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Storm and Cloud

Dynamics

William R. Cotton

DEPARTMENTOF ATMOSPHERICSCIENCE

FORTCOLLINS,COLORADO

COLORADO S T A r E U N I V E R S I T Y

Richard A. Anthes

NATIONALCEWTERFOR ATMOSPHERICRESEARCH BOULDER,COLORADO

ACADEMIC PRESS, INC.

Harcourl Brace Jovanovich, Publishers

San Diego New York Boston

London Sydney Tokyo Toronto

Preface

The focus of this book is on the dynamics of clouds and of precipitating

mesoscale meteorological systems. Mesoscale meteorology is concerned with weather systems that have spatial and temporal scales between the domains of macro- and micrometeorology. Generally, macrometeorology is concerned with weather systems having spatial scales greater than 1000 km and tem-

poral scales on the order of several days or longer. Micrometeorology is the

science dealing with atmospheric dynamics having spatial scales of tens to

hundreds of meters and time scales on the order of minutes. Mesoscale

meteorology can therefore be thought of as the science dealing with any weather system lying between these two extreme temporal and spatial scales. Orlanski (1975) subdivided the classification of mesoscale systems into three scales: meso-a, meso-p, and meso-y (see the accompanying figure). He sug- gested that the term meso-a should be applied to weather systems such as frontal systems and hurricanes having horizontal scales of 200-2000 km and temporal scales of 1 day to 1 week. The term meso-p should be applied to such systems as the nocturnal low-level jet, squall lines, inertial waves, cloud clusters, and mountain and lakekoastal circulations. These systems have

horizontal scales on the order of 20-200 km and temporal scales on the order

of several hours to 1 day. Finally, he suggested that the meso-y regime should include thunderstorms, internal gravity waves, clear air turbulence, and urban

effects with horizontal scales of 2-20 km and temporal scales on the order

of one-half hour to several hours. In this book, we shall generally adhere to this terminology. Clouds and precipitating mesoscale systems represent some of the most important and scientifically exciting weather systems in the world. These are the systems that produce torrential rains, severe winds including downbursts and tornadoes, hail, thunder and lightning, and major snow storms. Fore-

casting such storms represents a major challenge since they are too small to

ix

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Preface

I MONTH(flL,)-' I I I D A Y ( l ). ' 1

I 1

I

I

MACRO f l

I

MESO- SCALE

MEW SCALE ry

Scale definitions and different processes with characteristictime and horizontal scales. [Adapted from Orlanski (1975).]

xii Preface

described not so much from the point of view of a detailed examination of

the physics of the process as from the perspective of what essential elements of the processes most strongly influence the modeling of clouds and mesoscale systems. In other words, we discuss the parameterization of the detailed physical processes. In Part 11, we describe the physics and dynamics of various cloud systems, ranging from the least dynamic, fogs and stratocumulus clouds, to the most dynamic, severe convective clouds. A discussion follows of the physics and dynamics of the dominant precipitating mesoscale systems, including squall lines, cloud clusters, mesoscale convective systems, and the subsynoptic struc- ture of tropical and extratropical cyclones. We conclude with discussions of the physics and dynamics of middle and high clouds and stable orographic clouds. In our discussion of each cloud type, we attempt to describe the cur- rent state of knowledge as derived from the marriage of theoretical modeling

and observational analysis. The detailed examination of the theory in Part I

is not essential to the interpretation of Part 11. However, we recommend that

the reader become familiar with the notations in Part I in order to follow

more readily the discussions in Part 11. We appreciate the essential help of Brenda Thompson in typing the manuscript, requesting figure authorizations, editing, and keeping figures and the many drafts of this text organized. Lillian Vigil, Nancy Duprey, and Ann Modahl also assisted in typing. The editorial assistance of Annette Claycomb, Hope Hamilton, and Ann Modahl is acknowledged. Lucy McCall drafted the original figures in the text. The manuscript was greatly improved by the comments of Mitch Moncrieff, who reviewed the entire text. Reviewers of selected portions of the text in- clude Charlie Chappell, Paul Ciesielski, Terry Clark, Steve Cox, Leo Don- ner, Dale Durran, Piotr Flatau, Bob Houze, Dick Johnson, Joe Klemp, Kevin Knupp, Hung-Chi Kuo, Bob Maddox, Ray McAnelly, Mike Moran, Roger Pielke, Bob Rauber, Dave Reynolds, Wayne Schubert, Joanne Simpson, Ron Smith, Graeme Stephens, Duane Stevens, Sean Twomey, Melanie Wetzel, and Michio Yanai. Original research results reported in the text were supported by the Na- tional Science Foundation (NSF) under grants ATM-8512480, ATM-8312077, and ATM-8113082; the National Center for Atmospheric Research, which is sponsored by NSF; Air Force Geophysics Lab Contract #F19628-84-C-0005; and Office of Naval Research Contract #N00014-83-K-0322.

Orlanski, 1. (1975). A rational subdivision of scale for atmospheric processes. Bull. Am. Mereoml. SOC. 56. 527-530.

Chapter 1 I Clouds

Clouds are pictures in the sky They stir the soul, they please the eye They bless the thirsty earth with rain, which nurtures life from cell to brain- But no! They're demons, dark and dire, hurling hail, wind, flood, and fire Killing, scarring, cruel masters Of destruction and disasters Clouds have such diversity- Now blessed, now cursed, the best, the worst But where would life without them be?

Vollie Cotton

1.1 Introduction

Since the late 1940s, when the experiments by Langmuir (1948') and Schaefer

(1948) suggested that seeding of certain types of clouds could release

additional precipitation, there has been intensive investigation into the physics of clouds. The major focus of these studies has been on the micro- physical processes involved in cloud formation and the production of precipitation. As the studies have unraveled much about the detailed micro- physics of clouds, it has become increasingly apparent that these processes are affected greatly by macroscale dynamics and thermodynamics of the cloud systems. We have also learned to appreciate that the microphysical processes can alter the macroscale dynamic and thermodynamic structure of clouds. Thus, while the focus of this book is on the dynamics of clouds, we cannot neglect cloud microphysical phenomena. The title of this book implies a perspective from which we view the cloud or cloud system as a whole. From this perspective, cloud microphysical processes can be seen as a swarm or ensemble of particles that contribute collectively and in an integrated way to the macroscale dynamics and thermodynamics of the cloud. We take a similar perspective of small-scale air motions in clouds. Again, we will not use our highest power magnifying lens to view the smallest scale

1

1.2 The Classification of Clouds 3

masses, or rolls, which are sometimes partially fibrous or diffuse and which may or may not be merged; most of the regularly arranged small elements usually have an apparent width of 1-5”.

Altostratus-Greyish or bluish cloud sheet or layer of striated, fibrous,

or uniform appearance, totally or partially covering the sky, and having parts thin enough to reveal the sun at least dimly, as through ground glass. Altostratus does not produce halos. Nimbostratus-Grey cloud layer, often dark, the appearance of which is rendered diffuse by more or less continuously falling rain or snow, which in most cases reaches the ground. It is thick enough to completely obscure the sun. Low, ragged clouds frequently occur below the nimbostratus layer. Strutocumulus-Grey or whitish, or both grey and whitish, patches, sheets, or layers of cloud which almost always have dark parts, composed of crenellations, rounded masses, or rolls, which are nonfibrous (except when virga-inclined trails of precipitation-are present) and which may or may not be merged; most of the regularly arranged small elements have an apparent width of more than 5”. Stratus-Generally grey clouds with a fairly uniform base, which may produce drizzle, ice prisms, or snow grains. If the sun is visible through the cloud, its outline is clearly discernible. Stratus clouds do not produce halo phenomena except, possibly, at very low temperatures. Sometimes stratus clouds appear in the form of ragged patches. Cumulus-Detached clouds, generally dense and with sharp outlines developing vertically in the form of rising mounds, domes, or towers, of which the bulging upper part often resembles a cauliflower. The sunlit parts of these clouds are mostly brilliant white; their base is relatively dark and nearly horizontal. Sometimes cumulus clouds are ragged. Cumulonimbus-Heavy, dense clouds, with a considerable vertical extent, in the form of a mountain or huge tower. At least part of their upper portion is usually smooth, fibrous, or striated and is nearly always flattened; this part often spreads out in the shape of an anvil or vast plume. Under the base of these clouds, which is generally very dark, there are frequently low ragged clouds and precipitation, sometimes in the form of virga.

In general we will not have to refer to the definitions of the clouds species or varieties used in the “International Cloud Atlas.” The exceptions mainly concern cumulus clouds, which we refer to as follows:

Cumulus humilis-Cumulus clouds of only a slight vertical extent; they

Cumulus mediocris-Cumulus clouds of moderate vertical extent, the

generally appear flattened.

tops of which show fairly small protuberances.

4 I Clouds

Cumulus congestus-Cumulus clouds which exhibit markedly vertical development and are often of great vertical extent; their bulging upper part frequently resembles a cauliflower. We also may have occasion to refer to the following supplementary features and accessories of clouds:

Mamma-Hanging protuberances, like udders, on the under surface of

a cloud. Virgo-Vertical or inclined trails of precipitation (fall streaks) falling from the base but reaching the earth’s surface. Pileus-An accessory cloud of small horizontal extent, in the form of a cap or hood above the top or attached to the upper part of a cumuliform cloud which often penetrates it.

Fog is not treated as a separate cloud genus in the “International Cloud Atlas.” Instead it is defined in terms of its microstructure, visibility, and proximity to the earth’s surface as follows:

Fog-Composed of very small water droplets (sometimes ice crystals) in suspension in the atmosphere; it reduces the visibility at the earth’s surface generally to less than 1OOOm. The vertical extent of fog ranges between a few meters and several hundred meters. We include the discussion of fog in the chapter on stratocumulus clouds, since we shall see there is not always a clear distinction between the formative mechanisms of a marine stratocumulus cloud whose base is elevated from the surface and a fog which reaches the surface. Another cloud form discussed in this text that is not treated in the “International Cloud Atlas” as a separate cloud genus is the orographic cloud. According to the “Glossary of Meteorology” (Huschke, 1959), an orographic cloud is a cloud whose form and extent is determined by the disturbing effects of orography upon the passing flow of air. Since orography can also initiate convective clouds, we shall often refer to a stable, orographic cloud as the cloud form typically encountered in the wintertime during periods when the atmosphere is stably stratified. The cap cloud is the least complicated form of the orographic cloud and refers to a nearly stationary cloud that hovers over an isolated peak. The crest cloud is like the cap cloud with the exception that it hovers over a mountain ridge. The chinook arch or foehn wall cloud refers to a bank or wall of clouds associated with a chinook or foehn wind storm. Finally, the lenticular cloud, or lenticularis, is a lens-shaped cloud that forms over or to the lee of orographic barriers as a result of mountain waves. As the name implies, lenticular clouds generally have a smooth shape with sharp outlines, sometimes vertically stacked with clear air separating each lenslike element.

6 1 Clouds

mixing ratio of only 5 g kg-I. Thus, if these two clouds have equal depths, the one with the warmer cloud base has a much greater potential for producing rainfall. Cloud-top temperature is important for similar reasons, because the greater the difference between the cloud-base temperature and cloud-top temperature, the greater the potential for rainfall. Furthermore, if the cloud-top temperature is below O'C, then ice is possible, which greatly affects precipitation and radiation processes. Turbulence, the last consideration in our discussion of macroscopic cloud parameters, is important because it mixes properties of the cloud and interacts closely with the other parameters. When we speak of "characteris- tic" time scales, vertical velocities, liquid-water contents, and temperatures, the level of turbulence determines how representative these "characteristic" scales really are. For example, in some convective clouds the average updraft velocity may be 1 m s-', while the standard deviation of the vertical velocity may be as large as 3 m sC'. The level of turbulence also affects the precipita- tion processes, due to the formation of higher peak supersaturations and to increased interactions among cloud particles of different types and sizes.

Turbulence is also likely to affect the radiative properties of a cloud. In a

turbulent cloud the cloud top is likely to be very lumpy, and large fluctuations in liquid water will exist. As a consequence, the cloud-top radiative emittance and absorptance will differ significantly from that found in a more homogeneous cloud. Let us next consider how the characteristics just introduced differ in several cloud forms that we will study in this book.

1.3.1 Fog Fog may be considered the least dynamic of clouds. Fogs typically have

lifetimes (T,) of 2 to 6 h. The mean vertical velocity in fog is usually quite

small. If we assume a mean updraft of 0.01 m sC1 for a 100-m-deep fog, the time scale for a parcel entering cloud base and exiting cloud top would be T ~ = 100 m/0.01 m sC' = lo4 s, that is, Tp is on the order of 3 h. This represents the time scale in which cloud microphysical processes must operate in order to generate precipi- tation. However, the liquid-water content in fog typically ranges from 0.05 to 0.2 g mC3.Thus, precipitation is unlikely in all but the deepest, wettest, and most maritime fogs, even though the mean vertical velocity might indicate

a potential for precipitation. If^ we use our estimate of^ w^ of 0.01 m s-', we

determine that the cooling rate due to wet adiabatic cooling is on the

order of CR, = (0.5"C/ 100 m)0.01 m sC1= 5 x loC5"C sC',

1.3 Time Scales, Vertical Velocities, and Water Contents 7 which is approximately 0.2"C h-I. By comparison, the rate of cooling by longwave radiation flux divergence at the top of the fog can easily range from 1 to 4°C h-I. Thus, we see that fogs can be dominated by radiative cooling. The absolute magnitude of turbulence in fogs is usually small, although there have been reports of vertical velocity fluctuations in some valley fogs as large as 1 m Ci. However, if we consider turbulence in terms of fluctu- ations from the mean motions, it appears that because both horizontal and vertical mean velocities are typically small in fogs, a fog is dominated by turbulence. Thus, turbulence affects transport and nearly all physical processes in fogs, even though its absolute magnitude is generally small.

1.3.2 Stratus and Stratocumulus Clouds Stratus clouds and stratocumulus clouds d o not differ markedly from fogs in terms of time scales, liquid-water contents, o r turbulence levels. The lifetimes of stratus and stratocumulus clouds are longer, ranging from 6 to 12 h. As in fog, the time scale for a parcel to enter a stratus having a mean vertical velocity of 0.1 m sP1 and rising through a depth of, say, 1000 m may be 3 h. Typical liquid-water contents in stratus clouds range from 0.05 to 0.25 g mP3, with some maxima of over 0.6 g m-3 reported. This combination of time scales and liquid-water contents results in precipitation in the deepest, wettest stratus and stratocumulus clouds in the form of drizzle. Again, assuming vertical velocities of 0.1 m s - ' , the wet adiabatic cooling

rates are on the order of 2°C h-I. Thus, radiation and wet adiabatic cooling

are approximately equal contributors to the destabilization of stratus and stratocumulus clouds. The turbulence level in stratus clouds is low in absolute magnitude, just as it is in fog. However, since mean vertical velocities are also small, turbulence is a significant contributor to vertical transport processes, ener- getics, and the physics of stratus clouds.

1.3. Cumulus clouds whose vertical extent may be 1500 m have a lifetime (T,) of 10-30min, which is shorter than that for the preceding two types of clouds. If we consider an average vertical velocity of 3 m s - ' , the time scale

for a parcel to enter cloud base and exit cloud top is on the order of

Tp= 1500 m/3 m s-I = 500 s = 10 min.

The liquid-water content of small cumuli rarely exceeds 1.0 g m-3 and is typically approximately 0.3 g m-3. Thus, for such short time scales and low

Cumulus (Humilis and Mediocris) Clouds

1.3 Time Scales, Vertical Velocities, and Water Contents 9

greater. These high liquid-water contents compensate, to some extent, for the short time scale. The short time scale sometimes limits the formation of precipitation, which accounts for the weak echo regions (WERs) that are often observed by radars. I t should be noted that such intense updrafts as those present in WERs are not characteristic of the entire convective storm. Because turbulence levels can be so intense, there is considerable opportunity for air parcels to experience much longer lifetimes than are encountered rising in the main updraft. With the exception of the anvil outflow region of cumulonimbi, wet adiabatic processes dominate over radiative cooling. However, radiative cooling may contribute significantly to the destabilization and maintenance of the weak updraft regions of cumulonimbus anvils.

1.3.6 Stable Orographic Clouds Let us consider now a wintertime stable orographic cloud that is above a 1400-m-high mountain with a half-width of 18 km (Fig. 1.1). For this type of cloud, the cloud lifetime could be many hours or even days. However, the time scale for precipitation processes to operate if the

winds are about 15 m s-' is only

T ~ = 18,000 m/15 m s-I= 1200 s = 2 0 min Thus, the time scale Tp is longer than that for cumuli but considerably shorter than that for stratus clouds. The liquid-water contents of wintertime stable orographic clouds do not differ substantially from those of stratocumuli; they are typically less than 0.2gm-3. I t is only in highly efficient maritime clouds or the colder ice-phase-dominated clouds that precipitate occurs occasionally. If we consider typical updraft speeds near the mountain barrier to be about 1 m s-', we have an estimate of wet adiabatic cooling rates of CR, = 18°C h-I,

which is greater by an order of magnitude than radiative cooling rates.

f

1

1400 m

Fig. 1.1. Schematic diagram of a stable orographic cloud.

10 1 Clouds

Thus, near the barrier crest, wet adiabatic processes remain dominant. At distances removed from the barrier crest, however, where a blanket cloud may reside, or in weaker wind situations, one can anticipate that radiative processes become more significant in such clouds. There has been very little characterization of the levels of turbulence in wintertime stable orographic clouds. At cloud levels near the barrier crest, surface-generated turbulence could be quite significant. At higher cloud levels, however, turbulence levels can be expected to be relatively weaker under the typically stable conditions. We can see from these simple comparisons and contrasts that clouds form in a broad range of conditions that control the ultimate destiny of the cloud. Depending on the vertical velocity, liquid-water content, and cloud time scale, precipitation processes may or may not affect significantly the dynamics of the cloud. Similarly, radiation processes may or may not be an important destabilizing influence on the cloud. It should be remembered that these are only rough estimates and that one can expect considerable variability within a given cloud category. To account for such variability we must construct sophisticated models of each of the cloud types. In the following chapters, we present the foundation for constructing such models of the dynamics and physics of various cloud systems.

References

Howell, W. E. (1951). The classification of cloud forms. Clouds, fogs and aircraft icing. I n "Compendium of Meteorology" (T. F. Malone, ed.), pp. 1162-1 166. Am. Meteorol. SOC., Boston, Massachusetts. Huschke, R.^ E.,^ ed.^ (1959).^ "Glossary^ of^ Meteorology."^ Am.^ Meteorol.^ SOC., Boston, Massachusetts. Langmuir, 1. (1948). The growth of particles in smokes and clouds and the production of snow from supercooled clouds. Roc. Am. Philos. Sac. 92, 167. Schaefer, V. J. (1948). The production of clouds containing supercooled water droplets or ice crystals under laboratory conditions. Bull. Am. Meteorol. Sac. 29, 175. Scorer, R. S. (1963). Cloud nomenclature. Q. J. R. Meteorof. Sac 89, 248-253. Scorer, R. S., and H. Wexler (1967). "Cloud Studies in Colour." Pergamon, Oxford. World Meteorological Society (1956). "International Cloud Atlas," Vol. 1. Geneva.

14 2 Fundamental Equations Governing Cloud Processes Let us consider a system composed of dry air with density p a , water vapor density p v , and total water condensate p w (i.e., cloud water, rain water, and ice water) such that

P, = P"+ P w , (2.1)

where pL is the total water density.

can be written:

Assuming that the system behaves as an ideal gas, the equation of state

p = R,p,T + Rvp, T = pd + e, (2.2)

where R , and R , are the gas constants for dry air and water vapor (287. and 461.50 J kg-' K - ' , respectively), and pd and e are the partial pressure of dry air and water vapor. Equation (2.2) can be rewritten as

p = P , R , T ( 1 + R"P"/R,P,). (2.3)

The quantity p v / p a is defined as the mixing ratio of water vapor rv, and R , / R , = 1.61, thus,

p = p , R , T ( I + 1.61rv). (2.4)

It should be noted that Eq. (2.4) is written in terms of the dry air density pa and the dry gas constant R , and that no approximations have been made. Another more familiar form of the equation of state can be found by rewriting Eq. (2.2) as

m,R,+ mVRv P = P m m , + m , T, (2.5)

where m , and m , are the masses of dry air and water vapor, respectively, and

m a + m, P m = - - - P , + P v , U

and u is the volume of gas. Equation (2.5) can be rewritten as

1 + ( m " / m a ) ( R " / R a )T.

P = pmRa

1 + mv/ma

The mixing ratio of water vapor rv can be written as

so that Eq. (2.7) becomes

(2.7)

2.2 General Equations 15 where we have again let R , / R a = 1.61. Comparing Eqs. (2.4) and (2.9), one should note that the equation of state, Eq. (2.9), contains the density of the mixture p m , whereas Eq. (2.4) contains the density of dry air p a. Equation (2.9) can be rewritten as

We define the quantity specific humidity qv as

qv=---. m , + m a l + r v

m , - r,

Thus Eq. (2.10) can be written p=pmR,(1+0.61q,)T.

(2.10)

(2.11)

(2.12) Since vapor mixing ratios rarely exceed 22 g kg-' even in the tropics, qv<< 1; therefore 4,- r, and Eq. (2.12) may be approximated as p - pmRa( 1 +0.61rv) T. (2.13) Comparing Eq. (2.4) to Eq. (2.13), we note that the coefficient 0.61 multiplies rv when the density of the mixture is used in the equation of state, and the coefficient 1.61 multiplies r, when pa is used. We emphasize that this is often a source of confusion for a moist system.

It is common for meteorologists to define a virtual temperature Tv as

T, = ( 1 + 0.61 q v ) T = ( 1 + 0.61 r,) T, (2.14)

thus Eq. (2.12) or (2.13) becomes

p = P m R a T v. (2.15)

It should be noted that in a cloud system containing hydrometeors, the equation of state-Eq. (2.10), (2.12), or (2.15)-only describes the relation- ship among p , T, and p m , or the density of the gaseous components of the system. The total density of the system p is equal to

P = P n l + P w = P a + Pt. (2.16)

2.2.2 Equations of Motion The equations of motion of a parcel of moist air having density p m can be

written [see basic texts such as Dutton (1976) or Holton (1972) for deri-

vation]

P m ( d u i / d t ) = -ap/axi - p m g S i 3 - p w g S i 3 + P m E i j k U j f k + P m f r , (2.17)