Houze Robert A., Jr. Cloud Dynamics

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9.2 The Squall Line with Trailing Stratiform Precipitation 379

location within the stratiform region.P? The upward velocity of

10 em s-I near

the ground in curve 2 appears because this profile was taken in the vicinity of the

wake low (Sec. 9.2.3.5).

The association of the mesoscale downdraft with the melting layer is seen in

another way in Fig. 9.41. Panel a displays areal mean vertical velocity profiles for

both the convective and stratiform regions of the same mesoscale convective

system for which vertical profiles for specific locations are shown in Fig. 9.40. In

panel b of Fig. 9.41, the stratiform region profile is decomposed into three subre-

gions. Curves A and B represent the core of heaviest stratiform precipitation

(located in the

"secondary

maximum" of radar echo in the trailing stratiform

region, as described schematically in Fig. 9.9, Sec. 9.1.2.2). They represent the

region of stratiform precipitation with low-level radar reflectivity exceeding 25

dBZ for at least 2.5 h. This precipitation is that lying directly under the strong

radar bright band seen in Fig. 9.31. Curve A is for the heaviest stratiform rain

within this zone (radar echo >35

dBZ

for more than 1.5 h), while curve B repre-

sents core stratiform rain of more intermediate intensity (25-35

dBZfor

more than

2.5 h). Curve C is for the lighter stratiform region lying outside the secondary

maximum.

From

these three curves it is seen that the mesoscale downdraft is

concentrated within the zone of heaviest stratiform rain, namely that associated

with the well-defined melting layer marked by the bright band (curves A and B).

The mesoscale downdraft disappears in the average outside of the core of heavy

stratiform rain (curve C). At the same time, the mesoscale updraft appears with

the same intensity in all three subregions. Evidently, the horizontal scale of the

mesoscale downdraft is set by the width of the region of strong melting, while the

mesoscale updraft at higher levels is of a larger horizontal scale.

extends rather

uniformly across the entire stratiform region, as the positively buoyant air from

the upper reaches of the convective regions is spread across the stratiform region

by the front-to-rear flow at upper levels.

259 See Sec. 4a of Houze (1989) for further examples, including vertical profiles of w inferred from

sounding analysis, Doppler radar, and profiler measurements in tropical, midlatitude, continental, and

oceanic mesoscale convective systems.

Figure 9.37 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.

9.21.

Cross section is through the middle to rear portion of the stratiform region. (a) Radar reflectivity. (b)

Vertical air velocity. (c) Pressure perturbation. (d) Buoyancy expressed in temperature units (K) by

the quantity

(Jo' (From Sun and Roux, 1988.)

Figure 9.38 Thermodynamic fields obtained by the Doppler radar retrieval technique for the

trailing stratiform region of a tropical squall-line system observed by dual-Doppler radar in Ivory

Coast, west Africa, on

27-28

May 1981. Cross section is located near the back edge of the stratiform

region. (a) Radar reflectivity. (b) Vertical air velocity. (c) Pressure perturbation. (d) Buoyancy

expressed in temperature units (K) by the quantity

(Jo' (From Sun and Roux, 1989. Reprinted with

permission from the American Meteorological Society.)

Figure 9.39

.6.4

o .2

(ms-

)

-.4

~

-=:

- - - -

~/-:----

-.6

E 12

c10

I-

a 8

iii 6

'---j,;---'-----7---'-----:,----'-"-7--'-'-----±----'--.l~.L..-...J.

Figure 9.40

100

(a)

-0-

Convectiv

- - - Stratiform

200

::>

(/)

400

600

800

1000

Figure 9.41

16.5

(b)

---C

----8

14.5

--0--

12.5

10.5

8.5

iii

6.5

4.5

2.5

9.2 The Squall Line with Trailing Stratiform Precipitation

381

9.2.3.4 Kinematic

and

Thermodynamic Structure at the

Top

the Stratiform Cloud

So far we have examined only the portion of the trailing stratiform cloud from

which precipitation is falling. One reason for this is that radar observations are

restricted to regions occupied by precipitation particles. Rawinsonde data can be

used to examine the thermodynamic structure and winds in a region that extends

outside the precipitation zones. However, the time and space resolution of sound-

ing data is typically very coarse. Sometimes by making time-to-space conversions

it is possible to form a composite analysis of sounding data taken in and around a

storm over a period of time in which the storm was not changing its structure

rapidly. Some results from such a sounding composite are shown in Fig. 9.42. The

cross sections are divided into four regions: the environment ahead of the squall

line, the convective precipitation region, the trailing stratiform rain area, and the

poststratiform rain area. The convective and stratiform rain regions were charac-

terized by temperature and water-vapor perturbation fields generally consistent

with the results seen in Figs. 9.35-9.38. The maximum magnitude of the peak

temperature perturbation in the stratiform cloud is, however, only

-laC,

which is

smaller than indicated in previous discussions. However, the sounding data are of

low resolution and were put into a composite coordinate framework and objec-

tively analyzed. All

these factors contribute to smoothing out the perturbations.

Thus, these fields are not really inconsistent with those shown previously. What is

gained from these lower-resolution analyses is some knowledge of the regions

immediately ahead of, above, and to the rear of the convective and stratiform

precipitation areas, which cannot be obtained readily from radar. The main new

feature seen in this analysis is in the stratiform cloud region at upper levels,

toward the back of the storm in the rear half of the stratiform region and in the

poststratiform zone. A negative temperature perturbation is found, which may

have been the result

radiative cooling in the upper layers of the trailing strati-

form cloud.

Figure 9.39 Schematic vertical cross section illustrating the relationship of the buoyancy (B) of

the trailing stratiform cloud to the pressure perturbation

(p*).

The difference between the pressure

perturbation at the back

(pT) and leading portion

(pt)

of the stratiform region is indicated by Sp,

(Adapted from Lafore and Moncrieff, 1989. Reproduced with permission from the American

Meteorological Society.)

Figure 9.40 Stratiform region vertical velocity profiles for a squall line with trailing stratiform

precipitation. All three profiles were derived by single-Doppler radar analysis (using the VAD method

described in Sec. 4.4.5). Other aspects of this storm are illustrated 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. (From Houze, 1989. Reprinted with permission from the Royal

Meteorological Society.)

Figure 9.41 Mean vertical air motion in a squall line with trailing stratiform precipitation. In (a),

the curves are for the convective (solid) and entire stratiform (dashed) regions. In (b), curves are

shown for the stratiform region excluding the secondary band C, the secondary band excluding the

enhanced portions B, and enhanced portions of the secondary band A. The air motions were derived

by dual-Doppler radar observation. The height of the

ooe

level is shown. 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, 9.43, 9.44, 9.45, 9.48,

9.53, and 9.54. (From Biggerstaff and Houze, 1991a. Reproduced with permission from the American

Meteorological Society.)

PRE-LINE CONVECTIVE STRATIFORM

POST-

STRATIFORM

300

<sto~m,

motion

\ - >

I / _

o \ -0.5 - r: - - -

-c,

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

-'-

~~---~-~

-::: (

- - -

--0.5-'

---_

o 100 200

DISTANCE (km)

600

800

200

400

Figure 9.42 Composite analysis of radiosonde data obtained in and around a tropical squall-line

system

over

the eastern Atlantic Ocean. Cross sections are along a line perpendicular to the leading

convective region. (a) Temperature perturbation (K); maxima indicated by W, minima by C. (b) Water

vapor mixing ratio perturbation (g kg

:');

maxima indicated by M, minima by D. Other aspects of this

storm are illustrated in Figs. 9.50 and 9.59. (From Gamache and Houze, 1985. Reproduced with

permission from the American Meteorological Society.)

Figure9.43 Analysis emphasizing the structure at and above the top of the squall line with trailing

stratiform precipitation shown in Figs. 9.15, 9.18,

9.31,9.40,9.41,9.44,9.45,9.48,9.53,

and 9.54. This

cross section is taken along the direction of motion of the squall line during the system's later stages of

development. Shown are the streamlines for system-relative flow, potential temperature isotherms

(K), and relative humidity (with respect to ice at temperatures below freezing, values greater than 80%

indicated by shading). Infrared (IR) satellite data were used to determine the height at cloud top.

Airflow and thermal structure are deduced from soundings and assumptions about the infrared

radiative cooling rate at cloud top. Dotted line indicates where vertical air motion (expressed as

Dp/Dt) is diagnosed to have been zero. (From Johnson et al., 1990. Reprinted with permission from

the American Meteorological Society.)

9.2 The Squall Line with Trailing Stratiform Precipitation

383

Another feature of the mesoscale trailing stratiform region for which there

appears to be some observational support in rawinsonde data is a thin layer of

downward air motion in the front-to-rear flow at and above cloud top (Fig.

9.43).260

has been hypothesized that this feature of the trailing region is associ-

ated with the tropopause settling back downward after being displaced upward by

the propagating convective zone. The downward settling of the stratiform cloud

top may also be a manifestation of the outflow layer from the cumulonimbus

clouds in the leading convective line undergoing a

"collapse"

similar to that

described in Sec. 5.3.3 for the upper-level outflow from an individual cumulonim-

bus (Figs. 5.32 and 5.33).

9.2.3.5 The Wake

Low

The sounding analyses in Fig. 9.42 show that the major feature immediately to

the rear of the stratiform precipitation zone is a strong positive-temperature maxi-

mum at low levels. This warming produces the wake low at the back edge of the

stratiform precipitation (Fig. 9.13). A schematic view of the process producing the

low is given in Fig. 9.44, which reflects the opinion that the wake low is a surface

manifestation of the unsaturated descent of part of the rear inflow air. The warm-

ing appears to be maximized at the back edge of the stratiform precipitation area,

where the air is subsiding especially strongly and there is insufficient evaporative

cooling to offset the strong adiabatic warming.

9.2.3.6 The Rear-to-Front Current

and

Rear

Inflow

Sounding data to the rear of the stratiform precipitation region have also ex-

tended knowledge of the rear inflow. Although the schematic in Fig. 9.13 shows

descending rear inflow entering the storm at the back of the stratiform region, it

does not indicate how

strong the rear inflow is. Figure 9.45 shows an example of

an especially strong rear inflow current, which is shown by Doppler radar data to

be entering the back edge of the stratiform precipitation radar echo at a speed

exceeding 15 m

S-I

relative to the storm. This speed, however, is rather excep-

tional. When the sounding data from the environment to the rear of many squall

lines with trailing stratiform precipitation are examined, it is found that only a few

cases have strong inflow from the environment. Profiles of the storm-relative flow

from soundings taken to the rear of such cases have been averaged and are

referred to in Fig. 9.46 as strong rear inflow cases. The example in Fig. 9.45 was

one of the cases included in the average. Many cases have weaker rear inflow at

midlevels; many have essentially zero relative flow. These latter cases have been

referred to as stagnation zone cases. All

ofthe

cases, however, have similar shear.

The relative flow normal to the line tends to be front-to-rear at both upper and

lower levels, with the front-to-rear flow decreasing at midlevels. The rear inflow

cases are the ones in which the sign of the relative flow in the midlevel minimum is

reversed, so that environmental air flows across the back edge of the precipitation

area. Roughly half of the storms which have been studied are stagnation zone

260 This feature has also been noted in pro/Her data obtained in the tropics (Balsley et al., 1988).

384 9 Mesoscale Convective Systems

(a)

(b)

---:d=------=---

::!-:::-

- -

---

100 km

Figure 9.44 Schematic view of the process producing the wake low at the rear of a squall line with

trailing stratiform precipitation. (a) Vertical cross section through wake low. (b) Plan view of surface

winds and precipitation. Winds in (a) are system relative, with dashed line denoting zero relative wind.

Arrows indicate streamlines, not trajectories, with those in (b) representing ground-relative wind.

Note that horizontal scales are different in the two schematics. Other aspects of this storm are

illustrated in Figs. 9.15, 9.18, 9.31, 9.34, 9.40, 9.41, 9.43, 9.45, 9.48, 9.53, and 9.54. (From Johnson and

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

cases. These cases are dominated by, but not restricted to, tropical squall lines,

while the strong rear inflow cases have been found in midlatitudes over land.

In the stagnation zone cases, the pattern of divergence and vertical velocity of

the mesoscale circulation in the trailing stratiform region does not appear to be

essentially different than in the strong rear inflow cases. The ascending front-to-

rear flow in the stratiform cloud itself remains in the form illustrated by Fig. 9.13,

and midlevel convergence is implied in these cases by the zone of stagnation lying

adjacent to the upward-sloping rearward relative flow. As in the rear inflow cases,

this convergence is linked to both the mesoscale ascent in the cloud layer above

and to mesoscale descent below the cloud layer.

has also been found, from

9.2 The Squall Line with Trailing Stratiform Precipitation 385

aircraft and radar observations in stagnation zone cases, that rear-to-front flow

develops

internally (i.e., within the trailing rain area itself, storm frontward flow

develops and penetrates forward and into the cold pool of the convective region,

even though no air enters from the environment at the rear of the storm). An

example of this type of storm is the tropical squall line that we have examined

previously in Figs. 9.7, 9.8, and 9.20. In Fig. 9.47 we see that the profile of the

relative wind component normal to the line was strongly frontward just to the rear

of the convective region but decreased to a stagnation value at the back edge of

the stratiform region. Thus, it is clear that the squall line system generates its own

rear-to-front flow in the stratiform region, but that in some cases (especially the

strong rear inflow cases) this frontward flow is enhanced by inflow from the

environment.

The inflow from the environment in a strong rear inflow case has been studied

in the context of a

mesoscale model, which is a limited-area numerical weather

prediction

model-not

a convective cloud model of the type described in Sec. 7.5.

The convective cloud model starts with a single sounding (i.e., uniform and

steady-state large-scale environment) and uses nonhydrostatic equations to pre-

dict the motions internal to a cloud which develops from a specified perturbation

to the otherwise constant environment. The mesoscale model, in contrast, is

concerned with predicting changes in the large-scale environment over an area

much larger than that of the individual convective clouds. The environment may

be initially nonuniform and vary with time, as predicted by the mesoscale model.

The horizontal grid resolution of the model is typically 15-75 km. A variety of

approaches to this type of model have been used. Often, the motions are calcu-

lated with the hydrostatically balanced equations and the convective-scale mo-

tions are parameterized, which means that the net effect of the convective-scale

motions on the larger-scale environment is included in the turbulence terms in the

equation of motion and the thermodynamic equation. These terms are expressed

as functions of the resolvable-scale variables. A typical approach is to assume

that, if the environment becomes conditionally or potentially unstable and suffi-

cient resolvable-scale vertical motion is present to release the instability, the

thermodynamic stratification is overturned by the convection, according to some

prescribed scheme, to restore stability. In the case of a mesoscale convective

cloud system, such as a squall line with a trailing stratiform region, this type of

model resolves the air motions and cloud structure of the stratiform region, while

the motions in the smaller-scale updrafts and downdrafts of the convective region

must be represented by the parameterization scheme.>!

In Fig. 9.48a, we show results of a mesoscale model simulation of a midlatitude

squall line with a trailing stratiform region. This particular simulation used a

nested grid, which was 75 km in resolution except in the vicinity of the convec-

tion, where the grid spacing was reduced to 25 km. The case represented is the

261 See Frank (1983) for reviews of traditional methods of convective parameterization. More

recent ideas are discussed by Betts (1986)and Frank and Cohen (1987). Still more recently, mesoscale

models have replaced the parameterization approach with nested grids that allow explicit nonhydro-

static calculation of the convective-scale processes.

Figure 9.45

Figure 9.46

1oo....---r-----r---r---,.----,----,

200

300

400

!'! 500

:::J

600

700

800

900

00~ILOr---3.L0r---.J..20~O:'-.L1

0----l.0--1:":0---:'20

Relative Flow Normal to Squall Line (m 5-

9.2 The Squall Line with Trailing Stratiform Precipitation 387

one for which the rear inflow was shown in Fig. 9.45. Other aspects of the struc-

ture of the storm have been presented in several other figures (see caption of Fig.

9.48).

was a strong rear inflow case. Comparison of Figs. 9.45 and 9.48a shows

that the model represents the general structure quite well, with the rear inflow

jet

entering strongly from the environment to the rear of the stratiform region. From

the horizontal scale of Fig. 9.48 it is evident that the model results cover a region

much broader than the precipitation region shown in Fig. 9.45. Thus, it is evident

that the strong rear inflow extends far out into the environment to the rear of the

storm. Several model runs were made, under different sets of assumptions. These

experiments reveal that, in this case, the inflow from the environment at upper

levels at the back of the system was not pulled in by processes internal to the

storm itself but rather was associated with the baroclinity of the large-scale flow in

which it was embedded. (The squall line lay ahead of a well-defined short-wave

trough in the westerlies.) With the diabatic heating set equal to zero, which is

tantamount to removing all the dynamical effect of the cloud system on the resolv-

able-scale flow, only the upper-level (above 400 mb) part of the rear inflow (i.e.,

that to the rear of the rain area) developed. The mid- to lower-level part of the rear

inflow (i.e., that within the rain area) was absent. This result is illustrated by Fig.

9.48b, where the result with no diabatic heating has been subtracted from the total

result in Fig. 9.48a. All of the rear inflow internal to the storm remains, where the

frontward flow at midlevels descended toward the convective region. The rear

inflow entering from the environment at the rear of the storm is entirely absent

from the difference field. Thus, it appears that the part

ofthe

rear inflow that made

this case one of strong rear inflow (i.e., entering across the back edge of the storm)

was not driven by processes internal to the storm but rather was determined by

the large-scale environment in which the storm was embedded. The large-scale

baroclinity provided deep and favorable rear-to-front flow within the upper half of

the troposphere. This result is a further indication that the rear-to-front flow

within the squall line with a trailing stratiform region is fundamentally the result of

processes internal to the storm, while the factor which determines whether a given

case has strong rear inflow, weak rear inflow, or stagnation at the back edge of the

stratiform region depends on the environment in which the storm occurs.

Figure 9.45 Doppler radar data showing the strength of the rear inflow current entering the back

edge of the stratiform region of the squall-line system 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. This particular cross section was shown by a single radar at a

particular moment. Thus, it was not subjected to smoothing as were the composites in Figs. 9.31 and

9.43, and it therefore shows more details of the flow. Panels (a) and (c) depict radar reflectivity (dBZ).

Panels (b) and (d) show system-relative horizontal velocity

S-I),

respectively, along the 310

and

1300

azimuth directions. Positive velocities represent flow away from the radar, while negative

velocities denote flow toward the radar. Arrows indicating flow direction are also shown. Rear inflow

is highlighted by shading in (b) and (d). (From Smull and Houze, 1987. Reproduced with permission

from the American Meteorological Society.)

Figure 9.46 Profiles of the storm-relative flowfrom soundings taken to the rear of squall lines with

trailing stratiform precipitation. (From Smull and Houze, 1987. Reproduced with permission from the

American Meteorological Society.)

388 9 Mesoscale Convective Systems

Korhogo

220681

0547 GMT

(a)

Figure 9.47

Figure 9.48

200

100

D..

(a)

200km

c::l10-30

D1IIIII130-40

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_>50dBZ

sto~mn>

motto

HORIZONTAL

DISTANCE

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-20 10

(b)