Download How Does a Tropical Squall Line Work?

How Does a Tropical Squall Line Work?
Michael Herman
April 28, 2009
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Introduction
Confounded by the study of complex behavior, one inevitably yearns for a personal, unclouded view whereby
tenuous obfuscation condenses into a discrete, salient core. In the tropics, sufficiently convoluted systems
do develop and a small subset of those includes the squall line. In this paper, I hope to present a layman’s
description of the mechanisms driving the formation and persistence of the tropical squall line employing
both empirical and theoretical knowledge. To this end, I will explore the characteristics of these convective
features as seen by the observer and the mathematician/physicist alike.
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Characteristics of the Squall Line
A squall is a sudden burst of wind that persists for just a few minutes. A squall line is a type of mesoscale
convective feature in which several active thunderstorms are arranged in a pattern that is significantly longer
than it is wide. Thus, the system, when viewed from above, resembles a line. The term mesoscale refers
to phenomena occurring on length scales of a few to several hundred kilometers. Finally, these systems are
preceded by a squall, i. e., the observer, confronted with an oncoming squall line initially experiences a
short, fierce wind (AMS, 2009).
Studied observations of these systems reveal more phenomena at finer detail. Perhaps the best example
of studied observations of squall lines was the Global Atmospheric Research Program’s Atlantic Tropical
Experiment (GATE), a 1974 field experiment in which a large group of mesoscale features were exhaustively
recorded using a wide variety of meteorological instruments. As one researcher admitted recently at an NCEP
meeting on atmospheric modeling, this 35 year old experiment continues to provide useful data to atmospheric
scientists largely because of the broad scope of data collected (workshop, 2009). Among the instruments
employed were: 4 ships carrying radar (sampling at 15 min intervals), upper air rawinsondes (sampling
horizontal winds, temperature, relative humidity and pressure at 5 hPa resolution), surface instruments
(sampling horizontal winds, temperature, relative humidity and radiation in three minute averages), a rain
gauge (sampling at 30 minute to 1 hour intervals), aircraft in situ instruments and cloud photos (Houze,
1977).
From this myriad of data, Houze and others published a series of papers presenting interpretations of the
empirical data in an effort to explain the dynamic operation of the systems. In one paper, Leary and Houze
suggest there is a predictable set of four stages that a tropical cloud cluster undergoes over its lifetime. In
particular, “there exists a characteristic mesoscale organization of precipitation in tropical cloud clusters.”
Furthermore, they assert that squall lines, being a type of mesoscale convective feature, pass through the
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same stages. In the following section, I will outline the stages they observed (Leary and Houze, 1979).
2.1
A Theory of Mesoscale Precipitation Features
Initially, as witnessed in the GATE observations, mesoscale precipitation features exhibit a formative stage,
which is typified by a long, narrow line of thin, short convective towers precipitating at an approximate rate
of 10 mm h−1 . The small towers are seen on radar images as discrete specters of high reflectivity within the
system. The horizontal gradient of the reflectivity is very high adjacent to the towers, since the region of
precipitation within is truncated abruptly inside the edge of the cell.
One interesting point the authors make is that, the same basic structure is seen in both intensifying and
decaying towers, which suggests that the form of the structure itself is neither a predictor, nor a cause of its
subsequent development, but rather the towers are guided by the dynamical conditions of their environment.
Illustrating this distinction is the fact that towers which are aligned parallel to the surrounding low-level
winds tend to move with the winds and die out over time, whereas ones aligned perpendicular to the winds
tend to march into the wind, and gradually intensify. In the intensifying case, the oncoming low-level winds
meet the downdrafts associated with the convective towers, causing convergence ahead of the leading edge
of the line. This allows new cells to form due to mass continuity, which lifts low-level air above the region
of convergence (see figure 1). If the air is lifted above its level of free convection, the cell’s growth can be
sustained over time.
Figure 1: On the left is a bird’s-eye view of a line of convective cells oriented perpendicular to the low-level
winds, while the right side shows a side view of one of the cells as a contour of radar reflectivity. In both
frames, convective-scale downdrafts are shown radiating outwards and meeting the oncoming low-level winds.
The combined flows are convergent ahead of the line and result in favorable conditions for convection within
the dashed outline shown. (Leary and Houze, 1979).
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This process of convection assisted by low-level convergence defines the intensifying stage of the system,
wherein new convective cells arise ahead of the cluster and old ones dissipate behind. This cycle of arising and
passing away of convective cells effects a forward motion of the system into the oncoming low-level winds.
Another aspect of this stage is that the cells in front, which are initially quite shallow (short in height),
shoot up toward the tropopause due to the increasing strengths of the established downdrafts generating
new cells. The intense convective behavior leads to significantly increased rainfall within the cells (up to
100 mm h−1 ). High winds associated with divergence at the tops of the towers act to transport the moisture
and hydrometeors in the convective updrafts away from the towers. This sweeping out of the convective tops
generates an enormous roof covering the system, called a cirrus shield (see figure 2), which is most visible
in satellite images of the system (Leary and Houze, 1979).
In the mature stage, the cirrus shield persists as precipitation particles generated in the convective updrafts continue to overshoot the tropopause and get blown downwind. Beneath the shield, dying convective
cells merge together into a region of uniform precipitation extending far beyond the smaller locale of intensification at the leading edge. Here, the rain rate (typically about 3 mm h−1 ) is considerably less than that
of the intense cells out front.
Figure 2: The mature stage of a tropical cloud cluster is illustrated in radar reflectivity diagrams of vertical
and horizontal cross-sections (the latter taken along the transect from C to C’ in the diagram at left). In
the figure on the left, the line of intense cells is shown (their strong precipitation evinced by the black ovals
at the leading edge), with the uniform (weaker) precipitation region trailing behind. The cirrus shield is
indicated as a lower reflectivity contour above (dots), and vertical wind shear is illustrated by bold arrows in
front of the system. The cells at the leading edge are strongest, with weaker ones trailing behind, merging
with the uniform region. The melting layer is the horizontal reflectivity contour at 4 km in the uniform
region (Leary and Houze, 1979).
Within this region of uniform precipitation, there can be seen a band of high reflectivity at the melting
layer (the region where the vertical temperature gradient surpasses 0◦ celcius) on vertical cross-section radar
images of the system. This band illustrates the fact that melting H2 O particles have higher reflectivity in
the radio band than particles in the solid phase (Lopez-Carillo, 2009). Thus, as precipitation falls through
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this layer, it melts slightly, forming a thin liquid surface over the solid cores. Since the melting particles
initially have about the same size and spatial distribution as they had in the solid phase, they present a
numerically dense region of large, highly reflective particles to the radar source. As they continue to fall, the
particles melt and shrink in diameter, which reduces their drag. The now liquid droplet then accelerates,
which causes the number density of the droplet distribution to decrease; there is thus less reflectivity below
the bright band (Battan, 1962).
Another characteristic of the uniform region is a cool mesoscale downdraft below the cirrus shield and
behind the smaller convective cells. It is thought that particles falling out of the cirrus shield in solid
and liquid phases drive this downdraft when their respective phase changes draw latent heat from the
surrounding environment. The resulting cooler atmosphere is negatively buoyant and thus helps to force the
cool downdraft (Emanuel, 2004).
The final stage of the tropical cloud cluster is the dissipating stage, in which the intense, leading cells
become shorter (or rather, they don’t approach the heights that they did in earlier stages), and emit less
precipitation. Eventually, they stop forming, and the remaining cells simply merge with the trailing mesoscale
region, which continues to precipitate for a long time thereafter (typically, about 8 h), the melting layer band
persisting with it (Leary and Houze, 1979).
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A Scrutiny of Squall Line Attributes and Causality
Squall lines are among the most severe forms of mesoscale precipitation features. Herein I will discuss aspects
of this powerful engine and present concepts that can ultimately be linked into a simple, yet nontrivial
retelling of the phenomenon of squall lines as they appear over tropical oceans.
Robert Houze spent 20 days on a ship off the west coast of Africa in 1974 (during GATE) and published a
paper detailing the passing of a squall line overhead. Some of the data is actually presented as a time-series
in the rest frame while the system moves past. It is careful analysis of this data, coupled with aircraft
observations of the overall structure of the system in its own frame of reference that lends a fair description
of the updraft and downdraft processes inherent in the dynamics of the squall line.
3.1
The Mesoscale and Convective Scale Downdrafts
In cloud terminology, the convective scale cell, or tower, that drives the system is a cumulonimbus convective center. The AMS glossary defines the cumulonimbus form as “exceptionally dense and vertically
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Figure 3: The large-scale features of a squall line. The shaded regions indicate contours of reflectivity or
precipitation. The convective-scale cell is to the left, drawing BL air up over the expanding downdrafts that
emit from below the cell. The cirrus shield is indicated by the wavy outline extending to the right below
the tropopause. At the base below the system is the resulting stable layer, where moist entropy has been
inverted from the usual low-level gradient (Houze, 1977).
developed...[appearing] as mountains or huge towers”. Perhaps their most important characteristic is summarized thus: “cumulonimbus is a vertical cloud factory” (AMS, 2009). Indeed, we have already seen this
characteristic generating the cirrus shield described above. The towers give rise to intense rainfall that drives
downdrafts at their cores due to drag forces on the raindrops. The downdrafts are subsequently cooled by
the drops falling through unsaturated air entrained through the sides of the cells by the turbulent updrafts
on the cells’ perimeters. The notion of raindrops dragging the air down with it seems well entrenched in the
literature, as it was first proposed by Brooks nearly a century ago, who contended, “[in thunderstorms] the
raindrops drag the air along with them, thereby establishing a descending current.” (Brooks, 1922). Perhaps
the chief product of the convective cells is the mesoscale downdraft located behind them beneath the cirrus
shield, for it is associated with approximately 40% of the rainfall of the system, and a much greater portion
of its horizontal extent.
In their paper on the development of tropical cloud clusters, Leary and Houze (1979) present and analyze
evidence complimenting our understanding of the characteristics of the mesoscale downdraft. Analysis of
time series in situ data from low-flying research craft through one of the clusters gives pertinent information
in this regard (see figure 4, below). Perhaps the most striking detail from the plot of the flight data is the
drop in temperature in the mesoscale region. This is indicated by lines representing T and T d in plot (b).
Before the craft has entered the system, it is flying through moist, warm air, as you would expect in the
tropical boundary layer. The warmth is clearly indicated, since the temperature is about 295 K, while the
dewpoint is nearly the same. A rough calculation of the relative humidity using
RH = 100 − 5(T − T d)
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(1)
Figure 4: Time series from research aircraft flying at a height of 450 m through a tropical cloud cluster
during GATE. a) contours of radar reflectivity plotted on z vs. time; b) temperature and dewpoint vs. time;
c) wet-bulb potential temperature vs. time. The period near 1250 is immediately preceding the convectivescale cells in front of the cluster. The interval from 1220 to 1215 is within the mesoscale downdraft region.
Discontinuities are due to bad data (Leary and Houze, 1979).
gives RH ∼
= 95% in this region (1250 GMT). In contrast, in the mesoscale downdraft region (1215-1220
GMT), the temperature and dewpoint both drop, indicating cooler air.
The behavior of the wet-bulb potential temperature (θw ), coupled with the associated relative humidity
invites discussion of a debate regarding the origin of the downdraft. Throughout most of the flightpath, θw
is around 295 K, whereas in the mesoscale downdraft region, it drops to around 293.5 K. Due to warming
by radiative heat fluxes at the surface, the equivalent potential temperature, and thus θw , tend to decrease
with height in the tropics in the boundary layer, and thus we expect that in situ data from such a low
elevation maintains the higher value of θw characteristic of this heating (Raymond, 2009). However, in the
mesoscale downdraft region, we see decreased θw . Since it is conserved in pseudoadiabatic processes, the
authors conclude that the air originated at a higher level, and was carried downward, suggesting a downdraft
in this region. Figure 5, below, illustrates how the low θe air arrives near the surface in the downdraft region.
The origin of this downdraft is thought to be due to two possible mechanisms: 1) One is strictly dynamical,
i. e. the divergent cold-pool that originated due to the convective-scale downdrafts associated with the cells
at the front of the squall line draws air down from above into the cold-pool by mass continuity; 2) the other is
thermodynamic in nature, summarized as the evaporation of rainfall from the overarching anvil cloud, which
in turn cools the surrounding air, causing it to lose buoyancy and sink. In a modeling study done thirty
years ago, Brown found that evaporation is necessary to drive the downdrafts to match conditions witnessed
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in observations (Brown, 1979). However, Houze pointed out that some observations call into question the
notion that evaporation is the primary forcing mechanism (Houze, 1977). Indeed, by 1994, Emanuel felt it
necessary to mention that the cold-pool might be a significant factor in driving the downdraft (Emanuel,
1994).
Figure 5: Low θe air from the mid troposphere caught in the downdraft in the mesoscale rainfall region
beneath the anvil subsides and diverges in the low-level cold-pool, while moist, warm air from the boundary
layer is lifted above (Zipser, 1969).
The analysis of Leary and Houze speaks toward Brown’s conclusion. Since some of the air in the downdraft
region is considerably drier than air in other parts of the system (RH ∼
= 80%at 1220 GMT), the air has
plenty of capacity to evaporate liquid. As Zipser pointed out in his investigation of convective downdrafts,
“The cooling in the downdraft air [could not] take place by evaporation of raindrops into ambient low-level
air. ...If rain simply cooled the ambient air without replacing it with air from aloft, a temperature decrease
and dew-point increase would be the only results, with θe remaining unchanged” (Zipser, 1969). In contrast,
Leary and Houze found decreased temperature and dew-point with reduced θe , which suggests that the air
was cooled by evaporation within the drier air above, and then transported down into the boundary layer.
The downdraft air is still dry in comparison to that of the surrounding boundary layer air, as evinced by
the lower Td . Ultimately, the implication is that the downdraft is initiated by evaporation at higher levels
(Leary and Houze, 1979).
A question remains from the analysis above. If the air is falling in part due to evaporation, one would
expect higher values of humidity in the downdraft region. A time-series plot of the liquid content from
the rest frame (described above) tells the whole story (see figure 6). Before the squall line passes, the lowlevel humidity and mixing ratio are both high, as you’d expect in the boundary layer (data is from in situ
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Figure 6: Mixing ratio and relative humidity from the rest frame as the squall line passes by. The passing
of the squall front is indicated as ’SF’ on the plot (Houze, 1977).
observations on-board the ship Oceanographer ). At the time of the squall front passage (indicated on graph),
the humidity increases sharply, since moistened air from the convective-scale downdraft is rushing toward
the surface; however, the mixing ratio is considerably lower than the typical value in the BL. This makes
sense, since the air coming from above was initially drier than the BL air. While saturation vapor pressure,
and thus relative humidity are temperature dependent (so that RH is higher above the BL for a given mixing
ratio than within), while the mixing ratio is not. Past the system front, the higher relative humidity and
lower mixing ratio persist throughout the passage of the extensive mesoscale downdraft region, again due to
the evaporation thought to drive that phenomenon. Lastly, after the system has passed (1900 GMT), the
relative humidity is lower than it is in the surrounding boundary layer, since the saturation mixing ratio is
higher there (Houze, 1977).
3.2
Generation and Sustenance of the Convective Cells
According to Kerry Emanuel, squall line genesis in the tropics is often predicated on the existence of a single,
isolated convective cell, perhaps arising near the pressure anomaly of a propagating easterly wave. If the
cell generates rain, a cold pool develops at its base due to evaporative cooling of raindrops, and the pool
spreads out away from the cell. Along the arc-shaped edge of this pool, squall lines may form under certain
conditions (Emanuel, 1994; Houze, 1977).
The conditions needed for this to occur are a major subject of debate by the community of scientists
studying the phenomenon. In their discussion of the genesis of tropical cloud clusters, Leary and Houze
present the general condition for convection in these structures as the coincidence of low-level winds with
opposing outflow from existing cells; however, the details of where the winds must occur with respect to the
outflow and their relative strength is controversial.
In their 2004 defense of the RKW theory of squall line convection via wind-shear/cold-pool interaction,
Rotunno and Weisman summarize the debate as follows. Coniglio and Stensrud (2001), using a mesoscale
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forecast model, found that deep vertical wind shear leads to strong, long-lived squall lines, while Evans and
Doswell (2001) found that relatively weak shear confined to low levels could generate fairly powerful cells.
Furthermore, Lafore and Moncrieff (1990) used simulations to conclude that the vertical shear of the entire
atmospheric column must be considered, rather than just the low-level shear, and that the effects of the
squall line on its environment alter the environment too much to assume that local interactions between
the cold pool and ambient wind shear are sufficient predictors of squall line cell convection (Weisman and
Rotunno, 2004).
This debate is ongoing, but it is interesting to look into one of the theories in greater detail to see how
it relates to the stated characteristics of squall lines. The above-mentioned RKW theory will be discussed
further along; however, first I’ll take a brief look at vorticity.
3.2.1
A Look at Vorticity
We can analyze vorticity from a mathematics perspective to see what gives rise to it. Vorticity is the tendency
of a velocity field to move in a circular path. This idea is expressed in the following definition, which is
simply the curl of the velocity field:
~ × ~v
ζ~ ≡ ∇
(2)
Since the curl is comprised of sums and differences of spatial derivatives, we can first agree that any
velocity field lacking variation along its spatial dimensions will likewise have a curl of zero. In this case, all
attributes of circular motion would be absent and the vorticity would be zero. We can now look at causes
of vorticity by using the conservation of momentum in an incompressible flow in a non-rotating reference
frame.
Starting with the Boussinesq approximation to the Navier-Stokes momentum equation in advective form
(Raymond, 2009)
d~v ~
+ ∇π − bẑ − ν∇2~v = 0,
dt
(3)
we can find the vorticity equation by taking the cross product:
d~v ~ p0 (z)
ρ0
2
∇×
+∇
+ g ẑ − ν∇ ~v = 0.
dt
ρ0
ρ0
The curl of the density perturbation gradient p0 (z) must be zero, and the other terms become:
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(4)
g
dζ~
+
dt
ρ0
∂ρ0 ∂ρ0
,
, 0 − ν∇2 ζ~ = 0.
∂y ∂x
(5)
The y-component of the vorticity equation is then:
dζy
g ∂ρ0
=
+ ν∇2 ζy
dt
ρ0 ∂x
(6)
The above equation suggests that vorticity along the y-direction (CW vorticity, into the page) will increase
if the gradient of the density perturbation in the x-direction (to the right) is positive. This means that the
ambient density gradient must be negative to the right, so that a parcel of air moving rightward would ’feel’
heavier as it moved. Such a parcel, displaced at a given level to the right would be forced down (by gravity)
and left, since it ’wants’ to fall against the gradient of ambient density, i. e., it has negative buoyancy in
that direction. Likewise, a parcel displaced to the left would feel lighter, and would thus be forced up and
to the right. It isn’t too hard to imagine these parcels moving in a circle based on these initial motions.
The equation has another term leading to increased vorticity into the page: the laplacian of the vorticity
in the y-direction scaled by the viscosity of the fluid. For this term to be non-zero, the y-direction vorticity
must not only vary in some direction, but it must vary variably, i. e., some spatial 2nd derivative of the
y-vorticity must exist. It is this degree of significant spatial variation in the velocity field that invites viscous
effects upon the momentum of the field, which likewise affects the vorticity of the field.
3.2.2
RKW Theory
Having examined the notion of vorticity and its causes to some degree, let’s take a look at one theory
of how horizontal vorticity aids convection in squall lines. Weisman and Rotunno hereafter WR, wrote a
paper (2004) defending their findings which, expanding on conclusions of Thorpe et al. (1982), found in
2d models that lifting of boundary layer air by the cold pool circulation is enhanced by low-level vertical
wind shear, and that when the shear is “moderate to strong”, the lifting is optimal. In 3d models, they
further found that optimal lifting conditions occurred for moderate to strong vertical shear in the lowest 2.5
km of the atmosphere when the wind was directed perpendicular to the squall line. They also found that
stronger low-level shear gave bow-shaped lines of convective cells (an important ingredient for strong squall
lines), but that stronger shear was not as effective for generating continuous lines of cells (Weisman et al.,
2004, 364). Although it is unlikely that their model results are incorrect since the model speaks for itself
within its defined parameter space, it is another matter to accept those results as describing general natural
phenomena. Debate over this issue subsequently rose up since RKW first published their ideas, and to stem
the cause of dissent, they increased their model resolution and honed their analysis.
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The authors began their study with the above equation for horizontal vorticity, coupled with the remaining
governing equations, the buoyancy equation
db
= ν∇2 b,
dt
(7)
and the vorticity as given by the laplacian of the streamfunction.
∇2 Ψ = ζ y .
(8)
They then non-dimensionalized the equations, defined relevant boundary conditions and set the viscosity
to a value which “is large enough to control the small-scale instability that occurs in the inviscid problem,
but small enough to preserve the large-scale character of the solutions” (Weisman and Rotunno, 2004).
Figure 7: In the absence of ambient shear, the cold-pool slumps outward into the surrounding fluid. The
cold-pool is indicated by shading. Distorted horizontal lines are tracers to indicate the vertical displacement
of the originally uniformly stratified fluid. Dotted lines describe the streamfunction, indicating the vorticity
at the edges of the falling pool (Weisman and Rotunno, 2004).
The pertinent question here is: What mechanism lifts low-level air to the highest level? If we can
understand that in the context of spreading cold pools in ambient wind, we have a piece of the puzzle of
squall-line persistence solved, since lifting moist low-level air to its level of free convection allows convective
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cells to persist and the squall line to strengthen. To this end, WR initialized their 2D model with a single
parcel of relatively dense fluid amidst a surrounding less-dense fluid (hereafter, colloquially referred to as
heavier and lighter, respectively). This is a reenactment of the ’dam-break problem’, wherein a relatively
heavy fluid is suddenly released into a lighter one, and allowed to flow outwards. The purpose of this
experiment was to simulate the spreading of a cold-pool into a region of warmer air. Since the cold-pool is
necessarily denser due to the inverse relationship between temperature and density inherent in the ideal gas
law, the dam-break problem is thus a pertinent model.
When the model is run, the heavier fluid falls down and outward, pushing the lighter fluid as it moves.
Plots of the fluid positions after certain time intervals reveal the behavior of interactions between the two
fluids (see figure 7, above). Particularly illustrative in these plots are tracer lines, which indicate how initial
height strata behave during the flow. These lines show precisely how high a given parcel of low-level air
reaches in the evolution of the dam break sequence. It is easy to see what is happening to the lighter fluid:
1) The heavier fluid falls downward and outward at its sides where it is least constrained (in the center, it
is constrained by itself). 2) As it moves outward, the lighter fluid must move upward, for it is constrained
by itself everywhere along the same level. 3) The top, outer edge of the dense fluid caves downward as the
lower edge slumps out, leaving a cavity that is immediately filled by the lighter fluid above it. 4) The sum
of these motions effects positive horizontal vorticity along the front edge of the heavy fluid, as illustrated in
the plots by the streamfunction contours. Simpson described an actual experiment involving filling a large
box with dense gas on a calm day and letting the gas fall outwards into the surrounding environment. The
image below from the experiment gives an idea of how the horizontal vorticity at the edge of the cold pool
takes on a toroidal shape along the outer edge (see figure 8, below).
Figure 8: The dam-break experiment as seen from above on a calm day (Simpson, 1968).
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Having modeled the isolated cold-pool flow as a simple density current, WR then added wind shear to the
model. To check the above ideas about shear strength and position, they tested three regimes with various
shear strengths: surface-based shear, shear centered on the top edge of the cold-pool, and shear spanning the
depth of the modeled atmosphere. In each regime, different shear–cold-pool interactions occurred. Initially,
WR determined that, indeed, the greatest lifting of low-level air occurred for low-level, or surface-based
shear, i. e., shear that spans a vertical distance from the surface to the upper level of the cold pool. This
conclusion was based on the result that, over the range of shear strengths (the difference in horizontal wind
velocity over the depth of the shear layer), the surface-based shear gave the greatest lifting. Furthermore,
they determined that, for the surface-based case, lifting is optimized for moderate to strong shear (Weisman
and Rotunno, 2004).
It is illustrative to examine the mechanics of each case. For the lifted shear layer case, the cold pool
simply slumps beneath the shear layer, pushing the lighter air up into the opposing shear. Thus, the low-level
air doesn’t gain much altitude, but is merely pushed laterally away from its initial location along the top
edge of the cold-pool. In the case of shear extending the full height of the model, the circulation due to the
cold-pool seems dwarfed by the ambient shear circulation, such that the low level air gains some altitude,
but circulates at a very low level, so the net gain is minimal. In the case of the surface-based shear at
very high shear magnitudes, the ambient shear forces the cold-pool to slump toward the oncoming portion
of the shear, so that the low-level shear is merely supporting the cold-pool from sinking. In this case, the
surrounding lighter air is pushed under the cold-pool, and hardly elevated at all as a result. Finally, in the
optimal case, there is just enough shear to assist the cold-pool circulation in displacing the low-level air
to maximum height. In this case, the two opposing circulations work in concert to push the air upwards,
as opposing drums force paper through a printing press. It is thus the authors’ conclusion that when the
circulations due to the cold-pool and the (low-level) ambient shear are similar in magnitude, the lifting of
low-level air is optimized (see figure 9, below).
In further simulations of squall lines using a 3D model, the authors found similar results. In terms of the
relative strengths of the cold-pool circulation (determined primarily by the speed and depth of its outflow)
and the ambient vertical wind shear, they determined that incipient convective cells forming at the outer
edge of a cold pool in ambient wind shear will develop more readily due to optimal lifting of low-level air
when C ∼
= ∆U , i. e., the strength of the cold-pool circulation C is approximately equal to the strength
of the ambient wind shear ∆U . Specifically, total 6h rainfall, total condensation, average and maximum
surface winds are all increased when this condition is met. However, another indicator of squall line strength
is the maximum vertical wind speed, which they found to be optimized when the center of the shear layer
is elevated to the level of the top of the cold-pool. This seems related to the fact that such shear seems to
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drive a sparser convective cell distribution along the edge of the cold-pool (Weisman and Rotunno, 2004).
Figure 9: The optimal condition for lifting low-level air is illustrated by low-level vertical wind shear of
moderate strength, ranging from the surface up to the original depth of the cold-pool. Note that, initially
(t = 2), the low-level shear retains the cold-pool from advancing into the ambient fluid, while the lighter fluid
is pushed up over the edge of the pool. Later (t = 4), the pool has succeeded in falling outward, which helps
to drive the CCW circulation. Meanwhile, the CW circulation due to the shear pushes the fluid trapped
between the vortices upward (Weisman and Rotunno, 2004).
WR concluded their study by presenting a simplified view of the evolution of squall lines as pertains
to their relationship to the ambient wind. The stature of the convective system, and thereby its ability to
convect efficiently, is determined by the nature of the horizontal vorticity in the region, which is likewise
determined by the cold-pool–wind-shear interaction:
System Orientation is



downshear if C < ∆U




upright if C = ∆U if C < ∆U






upshear if C > ∆U
,
(9)
where C is the circulation due to the cold-pool, and ∆U is the strength of the ambient shear. These cycles
are illustrated in the figure. All squall lines pass through some variation of these phases; however, if the
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cold-pool–shear interaction is optimal during the upright phase, the squall line will be very strong and persist
for a long time.
Figure 10: The 3 stages of convective system development. a) A young cell in the vicinity of low-level wind
shear. Initially, the shear is more powerful than the cell’s nascent cold-pool and the system bends away
from the low-level shear due to the net vorticity in the region. b) The developed cold-pool drives circulation
opposing that of the shear, and system stands upright. c) The cold-pool is more powerful than the shear, so
the system bends away from the shear, forming a rear-inflow jet where vorticity due to the cell and its cold
pool conspire to draw air inwards. The cold-pool is the shaded region, while the shear is indicated on the
lower right of each frame (Weisman and Rotunno, 2004).
4
Conclusion
Having looked at the squall line in some detail, I’ll now describe a series of events linked by the relationships
I have discussed above.
Imagine an impetus, such as an African wave that directs a subtle pressure anomaly westward across the
sea at some altitude, say 850 hPa. The local atmosphere attempts to regain equilibrium via the pressuregradient force so that horizontal winds push air radially into the pressure minimum of the wave. The Coriolis
force, redirecting the flow according to the sign of the pressure anomaly, effects a vertical wind gradient in the
vicinity of a lone convective cell busily establishing radiative-convective equilibrium in the tropics by lifting
the moist, sun-warmed air above the lifting condensation level (LCL). Struggling against the convective
inhibition that impedes its progress, the young cell after a time manages to lift the moist air above the LCL,
from where it can go continue to the level of free convection. From the LFC, the saturated air becomes an
16
important source of fuel via condensation and release of latent heat. Depending on the amount of convective
available potential energy, the parcels are driven to the top of the troposphere, from where the energy can
make its way back into space. As the sun climbs higher, the cell grows stronger, and begins to rain out the
condensed ocean water it has transported upward.
The rain evaporates while falling through the dry mid-tropospheric air that has entrained though the
sides of the convective plume and thus pushes cold air downwards, pushing the cold-pool outward in all
directions underneath the warm boundary-layer air. The surrounding warm air goes up and over the top of
the pool, effecting a toroidal circulation around the pool’s edge. The afore-mentioned ambient vertical wind
shear generates opposite vorticity along one side of the pool and helps to lift a new parcel of warm, moist
air to the LFC, forming a new convective cell there. This process continues for some time, as the cold pool
and convective cells advance into the low-level shear, gaining strength and shooting condensed hydrometeors
above the tropopause, where they diverge in all directions forming a broad cirrus shield.
Eventually, the vorticity of the powerful cold-pool causes the system to lean away from the oncoming
low-level shear, and, due to the interaction of horizontal vorticity of the cold-pool and convective outflow,
an inflow of dry air arrives beneath the cirrus shield. Water from the convective cells precipitates out if the
cirrus shield and falls through the dry mid-tropospheric inflow below it. The rain evaporates as it falls, and
in doing so, drives a cool, yet hydrostatic downdraft back toward the surface. The downdraft reduces the
moist entropy near the surface in the atmosphere and in so doing, works to stabilize the environment.
17
References
[1] AMS Glossary of Meteorology 2009: (on line version) <http://amsglossary.allenpress.com/glossary>.
[2] Battan, L. J., 1962: Radar Observes the Weather. Anchor, 158 pp.
[3] Brooks, C. F., 1922: The Local, or Heat Thunderstorm. Mon Wea. Rev., 50.
[4] Brown, J. M., 1979: Mesoscale Unsaturated Downdrafts Driven by Rainfall Evaporation: A Numerical
Study. J. Atmos. Sci., 36.
[5] Emanuel, K. A., 1994: Atmospheric Convection. Oxford University Press, 580 pp.
[6] First NCEP-CPO Numerical Weather and Climate Modeling Workshop, 2009: (group discussion about
how field programs inform the modeling community).
[7] Houze, R. A., Jr., 1977: Structure and Dynamics of a Tropical Squall-Line System. Mon. Wea. Rev.,
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[8] Leary, C. A., and R. A. Houze, 1979: The Structure and Evolution of Convection in a Tropical Cloud
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[9] Lopez Carillo, C., 2009: (conversation about radar observations).
[10] Raymond, D., 2009: Atmospheric Convection, PHYS 536 (class notes, lecture).
[11] Rotunno R., J. B. Klemp, M. L. Weisman, 1988: A Theory for Strong, Long-Lived Squall Lines. J.
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[12] Simpson, J. E., 1968: Gravity Currents in the Environment and the Laboratory. Cambridge University
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[13] Weisman, M. L, and R. Rotunno, 2004: “A Theory for Strong Long-Lived Squall Lines” Revisited. J.
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[14] Xu, Qin, 1992: Density Currents in Shear Flows-A Two-Fluid Model. J. Atmos. Sci., 49.
[15] Zipser, E. J., 1979: The Role of Organized Unsaturated Convective Downdrafts in the Structure and
Rapid Decay of an Equatorial Disturbance. J. Appl. Meteor., 8.
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