Houze Robert A., Jr. Cloud Dynamics
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Contents ix
9.2 The Squall Line with Trailing Stratiform Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
9.2.1 General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
9.2.2 The Convective Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
9.2.3 The Stratiform Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
9.3 General Kinematic Characteristics of Mesoscale Convective Systems . . . . . . . . . . . . . . 394
9.3.1 Divergence Associated with Mesoscale Convective Systems . . . . . . . . . . . . . . . . 394
9.3.2 Vorticity in Regions Containing Mesoscale Convective Systems
....
.. .. .. .. .
401
Chapter 10 Clouds in Hurricanes
10.1 General Features of Hurricanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
10.1.1 Definition and Regions of Formation 406
10.1.2 General Pattern of Clouds and Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
10.1.3 Storm-Scale Kinematics and Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 406
10.2 The Inner-Core Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
10.3 Basic Hurricane Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
10.4 Clouds and Precipitation in the Eyewall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
10.4.1 Slantwise Circulation in the Eyewall Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
10.4.2 Strength of the Radial-Vertical Circulation in the Eyewall Cloud . . . . . . . . . . 427
10.4.3 Vertical Convection in the Eyewall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
10.4.4 Downdrafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
10.4.5 Eyewall Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
10.5 Rainbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
Chapter 11 Precipitating Clouds in Extratropical Cyclones
11.1 Structure and Dynamics of a Baroclinic Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
I
I. 1.1 Idealized Horizontal and Vertical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
I I. 1.2 Dynamics Governing Large-Scale Vertical Air Motion . . . . . . . . . . . . . . . . . . . 442
11.1.3 Application of the Omega Equation to a Real Baroclinic Wave . . . . . . . . . . . . 445
11.1.4 Low-Level Cyclone Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
11.2 Circulation at a Front . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
11.2.1 Quasi-Geostrophic Frontogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
451
11.2.2 Semigeostrophic Frontogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
11.2.3 Moist Frontogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
11.2.4 Some Simple Theoretical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
461
11.3 Horizontal Patterns of Frontal Zones in Developing Cyclones . . . . . . . . . . . . . . . . . . . . 463
11.4 Clouds and Precipitation in a Frontal Cyclone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
11.4.1 Satellite-Observed Cloud Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
11.4.2 Distribution of Precipitation within the Cloud Pattern . . . . . . . . . . . . . . . . . . . .
472
11.4.3 Narrow Cold-Frontal Rainbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
475
11.4.4 Wide Cold-Frontal Rainbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
481
11.4.5 Warm-Frontal Rainbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
484
11.4.6 Clouds and Precipitation Associated with the Occlusion . . . . . . . . . . . . . . . . . . 489
11.5 Clouds in Polar Lows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
496
11.5.1 Comma-Cloud System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
11.5.2 Small Hurricane-like Vortex
499
Chapter 12 Orographic Clouds
12.1 Shallow Clouds in Upslope Flow
502
12.2 Wave Clouds Produced by Long Ridges .. . .. . .. . .. . .. . .. .. . . . . . .. .. .. .. . .. .. . .
502
X Contents
12.2.1 Flow
over
Sinusoidal Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
12.2.2 Flow
over
a Ridge of Arbitrary Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
12.2.3 Clouds Associated with Vertically Propagating Waves . . . . . . . . . . . . . . . . . . . 508
12.2.4 Clouds Associated with Lee Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
12.2.5 Nonlinear Effects: Large-Amplitude Waves, Blocking, the Hydraulic Jump,
and Rotor Clouds . 512
12.3 Clouds Associated with Flow over Isolated Peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
12.4 Orographic Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
12.4.1
Seeder-Feeder
Mechanism over Small Hills . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
12.4.2 Upslope Condensation . .. .
...
. . .. .
...
. ..
....
.. . .. . ..
...
. .. . ..
...
. . .. . . 531
12.4.3 Orographic Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
Index
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. 557
Preface
Clouds are a vital link in the global climate and water cycle and an integral part of
weather forecasting and analysis. Serious students of the earth's atmosphere can
little afford to ignore the physics of clouds and their effects on the atmosphere.
Over the past twenty years, a two-quarter course of study has been developed at
the University of Washington to provide the necessary background to students
destined to work in some phase of atmospheric science. The course notes have
evolved substantially in concert with advances in modeling, theory, and observa-
tions. Within the last few years the course notes have stabilized, and they now
treat rather comprehensively and cohesively the air motions and larger-scale
physics of clouds and systems of clouds. Hence, the decision was made to formal-
ize the material into a book that could be of use to a wider community of atmo-
spheric scientists.
It
should be useful to researchers, operational meteorologists,
graduate students, and advanced undergraduates.
One of the most gratifying aspects of writing this book has been the help I have
received from both individuals and organizations. I am particularly indebted to
those who have read and commented on large portions of the text. These include
Marcia Baker, Scott Braun, Randy Brown, Christopher Bretherton, Richard E.
Carbone, Shuyi S. Chen, Dale R. Durran, Spiros G. Geotis, Peter V. Hobbs,
James R. Holton, Brian E. Mapes, Clifford F. Mass, Arthur
L. Rangno, Richard
J. Reed, James Renwick, Steven Rutledge, Christoph Schar, Lloyd Shapiro, Rob-
ert Solomon, Matthias Steiner, Ming-Jen Yang, and Sandra Yuter. The detailed
editing of the manuscript and darkroom photography were expertly performed by
Grace C. Tutt-Gudmundson, while the graphic arts were produced by Kay M.
Dewar. Deborah Houze served admirably as editorial assistant. Many authors
have graciously allowed me to reproduce figures from their texts, and in many
cases they provided original copies for my use. They are all acknowledged in the
figure captions. A wealth of photos and satellite pictures, from which I was able to
select examples for this text, were provided to me by Ernest M. Agee, Robert
Breidenthal, Steven Businger, Howard B. Bluestein, Kelvin K. Droegemeier,
Dale R. Durran, Ronald Holle, Joachim P. Kuettner, Arthur
L. Rangno, Shen-
qyang Shy, Aarnout van Delden, and Morton G. Wurtele. A large part of this book
reflects my own research on clouds and precipitation, which has been sponsored
by the National Science Foundation, the National Oceanic and Atmospheric Ad-
xi
xii Preface
ministration, and the National Aeronautics and Space Administration. I began this
book in 1988-1989, while I was on sabbatical leave from the University of Wash-
ington and serving as
Guest
Professor at the Swiss Federal Institute of Technol-
ogy in Ziirich, Switzerland. Without that year of focused effort, I would probably
never have
been
able to complete the project. I am indebted to both universities
for making that year possible.
Introduction
A cloud is defined as
"a
visible aggregate of minute particles of water or ice, or
both, in the free
air."
I Clouds
cover
about half of the earth at any given time.
Thus, from space, the earth appears as a planet semi-enshrouded by these "visible
aggregates" of drops and ice crystals (see the frontispiece). The pattern of clouds
seen from space fluctuates strongly as they form, dissipate, and move in conjunc-
tion with the fluid motion of the air. These masses of cloud are an integral part of
weather, climate, and the global water cycle, and they have been the object of
serious scientific
study-as
well as art, music, history, religion, poetry, proverbs,
mysticism, and
mythology-since
at least the time of Aristotle, and probably long
before.
2
About 1940, the discipline of cloud physics began to emerge as an identifiable
specialty in meteorology. The emphasis in these early years was on cloud micro-
physics, the study
of
the formation and growth of the "minute particles" making
up the "visible aggregates." As early as 1957, B.
J. Mason recognized that cloud
microphysics was really only one branch of cloud studies, and that another branch
needed to be developed. He pointed out that the microphysical processes
"are
largely controlled by the atmospheric motions that are manifest in clouds. These
macrophysical features of cloud formation and growth, which might more prop-
erly be called a dynamics, provide a framework of environmental conditions
confining the rates and duration of the microphysical
events."
In 1971, Mason
reiterated
"the
importance of acquiring a much deeper understanding of cloud
dynamics for the development of the subject [of cloud studies] as a whole."?
The focus of this book is on the air motions associated with clouds. In keeping
with
Mason's
terminology, we refer to this discipline as cloud dynamics. The
development of cloud dynamics has trailed that of cloud microphysics largely
because the technologies required to observe and model cloud dynamics are so
demanding. The proper documentation of cloud dynamics entails scales of air
motion from
< 1 km to > 1000 km. At the same time that the air motions are
documented across these scales, the microphysical processes, occurring in the
context
ofthe
dynamics, must continue to be accounted for, at least in some gross
I From the International Cloud Atlas, Volume I (World Meteorological Organization, 1956).
2 According to Hobbs (1989), studies of the physics of clouds may have begun with the Chinese in
135
B.C.,
when it was noted that snow crystals are six-sided.
J From The Physics
of
Clouds, by B. J. Mason, Preface to the First Edition (1957) and Preface to
the Second Edition (1971). Both prefaces are printed on pp.
v-ix
of the second edition.
xiii
xiv Introduction
fashion. To accomplish necessary documentation and understanding across so
many spatial scales," special aircraft, radars, computers, satellites, and numerical-
modeling techniques must be employed.
Much of the technology needed to study cloud dynamics now exists. Conse-
quently, the subject has reached sufficient maturity that most of the salient dy-
namics of all the different types of clouds in the
earth's
atmosphere have been
identified and
can
be discussed as a coherent discipline together in a single vol-
ume. That is the purpose of this text.
The book is divided into two parts. Part I is called
"Fundamentals"
and con-
sists of the first four chapters.
It
is devoted to a review of the fundamental
scientific background needed to study cloud dynamics. In Chapter 1 we review the
variety of clouds that exist in the atmosphere and the nomenclature used to
identify them. Air motions throughout the atmosphere are governed by the laws of
classical fluid dynamics, and Chapter 2 summarizes the principles of atmospheric
dynamics that are essential to the study of cloud dynamics. The dynamics of the
air motions are inseparable from the microphysical processes; the air motions
determine whether the air is receptive to the formation and development of the
microscopic particles composing the cloud, while the heat released or consumed
by phase changes of water in clouds and the friction between the particles and the
air constitute feedback of the cloud microphysics onto the dynamics. Since
knowledge of cloud microphysics is essential to understanding cloud dynamics,
Chapter 3 gives an overview
of
cloud microphysics. One of the primary tools for
observing clouds, especially precipitating clouds, is meteorological radar, which
is a remote-sensing tool with a variety
of
special characteristics that should be
borne in mind by the student of cloud dynamics. Hence, Chapter 4 offers a
summary
of
the subject
of
radar meteorology.
Part II is
called'
'Phenomena."
It
treats the dynamics of each type of cloud and
cloud system that occurs in the atmosphere.
Each
of the chapters in Part II
(Chapters 5-12) examines a particular category of cloud. The discussions com-
prising these chapters draw upon the reservoir of observational and theoretical
fundamentals provided in Part
I.
The
reader already familiar with the fundamen-
tals reviewed in Part I may find it possible to proceed directly to Part II.
Thosejust
being introduced to the topics in Part I may wish to supplement that material by
seeking
out
more detailed texts, several of which will be mentioned in footnotes of
Part
I.
For
all readers (as well as the author), Part I serves as a handy reference,
both while reading Part II and when studying the current scientific literature on
cloud dynamics.
4 Hobbs (1981) noted that the phenomena involved in cloud dynamics range from
"the
nucleation of
cloud particles to baroclinic waves. In terms of spatial scales, 15 orders of magnitude are involved,"
which is the same as
"the
ratio of the linear dimensions of the Milky Way to those of the
earth."
List
of
Symbols
A an area
S!l
an arbitrary variable
S!l#
turbulent deviation from
S!l,(r)
A
c
autoconversion
S!lc
value of a variable
S!l
in a cloud;
S!l
may be
ft,
T,
p,
qi,
U,
W,
or p
S!le
value of a variable
S!l
in the environment of a cloud;
S!l
may be
ft,
T,
p,
qi,
U,
W,
or p
Am
effective cross-sectional area swept out by a particle of
mass m
AT total area covered by rain in a given region
Ax
x-gradient of nondimensional pressure perturbation
A
z
contribution to z-gradient of nondimensional pressure
perturbation by advection and turbulence
S!lBL value of
S!l
in a well-mixed boundary layer
S!lSFC value of
S!l
at the sea surface
A
o,
Eo positive constants in the expression for the radiative flux
divergence in an ice-cloud outflow from cumulonimbus
.4.,
B,
C constants
AE(r)
total area covered by echoes within an annular range ring
centered at range
r
S!lr(r)
basic radial distribution of
S!l*
across a cloud
A(9t
r
)
area covered by rain with rates exceeding 9t
r
A(Ze, r) area covered by echoes within an annular range ring
centered at range
r with reflectivity between
Z,
and
Z,
+
az,
(!:.S!lc/
!:.th rate of change of
S!lc
that would occur if a parcel were not
exchanging mass with the environment
a expansion coefficient
a a positive constant relating the buoyancy generation of
eddy kinetic energy and the overall generation of eddy
kinetic energy
a proportionality constant relating tangential velocity to
radius in the inner region of a Rankine vortex
an half-width of a mountain ridge
a[
constant in the expression for
N[
xv
B
x
BPGA
b
xvi List of Symbols
a.;
at.
b., a-, b
2
coefficients in the Fourier decomposition of the mean
radar radial velocity
aT autoconversion threshold
_
2<TLV
a = PLRvT
a, b, aI, b
l
,
a2,
b
2
positive constants in empirical formulas relating radar
reflectivity to rainfall rate, rainwater mixing ratio, and
precipitation particle fall speed
a specific volume
(p-
I
)
aa azimuth angle (measured clockwise from the north) toward
which radar beam is pointing
a
e
elevation angle of radar beam
a, proportionality factor relating the volume of a polyhedron
to that of an inscribed sphere
a
o
adjustable parameter relating sensible heat fluxes at cloud
base to those at cloud top
ai positive constant in the expression for
Cf',2
a
e
an empirical constant determined in laboratory
experiments on turbulent elements
a proportionality constant in formula for autoconversion
eX,
/:3
constants
~
creation (destruction)
of
'J{ by thermally direct (indirect)
flow perturbations
B buoyancy
lB
i
time rate of change
of
the concentration of drops per unit
size interval in_size range
i resulting from drop breakup
B
-
ae
a -
ae
a
T=U-+W-
ax
az
x-gradient of apparent potential temperature perturbation
buoyancy pressure gradient acceleration
proportionality constant relating tangential velocity to
inverse radius in the outer region of a Rankine vortex
b In Chapter 7, b represents the radius of a turbulent
element; in Chapter 11, it is defined as the quantity
ge/{)
b _ 3ivH m
sM
w
47Tp
L
M
s
{3i
proportionality factor relating the surface area of a
polyhedron to that of an inscribed sphere
{3T
proportionality factor in the expression for the eddy flux of
cloud virtual potential temperature
C(6
rate at which 'J{ is created by conversion from mean-flow
kinetic energy, when down-gradient eddy momentum
fluxes
occur
C condensation of vapor
List of Symbols xvii
C
A
empirical coefficient in the bulk aerodynamic formula for
surface flux of
.oil
C
c
condensation of cloud water
CD empirical coefficient (drag coefficient) in the bulk
aerodynamic formula for surface flux of
.oil
= m
C« deposition rate
(£i time rate of change of the concentration of drops per unit
size interval in size range
i resulting from collection
C
R
a constant depending on the characteristics of a particular
set of radar equipment
C
s
empirical coefficient in the bulk aerodynamic formula for
surface flux of
.oil
= c
p
In ()e
CAPE convective available potential energy
CDR circular depolarization ratio
C shape factor analogous to electrical capacitance
c one-half the horizontal convergence in a one- or two-cell
vortex
C phase speed
Co speed of light
c
p
specific heat of dry air at constant pressure
c, specific heat at constant pressure of soil
c, specific heat of dry air at constant volume
c., specific heat of water
f: specific heat of a homogeneous fluid
D particle diameter
;t! domain of radar observations
CZlJ
«0)
frictional dissipation of ';j{ by eddies or molecular
friction
D
h
diameter of a hailstone
;t!i time rate of change of the concentration of drops per unit
size interval in size range
i resulting from vapor diffusion
(condensation and/or evaporation)
DR parameterization of the vertical pressure gradient
acceleration of a rising bubble
("drag")
D;
diffusion coefficient for water vapor in air
;t!i, time rate of change of the concentration of drops per unit
size interval in size range
i resulting from condensation
;t!i
e
time rate of change of the concentration of drops per unit
size interval in size range
i resulting from evaporation
2il
==
v'
~,
a measure of turbulent dissipation of the mean
flow
b viscosity
d constant proportionality factor relating the tangential
velocity to the inverse of the radius of a one-cell vortex
8
h
homogeneous freezing factor
xviii List of Symbols
E electric field vector
E; evaporation of cloud water
E, evaporation of rainwater
w,/
dynamic entrainment
W,2
entrainment by lateral eddy mixing
W,3
entrainment by the convergence of the vertical eddy flux
across the top and bottom of an infinitesimal layer of cloud
e, saturation vapor pressure over a plane surface of water
esi saturation vapor pressure with respect to a plane surface
of ice
esi(oo)
saturation vapor pressure over a plane surface of ice
AE
net energy (Gibbs free energy) required to accomplish
nucleation of a particle of water or ice bubble
~c
collection efficiency
~rc
collection efficiency of raindrops collecting cloud drops
e small positive fraction parameterizing the near adjustment
of frontal clouds to moist symmetric neutrality
e, time rate of change of the concentration of drops per unit
size interval in size range
i resulting from entrainment
F molecular friction force
F net convergence of the vertical flux of liquid water relative
to the air (sedimentation of liquid water)
F
B
buoyancy source for unaveraged pressure perturbation
F
D
=RvT(oo)D;:1 e;l(oo) (Chapter 3); dynamic source in
diagnostic equation for unaveraged pressure perturbation
(Chapters
7-9)
F
g
sedimentation of snow and graupel
iSi
time rate of change of the concentration of drops per unit
size interval in size range
i resulting from sedimentation
(or fallout)
F, sedimentation of rainwater
'?fir
turbulence term in equation for
qr
F, sedimentation of snow
'?fir
turbulence term in equation for the total water mixing ratio
'?fi
u turbulence term in the x-component of the equation of
motion
'?fi
v vertical flux of water vapor
'?fi
w turbulence term in the vertical component of the equation
of motion
'?fie
vertical flux of sensible heat
F
K
= L2K;;\
R;\
T-2(oo)
F
Di
= RvT(oo)D;le;;l(oo)
F
Ki
=
L~K;;lR~1
T-2(oo)
ft, c conservative properties of a parcel of air