AnIntroductiontoClouds - Cambridge University Pressassets.cambridge.org/97811070/18228/frontmatter/... · 2016-06-29 · AnIntroductiontoClouds FromtheMicroscaletoClimate Clouds,

An Introduction to CloudsFrom the Microscale to Climate

Clouds, in their various forms, are a vital part of our lives. Their effects on the Earth’s energy bud-get and the hydrological cycle depend on processes on the microphysical scale, encompassing theformation of cloud droplets, ice crystals and precipitation. Cloud formation, in turn, depends on thelarge-scale environment as well as the characteristics and availability of aerosol particles. An inte-grated approach drawing on information from all these scales is essential to gain a complete pictureof the behavior of clouds in the atmosphere.

An Introduction to Clouds provides a fundamental understanding of clouds, ranging from cloudmicrophysics to the large-scale impacts of clouds on climate. On the microscale, phase changesand ice nucleation are covered comprehensively, including aerosol particles and the thermodynamicsrelevant for the formation of clouds and precipitation. At larger scales, cloud dynamics, mid-latitudestorms and tropical cyclones are discussed, leading to the role of clouds in the hydrological cycle andtheir effect on climate.

Each chapter ends with problem sets and multiple-choice questions that can be completed online;important equations are highlighted in boxes for ease of reference. Combining mathematical formula-tions with qualitative explanations of the underlying concepts, this accessible book requires relativelylittle previous knowledge, making it ideal for advanced undergraduate and graduate students inatmospheric science, environmental sciences and related disciplines.

Ulrike Lohmann is a professor at the Institute for Atmospheric and Climate Science, ETH Zurich.She obtained her Ph.D. in climate modeling and her research now focuses on the role of cloudsand aerosol particles in the climate system, with an emphasis on clouds containing ice. ProfessorLohmann has published more than 200 peer-reviewed articles and several book chapters, and was alead author of the Fourth and Fifth IPCC Assessment Reports. She was awarded the Canada ResearchChair in 2002 and was the recipient of the AMS Henry G. Houghton Award in 2007. She is a fel-low of the American Geophysical Union and the German Academy of Sciences, Leopoldina. UlrikeLohmann has been teaching classes in cloud microphysics and cloud dynamics for almost 20 yearsat both undergraduate and graduate levels.

Felix Lüönd is a researcher at the Swiss Federal Institute of Metrology, METAS. He obtained his Ph.D.in atmospheric ice nucleation, for which he was awarded the ETH medal. His experimental workfocused on cloud microphysics. He specialized in the development of dedicated instrumentation tostudy the aerosol-induced freezing of cloud droplets and the interpretation of the resulting exper-imental data in the framework of nucleation theory and its advancements. Currently, Dr. Lüönd’sresearch activities are concentrated on aerosol metrology, particularly in the generation of ambient-like aerosols dedicated to establish traceability in measurements of ambient particulate matter andparticle number concentration.

Fabian Mahrt is a Ph.D. student at the Institute for Atmospheric and Climate Science, ETH Zurich.

He obtained a Master’s degree in Atmospheric and Climate Sciences from ETH. Early in his career

he developed a passion for cloud microphysics. He is particularly interested in aerosol particles and

their role in cloud droplets and ice crystal formation. Fabian Mahrt’s work is experimental in nature,

measuring and understanding aerosol–cloud interactions in both the laboratory and the field.

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Cambridge University Press978-1-107-01822-8 - An Introduction to Clouds: From the Microscale to ClimateUlrike Lohmann, Felix Lüönd and Fabian MahrtFrontmatterMore information

http://www.cambridge.org/9781107018228

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An Introduction to CloudsFrom the Microscale to Climate

U L R I K E L O H M A N N , F E L I X L Ü Ö N D A N D FA B I A N M A H R TETH Zurich, Institute for Atmospheric and Climate Science, Switzerland






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c© Ulrike Lohmann, Felix Lüönd and Fabian Mahrt 2016

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To our familiesKassiem, Stefanie, Claudia, Jana and Rainer











Contents

Preface page xiiiList of symbols and acronyms xvi

1 Clouds 11.1 Definition and importance of clouds 11.2 Macroscopic cloud properties and cloud types 3

1.2.1 Low-level layered clouds 51.2.2 Low-level clouds with vertical extent 81.2.3 Mid-level clouds 101.2.4 High-level clouds 101.2.5 Other cloud types 13

1.3 Microphysical cloud properties 151.3.1 Cloud phase 151.3.2 Size distributions and water contents 17

1.4 Exercises 23

2 Thermodynamics 262.1 Basic definitions 26

2.1.1 Thermodynamic states and variables of state 262.1.2 Intensive and extensive variables 272.1.3 Open, closed and isolated systems 282.1.4 Thermodynamic equilibrium 282.1.5 Reversible and irreversible processes 29

2.2 Dry air 312.2.1 Ideal gas law 322.2.2 First law of thermodynamics 322.2.3 Special processes 352.2.4 The Carnot process 362.2.5 Air parcels 382.2.6 Specific entropy 39

2.3 Thermodynamic charts 402.4 Thermodynamics of phase transitions 41

2.4.1 The role of the Gibbs free energy in phase transitions 422.4.2 Phase transitions in thermodynamic equilibrium: the

Clausius–Clapeyron equation 452.4.3 Saturation vapor pressure below 273.15 K 48

vii






viii Contents

2.5 Moist air 522.5.1 Water in the atmosphere 522.5.2 Partial pressure 522.5.3 Water vapor mixing ratio and specific humidity 532.5.4 Virtual temperature 532.5.5 Relative humidity 542.5.6 Dew point temperature 552.5.7 Wet-bulb temperature, wet-bulb potential temperature and

lifting condensation level 572.5.8 Isentropic condensation temperature 592.5.9 Equivalent potential temperature and equivalent temperature 602.5.10 Saturation equivalent potential temperature and saturation

equivalent temperature 612.5.11 Wet adiabatic processes 62

2.6 Exercises 63

3 Atmospheric dynamics 683.1 Basic equations and buoyancy force 68

3.1.1 Navier–Stokes equation 683.1.2 Coriolis and centrifugal force 693.1.3 Hydrostatic equation 703.1.4 Hypsometric equation 703.1.5 Buoyancy force 71

3.2 Stability in dry air 723.2.1 Dry adiabatic lapse rate 723.2.2 Lapse rate and stability 733.2.3 Brunt–Väisälä frequency 74

3.3 Stability in condensing air 763.4 Instability of layers 793.5 Horizontal restoring forces 81

3.5.1 Geostrophic wind 813.5.2 Thermal wind 843.5.3 Inertial instability 85

3.6 Slantwise displacement 883.7 Exercises 90

4 Mixing and convection 954.1 Mixing 95

4.1.1 Isobaric mixing 954.1.2 Adiabatic mixing 98

4.2 Convection 994.2.1 Level of free convection 994.2.2 Convective condensation level 994.2.3 Elementary parcel theory 103






ix Contents

4.2.4 Modification of the elementary parcel theory 1054.3 Exercises 112

5 Atmospheric aerosol particles 1155.1 Chemical and physical characteristics of aerosol particles 115

5.1.1 Chemical characteristics 1155.1.2 Physical characteristics 116

5.2 Aerosol size distributions 1185.2.1 Discrete size distributions 1185.2.2 Size distribution function 1185.2.3 Logarithmic normal distributions 1215.2.4 Surface and volume distributions 1235.2.5 Observed aerosol size distributions 126

5.3 Aerosol sources 1295.3.1 Formation mechanisms of aerosol particles 1295.3.2 Aerosol emissions 131

5.4 Aerosol sinks 1355.4.1 Dry scavenging 1355.4.2 Wet scavenging 1375.4.3 Atmospheric processing of aerosol particles 143

5.5 Burden and lifetime of aerosols 1445.6 Summary of aerosol processes 1475.7 Exercises 148

6 Cloud droplet formation and Köhler theory 1556.1 Nucleation 155

6.1.1 Initiation of phase transitions 1566.1.2 Cluster formation 158

6.2 Kelvin equation 1606.3 Hygroscopic growth 1636.4 Raoult’s law 1666.5 Köhler curve 170

6.5.1 Stable and unstable equilibrium 1726.5.2 The role of particle size and chemistry for Köhler

activation 1766.6 Measurements of cloud condensation nuclei 1776.7 Summary of cloud droplet formation by Köhler activation 1806.8 Exercises 182

7 Microphysical processes in warm clouds 1867.1 Droplet growth by diffusion and condensation 186

7.1.1 Diffusion equation for water vapor 1887.1.2 Heat conduction equation 1897.1.3 Droplet growth equation 190






x Contents

7.1.4 Solution of the droplet growth equation 1937.1.5 Growth of a droplet population 1937.1.6 Application of the droplet growth equation 195

7.2 Droplet growth by collision–coalescence 1987.2.1 Initiation of the collision–coalescence process 1987.2.2 Collision and coalescence efficiencies 2007.2.3 Terminal velocity of cloud droplets and raindrops 2027.2.4 Growth model for continuous collection 2047.2.5 Growth model for stochastic collection 207

7.3 Evaporation and break-up of raindrops 2087.3.1 Evaporation of cloud droplets and raindrops 2087.3.2 Maximum raindrop size 2097.3.3 Energy transformation during collision–coalescence 2107.3.4 Types of raindrop break-up 212

7.4 Exercises 213

8 Microphysical processes in cold clouds 2188.1 Ice nucleation 218

8.1.1 Homogeneous ice nucleation 2198.1.2 Heterogeneous ice nucleation 2268.1.3 Ice nucleating particles 2308.1.4 Dependence of ice nucleation on temperature and

supersaturation 2328.2 Ice crystal habits 2368.3 Ice crystal growth 237

8.3.1 Growth by diffusion 2398.3.2 Snow formation by aggregation 2418.3.3 Growth by accretion and terminal velocity of snowflakes 241

8.4 Collapse of ice particles 2458.4.1 Ice multiplication 2458.4.2 Melting and sublimation of ice and snow 246

8.5 Summary of microphysical processes in warm and cold clouds 2468.6 Exercises 248

9 Precipitation 2519.1 Precipitation rates 2519.2 Size distributions of hydrometeors 252

9.2.1 Raindrop size distribution 2529.2.2 Snowflake size distribution 255

9.3 Radar 2569.3.1 Scattering regimes 2579.3.2 Radar reflectivity 2589.3.3 Relation of radar reflectivity to precipitation rate 2609.3.4 Radar images 261






xi Contents

9.4 Types of precipitation 2619.4.1 Stratiform precipitation 2639.4.2 Convective precipitation 267

9.5 Synoptic and mesoscale structure of precipitation 2699.5.1 Norwegian cyclone model 2709.5.2 Conveyor belt approach 2719.5.3 Orographic precipitation 274

9.6 Precipitation in the present and future climate 2759.7 Exercises 279

10 Storms and cloud dynamics 28510.1 Isolated thunderstorms and hail 285

10.1.1 Life cycle of an ordinary thunderstorm 28610.1.2 Hail 288

10.2 Lightning and thunder 29010.2.1 Global electrical circuit 29010.2.2 Charge separation within clouds 29110.2.3 Ground flashes 293

10.3 Multicell and supercell storms 29510.3.1 Multicell storms 29710.3.2 Vorticity 29810.3.3 Supercell storms 30110.3.4 Tornadoes 304

10.4 Mesoscale convective systems 30710.5 Tropical cyclones 310

10.5.1 General characteristics 31010.5.2 Prerequisites for tropical cyclone formation 31210.5.3 Circulation within a tropical cyclone 31310.5.4 Differences between tropical and extratropical cyclones 31310.5.5 Tropical cyclone as a heat engine 31410.5.6 Decay of tropical cyclones 317

10.6 Cyclones and climate change 31710.7 Exercises 318

11 Global energy budget 32311.1 Energy balance at the top of the atmosphere 32311.2 Energy balance in the atmosphere 32611.3 Energy balance at the surface 32811.4 Cloud radiative effects 32911.5 Exercises 333

12 Impact of aerosol particles and clouds on climate 33512.1 Aerosol radiative forcing 335

12.1.1 Radiative forcing due to aerosol–radiation interactions 337






xii Contents

12.1.2 Radiative forcing due to aerosol–cloud interactions 34012.1.3 Comparison of anthropogenic forcings 343

12.2 Clouds and climate 34512.2.1 Clouds at different altitude levels 34512.2.2 Cloud regimes 34712.2.3 Trends in cloud cover 349

12.3 Climate feedbacks 35012.3.1 Planck feedback 35112.3.2 Water vapor, lapse rate and ice-albedo feedback 35212.3.3 Cloud feedback 353

12.4 Climate engineering involving aerosol particles and clouds 35612.4.1 Stratospheric aerosol injections 35812.4.2 Marine cloud brightening 36012.4.3 Cirrus modification 36112.4.4 Summary of the climate engineering discussion 363

12.5 Exercises 363

References 368Index 382

The plate section is to be found between pages 214 and 215.






Preface

Clouds, in their various forms, are a vital part of our lives. They are a crucial part ofthe global hydrological cycle, redistributing water to Earth’s surface in the form of pre-cipitation. In addition, they are a key element for the global energy budget since theyinteract with both shortwave (solar) and longwave (terrestrial) radiation. These so-calledcloud–radiation interactions depend strongly on the type of cloud. Clearly clouds affect theglobal climate and thus understanding clouds is an important factor for future climate pro-jections. The effects on Earth’s energy budget and on the hydrological cycle both dependon processes on the microphysical scale, encompassing the formation of cloud droplets,ice crystals, raindrops, snowflakes, graupel and hailstones.

Establishing an understanding of clouds and precipitation requires a knowledge of theenvironment in which they form, i.e. the atmosphere, with all the gases and airborne par-ticles present there. The latter are usually referred to as aerosol particles and encompassa wide range of solid and liquid particles suspended in air. Some aerosol particles can actas nuclei to form cloud droplets or ice crystals and thus initiate the formation of clouds orchange their phase from liquid to solid. Thus they influence the microphysical propertiesof clouds. In turn aerosol particles are removed from the atmosphere when clouds precip-itate. In order to gain a complete picture of the behavior of clouds in the atmosphere, thestrong interplay between aerosol particles and clouds requires one to tackle the subject inan integrated approach.

This book is intended to offer a fundamental understanding of clouds in the atmosphere.It is primarily written for students at an advanced undergraduate level who are new tothe field of atmospheric sciences. The content of this book evolved from the atmosphericphysics lectures held at ETH Zurich. This book is intended to serve students with a mul-tidisciplinary background as an introduction to cloud physics, assuming that most readerswill have a basic understanding of physics.

The book is organized into 12 chapters, each focusing on a particular topic. Chapter 1introduces the major cloud types found in the atmosphere and discusses them from amacroscopic point of view. Chapters 2–4 focus on the meteorological conditions and atmo-spheric dynamics needed for cloud formation and the thermodynamic principles needed todescribe atmospheric processes, including phase transitions.

Chapter 5 treats atmospheric aerosol particles and their physical characteristics. Thesources and sinks of aerosol particles are discussed at the process level as well as in termsof their global distributions and lifetimes.

Chapters 6–8 cover cloud microphysics. Chapter 6 discusses the fundamental equationsthat describe the formation of cloud droplets. Chapter 7 introduces the processes which

xiii






xiv Preface

ultimately lead to the formation of rain drops. Ice formation and other microphysicalprocesses occurring in cold clouds are presented in Chapter 8.

Chapter 9 combines the macroscopic view of Chapter 1 with the microscopic viewneeded to understand the physics of precipitation as well as the differences between strati-form and convective precipitation. Also, the change in precipitation since pre-industrialtimes and projections into the future are included.

To understand convective clouds, knowledge about cloud dynamics is needed. This isprovided in Chapter 10, where convective clouds at all scales, from isolated thunderstormswith lightning and thunder to multicells, supercells and mesoscale convective systems,including tropical cyclones, are discussed.

Finally, Chapters 11 and 12 bring the reader to the global scale. Chapter 11 outlines thephysical principles of the global energy budget and discusses the effects of clouds on it. Onthe basis of the information in Chapter 11 the impact of aerosols and clouds on the climatesince pre-industrial times and in future climate projections is considered in Chapter 12.

To strengthen concepts and test the reader’s understanding, qualitative exercises andmathematical problems are provided at the end of each chapter. This allows the reader toapply directly the material of the text and provides an opportunity for further learning. Tothis end, online solutions are provided and can be accessed at www.cambridge.org/clouds.For some of the problem sets the usage of a tephigram will be helpful. This, along withsome other material can be accessed from: www.cambridge.org/clouds. Some useful onlineinformation about atmospheric science includes the following links:

• Glossary of Meteorology: http://glossary.ametsoc.org/wiki• Encyclopedia of Atmospheric Sciences:

http://app.knovel.com/web/toc.v/cid:kpEASV0002/viewerType:toc/root_slug:encyclopedia-atmospheric/url_slug:encyclopedia-atmospheric/?

• NOAA glossary: http://w1.weather.gov/glossary/• Fifth Assessment Report of the Intergovernmental Panel on Climate Change:

http://www.climatechange2013.org

Throughout the book, important equations are underlaid in gray. All quantities are givenin SI units unless stated otherwise. However, as we often refer to processes occurring aboveor below 0 ◦C, we will use degrees celsius whenever convenient, keeping in mind thattemperatures need to be in kelvins in the equations given (if not noted otherwise).

The outline of the book follows a similar structure to the classic book A Short Coursein Cloud Physics by Rogers and Yau (1989), which served the present authors not onlyfor their own studies but also for over a decade of teaching at undergraduate level in theatmospheric physics course. Inspired by the straightforwardness of Rogers and Yau (1989)in explaining complex concepts of cloud physics and their style of imparting knowledgeto readers new to the atmospheric sciences, paired with the enormous developments in thisfield over recent years, the authors decided to come up with this new introductory textbook,which places a stronger focus on ice clouds, cloud dynamics and climate change.

We felt that, although there are many excellent textbooks at the graduate level, a textbookintroducing the physics of clouds, aerosols and precipitation in an integrated manner com-bining quantitative discussions at the undergraduate level was lacking. We believe that this






xv Preface

book fills this niche in giving intuitive interpretations of the physical processes discussed.Through this approach we hope to present the fascination of clouds that has captured usand thus to stimulate the interest of the readers in this diverse field. The book provides afundamental understanding, which can be deepened by the excellent further literature thatis available.

Writing this book would not have been possible without the knowledge we received frommany pioneers of the field of atmospheric sciences; these are named in the appropriatecontext throughout the book. Equally important, the development of this book relied onthe help and support from many colleagues and we are very grateful for help in differentaspects. We owe a great debt to Anina Gilgen for her invaluable contribution in puttingtogether the exercises. Chief among those who provided excellent support are the membersof our research group, who discussed drafts of different chapters and were a great sourceof ideas.

The authors wish to thank explicitly Manuel Abegglen, Alexander Beck, YvonneBoose, Robert David, Remo Dietlicher, Sylvaine Ferrachat, Blaz Gasparini, Anina Gilgen,Franziska Glassmeier, Olga Henneberg, Jan Henneberger, Katty Huang, Luisa Ickes,Zamin Kanji, Christina Klasa, Monika Kohn, Larissa Lacher, Claudia Marcolli, AmewuMensah, Angela Meyer, Baban Nagare, David Neubauer, Mikhail Paramonov, FabiolaRamelli, Carolin Rösch, Christina Schnadt, Sarah Schöpfer, Berko Sierau, Janina Stäu-dle, Kathrin Wehrli and Heini Wernli for very valuable discussions and suggestions thatgreatly improved the textbook.

Besides, we are indebted to Björn Baschek, Lea Beusch, Sebastian Bretl, Joel Corbin,Betty Croft, Daniel Cziczo, Corinna Hoose, Hanna Joos, Miriam Kübbeler, Glen Lesins,Rebekka Posselt, Jacopo Riboldi, Vivek Sant, Linda Schlemmer, Peter Spichtinger, EricSulmoni, André Welti and Marc Wüest. Finally, we are grateful for all the valuable feed-back we obtained from students of the atmospheric physics lectures, which has beenessential for continuous improvements of the book.

The authors want to thank Remo Dietlicher, Simon Förster, Anina Gilgen, FranziskaGlassmeier, Pascal Graf, Miriam Kübbeler, Jeremy Michael, David Neubauer, SarahSchöpfer and André Welti for their help with figures.

Photographs illustrating various aspects within our textbook were kindly provided byKouji Adachi, Laurent Barbe, Robert David, Martin Ebert, Blaz Gasparini, ChristianGrams, Zachary Hargrove, Jan Henneberger, Otte Homan, Luisa Ickes, Brian Johnson,Laurie Krall, Larissa Lacher, Sandra LaCorte, Kenneth Libbrecht, Julian Quinting, MilosVujovic and Thomas Winesett.

We specially thank the very helpful staff at Cambridge University Press, namely SusanFrancis, Cassi Roberts and Zoë Pruce in guiding the development of this book and also ourcopy-editor Susan Parkinson for valuable comments and suggestions.






Symbols and acronyms

Symbols

Symbol Value/unit Description

A, B Different substances in Raoult’s lawAi, Bi Empirical constants for the saturation vapor pressure over iceAw, Bw Empirical constants for the saturation vapor pressure over

waterA m2 Areaa m Coefficient of the curvature term in the Köhler equationaw Water activityB Buoyancy termBλ W m−2 Black body source functionb m3 Coefficient of the solution term in the Köhler equationb Coefficient in the Hatch–Choate equationC cm3 CCN concentration at 1% supersaturationC F/m Capacitance for ice crystalsCc Cunningham correction factorCD Drag coefficientCKE J Collision kinetic energyCR Constant for radar reflectivitycl 4219.9 J kg−1 K−1 Specific heat capacity of liquid waterci J kg−1 K−1 Specific heat capacity of icecp 1005 J kg−1 K−1 Specific heat capacity of dry air at constant pressurecpv 1884.4 J kg−1 K−1 Specific heat capacity of water vapor at constant pressurecv 718 J kg−1 K−1 Specific heat capacity of dry air at constant volumecvv 1418.4 J kg−1 K−1 Specific heat capacity of water vapor at constant volumeDa, Dv m2 s−1 Diffusivities of aerosol particles or water vapor in airE, E, E Collision, collection, coalescence or coagulation efficienciesEcoal J Total energy of coalescencee Pa Partial pressure of water vaporemix, e′

mix Pa Mean water vapor pressure of isobarically mixed air beforeand after condensation

es,i, es,w Pa Saturation vapor pressures with respect to ice or wateres0 611.2 Pa Saturation vapor pressure at T0 = 273.15 Ke∗ Equilibrium vapor pressure over a solutionF J Helmholtz free energy�F N Force vector

xvi






xvii Symbols and acronyms

FB m s−2 Buoyancy force per unit mass�FC m s−2 Coriolis force per unit massFd s m−2 Vapor diffusion term in droplet radius growth

equationFi

d , Fld m s kg−1 Vapor diffusion terms in the mass growth equations

for ice crystals and cloud dropletsFD kg m s−2 Drag force�FF m s−2 Dissipation term for momentum, per unit mass, i.e.

frictionFg kg m s−2 Gravity forceFk s m−2 Thermodynamic term in droplet radius growth

equationFi

k, Flk m s kg−1 Thermodynamic terms in the mass growth equations

for ice crystals and cloud dropletsFLW , Fcs

LW W m−2 Net longwave radiative fluxes at the TOA in all-skyand clear-sky conditions

F↑LW , F↓

LW W m−2 Upward- and downward-directed longwave radiativefluxes

FSun 3.85 × 1026 W Radiation emitted by the SunFSW , Fcs

SW W m−2 Net shortwave radiative fluxes at the TOA in all-skyand clear-sky conditions

F↓SW W m−2 Downward-directed shortwave radiative fluxes

�FPG m s−2 Pressure gradient force per unit massf s−1 Coriolis parameter, i.e. planetary vorticityf Compatibility parameter for heterogeneous

nucleationfact, ff Activation and frozen fractionsfv Mean ventilation coefficientG J Gibbs free energyGs,hom, Gv,hom, Gv,het J Surface and volume terms of the Gibbs free energy

for a pure liquid droplet and for a solution dropletGex(n) J Excess Gibbs free energy due to cluster formationG(n) J Total Gibbs free energy of the clusterg 9.81 m s−2 Acceleration due to gravityg, gv, gl J kg−1 Specific Gibbs free energy in general and in the

vapor or liquid phasesH J EnthalpyH W m−2 Heat flux into the oceanH m2 s−2 Helicityh m Height above Earth’s surface, vertical distanceIλ W m−2 Wavelength-dependent intensity of radiationI, I0 W m−2 Intensity of radiation in general and at TOAi Van ’t Hoff factorJ, Ji, Jw cm−3 s−1 General nucleation rate and nucleation rates for ice

in vapor and water in vaporK cm−3 s−1 Kinetic prefactor for the nucleation rateK J m−1 s−1 K−1 Coefficient of thermal conductivity in airK m3 s−1 Collision or collection kernel






xviii Symbols and acronyms

|K|2 Modulus squared of the complex index ofrefraction

k 1.38 × 10−23 J K−1 Boltzmann constantk Slope of the CCN−S relationshipkλ,abs = kabs m−1 Wavelength-dependent absorption

coefficient for greenhous gases, aerosolparticles and cloud hydrometeors

kλ,ext = kext m−1 Wavelength-dependent extinction coefficientfor greenhous gases, aerosol particles andcloud hydrometeors

kλ,scat = kscat m−1 Wavelength-dependent scattering coefficientfor greenhous gases, aerosol particles andcloud hydrometeors

L m Characteristic length scale for geostrophicflow

L2,1 J kg−1 Latent heat for the phase change from phase1 to phase 2

Lf J kg−1 Latent heat of fusionLf 0 = Lf (T0) 0.333 × 106 J kg−1 Latent heat of fusion at T0 = 273.15 KLs Latent heat of sublimationLs0 = Ls(T0) 2.834 × 106 J kg−1 Latent heat of sublimation at T0 = 273.15 KLv J kg−1 Latent heat of vaporizationLv0 = Lv(T0) 2.501 × 106 J kg−1 Latent heat of vaporization at T0 = 273.15 KM m s−1 Absolute momentumMF kg s−1 Mass fluxMd 28.96 g mol−1 Molecular weight of dry airMl kg m−3 Cloud liquid water content in units of mass

per unit volumeMm g mol−1 Molecular weight of moist airMs g mol−1 Molecular weight of a soluteMw 18 g mol−1 Molecular weight of waterMFd , MFu kg s−1 Downward and upward mass fluxesm, mw, ms kg Masses of air parcel, bulk water and solutemd , mm, mv kg Masses of dry air, moist air and water vaporm0 kg Masses of one water moleculemi, ml, mR, m(r) kg Masses of an ice crystal, cloud droplet and

collector drop and of hydrometeors ingeneral

ma, mtot kg Total mass of aerosol particles and of thesolution droplet

N s−1 Brunt–Väisälä frequencyN Number of moleculesNA 6.022 × 1023 mol−1 Avogadro’s constantN0 cm−4 Intercept parameter for hydrometeor size

distributionsN, Na, NCCN , Nc,Nd , Ni, Nr

cm−3 Number concentrations in general and ofaerosol particles, CCN, cloud droplets,drizzle drops, ice crystals and raindrops

Nj Number of particles of type j






xix Symbols and acronyms

n Number of moles or moleculesni, nv m−3 Number concentrations of gas molecules and of water

vapor moleculesne

m(r) g cm−3 Mass concentration of hydrometeorsnN (r) cm−3 µm−1 Number concentration of aerosol particles per

micrometer sizenN (r) m−3 mm−1 or m−3 m−1 Number concentration of hydrometeors per unit lengthne

N (r) cm−3 Number concentration of aerosol particles on alogarithmic scale

ns, nw Numbers of solute and water moleculesnS(r) µm2 cm−3 µm−1 Surface concentration of aerosol particles per

micrometer sizene

S(r) µm2 cm−3 Surface concentration of aerosol particles on alogarithmic scale

nV (r) µm3 cm−3 µm−1 Volume concentration of aerosol particles permicrometer size

neV (r) µm3 cm−3 Volume concentration of aerosol particles on a

logarithmic scaleP ProbabilityPR W Power received at a radar antennap Pa Atmospheric pressurep0 1000 hPa Reference pressurepc Pa Pressure of the lifting condensation levelpi, pA, pB Pa Partial pressure of particle type i and of substances A

and Bpn Pa Pressure within a clusterps Pa Saturation vapor pressureptot Pa Total vapor pressure of a solutionQ J Heat energyQ Generic quantity in thermodynamicsQ1 m−1 Thermodynamic variable in supersaturation equationQ2 Thermodynamic variable in supersaturation equationQλ,ext Extinction efficiencyq J kg−1 Specific heat energyqi kg kg−1 Cloud ice mass mixing ratioql kg kg−1 Cloud liquid water mass mixing ratioqs, qs,i kg kg−1 Saturation specific humidity with respect to water and

iceqv kg kg−1 Specific humidity: mass of water vapor per unit mass

of moist airqv,cl kg kg−1 Specific humidity in a cloudy air parcelqv,env kg kg−1 Specific humidity in the environmentqv,mix kg kg−1 Mean specific humidity in well-mixed airqx kg kg−1 Condensate mixing ratio: mass of condensate per unit

mass of dry airR m Radius of a collector dropR mm h−1 Precipitation or rain rateRd 287 J kg−1 K−1 Gas constant of dry airRi m Melted radius of a snowflake






xx Symbols and acronyms

Rm J kg−1 K−1 Gas constant of moist airRSun 6.98 × 108 m Radius of the SunRv 461.5 J kg−1 K−1 Gas constant of water vaporR∗ 8.314 J mol−1 K−1 Universal gas constantR50 m Radius at which 50% of aerosol particles are activatedRe Reynolds numberRH, RHi % Relative humidities with respect to water and iceRo Rossby numberr m Radius, distance in spherical coordinatesract m Critical radius for activationrc m Critical radiusrd , rh, ri, rr m Radii of a droplet, hydrometeor, ice particle and raindroprd m Mean volume radiusreq m Equivalent radius for a raindrop or for the drop that is

formed when a snowflake meltsrdry m Dry radius of an aerosol particlerEarth 6.371 × 109 m Radius of the Earthrmax m Maximum raindrop radiusrSun−Earth 1.5 × 1011 m Sun–Earth distanceS J K−1 EntropyS m2 Surface areaS = Sw, Si Ambient saturation ratios with respect to water and iceSa µm2 cm−3 Total aerosol surface area concentrationSact Activation saturation ratioSc J Surface energyScry Crystallization saturation ratioSdel Deliquesence saturation ratioSmax Maximum supersaturation reached in a cloudS(r) Size-dependent saturation ratio of a solution droplet with

radius rS0 1360 W m−2 Solar constantSc Schmidt numbers J kg−1 K−1 Specific entropys m Path lengths, scl, senv J kg−1 Moist static energies in general and for cloudy or

environmental airs % Supersaturationsact % Supersaturation required for activationT K Temperature of an air parcelT m s−1 Characteristic time scale for geostrophic flowT0 273.15 K Melting point temperature (0 ◦C)Tatm K Average temperature of the atmosphereTcl K Temperature of a cloudy air parcelTenv K Temperature of the environmentTc K Isentropic condensation temperatureTd K Dew point temperatureTe K Effective temperatureTe, Tes K Equivalent and saturation equivalent temperature






xxi Symbols and acronyms

Tin, Tout K Input and output temperature of the Carnot cycleTmix, T ′

mix K Mean temperature in isobarically mixed air before andafter condensation

Tp K Temperature of the air parcelTp0 , Ttropo K Temperatures at 1000 hPa and at the tropopauseTrd K Temperature at a droplet’s surfaceTs K Annual global mean temperature at the Earth’s surfaceTSun 5769.56 K Temperature of the SunTv, Tv,env K Virtual temperature in general and of the environmentTw K Wet-bulb temperaturet s TimeU J Internal energyU m s−1 Characteristic velocity scale for geostrophic flowu J kg−1 Specific internal energyu, v m s−1 Horizontal velocity components in x- and y- directionsug, vg m s−1 Geostrophic wind components in x- and y- directionsV , Vn m3 Volume in general and of the clusterVa µm3 cm−3 Total aerosol volume concentrationVsweep m3 Sweep-out volume�v m s−1 Three-dimensional velocity vector�vh m s−1 Horizontal velocity vectorv, vi, vw m3 kg−1 Specific volume in general and of ice and waterv0 m3 Volume of an individual moleculevD m s−1 Doppler velocityvh m s−1 Fall velocity of hydrometeorsvr m s−1 Relative velocity of two falling hydrometeorsvT , vT ,snow m s−1 Terminal velocity in general and for snowW J Workw J kg−1 Specific external workw, wcl m s−1 Vertical velocity in general and for a cloudy air parcelwj mass fractionwl kg kg−1 Adiabatic cloud liquid water mixing ratiows kg kg−1 Saturation water vapor mixing ratiowv kg kg−1 Water vapor mixing ratio: mass of water vapor per unit

mass of dry airx Dimensionless size parameter for scatteringx0 m Impact parameter within which a collision is certain to

occurZ mm6 m−3 Radar reflectivity factorZe mm6 m−3 Equivalent radar reflectivity factorz m Heightα, αi, αl, αv m3 kg−1 Specific volumes of air, ice, liquid water and water vaporαm Accommodation coefficient for ice crystal growthαc Cloud albedoαp Planetary albedoβ m−1 s−1 Meridional gradient of Coriolis parameter fγ , � K m−1 Lapse rates of the ambient air and of an air parcelγ Radii ratio of collector drop to smaller droplet






xxii Symbols and acronyms

�d 9.8 K km−1 Dry adiabatic lapse rate�s K km−1 Pseudoadiabatic lapse rate�F = RF W m−2 Radiative forcing�FLW , �FSW W m−2 Changes in FLW and FSW at the TOA�H W m−2 Heat uptake by the ocean�G J Change in Gibbs free energy�G∗, �G∗

het J Gibbs free energy barrier in general and forheterogeneous nucleation

�Gs, �Gv J Surface and volume terms of the change inGibbs free energy

�Gs,hom, �Gs,sol J Surface terms of the change in Gibbs freeenergy in pure water and in a solution

�Gv,hom, �Gv,sol J Volume terms of the change in Gibbs freeenergy in pure water and in a solution

�Gw,v, �Gi,w, �Gi,v J Changes in Gibbs free energy betweenwater and vapor, ice and water, and ice andvapor

�R W m−2 Net radiative imbalance at the TOA�Ts K Change in global mean surface temperatureδ infinitesimal changeε, ελ Emissivity in general and

wavelength-dependent emissivityε Entrainmentε 0.622 Ratio Rd/Rv = mw/mdζ s−1 z-component of the relative vorticityη s−1 x-component of the relative vorticityη Thermodynamic efficiency of the Carnot

processθ Contact angleθ K Potential temperatureθe, θes K Equivalent and saturation equivalent

potential temperaturesθmix K Mean potential temperature in well-mixed

airθw K Wet-bulb potential temperatureκ 0.286 Ratio Rd/cp

κ Hygroscopicity parameter� m−1 Entrainment rate� cm−1 Slope of hydrometeor size distributions�B s−1 Scavenging coefficientλ m Wavelengthλ W m−2 K−1 Climate sensitivity parameterλ0 W m−2 K−1 Null climate sensitivity parameterμ Shape parameter of hydrometeor size

distributionsμ kg m−1 s−1 Dynamic viscocity of airμ J s−1 Chemical potential






xxiii Symbols and acronyms

μ, μS, μV , μm m Number mean radius and arithmetric meansof the surface, volume and mass radii

μg, μg,S, μg,V , μg,m m Geometric means of the number, surface,volume and mass distributions of aerosolparticles

μ, μ m Number mode radius and radius of averagemass

ν m2 s−1 Kinematic viscocityξ s−1 y-component of the relative vorticityρa kg m−3 Density of an aerosol particleρd kg m−3 Density of dry airρenv kg m−3 Density of ambient airρl, ρi, ρs kg m−3 Densities of liquid water, ice and a solution

dropletρ, ρm kg m−3 Density in general and of moist airρv, ρv,rd , ρvs kg m−3 Ambient water vapor density, water vapor

density at a droplet’s surface and saturationwater vapor density

σ Arithmetic standard deviationσ 5.67 × 10−8 W m−2 K−4 Stefan–Boltzmann constantσ N m−1 Surface tensionσi,a, σi,v N m−1 Surface tension of ice in air or vaporσw,a = σw N m−1 Surface tension of water in airσw,v 0.0756 N m−1 Surface tension of water in water vapor at

273.15 Kσi,w N m−1 Surface tension between ice and waterσINP,i, σINP,v, σINP,w N m−1 Surface tensions between an INP and ice,

vapor or waterσ , σi m Standard deviations of the aerosol size

distribution in mode iσg Geometric standard deviation of the aerosol

size distributionτ Optical depthτAP Aerosol optical depthφ ◦, degrees Latitudeϕ(Vn) J Gibbs free energy of the interface between

a cluster and the parent phase� 7.29 ×10−5 s−1 Earth’s rotationω Pa s−1 Vertical velocity in the p-system�ω s−1 Three-dimensional vorticity vector�ωh s−1 Horizontal vorticity vector






xxiv Symbols and acronyms

Acronyms

AEJ African easterly jetAEROCOM Aerosol Intercomparison projectAERONET Aerosol Robotic NetworkAOD Aerosol optical depthAOGCM Coupled atmosphere–ocean general circulation modelAR4 Fourth Assessment Report of the Intergovernmental Panel on Climate ChangeAR5 Fifth Assessment Report of the Intergovernmental Panel on Climate Changeaci Aerosol–cloud interactionsari Aerosol–radiation interactionsa.u. arbitrary unitsBC Black carbonBWER Bounded weak echo regionCALIPSO Cloud–Aerosol Lidar and Infrared Pathfinder Satellite ObservationCAPE Convectively available potential energy (J kg−1)CCB Cold conveyor beltCCL Convective condensation levelCCN Cloud condensation nucleiCCNC Cloud condensation nuclei counterCERES Capacité de Renseignement Electromagnétique SpatialCIN Convective inhibitionCKE Collision kinetic energyCNT Classical nucleation theoryCRE Cloud radiative effectCRH Crystallization relative humidityCTP Cloud top pressureDCAPE Downdraft convectively available potential energy (J kg−1)DJF December, January, FebruaryDMS Dimethyl sulfideDRH Deliquescence relative humidityDU Mineral dust particlesEC Elemental carbonECA Emission controlled areaECHAM6 GCM Global climate model from the Max Planck Institute for Meteorology in

Hamburg, GermanyECMWF European Centre for Medium-Range Weather ForecastERA-interim ECMWF Re-analysis interimERFaci Effective radiative forcing due to aerosol–cloud interactionsERFari Effective radiative forcing due to aerosol–radiation interactionsERFacitari Effective radiative forcing due to aerosol–cloud and aerosol–radiation

interactionsGCCN Giant CCNGCM Global climate modelGeoMIP Geoengineering Model Intercomparison ProjectGHG Greenhouse gases






xxv Symbols and acronyms

GPCC Global Precipitation Climatology CentreHTI Height–time indicatorINP Ice nucleating particleIPCC Intergovernmental Panel on Climate ChangeISA International standard atmosphereISCCP International Satellite Cloud Climatology ProjectITCZ Intertropical Convergence ZoneIWC Ice water contentJJA June, July, AugustLAADS Level-1 and Atmosphere Archive and Distribution SystemLCRE Longwave cloud radiative effectLCL Lifting condensation levelLFC Level of free convectionLH Latent heat fluxLNB Level of neutral buoyancyLW LongwaveLWC Liquid water contentMCC Mesoscale convective complexMCS Mesoscale convective systemMEE Mass extinction efficiencyMISR Multi-angle imaging spectroradiometerMODIS Moderate resolution imaging spectroradiometerNCFR Narrow cold frontal rainbandNOAA National Oceanic and Atmospheric AdministrationOC Organic carbonOLR Outgoing longwave radiationPBL Planetary boundary layerPOA Primary organic aerosolPOM Particulate organic matterPPI Plan position indicatorQLL Quasi-liquid layerRadar Radio detection and rangingRCP Representative concentration pathwayRF Radiative forcingRFaci Radiative forcing due to aerosol–cloud interactionsRFacitari Radiative forcing due to aerosol–cloud and aerosol–radiation interactionsRFari Radiative forcing due to aerosol–radiation interactionsRH Relative humiditySCE Stochastic coalescence equationSCRE Shortwave cloud radiative effectSH Sensible heat fluxSOA Secondary organic aerosolsSPCZ South Pacific Convergence ZoneSRM Solar radiation managementSST Sea surface temperatureSS Sea salt






xxvi Symbols and acronyms

SU SulfateTC Tropical cycloneTDE Thermodynamic equilibriumTOA Top of the atmosphereWCB Warm conveyor beltWCFR Wide cold frontal rainbandWFR Warm frontal rainbandWMGHG Well-mixed greenhouse gasesWMO World Meteorological Organization






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AnIntroductiontoClouds - Cambridge University Pressassets.cambridge.org/97811070/18228/frontmatter/... · 2016-06-29 · AnIntroductiontoClouds FromtheMicroscaletoClimate Clouds,