Physics and chemistry of clouds

abil-This textbook provides students – whether seasoned or new to the atmospheric sciences –with a quantitative yet approachable path to learning the inner workings of clouds.Comprehensi

P H Y S I C S A N D C H E M I S T RY O F C L O U D S

Clouds affect our daily weather and play key roles in the global climate Through their ity to precipitate, clouds provide virtually all of the fresh water on Earth and are a cruciallink in the hydrologic cycle With ever-increasing importance being placed on quantifiablepredictions – from forecasting the local weather to anticipating climate change – we mustunderstand how clouds operate in the real atmosphere, where interactions with natural andanthropogenic pollutants are common

abil-This textbook provides students – whether seasoned or new to the atmospheric sciences –with a quantitative yet approachable path to learning the inner workings of clouds.Comprehensive treatments are given of the mechanisms by which cloud droplets formand grow on soluble aerosol particles, ice crystals evolve into diverse shapes, precipitationdevelops in warm and cold clouds, trace gases and aerosol particles are scavenged from theatmosphere, and electrical charge is separated in thunderstorms

Developed over many years of the authors’ teaching at Penn State University, Physics and Chemistry of Clouds is an invaluable textbook for advanced students in atmospheric

science, meteorology, environmental sciences/engineering, and atmospheric chemistry It

is also a useful reference text for researchers and professionals

D E N N I S L A M B is Professor Emeritus of Meteorology at the Pennsylvania StateUniversity He has been fascinated with clouds ever since growing up in the MidwesternUnited States, and the true nature of clouds and the processes that form them have beengradually revealed to him through years of formal training and self study Professor Lambworked as a researcher for nearly 14 years at the Desert Research Institute (Reno) beforeembarking on a teaching career at Penn State University With more than 40 years of obser-vational and laboratory research experience, and more than 20 years teaching cloud physicsand atmospheric chemistry at both the undergraduate and graduate levels, he now realizesthat the best path toward understanding clouds is to understand water itself, at the molecu-lar level The deeper the understanding, the greater becomes the appreciation of clouds asgate keepers in the water cycle and energy budget of Earth This book is the culmination

of his career studying the physics and chemistry of water and clouds

H A N S V E R L I N D E is an Associate Professor of Meteorology at the Pennsylvania StateUniversity He is an observational meteorologist who has studied clouds in the Antarctic,

at the equator, and in the Arctic He is currently the site scientist for the US Department

of Energy Atmospheric Radiation Measurement Program Climate Research Facility atBarrow on the North Slope of Alaska, and he teaches classes in atmospheric thermo-dynamics, cloud physics, mesoscale meteorology, and radar meteorology at Penn StateUniversity After a start in meteorology as a weather forecaster, he developed a passion

inside out He enjoys seeing the surprised looks on student faces when, on the firstday of every semester, he asks “Who can tell me what clouds are in the sky today?”which inevitably leads to the next question, “Who can tell me what the sky looks liketoday?”

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 Dennis Lamb and Johannes Verlinde 2011

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To our families

Pat and Julie

Terri, Anneke, Kris, Katrina, and Maarten

3.2 Thermodynamic perspective of phase equilibrium 130

14.4 Discharge events 543

Clouds contribute to our lives in both direct and indirect ways Clouds are at once the mostvisible elements of the sky and the dominant contributors to the weather we experienceevery day Less apparent, but perhaps even more important, are the roles clouds play in theglobal energy and water budgets that determine the climate of Earth Through their ability

to precipitate, clouds provide virtually all of the fresh water on Earth and a crucial link inthe hydrologic cycle Clouds are also the most effective agents cleansing the atmosphere,although some terrestrial and aquatic ecosystems pay the price for anthropogenic emissions

of chemicals into the air With ever-increasing importance being placed on quantifiablepredictions, whether to forecast the local weather or to anticipate changes in global climate,

we must learn how clouds operate in the real atmosphere, where two-way interactions withnatural and anthropogenic pollutants are common

Clouds have been the subject of observation for centuries, but serious systematic tigations began only a few decades ago For all practical purposes, the study of cloudscan be traced back to Luke Howard, the English pharmacist who began, around 1803, thesystem of naming cloud types that we still use today (see Appendix A) Speculation aboutthe composition and nature of clouds persisted for many years Direct observations fromballoons and aircraft helped greatly to develop a base of empirical knowledge upon whichthe research community could later build testable hypotheses With ongoing improvements

inves-in inves-instrumentation and measurement techniques, the inves-invention of cloud chambers, and anability to test hypotheses quantitatively, the research community of atmospheric scientistshas gradually developed a broad and quantitative understanding of clouds

The atmosphere, with all its dynamical and chemical complexity, is the environment

in which clouds form We cannot understand clouds divorced from that parental setting.The atmosphere is a mixture of a huge number of chemical compounds, some gaseous,some particulate in nature Indeed, water is just one of those myriad components, but theonly one of note that changes phase under ordinary conditions The atmosphere is far morethan “dry air” and water vapor, so any modern treatment of clouds must deal with thismixture head-on Indeed, cloud droplets form on the more soluble subset of the particulatematter, and they subsequently absorb some of the trace gases The microphysical proper-ties, even the macrophysical forms, of clouds are significantly affected by the chemicals inthe air In turn, many of those chemicals are altered and removed from the atmosphere by

xi

clouds and the precipitation they produce The physics and chemistry of the atmosphere

go hand in hand when developing a complete picture of clouds and how they behave in theatmosphere

The need for a new textbook arose partly out of our frustrations with identifyingtextbooks suitable for teaching cloud physics, mainly at the graduate level, but also aspart of the undergraduate curriculum that meteorology majors take Many of our first-year graduate students come from disciplines other than meteorology or the atmosphericsciences They typically have strong backgrounds in science, engineering, or math, but fewhave had any formal course dealing with clouds The graduate course offered at Penn StateUniversity therefore starts out with few assumptions other than that the students are brightand skillful in mathematics and scientific reasoning An ideal text parallels the coursestructure by presenting the atmospheric context and showing how fundamental scientificprinciples lead to the phase changes of water we know of as clouds We hope that we havemet the challenge with this textbook by emphasizing the basic disciplines of physics andchemistry

This textbook offers students, whether seasoned or new to the atmospheric sciences, aquantitative, yet approachable path to learning the inner workings of clouds Comprehen-sive treatments are given of the mechanisms by which cloud droplets form and grow onsoluble aerosol particles, ice crystals evolve into diverse shapes, precipitation develops inwarm and cold clouds, trace gases and aerosol particles get scavenged from the atmosphere,and electrical charge becomes separated in thunderstorms Overall, the book emphasizeshow clouds ultimately depend on the molecular properties of matter

The book is broken down into five parts to allow the reader to focus separately on the eral main areas Part I provides background material of use to those either unfamiliar withthe atmospheric sciences or wishing a brief refresher of concepts and terminology This firstpart could serve as the basis for a survey course in physical meteorology Alternatively, itmay be skimmed or skipped by readers with strong backgrounds in atmospheric physicsand chemistry Part II shows how transformations, both physical and chemical, come about

sev-in nature when a system deviates from equilibrium Special attention is paid to the concepts

of equilibria pertinent to phase changes because of their central role in theories of cloudformation Part III discusses clouds from a macroscopic point of view At this level, oneneed not know much about the composition of clouds other than that they are composed ofwater in condensed form Part IV elucidates the processes responsible for the microstruc-ture of clouds, the phases, sizes, and shapes of the individual particles making up a cloud.Part V brings the reader back to the cloud scale and the effects of large populations ofcloud particles

The units used for dimensioned quantities in this book are based on the InternationalSystem of Units (Système International d’Unités, SI) The SI uses decimal units of mea-sure, with the base units being the meter [m], kilogram [kg], second [s], ampere [A],kelvin [K], and mole [mol] A standard set of prefixes are used to allow quantities to bespecified with convenient values Some accommodation has been made in this book fornonstandard units that are still in common use For instance, hPa is the SI equivalent of

Preface xiii

mbar [or mb], the unit of pressure so commonly used by meteorologists It is expectedthat readers are familiar with or have access to the complete guidelines of SI symbols andusage

This textbook is intended to augment lectures in upper-division and graduate courses

in physical meteorology or cloud physics Introductory material in each major section isintentionally descriptive in nature in order to present students with a qualitative feel for thesubject Where the subject matter is presented from a theoretical viewpoint, mathematicsthrough vector calculus and differential equations is employed It is intended that students

in a graduate course would read further into each subject than would undergraduates Theinstructor is best able to decide the dividing points Each chapter ends with a bibliographyfor further reading and a set of problems to emphasize certain points and give opportunitiesfor further learning The instructor should feel free to modify or expand on problems tomeet the particular goals of his/her course

Authors of textbooks invariably depend on the hard work of and discussions with manyothers The research literature has been heavily exploited, but citations have been lim-ited to sources of graphical material in order to ease the reading of technical material

by beginning students We are indebted to the many authors of prior texts and referencebooks, upon which we have relied to develop material for teaching the subjects of cloudphysics and atmospheric chemistry over many years Among the books we have relied on

most are those by Pruppacher and Klett (Microphysics of Clouds and Precipitation, 2nd edn.), Rogers and Yau (A Short Course in Cloud Physics, 3rd edn.), Seinfeld and Pandis (Atmospheric Chemistry and Physics), Cotton and Anthes (Storm and Cloud Dynamics), and Houze (Cloud Dynamics) We think this book should find a niche somewhere between

the short course by Rogers and Yau and the extensive reference book of Pruppacher andKlett We would also like to think of it as complementing the comprehensive work onatmospheric chemistry by Seinfeld and Pandis

Special acknowledgment is graciously extended to the many individuals who have, inone way or another, enabled us to carry out this ambitious project At the onset, RaymondShaw graciously provided a quality environment in the Physics Department at MichiganTechnological University, where the first author spent a sabbatical leave in 2006 and beganthe actual process of writing Many subsequent discussions with him and other colleaguesthere and elsewhere have contributed enormously over the years to the development ofthe material presented in this book Among those individuals, the authors wish to thank(in alphabetical order) Alex Avramov, Chad Bahrman, William Brune, Will Cantrell, J.P.Chen, Eugene Clothiaux, William Cotton, Graham Feingold, Jose Fuentes, Barry Gardiner,Jerry Harrington, Alex Kostinski, Zev Levin, Nathan Magee, Paul Markowski, AlfredMoyle, Yvette Richardson, Lindsay Sheridan, Nels Shirer, Ariel Stein, and Huiwen Xue.The first author also benefited greatly from the opportunity, offered by Huiwen Xue andChunsheng Zhao, to teach part of a graduate course in cloud physics in the Department ofAtmospheric Sciences at Peking University in 2009 The feedback on various chapters ofthe book that was received from the students there and at Penn State University has helped

us greatly during revisions of the text We are especially grateful to Eugene Clothiaux,

Barry Gardiner, and Nels Shirer for their careful and critical reading of parts of themanuscript at various stages The publication process was made relatively painless by theable assistance provided by Laura Clark and Matt Lloyd at Cambridge University Press.Finally, we are ever thankful for the patience of and encouragement given by our respectivefamilies, to whom this book is dedicated.

Part I

Background

in the absence of atmospheric water and clouds A world without clouds would be differentindeed.

Clouds contribute to the environment in many ways Clouds, through a variety of ical processes acting over many spatial scales, provide both liquid and solid forms ofprecipitation and nature’s only significant source of fresh water Under extreme circum-stances, however, clouds and precipitation may not form at all, leading to prolongeddroughts in some regions At other times and places, too much rain or snow falls, giv-ing rise to devastating floods or blizzards Liquid rain drops bring usable water directly tothe surface, while simultaneously carrying many trace chemicals out of the atmosphere andinto the ecosystems of the Earth Chemical wet deposition thereby supplies nutrients (andsometimes toxic compounds) to both terrestrial and aquatic lifeforms, as well as the weakacids responsible for the weathering of the Earth’s crust The solid forms of precipitationcontribute in additional ways to the world as we know it Snow, for instance, forms the win-ter snowpacks that dramatically affect the radiation balance and climate of high latitudes

phys-on a seasphys-onal basis In mountainous regiphys-ons, snow simultaneously yields a lphys-ong-lastingsupply of water and lucrative opportunities for human recreation Snow that accumulatesfrom one year to the next gives rise to glaciers that carve out valleys as they slowly flowdownhill under their enormous weight Atmospheric clouds and the precipitation they yieldare responsible for much of the world that we take for granted

Many aspects of weather revolve around the presence or absence of clouds The weathersystems that routinely pass through the mid-latitudes transform invisible water vapor intosometimes beautiful, sometimes dreary clouds of many sizes and types These clouds affectthe radiation balance of the region and hence the temperature of the air and exposed sur-faces The precipitation they generate removes the water and trace chemicals from the sky,serving simultaneously to dry and cleanse the air Forecasting the meteorological events of

3

the next day or of the coming season is becoming ever more crucial to our individual livesand to the economy of our society Being able to anticipate the amount and nature of theclouds with assurance is an important skill of every forecast meteorologist, for which oneneeds a thorough understanding of the atmosphere and the processes responsible for cloudformation.

Less apparent than the weather we see and feel, but which is nevertheless important

to the workings of the atmosphere, are the roles clouds play in the atmospheric energybudget Clouds reflect incoming solar radiation back to space, thus helping regulate theoverall input of solar energy and its distribution around the world Clouds also interceptinfrared radiation emitted from the surface that would otherwise be lost to space; reradia-tion of infrared radiation by the same clouds helps warm the surface Energy deposited inthe oceans helps evaporate water and provides the primary ingredient for cloud formation,water vapor The transformation of water vapor into the many liquid and solid particlesthat compose clouds necessarily results in a warming of the air This energy consequence

of a physical change of phase determines in part the macroscopic shape and behavior ofclouds, whether they are convective or stratiform in nature On a much larger scale, thethermal energy “released” by the phase transformations in the large convective clouds ofthe tropics becomes an important component of the Earth’s energy balance Major circu-lation patterns in the atmosphere are thus spawned, helping redistribute the surplus energyfrom the tropical regions to other parts of the world, where less energy is received from theSun than is lost to space by thermal infrared radiation

The composition of the atmosphere, especially regarding its trace gases and late matter, is greatly influenced by clouds The precipitation resulting from clouds serves

particu-as a carrier of the material taken up by the cloud and precipitation particles Cloud andprecipitation “scavenging” thus serves as a remarkably efficient mechanism by which theatmosphere is cleansed of the diverse gases and particles continually emitted into the air,thereby preventing the build-up of natural and anthropogenic pollutants At the same timethat air quality is improved by precipitating clouds, the precipitation itself becomes corre-spondingly fouled, leading to such ecosystem problems as acidic rain, for instance Even inthe absence of precipitation, clouds offer several important opportunities for transformingtrace components of the atmosphere into other compounds In the lower atmosphere, suchin-cloud reactions oxidize sulfur and nitrogen compounds, leading to enhanced summer-time hazes across industrial regions In the middle atmosphere, chemical balances may bealtered rather profoundly by reactions occurring in or on the surfaces of aerosol and cloudparticles, causing ozone to be lost The chemistry of clouds thus becomes as important asthe physics of clouds toward the workings of the atmosphere

The study of clouds offers rich opportunities for applying our understanding of physicsand chemistry to real-world phenomena Clouds give direct evidence of changes takingplace in the atmosphere By our conventional ways of categorizing the disciplines of sci-ence, we would say that some of these changes are physical in nature, some are chemical

in nature Nature, of course, knows no such distinction, so we need to realize that dividingthe atmospheric sciences into “physical” and “chemical” domains is largely a matter of

1.2 Observed characteristics of clouds 5

convenience Physics, the science of matter, energy, and their interactions, is the disciplineused in traditional cloud physics to understand the fundamentals of cloud and precipita-tion formation, the microscale structure of clouds, cloud electrification, and the impacts ofclouds on climate The conventional restriction to the physics of clouds, however, ignoresseveral important chemical attributes of clouds Chemistry, the science of the composition,structure, and properties of substances and their transformations, is needed to understandthe very nature of water itself, as well as how water interacts with aerosol particles to per-mit clouds to form under atmospheric conditions Chemistry is also needed to understandhow those aerosol particles that serve as the sites of condensation came to exist in thefirst place The atmospheric phenomena of acidic haze formation, acid rain, stratosphericozone depletion, and some aspects of the natural biogeochemical cycles and climate can

be understood only via the traditional discipline of chemistry Throughout this book, wewill find frequent occasion to jump between physical and chemical concepts, often withoutmention It is only important to recognize that the fundamental principles of science guide

us aptly as we try to understand atmospheric clouds in their natural, complex setting

1.2 Observed characteristics of clouds

1.2.1 Overview

Careful observations of the atmosphere reveal much about clouds Some, “macroscopic”characteristics of clouds are readily seen with the unaided eye, whereas other “micro-scopic” properties require elegant instrumentation At all levels, we find it natural andhelpful to give names to phenomena, properties, and concepts The nomenclature and jar-gon of the science become the means by which we communicate effectively with oneanother and so must be learned along with the scientific concepts Some attention istherefore given to the proper use of terminology throughout the text

Cloud formation requires moisture, aerosol particles, and a process for cooling the air.The abundances of moisture and aerosol particles determine the total mass of condensateand the number concentration, respectively, and they affect the ability of clouds to pro-duce precipitation These two components also regulate the radiative properties of cloudsand how we perceive them visually The necessary cooling to form a cloud may arisefrom any one or combination of processes: radiative cooling, turbulent mixing of air acrossmoisture/temperature gradients, or expansion of air during forced ascent or free convection.The observed characteristics of a cloud depend on how the atmosphere organizes itself toprovide these key ingredients Atmospheric moisture, derived from evaporation of surfacewater or transpiration of plants, originates at or near the Earth’s surface The fact thatmost clouds are observed well above the surface suggests that surface moisture must betransported upward by atmospheric motions The surface is likewise the dominant sourcefor aerosol particles, although these particles may also be formed in the atmosphere throughgas-to-particle conversion The processes responsible for upward moisture transport alsoresults in a cooling of the air, the other requirement for cloud formation The type of vertical

motion is the major determinant of the cloud forms we commonly see Slow, large-scaleascent results in broad, featureless clouds, whereas rapid ascent of smaller parcels of airresult in cloud turrets The mixing of warm, moist air with cooler air leads to transientclouds of limited spatial extent.

Once formed, a cloud changes in response to the relative rates of the processes ble for condensate formation and loss Continued cooling from the net loss of radiation, adi-abatic expansion, and/or moisture advection adds condensate; conversely, radiative heating,adiabatic compression, mixing with drier atmospheric air, and precipitation all removecondensate The radiative heating rates are determined by a combination of the macro-scopic (large-scale) and microscopic (small-scale) characteristics of the cloud The verticaldistribution of diabatic heating and cooling plays a further role in changing the atmosphericstability profile, the impact of which is to enhance (suppress) vertical motions

responsi-The vertical velocities in a cloud determine the time an air parcel spends inside thecloud This in-cloud duration limits the time available for condensate to grow to sizes largeenough to fall against the updraft and remove condensate Spatial variations in verticalvelocities induced by turbulence result in spatial variations of microscopic properties, andare responsible for lumpiness in the visually observed cloud outline Turbulence furtherserves to mix drier atmospheric air into the cloud, leading to the loss of condensate throughevaporation The interactions between the macroscopic air motions and the microscaleprocesses ultimately determine the characteristics of the clouds we observe

1.2.2 Macroscopic forms

The sky is rich in information about the state of the atmosphere and the diverse processesthat bring about changes One needs to learn how to read the sky much as one does toread a book In both cases, we depend on our sense of vision to recognize patterns (theshape of a cloud, or the words on a page) and on our mind to interpret what we see

“Sky reading”, the art of interpreting observed properties of the sky in terms of gories and processes, is practiced by many, amateurs and professionals alike, as a way

cate-of understanding atmospheric phenomena and foretelling weather events By combiningthe ever-changing visual clues presented by clouds with an understanding of physical pro-cesses, much can be gleaned about the current or anticipated weather We start with basicterminology and categorization before explaining the processes that bring clouds into beingand eventually to their demise

Clouds can be seen at various times from virtually every point on the Earth’s surface, but

it is often challenging to know what to call them or how they evolve Despite difficulties indetermining the sizes and altitudes of clouds with precision, level in the atmosphere is goodfor telling one cloud type from another We can usually distinguish low-lying clouds fromthose higher in the atmosphere, for instance Thus, clouds may be categorized as “low” (up

to about 2 km above the surface), “mid-level” (2 to 7 km), or “high” (above 7 km) Cloudsconfined to distinct levels often take on a “stratiform” appearance, one exhibiting dimen-sions in the horizontal that are substantially greater than those in the vertical Stratiform

1.2 Observed characteristics of clouds 7

clouds form in air that is thermodynamically stable, meaning that small vertical ments have little effect on the overall air motions “Cumuliform” clouds, by contrast, tend

displace-to extend farther in the vertical than in horizontal directions Cumuliform clouds are times said to be convective because they form in air that is locally unstable, meaning thatsmall vertical displacements lead to further displacements and convective overturning ofthe air The stability of the air is determined by how rapidly the temperature and humiditychange with altitude Large cumuliform clouds can span all altitude categories, from “low”

some-to “high” The conventional names given some-to the various cloud forms are derived from visualobservations taken at the ground (see Appendix A for a summary)

The observed forms of clouds differ substantially within a given category Often,the shape of a cloud itself best reveals its type A few photographic examples illustrate thediverse forms clouds can take in various settings As Fig 1.1shows, the view from theground often reveals multiple cloud types at one time The cloud elements near the bottom

of the figure are individually cumuliform in nature and indicative of a turbulent, nearlywell-mixed boundary layer Such disconnected clouds are classified as cumulus (Cu) If theedges of the cloud elements were touching, the deck would be classified as stratocumulus(Sc) The particles constituting these clouds are liquid water droplets, the result of vaporcondensation at relatively high temperatures The clouds toward the top of Fig.1.1have

a fibrous appearance indicative of high cirrus clouds (Ci), perhaps the result of a jet craft The cloud particles are ice crystals, evidence for which is the coloration (bright spotsleft and right of center) arising from the refraction of sunlight through adjacent facets ofthe crystal (causing a “circumhorizontal arc” in this case) Another example of cirrus, inthis case Ci uncinus, is shown in Fig.1.2 Such high clouds are made of relatively large

air-Figure 1.1 Diverse cloud forms over eastern Oregon The two bright spots in the upper third are from

a circumzenithal halo, which forms when sunlight refracts through hexagonal ice crystals Photo by

D Lamb

Figure 1.2 Cirrus uncinus clouds over Victoria, British Columbia Photo by D Lamb

ice particles that sediment rather rapidly Ci uncinus in effect, represent snow that neverreaches the ground

Mid-level clouds are often relatively thin and take on a variety of sub-forms Perhapsthe most diverse types occur with altocumulus (Ac) Figure1.3a shows an example of Acundulatus, cumuliform elements that formed in a relatively thin layer where moisture accu-mulated preferentially A distinctly different form of Ac is shown in Fig.1.3b In this case,stable air was forced over an upstream mountain, forming a gravity wave with clouds in thecrest Such a cloud is commonly called a wave cloud, although the scientific designation is

Ac lenticularis because of the lens-like shape Figure1.3c shows the edge of an altostratusdeck (As), a continuous deck of clouds at mid levels Where precipitation is falling out, thecloud is called nimbostratus (Ns) It is hard to tell if the precipitation is rain or snow here,but any precipitation that evaporates before reaching the ground is termed virga

Clouds sometimes look tall and vertically extended relative to their horizontal sion Such cumuliform clouds arise when moist air rises rapidly in an unstable atmosphere.Examples of cumulus clouds in the trade winds of the Pacific Ocean are shown in Fig.1.4.The flat bases indicate that each of the clouds was derived from boundary-layer air havingcommon thermodynamic properties The towering nature of these clouds shows the impor-tance of buoyancy generated by the release of the latent heat of condensation Particularlyimpressive cumulus and cumulonimbus clouds (Cb) can develop when air moves upwardsrapidly in moist air that it unstable over large depths The cloud shown in Fig 1.5, forinstance, towered over the Grand Canyon in Arizona and was just about to develop ananvil and begin raining at the time the photograph was taken Such a cloud with hints

dimen-of an anvil is called Cb calvus A fully developed Cb is shown Fig.1.6 Note the activeconvection on the upshear (left-hand) side and the extended anvil on the downshear side of

1.2 Observed characteristics of clouds 9

Figure 1.3 Examples of mid-level clouds a Altocumulus (Ac) undulatus over Pennsylvania b Aclenticularis over Alberta c Nimbostratus (Ns) Photos by D Lamb

Figure 1.4 Trade-wind cumuli off the shore of Kauii Photo by D Lamb

Figure 1.5 Towering cumulus cloud over the Grand Canyon Photo by D Lamb.

Figure 1.6 Cumulomnimbus cloud with long anvil along east coast of the United States Photo by

D Lamb

1.2 Observed characteristics of clouds 11

Figure 1.7 Squall line over the middle United States Image from NOAA satellite

the central cloud Large cumulonimbi can develop airflow patterns that actively suppressthe development of neighboring clouds and so appear isolated Cumuliform clouds some-times organize themselves into well-defined circulations, which we recognize at differenttimes as squall lines (Fig.1.7) or hurricanes (Fig.1.8) Still photographs show impressivemacro-features of clouds, but they cannot do justice to the evolution and microphysicalproperties of clouds

1.2.3 Microscopic properties

The individual particles that make up a cloud are not generally visible to the human eye Wesee the macroscopic, overall form that the cloud takes in the sky, the net effect of sunlightbeing scattered by the many water droplets and ice crystals within the boundaries of thecloud, but the cloud particles themselves are simply too small to be resolved from outsidethe cloud Raindrops and snowflakes falling near us may be seen individually, but not thevast majority of cloud particles, which are truly microscopic We seek here to expose theproperties of those many minute particles that make up the cloud “microstructure”

A large cloud can look imposing, a potential hazard were one to venture into its rior However, one would not encounter a wall of water as one would upon jumping into

inte-a swimming pool Rinte-ather, entering inte-a cloud would be inte-akin to leinte-aving one’s house inte-and

Figure 1.8 Satellite view of hurricane Katrina in the Gulf of Mexico in 2005 Image from NOAAsatellite.

walking into a morning fog You might find the scene eerie perhaps, but you certainlywould find little to impede your progress, save the limited visibility Clouds are not muchdifferent Indeed, fogs are actual clouds, just ones that contact the ground We must appre-ciate the fact that clouds are mostly air, the many particles being dispersed widely andmore or less randomly throughout the cloud interiors

The microstructure of a cloud can be appreciated at a qualitative level by a eration of scales, the relative sizes of the various constituents that make up a cloud.Figure1.9shows a “telescoping” view of a cloud The cloud itself (top panel) forms on thecloud macroscale, which overlaps the meteorological mesoscale (kilometers to hundreds

consid-of kilometers) from moisture carried alconsid-oft by large-scale air motions Supersaturations aredeveloped as the air cools by adiabatic expansion and allow condensation to take place

on aerosol particles Any small part of this cloudy air contains many liquid water droplets

of diverse sizes (second panel) It is on this microscale that the particles compete for theavailable water vapor, causing the interstitial supersaturation to be less than that determinedthermodynamically Further extension of our telescoping view (third panel) would show anindividual droplet surrounded by the vapor from which it grows by condensation Gradi-ents of both vapor concentration and temperature would be found on this particle scalebecause of the resistances to mass and heat transport imposed by the air The droplet massincreases during condensational growth, when the interstitial vapor concentration exceedsthe equilibrium value, and it decreases during evaporation, when the vapor concentration

1.2 Observed characteristics of clouds 13

CLOUD MACROSCALE

Thermodynamic forcing Supersaturation development

r

n v (r)

Figure 1.9 Relative scales of clouds and particles

falls below this threshold value If we were to ever see the true molecular-scale processesnear the droplet surface (bottom panel), we would be amazed at the rapidity and complex-ity of action The water molecules continually scurry about just above the surface, beingimpacted randomly by the molecules that make up the air (mostly nitrogen and oxygen).The vapor molecules that collide with the surface of the droplets may stick for a short whilewhere they landed, then move around on the surface a bit, before they either escape backinto the vapor phase or enter the bulk liquid and add their mass to the droplet All of themany possibilities for molecular “incorporation” into the condensed phase are summed up

in the “condensation coefficient”, a parameter used in theoretical models to account for themany molecular-scale processes we can only speculate about The science of cloud physicsmust deal with a wide range of scales (from molecules to whole cloud systems), a rangeencompassing many factors of ten (called “orders of magnitude”)

The particles making up a cloud may be solid, liquid, or a mixture of both states ofmatter Clouds made solely of liquid droplets are termed “warm” clouds, whereas thosecontaining ice particles are said to be “cold” clouds These terms probably arose from ourgeneral realization that liquid water exists at relatively high temperatures (above 0◦C) and

that ice can form only at lower temperatures However, the distinction between “warm”and “cold” clouds hinges on the phase of the particles, not on the temperature Some parts

of “cold” clouds may also contain liquid drops, which are termed “mixed-phase” regions.Later, we will come to appreciate why the lower parts of deep clouds tend to be “warm”,the middle parts are often “mixed phase”, while the upper-most parts may be all ice Wewill also talk about “warm-cloud” microphysical processes, those involving liquid drops;ice particles may be present, or not, but they do not influence how the liquid drops interact

“Cold-cloud” processes, by contrast, can involve liquid drops, as during hail formation,although only ice particles may be involved in other situations, such as during crystalaggregation and snow formation

Warm-cloud microstructure

“Warm” clouds often contain liquid droplets of many different sizes An appreciation ofthe diversity of sizes can be gained from diagrams that compare the sizes directly, such asFig.1.10 Here, we see the various categories of cloud particles and their representativesizes drawn to scale The familiar raindrop (only half of which is shown to conserve space)

is huge in comparison with the other categories of particles Something like a thousanddrizzle drops could fit into the same volume occupied by a single raindrop (Rememberthat the particles are spherical and that the volume of a sphere increases as the cube of thediameter.) Likewise, a thousand cloud droplets of 10μm diameter could fit into the vol-ume of a single drizzle drop So, every raindrop that falls to earth represents the effectivegathering of a million cloud droplets or more It is important to note, however, that thecloud droplets do not just happen to gather together to form a raindrop Specific mecha-nisms must be operating within the cloud to allow raindrops to grow, via processes coveredlater One hint of those processes can be seen, however, by contrasting the concentrations

of the respective categories Note that many fewer raindrops exist than do drizzle drops orcloud droplets In fact, the ratio of concentrations is just the inverse of the ratio of sizes,suggesting that the large drops indeed form from the smaller drops, conserving the overallmass of liquid water in a given volume of cloudy air The large drops gain mass at theexpense of the smaller drops, but the process by which this “coalescence” takes place isanything but simple

At the small end of the range of droplet sizes we see a different pattern emerging.Haze droplets are yet another order of magnitude smaller in size, but their concentrationsare comparable to those of the cloud droplets If the cloud droplets formed from the hazedroplets, then clearly the mass of liquid water was not conserved in the process The mass

of water added to a given haze droplet to form a cloud droplet must have come from where other than the already-formed liquid phase Indeed, it is the process of condensation,whereby individual water molecules leave the gas phase and enter the liquid phase, thatcauses this mass increase It is, therefore, not a coincidence that the concentrations of hazeand cloud droplets are similar, just as it is no coincidence that the even smaller “cloud con-densation nuclei” (CCN) are found in comparable concentrations We will come to realizethat condensation preferentially takes place on existing surfaces, and it is the CCN that

some-1.2 Observed characteristics of clouds 15

At a quantitative level, the microstructure of a warm cloud is described by the way inwhich the cloud droplets are distributed in size Such “drop spectra” tell us how many ofwhat size drops are present Drop spectra are often determined empirically, for instance, byflying through a cloud and sampling the droplets with special instrumentation An example

of what one would find by letting the droplets impinge for a known length of time onto asticky surface that leaves a permanent impression (via a Formvar replicator) is shown in thetop part of Fig.1.11 Each of the circles here represents the region where the momentum ofimpact pushed aside some of the sticky coating, leaving a visible crater What we see there-fore are the impact craters, not the droplets themselves Nevertheless, a bit of work behindthe scenes allows one to relate the crater diameters to the sizes of the droplets causingthe craters (compare scales along the bottom axis) One must also compute the volume ofcloudy air sampled in order to convert the numbers of droplets sampled to concentrations

or number densities (vertical axis)

What results from performing such a sampling procedure? First, note that all of thedroplets here (Fig 1.11) may be correctly classified as “cloud droplets”, but that theynevertheless range considerably in size Droplets vary more or less continuously in size,but we must always define small subcategories or “bins” of well-defined size intervalsbefore arriving at a true size distribution We are concerned only with the number ofdroplets within a given size interval because we can never keep track of every droplet

in a cloud, only some statistical measure of the droplet population When we count thenumber of droplets in each category from the sample shown in Fig 1.11, for instance,

we obtain the “histogram” at the bottom of the figure, in which the ordinate specifies thedroplet concentration per bin (even when the labeling is not so specific) Here, we see

0 10 20

Figure 1.11 Example of in-cloud data from a Formvar replicator a Craters made in the Formvar

b Histogram derived from the drops shown in (a) (LWC= Liquid water concentration.) From JohnHallett, used with permission

that most of the cloud droplets fall into the 20- to 23-μm category We typically take themid-point (21.5 μm) of the bin containing the most droplets to be the “modal” diame-

ter of the sample The variation in the number densities of sampled droplets across thevarious size bins gives us some sense of how the droplet population in the cloud varies

1.2 Observed characteristics of clouds 17

where D j is the mid-point value of bin j The collective surface area in a unit

vol-ume of cloudy air can also be calculated readily by noting that each small drop closely

approximates the geometry of a sphere So, if we use A tot [possible unitsμm2m−3] todesignate the combined surface area concentration of the drops in the sample and recall

that the area of a single sphere of diameter D is A = π D2, we find

inter-water in each bin, recognizing that the mass of a single drop of diameter D and mass

den-sityρ L is m D = ρ L v D, wherev D = π/6 · D3is the drop volume Thus, the liquid waterconcentration of the sample is given by

Note the similarity of the expressions being summed in each of the previous equations:

each contains n j and D j raised to some power We use the exponent of D j to designatethe type of statistic derived from the given drop spectrum Thus, the statistical measures

of drop concentration (Eq (1.1)), mean diameter (Eq (1.2)), surface area concentration(Eq (1.3)), and liquid water concentration (Eq (1.4)) are said to come, respectively, fromthe zeroth, first, second, and third moments of the distribution The sixth moment of thedrop size distribution is important for radar studies

The microstructure of a cloud varies with location within the cloud, as well as withtime Typically, the properties vary most in the vertical direction, in part because pressuredecreases rapidly with height, as do the thermodynamic variables that cause cloud to form

in the first place An example of how the microstructure of a small cumuliform cloud varieswith distance above cloud base is presented in Fig.1.12 The set of curves along the right-hand side show the drop spectra as measured by instrumentation aboard an aircraft thatflew at five different heights The spectra are seen to broaden (span a wider range of sizes)with increasing altitude and shift toward larger sizes Care must be taken when viewingand interpreting these curves, for the concentrations are plotted on a logarithmic scale andrefer to the number densities within each bin The total concentration of drops at eachlevel would be computed via Eq (1.1), whereas the mean diameter of the drops sampled

at each level would be calculated from Eq (1.2) The variation with height of the totalconcentration is shown in the left-hand side of Fig.1.12 We clearly see that the numberdensity of drops decreases with height (at least above 0.4 km) at the same time that the

average size of the drops increases

0 0.4 0.8 1.2 1.6

100 10 1

100 10 1

100 10 1

100 10 1

Environment Canada (1980)

An important function of cloud physics research is to understand the causes of variousobserved microstructures Why do the spectra of this cumulus cloud broaden with height?What causes the drops to be larger near the top of the cloud, but fewer in number? Someadditional information, shown in Fig.1.13, may help us answer such questions Compu-tations of the maximum and average liquid water concentration show the total mass ofwater to increase with height above cloud base, as might be expected from continuousgrowth by condensation as the droplets rise in the atmosphere The maximum observedLWC approached the “adiabatic” value, the maximum possible for the given thermody-namic conditions, but the average LWC was only about half of the adiabatic values Oneexplanation consistent with these data is based on “entrainment”, the mixing in of drierenvironmental air surrounding the cloud Some parts of the cloud at each level below 1 kmmay have represented cloudy air that ascended undiluted from cloud base, but much of thecloud experienced the effects of dilution Some of the droplets in the mixed air would prob-ably have disappeared completely from the population, causing the number concentration

to be lowered At the same time, it appears that those droplets that did survive were able

to continue growing larger, perhaps even faster than if entrainment had not occurred Wewill see later how fewer droplets in a given parcel of air can give rise to faster growth rates.Real clouds are always complicated, even when the only condensed phase present is liquid

1.2 Observed characteristics of clouds 19

Average

Adiabatic

0 0.4

A few examples illustrate the wide diversity of ice forms found in the atmosphere A lection of snow crystals gathered over several hours in Antarctica is shown in Fig.1.14

col-We see, from a single event, both “columns” (long, pencil-like forms) and “plates” (thin,flat hexagons) of various sizes The crystals that overlap in this image most likely formedindividually in the atmosphere by vapor deposition and then landed on top of one anotherbefore the photograph was taken Snow falling in more temperate climates typically devel-ops more complicated shapes, such at the crystal shown in Fig.1.15 The “habit” of thiscrystal is also a “plate”, but we see a tendency for the corners of the hexagon to developmore than the sides We also see multiple hexagons, as if one formed on top of another.Indeed, microscopic inspection of many crystals originating at temperatures in the−10

to−12◦C range show plates separated by small distance As the diagram in Fig. 1.16suggests, plates form on opposite sides of a cloud droplet after it freezes into a singleice crystal The two plates align perfectly with one another because each arises (via vapor

Figure 1.14 Diverse snow crystals at the South Pole The air temperature near the surface was

−60◦C, but probably increased to−40◦C near the top of the inversion Photo by S Warren, usedwith permission

Figure 1.15 Photo of a sector plate that may be a double plate Photo by D Lamb

1.2 Observed characteristics of clouds 21

c axis

Figure 1.16 Schematic showing the geometry of a double plate Left: view from the top Right: viewfrom the side showing the c-axis perpendicular to the basal plane

Figure 1.17 Examples of polycrystals a Bullet rosette Photo by A Heymsfield, used withpermission b Two bullets still attached Photo by D Lamb

deposition) from the same initiating crystal (the frozen droplet) At lower temperature, such

as that found in cirrus clouds, each droplet freezes into a “polycrystal”, a single ice cle containing several crystalline grains formed during a common freezing event Each ofthe individual crystals in the particle subsequently grows by vapor deposition into either aplate or a column depending on the temperature Figure1.17shows examples Figure1.17ashows a bullet rosette formed as the crystals grew as columns The term “bullet” comesfrom the shape of the individual crystals emanating from the central frozen droplet, asshown in Fig.1.17b One can readily appreciate how complex ice particles can arise.Many attempts have been made over the years to systematize the complicated patterns

parti-of the ice crystals found in the atmosphere The most important variables controlling theshape or “habit” of a crystal formed by vapor deposition are temperature and the humidity(often expressed as an amount of water vapor above saturation) One summary for sin-gle snow crystals that grew at relatively high temperatures is provided schematically in

–20 –30

300

stellar crystals dendrites

solid plates solid

columns

solid columns

sector plates

broad-branch plates bullet

Figure 1.18 Categorization of snow crystals by temperature and excess vapor density

Fig.1.18 Because of the complexity in shapes (habits), we need to simplify our tions as much as possible First, note that all single crystals can be classed as either “plates”

descrip-or “columns”, giving us the first-descrip-order categdescrip-ory fdescrip-or crystal shape called the “primary habit”.Observations in the atmosphere and in laboratory experiments show that the primary habit

of vapor-grown ice crystals is determined mainly by the growth temperature, in the ner shown in Fig.1.18 Plate-like crystals are found to grow under the warmest conditions,within about 3◦C below the melting temperature, but they are most commonly found inthe lower temperature range of about−8 to −22◦C Columnar crystals, by contrast, arefound in the temperature ranges of−3 to −8◦C and below−22◦C The primary habit isthus seen to alternate with temperature, with transition temperatures at approximately−3,

man-−8, and −22◦C.

The complexity of crystal shape goes well beyond the designation of primary habit.Characteristic features superimposed on the primary habits are called “secondary habits”.For instance, the indentations along the edges of plates, seen earlier in Fig.1.15, subdi-vide each face into sectors, so such crystals are called “sector plates” Plate-like crystalsoften grow preferentially at the corners of the hexagons, because of variations in the con-centration of vapor in the vicinity of the crystal When this tendency for growth on thecorners is carried to an extreme, “dendrites” result, an example of which is shown inFig.1.19 The branches of dendritic crystals seem to sprout randomly along each spine, butresearch suggests that they develop from fluctuations in the ambient humidity (degree ofsupersaturation) Columns, too, can generate secondary habits, but the range of variations

1.2 Observed characteristics of clouds 23

Figure 1.19 A dendritic snow crystal Photo by D Lamb

is less extensive than that of plates Mostly, columns vary in the length-to-width ratio, ing from compact (short) columns to needles (very long columns) Columns may also growwith hollowed features that are sometimes called “sheath” crystals Particularly interestingcrystals are combinations of columns and plates, such as the “capped column” of Fig.1.20.The range of possibilities for crystal shape is vast, especially at high humidities andlow temperatures As seen in Fig.1.18, the crystal morphology becomes more intricate

lead-as the excess vapor density increlead-ases The secondary habits are much more dependent onthe humidity than they are on the temperature at the time of growth Even the distinctionbetween plates and columns is less clear cut at low temperatures, as shown in Fig.1.21.Some of the crystal habits found by scientists may arise from the manor in which the stud-ies have been carried out, but it seems clear that nature has found many ways to confoundour attempts to understand how so many different forms of ice crystals can arise by vapordeposition

Once crystals grow large enough to sediment, that is, fall relative to the local air in whichthey are embedded, they can collide with other crystals or with cloud droplets Individualice crystals often collide and stick to one another, in which case an “aggregate” or “flake”forms (Fig.1.22) (The common usage of the term “flake” for single (usually dendritic)crystals of snow is a misnomer.) Typical aggregates can contain anywhere from several

to hundreds of individual crystals On the other hand, collisions with supercooled (liquid)water droplets that freeze on contact is termed riming At the earliest stage of riming, onefinds lightly rimed crystals, such as that shown in Fig.1.23a The underlying crystal is

Figure 1.20 Capped column, also known as a tsusumi crystal Photo by D Lamb.

Irregular

Plates

Columns Thick Plates

Plates

Polycrystals Needles

Needles

Columns

Rosettes Rosettes

Crossed Plates

Side Planes

Side Planes Rosettes Rosettes Rosettes

Rosettes

Sheaths

Sector Plates

Very Long Columns

Sheaths

Spearheads Crossed Plates Long Columns

Assemblages of Plates Skeletal Plates

Spearheads

Liquid–w ater satur ation

Columns Short Columns

–20 –30

–40 –50

–60 –70

1.2 Observed characteristics of clouds 25

Figure 1.22 A complex snow crystal, viewable in stereo by the cross-eyed method Photo by

D Lamb

Figure 1.23 Stages in the riming of snow crystals a Light riming Photo by N Magee, used withpermission b Heavy riming, sufficient to obscure the underlying crystal Photo by D Lamb c Wetaccretion of supercooled water on a hailstone