Houze Robert A., Jr. Cloud Dynamics

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9.2 The Squall Line with Trailing Stratiform Precipitation 369

source, supplying the cold pool with negatively buoyant air to maintain the sur-

face high-pressure area under the cold-pool head and thereby the strength of the

surface outflow current (Fig. 9.29), and as a source of vorticity for the cold pool.

In the next section, we examine the structure and dynamics of the stratiform

region, of which the rear inflow is

just

one important aspect.

9.2.3 The Stratiform Region

We have seen in

Sees, 9.2.1 and 9.2.2 that in the squall line with trailing stratiform

precipitation the dynamics of the leading convective region are intimately tied to

the trailing stratiform region, with the rear inflow current being the primary agent

by which the stratiform region feeds back to the convection. When the circulation

associated with the stratiform region appears and interacts with the convective

region, the latter is no longer controlled

just

by the large-scale undisturbed envi-

ronment but is controlled by the stratiform region dynamics as well. We will now

examine the mesoscale circulation of the stratiform region, insofar as is possible

from available observations and modeling results.

9.2.3.1 Upward

Air

Motion and Precipitation

Development in the Stratiform Cloud

We begin by looking at the results of a model simulation. In Fig. 9.25, we saw

the time-averaged structure of a model simulation of a squall line with a trailing

stratiform region. A realistic convective region was simulated but no ice was

allowed to form, and a realistic stratiform region did not appear. In Fig. 9.30, we

show a time-averaged line structure for the same model but with a scheme for

representing the ice-phase microphysics included. A bulk microphysical scheme

of the type described in Sec. 3.6.2 was used in the water-continuity equations. The

only form of precipitating ice allowed to form was snow.

256 As can be seen from

Fig. 9.30a, a qualitatively realistic radar-echo pattern was obtained. The region of

precipitation reaching the surface extends across a horizontal distance of about 80

km. A radar bright band and secondary maximum of surface precipitation inten-

sity are found in the stratiform region. The structure of the precipitation is very

similar to that in Fig. 9.13. The time-averaged kinematic and thermodynamic

structure in Fig. 9.30b and c is not qualitatively different from that seen in the no-

ice case in Fig. 9.25. There are some quantitative differences, however, and the

case with ice included compares very well with data. For example, the radar

reflectivity and vertical velocity fields derived from Doppler radar data in Fig. 9.31

are nearly identical to the model fields in Fig. 9.30a and e. The observed case in

Fig. 9.31 was obtained as a composite of several volumes of Doppler radar obser-

vations centered at different locations and times within the mesoscale system. All

the data in a 60-km-wide strip oriented perpendicular to the convective line and

extending across the system were combined, averaged, and filtered to obtain the

256 Less realistic results were obtained when graupel was allowed to form because graupel falls out

too quickly.

370 9 Mesoscale Convective Systems

0.0-

o-c

E 9.0

:I:

(!) 4.5

:I:

0.0

!§Tc)

336

Ie-

~24-

324

...--

)~~

ire

(e)

9.0

4.5-

_________________

J /

'" "

<:»

o-c

20 30 40 50 60

HORIZONTAL

DISTANCE

(km)

sto~m>

mohon

Figure 9.30 Time-averaged numerical-model simulation of a squall line with trailing stratiform

region with ice-phase microphysics included: (a) Simulated radar reflectivity (in intervals of 5 dBZ). (b)

Streamlines of system-relative airflow. (c) Equivalent potential temperature (intervals of 3 K). (d)

System-relative horizontal wind (intervals of 3 m

S-I,

solid left-to-right, dashed right-to-left); (e)

Vertical air velocity (m

S-I);

relative humidity <60% indicated by shading. 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.)

Figure 9.31 Composite radar reflectivity and vertical velocity fields constructed from Doppler

radar observations obtained at different locations and times within a squall line with trailing stratiform

precipitation. Other aspects of this storm are illustrated in Figs. 9.15, 9.18,9.34,9.40,9.41,9.43,9.44,

9.45,9.48,9.53,

and 9.54. All the data in a 60-km-wide strip oriented perpendicular to the convective

line and extending across the system were combined, averaged, and filtered to obtain the mean cross

section. X is the coordinate axis perpendicular to the line. The storm was moving from left to right.

Radar reflectivity (dBZ) is shown by shading. Vertical wind component is shown by contours for

-0.9,

-0.45, -0.15,

0.15, 0.45, 0.9, 1.5, 2.4, and 3.6 m

S-l

with negative values dashed. (From Biggerstaff

and Houze, 1993. Reproduced with permission from the American Meteorological Society.)

720

600

CONVECTIVE

---

.....

...

I STRATIFORM

,,..,,-

....

---"

120

'iii'

:::I

iii

!;;(

II:

..J

240 360 480

TIME (min)

Figure 9.32 Area-integrated rain rate in a two-dimensional numerical-model simulation of a squall

line with trailing stratiform region with ice-phase microphysics included. Rain amounts are summed

separately for rain falling at grid points designated as convective and stratiform for each time step

throughout the lifetime of the storm. (From Tao and Simpson, 1989. Reprinted with permission from

the American Meteorological Society.)

372 9 Mesoscale Convective Systems

mean cross section. The similarity with the model results in Fig. 9.30a and e is

striking. However, the model version of the storm structure is scaled down.

not as broad or tall as the real case. The reason for the difference in scale remains

to be understood. In most other ways though, the model results are verified.

In both the time-mean model cross section in Fig. 9.30e and the example

composite observed case (Fig. 9.31), the vertical air motion is seen to be positive

nearly everywhere at mid- to upper levels in the stratiform region. The only

exception is in the zone of minimum radar reflectivity between the convective

region and the secondary maximum of stratiform precipitation below the bright

band, where there is a column of downward motion. This zone is where the upper-

level downdrafts tend to occur behind the strongest updraft cells (as seen in Fig.

9.18). The

net

effect of these strong upper-level downdrafts on the average verti-

cal velocity field is to produce the column of mean downward motion. The general

ascent found at mid- to upper levels behind the zone of mean downward motion is

typical of squall lines with trailing stratiform precipitation. Generally, the mean

vertical motion is zero at a height of

0-2

km above

O°C,

upward below this level

(corresponding to the front-to-rear ascent in Fig. 9.13), and downward below

(corresponding to the subsiding rear inflow in Fig. 9.13). To understand the pre-

cipitation process in the stratiform region, it is important to note the

magnitude of

the vertical motions in the stratiform region. They are generally (though not

uniformly) <0.5 m

S-I,

whereas the fall speeds of precipitating ice particles (ice

crystals, aggregates, graupel) are

-0.3-3

S-1

(Sec. 3.2.7, Figs. 3.12, 3.13, and

3.14). Thus, condition (6.1) is satisfied, and the precipitation is of a stratiform

character, as described in Sec. 6.1.

Results from another model simulation are shown in Figs. 9.32 and 9.33. This

simulation is very similar to that illustrated in Fig. 9.30. A bulk parameterization

of the ice-phase microphysics was used in the calculation and a region of strati-

form precipitation formed behind the convective line.

For

the first 2 h the precipi-

tation was primarily from the leading convective line, while during the last 4 h the

amounts of convective and stratiform rain were about equal (Fig. 9.32). Integrated

over the lifetime of the storm, about 37% of the precipitation from the storm was

stratiform. This behavior compares well with the typical observed evolution and

relative amounts of convective and stratiform precipitation illustrated by the ex-

ample in Fig. 9.12. The observed case, however, extends over a considerably

longer time period than the model case.P? The structure of the model storm,

during the time when the total convective and stratiform rain rates were approxi-

mately equal, is shown in Fig. 9.33. Surface precipitation extends over a 100-km-

wide region, and the stratiform region is well represented with a radar bright band

at the melting level.

Although the two model simulations we have referred to in Figs. 9.30,9.32, and

9.33 produced storms of somewhat smaller spatial and temporal scales than their

observed counterparts, they produced stratiform precipitation areas qualitatively

257 The case in Fig. 9.12 was particularly long-lived. Lifetimes

-12

h are more common for squall

lines with trailing-stratiform precipitation.

Figure 9.33 Vertical cross section of the numerically simulated squall line with trailing stratiform

precipitation whose rain rate is indicated in Fig. 9.32. The structure of the storm is shown for a time

(504 min after the beginning

ofthe

simulation) when the total convective and stratiform rain rates were

approximately equal. The simulated radar reflectivity is shown in contours of dBZ. In the darker

shaded areas,

w > 0.5 m

S-I,

and in the lighter shaded areas, w <

-0.5

S-I.

(From Tao and Simpson,

1989. Reprinted with permission from the American Meteorological Society.)

Cloud shield !

Gust

Front

region

Convective

zone

Transition

,, se,condary band

I Enhanced

Stratiform region

Figure 9.34 Schematic of the two-dimensional hydrometeor trajectories through the stratiform

region of a squall line with trailing stratiform precipitation. Trajectories were based on fall speeds and

air motions measured by Doppler radar. Other aspects of this storm are illustrated in Figs. 9.15, 9.18,

9.31, 9.40, 9.41, 9.43, 9.44, 9.45, 9.48, 9.53, and 9.54. (From Biggerstaff and Houze, 1991a.

Reproduced with permission from the American Meteorological Society.)

9.2 The Squall Line with Trailing Stratiform Precipitation

375

of the order of several degrees Celsius. Sandwiched between the warm and

cool layers is the pronounced, mainly hydrostatic pressure perturbation minimum

(Fig. 9.35c).

The model thermodynamic fields correspond well to data analyses. Thermody-

namic fields obtained by the Doppler radar retrieval technique (Sec. 4.4.7) are

shown in Figs. 9.36-9.38. Figure 9.36 cuts across the leading portion of the

stratiform region,

just

behind the convective region (which lies just to the left of

the cross section). Figure 9.37 is in the middle to rear portion of the stratiform

region-the

bright band is evident all across this region but decreasing in intensity

toward the rear of the system (i.e., toward higher

x). Figure 9.38 is located near

the back edge

ofthe

stratiform region. In all three figures, the vertical air motion is

upward above about 4 km altitude and downward below. Inspection of panel b in

each figure shows that the mesoscale updraft is

-50

S-1

at the back edge

ofthe

convective region,

-20

S-1

in the center of the stratiform region, and

-0-2

S-1

at the back edge of the system. The mesoscale downdraft at lower levels has a

maximum magnitude of

-25

S-I

(Fig. 9.36b).

The c and d panels of Figs. 9.36-9.38 show the thermodynamic structure of the

stratiform region.

is evident that the mesoscale updraft region aloft is positively

buoyant and that a pressure perturbation minimum lies at the base of the meso-

scale updraft zone aloft all across the stratiform region. This diagnosed pattern is

consistent with the model results in Fig. 9.35, where the pressure perturbation

minimum was seen to lie at the base of the positively buoyant layer offront-to-rear

ascent atop the cold pool. The magnitude of the total buoyancy perturbation,

expressed in temperature units by the quantity

(Ja in the d panels of Figs. 9.36-

9.38, has peak values of 2-4°C. Negative buoyancy of similar magnitude is seen in

the mesoscale downdraft at lower levels. In the stratiform region, where the

loading of liquid water and ice is not great, this total buoyancy perturbation

approximates the potential temperature perturbation itself and may therefore be

compared with the model results in Fig. 9.35a, where the peak values are 4-5°C.

Since the model represents a midlatitude storm while the retrieval results are for a

tropical case, and there are many uncertainties in both the model and retrieval

methodologies, we may take these values as being essentially in agreement.

A conceptual model shown in Fig. 9.39 ties together the buoyancy of the

trailing stratiform region, the pressure perturbation minimum at the base of the

buoyant cloud, and the rear inflow current. As we have seen from Figs. 9.35-9.38,

the trailing stratiform cloud layer is positively buoyant. Immediately to the rear of

the convective region, the cloud layer is thicker and the buoyancy is greater. The

buoyancy decreases and the cloud layer thins toward the rear of the system.

Hence the magnitude of the pressure perturbation at the base of the buoyant layer

is greater in the interior of the system,

just

behind the convective region. The

resulting horizontal difference of pressure perturbation across the stratiform re-

gion accelerates air from rear to front. This mesoscale difference of pressure

perturbation

(Ap

in Fig. 9.39) drives the rear-to-front flow across the stratiform

region. As ice particles fall from the stratiform cloud layer aloft into the rear-to-

front current, the air is chilled by sublimation, melting, and evaporation and

subsides while it flows horizontally toward the convective region.

374 9 Mesoscale Convective Systems

quite similar to those observed. We have seen this similarity in both the structure

of their radar reflectivity and the evolution and amount of surface precipitation,

and we have noted that this similarity is achieved only when the ice-phase micro-

physics are included in the model simulations. Thus, it must be concluded that the

production of ice in the upper levels of the convective region and its advection

rearward by the front-to-rear ascent are crucial to the formation of the trailing

stratiform region. As indicated by the horizontal wind pattern in Fig. 9.30d, slowly

falling snow particles grown in the upper levels of the convective cells in the

convective region are advected by front-to-rear flow in the manner depicted sche-

matically in Figs.

6.1lfand

9.13.

A more detailed schematic of these processes is provided in Fig. 9.34. The

trailing nimbostratus cloud deck is supplied with precipitation-sized ice particles,

which are spread across the trailing region. These particles fall (at speeds of

-1-3

S-I)

through the "mesoscale updraft" zone of weak vertical air motions. They

first cross the region of mean downward motion

just

behind the convective region.

In this "transition

zone,"

the mass of precipitation particles cannot increase, and

the particles partially evaporate. The more slowly falling particles from upper

levels are, however, quickly advected across the region of downward motion into

the region of the mesoscale updraft, where they grow significantly by vapor depo-

sition while continuing their slow descent to the melting layer. The upward air

motions of the order of tens of centimeters per second are great enough to con-

dense a considerable amount of vapor but small enough for all the ice particles to

fall [condition (6.1) is met]. The precipitation is stratiform in character. Before

reaching the melting layer, and possibly within it, the ice particles may aggregate

and by virtue of the large particles produced enhance the radar reflectivity inten-

sity in the bright band. The aggregation, however, does not increase the bulk mass

of the falling snow; it only changes the particle size distribution. Once melted, the

ice particles fall to the ground as rain.

As shown in Fig. 9.34, the maximum of the stratiform rain rate at the surface

below the mesoscale updraft may be attributed to the enhancement of the strati-

form precipitation by the mesoscale updraft above the melting layer. The mini-

mum in rain rate and radar reflectivity at low levels between the convective region

and the enhanced stratiform rain below the mesoscale updraft is associated with

particles falling out of convective cells but not being able to grow effectively in the

transition-zone downdraft region.

9.2.3.2 Thermodynamic Structure

the Stratiform Region

The thermodynamic structure of the stratiform region is also indicated by

model simulations. The perturbation fields of potential temperature, water-vapor

mixing ratio, and pressure for the time-averaged simulation of Fig. 9.30 are shown

in Fig. 9.35. A major feature is that the stratiform region is marked by a potential

temperature perturbation maximum of

-5°C

all the way to the back edge of the

storm (Fig. 9.35a). This feature is accompanied by a positive water vapor pertur-

bation (Fig. 9.35b). Lying below this warm, positively buoyant layer is a cold,

negatively buoyant layer, characterized by potential temperature perturbations

(b)

I-----------=~

E9.0

m4.5

I I I

70 80

storm

~otion>

Figure 9.35

100

<sto~m

mot

ion.

100

(b) w

(em

s-l)

--25

100

50 25

100 0

DISTANCE

(km)

100

(a)

dBZ

O+~..__.......,.......,,...,.---r-....,.._._,--r-.,...J

10....,..~

.........

---::::_-==____,1

0-r7."'":'"........,--=:::::::----;~-_r___,

I-

£2

Figure 9.36

9.2 The Squall Line with Trailing Stratiform Precipitation 377

9.2.3.3 The Mesoscale Downdraft

Mesoscale convective systems tend to form in air masses characterized by low

relative humidity (Sec. 3.1.1) and a minimum of

in the midtroposphere. Conver-

gence of air at midlevels, below the base of the positively buoyant upper-level

stratiform cloud deck, brings this dry, low-s, air into the storm. The sublimation

and/or evaporation of precipitation particles falling into the low-s, air makes the

air

just

below cloud base negatively buoyant. In addition, melting of the ice

particles falling from the upper-level cloud produces a cooling of -1-lOoC h-

the

-0.5-1-km-thick

melting layer (marked by the radar bright band in Fig.

9.12).258

The response to these cooling effects is the formation of a mesoscale

downdraft in the region of stratiform precipitation. Such a downdraft is found in

most well-developed mesoscale convective systems, not

just

the squall line with

trailing stratiform precipitation being considered here. In this particular type of

system, the ascending front-to-rear flow spreads ice particles across the trailing

portion of the storm (Fig. 9.13). A wide

(-100

km) lower tropospheric region of

negative buoyancy extends across the entire rear portion of the storm, and a

mesoscale downdraft develops across this region.

The vertical profile of the vertical velocity

w in the mesoscale downdraft (and

the mesoscale updraft above) exhibits considerable similarity from one mesoscale

system to another. Figure 9.40 shows the vertical profiles of

w seen at three

locations in the stratiform region of the storm shown in Figs. 9.15, 9.18, 9.31,9.34,

9.41, 9.43, 9.44, 9.45, 9.48, 9.53, and 9.54. The maximum magnitudes of down-

ward motion in the lower troposphere were 45-65 em

S-I,

while the peak upward

motion at upper levels was 50-60 em s

-1.

Curves 1 and 2 were obtained near the

northern edge

the stratiform region (Fig. 9.15). The top of the mesoscale down-

draft was 2 km above the

O°C

level in these two curves, while in curve 3, obtained

farther south, nearer the center

ofthe

stratiform region, the top

ofthe

descent was

at the

O°C

level. These profiles are quite typical; the level separating the upward

from downward motion is usually 0 to 2 km above the

O°C

level, depending on

258 In a study of five tropical squall lines, Leary and Houze (l979b) determined that the cooling rate

by melting ranged from 1 to 7°C h-

Figure 9.35 Time-averaged numerical-model simulation of a squall line with a trailing stratiform

region with ice-phase microphysics included. (a) Potential temperature perturbation (K). (b)

Water-vapor mixing ratio perturbation (intervals of 0.7 g kg:"). (c) Pressure perturbation (intervals of

0.4 mb). (From Fovell and Ogura, 1988. Reprinted with permission from the American Meteorological

Society.)

Figure 9.36 Thermodynamic fields obtained by the Doppler radar retrieval technique for the

trailing stratiform region of the tropical squall line whose convective structure was shown in Fig. 9.20.

Cross section is through the leading portion of the stratiform region,

just

behind the convective region,

which lies

just

to the left of the cross section. (a) Radar reflectivity. (b) Vertical air velocity. (c)

Pressure perturbation. (d) Buoyancy expressed in temperature units (K) by the quantity

ea'

(From Sun

and Roux, 1988.)

100

motion.

1000

DISTANCE

(krn)

378 9 Mesoscale Convective Systems

(a)

dBZ

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

",,---

10_

---

'----20

~:~~71

0 50 100 0

~-,.--------==-------,

Figure 9.37

200

sto~m

motion

100

(b) w (em

s-I)

200

DISTANCE (km)

100

O-+---r--..-----,-------,------'

15~-----------~

:::.

I-

(d)

(K)

Figure 9.38