divergence Associated with Mesoscale

Convective Systems

The vertical distribution of divergence in a mesoscale convective system whose

precipitation is organized into a convective and trailing stratiform region is illus-

trated in Fig. 9.55. These profiles of divergence were determined for a storm of the

type shown conceptually in Fig. 9.13. The divergence averaged

over

the convec-

tive region is characterized by convergence in the lower troposphere and diver-

gence in the upper troposphere. In the stratiform region, the profile shows conver-

gence in the middle troposphere, with a maximum at about the 600-700-mb level,

with divergence at upper and lower levels.

263 The profile of net divergence for the

storm as a whole is the area-weighted sum of the convective and stratiform pro-

files.

shows weak divergence (positive in this case, but not significantly different

from zero) at low levels, where the divergence in the stratiform region tends to

cancel the convergence characterizing the convective line. The level of maximum

convergence in the net profile is thus elevated well above the surface. In this case,

it is found between 900 and 700 mb, where both the convective and stratiform

regions are convergent. The maximum divergence is at high levels, where both the

convective and stratiform regions are divergent.

263 These profiles are typical of mesoscale convective systems consisting of a leading line of con-

vective precipitation trailed by a stratiform rain area. See Houze (1989) for a comprehensive review.

100

200

300

400

500 I

500

:::>

CI)

600

Convective

600-

I:>.

a..

,/,

700

800

",Stratiform

800

900

€ombined~""

900

1000

-15 -10

-5

0 5 10

DIVERGENCE

(10-

st)

Figure 9.55

Figure 9.56

Figure 9.57

Figure 9.58

Figure 9.55 Average divergence

over

the convective (dashed), stratiform (solid), and combined

(dotted) regions of a tropical squall-line system. Other aspects of this storm are represented in Figs.

9.42 and 9.50. (From Gamache and Houze, 1982. Reproduced with permission from the American

Meteorological Society.)

Figure 9.56 Mean divergence in the vicinity of MCCs. (From Maddox, 1981.)

Figure 9.57 Composite 700-mb wind in the vicinity of MCCs. The parallelogram is the region of

the MCCs, and the wind is reckoned relative to the MCCs. A full wind barb is for 10knots or

-5

S-I.

Vertical air motion (expressed as w

Dp/Dt)

is indicated in units of 10-

S-I

(contours for positive

values, indicating downward motion, are dashed). Map of the United States is shown in the

background to help indicate scale. The sides of the quadrilateral are approximately 700 km in length.

(From Maddox, 1981.)

Figure 9.58 Composite analysis of 200-mb wind in the vicinity of MCCs. The parallelogram is the

region of the MCCs, and the wind is reckoned relative to the MCCs. A full wind barb is for 10 knots or

-5

S-I.

Vertical air motion (expressed as w

Dp/Dt)

is indicated in units of 10-

S-I

(contours

for positive values, indicating downward motion, are dashed). Map of the United States is shown in the

background to help indicate scale. The sides of the quadrilateral are approximately 700 km in length.

(From Maddox, 1981.)

396 9 Mesoscale Convective Systems

The divergence profiles in Fig. 9.55 are typical not only of the squall line with

trailing stratiform structure but also of mesoscale convective systems that exhibit

a wider variety of mesoscale organizations. To illustrate this fact, we now exam-

ine the largest of the mesoscale convective

systems-the

MCC, whose satellite-

observed cloud shield satisfies the criteria listed in Table 9.

By focusing on these

large and long-lasting systems, we expect stronger and clearer kinematic signals.

There is evidence, however, that the types of mesoscale organization in smaller,

less intense mesoscale convective systems are qualitatively similar to those of

MCCS.264

Thus, much of what is learned from the MCCs should be applicable to

smaller mesoscale convective systems.

Mean kinematic characteristics of MCCs are shown in Figs. 9.56-9.59. The

mean divergence for the cloud cluster is shown by the solid curve in Fig. 9.56.

was calculated from a composite of the rawinsonde-measured winds in the vicinity

of cloud clusters. The composite wind fields at 700 and 200 mb are shown in Fig.

9.57 and 9.58. The cloud cluster location is the parallelogram. The divergence in

Fig. 9.56 is the average over the region of the parallelogram.

There is a strong qualitative similarity in the shape of the profile of net diver-

gence associated with the MCC and the shape of the curve of net divergence for

the squall line with trailing stratiform precipitation (cf. Figs. 9.55 and 9.56). As in

the case of the squall line with trailing stratiform precipitation, the mean MCC

divergence is approximately zero near the ground, where the strong convergence

in the boundary layer, where air rises into the bases of the convective downdrafts

at gust-front convergence lines, is offset in the mean by divergence associated

with the spreading of downdraft air below cloud. Thus, the net divergence over

the entire area of the MCC is near zero close to the surface. The strongest net

convergence is again found to be elevated well above the surface. In the MCC

profile, the maximum convergence is at 700 mb. Also similar to the squall line with

trailing stratiform precipitation, the MCC exhibits a strong peak of divergence at

high levels (200 mb). The strongly divergent character of the MCC winds at the

200-mb level is seen clearly in the streamline and isotach patterns of the composite

relative flow shown in Fig. 9.58. When the winds are filtered to remove the

synoptic-scale basic state flow, the mesoscale divergence and anticyclonic out-

flow are even more striking (Fig. 9.59). At this level, both the convective region

and the stratiform region of a mesoscale convective system are characterized by

divergence, and the two components of the MCC reinforce to produce the strong

divergent signal on the mesoscale.

Further insight has been gained into the vertical profile of the divergence in

mesoscale convective systems by aircraft flights into mesoscale convective sys-

tems of the type that have a more highly varied internal structure than the squall

line with a trailing stratiform region. During a field experiment conducted over the

ocean north of Australia, an aircraft with a Doppler radar on board flew through

264 In a study of major rainstorms

over

Oklahoma during springtime over a 6-year period, Houze et

al. (1990) found no difference in the mesoscale rainfall structures of MCCs and weaker mesoscale

convective systems.

9.3 General Kinematic Characteristics of Mesoscale Convective Systems 397

Figure 9.59 Composite analysis of 200-mb wind in the vicinity of MCCs band-pass filtered to

remove the larger, synoptic-scale basic state flow and smaller. convective-scale motions. The

parallelogram is the region of the MCCs, and the wind is reckoned relative to the MCCs. A full wind

barb is for 10 knots or

-5

S-I.

Letters A and C indicate anticyclonic and cyclonic centers,

respectively. Contours indicate divergence in units of 10-

S-I.

Map of United States is shown in the

background to help indicate scale. The sides of the quadrilateral are approximately 700 km in length.

(From Maddox, 1981.)

mesoscale convective systems in the manner illustrated by the example in Fig.

9.60. Generally, the mesoscale systems investigated in this study were not squall

lines with trailing stratiform precipitation. However, they fit the conceptual model

of rain area evolution described in Fig. 6.11, where a succession of convective

rain areas occurs. As each convective area ages it turns into a region of stratiform

precipitation. The entire rain area of the mesoscale convective system at a given

time then consists of a nonsteady pattern of relatively new convective areas

amidst a mass of stratiform precipitation formed from the decay of earlier active

convection. The aircraft flew a zigzag flight track back and forth across the rain

area. A Doppler radar beam pointing normal to the flight track (while scanning

vertically) could then view the precipitation within each V-shaped region from

two different angles.

265

The wind components along the beams were then used to

calculate the divergence of the wind for a diamond-shaped region

-500

in an

area centered within each V of the flight track.

265 Current airborne Doppler radars use two beams: one pointing at an angle forward and the other

pointing aft. In this way the same precipitation is viewed from two different angles while the aircraft

flies a straight track.

398 9 Mesoscale Convective Systems

Figure 9.60 Radar reflectivity time-composite images from airborne radar observations in a

tropical mesoscale convective system

over

the Joseph Bonaparte Gulf off the northwestern coast of

Australia on 27 January 1987. The reflectivity shown at each point is the maximum observed during the

period of the flight. Flight tracks are shown in white and proceed left to right in (a), right to left in (b),

and so forth. Ground

echo

from the Australian continent appears at lower right. (From Mapes and

Houze, 1993a. Reprinted with permission from the Royal Meteorological Society.)

The precipitation enclosed by each V of the flight track was classified according

to whether it was

convective, stratiform, or

intermediary-meaning

that it was in

the process of conversion from convective to stratiform. On several occasions,

the aircraft observed the same area of precipitation in all three stages of develop-

ment. In the example shown in Fig. 9.60, the region at

13°S,

129SE

was observed

at four successive times. At the time shown in Fig. 9.60a, the precipitation was in

a highly convective stage. By the time of Fig. 9.60d, it was completely strati-