Houze Robert A., Jr. Cloud Dynamics
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9.3 General Kinematic Characteristics of Mesoscale Convective Systems 399
(e) Stratiform
(b) Intermediary
rr--"-'-'-l...."
I~I
/I~
'--r,
ILl'
"
-,--
,;.c
'"
."
~~I
::1
(a)
Conveetivel---_~~.rl
J-~-----+-~
-
III
"...!r;-
:c 200
.s
w 400
a:
::l
~
600
W
a:
Q. 800
-2 0 2
DIVERGENCE (10-
4
8-
1)
-2 0 2
DIVERGENCE (10-
4
8-
1)
-2 0 2
DIVERGENCE (10-
4
8-
1)
Figure 9.61 Mean (solid) and standard deviation (dotted) of divergence observed by airborne
Doppler radar in mesoscale convective systems over the tropical ocean north of Australia. Profiles
have been plotted against pressure so that area is proportional to mass divergence. (From Mapes and
Houze, 1993a. Reprinted with permission from the Royal Meteorological Society.)
(a)
(b)
(c)
1
CONVECTIVE
STAGE
INTERMEDIARY
STAGE
W
Strong
Positive
Buoyancy
~~//
Weak
Positive
Buoyancy
~
Strong
Negative
Buoyancy
-, -, ""
" " "-
Weak
Negative
Buoyancy
Radar
Echo
STRATIFORM
STAGE
C
,'
...
c:
,~
Pressure Force Center of
Field Lines Convergence
Figure 9.62 Conceptual model
ofthe
buoyancy and pressure gradient force field in the life cycle of
a precipitation area within a mesoscale convective system.
form-vertical
cross sections confirmed this categorization by showing a radar
bright band at the melting level (Sec. 6.1.2). At the times shown in Fig. 9.60b and
c, the precipitation was in the intermediary stage. By measuring the divergence in
93 V-shaped regions in nine different mesoscale convective systems, the mean
divergence profiles shown in Fig. 9.61 were found. Note that sensitivity of the
radar was not sufficient to observe the low intensity of the reflectivity at high
levels. Other data showed that the actual cloud tops were several kilometers
above the 200-mb level
(-12
km), which is the highest level at which the diver-
gence could be reliably measured by the radar. All the mean profiles show a net
convergence below 12 km. On the linear pressure scale used in Fig. 9.61 the area
under the divergence profiles is proportional to mass divergence. Since mass
400 9 Mesoscale Convective Systems
convergence and divergence must balance over a full vertical column, the net
convergence seen in Fig. 9.61 implies that the higher levels must have been
characterized by upward air motion and net divergence in all three cases. Consid-
ering the divergence profiles below 200 mb, we note that in the convective region
(Fig. 9.6Ia) the maximum convergence is elevated and found at about the 700-mb
level. Very little convergence is seen below 400 mb in the intermediary regions
(Fig. 9.6Ib), while maximum convergence is found at about 500 mb in the strati-
form regions (Fig. 9.6Ic). Although there was some underestimate of the winds at
low levels as a result
of
echoes from the sea surface.P" it is evident that the level
of maximum net convergence into the mesoscale convective systems (convective,
intermediary, and stratiform regions combined) must be elevated and found at a
level somewhere in the 500-700-mb layer. This result is consistent with those
contained in Fig. 9.55 and Fig. 9.56. Again, it is seen that convergence into
updrafts and divergence associated with downdrafts tend to cancel in and
just
above the boundary layer, such that the main convergence into the mesoscale
convective system is elevated. The aircraft sampling moreover shows clearly that
this net divergence profile is associated not
just
with squall lines with trailing
stratiform regions but also with mesoscale systems with more random configura-
tions of convective and stratiform precipitation.
The very high-level (above 400 mb) maximum of convergence found in the
intermediary precipitation areas (Fig. 9.6Ib) is of particular interest. It can be
understood in terms
of
the typical life cycle of a subarea of rain within the meso-
scale convective system. As indicated in Fig. 6.11, each subarea begins as a region
of convective elements and then evolves through an intermediary stage into an
area of stratiform precipitation. The subarea is thus a group of cells, each under-
going a life cycle of the type illustrated in Fig.
6.lb,
where a deep cumulonimbus
cell degenerates into a stratiform structure at the end of its lifetime. The diver-
gence profile associated with a cell undergoing such a life cycle can be understood
in terms
of
the principle illustrated in Fig. 7.1, which shows the pressure gradient
force field required by mass continuity to be associated with a uniformly buoyant
parcel. As discussed in Sec. 7.2, such a pressure force field is associated with any
given spatial distribution
of
buoyancy. Figure 9.62 depicts a buoyancy pressure-
gradient force field, of the type depicted in Fig. 7.1, that would be associated with
a convective cell undergoing a life cycle of the type illustrated in Fig.
6.lb.
In the convective stage of development the cell is dominated by an updraft,
which may be idealized as a deep vertical column of uniformly buoyant air, which
has a pressure force field like that indicated in Fig. 9.62a; air is being pushed out of
the path of the top of the cell and air is being forced in toward the buoyant updraft
in the lower troposphere. To keep the convective-stage picture simple, the down-
draft and its negative buoyancy in the lower part of the cloud have not been
sketched in Fig. 9.62a; however, the pressure gradient force field associated with
a low-level negatively buoyant downdraft is indicated (dashed field lines). In the
intermediary stage (Fig. 9.62b), the strong buoyant updraft element has been cut
off from its supply
of
buoyant air from below, and it has reached the stable
266 See Mapes and Houze (I993a) for further discussion.
9.3 General Kinematic Characteristics of Mesoscale Convective Systems
401
tropopause and begun to spread out.
It
collapses into a flattened buoyant element
in the manner illustrated in Fig. 5.33. The base of the strongly buoyant element is
thus found at ever higher levels as the element continues to rise and spread out.
The buoyancy pressure gradient force, as shown by the field lines in Fig. 9.62b,
continues to push air in under the element to maintain mass continuity. This
process accounts for the strong convergence concentrated at upper levels in the
intermediary stage seen in Fig. 9.61b. Below this region of maximum convergence
(marked by C
inFig.
9.62b), the cloud is filled with air that has been pushed in
under the rising element as its base has risen during the intermediary stage.
It
is
shown schematically as weakly positively buoyant air in Fig. 9.62b. Still farther
down, in the lower part of the cloud, downdrafts are becoming more dominant
than updrafts, and the buoyancy in the lower part of the cloud is negative on
average.
After the time of Fig. 9.62b, all of the region of strong local buoyancy compris-
ing the original convective element becomes so flattened and mixed with sur-
rounding air by entrainment that it loses its identity. Hence, no strongly buoyant
element is shown at upper levels in Fig. 9.62c. However, the air pushed in under
the rising element throughout the intermediary stage (Fig. 9.62b) came largely
from the surrounding stratiform cloud region, which at upper levels is made up
mostly of diluted but generally warm, moist air from previous convective ele-
ments. The air column above the melting layer is therefore filled with moderately
buoyant air by the time of Fig. 9.62c. At lower levels, the downdraft motion has
become firmly established across the cloud, from at or
just
above the melting layer
down to near the surface, and this lower portion of the cloud is filled with nega-
tively buoyant air, as shown by the hatching in Fig. 9.62c. Associated with this
negatively buoyant downdraft region is a pressure force field like that shown in the
lower part of Fig. 9.62c. This force field promotes convergence in the layer near
and
just
above the
OQC
level. As a result, the maximum convergence, found at high
levels in the intermediary stage (Fig. 9.61b and Fig. 9.62b), lowers to the midtro-
posphere in the stratiform stage (Fig. 9.61c and Fig. 9.62c).
9.3.2 Vorticity in Regions Containing Mesoscale
Convective Systems
It
is not uncommon for the region containing one or more mesoscale convective
systems to become characterized by cyclonic vorticity in the low to middle tropo-
sphere. Evidence of this vorticity structure is sometimes seen in satellite pictures.
In particular, large mesoscale convective systems such as MCCs (Sec. 9.1.1) often
exhibit a vortical cloud pattern in the middle-level cloud after the upper-level
cloud shield has dissolved in the late stages of the cloud system's lifetime (Fig.
9.63). In Sec. 9.2.3.7, we saw a tendency for mesoscale cyclonic vorticity centers
to form in low to middle levels
within squall lines with trailing stratiform precipita-
tion. Here, we refer to a cyclonic vorticity that characterizes a region somewhat
larger than but containing the mesoscale convective system.
The spinup of such a vortex in low to middle levels is not surprising in view of
the vertical profile of divergence observed in the vicinity of mesoscale convective
402 9 Mesoscale Convective Systems
Figure 9.63 (a) Infrared satellite view of a mesoscale convective complex (MCC) centered over
Oklahoma at
1131
GMT 7 July 1982. Gray shades are proportional to infrared radiative temperature at
cloud top, with coldest values indicated by light shading in the interior of the cloud system. The large
cold cloud shield marks the MCC. (b) Visible satellite image of the remnants of the same MCC at
1631
GMT. A cyclonic circulation is seen in the cloud pattern over northwestern Arkansas. (Photos
provided by J.M. Fritsch.)
systems. The profiles of net divergence around both the squall line with trailing
stratiform precipitation (Fig. 9.55) and the MCC (Fig. 9.56) exhibit a maximum of
convergence in the lower troposphere, but well above the surface (between 700
and 900 mb). The three profiles of divergence for the convective, intermediary,
and stratiform stages of subareas tropical oceanic of mesoscale convective sys-
9.3 General Kinematic Characteristics of Mesoscale Convective Systems 403
terns in Fig. 9.61 combine (regardless of area weighting) to yield a net convergence
in the low to middle troposphere but well above the surface. Thus, mesoscale
convective systems, regardless of type, exhibit a maximum of net convergence at
low levels but above the boundary layer.
The significance of this observation for the development of vorticity can be
seen by first rewriting the vorticity equation (2.59) as
(9.1)
where the symbols are as defined in Sec. 2.4. The subscript
H designates horizon-
tal components of vector quantities. Term (i) is the horizontal advection, (ii) is the
vertical advection,
(iii) is the stretching or intensification of existing absolute
vorticity, and (iv) is the tilting of horizontal vorticity
WH into the vertical. (9.1) is
identical to (8.9), except that here the advection terms are separated into horizon-
tal and vertical components and the earth's vorticity
fis
retained. In Sec. 9.2.3.7
we saw how, in the case of squall lines with trailing stratiform regions, the inter-
play of horizontal advection, tilting, and stretching accounts for the details of the
vorticity pattern within that type of mesoscale convective system. To apply (9.1)
to a somewhat larger area, containing one or more mesoscale convective systems,
it is convenient to rewrite (9.1) as
(9.2)
where the first term on the right is obtained by combining the horizontal advection
and stretching terms
[(i) +
(iii)],
with the aid of (2.55), while the second term on
the right is the combination of vertical advection and tilting [(ii)
+ (iv)]. If (9.2) is
averaged over an area
A, it becomes
a,
1 f 1 f
aV
t
-=--
v
(S+f)df--
w-df
at
A n A
az
(9.3)
where the line integrals are taken along the boundary of
A,
de is an increment of
distance along the boundary, and
V
n
and V
t
are the horizontal wind components
normal and tangential to the boundary, respectively. If the boundary is in the clear
air surrounding the cloud system, the vertical velocity in the second term on the
right will tend to be small. The first term is usually the dominant one.
It
is simply
the net flux of vorticity across the boundary.
Iffis
taken to be constant, it may be
written as
(9.4)
404 9 Mesoscale Convective Systems
The first term on the right is the concentration, or stretching, of the
earth's
vorticity. If the mesoscale systems within the region A are the only important
contributors to the average horizontal divergence in the region, then the net
convergence, which we have seen prevails in the low to middle troposphere in
those systems, leads to spin-up
of
mean cyclonic vorticity over the region at low
to middle levels.
For
example, a convergence of
-10-
5
S-I
(like that near 700 mb
in Fig. 9.55) leads to an
e-folding of vorticity if it operates for a period
-1
day at a
midlatitude location.
Chapter
10
Clouds in Hurricanes
"
...
when there are no hurricanes, the weather of the hurricane
months is the best of all the
year"267
As we have proceeded through discussions of cumulus clouds, thunderstorms,
and mesoscale convective systems in the previous three chapters, we have seen
convective cloud dynamics involving successively larger scales of motion, ranging
from the turbulent eddies associated with entrainment in even the smallest of
cumulus clouds to the mesoscale updraft, downdraft, and rear inflow found in the
stratiform regions of mesoscale convective systems. We now move still farther
upscale and consider the clouds associated with hurricanes (Sec. 1.3.2). The
clouds in these small synoptic-scale cyclones play an integral role in the storm
dynamics. The clouds within a hurricane are primarily of the convective genera
(cumulus and cumulonimbus) and are typically organized into large rings and
bands, which have cloud and precipitation structure (including regions of nimbo-
stratus and stratiform precipitation) similar to the mesoscale convective systems
described in the last chapter. But in addition, the air motions in the clouds are
strongly tied to the cyclone-scale dynamics. To see the connection between the
clouds and the cyclone, we cannot depend on convective dynamics and hydro-
static reasoning alone, as we have sought to do with the mesoscale convective
systems. The dynamics of the clouds in the hurricane need to be examined to-
gether with consideration of the dynamics of the cyclone itself, which is organized
on a larger scale than any we have considered thus far. In this chapter, we
therefore consider the clouds of hurricanes in relation to the horizontal and verti-
cal air motions characterizing the hurricane vortex.
We begin in Sec. 10.1 with a definition of the hurricane and a review of some its
generally observed features, including its regions of formation and occurrence
over the globe, the general pattern of clouds and precipitation in a typical storm,
and the broader aspects of storm-scale kinematics and thermodynamics. After this
general background, in Sec. 10.2, we will take a more detailed look at the ob-
served structure
ofthe
inner-core region of the storm. The dynamics of this part of
the storm are particularly crucial to understanding its clouds and precipitation. In
Sec. 10.3, we take a theoretical look at some basic aspects of hurricane dynamics.
Then we return in Sees. 10.4 and 10.5 to the observations of clouds and precipita-
tion to examine the consistency of the observed structures with the theoretical
267
From The Old Man
and
the Sea, by Ernest Hemingway.
405
406 10 Clouds in Hurricanes
view. In Sec. 10.4, we focus on the observations of the inner-core region, while in
Sec. 10.5, we examine the cloud and precipitation structures that
occur
outside
the inner-core region.
10.1 General Features of Hurricanes
10.1.1 Definition and Regions of Formation
A tropical cyclone is considered to be a hurricane when the winds near the
center
of the vortex exceed 32 m
S-I.
These storms form in the regions shown in Fig.
10.1. They form at low latitudes, generally between 5° and 20°, but not at the
equator, where there is no Coriolis force. Some vorticity of the large-scale envi-
ronment is required, and the formation regions are characterized by higher than
average surface vorticity for these latitudes. The most critical characteristic
ofthe
formation zones, however, is that the sea-surface temperature must be above
26SC.
Otherwise, there is insufficient boundary-layer energy to fuel the storm.
Other characteristics of these regions are that the stratification of temperature and
humidity is such that the air is moderately conditionally unstable (Sec. 2.9.1) and
the vertical shear of the horizontal wind is weak. This latter property is necessary
to prevent strong relative flow through developing storms. Such flow-through
ventilates the storms in such a way that they cannot build up to hurricane inten-
sity. Once hurricanes are formed, they tend to move along tracks such as those
indicated in Fig. 10.2. They appear to be largely steered by midlevel winds;
however, the factors that control their movement are complex. Forecasting hurri-
cane tracks remains difficult, and empirical methods are often employed.
10.1.2 General Pattern of Clouds and Precipitation
In satellite pictures (e.g., Fig. 1.28), the clouds in a hurricane are seen to consist of
low-level clouds spiraling cyclonically inward and upper-level cirriform cloud
spiraling anticyclonically outward.P" The precipitation pattern embedded within
this cloud pattern is a better indication
ofthe
storm dynamics, and the rain is best
observed by radar.
The
typical radar echo pattern in hurricanes, as seen by
airborne
radar
during many research flights through hurricanes, is indicated sche-
matically in Fig. 10.3. The echo pattern in a real case is shown in Fig. 10.4. The
primary distinction to be made in these patterns is between the eyewall, which
surrounds the
center
(or eye) of the storm, and the rainbands, which occur outside
the eyewall.
Further
distinctions among the types of rainbands are indicated in the
figure and will be discussed again in Sec. 10.5.
10.1.3 Storm-Scale Kinematics and Thermodynamics
An example of the low-level wind field in a hurricane (Gloria 1985)is shown in Fig.
10.5. The winds have been constructed from standard rawinsonde data plus spe-
268 The cloud motions are easily seen when the satellite imagery is viewed in time lapse.
20'E
40'
60'
80'
100'
120' 140' 160'
180' 160' 140' 120' 100'
40'N
40'
'--
__
-=-"-
=_-='O:=""
__
.l2L
'-----~20'
'---
40'
Figure 10.1 Locations of tropical cyclone formation over a 20-year period. (From Gray, 1979.
Reprinted with permission from the Royal Meteorological Society.)
Figure 10.2 Tracks of tropical cyclones in relation to mean sea-surface temperature CC).
September temperatures are taken for the Northern Hemisphere. March temperatures are taken for
the Southern Hemisphere. (From Bergeron, 1954. Reprinted with permission from the Royal
Meteorological Society.)
Figure 10.3 Schematic repre-
sentation of the typical echo pattern
seen by airborne radar in flights
through hurricanes in relation to the
low-level wind pattern. (From Wil-
loughby
et al., 1984b. Reprinted
with permission from the American
Meteorological Society.)
Texas
Gulf of Mexico
I I I I I I I I
o6 12 24 48 72 96
km
Figure 10.4 Radar echo pattern seen in Hurricane Alicia (1983) labeled according to the schematic
of Fig. 10.3. Contours are for 25 and 40 dBZ. (From Marks and Houze,
1987. Reproduced with
permission from the American Meteorological Society.)
Figure 10.5 Low-level (900 mb) wind field associated with Hurricane Gloria (1985). (a)
Large-scale flow analysis. Tick marks indicate boundaries of three nested rectangular domains defined
for the analysis; in the inner domain, wavelengths less than about
150 km have been filtered out. In the
intermediate and outer domains, wavelengths less than about 275 and 440 km have been removed. (b)
High-resolution wind analysis, in which wavelengths less than about
16, 28, and 44 km have been
filtered out in the three successively larger domains, whose boundaries are indicated by tick marks.
Solid lines with arrows are streamlines. Dashed lines are isotachs labeled in m
S-I.
(Courtesy of James
Franklin, Hurricane Research Division, U.S. National Oceanic and Atmospheric Administration.)