Houze Robert A., Jr. Cloud Dynamics

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9.2

The Squall Line with Trailing Stratiform Precipitation

359

10 20 30

20 30

DISTANCE

(km)

DISTANCE

(km)

motion

Figure 9.21 Retrieved thermodynamic fields for the tropical squall-line system shown in Fig. 9.16.

(a) Buoyancy expressed in temperature units (K) by the quantity 8". (b) Pressure perturbation p*

(hPa). (From Roux, 1988. Reprinted with permission from the American Meteorological Society.)

9.0

4.5

(d) 6

~~::

10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

DISTANCE (km)

motion

Figure 9.22 Convective portion of a two-dimensional numerically simulated squall-line system.

(a) Simulated radar reflectivity (in intervals of 5 dBZ). (b) System-relative airflow. Vectors have been

scaled such that one the length of the grid interval represents

14 m S-I. Centers of low and high

pressure are indicated by

Land

H, respectively. (c) Cloud water mixing ratio (contour intervals of 0.5

g kg-I beginning with

0.1 g kg-I. Shading indicates equivalent potential temperature 8, < 327 K. Large

dot marks an air parcel that was traced. (d) Vertical air velocity in intervals

of2

m S-I with negative

(downward) values dashed. (e) System-relative horizontal wind perpendicular to the leading

convective line in intervals of 4 m S-I with negative (right-to-left) values dashed.

(f)

Potential

temperature perturbation (K). Heavy solid contour in (b), (d), (e), and

(f)

outlines cold pool (region of

negative potential temperature perturbation). (From Fovell and Ogura, 1988. Reprinted with

permission from the American Meteorological Society.)

Hence, the total buoyancy peak, which was found to be

-4°C

and collocated with

the strongest updraft, reflects a temperature perturbation larger than this value

since the weight of the condensate has been subtracted. A large value of radar

reflectivity in the region of the maximum suggests a large negative contribution

from the weight

ofthe

water. Thus, the maximum temperature perturbation could

360 9 Mesoscale Convective Systems

have been several degrees in excess of 4°C. Shown in Fig. 9.21b is the field of the

pressure perturbation, which is seen to display a minimum directly below the

region of positive buoyancy associated with the main convective cell. This re-

trieved pattern is consistent with the aircraft-observed

p* pattern in Fig. 9.19.

9.2.2.3 Multicellular

Aspect

the Convective Line

and Cell Life Cycles

Since the data on winds, thermodynamic structure, and water content in me-

soscale convective systems are rather limited, numerical cloud modeling of the

type discussed in Sec. 7.5.3 again becomes an important tool in furthering the

understanding of these cloud systems. Results of a two-dimensional numerical

simulation of the convective portion of a squall-line system are shown in Fig. 9.22.

This particular simulation did not include ice-phase microphysics. As a result, the

trailing stratiform region is not well represented. Later in this chapter, we will see

that when ice is allowed to occur in the model, a better representation of the

stratiform region is obtained. Despite the absence of ice, the convective region is

well represented in Fig. 9.22. The basic behavior of the model convective region is

similar to that of the line of multicell storms discussed in Sec. 8.11. A series of

convective cells, each undergoing the type of life cycle illustrated in Fig. 8.58,

extends across the convective region. The cells appear as distinct cores of high

radar reflectivity in Fig. 9.22a. The relative flow of air through the convective

region resembles that in the observed cases shown in Figs. 9.17 and 9.20. From

Fig. 9.22c, it can be seen that the slantwise upward flow over the cold pool

consists of'high-e, air originating in the boundary layer ahead of the storm. As this

air first rises over the gust front, a buoyant updraft forms and develops into a cell

near the gust front. According to Fig. 9.22d and f this updraft has a peak value of

>8 m

S-1

and a maximum potential temperature perturbation of about

8°C_

values generally consistent with the magnitudes implied by radar-retrieval results

in Figs. 9.20 and 9.21. (The case in Fig. 9.20 had thermal perturbations about half

this large, but it appeared to be a weaker case than the modeled case or the case in

Fig. 9.21.) Each cell is advected rearward in the slantwise relative flow. Thus, the

second cell behind the leading edge of the system is older.

too is marked by a

strong updraft and warm air. The third cell toward the rear is located at a still

higher altitude than the first two cells and is weaker (in reflectivity,

and thermal

perturbation) since it is in a decaying stage. As illustrated in Fig. 8.58, low-s, air

originally at midlevels ahead of the storm is pinched off between the first and

second cells and is incorporated into the downdraft. The large dot in Fig. 9.22c

identifies a parcel of

low-s, air that was traced, which ultimately descended into

the cold pool in the downdraft located between the first two cells. The convective-

scale downdrafts located on either side of each convective updraft are a part of the

convective structure associated with each cell. They correspond to the upper-

level downdrafts seen between the convective updrafts in the Doppler

radar-

derived W field in Fig. 9.18a. The regions of downward motion seen below the

second and third updraft cells in Fig. 9.22d are the lower-level, precipitation-

driven downdrafts. The layer of rear-to-front flow seen below the layer of rear-

9.2 The Squall Line with Trailing Stratiform Precipitation

361

ward-flowing updraft air in Fig. 9.22e is the descending rear inflow current de-

picted schematically in Fig. 9.13.

enters the convective zone from the stratiform

region and descends into the cold pool below the intense convective cells.

Although the multicell sequence seen in Fig. 9.22 is taken from a two-dimen-

sional model simulation, the results shown are very similar to the structure ob-

served across the convective zone of a real squall line with a trailing stratiform

region, especially if the cross section is taken parallel to the relative flow across a

part of the line where the cells are well defined. However, there is a considerable

amount of along-line variability in real squall line systems. A horizontal view from

a three-dimensional simulation of a squall line with trailing stratiform precipitation

is shown in Fig. 9.23. Along lines such as AB and CD in Fig. 9.23b, vertical cross

sections of the results are very similar to those in Fig. 9.22. The horizontal maps in

Fig. 9.23 show, however, that the only highly two-dimensional feature is the

ascent forced at the gust front at low levels; in Fig. 9.23a, the updraft at the l-km

level is seen to be continuous in a narrow along-line band. The convective down-

drafts to the rear of this leading updraft line are much more cellular. The continu-

ous two-dimensional line structure of the updraft disappears quickly with height.

By 2.8 km altitude (Fig. 9.23b), both the updrafts and downdrafts exhibit a highly

cellular structure.

9.2.2.4 Interaction with the Stratosphere

We have now seen that the convective updraft cells in the convective region of

the squall line intermittently form in the vicinity of the gust front, ascend, and

travel rearward relative to the storm. A typical snapshot of the air motions looks

like Fig. 9.17. When the updraft cells reach tropopause level, they perturb the

base of the stratosphere. In doing so, they act as traveling mechanical oscillators

that excite gravity waves in the nearly isothermal lower stratosphere. These

waves are illustrated by the results of a model simulation-f in Fig. 9.24. The

model used is of the type discussed in Sec. 7.5.3 and is essentially similar to that

used for the convective-line simulation illustrated in Fig. 8.58. In the case shown

in Fig. 9.24, a base state is assumed that has no flow relative to the storm at

stratospheric levels. The storm is shown in its mature stage, when the strato-

spheric response consists of waves whose phase lines tilt rearward and whose

periods match the primary periods of the forcing by the tropospheric updrafts.

Some very weak forward-tilting waves also occurred but can hardly be discerned

in the figure. In the earlier stages of squall-line development, the convective

updrafts generate more nearly equal amounts of forward- and rearward-propagat-

ing stratospheric gravity waves. The early period of the line is characterized by a

single vertically oriented updraft that impulsively strikes the tropopause at one

location, and both forward- and rearward-moving waves are excited. As discussed

in Sec. 8.11, the line of convection evolves into a less vertically oriented configu-

ration characterized by a series of weaker cells embedded in a rising, rearward-

tilted airflow. The predominance of the rearward-propagating waves at later times

254 Carried out by Fovell et al. (1992).

,;.,-..- -

......

"Ill

...

_ .. '

1'"

\ ..'

....

I '

, '

\ .._

....

, .

r ,

I '

. .

.......

x (km)

(a) w

Figure 9.23

200

300

X(km)

400

Figure 9.24

9.2 The Squall Line with Trailing Stratiform Precipitation

363

is attributed to the changeover to this latter flow configuration in which the cells

impinging on the stratosphere are moving systematically rearward.

9.2.2.5 Mean Structure

the Convective Zone

When the numerical model results are averaged in time, much of the transient

and spatially variable cellular structure in the convective region disappears, and

the smooth patterns seen in Fig. 9.25 appear. The mean streamline pattern (Fig.

9.25b) consists of two dominant and clearly identifiable currents. The main up-

draft current begins in the low to middle troposphere ahead of the storm, flows

horizontally toward the storm, slopes up through the convective precipitation

zone, and gradually becomes more horizontal toward the rear of the stratiform

precipitation zone where it exits the storm at middle to upper levels. The main

updraft current thus corresponds to the front-to-rear ascent shown in Fig. 9.13. In

the upper reaches of the convective zone, a part of the main updraft current splits

off and flows

out

of the forward side of the storm at upper levels. The second

primary current seen in Fig. 9.25b is the rear inflow entering the back of the storm

at the 3-4-km level and descending gradually into the cold pool in the convective

region. At the surface below the rear unflow is a thin layer of front-to-rear flow.

9.2.2.6 Overturning

the Environment

The two primary mean currents seen in Fig. 9.25b, the front-to-rear ascent and

the rear inflow, are two of the storm circulation features by which the storm

overturns the convectively unstable prestorm environment. However, the over-

turning process cannot be interpreted simply in terms of these average features.

The air entering the front-to-rear ascent in the low to middle troposphere has a

strong vertical gradient of

()e (far right side of domain in Fig. 9.25c). When the low-

()e air at the top of this inflow on the forward side enters the convective zone (at

about 53 km on the horizontal scale in Fig. 9.25), it fuels convective downdrafts

(as shown in Fig. 9.22c). On the other hand, the high-s, air at the bottom of the

inflow layer runs into the leading edge of the cold pool, is forced above its level of

free convection, and ascends in rapidly rising buoyant updraft cores. The convec-

tive region is thus a

crossover zone, where the low to middle tropospheric air

Figure 9.23 Horizontal patterns of vertical velocity in the convective region of a three-

dimensional simulation of a squall line with trailing stratiform precipitation. (a) I-km level. Positive

(solid) and negative (dashed) values are contoured respectively from I m

S-I

with intervals of 2 m

S-I

and from

-0.5

S-1

with intervals of I m

S-I.

Zero contour not shown. (b) 2.8-km level. Positive

(solid) and negative (dashed) values are contoured respectively from 2 m

S-I

with intervals of 4 m

S-I

and from

-I

S-1

with intervals

of2

S-I.

Zero contour not shown. (From Redelsperger and Lafore,

1988. Reprinted with permission from the American Meteorological Society.)

Figure 9.24 Numerically simulated squall line with trailing stratiform precipitation. The calculated

fields show gravity wave structure in the lower stratosphere (from about 13 km upward). Light lines

are potential temperature isotherms (4 K intervals). The cloud outline is represented by a dark solid

line, and heavy contours show vertical velocity (3 m

S-I

intervals, downdrafts dashed). (From Fovell

et al., 1992. Reprinted with permission from the American Meteorological Society.)

364 9 Mesoscale Convective Systems

30 40 50 60

DISTANCE

(km)

2010 80

sto~m>

motion.

Figure 9.25 Time-averaged numerical-model simulation of a squall line with trailing stratiform

precipitation. (a) Simulated radar reflectivity (in intervals of 5 dBZ). (b) Streamlines of system-relative

airflow. (c) Equivalent potential temperture (intervals of 3 K). Heavy solid contour outlines cold pool

(region of negative potential temperature perturbation). (From Fovell and Ogura, 1988. Reprinted with

permission from the American Meteorological Society.)

entering the front side of the storm overturns in transient convective-scale drafts.

This crossover is depicted in the schematic in Fig. 9.26.

is also represented in

terms of model results in Fig. 9.27, where the crossover in the convective region is

seen as a strong maximum-positive correlation of

wand

Oe,

which results from the

transient convective updrafts and downdrafts having systematically positive and

negative perturbations of

0., respectively. As a result of the crossover,

is not

conserved within the mean front-to-rear ascent. The stratification of

seen in

Fig. 9.25c changes markedly as soon as the front-to-rear flow encounters the cold

pool. The maximum

in the air finally flowing out the back edge of the domain at

about 7 km altitude is <300 K, compared to a maximum of about 336 K in the low-

level inflow.

9.2.2.7 Further Interpretation

the Pressure

Perturbation Field

A general overview of the pressure perturbation field in the squall-line system

was given in Sec. 9.2.1 (symbols

Land

H in Fig. 9.13). In Sec. 9.2.2.2, we

9.2 The Squall Line with Trailing Stratiform Precipitation

365

examined the small-scale midlevel low that is found below the sloping updraft of

the main convective cell in the convective region. Further aspects of the pressure

perturbation field in the convective zone can be seen in the time-averaged model

results. The pressure perturbation pattern corresponding to the time-averaged

model circulation in Fig. 9.25 is shown in Fig. 9.28. The total perturbation

p* (Fig.

9.28a) again displays the small-scale low in the convective zone.

is the strong

minimum at the top of the cold-pool head,

just

below the sloping front-to-rear

ascent, as seen in the aircraft data composite of Fig. 9.19. In addition, there are

three maxima of

p*: a small-scale peak of p* at the surface at the leading edge of

the cold-pool head, a shallow secondary maximum of

p* in the boundary layer

directly below the cold-pool head, and a broad maximum aloft extending over the

trailing stratiform region. In Fig. 9.28b and c, the total pressure perturbation is

decomposed into its dynamic and buoyancy components

and

Pb.

From these

additional cross sections, we can see the relative contribution of each component

to the total pressure perturbation field in Fig. 9.28a. Comparison of Fig. 9.28a and

b shows that the total field is dominated by the buoyancy component. The only

exception is that the small-scale peak of

p* seen at the surface at the leading edge

of the cold-pool head in Fig. 9.28a is not apparent in the buoyancy pressure-

perturbation field.

is entirely a dynamically produced feature, which is strongly

represented in Fig. 9.28c. This feature was described in Sec. 8.9 [Eq. (8.43)] as a

dynamically produced feature that occurs where the low-level inflow current is

stagnated and kinetic energy is converted to enthalpy. This interpretation is con-

firmed by its appearance only in the field of

Pb.

Another feature of interest in the

field is the pressure minimum that occurs in the middle of the cold-pool head.

This minimum is associated with the vorticity centered at this location in the

interface of the overlying rearward flow and the underlying rear-to-front flow in

the cold pool. A vortex is centered at this point in the mean flow pattern shown in

Fig. 9.25b. Such a vortex and an accompanying cyclostrophic pressure minimum

were seen to be characteristic of a density-current outflow head in Sec. 8.9

[Eq,

(8.44)]. From Fig. 9.28b and c, it is evident that this minimum of the dynamic

pressure perturbation component lies

just

forward of the minimum in the buoy-

ancy component, which is an effect of the deep layer of buoyant updraft air lying

above this point. The superposition of the two minima leads to the broader,

stronger minimum in the total field (Fig. 9.28a) than would be present from the

effect of buoyancy alone.

is thus an oversimplification to think of the pressure

minimum seen in data such as those in Fig. 9.19 as being either purely a hydro-

static or a purely dynamic pressure minimum.

9.2.2.8 Influence

the Stratiform Region on the

Convective Region

The foregoing observations and model results have led to the conceptualization

of the convective portion of the squall line with trailing stratiform precipitation in

Fig. 9.29. The low-e, (dry) rear inflow air enters the convective region from the

rear and descends into the cold-pool head, after passing through the trailing strati-

form precipitation

just

below the base of the trailing stratiform cloud deck. A

second source of low-s, air for the cold-pool head is the transient downdraft

Figure 9.26

Figure 9.27

x (km)

storm

motion

9.2 The Squall Line with Trailing Stratiform Precipitation 367

activity in the crossover zone, where dry air from ahead of the squall line also

comes down into the cold-pool head (dashed arrow emanating from ahead of the

storm in Fig. 9.29). In Sec. 8.11, the dynamics of the cold pool were discussed

entirely in terms of this second source of cold-pool air. Model simulations, how-

ever, show that the rear inflow accounts for most of the mass of the cold-pool

head, when the thunderstorm line is trailed by a stratiform precipitation region. In

the case of the squall line with trailing stratiform precipitation, it is thus primarily

the rear inflow that maintains the strength of the surface high in the center of the

cold-pool head and thus the strength of the storm's density-current outflow. The

dynamics of the cold pool should therefore be reconsidered in view of the primary

source of its air being the rear inflow.

In Sec. 8.11, the maintenance of a line of multicell thunderstorms was dis-

cussed in light of the two-dimensional vorticity equation (2.61). If that equation

(where the horizontal gradient of buoyancy is the only source of

g) is integrated

along a trajectory, such as the rear inflow trajectory of the conceptualized storm in

Fig. 9.29, an expression for the horizontal vorticity

g at any point along the

streamline can be obtained. That vorticity is given by the upstream value of

where the rear inflow enters the storm, plus the integrated effect of the baroclinic

generation

Bx) experienced by the parcel of air moving along the trajectory.

Since the rear inflow trajectory slopes downward through a region where there is

positive buoyancy ahead and negative buoyancy to the rear, it accumulates vortic-

ity as a result ofbaroclinity during the time it takes to reach the leading edge of the

storm. This final vorticity contributes strongly to the vorticity budget of the cold

pool and should be taken into account when considering a line of thunderstorms

with a trailing stratiform

region.l"

The idealization of the flow components in the convective region, as depicted in

Fig. 9.29, thus illustrates that the dynamics of the convective region of the squall

line with trailing stratiform precipitation are not separable from the dynamics of

the stratiform region. The rear inflow current arriving from the stratiform region is

important to the cold-pool dynamics of the convective region, both as a mass

255 See Lafore and Moncrieff

(989)

for further discussion of this problem.

Figure 9.26 Conceptual model of a tropical oceanic squall line with trailing stratiform

precipitation. All flow is relative to the squall line, which is moving from right to left. Numbers in

ellipses are typical values of equivalent potential temperature (K). (Adapted from Zipser, 1977.

Reproduced with permission from the American Meteorological Society.)

Figure 9.27

Updraft-downdraft

crossover zone, as seen in the results of a two-dimensional

numerical simulation of a squall line with trailing stratiform precipitation. (a) Stream function of

two-dimensional airflow (relative units) with the outline of the region of strong positive correlation of w

and (Je perturbations superimposed (contour is for correlation of 0.6). (b) Vertical eddy flux of (Je

associated with

wand

(Je perturbations in intervals of 5 K m s-) with maxima indicated by a +. The

crossover zone appears as the zone of strong eddy flux (implied by high correlation of

wand

(Je)

centered in the updraft region at x = 40 km and z = 5 km. (Adapted from Redelsperger and Lafore,

1988. Reproduced with permission from the American Meteorological Society.)

.(a)

~~::!~i~J~!~~~~;;;}!~!&

..... -...-.............................

I I I

(b)

P*B

1.0

----

::::::::::::::::::=Ei:::::::::::::::::::::::

.•....

-2.0··-···-··-···~

::::==:::::::...:...:...:..:...:...

................

::::::::::::-

......

-.-,::

.....

-:-:

I I

I I I

9.0

4.5

0.0

9.0

I-

:I:

iii

4.5

:I:

0.0

10 20 30

40 50 60

30 40 50 60

P*D

(c)

,--

--_

...

.................................

.........

4.5

9.0

30 40 50 60

DISTANCE

(km)

sto~m;j>

motto

Figure 9.28 Pressure perturbation field in the convective zone as seen in the time-averaged results

of a numerical-model simulation of a squall line with trailing stratiform precipitation. The patterns

correspond to the fields shown in Fig. 9.25. (a) Total pressure perturbation in intervals of 0.4 mb. (b)

Buoyancy component of pressure perturbation in intervals of 0.5 mb. (c) Dynamic component of

pressure perturbation in intervals of 0.2 mb. Negative values dashed. (From Fovell and Ogura, 1988.

Reprinted with permission from the American Meteorological Society.)

cloud

boundary

Figure 9.29 Conceptualization of the convective portion of the squall line with trailing stratiform

precipitation, with emphasis on flow of water vapor into and out of the storm.

B represents buoyancy.

(Adapted from Fovell, 1990. Reproduced with permission from the American Meteorological Society.)