Atmospheric Chemistry and Physics Wiley 1997

xxv

1

18

Preface

1 The Atmosphere

1.1 History and Evolution of the Earth's Atmosphere 11.2 Climate 41.3 The Layers of the Atmosphere 61.4 Variation of Pressure with Height in the Atmosphere 91.5 Large-Scale Motion of the Atmosphere 10

1.5.1 The General Circulation 101.5.2 Troposphere-Stratosphere Transport 14

1.6 Temperature and Water Vapor 161.7 Expressing the Amount of a Substance in the Atmosphere1.8 Composition of the Atmosphere 211.9 Radiation 23

1.9.1 Solar and Terrestrial Radiation 261.9.2 Absorption of Radiation by Gases 29

1.10 Energy Balance for Earth and Atmosphere 331.10.1 Solar Variability 371.10.2 Earth's Energy Balance 38

1.11 Spatial and Temporal Scales of Atmospheric Processes 40Appendix 1 Derivation of the Geostrophic Wind Speed 43References 47Problems 47

492 Atmospheric Composition, Global Cycles, and Lifetimes

2.1 Atmospheric Residence Times 502.1.1 Residence Time 51

2.2 Sulfur-Containing Compounds 552.2.1 Dimethyl Sulfide (CH3SCH3) 612.2.2 Carbonyl Sulfide (OCS) 622.2.3 Sulfur Dioxide (SO2) 632.2.4 The Atmospheric Sulfur Cycle 63

2.3 Nitrogen-Containing Compounds 672.3.1 Nitrous Oxide (N2O) 672.3.2 Nitrogen Oxides (NO x = NO + NO;) 702.3.3 Reactive Odd Nitrogen (NOy) 71

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ixCONTENTS

4 Chemistry of the Stratosphere

4.1 Chapman Mechanism 1644.2 HO x Cycles 1714.3 NO x Cycles 173

4.3.1 N2O Stratospheric Source of NO x 1734.3.2 NOx Cycles 175

4.4 ClO x Cycles 1774.5 Reservoir Species and Coupling of the Cycles 1804.6 Stratospheric Species Observations and Predictions 184

4.6.1 Upper Stratosphere 1844.6.2 Lower Stratosphere 186

4.7 Ozone Hole 1894.7.1 Polar Stratospheric Clouds 1924.7.2 PSCs and the Ozone Hole 1944.7.3 Antarctic Ozone Hole Measurements 1984.7.4 Arctic Ozone Hole 1994.7.5 Summary 202

4.8 Heterogeneous (Nonpolar) Stratospheric Chemistry 2034.8.1 Heterogeneous Hydrolysis ofN2Os 2034.8.2 Effect of Volcanoes on Stratospheric Ozone 2074.8.3 Summary of Midlatitude and Tropical Stratospheric

Ozone Chemistry 2104.9 Transport Between the Tropical and Midlatitude

Stratosphere 2104.10 Ozone-Depleting Potential of Halocarbons 2124.11 Effect of Aircraft Emissions on Stratospheric Ozone 2154.12 Carbonyl Sulfide (OCS) and the Stratospheric

Aerosol Layer 2164.12.1 Atmospheric Chemistry ofOCS and

OCS Lifetime 2174.12.2 Stratospheric Aerosol Layer 217

4.13 Projections of Future Ozone Change 218Appendix 4 Sensitivity/Uncertainty Analysis of Atmospheric

Chemical Mechanisms 2194.A.l Sensitivity Coefficients 2224.A.2 The Direct Decoupled Method 2234.A.3 Adjoint Methods 2244.A.4 Green's Function Methods 224

References 226Problems 230

5 Chemistry of the Troposphere

5.1 Basic Photochemical Cycle of N02, NO, and 03 2355.2 Atmospheric Chemistry of Carbon Monoxide and NOx 2395.3 Atmospheric Chemistry of Fonnaldehyde and NO x 244

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5.15 Atmospheric Chemistry (Gas Phase) of Sulfur Compounds 3145.15.1 Sulfur Oxides 3145.15.2 Reduced Sulfur Compounds (Dimethyl Sulfide) 315

5.16 Tropospheric Chemistry of Halogen Compounds 3175.16.1 Chemical Cycles of Halogen Species 3185.16.2 Tropospheric Chemistry ofCFC Replacements:

Hydrofluorocarbons (HFCs) andHydrochlorofluorocarbons (HCFCs) 319


3376 Chemistry of the Atmospheric Aqueous Phase

6.1 Liquid Water in the Atmosphere 3376.1.1 Cloud Types and Liquid Water Content 338

6.2 Absorption Equilibria and Henry's Law 3406.2.1 Gas/Aqueous-Phase Distribution Factor 343

.6.3 Aqueous-Phase Chemical Equilibria 3446.3.1 Water 3446.3.2 Carbon Dioxide/Water Equilibrium 3456.3.3 Sulfur Dioxide 3486.3.4 Ammonia/Water Equilibrium 3536.3.5 Nitric Acid/Water Equilibrium 3556.3.6 Equilibrium of Other Important Atmospheric Gases 356

6.4 Aqueous-Phase Reaction Rates 3616.5 S(IV) to S(VI) Transformation and Sulfur Chemistry 363

6.5.1 Oxidation of S(IV) by Dissolved 03 3636.5.2 Oxidation of S(IV) by Hydrogen Peroxide 3666.5.3 Oxidation of S(IV) by Organic Peroxides 3676.5.4 Uncatalyzed Oxidation of S(IV) by O2 3686.5.5 Oxidation of S(IV) by 02 Catalyzed by

Iron and Manganese 3696.5.6 S(IV) Oxidation by the OH Radical 3726.5.7 Oxidation ofS(IV) by Oxides of Nitrogen 3746.5.8 Reaction of Dissolved S02 with HCHO 3766.5.9 Comparison of Aqueous-Phase S(IV)

Oxidation Paths 3786.6 Aqueous-Phase Nitrite and Nitrate Chemistry 380

6.6.1 NO x Oxidation 3806.6.2 Nitrogen Radicals 381

6.7 Aqueous-Phase Organic Chemistry 3816.8 Oxygen and Hydrogen Chemistry 3836.9 Dynamic Behavior of Solutions with Aqueous-Phase

Chemical Reactions 3846.9.1 Closed System 385

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CONTENTS xiii

8.5.2 Aerosol Mobility and Drift Velocity 4758.5.3 Mean Free Path of an Aerosol Particle 478

8.6 Phoretic Effects 4808.6.1 Thermophoresis 4808.6.2 Diffusiophoresis 4838.6.3 Photophoresis 483

8.7 Aerosol and Fluid Motion 4848.7.1 Motion of a Particle in an Idealized Flow

(900 Corner) 4858.7.2 Stop Distance and Stokes Number 486

8.8 Diameters of Nonspherical Particles 488References 488Problems 489

4919 Thermodynamics of Aerosols

9.1 Thermodynamic Principles 4919.1.1 Internal Energy and Chemical Potential 491

. 9.1.2 The Gibbs Free Energy, G 4939.1.3 Conditions for Chemical Equilibrium 4959.1.4 Chemical Potentials of Ideal Gases and Ideal

Gas Mixtures 4999.1.5 Chemical Potential of Solutions 5019.1.6 The Equilibrium Constant 506

9.2 Aerosol Liquid Water Content 5079.2.1 Chemical Potential of Water in Atmospheric Particles 5089.2.2 Temperature Dependence of the DRH 5109.2.3 Deliquescence of Mu1ticomponent Aerosols 5149.2.4 Crystallization of Single and Multicomponent Salts 519

9.3 Equilibrium Vapor Pressure Over a Curved Surface:The Kelvin Effect 519

9.4 Thermodynamics of Atmospheric Aerosol Systems 5239.4.1 The H2SO4-H2O System 5239.4.2 The Sulfuric Acid-Ammonia-Water System 5299.4.3 The Ammonia-Nitric Acid-Water System 5319.4.4 The Ammonia-Nitric Acid-Sulfuric

Acid-Water System 5379.4.5 Other Inorganic Aerosol Species 539

References 541Problem 543

54510 Nucleation

10.1 Classical Theory of Homogeneous Nucleation:KineticApproach 54710.1.1 The Forward Rate Constant.Bi 55010.1.2 The Reverse Rate Constant Yi 551

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CONTENTS xv

11.2.5 Characteristic Time for Aqueous-PhaseChemical Reactions 617

11.3 Mass Transport and Aqueous-Phase Chemistry 61711.3.1 Gas-Phase Diffusion and Aqueous-Phase Reactions 61811.3.2 Aqueous-Phase Diffusion and Reaction 62011.3.3 Interfacial Mass Transport and Aqueous-Phase

Reactions 62111.3.4 Application to the S(IV)-Ozone Reaction 62311.3.5 Application to the S(IV)-Hydrogen Peroxide

Reaction 62611.3.6 Calculation of Aqueous-Phase Reaction Rates 62711.3.7 An Aqueous-Phase Chemistry/Mass

Transport Model 63411.4 Mass Transfer to Falling Drops 63511.5 Characteristic Time for Atmospheric Aerosol Equilibrium 636

11.5.1 Solid Aerosol Particles 63611.5.2 Aqueous Aerosol Particles 638

Appendix 11 Solution of the Transient Gas-Phase DiffusionProblem Equations (11.4) to (11.7) 641


64812 Dynamics of Aerosol Populations

12.1 Mathematical Representations of the AerosolSize Distributions 64812.1.1 Discrete Distribution 64812.1.2 Continuous Distribution 649

12.2 Condensation 64912.2.1 Solution of the Condensation Equation 652

12.3 Coagulation 65612.3.1 Brownian Coagulation 65612.3.2 Coagulation in Laminar Shear Flow 66412.3.3 Coagulation in Turbulent Flow 66512.3.4 Coagulation from Gravitational Settling 66512.3.5 Brownian Coagulation and External Force Fields 66612.3.6 The Coagulation Equation 67212.3.7 Solution of the Coagulation Equation 676

12.4 The Discrete General Dynamic Equation 68012.5 The Continuous General Dynamic Equation 68212.6 Evolution of an Aerosol Size Distribution During

Gas-to-Particle Conversion 68412.6.1 Diffusion-Controlled Growth 68512.6.2 Surface Reaction-Controlled Growth 68612.6.3 Volume Reaction-Controlled Growth 68812.6.4 Dimensionless Size Spectra Evolution 689

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CONTENTS xvii

14.1.2 Temperature Changes of a Rising (or Falling)Parcel of Air 770

14.2 Atmospheric Stability 772Problems 775

77715 Cloud Physics

15.1 Properties of Water and Water Solutions 77715.1.1 Specific Heat of Water and Ice 77815.1.2 Latent Heats of Evaporation and of Melting for Water 77815.1.3 Water Surface Tension 779

15.2 Water Equilibrium in the Atmosphere 78015.2.1 Equilibrium of a Flat Pure Water Surface

with the Atmosphere 78015.2.2 Equilibrium of a Pure Water Droplet 78115.2.3 Equilibrium of a Flat Water Solution 78315.2.4 Atmospheric Equilibrium of an Aqueous

Solution Drop 78415.2.5 Atmospheric Equilibrium of an Aqueous Solution

Drop Containing an Insoluble Substance 79015.3 Cloud and Fog Formation 793

15.3.1 Isobaric Cooling 79415.3.2 Adiabatic Cooling 79515.3.3 Cooling with Entrainment 79815.3.4 A Simplified Mathematical Description of

Cloud Formation 79915.4 Growth Rate of Individual Cloud Droplets 80115.5 Growth of a Droplet Population 80515.6 Cloud Condensation Nuclei 80915.7 Cloud Processing of Aerosols 812

15.7.1 Nucleation Scavenging of Aerosols by Clouds 81315.7.2 Chemical Composition of Cloud Droplets 81415.7.3 Nonraining Cloud Effects on Aerosol Concentrations 81615.7.4 Interstitial Aerosol Scavenging by Cloud Droplets 82115.7.5 Aerosol Nucleation Near Clouds 823

15.8 Other Forms of Water in the Atmosphere 82315.8.1 Ice Clouds 82415.8.2 Rain 828

15.9 Cloud Climatology 832References 834Problems 839

84116 Micrometeorology

16.1 Basic Equations of Atmospheric Fluid Mechanics 84116.2 Turbulence 847 .

16.3 Equations for the Mean Quantities 849

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CONTENTS xix

18.3 Summary of Gaussian Point Source Diffusion Fonnulas 92318.4 Dispersion Parameters in Gaussian Models 926

18.4.1 Correlations for uyand Uz Based onSimilarity Theory 926

18.4.2 Correlations for uyand Uz Based onPasquill Stability Classes 929

18.5 Plume Rise 93118.6 Analytical Properties of the Gaussian Plume Equation 93318.7 Functional Fonns of Mean Wind Speed and Eddy Diffusivities 938

18.7.1 MeanWindSpeed 93818.7.2 Vertical Eddy Diffusion Coefficient Kzz 93818.7.3 Horizontal Eddy Diffusion Coefficients Kxx and K yy 942

18.8 Solutions of the Steady-State Atmospheric Diffusion Equation 94318.8.1 Diffusion from a Point Source 94318.8.2 Diffusion from a Line Source 944


95819 Dry Deposition

19.1 Deposition Velocity 95819.2 Resistance Model for Dry Deposition 960

19.2.1 Aerodynamic Resistance 96219.2.2 Quasi-Laminar Resistance 96319.2.3 Surface of Canopy Resistance 96519.2.4 Relative Magnitudes of ra, rb, and rc 968

19.3 Dry Deposition of Particles 96919.4 A Model for Dry Deposition Calculations 97119.5 Measurement of Dry Deposition 977

19.5.1 Direct Methods 97819.5.2 Indirect Methods 97919.5.3 Comparison of Methods 980

19.6 Some Comments on Modeling and Measurement ofDry Deposition 980

19.7 Interaction Between Equilibration Processes andDry Deposition 98219.1.1 Solution of the Model Equations 98719.7.2 TheDepositionRatio 98819.7.3 Effects of Equilibration Processes on

Dry and Wet Deposition 989References 993Problems 995

99720 Wet Deposition

20.1 General Representation of AtmosphericWet Removal Processes 997

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S~3.LNO;)xx

CONTENTS xxi

1135

22 Radiative Effects of Atmospheric Aerosols: Visibility and Climate

22.1 Scattering and Absorption of Light by Small Particles 111422.1.1 Rayleigh Scattering Regime 112022.1.2 Geometric Scattering Regime 112222.1.3 Scattering Phase Function 112322.1.4 Extinction by an Ensemble of Particles 1123

22.2 Visibility 112622.3 Scattering, Absorption, and Extinction Coefficients from

Mie Theory 113122.4 Calculated Visibility Reduction Based on Atmospheric Data22.5 Direct Effect of Aerosols on Climate 1139

22.5.1 Optical Depth 114322.5.2 Upscatter Fraction 114622.5.3 Scattering Model of an Aerosol Layer 114722.5.4 Cooling Versus Heating of an Aerosol Layer 115222.5.5 Scattering Model of an Aerosol Layer for a

NonabsorbingAerosol 115422.5.6 Direct Aerosol Forcing of Climate by

Sulfate Aerosols 115622.5.7 Effect of Mineral Dust on Radiative Forcing

of Climate 116022.5.8 Effect of Carbonaceous Aerosols on Radiative

Forcing of Climate 116622.5.9 Internal and External Mixtures 1166

22.6 Indirect Effect of Aerosols on Climate 117022.6.1 Radiative Model for a Cloudy Atmosphere 117322.6.2 Sensitivity of Cloud Albedo to Cloud Drop

Number Concentration 117522.6.3 Relation of Cloud Drop Number Concentration to

Aerosol Concentrations 117722.6.4 Estimates of Indirect Radiative Forcing of Aerosols

22.7 Summary: Estimates of Contributions to Radiative Forcing ~22.8 Climate Response to Anthropogenic Aerosol Forcing 1182Appendix 22 Calculation of Scattering and Extinction Coefficients

by Mie Theory 1184References 1185Problems 1190

11791180

23 Atmospheric Chemical Transport Models

23.1 Introduction 119323.1.1 Model Types 1194? ~ 1 2 Tvne~ of Atmosoheric Chemical Transport Models 1195

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CONTENTS xxiii

24.6 Alternative Forms of Air Quality Standards 127724.6.1 Evaluation of Alternative Forms of the Ozone Air Quality

Standard with 1971 Pasadena, California, Data 127924.6.2 Selection of the Averaging Time 1281

24.7 Relating Current and Future Air PollutantStatistical Distributions 1281


1289Appendix A Units and Physical Constants

A.l SI Base Units 1289A.2 SI Derived Units 1289A.3 Fundamental Physical Constants 1292A.4 Properties of the Atmosphere and Water 1293A.5 Units for Representing Chemical Reactions 1294A.6 Concentrations in the Aqueous Phase 1295A.7 Symbols for Concentration 1295References 1295

Appendix B Rate Constants of Atmospheric Chemical Reactions

References 1307

1297

Index 1309

The study of atmospheric chemistry as a scientific discipline goes back to the 18th century,when the principal issue was identifying the major chemical components of the atmos-

phere, nitrogen, oxygen, water, carbon dioxide, and the noble gases. In the late 19th andearly 20th centuries attention turned to the so-called trace gases, species present at less than1 part per million parts of air by volume (1 JLmol per mole). We now know that the atmos-phere contains a myriad of trace species, some at levels as low as 1 part per trillion parts ofair. The role of trace species is disproportionate to their atmospheric abundance; they areresponsible for phenomena ranging from urban photochemical smog, to acid deposition, tostratospheric ozone depletion, to potential climate change. Moreover, the composition ofthe atmosphere is changing; analysis of air trapped in ice cores reveals a record of strikingincreases in the long-lived so-called greenhouse gases, carbon dioxide (CO2), methane(CH4), and nitrous oxide (N 20). Within the last century, concentrations of troposphericozone (03), sulfate (SO~-), and carbonaceous aerosols in the Northern Hemisphere haveincreased significantly. There is evidence that all these changes are altering the basic chem-istry of the atmosphere.

Atmospheric chemistry occurs within a fabric of profoundly complicated atmosphericdynamics. The results of this coupling of dynamics and chemistry are often unexpected:witness the unique combination of dynamical forces that lead to a wintertime polar vortexover Antarctica, with the concomitant formation of polar stratospheric clouds that serve assites for heterogeneous chemical reactions involving chlorine compounds resulting from

anthropogenic chlorofluorocarbons-all leading to the near total depletion of stratosphericozone over the South Pole each spring; witness the nonlinear, and counterintuitive, depen-dence of the amount of ozone generated by reactions involving hydrocarbons and oxides ofnitrogen (NO x) at the urban and regional scale-although both hydrocarbons and NO x areozone precursors, situations exist where continuing to emit more and more NO x actuallyleads to less ozone.

The chemical constituents of the atmosphere do not go through their life cycles inde-pendently; the cycles of the various species are linked together in a complex way. Thus aperturbation of one component can lead to significant, and nonlinear, changes to other com-ponents and to feedbacks that can amplify or damp the original perturbation.

In many respects, at once both the most important and the most paradoxical trace gas inthe atmosphere is ozone (03). High in the stratosphere ozone screens living organismsfrom biologically harmful solar ultraviolet radiation; ozone at the surface, in the tropos-phere, can produce adverse effects on human health and plants when present at levels ele-vated above natural. At the urban and regional scale, significant policy issues concern howto decrease ozone levels by controlling the ozone precursors-hydrocarbons and oxides ofnitrogen. At the global scale, understanding both the natural ozone chemistry of the tro-posphere and the causes of continually increasing background tropospheric ozone levels isa major goal.

xxv

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3;)Vd31ld JAxx

PREFACE xxvii

for the benefit of the student and the instructor. The designation (A) indicates a problemthat involves a straightforward application of material in the text. Those problems denoted(B) require some extension of the ideas in the text. Problems designated (C) encourage thereader to apply concepts from the book to current problems in atmospheric science and gosomewhat beyond the level of (B) problems. Finally, those problems denoted (D) are of adegree of difficulty corresponding to (C) but generally require development of a computerprogram for their solution.

This book isa successor to John H. Seinfeld's Atmospheric Chemistry and Physics ofAir Pollution (Wiley, 1986), which has been widely used for a decade. Substantial addi-tions have been made in virtually all areas covered by the earlier book, reflecting the sig-nificant increase in our understanding of atmospheric processes that has emerged over thelast decade and reflecting the truly global scope of the science of atmospheric chemistryand physics.

We extend sincere appreciation to Marta Goodman and Laura Shaheen who provided somuch valuable assistance in making this book a reality and to Cecilia Lin who drafted thefigures so skillfully.

JOHN H. SEINFELD

SPYROS N. PANDIS

1

1.1 HISTORY AND EVOLUTION OF THE EARTH'S ATMOSPHERE

It is generally believed that the solar system condensed out of an interstellar cloud of gasand dust, referred to as the "primordial solar nebula," about 4.6 billion years ago. The at-mospheres of the Earth and the other terrestrial planets, Venus and Mars, are thought tohave formed as a result of the release of trapped volatile compounds from the planet itself.The early atmosphere of the Earth is believed to have been a mixture of carbon dioxide(COz), nitrogen (Nz), and water vapor (HzO), with trace amounts of hydrogen (Hz), amixture similar to that emitted by present day volcanoes.

The composition of the present atmosphere bears little resemblance to the compositionof the early atmosphere. Most of the water vapor that outgassed from the Earth's interiorcondensed out of the atmosphere to form the oceans. The predominance of the CO2 thatoutgassed formed sedimentary carbonate rocks after dissolution in the ocean. It is esti-mated that for each molecule of COz presently in the atmosphere, there are about 105 COzmolecules incorpor~ted as carbonates in sedimentary rocks. Since Nz is chemically inert,non-water soluble, and noncondensable, most of the outgassed Nz accumulate~ in the at-mosphere over geologic time to become the atmosphere's most abundant constituent.

The early atmosphere of the Earth was a mildly reducing chemical mixture, whereas thepresent atmosphere is strongly oxidizing. The dramatic rise of oxygen (Oz) as an atmos-pheric constituent over time was the result of the production of Oz as a by-product of pho-tosynthetic activity. It has been estimated that the current level of Oz in the atmosphere wasachieved approximately 400 million years ago (Cloud, 1983). The present level of Oz ismaintained by a balance between production from photosynthesis and removal throughrespiration and decay of organic carbon. If Oz were not replenished by photosynthesis, thereservoir of surface organic carbon would be completely oxidized in about 20 years, atwhich time the amount of Oz in the atmosphere would have decreased by less than 1 %(Walker, 1977). In the absence of surface organic carbon to be oxidized, weathering of sed-imentary rocks would consume the remaining O2 in the atmosphere, but it would take ap-proximately 4 million years to do so.

The Earth's atmosphere is composed primarily of the gases Nz (78%), Oz (21%), andAr (1 %), whose abundances are controlled over geologic time scales by the biosphere, up-take and release from crustal material, and degassing of the interior. Water vapor is the nextmost abundant constituent; it is found mainly in the lower atmosphere and its concentrationis highly variable, reaching concentrations as high as 3%. Evaporation and precipitationcontrol its abundance. The remaining gaseous constituents, the trace gases, comprise lessthan 1 % of the atmosphere. These trace gases playa crucial role in the Earth's radiative

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3HISTORY AND EVOLUTION OF THE EARTH'S ATMOSPHERE

The atmosphere is the recipient of many of the products of our technological society.These effluents include products of combustion of fossil fuels and of the development ofnew synthetic chemicals. Historically these emissions can lead to unforeseen consequencesin the atmosphere. Classical examples include the realization in the 1950s that motor vehi-cle emissions could lead to urban smog and the realization in the 1970s that emissions ofchlorofluorocarbons from aerosol spray cans and refrigerators could cause the depletion ofstratospheric ozone.

The chemical fates of trace atmospheric species are often intertwined. The life cycles ofthe trace species are inextricably coupled through the complex array of chemical and phys-ical processes in the atmosphere. As a result of these couplings, a perturbation in the con-centration of one species can lead to significant changes in the concentrations and lifetimesof other trace species and to feedbacks that can either amplify or damp the original pertur-bation. An example of this coupling is provided by methane. Methane is the predominantorganic molecule in the troposphere and it is the sec.ond most important greenhouse gas af-ter CO2. Methane sources such as rice paddies and cattle can be estimated and are increas-ing. Methane is removed from the atmosphere by reaction with the hydroxyl (OH) radical,at a rate that depends on the atmospheric concentration of OR. But, the OH concentrationdepends on the amount of carbon monoxide (CO), which itself is a product of C~ oxida-tion as well as a result of fossil fuel combustion and biomass burning. The hydroxyl con-centration also depends on the concentration of ozone and oxides of nitrogen. Change inC~ can affect the total amount of ozone in the troposphere, so methane itself affects theconcentration of the species, OR, that governs its removal.

Depending on their atmospheric lifetime, trace species can exhibit an enormous rangeof spatial and temporal variability. Relatively long-lived species have a spatial uniformitysuch that a handful of strategically located sampling sites around the globe are adequate tocharacterize their spatial distribution and temporal trend. As species lifetimes becomeshorter, their spatial and temporal distributions become more variable. Urban areas, for ex-ample, can require tens of monitoring stations over an area of hundreds of square kilome-ters in order to characterize the spatial and temporal distribution of their atmospheric

components.The extraordinary pace of the recent increases in atmospheric trace gases can be seen

when current levels are compared with those of the distant past. Such comparisons can bemade for CO2 and C~, whose histories can be reconstructed from their concentrations inbubbles of air trapped in ice in such perpetually cold places as Antarctica and Greenland.With gases that are long-lived in the atmosphere and therefore distributed rather uniformlyover the globe, such as CO2 and C~, polar ice core samples reveal global average con-centrations of previous eras. Analyses of bubbles in ice cores show that CO2 and C~ con-centrations remained essentially unchanged from the end of the last ice age some 10,000years ago until roughly 300 years ago, at mixing ratios close to 260 ppm by volumeand 0.7 ppm by volume, respectively. (See Section 1.4 for discussion of units.) About 300years ago methane levels began to climb, and about 100 years ago levels of both gases be-gan to increase markedly. Before the large-scale production of chlorofluorocarbons the nat-ural level of chlorine in the stratosphere was 0.6 part per billion (ppb) by volume; now it is3 ppb, a factor of 5 increase.

Activities of humans account for most of the rapid changes in the trace gases over thepast 200 years-combustion of fossil fuels (coal and oil) for energy and transportation, in-

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5CLIMATE

century. It has been estimated that a doubling of CO2 from its pre-Industrial Revolutionmixing ratio of 280 ppm by volume could lead to a rise in average global temperature of1.5 to 4.5°C. A 2°C warming would produce the warmest climate seen on Earth in 6000years. A 4.5°C rise would place the world in a temperature regime last experienced in theMesozoic Era-the age of dinosaurs.

Although an average global ~arming of a few degrees does not sound like much, itcould create dramatic changes in climatic extremes. It has been estimated, for example,that, in the event of an average global warming of 1.7°C, the frequency of periods of 5 daysor more exceeding 35°C (95°F) in the Com Belt of the United States would increase three-fold. Such conditions at critical stages of the growing season are known to harm com andlead to reduced yields. With a doubling of CO2, the number of days exceeding 38°C(100°F) and nights above 27°C (80°F) have been estimated to rise dramatically in manymajor American cities. Changes in the timing and amount of precipitation would almostcertainly occur with a warmer climate. Soil moisture, critical during planting and earlygrowth periods, will change. Some regions would probably become more productive, oth-ers less so. The North American Grain Belt, according to at least one climate model, willshift northward into Canada as warming produces hotter, drier conditions in the AmericanMidwest.

Of all the effects of a global warming, perhaps none has captured more attention thanthe prospect of rising sea levels. This would result from the melting of land-based glaciersand volume expansion of ocean water as it warms. Prevailing opinion is that a sea level riseof about 0.5 m could occur by 2100. In the most dramatic scenario, the West Antarctic icesheet, which rests on land that is below sea level, could slide into the sea if the buttress offloating ice separating it from the ocean were to melt. This would raise the average sealevel 5 to 6 m (Bentley, 1997). Even a 0.3 m (1 foot) rise would have major effects on theerosion of coastlines, salt water intrusion into the water supply of coastal areas, flooding ofmarshes, and inland extent of surges from large storms.

To systematically approach the complex subject of climate, the scientific communityhas divided the problem into two major parts, climate forcings and climate responses.Climate forcings are changes in the energy balance of the Earth that are imposed upon it;forcings are measured in units of heat flux-watts per square meter (W m-2). An exampleof a forcing is a change in energy output from the sun. Responses are the meteorological re-sults of these forcings, reflected in temperatures, rainfall, extremes of weather, sea levelheight, and so on.

Much of the variation in the predicted magnitude of potential climate effects resultingfrom the increase in greenhouse gas levels hinges on estimates of the size and direction ofvarious feedbacks that may occur in response to an initial perturbation of the climate.Negative feedbacks have an effect that damps the warming trend; positive feedbacks rein-force the initial warming. One example of a greenhouse warming feedback mechanism in-volves water vapor. As air warms, each cubic meter of air can hold more water vapor. Sincewater vapor is a greenhouse gas, this increased concentration of water vapor further en-hances greenhouse warming. In turn, the warmer air can hold more water, and so on. Thisis an example of a positive feedback, providing a physical mechanism for multiplying theoriginal impetus for change beyond its initial amount.

Some mechanisms provide a negative feedback, which decreases the initial impetus. Forexample, increasing the amount of water vapor in the air may lead to forming more clouds.Low-level, white clouds reflect sunlight, thereby preventing sunlight from reaching the

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7'HE LAYERS OF THE ATMOSPHERE

Stratosphere. Extends from the tropopause to the stratopause (-45 to 55 kIn altitude);temperature increases with altitude, leading to a layer in which vertical mixing isslow.

Mesosphere. Extends from the stratopause to the mesopause (-80 to 90 kIn altitude);temperature decreases with altitude to the mesopause, which is the coldest point inthe atmosphere; rapid vertical mixing.

Thermosphere. The region above the mesopause; characterized by high temperaturesas a result of absorption of short wavelength radiation by N2 and O2; rapid verticalmixing. The ionosphere is a region of the upper mesosphere and lower thermospherewhere ions are produced by photoionization.

Exosphere. The outermost region of the atmosphere (>500 kIn altitude) where gas mol-ecules with sufficient energy can escape from the Earth's gravitational attraction.

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3'M3HdSOW.LV 3ffi8

VARIATION OF PRESSURE WITH HEIGHT IN THE ATMOSPHERE 9

Absorption of solar ultraviolet radiation by 03 causes the temperature in the stratosphere tobe much higher than expected, based on simply extending the troposphere's lapse rate intothe stratosphere.

1.4 VARIATION OF PRESSURE WITH HEIGHTIN THE ATMOSPHERE

The variation of pressure with height in the atmosphere can be addressed with the hydro-static equation,!

dp(z)dz .p(z)g (1.1)=

where p(z) is the mass density of air at height z and g is the acceleration due to gravity.From the ideal gas law,

MairP(Z)

RT(z)p(z) = (1.2)

where Mair is the average molecular weight of air (28.97 g mol-I). Thus

dp(z)dz

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RT(z)(1.3)-

which we can rewrite as

(1.4)d lnp(z) - -~dz - H(z)

where H(z) = RT(z)/ Mairg is a characteristic length scale for decrease of pressure with

height.The temperature in the atmosphere varies by less than a factor of 2, while the pressure

changes by six orders of magnitude (see Table A.8). If the temperature can be taken to beapproximately constant, just to obtain a simple approximate expression for p(z), then the

'Units of pressure. Because instruments for measuring pressure, such as the manometer, often contain mercury,commonly used units for pressure are based on the height of the mercury column (in millimeters) that the gaspressure can support. The unit mm Hg is often called the Torr in honor of the scientist, Evangelista Torricelli. Arelated unit for pressure is the standard atmosphere (abbreviated atm):

1 standard atmosphere = 1 atm = 760 mm Hg = 760 Torr

The unit of pressure in the International System of Units (SI) is newtons per meter squared (N m-'), which iscalled the pascal (Pa). In terms of pascals, the standard atmosphere is 1.01325 x 10s Pa. Another commonly usedunit of pressure in atmospheric science is the millibar (mbar), which is equivalent to the hPa (see Tables A.5 andAR) Thp .t"nti"rti "tmn.nhprP i. 101, ?~ mh"r

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11ARGE-SCALE MOTION OF THE ATMOSPHERE

to the tropics must pass through more atmosphere and intercept a larger surface area. Theuneven distribution of energy resulting from latitudinal variations in insolation and fromdifferences in absorptivity of the Earth's surface leads to the large-scale air motions of theEarth. In particular, the tendency to transport energy from the tropics toward the pola( re-gions, thereby redistributing energy inequalities on the Earth, is the overall factor govern-ing the general circulation of the atmosphere.

In order to visualize the nature of the general circulation of the atmosphere, we can thinkof the atmosphere over either hemisphere as a fluid enclosed within a long, shallow con-tainer, heated at one end and cooled at the other. Because the horizontal dimension of the"container" is so much greater than its vertical dimension, the curvature of the Earth can beneglected, and the container can be considered to be rectangular. If such a container wereconstructed in the laboratory and the ends differentially heated as described above, onewould observe a circulation of the fluid, consisting of rising motion along the heated walland descending motion along the cooled wall, flow in the direction of warm to cold at thetop of the box, and flow in the direction of cold to warm along the bottom of the box. In theatmosphere, then, the tendency is for warm tropical air to rise and cold polar air to sink,with poleward and equatorward flows to complete the circulation.

However, the general circulation of the atmosphere is not as simple as just described.Another force arises because of the motion of the Earth, the Coriolis force. At the Earth'ssurface an object at the equator has a greater tangential velocity than one in the temperatezones. Air moving toward the south cannot acquire an increased eastward (the Earth rotatesfrom west to east) tangential velocity as it moves south and thus, to an observer on theEarth, appears to acquire a velocity component in the westward direction. Thus air movingsouth in the Northern Hemisphere appears to lag behind the Earth. To an observer on theEarth it appears that the air has been influenced by a force in the westward direction. To anobserver in space, it would be clear that the air is merely trying to maintain straight-linemotion while the Earth turns below it. Friction between the wind and the ground dimin-ishes this effect in the lower atmosphere.

From the standpoint of air motion, the atmosphere can be segmented vertically into twolayers. Extending from the ground up to about 1000 m is the planetary boundary laye!; thezone in which the effect of the surface is felt and in which the wind speed and direction aregoverned by horizontal pressure gradients, shear stresses, and Coriolis forces. Above theplanetary boundary layer is the geostrophic laye!; in which only horizontal pressure gradi-ents and Coriolis forces influence the flow. .

To predict the general pattern of macroscale air circulation on the Earth we must con-sider both the tendency for thermal circulation and the influence of Coriolis forces. Figure1.2 shows the nature of the general circulation of the atmosphere. At either side of the equa-tor is a thermal circulation, in which warm tropical air rises and cool northern air flows to-ward the equator. The circulation does not extend all the way to the poles because radiativecooling of the upper northward flow causes it to subside (fall) at about 30° Nand S latitude.The Coriolis force acting on these cells leads to easterly winds, called the trade winds. Thesame situation occurs in the polar regions, in which warm air from the temperate zonesmoves northward in the upper levels, eventually cooling by radiation and subsiding at thepoles. The result is the polar easterlies.

In the temperate regions, between 40° and 55° latitude, influences of both tropical andpolar regions are felt. The major feature of the temperate regions is large-scale weather sys-tems, which results in the circulation shown in Figure 1.2. The surface winds in theNorthern Hemisphere are westerlies because of the Coriolis force.

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exchange is that air is forced into the stratosphere by tropical cumulus convective turrets.More consistent, however, is that the net flux from the tropical troposphere to the stratos-phere is actually a result of the wave-driven pumping from the extratropical stratosphere(the large horizontal arrows in Figure 1.3). It is this pumping that is the cause of the steadyascent of air in the tropical stratosphere (Holton et al., 1995). The shaded region of thestratosphere, the lowermost stratosphere, is the only part of the stratosphere that can re-ceive material from the troposphere by transport along surfaces of constant potential tem-

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TEMPERATURE AND WATER VAPOR

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LatitudeFIGURE 1.4 Mean atmospheric temperature over the period 1980 to 1989 between 1000 mbar and50 mbar averaged around a latitude band (Salstein. 1995). Data not available in blackened areas.

the average temperature exceeds 295 K. The annual mean temperature structure is largelysymmetric about the equator (although the highest temperature occurs at about 10° N),with the difference in mean surface temperature between the tropics and the poles about35°C. At the top of the troposphere, about the 200 mbar level, the meridional temperaturegradient begins to reverse; at 100 mbar, for example, temperature increases poleward byabout 20°C.

Water vapor is distributed throughout the lower troposphere, at highly variable levels.The water vapor content of the atmosphere can be expressed in a variety of ways:

1. Mole (or volume) mixing ratio--moles of water vapor per mole of air (see Section1.7).

2. Amount of water vapor to dry air by mass [g H2O (kg dry air)-'].3. Specific humidity-proportion of water vapor to total air [g H2O (kg air)-'].4. Relative humidity-ratio of the specific humidity to the maximum specific humid-

ity possible at a given temperature and pressure (dimensionless). (See Section 1.7.)

5. Mass concentration g H2O (m3 air)-'.6. Mass mixing ratio g H2O (g air)-'.

Figure 1.5 shows the zonal mean specific humidity for the period 1980 to 1989. Maximumspecific humidities are reached in the tropics, about 16 g kg-I. By the 500 mbar altitude,the value over the tropics has decreased to 2 g kg-I. This value of 2 g kg-I also holds inthe northern and southern polar regions.

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81 3~3HdSOW.LY3H.L

EXPRESSING THE AMOUNT OF SUBSTANCE IN THE ATMOSPHERE 19

Thus the mixing ratio ~i and the molar concentration are related by

Cj~ j = -;;jiiT

(1.8)

-~=~- pfRT p

where Pi is the partial pressure of i.Concentration (mol m-3) depends on pressure and temperature through the ideal gas

law. Mixing ratios, which are just mole fractions, are therefore better suited than concen-trations to describe abundances of species in air, particularly when spatial and temporalvariation is involved. The inclusion of water vapor in the totality of gaseous substances ina volume of air means that mixing ratio will vary with humidity. The variation can amountto several percent. Sometimes, as a result, mixing ratios are defined with respect to dry air.

It has become common use in atmospheric chemistry to describe mixing ratios by thefollowing units:

10-6

10-9

10-12

.umolnmolpmol

parts per million (ppm)parts per billion (ppb)parts per trillion (ppt)

These quantities are sometimes distinguished by an added v (for volume) and m (for mass),that is,

parts per million by volumeparts per million by mass

ppmvppmm

Unless noted otherwise, we will always use mixing ratios by volume and not use the addedv. The parts per million, parts per billion, and parts per trillion measures are not SI units;the SI versions are, as given above, JLmol mol-I, nmol mol-I, and pmol mol-I.

The concentration of air molecules at any temperature and pressure can be computedfrom the ideal gas law (1.7). At T = 298 K and p = 1 atm, for example, the concentration,expressed in molecules cm-3, is

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molm3

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21COMPOSITION OF THE ATMOSPHERE

1.8 COMPOSITION OF THE ATMOSPHERE

The atmosphere is composed primarily of nitrogen, oxygen, and several noble gases, theconcentrations of which have remained remarkably fixed over time. Also present are a

number of trace gases that occur in relatively small and sometimes highly variableamounts.

In spite of its apparent unchanging nature, the atmosphere is in reality a dynamic sys-tem, with its gaseous constituents continuously being exchanged with vegetation, theoceans, and biological organisms. The so-called cycles of the atmospheric gases involve anumber of physical and chemical processes. Gases are produced by chemical processeswithin the atmosphere itself, by biological activity, volcanic exhalation, radioactive decay,and human industrial activities. Gases are removed from the atmosphere by chemical reac-tions in the atmosphere, by biological activity, by physical processes in the atmosphere(such as particle formation), and by deposition and uptake by the oceans and earth. The av-erage lifetime of a gas molecule introduced into the atmosphere can range from seconds tomillions of years, depending on the effectiveness of the removal processes. Most of thespecies considered air pollutants (in a region in which their concentrations exceed substan-tially the normal background levels) have natural as well as man-made sources. Therefore,in order to assess the effect man-made emissions may have on the atmosphere as a whole,it is essential to understand the atmospheric"cycles of the trace gases, including natural andanthropogenic sources as well as predominant removal mechanisms.

The important atmospheric gases are listed in Table 1.1 arranged according to the natureof their global cycles. The total quantity of a species both in the atmosphere and dissolved

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23RADIATION

erals at the Earth's surface. Thus the oxygen concentration in the atmosphere is probably aresult of both accumulation and geochemical cycles.

While in the air, a substance can be chemically altered in one of two ways. First, the sun-light itself may contain sufficient energy to break the molecule apart, a so-called photo-chemical reaction. The more frequently occurring chemical alteration, however, takesplace when two molecules interact and undergo a chemical reaction to produce newspecies. Atmospheric chemical transformations can occur homogeneously or heteroge-neously. Homogeneous reactions occur entirely in one phase; heterogeneous reactions in-volve more than one phase, such as a gas interacting with a liquid or with a solid surface.

During transport through the atmosphere, all but the most inert substances are likely toparticipate in some form of chemical reaction. This process can transform a chemical fromits original state, the physical (gas, liquid, or solid) and chemical form in which it first en-ters the atmosphere, to another state that may have either similar or very different charac-teristics. Transformation products can differ from their parent substance in their chemicalproperties, toxicity, and other characteristics. These products may be removed from the at-mosphere in a manner very different from that of their precursors. For example, when asubstance that was originally emitted as a gas is transformed into a particle, the overall re-moval is usually hastened since particles often tend to be removed from the air more

rapidly than gases.In spite of the fact that the atmosphere is composed predominantly of relatively inert

molecules such as Nz and Oz, it is actually a rather efficient oxidizing medium. One reasonfor the atmosphere's oxidizing capacity arises because the atmosphere contains minuteamounts of very reactive molecular fragments, called free radicals. The most importantfree radical in the chemistry of the troposphere is the hydroxyl (OH) radical, which reactswith nearly every molecular species in the atmosphere. In addition, the atmosphere con-tains trace amounts of species less reactive than free radicals but nonetheless reactiveenough to attack a variety of airborne compounds. Ozone (03) is one important oxidizer,which also participates in the formation of the hydroxyl radical.

Once emitted, species are converted at various rates into substances generally charac-terized by higher chemical oxidation states than their parent substances. Frequently this ox-idative transformation is accompanied by an increase in polarity (and hence watersolubility) or other physical and chemical changes from the precursor molecule. An exam-ple is the conversion of sulfur dioxide (SOz) into sulfuric acid (HzS04). Sulfur dioxide ismoderately water soluble, but its oxidation product, sulfuric acid, is so water soluble thateven single molecules of sulfuric acid in air immediately become associated with watermolecules. The demise of one substance through a chemical transformation can becomeanother species in situ source. In general, then, a species emitted into the air can be trans-formed by a chemical process to a product that may have markedly different physico-chemical properties and a unique fate of its own.

1.9 RADIATION

Basically all the energy that reaches the Earth comes from the Sun. The absorption and lossof radiant energy by the Earth and the atmosphere are almost totally responsible for theEarth's weather, both on a global and local scale. The average temperature on the Earth re-

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RADIATION 25

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27RADIATION

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Wavelength, ~mFIGURE 1.8 Spectral irradiance (W m-2 p,m-l) of a blackbody at 300 K.

As can be seen from Figures 1.7 and 1.8, the higher the temperature, the greater is the emis-sive power (at all wavelengths). We also see that, as temperature increases, the maximumvalue of FB(A) moves to shorter wavelengths. The wavelength at which the maximumamount of radiation is emitted by a blackbody is found by differentiating (1.14) with re-spect to A, setting the result equal to zero, and solving for A. The result with A expressed

in nm and T in kelvin units is

2.897 X 106

T(1.15)Amax =

Thus hot bodies not only radiate more energy than cold ones, they do so at shorter wave-lengths. The wavelengths for the maxima of solar and terrestrial radiation are 480 nm andabout 10,000 nm, respectively. The Sun, with an effective surface temperature of about6000 K, radiates about 2 X 105 more energy per square meter than the Earth at 300 K.

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29RADIATION

If (1.14) is integrated over all wavelengths, the total emissive power F B (W m -1 of ablackbody is found to be

aT4 (1.16)

where u = 5.671 X 10-8 W m-2 K-4, the Stefan-Boltzmann constant.

1.9.2 Absorption of Radiation by Gases

Absorption of radiation by gases is one of the most important aspects of both global mete-orology and atmospheric chemistry. The solar spectrum is radically altered by absorptionas the radiation traverses the atmosphere. It is important to note that the molecules that areresponsible for the most pronounced absorption of both solar and terrestrial radiation arethe minor constituents of the atmosphere, not N2 and O2. Thus ozone in the upper atmos-phere effectively absorbs all solar radiation below 290 nm, whereas water vapor and car-bon dioxide absorb much of the long-wave terrestrial radiation. The most significantabsorbing gases in the atmosphere are O2, 03, H2O, and CO2, Figure 1.9 shows the solar ir-radiance at the top of the atmosphere and that at sea level. The absorption spectra are quitecomplex, but they do indicate that absorption is so strong in some spectral regions that nosolar energy in those regions reaches the surface of the Earth. For example, absorption byO2 and 03 is responsible for removal of practically all the incident radiation with wave-lengths shorter than 290 nm. However, atmospheric absorption is not strong from 300 to

about 800 nm, forming a "window" in the spectrum. About 40% of the solar energy is con-centrated in the region of 400 to 700 nm. Water vapor absorbs in a complicated way, andmostly in the region where the Sun's and Earth's radiation overlap. From 300 to 800 nm,the atmosphere is essentially transparent. From 800 to 2000 nm, terrestrial long-wave radi-ation is moderately absorbed by water vapor in the atmosphere. Table 1.2 summarizes the

attenuation of solar radiation by the atmosphere.Figure 1.10 shows the penetration of radiation as a function of height in the atmosphere.

Wavelengths shorter than about 100 nm are absorbed by O2 and N2 and do not penetrate be-low 100 krn. O2 absorbs strongly in the range 100 to 175 nm, the so-calledSchumann-Runge continuum, and also in the range 175 to 200 nm, the Schumann-Rungebands. Wavelengths in the 200 to 245 nm range are absorbed in the stratosphere, mainly byO2 (the weak Herzberg continuum). Wavelengths between 200 and 230 nm do penetrate aslow as 30 krn altitude. Ultraviolet absorption by ozone, which peaks near 254 nm (theHartley band of 03 absorption), attenuates solar radiation over the entire range of 230 to300 nm. As a result, solar radiation of wavelengths shorter than about 290 to 300 nm does

not reach the Earth's surface.Why molecules absorb in particular regions of the spectrum can be determined only

through quantum chemical calculations. In general, the geometry of the molecule explains,for example, why H2O, CO2, and 03 interact strongly with radiation above 400 nm but N2and O2 do not. In H2O, for instance, the center of the negative charge is shifted toward theoxygen nucleus and the center of positive charge toward the hydrogen nuclei, leading to aseparation between the centers of positive and negative charge, a so-called electric dipolemoment. Molecules with dipole moments interact strongly with electromagnetic radiation

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Wavelength, nmFIGURE 1.10 Depth of penetration of solar radiation through the atmosphere. Altitudes corre-spond to an attenuation of lIe (Kluwer Academic Publishers Aeronomy of the Middle Atmosphere,1984, Brasseur, G. and Solomon, S. with kind permission from Kluwer Academic Publishers).

because the electric field of the wave causes oppositely directed forces and therefore ac-celerations on electrons and nuclei at one end of the molecule as compared with the other.Similar arguments hold for ozone; however, nitrogen and oxygen are symmetric and thusare not strongly affected by radiation above 400 nm. The CO2 molecule is linear but caneasily be bent, leading to an induced dipole moment. A transverse vibrational mode existsfor CO2 at 15 JLm, just where the Earth emits most of its infrared radiation.

Considering the outgoing long-wave infrared radiation, the spectral region from about 7to 13 JLm is also a window region; nearly 80% of the radiation emitted by the Earth in this

region escapes to space. Most of the non-CO2 greenhouse gases, including 03, CH4, N2O,and the chlorofluorocarbons, all have strong absorption bands in this window region. Forthis reason, relatively small changes in the concentrations of these gases can produce a sig-nificant change in the net radiative flux. As the concentration of a greenhouse gas contin-ues to increase, it can absorb more of the radiation in its energy bands. Once an absorptionwavelength becomes saturated, further increases in the concentration of the gas have lessand less effect on radiative flux. This is called the band saturation effect. For CO2, for ex-ample, the 15 JLm band is already close to saturated. In addition, if a gas absorbs at wave-lengths that are also absorbed by other gases, then the effect of increasing concentrationson radiative flux is less than in the absence of band overlap. For example, there is signifi-cant overlap between some of the absorption bands of CH4 and N2O; this overlap must becarefully accounted for when calculating the effect of these gases on radiative fluxes.

Even with the band saturation effect, it is incorrect to conclude that because there is al-ready so much CO2 in the atmosphere, more CO2 can have no additional effect on absorp-tion of outgoing radiation. When gases are present in small concentrations, doubling theconcentration of the gas will approximately double its absorption. When an absorbing gasis present in high concentration the effect of further addition is not one-to-one but it is not

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33ENERGY BALANCE FOR EARTH AND ATMOSPHERE

in this portion of the spectrum. Away from this band, however, where CO2 is less stronglyabsorbing, the increase in CO2 does have an effect. As more and more CO2 is added to theatmosphere, more of its spectrum will become saturated, but there will always be regionsof the spectrum that remain unsaturated and thus capable of continuing to absorb infraredradiation. For example, the 10 .urn absorption band is about 106 times weaker than the peakof the 15 .urn band, but its contribution to the irradiance change in the lower frame is im-portant. And as CO2 concentrations increase, the importance of the 10 .urn band will con-

tinue to increase relative to the 15 .urn band.

1.10 ENERGY BALANCE FOR EARTH AND ATMOSPHERE

The Earth's climate is controlled by the amount of solar radiation intercepted by the planetand the fraction of that energy that is absorbed. The flux density of solar energy, integratedover all wavelengths, on a surface oriented perpendicular to the solar beam at the Earth'sorbit is about 1370 W m-2. This is called the solar constant. 3 Let the solar constant be de-

noted by So = 1370 W m-2. The cross-sectional area of the Earth that intercepts the solarbeam is 1TR2, where R is the Earth's radius. The surface area of the Earth that receives theradiation is 41TR2. Thus the fraction of the solar constant received per unit area of the Earthis (1TR2 /41TR1 = 1/4 of the solar constant, about 343 W m-2. Of this incoming solar radi-ation, a fraction is reflected back to space; that fraction, which we can denote by Rp, is theglobal mean planetary reflectance or albedo. Rp is about 0.3 (Ramanathan, 1987;Ramanathan et al., 1989). Contributing to Rp are clouds, scattering by air molecules, scat-tering by atmospheric aerosol particles, and reflection from the surface itself, the surfacealbedo (the surface albedo is denoted as Rs). The fraction 1 - Rp represents that fraction

of solar short-wave radiation that is absorbed by the Earth-atmosphere system. ForRp = 0.3, this corresponds to about 240 W m-2. This amount is matched, on an annual andglobal average basis, by the long-wave infrared radiation emitted from the Earth-atmos-phere system to space (Figure 1.12). The infrared radiative flux emitted at the surface of theEarth, about 390 W m-2, substantially exceeds the outgoing infrared flux of 240 W m-2 atthe top of the atmosphere. Clouds, water vapor, and the greenhouse gases (GAGs) both ab-sorb and emit infrared radiation. Since these atmospheric constituents are at temperatureslower than that at the Earth's surface, they emit infrared radiation at a lower intensity thanif they were at the temperature of the Earth's surface and therefore are net absorbers of

energy.The equilibrium temperature of the Earth can be estimated by a simple model that

equates incoming and outgoing energy (Figure 1.13). Incoming solar energy at the surface

of the Earth is

(1.17)SoFs = -(1 - Rp)

4

3Since the late 1970s, regular satellite measurements of the solar constant have been perfonned (Mecherikunnelet aI., 1988). Maximum differences in the value of So among the instruments is about 2 W m-2, corresponding toa little more than 0.1 % of the value of So. Over the period 1980 to 1986 the so-called SMM/ ACRIM instrumentmeasured an average value of So of about 1386 W m-2, whereas that on NIMBUS- 7 reported an average So of

about 1370 W m-2.

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Reflected

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For Rp = 0.30, this equation gives T e = 255 K. If the Earth were totally devoid of clouds,then the global albedo would be about Rp = 0.15. With this value of Rp, the equilibriumtemperature T e = 268 K. This simple equation predicts that T e varies about 0.5 K for a10 W m-2 (0.7%) variation in the solar constant, or for a reflectance variation around Rp =0.3 of ~Rp = 0.005.

The net radiative energy input, F net = F s - F L, is zero at equilibrium. If a perturbation

occurs then the change in net energy input is related to the changes in both solar and long-

wave components by

= ~Fs - ~FL (1.20)

To reestablish equilibrium, a temperature change ~T e results, which can be related to ~F net

by a parameter }.O,

where Ao, having units K (W m-1-1 is called the climate sensitivity factor. If we neglectany feedbacks in the climate system, Ao can be estimated as (8Fe/8Te)-I,

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Global climate change is induced by a forcing that disturbs the equilibrium and leads toa nonzero average downward net flux at the top of the atmosphere (TO A),

(1.23)So-Foe! = -(1 - Rp) - FL

4

It is customary to write (1.23) in terms of downward flux, -Fnet, at the TOA; an increaseof - F net corresponds to heating of the planet. Primary forcing can occur as a result ofchanges of So, Rp, or FL, Changes in incoming solar radiation have resulted from changesin the Earth's orbit and fromyariations in the Sun's output of energy. Changes in the plan-etary albedo Rp can result from changes in surface reflectance from human activity (agri-culture, deforestation), from changes in the aerosol content of the atmosphere from bothnatural (volcanoes) and anthropogenic (industrial emissions, biomass burning) causes, andto a lesser extent from changes in levels of gases that absorb solar wavelengths (e.g.,ozone). Changes in the emitted long-wave flux F L result primarily from changes (increases)of absorbing gases in the atmosphere and to a lesser extent from changes in aerosols. As wehave seen, in the long-wave portion of the spectrum gases and aerosols absorb much of theradiation emitted by the surface and reemit radiation to space at their lower temperature.

1.10.1 Solar Variability

The amount of solar radiation reaching Earth and Earth's changing orientation to the Sunhave been the major causes for climatic change throughout its history. If the Sun's radia-tion intensity declined 5 to 10% and there were no other compensating factors, ice wouldengulf the planet in less than a century. Although no theory exists to predict future changesin solar output, the effect of changes in Earth's orbit as it travels around the Sun is begin-ning to be understood. During the past million years, Earth has experienced 10 major and40 minor episodes of glaciation. All appear to have been controlled by three so-called or-

bital elements that vary cyclically over time.First, Earth's tilt changes from 22° to 24.5° and back again every 41,000 years. Second,

the month when Earth is closest to the Sun also varies over cycles of 19,000 and 24,000years. Currently, Earth is closest to the Sun in January. This month-of-closest-approachfactor can make a difference of 10% in the amount of solar radiation reaching a particularlocation in a given season. Last, the shape of Earth's orbit varies from being nearly circu-lar to being more elliptical with a period of 100,000 years. The climatic cycles caused bythese orbital factors are called Milankovitch cycles after the Serbian mathematicianMilutin Milankovitch, who first described them in 1920. Superimposed on theMilankovitch cycles are changes in the Sun that occur over days or months or a few years.Over the period 1979 to 1990, for example, total solar irradiance varied by about 0.1 %

(Hickey et al., 1988; Willson and Hudson, 1988).Even though studies of ocean cores have shown that these orbital changes are the prin-

cipal determinant of the times of glaciation, the exact mechanisms by which Earth re-sponds to the orbital changes have not been established. Orbital changes alone appear notto have caused the vast climate shifts associated with glaciation and deglaciation.Feedbacks, such as changes in Earth's reflectivity, amount of particles in the atmosphere,and the carbon dioxide and methane content of the atmosphere, act together with orbitalchanges to enhance global warming and cooling. The levels of carbon dioxide and

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~OENERGY BALANCE FOR EARTH AND ATMOSPHERE

from the Earth, and nonradiative processes. Of the 100 units of incoming solar flux:

-26 units are absorbed within the atmosphere (-22 by cloud-free air and -4 by

clouds)- 30 units are reflected back to space 4 (- 7 from the cloud-free atmosphere, -17 from

the cloudy atmosphere, and -6 from the Earth's surface)-44 units absorbed by the Earth's surface

The Earth-atmosphere system emits thermal infrared radiation. The upward flux from theEarth's surface is -115 units. The cloud-free atmosphere emits -33 units back to theEarth's surface and -34 units out to space. The cloudy atmosphere emits -67 units backto Earth and -36 units out to space. Thus -70 units of infrared radiation leave the top ofthe atmosphere, balancing the net -70 units of solar radiation penetrating the top of the at-mosphere. The net upward flux of infrared radiation at the surface of the Earth is -15 units,consisting of -115 units emitted by the Earth and -100 units radiated back to Earth by the

cloud-free and cloudy atmosphere.The incoming solar energy absorbed by the Earth is -44 units; this is balanced by the

net upward flux of infrared radiation of -15 units, plus -6 unit loss by sensible heat con-duction, and - 23 unit loss by latent heat. The Earth emits -115 units of infrared radiationto the atmosphere, whereas the atmosphere emits -170 units of infrared radiation, a netdeficit of -55 units. Since the atmosphere absorbs -26 units of solar radiation, the net ra-diative loss from the atmosphere is -29 units; this is made up for by the sensible and latentheat fluxes. The net radiative cooling of the atmosphere is thus balanced by the latent heatof condensation released in precipitation processes and by the convection and conduction

of sensible heat from the surface.The average annual ratio of sensible to latent heat loss at the surface is called the Bowen

ratio. With -6 units of sensible heat loss and -23 units of latent heat loss, the Bowen ra-

tio is -0.27.Figure 1.16 shows the zonally annual averaged absorbed solar and emitted infrared

fluxes, as observed from satellites. We note a net gain of radiative energy between about40° Nand 40° S, and a net loss of energy in the polar regions. This pattern results largelyfrom the decrease in insolation to the polar regions in winter and from the high surfacealbedo in the polar regions. The outgoing infrared flux displays only a small latitudinal de-pendence. The tendency for the outgoing infrared flux to be greatest in the tropics wherethe surface temperature is largest is muted by the larger amount of atmospheric water va-por and the higher and colder clouds in the tropics. As a result of the net gain of radiativeenergy in the tropics and the net loss in the polar regions, an equator-to-pole temperature

gradient is generated.

'The average value of the albedo, the incoming radiation that is reflected or scattered back to space without ab-sorption, is usually taken to be somewhere in the range of 30 to 34%. It is important to note that the albedo variesconsiderably, depending on the surface of the Earth. For example, in the polar regions, which are covered by iceand snow, the reflectivity of the surface is very high. On the other hand, in the equatorial regions, which arelargely covered with oceans, the reflectivity is low, and most of the incoming energy is absorbed by the surface.

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SPATIAL AND TEMPORAL SCALES OF ATMOSPHERIC PROCESSES 41

Regional or Synoptic toMesoscale Glohal ~cale

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dimensions. Four rough categories have proved convenient to classify atmospheric scalesof motion:

1. Microscale. Phenomena occurring on scales of the order of 0 to 100 m, such as themeandering and dispersion of a chimney plume and the complicated flow regime inthe wake of a large building.

2. Mesoscale. Phenomena occurring on scales of tens to hundreds of kilometers,such as land-sea breezes, mountain-valley winds, and migratory high- and low-pressure fronts.

3. Synoptic Scale. Motions of whole weather systems, on scales of hundreds to thou-sands of kilometers.

4. Global Scale. Phenomena occurring on scales exceeding 5 X 103 kin.

Spatial scales characteristic of various atmospheric chemical phenomena are given inTable 1.3. Many of the phenomena in Table 1.3 overlap; for example, there is more or lessof a continuum between (1) urban and regional air pollution, (2) the aerosol haze associ-ated with regional air pollution and aerosoVclimate interactions, (3) greenhouse gas in-creases and stratospheric ozone depletion, and (4) tropospheric oxidative capacity andstratospheric ozone depletion. The lifetime of a species is the averal!:e time that a molecule

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FIGURE 1.17 Spatial and temporal scales of variability for atmospheric constituents.

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DERIVATION OF THE GEOSTROPHIC WIND SPEED 43

atmosphere's scales of motion. Much of this book will be devoted to understanding the ex-quisite interactions between chemical and transport processes in the atmosphere. In antici-pation of much of the remainder of this book, Table 1.4 summarizes atmospheric effects oftrace gases.

DERIVATION OF THE GEOSTROPffiC WIND SPEEDAPPENDIXl

The direction of winds in the geostrophic layer is determined by horizontal pressure gradi-ents and Coriolis forces. As we have discussed, an air parcel moving southward in theNorthern Hemisphere as a result of pressure gradients is accelerated toward the west by theCoriolis force. We can actually compute the wind speed and direction at any latitude as afunction of the prevailing pressure gradient if we assume that only pressure and Coriolisforces influence the flow.

It can be shown that the acceleration experienced by an object on the surface of theEarth (or in the atmosphere) moving with a velocity vector u consists of two components,-0 x (0 x r) and - 2(0 x D), where 0 is the angular rotation vector for the Earth and

r is the radius vector from the center of the Earth to the point in question. The first term issimply the centrifugal force, in a direction that acts normal to the Earth's surface and iscounterbalanced by gravity. The second term, 0 x u, is the Coriolis force. This forcearises only when an object, such as an air parcel, is moving; that is U :;t: O. Even thoughthe Coriolis force is of much smaller magnitude than the centrifugal force, only the Coriolisforce has a horizontal component. Since the winds are horizontal in the geostrophic layer,the Coriolis acceleration is given by the horizontal component of the Coriolis term, namely,2uG Q sin cf>, where Q is the rate of rotation of the Earth and cf> is the latitude. The direc-tion of the Coriolis force is perpendicular to the wind velocity, as shown in Figure I.A.I.Wind speed UG at latitude cf> lies in the horizontal plane.

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45DERIVATION OF THE GEOSTROPHIC WIND SPEED

Low p

~ Parcel initiallyat rest here

FIGURE 1.A.2 Approach to geostrophic equilibrium.

We usually denote 20 sin r/> by f, called the Coriolis parameter. From the continuity equa-tion (I.A.I), we see that au/ax = 0, since v = w = O. Thus from (I.A.5) op/ox = 0, and

the direction of flow is perpendicular to the pressure gradient op/oy. In addition, from(I.A.6), we see that the component of the Coriolis force, -ju, is exactly balanced by thepressure gradient, (1/ p) op/oy. Therefore the geostrophic wind speed UG is given by

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The approach to the geostrophic equilibrium for an air parcel starting from rest, acceleratedby the pressure gradient and then affected by the Coriolis force, is shown in Figure I.A.2.

The geostrophic balance determines the wind direction at altitudes above about 500 m.In order to describe the air motions at lower levels we must take into account the frictionof the Earth's surface. The presence of the surface induces a shear in the wind profile, as ina turbulent boundary layer over a flat plate generated in a laboratory wind tunnel. In ana-lyzing the geostrophic wind speed we found that for steady flow a balance exists betweenthe pressure force and the Coriolis force. Consequently, steady flow of air at levels near theground leads to a balance of three forces: pressure force, Coriolis force, and friction forcedue to the Earth's surface. Thus, as shown in Figure 1.A.3, the net result of these threeforces must be zero for a nonaccelerating air parcel. Since the pressure gradient force F pmust be directed from high to low pressure, and the frictional force F f must be directed op-posite to the velocity u, a balance can be achieved only if the wind is directed at some an-gle toward the region of low pressure. This angle between the wind direction and theisobars increases as the ground is approached since the frictional force increases. At theground, over open terrain, the angle of the wind to the isobars is usually between 10° and20°. Because of the relatively smooth boundary existing over this type of terrain, the windspeed at a 10 m height (the height at which the so-called surface wind is usually measured)

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PROBLEMS 47

REFERENCES

Bentley, C. R. (1997) Rapid sea-level rise soon from West Antarctic Ice Sheet collapse? Science, 275,1077-1078.

Boering, K. A. et al. (1995) Measurements of stratospheric carbon dioxide and water vapor at north-ern midlatitudes: implications for troposphere-to-stratosphere transport, Geophys. Res. Lett., 22,2737-2740.

Brasseur, G., and Solomon, S. (1984) Aeronomy of the Middle Atmosphere. Reidel, Dordrecht, TheNetherlands.

Cloud, P. (1983). The biosphere. Sci. Am., 249, 176-189.

Graedel, T. E., and Crutzen, P. J. (1989) The changing atmosphere, Sci. Am., 261,58-68.Hickey, J. R., Alton, B. M., Kyle, H. L., and Hoyt, D. (1988) Total solar irradiance measurements by

ERB/Nimbus-7: a review of nine years, Space Sci. Rev., 48,321-342.Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B., and Pfister, L. (1995)

Stratosphere-troposphere exchange, Rev. Geophys., 33,403-439.Intergovernmental Panel on Climate Change (IPCC) (1995) Climate Change 1994: Radiative

Forcing of Climate Change and an Evaluation of the 1PCC IS92 Emission Scenarios. CambridgeUniversity Press, Cambridge, UK.

Iqb~l, M. (1983) An Introduction to Solar Radiation. Academic Press, Toronto.Liou, K. N. (1992) Radiation and Cloud Processes in the Atmosphere. Oxford University Press,

Oxford, UK.Mecherikunnel, A. T., Lee, R. B., Kyle, H. L., and Major, E. R. (1988) Intercomparison of solar total

irradiance data from recent spacecraft measurements, J. Geophys. Res., 93,9503-9509.Prather, M., McElroy, M., Wofsy, S., Russell, G., and Rind, D. (1987) Chemistry of the global tro-

posphere: fluorocarbons as tracers of air motion, J. Geophys. Res., 92,6579-6613.Ramanathan, V. (1987) The role of earth radiation budget studies in climate and general circulation

research, J. Geophys. Res., 92,4075-4095.Ramanathan, V., Cess, R. D., Harrison, E. F., Minnis, P., Barkstrom, B. R., Ahmad, E., and Hartmann,

D. (1989) Cloud-radiative forcing and climate: results from the earth radiation budget experiment,Science, 243,57-63.

Salstein, D. A. (1995) Mean properties of the atmosphere, in Composition, Chemistry, and Climateof the Atmosphere, edited by H. B. Singh. Van Nostrand Reinhold, New York, pp. 19-49.

Trenberth, K. E., and Guillemot, C. J. (1994) The total mass of the atmosphere, J. Geophys. Res., 99,23079-23088.

Walker, J. C. G. (1977) Evolution of the Atmosphere. Macmillan, New York.Willson, R. C., and Hudson, H. S. (1988) Solar luminosity variations in solar cycle 21, Nature, 332,

810-812.

PROBLEMS

l.lA Calculate the concentration (in molecules cm -3) and the mixing ratio (in ppm) of wa-ter vapor at ground level at T = 298 K at RH values of 50%, 60%, 70%, 80%, 90%,95%, and 99%.

The vapor pressure of pure water as a function of temperature can be calculatedwith the following correlation:

.976a2 - O.6445a3 - O.1299a4]PH10(T) = Ps exp[13.3185a-

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Virtually every element in the periodic table is found in the atmosphere; however, whenclassifying atmospheric species according to chemical composition it proves to be conve-nient to use a small number of major groupings such as:

1. Sulfur-containing compounds.

2. Nitrogen-containing compounds.

3. Carbon-containing compounds.

4. Halogen-containing compounds.

Obviously these categories are not exclusive; many sulfur-containing compounds, forexample, also include atoms of carbon. And virtually all the atmospheric halogens involvea carbon atom backbone. We do not include in the above list species of the general formulaHxOy; with the exception of water and hydrogen peroxide (H2O2), these are all radicalspecies (e.g., hydroxyl, OH) that play key roles in atmospheric chemistry but do not nec-essarily require a separate category. Every substance emitted into the atmosphere is even-tually removed so that a cycle of the elements in that substance is established. This is calledthe biogeochemical cycle of the element. The biogeochemical cycle of an element or acompound refers to the transport of that substance among atmospheric, oceanic, bio-spheric, and land compartments, the amounts contained in the different reservoirs, and therate of exchange among them. The circulation of water among oceans, atmosphere, andcontinents is a prime example of a biogeochemical cycle. The term biogeochemical cycleis often used to describe the global or regional cycles of the "life elements," C, 0, N, S, andP, with reservoirs including the atmosphere, the ocean, the sediments, and living organisms

(Rodhe, 1992).A condition of "air pollution" may be defined as a situation in which substances that re-

sult from anthropogenic activities are present at concentrations sufficiently high abovetheir normal ambient levels to produce a measurable effect on humans, animals, vegeta-tion, or materials. This definition could include any substance, whether noxious or benign;however, the implication is that the effects are undesirable. Traditionally, air pollution hasbeen viewed as a phenomenon characteristic only of large urban centers and industrializedregions. It is now clear that dense urban centers are just "hotspots" in a continuum of tracespecies concentrations over the entire Earth. Both urban smogs and stratospheric ozone de-pletion by chlorofluorocarbons are manifestations of what might be termed in the broadestsense as air pollution.

The first recognized type of air pollution was that typified by high concentrations of sul-fur compounds (S02 and sulfates) and particles, resulting from combustion of coal andhigh-sulfur-containing fuels. Cities with this characteristic type of air pollution are often incold climates where electric power generation and domestic heating are major sources ofemissions. 49

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ATMOSPHERIC RESIDENCE TIMES 51

from direct emissions of particles but also from emissions of certain gases that either con-dense as particles directly or undergo chemical transformation to a species that condensesas a particle. A full description of atmospheric particles requires specification of not onlytheir concentration but also their size, chemical composition, phase (i.e., liquid or solid),and motphology.

Once particles are in the atmo~phere, their size, number, and chemical composition arechanged by several mechanisms until ultimately they are removed by natural processes.Some of the physical and chemical processes that affect the "aging" of atmospheric parti-cles are more effective in one regime of particle size than another. In spite of the specificprocesses that affect particulate aging, the usual residence time of particles in the lower at-mosphere does not exceed several weeks. Very close to the ground, the main mechanismsfor particle removal are settling and dry deposition on surfaces; whereas at altitudes aboveabout 100m, precipitation scavenging is the predominant removal mechanism.

As air rises through a cloud and becomes slightly supersaturated with water vapor (i.e.,as its relative humidity exceeds 100%), cloud droplets form on condensation nuclei-usu-ally soluble aerosol particles (e.g., microscopic particles of various salts) that exist in theatmosphere at concentrations of 100 to .1000 cm-3-and grow by condensation of watervapor. As the droplets grow and collide with each other they become raindrops, whichgrow rapidly as they fall and accrete cloud droplets.

2.1.1 Residence Time

The fundamental physical principle governing the behavior of a chemical in the atmos-phere is conservation of mass. In any imaginary cube of air the following balance musthold:

Rate of the

speciesflowing in

Rate of the

speciesflowing out

Rate ofremoval of- the species =

Rate of intro-duction (emis-

sion) of thespecies

Rate of accumu-lation of thespecies in the

imaginary volume

+

This balance must hold from the smallest cube of air all the way up to the entireatmosphere.

If we let Q denote the total mass of the substance in the volume of air, Fin and Foul themass flow rates of the substance in and out of the air volume, respectively, P the rate of in-troduction of the species from sources, and R the rate of removal of the species, then con-servation of mass can be expressed mathematically as

dQdt

(2.1)(Fin - Fout) + (P - R)

If the amount Q of the substance in the volume or reservoir is not changing with time,then Q is a constant and dQ/dt = O. In order for Q to be unchanging, all the sources of the

substance to the reservoir must be precisely balanced by the sinks of the substance. Thismeans that

Fin + P = Foul + R (2.2)

In such a case steadv-state conditions are said to hold

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S3WI.L3d11 aNY 'S3'IJAJ 'IVaO'ID 'NOI.LISOdWOJ JI1I3HdSOW.LV

ATMOSPHERIC RESIDENCE llMES 53

The stratosphere can be considered well mixed vertically only for atmospheric specieswith residence times greatly exceeding 50 years. In fact, one of the only examples of sucha long-lived species is He, which has its source at the Earth's surface and its sink as escapethrough the very top of the atmosphere into space. Thus the stratosphere is poorly mixedvertically for essentially all atmospheric trace constituents.

Frequently the rate at which a chemical is removed from the atmosphere is proportionalto its concentration (first-order loss)-the more that is present, the faster its rate of re-moval. This is generally the case for both dry deposition at the Earth's surface and scav-enging by cloud droplets. Consider a species for which steady-state conditions hold andwhich is removed at a rate proportional to its concentration with a proportionality constantA. Such a species is 85Kr, the only significant removal process for which is radioactive de-cay. For 85Kr, then

Q 1-)..Q -)..

Thus to estimate the residence time of 85Kr does not even require knowledge of its atmos-pheric abundance Q, but only of the radioactive decay constant. Consequently, it does notmatter whether 85Kr is uniformly mixed throughout the entire atmosphere or not to estimateits lifetime. In a case where the removal process is first order, then even for a poorly mixedspecies a simple and accurate estimate for its residence time can be obtained provided thatits removal rate constant can be accurately estimated.

Now consider a species with mass Q in the atmosphere that is removed by two inde-pendent processes, the first at a rate kl Q and the second at a rate k2 Q, where kl and k2 arethe first-order removal coefficients. Its overall residence time is given by

or

~ = kl + k21:

Process 1. for example. could be dry deposition and process 2 cloud scavenging. We canactually associate time constants with the two individual removal processes,

.. = T2 =-kl

-k2

where ., can be thought of as the residence time of the species if the only removal processis process 1, which is also true for .2. From (2.8) and (2.9) we can express the overall res-idence time. in terms of the two individual removal times ., and .2 by

(2.10)..:.=..:.+..:.. .1 .2

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55SULFUR-CONTAINING COMPOUNDS

The loss processes are usually represented as first order; for example, Rt = kt Qi'

where the first-order rate constants, which we will denote by k's, must be specified. Thus(2.13) becomes

dQidt

= p.n + p.Q + p.C - (k~ + k!lJ + k'! + k~)Q,', I , I , , , (2.14)

If the concentration of the species is not changing, then a steady state may be presumedin which

p.n + p.a + p.C - ( kd + k!1' + k': + k~ ) Q, ' = 0

, , , , , , I

The mean residence time of species j can be calculated by either

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kd + k!V + k,: + k~, , I I

or

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p!' + p.a + p.CI I I

To use (2.16) the individual first-order rate constants for removal must be estimated,whereas in (2.17), estimates for the total number of moles in the troposphere, which can bederived from a concentration measurement, and for the source strength terms are needed.If the k; values are difficult to specify, mean residence times are often estimated from

(2.17).

2.2 SULFUR.CONTAINING COMPOUNDS

Sulfur is present in the Earth's crust at a mixing ratio of less than 500 parts per million bymass and in the Earth's atmosphere at a total volume mixing ratio of less than I ppm. Yet,sulfur-containing compounds exert a profound influence on the chemistry of the atmo-sphere and, likely, on climate. The main questions that we will seek to answer with respectto sulfur compounds, and indeed for all classes of atmospheric compounds, are:

1. What are the species present in the atmosphere? What are their natural and anthro-pogenic sources?

2. What chemical reactions do they undergo in the atmosphere? How fast are these re-actions?

3. What are the products of atmospheric transformations?

4. What effect does the presence of the compound and its chemical transformationproducts have on the atmosphere?

In this chapter we focus on the first question.

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61SULFUR-CONTAINING COMPOUNDS

TABLE 2.3 Observed Mixing Ratios of Atmospheric Sulfur Gases

Average Mixing Ratio (ppt)Compound and Location

3.6-7.565

35-60450-840

3656-8.5

80-1108-60

1.5-15

2-1835-1205-7

500500545

2050

160260

1500

H2SMarine surface layerCoastal regionsForestsWetlandsUrban areasFree troposphere (2-5 kin)

CH3SCH3Marine surface layerContinental surface layerFree troposphere (2-5 kin)

CS2Marine surface layerContinental surface layerFree troposphere (2-5 kin)

OCSTotal troposphereMarine surface layerContinental surface layer

SO2Marine surface layerFree troposphere (>5 km)-

Europe/North Sea/ArcticNorth America clean continentalCoastal EuropePolluted continental air

Source: Berresheim et al. (1995) (detailed references given by the authors).

2.2.1 Dimethyl Sulfide (CH~CH3)

Dimethyl sulfide (DMS) is the dominant sulfur compound emitted from the world'soceans. DMS was discovered in the surface ocean by Lovelock et al. (1972), who sug-gested that DMS may be the biogenic sulfur species that was needed at the time to balancethe global sulfur budget.

DMS is produced in oceanic waters by both benthic and planktonic marine organisms(Dacey and Wakeham, 1986), suggesting that it may be ubiquitous in the surface ocean(Barnard et al., 1982). It is thought to originate from the decomposition of dimethyl-sulfo-niopropionate produced by marine organisms, in particular, phytoplankton (Andreae,1990). Its concentration in the upper layer of the ocean varies between a few nanograms ofS per liter to a few micrograms of S per liter (Lovelock et al., 1972; Barnard et al., 1982;Andreae and Raemdonck, 1983; Cline and Bates, 1983; Nguyen et al., 1984, 1988). TheDMS surface seawater concentration is highly nonuniform; its average concentration is ap-proximately 100 nanograms (ng) of S per liter. It has been observed that the concentrationof DMS is dependent on diurnal (Andreae and Barnard, 1984) and seasonal variations(Turner and Liss, 1985), and on depth and location (Andreae and Raemdonck, 1983).

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SULFUR-CONTAINING COMPOUNDS 63

MarineAtmosphere

3.2

ContinentalAtmosphere

1.6-: Human "

" Artivity ..<

Soils andLand.

3x

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! 300

MarineBiota

?,.

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FIGURE 2.2 Major reservoirs and burdens of sulfur, in Tg(S) (Charlson et al., 1992). Reprinted bypermission of Academic Press.

and 0.57 Tg in the stratosphere. Based on the estimated global OCS source strength of0.73 Tg yr-I, the global atmospheric lifetime of OCS is estimated to be about 7 years. Wewill return to the global cycle and chemistry of OCS in Chapter 4 in connection with thestratospheric aerosol layer.

2.2.3 Sulfur Dioxide (S02)

Sulfur dioxide is the predominant anthropogenic sulfur-containing air pollutant. Mixing ra-tios of S02 in continental background air range from 20 ppt to over I ppb; in the unpollutedmarine boundary layer levels range between 20 and 50 ppt. Urban S02 mixing ratios canattain values of several hundred parts per billion. We will consider the atmospheric chem-istry of S02 in Chapter 5.

2.2.4 The Atmospheric Sulfur Cycle

Figure 2.2 depicts the major reservoirs in the biogeochemical cycle of sulfur. with esti-mated quantities (in Tg(S» in each reservoir. Directions of fluxes between the reservoirsare indicated by arrows. The major pathways of sulfur compounds in the atmosphere aredepicted in Figure 2.3. The numbers on each arrow refer to the description of the processgiven in the caption to the figure (not to fluxes). All the processes indicated schematicallyin Figure 2.3 will be studied later in this book.

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SULFUR-CONTAINING COMPOUNDS 65

The mean residence time of SO" is

QS02a7:S02 = P;02 + PS02

k~o, + k~O2 + kso,

whereas that for sulfate is

QSO4

kSO,QSO21'SO. =

kSO4d + kSO4

The mean residence time of a sulfur atom is

QSO2 + QSO4

P;O2 + P:~t's =

which can be expressed in terms of the two previous mean residence times as

1:S = 1:S02 + b1:s04 (2.23)

where

ksoz Qs~PSOz + Ps~

b= (2.24)

the fraction of S converted to SO~- before being removed.We can also define individual characteristic times such as

d ( d' 'so, = kso, .502 = (ks02) d ( d' t'SO4 = kSO4,

so that

~1"S04

wTSO,

-1"S04

We can also define the mean residence time of a sulfur atom before surface removal or pre.

cipitation scavenging by

Qs~ + QS04

kd,w Q + kd.wQSO, S02 SO. S04

d,w -TS -

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NITROGEN-CONTAINING COMPOUNDS 67

2.3 NITROGEN-CONTAINING COMPOUNDS

Aside from N2, which is extremely stable chemically and is not involved in the chemistryof the troposphere or stratosphere, the important nitrogen-containing trace species in theatmosphere are nitrous oxide (N2O), nitric oxide (NO), nitrogen dioxide (NOJ, nitric acid(HNO3), and ammonia (NH3). The first of these, nitrous oxide (N2O), is a colorless gas thatis emitted almost totally by natural sources, principally by bacterial action in the soil. Thegas is employed as an anesthetic and is commonly referred to as "laughing gas." The sec-ond, nitric oxide (NO), is emitted by both natural and anthropogenic sources. Nitrogendioxide (NOJ is emitted in small quantities from combustion processes along with NO andis also formed in the atmosphere by oxidation of NO. The sum of NO and NO2 is usuallydesignated as NOx' Nitric oxide is the major oxide of nitrogen formed during high-temper-ature combustion, resulting from both the interaction of nitrogen in the fuel with oxygenpresent in the air and the chemical conversion of atmospheric nitrogen and oxygen at thehigh temperatures of combustion. Other oxides of nitrogen, such as NO3 and N20S, existin the atmosphere in relatively low concentrations but nonetheless participate importantlyin atmospheric chemistry. Nitric acid is an oxidation product of NO2 in the atmosphere.Ammonia (NH3) is emitted primarily by natural sources. Finally, nitrate and ammoniumsalts are not emitted in any significant quantities but result from the atmospheric conver-sion of NO, NO2, and NH3'

Nitrogen is an essential nutrient for all living organisms. The primary source of this ni-trogen is the atmosphere. However, N2 is not useful to most organisms until it is "fixed" orconverted to a form that can be chemically utilized by the organisms. (Nitrogen fixationrefers to the chemical conversion ofN2 to any other nitrogen compound.) The "natural" fix-ation of N2 occurs by two types of processes. One is the action of a comparatively few mi-croorganisms that are capable of converting N2 to ammonia, ammonium ion (NHt), andorganic nitrogen compounds. The other natural nitrogen fixation process occurs in the at-mosphere by the action of ionizing phenomena, such as cosmic radiation or lightning, onN2. This process leads to the formation of nitrogen oxides in the atmosphere, which are ul-timately deposited on the Earth's surface as biologically useful nitrates.

In addition to natural nitrogen fixation, human activities have led to biological and in-dustrial fixation and fixation by combustion. Humans have increased the cultivation oflegumes, which have a symbiotic relationship with certain microorganisms capable of ni-trogen fixation. Legumes provide an increase in the soil nitrogen and serve as a valuablefood crop. Industrial nitrogen fixation consists primarily of the production of ammonia forfertilizer use. Combustion can also lead to the fixation of nitrogen as NOx' In the process ofnitrification, ammonium is oxidized to N°"i and NO3 by microbial action. N2O and NOare by-products of nitrification; the result is the release of N2O and NO to the atmosphere.Reduction of NO3 to N2, NO2, N20, or NO is called denitrification. Denitrification is ac-complished by a number of bacteria and is the process that continually replenishes the at-mosphere's N2. Figure 2.4 depicts the atmospheric nitrogen cycle.

2.3.1 Nitrous Oxide (N2O)

Nitrous oxide (N2O) is an important atmospheric gas that is emitted predominantly by bio-logical sources in soils and water. Although by comparison to CO2 and H2O, N2O has a farlower concentration, it is an extremely influential greenhouse gas. This is a result of its long

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TABLE 2.4 Estimated Sources and Sinks of N2O Typical of the Last Decade

Likely (Tg(N) yiRange (Tg(N) yr-l)Sources

31-5

31

2.2-3.70.5-2.0

0.1-2.00.5-2.0

9

NATURAL

OceansTropical soils

Wet forestsDry savannas

Temperate soilsForestsGrasslands

Total natural sources

3.50.51.30.4

1.8-5.30.2-1.00.7-1.80.2-0.5

ANTHROPOGENIC

Cultivated soilsBiomass burningIndustrial sourcesCattle and feedlots

Implied total sources(atmospheric increase + total sinks)a

"The observed atmospheric increase implies that sources exceed sinks by 3.9 Tg(N) yr-i.

Source: IPCC (1995).

the stratosphere. We will return to this process in Chapter 4. Sources of N2O exceed esti-mated sinks by 2.4 Tg(N) yr-i.

Estimates for the atmospheric lifetime of N2O come from stratospheric chemical trans-port models that have been tested against observed N2O distributions. The best current es-timate for the lifetime ofN2O is 120 :t 30 years. Because of its long lifetime N2O exhibitsmore or less uniform concentrations throughout the troposphere. Ice core records of N2Oshow a preindustrial mixing ratio of about 276 ppb. N2O levels have risen approximately15% since preindustrial times, reaching 311 ppb in 1992 (IPCC, 1995; Machida et al.,1995) (Figure 2.5). This observed atmospheric increase is consistent with a difference of3.9 Tg(N) yr-1 excess of sources over sinks, which is in reasonable agreement, given theuncertainties, with the mismatch based on attempting to estimate sources and sinks inde-

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71NITROGEN-CONTAINING COMPOUNDS

Detailed emissions inventories are available for Canada, the United States, and westernEurope that describe the spatial patterns of NOx emissions from combustion of fossil fuelsand from industrial processes (Lubkert and Zierock, 1989; Placet et al., 1990). Between 40and 45% of all NOx emissions in the United States are estimated to come from transporta-tion, 30 to 35% from power plants, and about 20% from industrial sources. About half theNOx emissions associated with transportation come from light-duty gasoline trucks andcars and approximately one-quarter are from heavy-duty gasoline and diesel vehicles.3

2.3.3 Reactive Odd Nitrogen (NO,)

Reactive nitrogen, denoted NO" is defined as the sum of the two oxides of nitrogen(NOx = NO + NOJ and all compounds that are products of the atmospheric oxidation ofNOx' These include nitric acid (HNO3), nitrous acid (HONO), the nitrate radical (NO3),dinitrogen pentoxide (N2Os), peroxynitric acid (HNO4), peroxyacetyl nitrate (PAN)(RC(O)OONOJ and its homologues, alkyl nitrates (RONOJ, and peroxyalkyl nitrates(ROONOJ. Nitric acid (HNO3) is the major oxidation product of NOx in the atmosphere.Because of its extreme water solubility, HNO3 is rapidly deposited on surfaces and in wa-ter droplets. Also, in the presence of NH3, HNO3 can form an ammonium nitrate (NH4NO3)aerosol. The nitrate radical (NO3) is an important constituent in the chemistry of the tro-posphere, especially at night. NO3 is present at night at mixing ratios ranging up to 300 pptin the boundary layer. Nitrous oxide (N2O) and ammonia (NH3) are not considered in this

context as reactive nitrogen compounds.Measurement of total NO, in the atmosphere provides an important measure of the total

oxidized nitrogen content. Concentrations of individual NO, species relative to the total in-dicate the extent of interconversion among species. NO, is indeed closer to a conserved

quantity than any of its constituent species (Roberts, 1995).There is a sizable body of data on the concentrations of NOx in the atmosphere, but cau-

tion must be exercised in drawing conclusions from these measurements. Many measure-ments of NO x have been made by devices that convert NO2 to NO, which is then measuredby the phenomenon of chemiluminescence. Comparison of these measurements with morespecific techniques suggests that surface converters that can convert NO2 to NO also con-vert other reactive nitrogen oxide species, such as peroxyacetyl nitrate (PAN), to NO,thereby causing interference. In urban locations, where the local NO sources are typicallylarge, NO and NO2 are probably the dominant constituents of the total reactive nitrogenNO,. Thus, in urban areas, interference from PAN and other oxides of nitrogen is believedto be relatively small. In rural and remote locations, however, the interference can be sub-stantial. For this reason, all non urban NOx measurements made with surface convertersmust be considered upper limits (biased toward a high measurement).

Given the dominant role of anthropogenic emissions in the budget of atmospheric NOxand the fact that the sources of these emissions tend to be located in or near urban areas, el-evated concentrations of NOx are to be expected in these locations. Observations of NOxsupport this expectation. The range and variability of NOx measurements are reflected inmeasurements made in 29 cities across the eastern and southern United States during the

3It is estimated that in 1994 there were 147,000,000 light-duty motor vehicles in the United States, 48,000,000trucks (85% light-duty), and 676,000 buses. Total vehicle miles traveled were estimated as 235 X 10'2, with

1.4 X 10'igallons of gasoline consumed.

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TABLE 2.6 Typical Boundary Layer NOxMixing Ratios

Urban-suburbanRuralRemote tropical forestRemote marine

Source: National Research Council (1991).

rural sites and generally range from a few tenths to 1 ppb. Measurements of NOx in the at-mospheric boundary layer and lower free troposphere in remote maritime locations havegenerally yielded mixing ratios of 0.02 to 0.04 ppb (20 to 40 ppt). Although the database isstill quite sparse, mixing ratios in remote tropical forests (not under the direct influence ofbiomass burning) appear to range from 0.02 to 0.08 ppb (20 to 80 ppt); the somewhathigher NOx concentrations found in remote tropical forests, as compared with those ob-served in remote marine locations, could result from biogenic NOx emissions from soil.

A summary of the NOx measurements made in the four regions of the globe mentionedabove is presented in Table 2.6. It can be seen that NOx concentrations decrease sharply asone moves from urban and suburban to rural sites in the United States and then to remotesites over the ocean and tropical forests. The striking difference of three orders of magni-tude or more between NOx concentrations in urban-suburban areas and remote locations iscompelling evidence for the dominant role of anthropogenic emissions of NOx over stronganthropogenic source regions such as North America. Because the ability to measure Naywas developed only recently, the rural and remote Nay database is even more limited thanthat for NOx' However, there are enough data to establish a rough indication of the Nay dis-tribution. Average Nay concentrations observed at many sites in the United States are quitesimilar; median mixing ratio values range from 3 to 10 ppb. These are somewhat lowerthan NOx mixing ratios typically observed in urban and suburban locations, which rangefrom 10 to 1000 ppb.

The contrast in Nay concentrations found in rural areas of the continental United Stateswith those observed in the remote troposphere is illustrated in Figure 2.7. The measure-ment sites are Scotia, Pennsylvania, a rural site in the eastern United States; Niwot Ridge,Colorado, an isolated inland site in the western United States; Point Arena, California, asite on the West Coast that often receives air from the Pacific Ocean; and Mauna Loa,Hawaii, a remote maritime site. Two of the sites, Mauna Loa and Niwot Ridge, are at highelevations (approximately 3 kin), and thus the air sampled there is not necessarily repre-sentative of the boundary layer. There is a progressive decrease in the contribution of NOxto Nay as one moves toward more remote regions. On average, NOx at Scotia accounted for59% of the observed Nay. At Niwot Ridge in 1987, NOx accounted for 32% of the Nay,and at Mauna Loa, NOx accounted for only 15% of the Nay. Because Nay enters the at-mosphere as NOx, the decrease in the ratio of NOx to Nay as one moves to more remotesites can be understood in terms of the increasing chemical conversion of NOx to organicnitrates (principally PAN) and to inorganic nitrates (principally HNO3) with increasing dis-tance of the site from major anthropogenic sources. The most remote sites are characterizedby the lowest ratios of NOxINOv' Those sites at hi.e:h altitudes have the lar.e:est ratio of

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75CARBON-CONTAINING COMPOUNDS

TABLE 2.7 Estimated Global Ammonia Emissions

Emission

(Tg(N) yr-1Source of Ammonia

,NTHROPOGENIC

Dairy cattleBeef cattle/buffaloPigsHorsesSheep/goatsPoultryFertilizerBiomass burning

Subtotal

5.58.72.81.22.51.36.42.0

3OA

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-1.:Q1.4,.Q45.0

NATURALWild animalsVegetationOcean

SubtotalTotal

Source: Dentener and Crutzen (1994).

are animal waste, ammonification of humus followed by emission from soils, losses ofNH3-based fertilizers from soils, and industrial emissions (Table 2.7). The ammonium(NHt) ion is an important component of the continental tropospheric aerosol. BecauseNH3 is readily absorbed by surfaces such as water and soil, its residence time in the loweratmosphere is expected to be quite short, about 10 days. Wet and dry deposition of NH3 arethe main atmospheric removal mechanisms for NH3' In fact, deposition of atmosphericNH3 and NH: may represent an important nutrient to the biosphere in some areas.Atmospheric concentrations ofNH3 are quite variable, depending on proximity to a source-rich region. NH3 mixing ratios over continents range typically between 0.1 and 10 ppb.

2.4 CARBON-CONTAINING COMPOUNDS

2.4.1 Classification of Hydrocarbons

Let us review briefly the classifications of carbon-containing compounds, particularlythose of interest in atmospheric chemistry. The carbon atom has four valence electrons andcan therefore share bonds with from one to four other atoms. The nature of the carbon-car-bon bonding in a hydrocarbon molecule basically governs the properties (as well as the

nomenclature) of the molecule.

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CARBON-CONTAINING COMPOUNDS 77

Molecules with two double bonds are called alkadienes, an example of which is

CH2=CH-CH=CH21,3-Butadiene

Molecules with a single triple bond are known as alkynes, the first in the series of whichis acetylene, HC ~ CR.

Double-bonded hydrocarbons may also be arranged in a ring structure. This class ofmolecules, of which the basic unit is benzene,

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is called aromatics. Other common aromatics are

CH3

arCH3

CH3

9CH3

p-Xylene

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6Toluene a-Xylene m-Xylene

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0

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whereas ketones have the structure

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Thus the distinction lies in whether the carbon atom is bonded to one or two alkyl groups.

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TABLE 2.9 Estimated Sources and Sinks of Methane (Tg(CH4) yr-1

TotalIndividual EstimateIdentified Sources

115 (55-150)20 (10-50)10 (5-50)15 (10-40)

160 (110-210)D

NATURAL

WetlandsTermitesOceansOther

Total identified natural sources

40 (25-50)30 (15-45)15 (5-30)?(1-30)

100 (70-120)b

85 (65-100)60 (20-100)40 (20-80)40 (20-70)25 (20-30)25 (15-80)

275 (200-350)

375 (300-450)"

ANTHROPOGENIC

Fossil-fuel related sourcesNatural gasCoal minesPetroleum industryCoal combustion

Total fossil-fuel relatedBiospheric carbon

Enteric fermentationRice paddiesBiomass burningLandfillsAnimal wasteDomestic sewageTotal biospheric

~

Total identified anthropogenic sources

Total identified sources

445 (360-530)40 (32-48)30 (15-45)

515 (430-600)

SinksTropospheric OH

StratosphereSoils

Total sinks

Total global burden: 4850 Tg (C~)

aA preindustrial level of 700 ppb would have required a source of2l0 Tg(CH.) yr-1 if the lifetime has remainedconstant, and 280 Tg (CH.) yr-1 if current tropospheric chemical feedbacks can be extrapolated back. The total

anthropogenic emissions of CH. based on identified sources, 375 (300--450), is slightly higher than the inferred

range from preindustrial levels, 270-340, but is well within the uncertainties.bpractional source from fossil carbon based on a measure of the atmospheric ratio of "CH. to 12CH..

Note: The observed increases in methane show that sources exceed sinks by about 35 to 40 Tg each year. All data

are rounded to the nearest 5 Tg.

Source: IPCC (1995).

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TABLE 2.10 Estimated Global Anthropogenic Emissions of

Nonmethane Volatile Organic Compounds

8252.5

FUEL PRODUCTION/DISTRIBUTION

Petroleum

Natural gasOil refiningGasoline distribution

FUEL CONSUMPTION

CoalWoodCrop residues (including waste)CharcoalDung cakesRoad transportChemical industrySolvent useUncontrolled waste burning

OTHER

Total

3.52514.52.53

362

208

10

142

Source: Middleton (1995).

pogenic VOC emissions included, for example, about 600 different compounds (Placet

et al., 1990).Motor vehicles are the dominant contributor to VOC emissions in the United States.

VOCs emitted from motor vehicles are mainly hydrocarbons that result from the incom-plete combustion of fuel or from its vaporization. These contributions are generally cate-gorized and reported as exhaust and evaporative emissions. Within the exhaust emissionscategory are included the unburned and partially burned fuel and lubricating oil in the ex-haust and gases that leak from the engine. The evaporative emissions category includesfuel vapor emitted from the engine and fuel system that can be attributed to several sources:vaporization of fuel as a result of the heating of the fuel tank, vaporization of fuel from theheat of the engine after it has been turned off (hot-soak emissions), vaporization of fuelfrom the (uel system while the vehicle is operating (running losses), fuel losses due to leaksand diffusion through containment materials (resting losses), and fuel vapor displacementas a result of filling fuel tanks (refueling losses). Motor vehicles are the major sources of

alkane and aromatic emissions.Estimates of global anthropogenic nonmethane VOC emissions in 1990 are given in

Table 2.10. In general, a breakdown by chemical compound is not yet available for globalanthropogenic VOC emissions. As seen in Table 2.10, transportation is the largest sourceofVOC emissions worldwide, with solvent use following as the second largest source.

As an illustration of the large number of organic compounds identified in the atmos-phere, Table 2.11 lists the median concentrations of the 25 most abundant nonmethane or-ganic species measured in the 1987 Southern California Air Quality Study.

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TABLE 2.12 Organic Compounds Emitted by Vegetation"

~=~>==Isoprene a-Pinene

Camphene IlJf3-Pinene

2-CareneSabinene

3~ -Carene

a-Terpinene

d-Limonene

y-Terpinene

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f:J-Phellandrene

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"In the simplified molecular structures here bonds between carbon atoms are shown. Vertices represent carbonatoms. Hydrogen atoms bonded to the carbons are not explicitly indicated.

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S3WI.L3dI'1 ON" 'S3'1JAJ '1"80'10 'NOI.LISOdWOJ JI~3HdSOW.L".,8


TABLE 2.13 Global Biogenic VOC Emission Rate Estimates by Source andClass of Compound (Tg yr-1

821

120

194

5

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127 260

.Other reactive biogenic VOCs (ORVOC).bThese totals include additional non-reactive VOCs not reflected in the columns to the left.

Source: Guenther et al. (1995).

biogenic hydrocarbon emissions in the southeastern United States is predicted to be aslarge as that in the tropics. An estimate of global biogenic VOC emissions appears in Table2.13. On a global basis, biogenic hydrocarbon emissions far exceed those of anthropogenic

hydrocarbons.

2.4.5 Carbon Monoxide

The global sources and sinks of CO are given in Table 2.14. Methane oxidation (by OH)is a major source of CO, as are technological processes (combustion and industrialprocesses), biomass burning, and the oxidation of nonmethane hydrocarbons. Un-certainties in each of these estimated sources are large. It is estimated that about two-thirds

TABLE 2.14 Estimated Sources and Sinks of COTypical of the Last Decade

TechnologicalBiomass burningBiogenicsOceansMethane oxidationNMHC oxidation

Sinks

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87HALOGEN-CONTAINING COMPOUNDS

As a group of atmospheric chemicals, halogen-containing compounds have a wide vari-ety of anthropogenic and natural sources. They are produced by biological processes in theoceans, from sea salt, from biomass burning, and from industrial synthesis. Their atmo-spheric lifetimes vary considerably depending on their mechanism of removal, rangingfrom a few days to several centuries.

Table 2.15 lists atmospheric halogenated organic species with global average concen-trations, atmospheric burdens, lifetimes, sources, and sinks.4 Of the exclusively man-madeorganic halogenated species, the chlorofluorocarbons are used as refrigerants (CFC-12,HCFC-22), blowing agents (CFC-ll, HCFC-22), and cleaning agents (CFC-113). Methylchloroform (CH3CCI3), methylene chloride (CHzClz), and tetrachloroethene (CzCI4) areused as degreasers and as dry cleaning and industrial solvents. Methyl bromide (CH3Br) isa widely used agricultural and space fumigant. All the monomethyl halides in Table 2.15have natural sources. Methyl chloride (CH3Cl) and CH3Br are also products of biomass

burning.Lovelock (1971) first detected SF6 and CFCl3 in the atmosphere using the electron cap-

ture detector. In landmark work in atmospheric chemistry for which they received the 1995Nobel Prize in Chemistry, Molina and Rowland (1974) showed that CFCs that are im-mune to removal in the troposphere could decompose photolytically in the stratosphere torelease Cl atoms capable of catalytic destruction of stratospheric ozone. The very lack ofchemical reactivity that makes chlorofluorocarbon molecules so intrinsically useful also al-lows them to survive unchanged in most commercial applications and eventually to be re-leased to the atmosphere in their original gaseous form. The usual tropospheric sinks ofoxidation, photodissociation, and wet and dry deposition are ineffective with the chloroflu-orocarbons. The only important sink for CFC13 and CFzClz is photodissociation in the mid-stratosphere (25 to 40 kill) by solar ultraviolet radiation with wavelengths shorter than230 nm. These same CFCs that lead to stratospheric ozone depletion are efficient absorbersof infrared radiation and potentially important greenhouse gases.

There is a sharp demarcation in atmospheric behavior between fully halogenated halo-carbons and those containing one or more atoms of hydrogen. Halocarbons containing atleast one hydrogen atom, such as CFzHCl, CHCI3, and CH3CCI3, are effectively brokendown in the troposphere by reaction with the hydroxyl radical before they can reach thestratosphere. Atmospheric lifetimes of these species range from months to decades. Someof these gases also react with seawater; it is estimated that 5 to 10% of the removal ofCH3CCl3 occurs by absorption into the ocean. The hydrohalogenated species such as

'The tenD hydrochlorofluorocarbons is the collective name given to a series of chemicals with varying number ofcarbon, hydrogen, chlorine, and fluorine atoms. The somewhat arcane system of numbering these compounds wasproposed by the American Society of Heating and Refrigeration Engineers in 1957. For the simpler hydrochloro-fluorocarbons, the numbering system may be summarized as follows:

1. The first digit on the right is the number of fluorine (F) atoms in the compound.

2. The second digit from the right is one more than the number of hydrogen (H) atoms in the compound.

3. The third digit from the right, plus one, is the number of carbon (C) atoms in the compound. When thisdigit is zero (i.e., only one carbon atom in the compound), it is omitted from the number.

4. The number of chlorine (CI) atoms in the compound is found by subtracting the sum of the fluorine andhydrogen atoms from the total number of atoms that can be connected to the carbon atoms.

CCI2F2 C2CI2F4 CHCIF2. CCI3FCFC-12 CFCI-114 CFC-22 CFC-II

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YearFIGURE 2.9 Annual emissions of industrially important halocarbons from 1972 to 1992 (IPCC.1995).

methyl chloroform (CH3CCI3) and the HCFCs are also significant infrared absorbers buttheir shorter atmospheric lifetimes reduce their radiative impact relative to the fully halo-genated CFCs.

Discovery of the stratospheric ozone-depleting potential of CFCs in the mid-1970s ledto a ban in the United States (announced in 1976 and effective in 1978) on the use ofCFCsas aerosol propellants and to similar restrictions in Canada and Scandinavia. When theAntarctic ozone hole was discovered, subsequently, an international protocol outlining pro-posed actions to protect the stratospheric ozone layer was signed in Montreal in September1987. The so-called Montreal Protocol specifies a 20% reduction from 1986 emissions offully halogenated CFCs by 1994 and a further 30% reduction by 1999. Global emissions ofCFCI3, CF2CI2, C2F3C13, CF2HC1, and CH3CC13 up to 1992 are shown in Figure 2.9. Theturn-down in emission rates reflects the results of the Montreal Protocol.

Atmospheric levels of CF2CI2, CFCI3, and CH3CC13 from 1978 to 1992 are shown inFigure 2.10. Mixing ratios increased steadily until about 1990. Methyl chloride (CH3Cl), atan atmospheric abundance of about 600 ppt, is the dominant halogen compound in the at-mosphere. To maintain the steady-state CH3Cl concentration, with an atmospheric lifetimeof order 2 years, requires a source strength of about 3.5 Tg yr-1 , most of which comes fromthe ocean. Southern Hemisphere (SH) CFC concentrations lag behind those in the NorthernHemisphere (NH) by about 1 year, reflecting the predominant source of CFCs in the NHand the approximate 1 year mixing time between the NH troposphere and the SH tropo-

sphere.At present, the atmosphere contains approximately 20 ppt of bromine, about half of

which is methyl bromide (CH3Br). Methyl bromide is an ubiquitous component of the at-mosphere, arising from both man-made and natural sources. A calculated atmospheric life-time of 1.7 to 1.9 years, based solely on removal by reaction with OH radicals, is consistentwith a global source of 90 to 110 Gg (109 g) yr-l (Singh and Kanakidou, 1993). A shorterlifetime of about 1.3 years (see Table 2.15) results if deposition/hydrolysis losses are alsoconsidered. Available data provide an estimate of global sources of CH3Br that divide 35%(20 to 50%) man-made and 65% (80 to 50%) natural. Oceans are supersaturated withCH3Br and constitute the major natural source of CH3Br of about 60 Gg yr-1, which could

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range from 40 to 80 Gg yr-l. CH3Br mixing ratios in the Northern Hemisphere ar,ound1992 were about 14 ppt, with a ratio of NH to SH mixing ratios varying between 1.2 and1.4 depending on season. The seasonal variation is a result of source strength and OH vari-ations. CH3Br levels have been increasing at a rate of 0.1 to 0.2 ppt yr-i. Despite the factthat CH3Br is largely removed in the troposphere by OH reaction, enough survives to enterthe stratosphere and contribute to halogen-induced stratospheric ozone depletion.

2.6 ATMOSPHERIC OZONE

Ozone (03) is a reactive oxidant gas produced naturally in trace amounts in the Earth's at-mosphere. Ozone was discovered by C. F. Schonbein in the middle of the last century; healso was first to detect ozone in air (Schonbein, 1840, 1854). Schonbein (1840) suggestedthe presence of an atmospheric gas having a peculiar odor (the Greek word for "to smell"is ozein). Spectroscopic studies in the late 19th century showed that ozone is present at ahigher mixing ratio in the upper atmospheric layers than close to the ground. Attempts toexplain the chemical basis of existence of ozone in the upper atmosphere began nearly 70years ago. Within the last 30 years, however, while increased understanding of the role ofother trace atmospheric species in stratospheric ozone was unfolding, it became apparentthat anthropogenically emitted substances have the potential to seriously deplete the nat-ural levels of ozone in the stratosphere. At about the same period, ironically, it was real-ized that anthropogenic emissions could lead to ozone increases in the troposphere.Whereas stratospheric ozone is essential for screening of solar ultraviolet radiation, ozoneat ground level can, at elevated concentrations, lead to respiratory effects in humans. Thisparadoxical dual role of ozone in the atmosphere has, on occasion, led to the dubbing ofstratospheric ozone as "good" ozone and tropospheric ozone as "bad" ozone.

Most of the Earth's atmospheric ozone (about 90%) is found in the stratosphere whereit plays a critical role in absorbing ultraviolet radiation emitted by the Sun. Figure 2.11

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from 1979 to 1991 have shown that broadly similar midlatitude losses have also occurredat equivalent latitudes in the Southern Hemisphere (IPCC, 1995). Figure 2.12 shows theannual, latitudinal variation of the total ozone trends calculated from the Dobson ground-based measurement record and satellite observations. The effect of the Antarctic ozonehole is seen in the data from 60° S to 90° S. Analysis of the total ozone mapping spec-trometer (TOMS) data over the period 1979 to 1989 between 69° S and 69° N reveals a to-tal global average ozone decrease of 3.5% over that 11 year period (Herman et al., 1991).Statisticaily significant decreases in total ozone are now being observed in all seasons inboth the Northern and Southern Hemispheres at middle and high latitudes (Stolarski et al.,1992).

2.6.2 Ozone Flux from the Stratosphere to the Troposphere

Ozone from the stratosphere is transported down across the tropopause by so-calledtropopause folding events (Danielson, 1968) in which tongues of stratospheric air intrudeinto the troposphere, usually at extratropicallatitudes (recall Figure 1.3 and associated dis-cussion). Estimates of the amount of 03 transported from the stratosphere to the tropos-phere on an annual basis rely on measurements of conserved tracers or on generalcirculation models but are quite uncertain. In the NH ozone fluxes seem to maximize inspring, being as much as five times the value in the fall. The NH stratosphere-to-troposphere ozone flux has been estimated to fall in the range of (3 to 8) X 1010 moleculescm-2 S-l (Crutzen, 1995). The SH flux may be about half as large. An estimate for the to-tal 03 production in the stratosphere is about 5 X 1013 molecules cm-2 S-I; only about0.1 % of all 03 produced in the stratosphere leaks down to the troposphere (Crutzen, 1995).The estimated global 03 loss from photolysis in the troposphere is 14 X 1010 moleculescm-2 S-I, which generously exceeds the amount of 03 from stratosphere-to-troposphere

exchange.

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I: ,10001-'II--illllllll'II!00 50 100 150

°3 Partial Pressure, nbarFIGURE 2.13 Selected annual means of ozone balloon soundings over Payeme, Switzerland(Staehelin and Schmid, 1991). The annual mean altitude of the tropopause at Payeme is about 10 kIn,varying from about 8 kIn in winter to 12 km in summer. (Reprinted from Atmos. Environ., 25A,Staehelin, J. and Schmid, W., Trend analysis of tropospheric ozone concentrations utilizing the 20-year data set of balloon soundings over Payeme (Switzerland), p. 1739,1991, with kind permissionfrom Elsevier Science Ltd, The Boulevard, Langford Lane, Kid1ington OX5 1GB, UK.)

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urban-suburban atmosphere, where maxima well above 200 ppb have been observed(Table 2.16). Ozone concentrations in rural areas tend to be more moderate and rarely ex-ceed 150 ppb. In remote locations, ozone concentrations typically range from 20 to 40 ppb.

2.7 PARTICULATE MATTER (AEROSOLS)

Particles in the atmosphere arise from natural sources, such as windbome dust, sea spray,and volcanoes, and from anthropogenic activities, such as combustion of fuels. Whereas anaerosol is technically defined as a suspension of fine solid or liquid particles in a gas, com-mon usage refers to the aerosol as the particulate component only (Table 2.17). Emitted di-rectly as particles (primary aerosol) or formed in the atmosphere by gas-to-particleconversion processes (secondary aerosol), atmospheric aerosols are generally consideredto be the particles that range in size from a few nanometers (nm) to tens of micrometers

TABLE 2.17 Terminology Relating to Atmospheric Particles

Aerosols, aerocolloids,aerodisperse systems

Dusts

Tiny particles dispersed in gases

Fog

Mists

Particle

Suspensions of solid particles produced by mechanical disintegration ofmaterial such as crushing, grinding, and blasting. Dp > I JLm.

A loose term applied to visible aerosols in which the dispersed phase isliquid. Usually, a dispersion of water or ice, close to the ground.

The solid particles generated by condensation from the vapor state, gen-erally after volatilization from melted substances, and often accompa-nied by a chemical reaction such as oxidation. Often the materialinvolved is noxious. Dp < I JLm.

An aerosol that impedes vision and may consist of a combination of wa-ter droplets, pollutants, and dust. Dp < 1 JLm.

Liquid, usually water in the form of particles suspended in the atmos-phere at or near the surface of the Earth; small water droplets floatingor falling, approaching the form of rain, and sometimes distinguishedfrom fog as being more transparent or as having particles perceptiblymoving downward. Dp > I JLm.

An aerosol particle may consist of a single continuous unit of solid orliquid containing many molecules held together by intermolecularforces and primarily larger than molecular dimensions (> 0.001 JLm).A particle may also be considered to consist of two or more such unitstructures held together by interparticle adhesive forces such that itbehaves as a single unit in suspension or upon deposit.

A term derived from smoke and fog, applied to extensive contaminationby aerosols. Now sometimes used loosely for any contamination ofthe air.

Small gas-borne particles resulting from incomplete combustion, con-sisting predominantly of carbon and other combustible material, andpresent in sufficient quantity to be observable independently of thepresence of other solids. Dp 2: 0.01 JLm.

Agglomerations of particles of carbon impregnated with "tar," formedin the incomplete combustion of carbonaceous material.

Soot

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15 5 24 II 4 37

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"Heintzenberg (1989).

bSolomon et aI. (1989).

to atmospheric aerosol have increased dramatically over the past century and have beenimplicated in human health effects (Dockery et al., 1993), in visibility reduction in urbanand regional areas (see Chapter 22), in acid deposition (see Chapter 20), and in perturbingthe Earth's radiation balance (see Chapter 22).

Table 2.18 presents data summarized by Heintzenberg (1989) and Solomon et al. (1989)on aerosol mass concentrations and composition in different regions of the troposphere. Itis interesting to note that average total fine particle mass (that associated with particles ofdiameter less than about 2 .urn) in nonurban continental, (i.e., regional) aerosols is only afactor of 2 lower than urban values. This reflects the relatively long residence time of par-ticles. Correspondingly, the average compositions of nonurban continental and urbanaerosols are roughly the same. The average mass concentration of remote aerosols is a fac-tor of 3 lower than that of nonurban continental aerosols. The elemental carbon component,a direct indicator of anthropogenic combustion sources, drops to 0.3% in the remoteaerosols, but sulfate is still a major component. This is attributable to a global average con-centration of non-sea-salt sulfate of about 0.5 .ugm-3. Rubidoux, California, located about100 km east of downtown Los Angeles, routinely experiences some of the highest particu-late matter concentrations in the United States.

2.7.3 Cloud Condensation Nuclei (CCN)

Aerosols are essential to the atmosphere as we know it; if the Earth's atmosphere were to-tally devoid of particles, clouds could not form. Particles that can become activated to growto fog or cloud droplets in the presence of a supersaturation of water vapor are termedcloud condensation nuclei (CCN). At a given mass of soluble material in the particle thereis a critical value of the ambient water vapor supersaturation below which the particle ex-ists in a stable state and above which it spontaneously grows to become a cloud droplet of10 JLm or more diameter. The number of particles from a given aerosol population that canact as CCN is thus a function of the water supersaturation. For marine stratiform clouds, forwhich supersaturations are in the range of 0.1 to 0.5%, the minimum CCN particle diame-ter is 0.05 to 0.14 tLm. CCN number concentrations vary from fewer than 100 cm-3 in re-

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PARTICULATE MAnER (AEROSOLS) 101

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roads, wind erosion of cropland, construction, etc.), and transportatIon sources (automo-biles, etc.).

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EMISSIONS INVENTORIES 103

Atmospheric particulate matter samples can be analyzed routinely for more than 50trace elements. Trace element emissions arise from a large number of different source typesin urban areas. For example, motor vehicles burning leaded fuel, electric arc steel furnaces,Kraft recovery boilers, and secondary lead smelters contribute to atmospheric lead con-centrations. The wide spectrum of sources, together with the fact that trace metals often areonly a minor fraction of the mass emissions from each source, obscure the relative impor-tance of the contributors to atmospheric trace element levels.

As with all atmospheric species, trace metal emissions undergo atmospheric transportand dilution before they reach a particular receptor site. Mathematical models can be con-structed based on the fundamentals of atmospheric chemistry and physics that will trackthe contributions from many emission sources as they undergo atmospheric transport.Indeed, the development of such models will receive considerable attention in this book. Inthe case of particulate emissions, an alternative is available. It is possible to attack thesource contribution identification problem in reverse order, proceeding from measured par-ticulate concentrations at a receptor site backward to the responsible emission sources (seeChapter 24). The unique metals content of the emissions from each source type is viewedas a fingerprint for the presence of material from that source in an ambient aerosol sample.

2.7.6 Carbonaceous Particles

Carbonaceous particles in the atmosphere consist of two major components-graphitic orblack carbon (sometimes referred to as elemental or free carbon) and organic material. Thelatter can be directly emitted from sources or produced from atmospheric reactions involv-ing gaseous organic precursors. Elemental carbon can be produced only in a combustionprocess and is therefore solely primary. Graphitic carbon particles are the most abundantlight-absorbing aerosol species in the atmosphere. Particulate organic matter is a complexmixture of many classes of compounds (Daisey, 1980). A major reason for the study of par-ticulate organic matter has been the possibility that such compounds pose a health hazard.Specifically, certain fractions of particulate organic matter, especially those containingpolycyclic aromatic hydrocarbons (PAHs), have been shown to be carcinogenic in animals

and mutagenic in in vitro bioassays.

2.8 EMISSIONS INVENTORIES

An estimate of emissions of a species from a source is based on a technique that uses"emission factors," which are based on source-specific emission measurements as a func-tion of activity level (e.g., amount of annual production at an industrial facility) with regardto each source. For example, suppose one wants to sample a power plant's emissions ofSO2 or NOx at the stack. The plant's boiler design and its BTU (British thermal unit) con-sumption rate are known. The sulfur and nitrogen content of fuel burned can be used to cal-culate an emissions factor of kilograms (kg) of SO2 or NOx emitted per metric ton (Mg) of

fuel consumed.The U.S. Environmental Protection Agency (EPA) has compiled emission factors for a

variety of sources and activity levels (such as production or consumption), reporting the re-sults since 1972 in "AP-42 Compilation of Air Pollutant Emission Factors," for which sup-olements are issued regularly. Emission factors currently in use are developed from only a

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AIR POLLUTION LEGISLATION 105

lationship that requires the U.S. Environmental Protection Agency (EPA) to developNational Ambient Air-Quality Standards (NAAQS) and empowers the states to implementand enforce regulations to attain them. The act also requires the EPA to set NAAQS forcommon and widespread pollutants after preparing criteria documents summarizing scien-tific knowledge of their detrimental effects. The EPA has established NAAQS for each ofsix criteria pollutants: sulfur dioxide, particulate matter, nitrogen dioxide, carbon monox-ide, ozone, and lead. At certain concentrations and length of exposure these pollutants areanticipated to endanger public health or welfare. The NAAQS are threshold concentrationsbased on a detailed review of the scientific information related to effects. Concentrationsbelow the NAAQS are expected to have no adverse effects for humans and the environ-ment. Table 2.20 presents the U.S. national primary and secondary ambient air-qualitystandards for ozone, carbon monoxide, nitrogen dioxide, sulfur dioxide, suspended partic-ulate matter, and lead.

In the Clean Air Act Amendments of 1970, Congress set 1975 as the deadline for meet-ing the NAAQS. By 1977,2 years after this deadline, many areas were still in violation ofthe ozone NAAQS. The 1977 amendments to the Clean Air Act delayed compliance withthe ozone and carbon monoxide NAAQS until 1982, and areas that demonstrated theycould not meet the 1982 deadline were given extensions until 1987. The 1990 amendmentsclassify nonattainment areas according to degree of noncompliance with the NAAQS. Theclassifications are extreme, severe, serious, moderate, or marginal, depending on the area'sozone design value and the percentage by which the value is greater than the NAAQS.Ozone design values are ozone concentrations that are statistically determined from air-quality measurements for each nonattainment area. If monitoring data for an area are com-plete, the design value is the fourth highest monitor reading over the past 3 years. Designvalues are used to determine the extent of control needed for an area to reach attainment.

The 1990 amendments of the Clean Air Act establish an interstate ozone transport re-gion extending from the Washington, DC metropolitan area to Maine. In this densely pop-ulated region, ozone violations in one area are caused, at least in part, by emissions inupwind areas. A transport commission is authorized to coordinate control measures withinthe interstate transport region and to recommend to the EPA when additional control mea-sures should be applied in all or part of the region in order to bring any area in the regioninto attainment. Hence areas within the transport region that are in attainment of the ozoneNAAQS might become subject to the controls required for nonattainment areas in that re-

gion.The Clean Air Act requires each state to adopt a plan, a so-called State Implementation

Plan (SIP), that provides for the implementation, maintenance, and enforcement of theNAAQS. It is, of course, emission reductions that will abate air pollution. Thus the states'plans must contain legally enforceable emission limitations, schedules, and timetables forcompliance with such limitations. The control strategy must consist of a combination ofmeasures designed to achieve the total reduction of emissions necessary for the attainmentof the air-quality standards. The control strategy may include, for example, such measuresas emission limitations, emission charges or taxes, closing or relocation of commercial orindustrial facilities, periodic inspection and testing of motor vehicle emission control sys-tems, mandatory installation of control devices on motor vehicles, means to reduce motorvehicle traffic, including such measures as parking restrictions and carpool lanes on free-ways, and expansion and promotion of the use of mass transportation facilities.

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901

HAZARDOUS AIR POLLUTANTS (AIR TOXICS) 107

2.11 HAZARDOUS AIR POLLUTANTS (AIR TOXICS)

Hazardous air pollutants or toxic air contaminants ("air toxics") refer to any substances thatmay cause or contribute to an increase in mortality or in serious illness, or that may pose apresent or potential hazard to human health. Title III of the Clean Air Act Amendments of1990 completely overhauled the existing hazardous air emission program. Section 112 ofthe Amendments defines a new process for controlling air toxics that includes the listing of189 substances, the development and promulgation of Maximum Achievable ControlTechnology (MACT) standards, and the assessment of residual risk after the implementa-tion of MACT. Any stationary source emitting in excess of 10 tons yr-1 of any listedhazardous substance, or 25 tons yr-1 or more of any combination of hazardous air contam-inants, is a major source for the purpose of Title III and is subject to regulation. Congressestablished a list of 189 hazardous air pollutants in the CAA itself. It includes organicchemicals, pesticides, metals, coke-oven emissions, fine mineral fibers, and radionuclides(including radon). This initial list may be revised by the EPA to either add or remove sub-stances. The EPA is required to add pollutants to the list if they are shown to present,through inhalation or other routes of exposure, a threat of adverse human health effects oradverse environmental effects, whether through ambient concentrations, bioaccumulation,deposition, or otherwise.

Congress directed the EPA to list by 15 November 1995, the categories and subcate-gories of sources that represent 90% of the aggregate emissions of:

. Alkylated lead compounds. Polycylic organic matter. Hexachlorobenzene. Mercury. Polychlorinated biphenyls. 2,3,7,8-Tetrachlorodibenzofuran. 2,3,7,8-Tetrachlorodibenzo-p-dioxin

Congress further directed the EPA to establish and promulgate emissions standards forsuch sources by 15 November 2000. The emissions standards must effect the maximum de-gree of reduction in the listed substance, including the potential for a prohibition on suchemissions, taking into consideration costs, any non-air-quality health and environmentalimpacts, and energy requirements. In establishing these emissions standards, the EPA mayalso consider health threshold levels, which may be established for particular hazardous airpollutants. Each state may develop and submit to the EPA for approval a program for theimplementation and enforcement of emission standards and other requirements for haz-ardous air pollutants or requirements for the prevention and mitigation of accidental re-leases of hazardous substances.

The California Air Resources Board (ARB) (1989) has developed a list of substances ofconcern in California, called "Status of Toxic Air Contaminant Identification." This list andthe organization of substances within it are subject to periodic revision, as needed. TheFebruary 1989 Status List groups substances into three categories. Category I includesidentified toxic air contaminants: asbestos, benzene, cadmium, carbon tetrachloride, chlo-rinated dioxins and dibenzofurans (15 species), chromium (VI), ethylene dlbromide and

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COMPARTMENTAL MODELS OF GLOBAL BIOGEOCHEMICAL CYCLES 113

Comparable balances on the two stratosphere compartments yield

(2.A.5)0 = - (k~H/SH + k~rT + k~H) Q~H + klH/NHQ~H + k~rsQ~H

0 = - (k~H/NH + k~fT + k~H) Q~H + k~H/SHQ~H + k~~SQrH (2.A.6)

Equations (2.A.3) to (2.A.6) constitute four equations in the four unknowns Q~H' Q~H'Q~H' and Q~H' It is useful to rewrite these equations as

0 = -alQI +a2Q2 +a3Q3 + PI (2oA.7)

0 = -a4Q2 + asQI + a6Q4 + P2 (2.A.8)

0 = -CX7Q3 + CXSQ4 + CX9QI (2.A.9)

0 = -aloQ4 + all Q3 + al2Q2 (2.A.IO)

where QI = Q~H' Qz = Q~H' Q3 = Q~H' Q4 = Q~H' PI = PNH, and Pz = PsH. Also,

- kT +kNH +kNHat - NH/SH TIS T

- kT kSH kSHa4 - SH/NH + TIS + T

- ks + kNH + kNHa7 - NH/SH SIT S

- ks +k SH +k SHalO= SH/NH SIT S

a2 = k§H/NH

a5 = k~/SH

as = k~H/NH

- ksall- NH/SH

a3 =

a6 =

a9 =

a.?=

Equations (2.A.9) and (2.A.lO) can be solved simultaneously to obtain Q3 and Q4 in termsofQ. and Q2'

Q3 = .81 Qz + .8ZQI

Q4 = .83QZ + .84QI

(2.A.II)

(2.A.I2)

where

The resulting equations for QI and Q2 are

(2.A.I3)0 = (a3.82 - at)Qt + (a2 + a3.8t)Q2 + PI

0 = (a~ + a"BJJ.) 01 + (a"B~ - aJJ.)O, + P, (2.A.14)

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SIT

k NH

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kSH.- TIS

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COMPARTMENTAL MODELS OF GLOBAL BIOGEOCHEMICAL CYCLES 115

It can be assumed that these masses divide equally between the NH and SH. With the av-erage molecular weight of air, Mair = 28.9 g mol-I, the tropospheric mass of a substance ofmolecular weight M that has a tropospheric mixing ratio of ~ T is

(2.A.19)

Similarly, for the stratosphere,

s~~sMMair

QS= (2.A.20)

(2.A.21)

If the tropospheric mass is divided into Q~H and QIH'

(2.A.22)

(2.A.23)-Mair

As an example, the average mixing ratios of OCS in the troposphere and stratosphereare (Chin and Davis, 1995)

~Jcs = 490 ppt = 490 x 10-12

~JcS = 380 ppt = 380 X 10-12

The total atmospheric mass ofOCS is (Mocs = 60 g mol-I)

0.72 X 1021

28.9

4.56 X 1021(490 x 10-11 +

, 28.9= 4.63 x 1012 g + 0.57 x 1012 g

= 4.63 Tg + 0.57 Tg

Q

5.2Tg

2.A.2 Application of the Compartment Model to Methyl Chloroform (CH3CCI3)

Methyl chloroform is a man-made substance, the total emissions of which to the atmos-phere are reasonably well known. Its atmospheric degradation occurs almost entirely byhydroxyl radical reaction. The CH3CCl3 mixing ratio in the atmosphere is well established;

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PROBLEMS 121

Went, F. W. (1960) Organic matter in the atmosphere and its possible relation to petroleum formation,Proc. Natl. Acad. Sci. (USA), 46,212-221.

Whitby, K. T., and Cantrell, B. (1976) Fine particles, in International Conference on EnvironmentalSensing and Assessment, Las Vegas, NV, Institute of Electrical and Electronic Engineers.

Winer, A. M., Arey, J., Aschmann, S. M., Atkinson, R., Long, W. D., Morrison, L. C., and Olszyk,D. M. (1989) Hydrocarbon emissions from vegetation found in California's Central Valley. FinalReport. Contract No. A 732-155. California Air Resources Board, Sacramento, CA.

World Meteorological Organization (WMO) (1986) Atmospheric Ozone 1985. Global OzoneResearch and Monitoring Project: Report No. 16, Geneva.

World Meteorological Organization (WMO) (1990) Report of the International Ozone Trends Panel:1988. Global Ozone Research and Monitoring Project: Report No. 18, Geneva.

Yokouchi, Y. (1994) Seasonal and diurnal variation of isoprene and its reaction products in a semi-rural area. Atmos. Environ., 28,2651-2658.

Yvon, S. A., Saltzman, E. S., Cooper, D. J., Bates, T. S., and Thompson, A. M. (1996) Atmospheresulfur cycling in the tropical Pacific marine boundary layer (120 S, 1350 W): a comparison offielddata and model results I. Dimethylsulfide, J. Geophys. Res., 101,6899-6909.

Zimmerman, P. (1979) Testing of hydrocarbon emissions from vegetation, leaf litter and aquatic sur-faces, and development of a method for compiling biogenic emission inventories. U.S.Environmental Protection Agency Report, EPA-450-4- 70-004, Research Triangle Park, NC.

Zimmerman, P., Greenberg, J., and Westberg, C. (1988) Measurements of atmospheric hydrocarbonsand biogenic emission fluxes in the Amazon boundary layer, J. Geophys. Res., 93, 1407-1416.

PROBLEMS

2.1A In the simplified calculation of the atmospheric sulfur cycle in Section 2.2.4, if thevalue of c, the S02 fraction of the total sulfur, is taken as 0.5, a sulfur atom residencetime of 50 hours is estimated. What is the value of b, the fraction of sulfur convertedto SO~- before being removed, that is consistent with this choice of c?

2.2A Prepare a plot of ozone mixing ratio versus altitude from ground level to 50 km. Totalmolecular number density of air can be obtained from Table A.8, and 03 molecularnumber density is given in Figure 2.11. Why do the molecular number density andmixing ratio peak at different altitudes?

2.3A One Dobson unit corresponds to 2.69 X 1016 molecules 03 cm-2 integrated over avertical column to the top of the atmosphere. Show how vertical ozone column datacan be converted to Dobson units.

2.4A Calculate the change in total ozone column, as measured in Dobson units, between1969 and 1988 for the ozone profiles in Figure 2.13.

2.5A Confirm the calculations presented in Section 2.A.2 on the concentration and lifetimeof methyl chloroform.

2.6B Derive the balance equations for a substance that is completely removed in the tro-posphere, but for which two tropospheric reservoirs should be considered (seeAppendix 2). Apply the balance to CO using the source and sink data from Table2.14. As a first approximation, assume that anthropogenic sources are totally concen-trated in the Northern Hemisphere and that biomass burning sources are totally in the

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atmospheric residence time. = p-l. Given values of land r,p can be calculatedfrom 1= rf(r + p) since these species have been emitted long enough so thatrt» 1. Plot/versusp (and .) for r = 0.15 yr-1 showing points corresponding

to the three compounds.c. Let us now assume that the troposphere can be divided into Northern and

Southern Hemispheres with an interhemispheric fractional mixing rate of m yr-i.The rate of removal from the atmosphere, p yr-l, is assumed to be the same inboth hemispheres. If all the manufacture and release of the compound are as-sumed to occur in the Northern Hemisphere, then let us find the ratio of concen-trations, R, between the Northern and Southern Hemispheres at any time t. Let

MN = mass of species in Northern Hemisphere

Ms = mass of species in Southern Hemisphere

Show that the hemispheric material balances are

dMNdt

dMsdt

= Poert - pMN + m(Ms - MN)

= m(MN - Ms) - pMs

MN(O) = Ms(O) 0

PoMN + Ms = _(err - e-pt)r+p

show that

e-pt

2(r + p + m)ert - (r + p + 2m)e-pt - (r + p)e-(2m+p)1MN(t)

Ms(t)R= --

2me,t - (r + p + 2m)e-pt + (r + p)e-(2m+p)t

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3 Atmospheric Photochemistryand Chemical Kinetics

3.1 RADIATIVE FLUX IN THE ATMOSPHERE

The essential energy flux in atmospheric chemistry is the flux of solar radiation. The radi-ant flux density F is the radiant energy flux across any surface element, without considera-tion of the direction; F is measured in watts per square meter (W m-1. The radiant fluxdensity is called the irradiance E when the radiation is received on a surface. Thus F andE are often used interchangeably. We will use F in general and E when we are referringspecifically to the radiant flux density on a surface. The radiance L is the radiant flux as afunction of the solid angle d{J) crossing a surface perpendicular to the axis of the radiationbeam; L is measured in watts per square meter per steradian (W m-2 sr-I). The radiance asa function of direction gives a complete description of the radiative field.

Consider a beam of radiation of radiance L crossing a surface dS with the beam axismaking an angle e to the normal to dS (Figure 3.1). dS projects as dS cos e perpendicularto the beam axis of the radiation, and the radiant flux density dF on dS is

dF = Lcos(J dw

The radiant flux density, or irradiance, on the surface dS is obtained by integrating the ra-diance over all angles,

E = f L case dw

When the radiance L is independent of direction, the radiative field is called isotropic. Inthis case, (3.2) can be integrated over the half space, n = 271; and the relation between the

irradiance and the radiance is

E = JrL

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RADIATIVE FLUX IN THE ATMOSPHERE 127

Sometimes the spectral radiant flux density is expressed as a function of frequency v,that is, F(v). Because the frequency v of radiation is related to its wavelength by (1.13),v = ciA, F(A) and F( v) can be interrelated. Since the flux of energy in a small interval ofwavelength dA must be equal to that in a small interval of corresponding frequency d v,

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~ )F(V)

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Generally we will deal with wavelength as the variable rather than frequency, althoughthey can easily be interrelated as indicated in (3.6).

3.1.1 Solar Radiation Received on Earth

Light absorption and scattering by atmospheric constituents attenuate the solar radiation asit passes through the atmosphere. The amount of attenuation depends on the nature andconcentration of gases and particles and on the pathlength through which the solar beampasses. The pathlength is a function of the angle of the Sun, which depends on time of day,latitude, and date. Also, reflection of radiation from the Earth's surface contributes to the

radiation at any point in the atmosphere.Table 3.1 gives the solar spectral irradiance, normalized to a solar constant of 1367

W m-z. Solar UV radiation, expressed in units of photons cm-z S-I nm-l, at the surface(0 kIn), 20, 30, 40, and 50 kIn is shown in Figure 3.3. (A discussion of the processes thatlead to the progressive attenuation of radiation was given in Chapter 1 in association withFigure 1.9.) Usually radiative transfer through the atmosphere is calculated by radiativetransfer models that divide the atmosphere into layers and the radiative spectrum intowavelength intervals (Goody and Yung, 1989; Liou, 1992; Lenoble, 1993). The verticaldistribution of trace gases and particles and the surface albedo serve as inputs to such mod-els. Near the Earth's surface the spectral distribution shows a steep cutoff, when movingfrom longer to shorter wavelengths, beginning at about 320 nm. Radiation below 290 nmdoes not reach the Earth's surface; as noted in Chapter 1, this cutoff is the result of absorp-tion of solar radiation by stratospheric ozone. There is no overlap between the absorptioncross section of the major atmospheric gases, Nz, Oz, COz, and HzO, and the solar spectrumat the Earth's surface. Overlap does exist, however, with a number of trace gases that are

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RADIATIVE FLUX IN THE ATMOSPHERE 129

TABLE 3.1 (Continued)

f;F(A')dA'(W m-2)J;F(X)dX

(W m-1F(A)

(W m-2 nm-1F(A)(W -2 -I,

m om A (nm)A (nm)13131319132513291332133613421346134913531355135713601362136413661367

0.0660.0540.0470.0410.0360.0310.0240.0190.0150.0120.0100.0080.0050.0030.0020.0010.000

11201140115911761191120512181230124112511260126712741281128712981307

0.4380.3870.3530.3230.2960.2730.2470.2340.2170.1870.1690.1480.1330.1260.1160.0930.075

Source: Frohlich and London (1986).

important in tropospheric chemistry. In spite of its stratospheric absorption, a sufficientoverlap exists between the solar UV spectrum at the Earth's surface and the absorptioncross section of ozone that 03 photolysis is also important in tropospheric chemistry.

3.1.2 Earth Geometry for Solar Radiation

Because of the rotation of the Earth around the Sun and its daily rotation around itself, thesolar irradiance actually received at a given location on Earth depends on the location onthe Earth, the date of the year, and the time of day. The Earth describes an ellipse aroundthe Sun. The shortest distance between the Earth and Sun, occurring around January 3, is1.471 X 108 kIn, and the largest distance, around July 4, is 1.521 X 108 kIn. The mean dis-

tance, the average of the two extremes, is 1.496 X 108 kIn.The Earth rotates in an eastward direction around the polar axis, which is inclined at

23 °27' from the normal to the ecliptic plane. The line joining the center of the Earth to thecenter of the Sun makes an angle 11 with the equatorial plane, which is called the Sun dec-lination with the equatorial plane. 11 reaches its maximum value of + 23 °27' at the summersolstice around June 21; it reaches its minimum value of -23°27' at the winter solstice,around December 21, and is zero at the spring and fall equinoxes. 11 can be computed at anyday of the year by 11 (in radians) = -0.4cos[27r(dn + 10)/365], where dn = 1 for January

1,2 for January 2, and so on.

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RADIATIVE FLUX IN mE ATMOSPHERE 131

FIGURE 3.4 Definition of latitude andlongitude of a point M on the Earth. Ozis the local vertical.

The period of the Earth's rotation is constant and is measured by the interval of time be-tween two successive passages of a star in the observer's meridian. This is called the side-real day. The interval of time between two successive passages of the Sun in the observer'smeridian, the solar day, is slightly longer (by about 4 minutes) than the sidereal day. Also,because of the ellipticity of the orbit and the inclination of the axis, the solar day is not con-stant throughout the year. For practical purposes, we use a mean solar day divided into 24hours. Local mean time (LMT) noon is defined on this basis. The real Sun passes in themeridian either earlier or later than the average Sun. The passage of the real Sun in the ob-server's meridian defines the local true solar time (TST) noon. The difference between thetrue solar time and the local mean time is ET = TST - LMT, which varies between :t 15

FIGURE 3.5 Horizontal coordinates of theSun: eo = solar zenith angle; h = altitude

angle; <Po = azimuthal angle.

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ABSORPTION COEFFICIENT AND ABSORPTION CROSS SECTION 133

3.2 ABSORPTION COEFFICIENT AND ABSORPTIONCROSS SECTION

Consider the propagation of radiation through a medium and select a layer of thickness dxperpendicular to a beam of intensity F (Figure 3.7). The loss of intensity F over the infini-tesimal slice dx as a result of light absorption is

dF = -baF dx (3.10)

where ba is the absorption coefficient (m-l) of the medium. For a finite path between Xl andX2, integration of (3.10) gives

F(X2) = F(x,) exp( -8a)

where

ba{x) dx (3.12)

is the absorption optical thickness (dimensionless) between Xl and X2' If the medium is ho-mogeneous, ba(x) = ba, independent of X, and

F(xV = F(XI)eXp[-ba(X2 -XI)] (3.13)

This result is known as the Beer-Lambert law of extinction. When x is measured verticallyin the atmosphere the optical thickness is called the optical depth.

The transmittance of the layer between XI and X2 along the direction of propagation isdefined byI

F(xV = exp( -b'a)

'f=~

Ildx

.. .

F(x.; F(~FIGURE 3.7 Propagation of radiation through a medium.

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ACTINIC FLUX 137

As indicated, the quantity on the R.H.S. multiplying nA is jA. The spectral actinic flux isthen the radiative quantity that drives the photodissociation, that is, the quantity that mul-tiplies rPA(A)aA(A) to produce a product that when integrated over all wavelengths pro-duces the photodissociation rate coefficient.

The spectral actinic flux I (A) is then

I(J..) = !L(J..,(},</» dw

w(3.23)

= f f L(A, 0, 4» sinO dO d4>

t/> IJ

The spectral irradiance E()") is the radiant energy crossing a surface (per unit surface area,time, and wavelength) and is calculated from L()", 0, 4» by (3.4),

E()") = f f L()", e, 4» cose sine de d4>

"'9(3.24)

The factor cos () reflects the change in the projected area of the surface as the angle of in-cidence is varied. This factor does not appear in the expression for the actinic flux becausethe projected area and the pathlengths offset exactly. As the angle of incidence is changedfrom overhead «() = 0°) to nearly glancing «() -+ 90°), the energy (irradiance) incidentupon the layer decreases, but the actinic flux remains unchanged because the lower inten-sity is exactly compensated for by the longer pathlength of light through the layer.

Two special cases exist, collimated and isotropic light, in which simple relationships ex-ist between actinic flux and irradiance (Madronich, 1987). These two limiting cases oftencan be used to approximate atmospheric situations. Collimated light can be considered tobe parallel, having originated from a very small solid angle Ll(JJ(j. An example is the directsolar beam, which subtends Ll(JJ(j ~ 7 X 10-5 sr at the Earth. Over this small solid anglethe radiance may be taken as constant, while at all other solid angles it equals zero:L«(}"p) = Lo = constant over the solid angle Ll(JJ(j centered about «(}o, CPo). In this case(3.23) and (3.24) become

10 = Lo~~

Eo = Lo cas (Jo ~~(3.25)

(3.26)

Thus, if Lo is the extraterrestrial solar radiance, Eo is the solar irradiance at the top of the at-

mosphere.The other special case is that of isotropic radiation, L«(J,4» = Ll = constant. In this

case

I = 21TLI

E = 1TL.(3.27)

(3.28)

Equation (3.28) is identical to (3.3).

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ACTINIC FLUX 139

TABLE 3.2 Relation Between the Slant Path OpticalDepth m and sec 80 for a Standard Rayleigh Atmosphere

SOU Ire: Kasten and Young (1989).

If Foo(A) is the spectral radiant flux density at the top of the atmosphere (TOA), that atground level on a plane perpendicular to the solar beam can be determined from an exten-sion 0(3.11),

F(A) = Foo(A) exp[ -m8(A)] (3.37)

where 8(A) is the total atmospheric optical depth at wavelength A, and m is the ratio be-tween the slant path optical depth for the actual solar zenith angle (Jo and the overhead Sunoptical depth (Figure 3.8). When the Sun is directly overhead «(Jo = 0°), m = 1.0 and at-mospheric attenuation is at its minimum. As the Sun approaches the horizon, (Jo increasestoward 90°, m increases and the attenuation of sunlight increases as a result of the increasedpathlength. When the sphericity of the Earth can be neglected,

1m = - = secf}o (3.38)cos eo

This relation holds for eo less than about 75°. For larger values of eo, m has to be com-puted, taking into account the path through the spherical atmospheric layers, the verticalprofile of absorbing and scattering species, and the curvature of the optical rays as a resultof refraction. Values of m are given in Table 3.2 for the molecular atmosphere, that is, the

Rayleigh scattering optical depth!

2The TOA radiative flux can be estimated by measuring E()..) on a surface at ground level for various solar zenithangles (Jo and plotting In E()..) versus m and extrapolating to m = O. The slope of the best-fit straight line is 8()..)

This method of calculating E-C)..) is called the Bouguer-Langley method. Integrating E_()..) over all wavelengths

produces the solar constant So'

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ATMOSPHERIC PHOTOCHEMISTRY 141

of radiation can only occur if an upper energy level of the molecule exists that is separatedfrom the lower level by an energy equal to that of the incident photon. Small moleculesgenerally exhibit intense electronic absorption at wavelengths shorter than do larger mol-ecules. For example, N2 and H2 absorb significantly at wavelengths less than 100 nm, whileO2 absorbs strongly for A < 200 nm, H2O for A < 180 nm, and CO2 for A < 165 nm.

As radiation penetrates deeper into the atmosphere the shorter wavelengths are progres-sively removed (recall Figure 1.10; also Figure 3.3). Photochemistry in the troposphere isconfined to molecules that absorb radiation of wavelengths exceeding about 290 nm.

The primary step of a photochemical reaction may be written

A+hv~A*

where A * is an electronically excited state of the molecule A. The excited molecule A * may

subsequently partake in:

DissociationDirect ReactionFluorescenceCollisional deactivationIonization

IA*--+-B1 + B2

2A* + B--+-CI + C2

3A*--+-A+hv

4A* +M--+-A+M

5A*--+-A+ +e

The quantum yield for a specific process involving A * is defined as the ratio of the num-ber of molecules of A * undergoing that process to the number of photons absorbed. Sincethe total number of A * molecules formed equals the number of photons absorbed, thequantum yield cf>i for a specific process i, say, dissociation, is just the fraction of the A *

molecules that participate in path i. The sum of the quantum yields for all possibleprocesses must equal 1.

The rate of formation of A * is equal to the rate of photon absorption and is written4

d[A *]dt

(3.41)= ;A [A]

where jA, having units S-I, is the first-order rate constant for photolysis or the so-calledspecific absorption rate; jA is normally taken to be independent of [A]. The rate of forma-tion of B 1 in step I is

(3.42)~ =cf>tjA [A]dt

where cf>l is the quantum yield of step 1.Photodissociation of a molecule can occur when the energy of the incoming photon ex-

ceeds the binding energy of the particular chemical bond. Thus the excited species A * can

lie energetically above the dissociation threshold of the molecule. One or more of the prod-

'In writing chemical reaction rate equations we will generally use [A] to denote the concentration of species A,r..thpr th.." r.

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Table 3.3 summarizes important light-absorbing molecules in atmospheric chemistry.Photodissociation of molecular oxygen is key to stratospheric chemistry and will be ad-

TABLE 3.3 Some Photochemical Reactions of Importance in Atmospheric Chemistry"

Reaction Comments

Photodissociation of molecular oxygen results pri-marily from absorption of solar radiation in the200-220 nm wavelength region. The 185-200 nmregion, the O2 Schumann-Runge band spectralrange, is also important since solar radiation pene-trates efficiently into the stratosphere at thosewavelengths. Recommended absorption cross sec-tions are given by DeMore et al. (1994).

03 absorption cross sections are given in WMOReport No. 16 (1986) and DeMore et al. (1994).DeMore et al. (1994) present a polynomial ex-pression for the quantum yield forO(ID) produc-tion, cP(OID), as a function of Ii and T in the range305-320 nm. The upper limiting value of cP(OID)is taken as 0.95 at 305 nm. Discrepancies exist be-tween published O(ID) quantum yields, which canbe separated into two groups: those that show cf> todrop to zero at about 315 nm (DeMore et al.,1994) and those that exhibit a "tail" extending be-yond 320 nm (Michelsen et al., 1994). In evaluat-ing ambient data against both groups of quantumyields, Hofzumahaus et al. (1995) found that thecf> data exhibiting a tail above 315 nm better repre-sent observed data. As noted in the text, the impli-cation of this finding is that solar photolysis of 03at wavelengths longer than 310 nm contributessignificantly more to tropospheric O(ID) forma-tion than that based on the recommended correla-tion of DeMore et al. (1994).

O2 +hv ~O + O('D) > 50km

~O+O

I03 + hV--02 + 0

2-- O2 + 0(10)

at 40 kID

at 10 kID

h = 10-3 S-I

h = 10-5 s-t

continued

SMadronich and Weller (1990) calculated tropospheric photolysis rate constants for N02, 03, HONO, HCHO, andCH3CHO using high spectral resolution (~A = 0.1 nm) and compared these to values calculated with ~A = I,

2,4,6,8, and 10 nm. Depending on the molecule, substantial errors were found to be introduced with the coarser

resolution calculations.

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TABLE 3.3 (Continued)

CommentsReactionI

HCHO + hv--+- H + HCO

2--+- H, + CO

CH3OOH + hv--products

Cl2 + hv~CI + CI

ClOG + hv-+CIO + 0

OCIO + hv--'O + CIO

HOCI + hv OH + CI

1CIONO2 + hv-+CI +NO3

2-+CIO + NO2

CCl3F + hv--+products

CCl2F2 + hjl~products

OCS + hv~CO + S

ICH3CHO + hv--+CH4 + CO

2--+CH3 + HCO

Formaldehyde photolysis is a significant source offree radicals in the troposphere. Absorption crosssections for HCHO are given by DeMore et al.(1994). DeMore et al. (1994) give quantum yields,cf>1 and cf>20 from 301 to 356 nm. Channell pre-dominates at shorter wavelengths and channel 2 at

longer wavelengths.

Absorption cross sections for CH3OOH from 210 to360 nm are given by DeMore et al. (1994).

Absorption cross sections for Clz from 260 to470 nm are given by DeMore et al. (1994).

Absorption cross sections for ciao from 220 to280 nm are given by DeMore et aI. (1994).

Absorption cross sections for OCIO from 272 to475 nm are given by DeMore et al. (1994).

Absorption cross sections for HOCI from 200 to 380nm are given by DeMore et aI. (1994).

Absorption cross sections for CIONOz from 196 to414 nm are given by DeMore et aI. (1994). Thepreferred quantum yield vaIues are cf>1 =0.6 (). < 308 nm), cf>. = 1.0 (). > 364nm),and cf>z = I - cf>1'

Absorption cross sections for CCI3F from 170 to 260nm are given by DeMore et al. (1994).

Absorption cross sections for CClzFz from 170 to240 nm are given by DeMore et aI. (1994).

Absorption cross sections for OCS from 186 to 296nm are given by DeMore et al. (1994). The rec-ommended quantum yield for photodissociationis 0.72.

Absorption cross sections for acetaldehyde havebeen measured by Martinez et al. (1992) at 300 :t2 K over the wavelength region 200-366 nm.Recommended quantum yields for channels I and2 have been tabulated by Atkinson et al. (1992).

Absorption cross sections and quantum yields foracetone have been summarized by Atkinson et al.(1992). An average photodissociation quantumyield for CH3CO formation is about 0.33 over thewavelength region 280-330 nm.

CH3C(O)CH3 + hv-CH3 + CH3CO

"Many of the rate constants for reactions important in atmospheric chemistry are surveyed periodically by a grouporganized through the Jet Propulsion Laboratory (JPL), Pasadena, CA. The latest report is that of De More et aI.(1997) Evaluation No. 12, JPL Publication 97-4. Recommended values of rate constants, absorption cross sec-

tions, and quantum yields appear in these reports.

145

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Photolysis Energy, cm-lFIGURE 3.10 Primary quantum yield for 0(10) formation from 03 photolysis at 298 K. Summaryof data presented by Michelsen et al. (1994).

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IL, nmFIGURE 3.12 Primary quantum yield for 0 formation from NO2 photolysis, as correlated byDemerjian et al. (1980).

wavelengths, there is insufficient energy to promote bond cleavage. The point at which dis-sociation fails to occur is not sharp because the individual molecules of NO2 do not possessa precise amount of ground-state energy prior to absorption. The gradual transition area(370 to 420 nm) corresponds to a variation in ground-state energy of about 40 kJ mol-I.This transition curve can be shifted slightly to longer wavelengths by increasing the tem-perature and therefore increasing the ground-state energy of the system. Table 3.5 givestabulated values of the NO2 absorption cross section and quantum yield at 273 and 298 K,and Table 3.6 illustrates the calculation of the photolysis rate jN02 for noon, July 1, at40oN.

Example 3.2 Atmospheric Heating Rates: The Chapman Function The nature ofthe attenuation that occurs as radiation penetrates the atmosphere can be seen by consider-ing the Beer-Lambert law of light absorption for a single absorbing component,

dF(A) = -a(A)NF(A) dx (3.47)

where a(A) is the absorption cross section (cm2 molecule-'), N is the concentration ofthe species (molecules cm - 3), F( A) is the spectral radiant flux density at wavelength A

(W m-2 nm-I), and dx is an increment of optical path. If the absorbing species is uni-formly mixed in the atmosphere, that is, it has a uniform mixing ratio, its concentrationcan be written as

N = Nt~ (3.48)

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TABLE 3.6 Calculation of the Photolysis Rate of NO2 at Ground Level, July 1,Noon, 40° N, 298 K

3.14 X 1012

3.35 X 1013

1.24 X 1014

2.87 X 1014

4.02 X 1014

5.08 X 1014

7.34 X 1014

7.79 X 1014

7.72 X 1014

8.33 X 1014

8.32 X 1014

9.45 X 1014

8.71 X 1014

9.65 X 1014

1.19 X 1015

1.07 X 1015

1.20 X 1015

9.91 X 1014

1.09 X 1015

1.13 X 1015

1.36 X 1015

1.64 X 1015

1.84 X 1015

1.94 X 1015

1.97 X 1015

9.69 X 1014

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1.221.431.742.022.332.652.973.283.613.914.184.514.755.005.235.415.575.695.845.865.935.865.895.785.735.78

Total jNO2 = 8.14 X 10-3 S-l

jNO2 = 0.488 min-1

a Actinic flux from Finlayson-Pitts and Pitts (1986).

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CHEMICAL KINETICS 153

where Nj is the number concentration of species i (cm-3), (8kT /;rmij)1/2 is the root-mean-square relative speed of the i and j molecules, k is the Boltzmann constant,mij = mimj/(mi + mj) is the reduced mass, and ;rUi} is the so-called collision cross sec-tion of molecules i andj. The characteristic time during which molecules in thermal motionin a gas are close enough to interact is brief, on the order of 10-12 to 10-13 s. At ambienttemperature and pressure the mean time between molecular collisions can be shown from(3.53) to be on the order of 10-9 s. Thus collisions are short in duration compared to thetime between collisions.

Whereas the collision of two molecules is a necessary condition for reaction, sufficientenergy must be available to break chemical bonds. Theory indicates that the fraction of col-lisions involving energy greater than a required energy E is given by exp (- E / kT). In thisform E has units of energy per molecule. More commonly, E is expressed in terms of en-ergy per mole, and we use exp( -E/ RT), where R is the universal gas constant. The rateof reaction is expressed in a form that accounts for both the frequency of collisions and thefraction that exceed the required energy,

(3.54)

The preexponential factor A(T) may depend on temperature since the translational kineticenergy and internal degrees of freedom of the molecules influence the probability of reac-tion in any collision event.

The rate of reaction is usually written as r = kcjcj, where the parameter k is called therate constant,6

E'RT

k = A(T) exp( - (3.55)

If A(T) is independent of T, we have the Arrhenius form, k = A exp( - E / RT). The max-imum possible value of the rate constant of a bimolecular reaction is achieved if every mol-ecular collision between molecules of i and j results in reaction. This is called thegas-kinetic collision rate, and the corresponding value of the second-order rate constant kat room temperature is about 2 X 10-10 cm3 molecule S-I. Most reactions have rate con-stants less than this. First, the activation energy E must be overcome for the reaction to pro-ceed. Second, molecules that are geometrically complex may have to be aligned properlyat the point of collision for reaction to take place and perfect alignment is not achieved inevery collision.

Consider the potential energy surface for the bimolecular reaction (most elementary re-actions can be considered to be reversible)

fA+BC~AB +C

b

~e rate constant k is not to be confused with the Boltzmann constant. The latter will always appear as a productwith T in this context.

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molecule denoted by A *, followed by decomposition of A * to give B + C,

A*~B + c

Note that A * may return to A by collision and transfer of its excess energy to an M. The rate

equations for this mechanism are

d[A]

The reactive intennediate in this mechanism is A *. The PSSA states that the rate of gener-ation of A * is equal to its rate of disappearance; physically, what this means is that A * is soreactive that, as soon as an A * molecule is fonned, it reacts by one of its two paths. Thus

the PSSA gives

kIf [A] [M] - k1b[A*][M] - k2[A*] = 0 (3.59)

From this we find the concentration of A * in terms of the concentrations of the stable

molecules A and M,

k1f[A][M]

k1b[M] + k2[A *] =

This expression can be used in (3.57) to give

d[A]dt (3.61)

- - klfk2[M][A]- k1b[M] + k2

We see that the single overall reaction A -+ B + C with a rate given by (3.61) dependson the concentration of M. If the background species M is in such excess that its concen-tration is effectively constant, the overall rate can be expressed as d[A]/dt = -k[A],

where k = k1fkz[M]/(k1b[M] + kz) is a constant. If k1b[M] »kz then d[A]/dt =-k[A], with k = k1fkz/k1b. On the other hand, if k1b[M] «kz, then d[A]/dt =-k]f[M][A], and the rate of the reaction depends on the concentration of M.

One comment is in order. The PSSA is based on the presumption that the rates of for-mation and disappearance of a reactive intermediate are equal. A consequence of this state-ment is that d[A*]/dt = 0 from (3.58). This should not, however, be interpreted to meanthat [A*] does not change with time. [A*] is at steady state with respect to [A] and [M].We can, in fact, compute d[A*]/dt. It is

d[A*]dt

(3.62)- ~ k)f[A][M]- dt k)b[M] + k2

= -k(f[A][M] + k1b[A*][M]dt

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:HEMICAL KINETICS 1-"7

The time behavior of 0 following irradiation beginning at t 0 is

[0]Rl

k3[O2]exp(-k3[OZ] [M]t)) (3.64)

At 80 km, T = 200 K, at which k3 = 1.4 X 10-33 cm6 molecule-2 S-I. The exponentialterm in (3.64) is <0.01 for t ~ 1.8 X 105 s (50 h). Thus the time needed for 0 to establisha steady-state concentration is much longer than that over which the solar intensity varies,and 0 is never in steady state at this altitude in the atmosphere. The reason why, at this al-titude, 0(10) achieves a steady state and 0 does not, is based on the relative rates of the re-moval reactions. That for 0('0) is sufficiently fast; that for 0 is too slow to "keep up with"the formation step. In the lower regions of the atmosphere, where the pressure is large, andhence the concentration of third bodies, M, is large, removal reactions for both 0 and0(10) are, under all conditions, sufficiently fast that steady states are rapidly establishedfor both species.

3.5.2 Pressure Dependence of Reactions

Certain reactions have an order that is variable with pressure; they are third order at lowpressure and second order at high pressure. Consider, for example, the combination of twooxygen atoms (0(3p) in the triplet- P ground state, which we will denote simply by 0) toform O2, Upon collision the newly formed O2 molecule possesses the combination energyof 0 + O. Unless some energy is removed within the time of one vibrational period, thefreshly formed O2 will decompose back to 0 + O. The excess energy is removed by thethird body, M. The overall reaction is written as

O+O+M-+O'J+M

But the elementary steps are

ot20+0

+O,+M

where the dagger-denotes vibrational excitation. The rate of formation of a product AB inthe general system

ABtA+B

ABO M +AB+M

d[AB]dt

kaks[A][B][M]ks[M] + kr

3.65)

If the newly formed molecule is larger than diatomic, there are several vibrational modesinto which the bond combination energy can be converted. In such a case, the lifetime ofthe newly formed molecule can extend over several vibrational neriods hefore the critical

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(3.72)

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PROBLEMS 161

Hofzumahaus, A., Kraus, A., and Milller, M. (1995) Comparison of tropospheric photolysis fre-quency data J(O'D) measured simultaneously by chemical actinometry and spectroradiometry:test of laboratory O(ID) quantum yield data, in Tropospheric Oxidation Mechanisms, edited byK. H. Becker. European Commission, Report EUR 16171EN, Luxembourg, pp. 71-76.

Kasten, F., and Young, A. T. (1989) Revised optical air mass tables and approximation formula, Appl.Opt. 28,4735-4738.

Lenoble, J. (1993) Atmospheric Radiative Transfer: A. Deepak Publishing, Hampton, VA.Liou, K. N. (1992) Radiation and Cloud Processes in the Atmosphere. Oxford University Press,

Oxford, UK.Madronich, S. (1987) Photodissociation in the atmosphere I. Actinic flux and the effects of ground

reflections and clouds, J. Geophys. Res., 92,9740-9752.

Madronjch, S., and Weller, G. (1990) Numerical integration errors in calculated tropospheric pho-todissociation rate coefficients, J. Atmos. Chem., 10, 283-300.

Martinez, R. D., Buitrago, A. A., Howell, N. W., Hearn, C. H., and Joens, J. A. (1992) The near UVabsorption-spectra of several aliphatic aldehydes and ketones, Atmos. Environ., 26, 785-792.

Merienne, M. F., Jenouvrier, A., and Coquart, B. (1995) The N02 absorption spectrum. I. Absorptioncross-sections at ambient temperatures in the 300-500 nm region, J. Atmos. Chem., 20, 281-297.

Michelsen, H. A., Salawitch, R. J., Wennberg, P.O., and Anderson, J. G. (1994) Production ofO(ID)from photolysis of 03, Geophys. Res. Left., 21,2227-2230.

Troe, J. (1983) Specific rate constants k(E, 1) for unimolecular bond fissions, J. Chem. Phys., 79,6017-6029.

Wayne, R. P. (1991) Chemistry of Atmospheres, 2nd ed. Oxford University Press, Oxford, UK.World Meteorological Organization (WMO) (1986) Atmospheric Ozone 1985. Global Ozone

Research and Monitoring Project, Report No. 16, Geneva.

PROBLEMS

3.1B Consider the following reaction system

A~BB+M~C

Assume M is present in great excess, so that [M] ~ constant. The concentrations ofB and C are zero at t = O.

8. Derive analytical expressions for the exact dynamic behavior of this system overtime. Show mathematically under what conditions the pseudo-steady-state ap-proximation (PSSA) can be made for [B].

b. Use the PSSA to derive a simpler set of equations for the concentrations of A, B,andC.

3.28 The most important oxidizing species for tropospheric compounds is usually the hy-droxyl (OH) radical. A standard way of determining the OH rate constant of a com-pound is to measure its decay in a reactor in the presence of OH relative to the decayof a second compound, the OH rate constant of which is known. Consider two com-pounds A and B, A being the one for which the OH rate constant is to be determinedand B the reference compound for which its OH rate constant is known. Show that the

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s

BASIC PHOTOCHEMICAL CYCLE OF N02, NO, AND 0, 235

BASIC PHOTOCHEMICAL CYCLE OF N02, NO, AND 035.1

When NO and NOz are present in sunlight, ozone formation occurs as a result of the pho-tolysis of NOz at wavelengths < 424 nm,

(5.1)

(5.2)

NO2+hv ~ NO+O

O+O2+M~O3+M

where M represents N2 or O2 or another third molecule that absorbs the excess vibrationalenergy and thereby stabilizes the 03 molecule formed. There are no significant sources ofozone in the atmosphere other than reaction 5.2. Once formed, 03 reacts with NO to re-

generate N02,

03 + NO -- N02 + O2

Let us consider for a moment the dynamics of a system in which only these three reac-tions are taking place. Let us assume that known initial concentrations of NO and NO2,[NO]o and [NO2]o, in air are placed in a reactor of constant volume at constant temperatureand irradiated. The rate of change of the concentration of NO2 after the irradiation begins

is given by

d[NO2]dt

- j5.1 [NO2] + k5.3[O3][NO]

Treating [02] as constant, there are four species in the system: N02, NO, 0, and 03, Wecould write the dynamic equations for NO, 0, and 03 just as we have done for N02. For ex-ample, the equation for [0] is

d[O]dt

= j5.I[NO2] - k5.2[O][O2][M]

However, if we were to evaluate the right-hand side numerically we would find that it isvery close to zero. Physically, this means that the oxygen atom is so reactive that it disap-pears by reaction 5.2 virtually as fast as it is formed by reaction 5.1. In dealing with highlyreactive species such as the oxygen atom, it is customary, as noted in Chapter 3, to invokethe pseudo-steady-state approximation (PSSA) and thereby assume that the rate of forma-tion is exactly equal to the rate of disappearance, for example,

jS.1 [NO2] = kS.2[O][O2][M]

The steady-state oxygen atom concentration in this system is then given by

jS.1 [NOz]ks.z[Oz][M]

[0]88 =

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Z/I . V z. I

BASIC PHOTOCHEMICAL CYCLE OF N02. NO. AND 0, 237

ing ratio of N02 with [03]0 = [NO]o = 0:

1001000

If, on the other hand, [NOz]o = [03]0 = 0, then [03] = O. This is clear since with no N02

there is no means to produce atomic oxygen and therefore ozone. Thus the maximumsteady-state ozone concentration would be achieved with an initial charge of pure NOz.The mixing ratios of ozone attained in urban and regional atmospheres are often greaterthan those in the sample calculation. Since most of the NOx emitted is in the form of NOand not NOz, the concentration of ozone reached, if governed solely by reactions 5.1 to 5.3,would be far too low to account for the actual observed concentrations. It must be con-cluded that reactions other than 5.1 to 5.3 are important in tropospheric air in which rela-tively high ozone concentrations occur. Shortly we will see what those reactions are.

Example 5.1 Measurement of the Photolysis Rate of NOz The photolysis of NOz isa key atmospheric reaction. Its photodissociation rate can be calculated if the actinic fluxI (A)- is known. However, such measurements require specialized apparatus that is complexand expensive. A method that allows one to determine the NOz photodissociation rate, j5.1,directly circumvents the need for elaborate measurements of the radiation intensity. By ex-posing a mixture of NOz and Nz to sunlight one can determine the value of j5.1 by com-paring the measured NOz decay as a function of time with that obtained by integration ofthe rate equations. To integrate the rate equations it is necessary to assume a value for j5.1.The desired value of j51 is that which produces agreement between the observed and pre-

dicted NOz decay.In the previous analysis we considered only reactions 5.1 to 5.3. There are several other

reactions that occur in the NOx-Nz system that should be included for a more complete

analysis. These are'

(5.

(5.

(5.

(5.

(5.

(5.

0 + N02 -+ NO + 02

0+N02 +M -+ N03 +M

NO+ N03 -+ 2N02

0 + NO + M -+ N02 + M

N02 + N03 + M -+ N20S + M

N20S + M -+ N02 + N03 + M

I Actually in the presence of sunlight NO3 photolyzes very rapidly (see Section 5.6) so that we do not expect day-

light NO, levels to be appreciable. NO, is added to the mechanism at this point largely for completeness.

11)

12)

13)

14)

15)

16)

31I3HdSOdO~.L 3H.L dO J..~SIW3HJ 8fZ

ATMOSPHERIC CHEMISTRY OF CARBON MONOXIDE AND NO, 239

6.0. I I I I I I

~~~~

6 3.0

.~~OJ) 2.0=><

~

N0Z 1.0

~~~

5.0

4. ~2 = 1 atm

k = 0.14 min-I. . .

kl = 0.32 min-

0

~~

. .

~

0,8 Experimental data 0 0

~ Integration of mechanism 00

0.61 I I I I I I ~01 23 4 56 7

Irradiation Time, minFIGURE 5.1 NO2 mixing ratio as a function of time in a system initially comprising 5 ppm NO2 inN2. Experimental data and the predictions of the mechanism in the text are shown for two light in-

tensities (Holmes et al., 1973).

5.2 ATMOSPHERIC CHEMISTRY OF CARBON MONOXIDE AND NO,

We noted that in order to explain frequently observed atmospheric ozone levels it is neces-sary that reactions other than 5.1 to 5.3 must be invoked. For these we must turn to the nextmajor class of tropospheric compounds, carbon-containing species. In some respects thesimplest atmospheric carbon-containing species is CO. Carbon monoxide does not, how-ever, react readily with any of the species present in the NOx-air system.

We already know from Section 4.2 that ozone photolysis to produce both ground-state(0) and excited singlet (O(ID)) oxygen atoms is important in both the stratosphere and tro-

posphere,

(5.21a)

(5.21b)

03 +hv -+- 0+02

-+- 0(10) + 02

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241ATMOSPHERIC CHEMISTRY OF CARBON MONOXIDE AND NO,

The atmospheric oxidation of CO can be summarized as follows:

~CO+OH. ~ CO2 + HO2'

HO2.+NO ~ NO2+0H.

NO2+hv ~ NO+O

O+O2+M~O3+M

co + 202 + hv--+ CO2 + 0,Net

Note that neither OH nor H02 is consumed in this reaction cycle, which can be viewed asa catalytic oxidation of CO to CO2- Net formation of 03 occurs because the conversion ofNO to N02 is accomplished by the H02 radical rather than by 03 itself. This set of reactionscan occur repeatedly until one of the molecules is removed in a termination reaction.

Termination of the chain can occur when OH and N02 react to form nitric acid,

OH. +NO2+M -+ HNO3 +M (5.26)

Again, we have already encountered this reaction in the stratosphere. (Termination can alsooccur when HO2 reacts with itself, but at this point we assume that NOx concentrations are

sufficiently large that the self-reaction of HO2 is not favored.)In analyzing this mechanism, the PSSA, as applied to this system, can be represented in

terms of the rates of the nine reactions as2'

[0]88Rs.I - RS.2 + RS.22 = 0jS.1 [N02] - kS.2 [0] [02] [M] + kS.22 [M] [0(10)] = 0

[O(IO)]SSRS.21b - RS.22 + RS.23 = 0kS.21b [03] - kS.22[M] [0(10)] - kS.23 [H2O] [0(10)] = 0

[OH]ss[HO2]ss

2Rs.23 - RS.24 + RS.2S - RS.26 = 0RS.24 - Rs.2s = 0

2kS.23 [H2O] [O( 1 D)] - kS.26 [OH] [N02] = 0

[03]88RS.2 - RS.3 - RS.21 = 0kS.2 [0] [02] [M] - kS.3 [03] [NO] - kS.21b [03] = {\

2In writing rate equations for reactions of the type A + B + M ~ AB + M, for example, reaction 5.26, one must

decide whether to express the rate of the reaction as k[A)[B][M] or k[A)[B]. This is simply an issue of notation,since the value of the rate constant k will depend on the concentration of the third body M through its appropriateformula, as given in Appendix B. We will often choose not to explicitly indicate [M] in the rate equation for such

three-body reactions, keeping in mind that the value of the rate constant will depend on [M] through its appropri-

ate formula.

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ATMOSPHERIC CHEMISTRY OF CARBON MONOXIDE AND NO. 243

The qualitative features of the set of CO/NOx reactions can be described as follows.Photolysis ofN02 produces NO and o. The 0 atom immediately combines with an oxygenmolecule to form 03, Ozone then reacts mainly with NO to regenerate N02o The cycle ofthese three reactions can be represented concisely as (where O2 is not indicated)

hvNO2 ~ NO+O3

The characteristic time of this cycle is usually short enough relative to the competing reac-tions so that a steady state is achieved quickly. The concentration of 03 at such a steady-state condition is given by the photostation~ state relation (5.8). If we now consider thereactions resulting when CO is present, we see that the simple reversible cycle above ismodified to be3

hvNOz ~ NO+03

r HOz I

The HO2 radical that converts NO back to NO2 is converted in the process to OH, whichthen is available to react with another molecule of CO. Thus we obtain two interwovencycles, a "fast" cycle and a "slow" cycle,

hvNOz ~

.NO + 01

CO + qH-E~.

.NO

The CO/NOx reaction mechanism is a chain reaction with OH as the chain carrier. Thechain length Lc of such a reaction is defined as the number of propagation steps occurringfor each termination step,

RS.2S

RS.26

RS.24

RS.26

kS.Z4[CO]

kS.z6[NOz]Lr = (5.31)=

Since the steady-state 03 concentration achieved in the fast cycle is proportional to the ra-tio of [N02] to [NO], the effect of the slow CO cycle is to slowly convert NO to N02 andtherefore to increase the steady-state 03 concentration. Thus, because of the rapidity of theN02/O3 cycle, an independent path that changes the ratio of [N02] to [NO] indirectly con-trols the ozone concentration. It is common to refer to such oxidation chains that are drivenby sunlight as photooxidations.

The basic reaction mechanism of the CO/NOx system exhibits many of the key featuresof those involving much more complex organic molecules. In particular, the role of OH as

-' The presence of water is also necessary to provide a path for formation of hydroxyl radicals after ozone photo]

ysis to give O('D).

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CHEMISTRY OF THE BACKGROUND TROPOSPHERE 245

The rate equations for the photooxidation of a mixture of NO2, NO, and HCHO are, as a re-

sult,

[HCHO]

The chain length of the HCHO photooxidation is given by

R5.25Lc =RS.Z6

2jS.32a + RS.33

RS.z6

1 + kS.33[HCHO]

kS.Z6[NOz]

We see that Lc is always greater than one as long as HCHO is present in the system. Eachmolecule of HCHO that photolyzes via reaction 5.32a leads to the conversion of two mol-ecules of NO to N02 and at the same time generates two OH radicals. The HCHO-OHreaction, on the other hand, leads to one NO to N02 conversion and produces a single OHradical.

The reactivity of the system is controlled by the amount of HCHO. Upon photolysis,HCHO provides two H02 radicals on one path and none on the other. Since these paths areroughly comparable in rate, we can say approximately that each HCHO molecule leads toone H02 molecule. (It leads to exactly one in the OH reaction.) The conversion of NO toN02 and the formation of 03 are therefore driven by HCHO through its production of H02.Thus the theoretical maximum amount of 03 that could be produced in this system is

[03] = [HCHO]o + [N02]o

When all the NOx is converted to HNO3, the system ceases reacting.

5.4 CHEMISTRY OF THE BACKGROUND TROPOSPHERE

We have begun a systematic development of the chemistry of the troposphere. We beganwith carbon monoxide since its atmospheric chemistry is the simplest, while exhibitingsome of the essential elements of hydroxyl radical attack, formation of the hydroperoxylradical, and conversion of NO to NO2. We then proceeded to formaldehyde, the atmos-pheric chemistry of which is slightly more complex than that of carbon monoxide. The nextlogical step would be to consider the simplest alkane, methane (CH4), and that is, in fact,what we will now do. It turns out, moreover, that methane is the principal hydrocarbonspecies in the chemistry of the background troposphere. Thus, in studying the atmosphericchemistry of methane, we are led naturally to the chemistry of the background troposphere.

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Methyl peroxynitrate, CH3OONOb thermally dissociates back to the reactants with a life-time with respect to thermal decomposition of ~ 1 second at room temperature and atmos-

pheric pressure, which increases to ~2 days for the temperature and pressure conditions inthe upper troposphere (Atkinson et aI., 1989; Atkinson, 1990). Methyl peroxynitrate canact as a temporary reservoir of NO2 and CH3O2 radicals in the upper troposphere.

The reaction of CH3O2 with the HO2 radicaIleads to the formation of methyl hydroper-oxide,

(5.42)CH302' + H02' ~ CH300H + 02

which can photolyze or react with the OH radical

(5.43)CH300H + hv --+- CH30, + OH.

CH300H + OH, ~ H2O + CH3O2'

~ H2O + CH200H-!- fast

(5.44a)

(5.44b)

HCHO + OH.

where the fractional splits indicated are those at 298 K. The lifetime of methyl hydroper-oxide in the troposphere resulting from photolysis and reaction with the OH radical is cal-culated to be - 2 days. Methyl hydroperoxide is then a temporary sink of radicals, with itswet or dry deposition being a tropospheric loss process for radicals.

The only important reaction for the methoxy radical under tropospheric conditions iswith O2 to form formaldehyde and the H02 radical,

CH30. + 02 ~ HCHO + H02' (5.45)

Formaldehyde is a "first-generation" product that reacts further, by photolysis by reac-tions 5.32a and 5.32b and with the OH radical, reaction 5.33. Formaldehyde is the first ma-jor product of C~ oxidation with a lifetime longer than a few seconds. The lifetimes ofHCHO resulting from photolysis and OH radical reaction are -4 hours and 1.5 days, re-spectively, leading to an overall lifetime of -3 hours for overhead sun conditions.

Major chain-terminating steps in C~ oxidation include nitric acid and hydrogen perox-ide formation,4

OH. + N02 + M -+ HN03 + M

H02. + H02. -+ H202 + 02

(5.26)

(5.46)

4 The recommended rate constant for reaction 5.46 is (Stockwell, 1995):

kS46 = (kc + kp)fw

kc = 2 X 10-13 exp(600/T)

kp = 1.7 X 10-33 [M] exp(IOOO/T)

fw = 1 + 1.4 X 10-21 [H2O] exp(2200/T)

where Tis in K and [M] and [H2O] are in molecules cm-3. kc is the bimolecular term, kp is the pressure-dependentterm, andfw is a water-vapor-dependent factor. Stockwell (1995) has shown that the contribution of the water-de-pendent term can be very important; at the surface the value of kS46 in air saturated with water vapor is over twicethe value of kS46 in dry air. Above about 15 km the water-dependent contribution is negligible and above 25 kmthe reaction is almost completely bimolecular.

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dation and assuming that the photostationary state holds at any instant, the local rate offormation of 03 as a result of the above cycle is

po] = {kS.2s[HO2] + kS.4o[CH302]} [NO]

As a result of peroxy radical-NO reactions, the photostationary state relation must beadjusted to (Parrish et al., 1986; Ridley et aI., 1992; Cantrell et aI., 1993)

[NO2]--[NO]

kS.3[O3] + kS.2S[HO2] + kS.4o[CH302]

j5.

Measurements made during the spring of 1988 at Mauna Loa, Hawaii, indicated that per-oxy radical mixing ratios of 60 ppt or so were required to account for observations of thisratio (Ridley et al., 1992).

Production of 03 in the CH4 oxidation chain is interrupted if the peroxy radicals H02and CH3O2 react with something other than NO, for example, themselves, N02, or 03 itself,or if NOx is removed from the active cycle by reaction with OH to form HN03. For the H02radical, besides reaction 5.46, another important reaction is

H02' + 03 -+- OH. + 202 (5.47)

Reaction 5.46 is the principal gas-phase source of H2O2 in the atmosphere.

5.4.3 Hydrogen Peroxide

Hydrogen peroxide is the dominant oxidant in clouds, fogs, or rain in the atmosphere.Photochemical activity largely determines the diurnal, seasonal, and latitudinal variationsof the H2O2 concentration. H2O21evels have been found to be higher in the afternoon, dur-ing the summer, and in the southern latitudes (Sakugawa et al., 1990). The major gas-phasedestruction pathways for H2O2 are its reaction with OH and its photolysis,

(5.48)

(5.49)

H202 + OR. ~ H2O + H02

H202 +hv ~ 2 OR.

The destruction of H2O2 in the aqueous phase, mainly by reacting with dissolved S02,is considered in Chapter 6. Van Valin et al. (1990), Boatman et al. (1990), and Daum et al.(1990) reported continuous airborne measurements of H2O2 over the northeastern UnitedStates in June 1987. The range of H2O2 mixing ratios was < 0.2 to 37 ppb, with an aver-age of 2 to 4 ppb. H2O2 concentrations are typically low near the surface, rise to a maxi-mum at the top of the boundary layer, then slowly decrease with height. 'Photochemicalmodel predictions indicate the H2O2 levels depend on whether the atmosphere is in a highor low NOx regime, according to whether radical production is greater or less than the NOxemission rate (Kleinman, 1991). In the low NOx regime, more radicals are formed that canreact with NOx, and the "excess" radicals are removed by radical-radical reactions that arethe source of peroxides (e.g., reaction 5.46). In this regime, peroxide formation is nearlyproportional to the difference between radical source strength and NOx emission rate. In thehigh NOx regime, peroxide formation is suppressed.

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3'M3HdSOdOll.L 3ill dO J..1I.LSIW3H:> OSZ

THE HYDROXYL RADICAL 251

Because the temperature dependences of these two rate constants are quite close, the at-mospheric oxidation rate ofCH4 can be scaled to that ofCH3CCI3. An atmospheric CH4 de-struction rate' of 440 :t 50 Tg yr-1 can be inferred in this way. From the currentatmospheric loading of CH4 of about 4850 Tg, a mean atmospheric lifetime of 11 (:t 10%)years is derived based solely on OH reaction. When loss in the stratosphere and removal insoils are also considered, the lifetime shortens to about 10 years.

Only in the past few years have reliable direct measurements been made of lower tropos-pheric OH radical concentrations (e.g., see, Felton et al., 1990; Eisele and Tanner, 1991;Hofzumahaus et al., 1991; Comes et al., 1992; Hard et al., 1992; Mount and Eisele, 1992;Eisele, 1995). These measurement show that, as expected, OH radical concentrations exhibita diurnal profile, with daytime maximum concentrations of several 106 molecules cm-3.

Ehhalt et al. (1991) have evaluated the extent of agreement between calculated and mea-sured OH concentrations on May 20, 1983, 0908 to 1130 hours, at Deuselbach, a rural areain Germany, assuming that OH and HO2 levels were governed by the CH4 oxidation cycle.Figure 5.3 shows the calculated concentrations and fluxes between species. Since inter-

,,°2

hv1.5 x 107

t

OCD)1.9 x 10-2

HCHO: 0.5 x 106HZ : 0.4 x 106°3 : 0.3 x 106

80Z : 0.1 x 106

"-N2;O2

H;O1.9 x

~ Ux 106 ;

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~/ 4.~')~/ 3.5 x 10

-~.~ .b~-\\O');

I~-. '-.

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A

HNO31.5x1011

°3: 2.2 x lO~

-;S'"'"104

Kaiiiout IHeterogeneous Removal Rainout

1.8 x 106 1.3 x 104

~ ~FIGURE 5.3 Concentrations and fluxes between OH and HO2 (Ehhalt et al., 1991). The calcula-tion simulates an airmass observed between 0908 and 1130 hours, May 20, 1983 at Deuselbach,Germany. Numbers in boxes are calculated concentrations (molecules cm-3); numbers on arrows areconversion rates ofOH and HO" (molecules cm-3s-').

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THE NITRATE RADICAL 253

5.6 THE NITRATE RADICAL

We recall from Chapter 4 that the gaseous NO3 radical is formed via the reactions (seeAtkinson, 1991, Wayne et al., 1991, and Platt and Heintz, 1994, for comprehensive reviewsof the nitrate radical),

(5.52)N02 + 03 -+ N03 + 02M

N02 + N03 ~ N20S (5.15,5.16)

with N2Os being in a relatively rapid (characteristic time to reach equilibrium -1 minute at298 K) equilibrium with N02 and the N03 radical. Nitrate radicals were first detected in thetroposphere in 1980. N03 is a strong oxidizing agent and reacts with a number of other at-mospheric species. The prerequisite for N03 radical production is the simultaneous pres-ence ofN02 and 03 in the same airmass, as reaction 5.52 is the only primary source ofN03in the troposphere. The equilibrium with N2Os, reactions 5.15 and 5.16, is an important fea-ture ofN03 chemistry.

During daytime N03 radicals photolyze rapidly via two paths (see Table 3.3),

(5.53a)

(5.53b)

N03 + hV(A < 700 om) -+ NO + O2

N03 + hV(A < 580 om) -+ N02 + 0

with a noontime lifetime of -5 seconds, and react with NO,

NO3 + NO ~ 2NO2 (5.13)

sufficiently rapidly that NO and N03 cannot coexist at mixing ratios of a few parts per tril-lion (ppt) or higher. For typical daytime conditions of [N02] = 40 ppb, [03] = 50 ppb,and [NO] = 40 ppb, the maximum N03 mixing ratio will be 0.6 ppt. At nighttime, how-ever, when NO concentrations drop near zero, due to reaction with 03, the N03 mixing ra-tio can reach 100 ppt. Under conditions typical of rural areas in industrialized countries(N02 mixing ratio of -1 ppb), N03 and N2Os concentrations are roughly the same order ofmagnitude. Whereas homogeneous reactions of N2Os with water vapor and other trace

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THE OZONE BUDGET OF THE TROPOSPHERE AND THE ROLE OF NO. 255

]...rfoQ)

x

LatitudeFIGURE 5.4 Meridianal cross section of 03 (in ppb) obtained during March and April 1987 viaozonesondes released from the research vessel Polarstern on a northern cruise in the Atlantic, mostlyalong 30° W. Approximate location of the tropopause is shown with crosses. (Figure presented inMonthly Update, Department of Energy Atmospheric Chemistry Program, originally presented bySmit et al., in Ozone in the Atmosphere, edited by R. D. Bojkov and P. Fabian, Deepak Publishing,1989.)

5.7.1 Tropospheric Sinks of Ozone

The principal photochemical sink of 03 in the troposphere is reactions 5.21b, 5.22, and5.23. Because this removal path depends on the concentration of water vapor, it is most ef-fective in low latitudes at low altitudes, where the radiation is intense and the humidity ishigh. An estimate of the magnitude of the local rate of 03 destruction by reactions 5.21b,5.22, and 5.23 can be obtained by assuming that [O(ID)] is in a pseudo-steady state as a re-sult of these three reactions. The pseudo-steady-state concentration of O(ID) is given by

j5.2Ib[O3][0(10)]88 =ks.zz[M] + kS.Z3[HzO]

Ozone destruction occurs whenever an OrO) reacts with H2O, since this removes OrO)from the system; otherwise 0(10) is just quenched back to 0 in reaction 5.22, and 0 im-mediately reforms 03 by reaction 5.2. Thus the rate of 03 removal by reactions 5.2Ib, 5.22,and 5.23 is

d[O3]dt

= -kS.23[O('D)][H2O]

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3~3HdSOdO~J. 3HJ. dO A~J.SIW3HJ 9SZ

257THE OZONE BUDGET OF THE TROPOSPHERE AND THE ROLE OF NO.

The fractional 03 photochemical loss in Figure 5.5 can be converted into absolute 24-hour averages of the normalized 03 destruction rate (in S-I) by multiplying the fractions inFigure 5.5 by the 24-hour average of j5.21b. For example, at 10° S at the surface,j5.21b ~ 7 X 10-6 S-l, and a photolysis lifetime of 03 is estimated as about 11 days. In con-trast, the lifetime of 03 resulting from dry deposition to the surface of the ocean can be es-timated as about 35 days on the b~sis of assuming a dry deposition velocity of 0.05 cm S-1(see Chapter 19) (Smit et al., 1989). Since reactions other than photolysis also contribute tophotochemical 03 loss, such as reaction 5.47, one concludes that photochemistry is likelythe major sink for 03 in the boundary layer at 10° S and not dry deposition (Ayers et al.,1992). In fact, ozone destruction by the photochemical processes 5.21b, 5.22, and 5.23 isestimated to account for roughly 75% of the tropospheric loss of 03 by gas-phase routes;the remainder is primarily the result of reaction 5.47. This conclusion is strengthened bythe lack of observed 03 decrease at night, which would occur if dry deposition to the oceanwere having a noticeable effect on 03, since photochemical destruction occurs only duringdaytime and dry deposition operates both day and night. (Over land the 03 dry depositionvelocity may be as much as an order of magnitude larger than that over the ocean, and witha nighttime boundary layer generally shallower than that over the ocean, dry deposition ofozone may compete effectively with chemical removal.)

5.7.2 Tropospheric Source of Ozone

The principal in situ chemical source of ozone in the troposphere is photochemical pro-duction through the methane oxidation chain. The level of NO is critical in this chain indictating the fate of the HO2 radical. Reaction 5.25,

+NO~ NO2+0H. (5.25)

leads to 03 production; reaction 5.47,

+03 ~ OH-+202 (5.47)

destroys ozone. The break-even concentration of NO, below which 03 is destroyed andabove which it is produced, depends on the local 03 concentration. Tropospheric air maybe called NOx rich when NO mixing ratios exceed those of 03 by more than the ratio of therate constants of reactions 5.47 and 5.25. The ratio of the rates of these two reactions is

RS.47

RS.2S

kS.47 [03]--kS.2S [NO]

=

The rate constant ratio, k5.47/k5.25 ~ 2.5 x 10-4. The 03 mixing ratio near the Earth's sur-face in the remote continental troposphere is about 20 ppb. Then R5.25 > R5.47 for NO mix-ing ratios exceeding about 5 ppt. This amount of NO is roughly equivalent to 15 to 20 pptNOx. A competition also exists between NO and the H02 radical for reaction with theCH3O2 radical, and the preferred route depends on the concentrations of H02 radicals andNO. The rate constants for the reaction of the CH3O2 radicals with NO (reaction 5.40) andH02 radicals (reaction 5.42) are of comparable magnitude (see Table B.l). Based on ex-pected H02 radical concentrations in the troposphere, Logan et al. (1981) calculated thatthe reaction of the CH3O2 radical with NO dominates over that with H02 for NO mixing ra-

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NOx, pptFIGURE 5.6 Calculated 24 hour average 03 production and loss rates for the free troposphereabove Hawaii during the MLOPEX as a function of the NOx mixing ratio (Liu et al., 1992).

of the reduced solar intensity. At 20° N, for example, it is estimated that 03 lifetimes at thesurface are about 5 days in summer and 17 days in winter, whereas at 40° N these increaseto 8 days in summer and 100 days in winter. At 20° N, at 10 kIn altitude, estimated summerand winter 03 lifetimes are 30 days and 90 days, respectively, increasing by about a factorof 6 from those at the surface.

The key to understanding background tropospheric ozone is to determine whether a re-gion is in a local 03-producing or 03-destroying condition. Because of the critical roleplayed by NOx, assessing the effect of anthropogenic NOx emissions on background tro-pospheric NOx is one of the major issues in tropospheric chemistry. Increasing NOx weak-ens the net photochemical sink of 03 in the background troposphere, leading to an overallincrease of 0,.

5.7.3 Fate of NO.,

At first glance it might appear that NOx released in urban and regional areas will have alifetime too short to permit its transport to the remote troposphere to influence background03. For typical OH levels, reaction 5.26,

N02 + OH. + M -+ HN03 + M (5.26)

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3113HdSOdO~ 3~ dO AlI.LSIW3H;) 09"

THE OZONE BUDGET OF THE TROPOSPHERE AND THE ROLE OF NO. 261

moval is indeed occurring, predicted HNO3 concentrations and the HNO3/ NOx ratio canbe reduced to a value close to those measured.

The heterogeneous hydrolysis of N2Os, reaction 5.54, has been suggested to play an im-portant role in tropospheric chemistry (Dentener and Crutzen, 1993). Particles on whichHNO3 has formed can be transported to the dry upper troposphere, where it is expected thatmost water and HNO3 would evaporate. From the point of view of explaining the reasonfor the mismatch in predicted and observed HNO3/ NOx ratios, reaction 5.54 does not help;if the HNO3 is indeed released the result should be, more or less, equivalent to that if theoriginal NO2 were simply converted to HNO3 by OH. Understanding the relationship be-tween HNO3 and NOx in the upper troposphere remains as an outstanding problem in at-

mospheric chemistry.

5.7.4 Ozone Budget of the Troposphere

The global tropospheric balance on ozone includes the following:

Production: transport from stratosphere; in situ chemical production

Loss: dry deposition at Earth's surface; in situ chemical destruction

Transport from the stratosphere and dry deposition rates can be estimated. The estimateddownward flux of 03 from the stratosphere is (3-8) X 1010 molecules cm-2 S-I. Loss of 03by dry deposition on the Earth's surface is estimated at about 8 X 1010 molecules cm-2 S-I(Galbally and Roy, 1980). The principal mechanism for in situ chemical destruction of 03is photolysis and subsequent reaction of 0(10) with H2O, estimated also to be about 8 X1010 molecules cm-2 S-I (Lelieveld et al., 1993). The most difficult term to estimate, of thefour, is the average rate of in situ chemical production. We know that in situ production of03 on the global scale is driven by the oxidation of CO and CH4. Thus a good starting pointis to estimate the amount of 03 that can be produced globally from the oxidation of CO andC~. Average destruction rates of CO and CH4 by OH reaction are 3 X 1011 moleculescm-2 S-I and 1 X lOll molecules cm-2 S-I, respectively (Lelieveld et al., 1993). If all theCO and CH4 oxidation were to occur in NOx-rich environments, yielding one 03 moleculeper each CO and 2.7 03 molecules for each C~ (this number accounts for oxidation of theformaldehyde formed as a product of C~ oxidation), the average global production rate6of 03 would be 3 X 1011 + 2.7 X lOll ~ 6 X 1011 molecules cm-2 S-I. This production rateexceeds substantially the amount of 03 that can be destroyed by reactions 5.21b and 5.23and that which can be removed by deposition at the Earth's surface. The conclusion onereaches is that large portions of the troposphere must contain so little NOx that these re-gions lie below the NO crossover concentration with respect to 03 formation. At present,the tropospheric 03 budget can be calculated by global chemical models, but the validity ofsuch calculations must be assessed by careful comparisons with field data that provide allinportant components of production and loss. Nonetheless, there is little doubt that pro-duction and loss of tropospheric ozone are dominated by in situ chemistry and not bydownward transport of 03 from the stratosphere.

Manzerall et al. (1996) have quantified the ozone budget over remote high northern lat-itudes in summer using chemical and meteorological measurements between 0 and 6 kIn

"Globally, the methane oxidation chain has been estimated to result in a net annual loss of about 0.22 moleculesof OH for every CH. molecule destroyed (Tie et aI., 1992). The associated average annual yield of CO frommethane oxidation is about 0.82 molecule of CO per molecule of CH. destroyed. The global methane oxidationchain is estimated to produce, as a result, about 1.15 molecules of ozone for each molecule of CH. destroyed.

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~3HdSOdO~.L 3RL dO A~.LSIW3HJ Z9Z

THE OZONE BUDGET OF THE TROPOSPHERE AND THE ROLE OF NO, 263

downdraft. Cumulonimbus clouds are classified by their cells, organization, and life cycles.Ordinary cumulonimbi contain a single cell that has a life cycle of 45 minutes to an hour.Many thunderstorms are composed of a number of cells, each having lifetimes of 45 to 60minutes. These multicell storms can last for several hours and vertically redistribute largequantities of ozone and its precursors. Supercell storms, composed of a single steady cell,with strong updrafts and downdrafts, can last 2 to 6 hours and inject large quantities of pol-lutants into the upper troposphere (Dickerson et aI., 1987; Pickering et aI., 1989). Not allcases of convection cause such transport (e.g., convective clouds above a cold front;Pickering et al., 1988). Convective redistribution of ozone precursors may lead to an in-crease in the production rate of ozone averaged through the troposphere (Pickering et aI.,

1990).

Example 5.3 The Troposphere/Stratosphere Transition The transition from tropos-phere to stratosphere is traditionally defined based on the reversal of the atmospheric tem-perature profile. That transition is also dramatically reflected in how the concentrations oftrace species vary with altitude below and above the tropopause. Of trace species. H02 andOH exhibit perhaps the most profound differences across the tropopause (Wennberg et al.,1995). In the lower stratosphere H02 and OH participate in HOx Cycle 4, which is the pre-dominant cycle involved in 03 removal in that portion of the stratosphere. We saw inChapter 4 that in the lower stratosphere the H02/0H ratio is described by

[HO2]

[OH]

k4.ll [03]

k4.36 [NO] +k4.14 f03]

The presence of NO short-circuits HO" Cycle 4 by reconverting H02 back to OH before ithas a chance to react with 03, This ratio varies from about 4 to 7 and decreases as [NO] in-creases. [OH] itself is essentiaIly independent of [NO] and depends almost entirely on so-lar zenith angle. This independence of OH on NO is a result of the fact that the increase ofOH that results from reaction 4.36 is offset almost exactly by a decrease of the rates of re-actions that generate OH, reactions 4.14, 4.40, and 4.41. This occurs because the HO2 thatparticipates in reaction 4.36 is not otherwise available for reactions 4.14 and 4.40.

The behavior of HO2 and OH in the upper troposphere is dominated by CO chemistry.(Because of its I to 3 month lifetime, CO is more or less uniformly mixed up to thetropopause. Above the tropopause, CO faIls off with increasing altitude. Because of themuch slower vertical transport rate in the stratosphere, the rate of the CO-OH reactioncompetes with the rate of vertical mixing.) Tropospheric CO oxidation proceeds accordingto reactions 5.24 and 5.25, coupled to reactions 5.1 to 5.3. (Note that 4.36 and 5.25 are thesame reaction.) From Section 5.2 we can obtain an expression for the HO2/OH ratio in theupper troposphere. Based on the steady-state relation for HO2, we obtain

[HOz]

[OH]

k5.24 [CO]k [ NO ].5.25, .

As one proceeds up in the troposphere, the NO2/NOx ratio decreases, achieving its low-est value at the tropopause, and then increases moving into the stratosphere. The increaseof NOz relative to NO in the lower stratosphere is the result of reaction 4.36 (5.25). (TheNOx /NOy ratio is more or less constant in the upper troposphere, falling off as one goes

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CHEMISTRY OF NONMETHANE ORGANIC COMPOUNDS IN THE TROPOSPHERE 265

These alkyl peroxy radicals can be classed as primary, secondary, or tertiary depending onthe availability of H atoms: RCHzOO.(primary); RR'CHOO. (secondary); RR'RNCOO.(tertiary). The alkyl radical-Oz addition occurs with a room-temperature rate constant of~IO-IZ cm3 molecule-1 S-l at atmospheric pressure. Given the high concentration of Oz,the R + Oz reaction can be considered as instantaneous relative to other reactions occur-ring such as those that form R in the first place. Henceforth, the formation of an alkyl rad-ical will be considered to be equivalent to the formation of an alkyl peroxy radical.

Under tropospheric conditions, these alkyl peroxy (ROz) radicals react with NO, via two

pathways,

(S.S9a)RO2' + NO -- RO. + NO2M-- RONO? (5.59b)

For alkyl peroxy radicals, reaction 5.59a can form the corresponding alkoxy (RO.) rad-ical together with NO2, or the corresponding alkyl nitrate, reaction 5.59b, with the yield ofthe alkyl nitrate increasing with increasing pressure and with decreasing temperature. Forsecondary alkyl peroxy radicals at 298 K and 760 Torr total pressure, the alkyl nitrateyields increase monotonically from <0.014 for a C2 alkane up to -0.33 for a Cg alkane(Atkinson, 1990). The rate constant for the CH3O2' + NO reaction is (see Table B.l): kS.40= 4.2 X 10-12exp(180/T) = 7.7 X 10-12cm3molecule-1 S-I at 298 K. Rate constants forhigher (;=:C2) alkyl peroxy radicals with NO are taken as (Atkinson, 1994): kS.S9 = 4.9 X10-12 exp( 180/ T) = 8.9 X 10-12 cm3 molecule-l S-I at 298 K.

Alkyl peroxy radicals react with NO2 by combination to yield the peroxynitrates (recallreaction 5.41),

RO2' +NO2 + M -.. ROONO2 + M (5.60)

Limiting high pressure rate constants for ~C2 alkyl peroxy radicals are identical to that forthe C2HsO2, radical: kS.60 = 9 X 10-12 cm3 molecule-I S-I, independent of temperatureover the range 250 to 350 K,

Alkyl peroxy radicals also react with HO2 radicals,

R02' + H02' -+ ROOH + 02 (5.61)

or with other RO2 radicals. The self-reaction of RO2. and RO2. proceeds by the three path.

ways

(5.62a)

(5.62b)

R(RzCHOz" + R(RzCHOz" -+ 2 R(RzCHO" + Oz

-+ R(RzCHOH+R)RzCO+Oz

-+ R)RzCHOOCHR)Rz + Oz (5.62c)

Pathway 5.62b is not accessible for tertiary ROz radicals, and pathway 5.62c is expected tobe of negligible impcrtance. Under urban conditions, and indeed possibly for much of thelower troposphere in anthropogenically influenced continental regions, reaction with NO isthe dominant reaction pathway for ROz radicals.

Alkoxy (RO.) radicals are formed in the reaction of alkyl peroxy (RO2') radicals withNO, reaction 5.59a. Subsequent reactions of alkoxy radicals determine to a large extent the

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The 2-pentoxy radical can then react with 020 decompose, or isomerize:

o.

IsomerizationDecomposition "

/CH3CHO + CH3CHzCHz

or

CH3. + CH3CH2CH2CHO

CH3CH(OH)CH2CH2CH2'CH3C(0)CH2CH2CH3 + H02 .

Rate constants for alkoxy radical isomerizations can be combined with rate constants foralkoxy radical decomposition and reaction with O2 to predict the relative importance of thethree pathways (Atkinson. 1994). Alkoxy radicals can also react with NO and N02. but un-der ambient tropospheric conditions these reactions are generally of negligible importance.

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l88j

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saua~IY r8'~

31I3HdSOdO~.L 3m dO J..~.LSIWHHJ 89Z


CH3CH2CH2CH202'

Nol -r CH3CH2CH2CH20NO2

CH3CH2CH2CH20.,,- I ;onm

°2 I V2!

CHJCH2O2° + ICH3CHOI irH ,rH.rH.rHOIICH,CH.C(O) CH, I

~ 102

CH2(02.) CH2CH2CH2OH

+ !NO + !NO

H02" HO"

2

CH3CH20" CH2(0.) CH2CH2CH20H

i 02 fsom.

@~ CH2(OH) CH2CH2CHOH

+

H02.

+

H02"

FIGURE 5.7 Atmospheric photooxidation mechanism for n-butane. The only significant reactionof n-butane is with the hydroxyl radical. Approximately 85% of that reaction involves H-atom ab-straction from an internal carbon atom and 15% from a terminal carbon atom. In the terminal H-atomabstraction path, the CH3CH2CH2CH2O. alkoxy radical is estimated to react with O2 25% of the timeand isomerize 75% of the time. The second isomerization is estimated to be a factor of 5 faster thanthe first isomerization of the CH3CH2CH2CH2 O. radical, so that competition with O2 reaction is notconsidered at this step. The predominant fate of a-hydroxy radicals is reaction with O2, For example,.CHzOH+Oz -+ HCHO+HOz', and CH3CHOH+Oz -+ CH3CHO+HOz', In the n-butanemechanism, the a-hydroxy radical, CHz(OH)CHzCHzCHOH reacts rapidly with O2 to form 4-hy-droxy-l-butanal, CHz(OH)CHzCHzCHO. In the internal H-atom abstraction path, the alkoxy radi-cal CH3CH2CH(0. )CH3 reacts with O2 to yield methyl ethyl ketone (MEK), CH3CH2C(0)CH3, anddecomposes to form CH3CHO and CH3CH2., which, after reaction with O2 and NO and O2 again,

yields another molecule of CH3CHO and H02.

The HOCH2CH20. radical then decomposes and reacts with O2:

HOCH2CH2O. ~ HCHO + .CH20H

HOCH2CH20. +02 ~ HOCH2CHO+ H02'

The numbers over the arrows indicate the fraction of the reactions that lead to the indicatedproducts at 298 K. Finally, the .CH2OH radical reacts with O2 to give formaldehyde and a

hydroperoxyl radical,

.CH20H + 02 --+ HCHO + H02fast

CH3CH2CH (~.) CH3

NOIr CH3CH2CH(ON02)CH3

CH3CH2CH (0.) CH 3

v~ l~" /

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followed by rapid addition of O2 to yield the corresponding {3-hydroxyalkyl peroxy radi-

cals,

OH OH 00.R)",I I /R3RJ, R~

M :c-c+ °2 -=--" .

c-c

"R4R/2 \R 4 R12

In the presence of NO, the {3-hydroxyalkyl peroxy radical reacts with NO to form either the

{3-hydroxylalkoxy radical plus NO2 or the {3-hydroxynitrate:9

OH 00'RI" I I /R3 (5.69),c-c:c-c + NO - NO2+

R/2 R4RI2 \R 4

Rate constants for the reactions of f3-hydroxyalkyl peroxy radicals with NO are essentiallyidentical to those for the reaction of NO with more than C2 alkyl peroxy radicals formed

from alkanes (Atkinson, 1994).The f3-hydroxyalkoxy radicals can then decompose, react with O2, or isomerize.

Available data show that, apart from ethene, for which reaction of the HOCH2CH20. radi-cal with O2 and decomposition are competitive, the f3-hydroxyalkoxy radicals formed sub-sequent to OH addition to ~C3 alkenes undergo decomposition and the reaction with O2 is

negligible.The decomposition reaction is

08 O.Rl~ I 1/

,C-C"

OH 0RI" I II

,C. + R3CR4R1

RI2 R12R4

Carbonyl yields from alkene-OH reactions are summarized in Table 5.1. The yields ofHCHO and RCHO arising from cleavage of the -C = C- bond of l-alkenesRCH = CHz decrease monotonically from ~0.90 for propene and I-butene to 0.21 to0.39 for l-octene. H-atom abstraction from the CHz groups in the l-alkenes is expected toaccount for an increasing fraction of the overall OH radical reaction as the carbon numberof the l-alkenes increases, with about 15% of the I-heptene reaction being estimated toproceed by H-atom abstraction from the secondary CHz groups. The propene-OH reactionmechanism is shown in Figure 5.8.

"The {3-hydroxynitrate formation pathway accounts for only -I to 1.5% of the overall NO reaction pathway at298 K for propene (Shepson et aI., 1985). The yields of {3-hydroxynitrates from the propene-OH and 1-butene-OH reactions are about a factor of 2 lower than those of alkyl nitrates from the propane-OH and n-bu-tane-OH reactions. These observations suggest that the formation yields of {3-hydroxynitrates from the OHreaction with higher l-alkenes could also be a factor of 2 lower than those from the reactions with the corre-

sDondinl! n-alkanes.


followed by rapid addition of O2 to yield the corresponding {3-hydroxyalkyl peroxy radi-

cals,

OHR'lRJ R~

M

R OR 00I", I II

.C-C.+ °2 -=--" .

c-c

R4R12R{ R4

In the presence of NO, the f'-hydroxyalkyl peroxy radical reacts with NO to form either thef'-hydroxylalkoxy radical plus NO2 or the f'-hydroxynitrate:9

OH 00.RI",! I/R3 (5.69):c-c:c-c + NO - NO2+

R/2 R4RI2 \R 4

Rate constants for the reactions of f3-hydroxyalkyl peroxy radicals with NO are essentiallyidentical to those for the reaction of NO with more than C2 alkyl peroxy radicals formed

from alkanes (Atkinson, 1994).The {3-hydroxyalkoxy radicals can then decompose, react with O2, or isomerize.

Available data show that, apart from ethene, for which reaction of the HOCH2CH20. radi-cal with O2 and decomposition are competitive, the f3-hydroxyalkoxy radicals formed sub-sequent to OH addition to 2:C3 alkenes undergo decomposition and the reaction with O2 is

negligible.The decomposition reaction is

08 O.Rl" I I /

,C-C"

08 0RI", I II

C. + R'tCR,iR1 -

RI2 R12R4

Carbonyl yields from alkene-OH reactions are summarized in Table 5.1. The yields ofHCHO and RCHO arising from cleavage of the -C = C- bond of 1-alkenesRCH = CHz decrease monotonically from ~0.90 for propene and I-butene to 0.21 to0.39 for l-octene. H-atom abstraction from the CHz groups in the 1-alkenes is expected toaccount for an increasing fraction of the overall OH radical reaction as the carbon numberof the 1-alkenes increases, with about 15% of the 1-heptene reaction being estimated toproceed by H-atom abstraction from the secondary CHz groups. The propene-OH reactionmechanism is shown in Figure 5.8.

"The {3-hydroxynitrate formation pathway accounts for only -I to 1.5% of the overall NO reaction pathway at298 K for propene (Shepson et aI., 1985). The yields of {3-hydroxynitrates from the propene-OH and 1-butene-OH reactions are about a factor of 2 lower than those of alkyl nitrates from the propane-OH and n-bu-tane-OH reactions. These observations suggest that the formation yields of {3-hydroxynitrates from the OHreaction with higher l-alkenes could also be a factor of 2 lower than those from the reactions with the corre-

sponding n-alkanes.

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This is followed by rapid O2 addition:

ONOzRI" I /R3

C-CR / I "R4

Z 00.

ONO2R"", I /R3

C-CR / o""R

2 4

+°2-

to produce the {3-nitratoalkyl peroxy radical, subsequent reactions of which are

+ NO2+NO -

(5.73)

ONO2 RR}, I / 3

"c -C,/ I "R4

R2 ONO2

The latter reaction is expected to be minor.Further reactions of {3-nitratoalkoxy radicals include

R ONOz RI" I / 4C-C

R / IIz 0

+ HO.2+°2-

if R3 = H

0 0II II

R)CR2 + R3CR4 + NO2

ONO2RI~ I /R3

C-CR / - I~R

2 0. 4

+ NOZ -

of which the last reaction is expeced to be minor. Figure 5.9 shows the mechanism of theorooene-NO, reaction.

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Atkinson, 1994; Horie et al., 1994 a, b; Neeb et al., 1995; Thomas et al., 1995; Neeb et al.,1996) and are reasonably well understood for a large number of the smaller alkenes. Themajor mechanistic issue concerns the fate, under atmospheric conditions, of the initiallyenergy-rich Criegee biradical, which can be collisionally stabilized or can undergo uni-molecular decomposition,

[RI CH2t(R2)O6]~ (5.76a)

(5.76b)

(5.76c)

(5.76d)

-+- RI CH2C(R2)O6 (stabilization)

-+- RICH2C(O)R2 + 0

-+- [RICH2C(O)OR2]'" -+- decomposition

-+- [RICH = C(OOH)R2]'" -+- RICHC(O)R2 + OH.

At atmospheric pressure, 0 atoms are not formed in any appreciable amount, so path 5.76bcan generally be neglected.

Hydroxyl radicals have been observed to be formed from alkene-O3 reactions, some-times with close to a unit yield (1 molecule of OH per 1 molecule of alkene reacted)(Atkinson and Aschmann, 1993). Atkinson et al. (1995a) reported .OH radical yields froma series of alkene-O3 reactions:

Alkene OH Yield

0.370.320.270.180.500.610.90

I-PenteneI-HexeneI-Heptenel-Octene2,3-Dimethyl-l-buteneCyclopenteneI-Methylcyclohexene

(Estimated uncertainties in these yields are a factor of -1.5.)At I atm, fractional yields of stabilized biradicals are estimated as (Atkinson, 1994):

0.370.2750.180.1740.30

Ethene

Propenetrans-2-Butene

2-Methylpropene2,- 3- Dimethy 1- 2-butene

The reaction pathways of Criegee biradicals are generally well established for the firsttwo compounds in the series although the exact fractions that proceed via each individualpath are still open to question (Horie and Moortgat, 1991):

M--+- CH200. (stabilization)

CO2 + H2

CO + H2O (5.77)0,

2HO2. +CO2

HtO + OH.

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Aromatics5.8.3

Aromatic compounds are of great interest in the chemistry of the urban atmosphere be-cause of their abundance in motor vehicle emissions and because of their reactivity with re-spect to ozone and organic aerosol formation. Understanding the atmospheric oxidationmechanisms of aromatics has long been cited as the most critical need in further develop-ment of reaction mechanisms for the urban and regional atmosphere (National ResearchCouncil, 1991). The major atmospheric sink for aromatics is reaction with the hydroxylradical. Whereas rate constants for the OR reaction with aromatics have been well charac-terized (Atkinson, 1994), mechanisms of aromatic oxidation following the initial OR at-tack have been highly uncertain. Aromatic compounds of concern in urban atmosphericchemistry are given in Figure 5.10.

CH~ CH3A

CH3A

CH3A,CH~~ ~

~ ~~ ij'CH~ y

CH3P - XyleneBenzene Toluene 0 - Xylene m - Xylene

CH3A

C2HsX

CH3A ~CH~

~~ yCH3

,2,4 Trimethyl benzene

,CH3 'CR3

,3,5 Trimethyl benzeneEthyl benzene

0 - Ethyl toluene m - Ethyl toluene p - Ethyl toluene

FIGURE S.10 Aromatic compounds of interest in tropospheric chemistry.

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The H-atom abstraction pathway leads mainly to the formation of aromatic aldehydes

oCHZ

6CH20.

602 °2

CHO6 + H028 (5.82)

Benzaldehyde

As noted above, this H-atom abstraction pathway is minor, accounting for <10% of theoverall OH radical reaction for benzene and the alkyl-substituted aromatic hydrocarbons.

The radicals resulting from OH addition to the aromatic ring are named as follows:

CH3

C

CH3l

CH3

6~Hf~Hc ~~H )"-OHH

Hydroxycyclohexadienylradical

(from benzene)

Methyl hydroxycyclohexadienylradicals

(from toluene)

For toluene, and other aromatics, there are several possible sites of attack for the OH radi-cal. Some sites are less sterically hindered than others or are favored because of stabiliza-tions resulting from group interactions. Andino et al. (1996) have performed ab initiocalculations to determine the most energetically favored structures resulting from OH ad-dition to aromatic compounds. For toluene the most favored structure is that resulting fromOH addition at the ortho position 1°:

CH3

6~H

100M addition to the meta and para positions of toluene yield structures that are only I to 2 kcal mol-I less favor-able than addition at the ortho site and thus cannot be ruled out categorically. For our purposes, we will consider

OH addition at the ortho site only.

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After bicyclic radical formation, O2 rapidly adds to the radical, forming a bicyclic per-oxy radical, for example,

CH3

.OO-&~H

This radical is then expected to react with NO to form a bicyclic oxy radical and NO2, for

example,

CH3. O_-r-;"~"~ ' H

~'OH

The only path for this bicyclic oxy radical is fragmentation via favorable /3-scission re-actions. For the above radical, such scission would produce

.0

OH1

H

O~

H

/' ~ - Scissi°!l. O~

'(-1/

Decomposition B

a1l

H H

OA~. + O~OH

+ .~H

H

0 ~-../'yOH I(

a'1(0

Observed ring-fragmentation products of the toluene-OH reaction include the follow

ing:

00/I /I

CH3C CHMethylglyoxal

0 CH 0II I 3 II

HCCH=C CHMethyl butenedial

0 0II II

HC CH =CH CH1.4-Butenedial

00II II

HCCHGlyoxal

5.8.4 Aldehydes

Aldehydes are important constituents of atmospheric chemistry. We have already seen therole played by formaldehyde in the chemistry of the background troposphere. Aldehydesare formed in the atmosphere from the photochemical degradation of other organic com-

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Peroxyacetyl nitrate, the first compound in the series of PANs, which itself is usuallycalled PAN. is formed from the OH reaction with acetaldehyde,

(5.92)

(5.93)

(5.94, 5.95)

CH3CHO + OH, -+- CH3CO + H2O

CH3CO + O2 -+- CH3C(0)02'

CH3C(0)02' +N02 + M ~ CH3C(0)02N02 + M

Reaction 5.94 must compete with the NO-to~NO2 conversion reaction

CH3C(O)OZ. + NO -.-+- NOz + CH3C(O)O. (5.96)

followed by

CH~C(O)O. ~ CH3O2' + CO2 (5.97)

Peroxyacetyl nitrate does not absorb radiation above 290 nm so this class of compoundsis not expected to photodissociate in the troposphere. Peroxyacetyl nitrate is not highly wa-ter soluble; it is more soluble than NO and NO2 but considerably less soluble, for example,than nitric acid. Thus aqueous-phase scavenging is not expected to be an important tropos-

pheric removal path for PANs.Once thought to be of importance only in polluted urban atmospheres, PANs are now

recognized to be ubiquitous, having been detected in urban, rural, and global environments(Roberts, 1990). By virtue of their photochemical inertness, relative insolubility in water,and low OH rate constant, PANs can have an appreciable atmospheric lifetime. The princi-pal loss mechanism is thermal decomposition by reaction 5.91 or 5.95 back to the peroxy-acyl radical and NO2. The thermal decomposition is highly temperature dependent; attemperatures of the upper troposphere PANs are quite stable and can be transported long

distances.The thermal decomposition rate constant for PAN, reaction 5.95, is both temperature

and pressure dependent, being in the falloff region at room temperature at and below at-mospheric pressure. Using the Troe falloff expression, over the temperature range 280 to

330K,

(5.98)

~

the specific values for PAN are

ko = 4.9 X 10-3 exp( -12100/ T) cm3 molecule-I S-I

koo = 4.0 X 1016 exp( -13600/ T) S-I

F=0.3

Thus koo = 6.1 X 10-4 S-I at 298 K and kS.9s = 5.2 X 10-4 s-t at 298 K and 760 Torr totalpressure. The decomposition rates of the higher peroxyacyl nitrates are expected to be sim-

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with 5.99a being the major reaction pathway. Subsequent reaction of this particular radicalwith NO leads to

00. O.I I

CH3CHC(0)CH3 + NO -.. N02 + CH3CHC(0)CH3

CH3C(0. )HC(0)CH3 -.. CH3CHO + CH3CO

The major reaction products from the atmospheric reactions of the ketones are aldehydes

and PAN precursors.Acetone is an ubiquitous atmospheric species having a mixing ratio of about 1 ppb in

rural sites in a variety of locations (Singh et al., 1994, 1995). Under extremely clean con-ditions, ground-level background mixing ratios of 550 ppt have been found throughout theNH troposphere. In the free troposphere, acetone mixing ratios on the order of 500 ppt arepresent at northern midlatitudes, declining to about 200 ppt at southern latitudes (Singh etal., 1995). From atmospheric data and three-dimensional photochemical models, a globalacetone source of 40 to 60 T g yr-1 has been estimated, comprised of 51 % secondary for-mation from the atmospheric oxidation of precursor hydrocarbons (principally propane,isobutane, and isobutene), 26% direct emission from biomass burning, 21 % direct biogenicemissions, and 3% primary anthropogenic emissions (Singh et al., 1994). Atmospheric re-moval of acetone is estimated to result from photolysis (64%), OH reaction (24%), and de-position (12%). Acetone photolysis, which produces the PAN-precursor CH3CO radical, isestimated to contribute 40 to 50 ppt of PAN in the middle and upper troposphere of theNorthern Hemisphere. Based on tropospheric models, up to 50% of observed PAN may beformed by this mechanism. The average lifetime of acetone in the atmosphere is estimatedto be 16 days (Singh et al., 1995).

By virtue of its photooxidation chemistry (Figure 5.11), acetone is a source of HOx rad-icals in the upper troposphere. Under the dry conditions of the upper troposphere, where0(10) + H2O is relatively slow, acetone makes an important additional contribution to

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with the first reaction pathway accounting for -85% of the overall reaction at 298 K.Since, as shown earlier, both the .CH20H and CH30. radicals react with O2 to yieldformaldehyde and H02, the overall methanol-OH reaction can be written as

~CH30H + OH. --+ H2O + HO2' + HCHO

The ethanol-OH reaction proceeds as follows:

OR. + CH3CH20H -.. H2O + CH2CH20H

-.. H2O + CH3CHOH

-.. H2O + CH3CH20.

(-5%)

(-90% )

(-5%)

(5.104a)

(5.104b)

(5.104c)

where the branching ratios are those at 298 K. The second two channels result in identicalproducts under atmospheric conditions, H02 + CH3CHO. The first channel forms the in-termediate CH2CH20H, which, under atmospheric conditions, leads to the same productsas the OH + ethene reaction. Using the ethene-OH mechanism given earlier, the overallethanol-OH reaction mechanism can be written as

C2HsOH + OH. +0.05 NO -+ 0.05 NO2 + 0.014 HOCH2CHO + 0.072 HCHO

+0.95 CH:1CHO + HO2. + H2O

with the principal products being acetaldehyde and the HO2 radical.Free tropospheric concentrations of methanol range from about 700 ppt at northern mid-

latitudes to about 400 ppt at southern latitudes (Singh et al., 1995). In general, ethanolabundance in the free troposphere is an order of magnitude lower than that of methanol.Average lifetimes of CH3OH and C2HsOH in the atmosphere are on the order of 16 days

and 4 days, respectively.

5.8.10 Acids

The atmospheric sources of formic and acetic acid are still open to question. In theShenandoah Cloud and Photochemistry Experiment conducted during 1990 in the ruralcontinental atmosphere at a mountaintop (1014 m) in Virginia, median mixing ratios forHCOOH and CH3COOH were 5.4 and 2.1 ppb, respectively (Talbot et al., 1995). Formicacid mixing ratios often approached or exceeded 10 ppb. An observed lack of correlationbetween HCOOH and CH3COOH with peroxide species argued against a significant sourcefrom permutation reactions of peroxy radicals (e.g., reaction 5.61). A strong correlation be-tween the mixing ratios of both acids was suggestive of a common source, although com-bustion emissions could be ruled out. Correlation between the seasonal variation of the twoacids and ambient temperature is consistent with a soil microbial source.

Together, the two acids contribute between 16 and 35% of the free acidity in NorthAmerican precipitation and between 25 and 98% of the free acidity in precipitation in re-mote areas. Photochemical production of organic acids occurs in the gas phase fromozone-alkene reactions and in cloud water by the hydrolysis of aldehydes followed byaQueous-phase reaction with OH radicals (see Chapter 6). These routes can explain, in part,

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L

THE SIZE DISTRIBUTION FUNCTION 409

TABLE 7.1 Example of Segregated Aerosol Size Information

1111120000300020001000750

1250563117160802

100300330350390450650830890910915916

10020030204060

200180602051

0.001-0.010.01-0.020.02-0.030.03-0.040.04-0.080.08-0.160.16-0.320.32-0.640.64-1.251.25-2.52.5-5.05.0-10.0

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set.

2001

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Diameter. J.1mFIGURE 7.3 Same as Figure 7.2 but plotted versus the logarithm of the diameter.

large-and small-particle regions are depicted, but it now erroneously appears that the dis-tribution consists almost exclusively of particles smaller than 0.1 j.Lm.

Using a number of size bins to describe an aerosol size distribution generally results inloss of information about the distribution structure inside each bin. While this may be ac-ceptable for some applications, our goal in this chapter is to develop a rigorous mathemat-ical framework for the description of the aerosol size distribution. The issues discussed inthe preceding example provide valuable insights into how we should express and present

ambient aerosol size distributions.

7.1.1 The Number Distribution nN(Dp)

In the previous section, the value of the aerosol distribution nj for a size interval i was ex-pressed as the ratio of the absolute aerosol concentration Nj of this interval and the sizerange ~Dp. The aerosol concentration can then be calculated by

Ni = ni ~Dp

The use of arbitrary intervals ~Dp can be confusing and makes the intercomparison of sizedistributions difficult. To avoid these complications and to maintain all the information re-garding the aerosol distribution, one can use smaller and smaller size bins, effectively tak-

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Diameter. IJ.tnFIGURE 7.4 Atmospheric aerosol number, surface, and volume continuous distributions versusparticle size. The diameter range 0 to 0.5 JLm for the number distribution is shown as an inset.

Example 7.1 For the distribution of Figure 7.4, how many particles of diameter 0.1 j),m. ')

exist.

According to the inset of Figure 7.4, nN(O.1 fLm) = 13,000 fLm-l cm-3. However, this

is not the number of particles of diameter 0.1 fLm (it even has the wrong units). To calcu-late the number of particles we need to multiply nN by the width of the size range ~Dp.But if we are interested only in particles with Dp = 0.1 fLm this size range is zero andtherefore there are zero particles of diameter exactly equal to 0.1 fLm.

Let us try to rephrase the above question.

Example 7.2. For the distribution of Figure 7.4, how many particles with diameter in therange 0.1 to 0.11 .urn exist?

The size distribution is practically constant over this narrow range with n N (0.1 JLm)= 13,000 JLm -I cm -3. The width of the region is 0.11 - 0.1 = 0.01 JLm and there are0.0 I X 13,000 = 130 particles cm -3 with diameters between 0.1 and 0.11 JLm for this

size distribution.

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The total aerosol volume per cm 3 of air, V, is

and is equal to the area below the nv(Dp) curve in Figure 7.4.If the particles all have depsity Pp (g cm-3) then the distribution of particle mass with

respect to particle size, nM(Dp), is

(,ug ,um-l cm-3) (7.7)Pp ) Pp )(7r,1"66 nv(Dp) = .106 "6,

where the factor 106 is needed to convert the units of density Pp from g cm -:I to ILg ILm -:I,and to maintain the units for nM(Dp) as ILg ILm -I cm -3.

Because particle diameters in an aerosol population typically vary over several orders ofmagnitude, use of the distribution functions, nN(Dp), ns(Dp), nv(Dp), and nM(Dp), isoften inconvenient. For example, all the structure of the number distribution depicted inFigure 7.4 occurs in the region from a few nanometers to 0.3 ILm diameter, a small part ofthe 0 to 10 ILm range of interest. To circumvent this scale problem the horizontal axis canbe scaled in logarithmic intervals so that several orders of magnitude in Dp can be clearlyseen (Figure 7.5). Plotting nN(Dp) on semilog axes gives, however, a somewhat dis-

D~nN(Dp)

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The units of n~ (In Dp) are cm-3 since InDp is dimensionless. The total number concen-tration of particles N is

N = {(X}

J -(X}(cm-3) (7.8)n~(In Dp) d In Dp

The limits of integration in (7.8) are from -00 to 00 as the independent variable is In Dp.The surface area and volume distributions as functions of In Dp can be defined similarly

to those with respect to Dp,

n~(lnDp) = 11" D;nN(ln Dp) (,um2 cm-3) (7.9)

(.um3cm-3) (7.10)

with

The above aerosol distributions can also be expressed as functions of the base 10 loga-rithm log Dp, defining nN(log Dp), ns(log Dp), and ny(log Dp). Note that nN, nN' andnN are different mathematical functions, and, for the same diameter Dp, they have differ-ent arguments, namely Dp,ln Dp, and log Dp. The expressions relating these functionswill be derived in the next section.

Using the notation dNjdSjdV = the differential number/surface/volume of particlesin the size range Dp to Dp + dDp we have

(7.13)

(7.14)

(7.15)

dN = nN(Dp) dDp = n~(ln Dp) d In Dp = n~(log Dp) d log Dp

dS = ns(Dp) dDp = ns(lnDp) d InDp = ns(log Dp) d log Dp

dV = ny(Dp) dDp = nt(ln Dp) d In Dp = ny(log Dp) d log Dp

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This procedure can be generalized to relate any two size distribution functions n(u) andn(v), where both u and v are related to Dp. The generalization of (7.17) is

n(u) du = n(v) dv (7.24)

and dividing both sides by dDp

(dvfdDp) (7.25)n(u) = n(v)(d~)

7.1.5 Properties of Size Distributions

It is often convenient to summarize the features of an aerosol distribution using one or twoof its properties (mean particle size, spread of distribution) than by using the full functionn N (D p) . Growth of particles corresponds to a shifting of parts of the distribution to largersizes or simply an increase of the mean particle size. These properties are called the mo-ments of the distribution, and the two most often used are the mean and the variance.

Let us assume that we have a discrete distribution consisting of M groups of particles,with diameters Dk and number concentrations Nk, k = 1,2, ..., M. The number concen-

tration of aerosols is therefore

M

N = L Nkk=l

(7.26)

The mean particle diameter, Dp, of the population is

(7.27)M

~ L NkDkN k=1

-. =Dp = =;- --~~1 NkDk

The variance, 0'2, a measure of the spread of the distribution around the mean diameter

Dp, is defined by

1 M

N L Nk(Dk -D rk=l P (7.28)

A value of a2 equal to zero would mean that every one of the particles in the distributionhas precisely diameter Dp. An increasing a2 indicates that the spread of the distributionaround the mean diameter Dp is increasing.

We will usually deal with aerosol distributions in continuous form. Given the numberdistribution nN(Dp), (7.27) and (7.28) can be written in continuous form to define the

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7.1.6 The Log-Normal Distribution

A measured aerosol size distribution can be reported as a table of the distribution values fordozens of diameters. For many applications carrying around hundreds or thousands ofaerosol distribution values is awkward. In these cases it is often convenient to use a rela-tively simple mathematical function to describe the atmospheric aerosol distribution. Thesefunctions are semiempirical in nature and have been chosen because they match well ob-served shapes of ambient distributions (Hinds, 1982). Of tbe various mathematical func-tions that have been proposed, the log-normal distribution (Aitchison and Brown, 1957)often provides a good fit and is regularly used in atmospheric applications. A series of other

distributions are discussed in the next section.The normal distribution for a quantity u defined from -00 < u < 00 is given by

(u - U)2

2a2 u

(7.31)

where u is the mean of the distribution, a; is the variance, and

N= j OO

-00

(7.32)n(u) du

The normal distribution has the characteristic bell shape, with a maximum at Ii". The stan-dard deviation, au, quantifies the width of the distribution, and 68% of the area below the

curve is in the range Ii"::!:: au.A quantity u is log-normally distributed if its logarithm is normally distributed. Either

the natural (In u) or the base 10 logarithm (log u) can be used, but since the former is morecommon, we will express our results in terms of In Dp. An aerosol population is thereforelog-normally distributed if u = In Dp satisfies (7.31), or

where N is the total aerosol number concentration, and Dpg and ag are for the time beingthe two parameters of the distribution. Shortly we will discuss the physical significance ofthese parameters. The distribution nN(Dp) is often used instead of nN(ln Dp)' Combining

(7.21) with (7.33)

A log-normal aerosol distribution with Dpg = 0.8,urn and O"g = 1.5 is depicted in Figure

7.7.

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The error function erf z is defined as

erfz

and erf(O) = O. erf( 00) = 1. If we divide the integral in (7.37) into one from -00 to 0 andthe second from 0 to (In D; - In D pg) 1.J2 In (1 g. then the first integral is seen to be equalto In 12 and the second to (In 12)erf[(ln D; -In Dpg)/.J2 In (1g]. Thus for the log-

normal distribution

Dpg. since erf(O) = 0For Dp

NF(Dpg) = "2

and we see that Dpg = Dmed is the median diametel; that is, the diameter for which exactlyone-half of the particles are smaller and one-half are larger. To understand the role of u g letus consider the diameter Dp17 for which Ug = Dp17 /Dpg. At that diameter, using (7.39),

1 1 ( 1 )2" + 2" erf "J2 = O.841NF(Dp,,) = N

Thus a g is the ratio of the diameter below which 84.1 % of the particles lie to the mediandiameter and is termed the geometric standard deviation. A monodisperse aerosol popula-tion has ag = I. For any distribution, 67% of all particles lie in the range from Dpg/ag toDpgag and 95% of all particles lie in the range from Dpg/2ag to 2Dpgag.

Let us calculate the mean diameter Dp of a log-normally distributed aerosol. By defin-ition, the mean diameter is found from

~ rooN Jo

(7.42)DpnN(Dp) dDpDp

which we wish to evaluate in the case of nN(Dp) given by (7.34). Therefore

( - 2 (In Dp -In Dpg)

exp -2 In2 a~

dDn

After evaluating the integral one finds that

Dp = Dpg exp

We see that the mean diameter of a log-normal distribution depends on both Dpg and D'g.

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narrow distribution and to a steep line in the log-probability graph (Figure 7.8). The geo-~etric standard deviation can be calculated as the ratio of the diameter Dp+a for whichFN(Dp+a) = 0.84 to the mean diameter

~15"

(7.47)ag =

7.1.8 Properties of the Log-Normal Distrjbution

We have discussed the properties of the log-normal distribution for the number concentra-tion. The next step is examination of the surface and volume distributions corresponding toa log-normal number distribution given by (7.34). Since ns(Dp) = 1T D;nN(Dp) and

ny(Dp) = (1T/6)D~nN(Dp). let us determine the forms of ns(Dp) and ny(Dp) when

n(Dp) is log-normal. From (7.34) one gets

- 2(In Dp -In Dpg)

"2i~By letting D; = exp (2 In Dp), expanding the exponential, and completing the square inthe exponent, (7.48) becomes

x exp

Thus we see that if the number distribution nN(Dp) is log-normal, the surface distributionns(Dp) is also log-normal with the same geometric standard deviation C1g as the parent dis-

tribution and with the surface median diameter given by

- - 2In Dpgs = In Dpg + 2 In Ug (7.50)

The above calculations can be repeated for the volume distribution and one can show

that

exp ( -- 2

(In Dp -In Dpg)

or by letting D~ = exp(3 In Dp), expanding the exponential, and completing the square inthe exponent, (7.51) becomes

(7.51a)

- 2 2[In Dp - (In Dpg + 2 In Ug)]

- 2 In2ug

( [lnDp - (lnDpg + 3 In2ag)fx exp -

2 In2 ag

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THE SIZE DISTRIBUTION FUNCfION 427

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Diameter. IJtT1 Diameter. IJtT1

FIGURE 7.10 Fitting of an urban aerosol number distribution with a power-law distribution (left) and

comparison of the corresponding volume distributions (right). Even if the power-law distribution ap-

pears to match the number distribution, it fails to reproduce the volume distribution.

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AMBIENT AEROSOL SIZE DISTRIBUTIONS 429

The Modified Gamma Distribution The modified gamma distribution (Deirrnendjian,1969) has been proposed as another function that approximates ambient aerosol sizedistributions,

nN(Dp) = AD; exp(-BD~) (7.55)

where A, b, B, and c are all positive parameters. This distribution form provides signifi-cant flexibility (Figure 7.11). but its use is often cumbersome. The total aerosol numberconcentration N is equal to

AB-(b+l)/c

c r(~N=

where r is the gamma function. The maximum of the distribution occurs at diameter Dm.

!!.-) I/c

Bc

Dm=

7.2 AMBIENT AEROSOL SIZE DISTRIBUTIONS

Atmospheric aerosol size distributions are often described as the sum of n log-normal dis-

tributions,( - 2 (log Dp -log Dpj)

exp -2 1 2og aj

where Ni is the number concentration, Dpi is the mean diameter, and O"i is the standard de-viation of the jib log-normal mode. In this case 3n parameters are necessary for the de-scription of the full aerosol distribution. Characteristics of model aerosol distributions arepresented in Table 7.3 following the suggestions of Jaenicke (1993).

7.2.1 Urban Aerosols

Urban aerosols are mixtures of primary particulate emissions from industries, transporta-tion, power generation, and natural sources and secondary material formed by gas-to-par-ticle conversion mechanisms. The number distribution is dominated by particles smallerthan 0.1 ILm, while most of the surface area is in the 0.1 to 0.5 ILm size range. On the con-trary, the aerosol mass distribution has usually two distinct modes, one in the submicronregime (referred to as the accumulation mode) and the other in the coarse particle regime

(Figure 7.12).The aerosol size distribution is quite variable in an urban area. Extremely high concen-

trations of fine particles (less than 0.1 ILm in diameter) are found close to sources (e.g.,highways), but their concentration decreases rapidly with distance from the source (Figure

~~

~8-~-==

Off'


0.01 0.10 1.00 10.00Diameter, IJIn

FIGURE 7.12 Typical urban aerosol number, surface, and volume distributions.

7.13). Figure 7.13 describes the number of particles as a function of their diameter (both inlogarithmic scales) for a variety of environments. There are roughly an order of magnitudemore particles close to the freeway compared to the average urban concentration. Figure7.14 illustrates the corresponding volume distributions. These distributions show that mostof the particles in an urban area are smaller than 0.1 JLm, while most of the particle mass is

found in particles with diameters larger than 0.1 JLm.An important feature of atmospheric aerosol size distributions is their multimodal char-

acter. Mass distributions, measured in urban centers, are characterized by three modes witha minimum between 1.0 and 3 JLm. The size range of particles larger than the minimum(supermicron particles) is termed "coarse," while the smaller particles are called "fine."The three modes present in the mass distribution of Figure 7.14 correspond to the nucleimode (particles below 0.1 JLm), accumulation mode (0.1 < Dp <' 1 JLm), and coarse mode(Dp > 1 JLm) (Whitby and Sverdrup, 1980). Thus the fine particles include both accumu-lation and nuclei modes. The boundaries between these sections are not precise (recall inChapter 2 that we divided fine and coarse modes at 2.5 JLm diameter). Note that our defin-ition of modes has been based on the mass (or volume distribution). The location of modesmay be different if they are based on the number or surface distribution.

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AMBIENT AEROSOL SIZE DISTRIBUllONS 433

The mass concentrations of the accumulation and coarse particle modes are comparablefor most urban areas. The nuclei mode, with the exception of areas close to combustionsources, contains negligible volume (Figures 7.12 and 7.14). Most of the aerosol surfacearea is in particles of diameters 0.1 to 0.5 jJ.m in the accumulation mode (Figure 7.12).Because of this availability of area, transfer of material from the gas phase during gas-to-particle conversion occurs preferentially on them.

The sources and chemical compositions of the fine and coarse particles are different.Coarse particles are generated by mechanical processes and consist of soil dust, sea salt, flyash, tire wear particles, and so on. Nuclei and accumulation mode particles contain primaryparticles from combustion sources and secondary aerosol material (sulfate, nitrate, ammo-nium, secondary organics) formed by chemical reactions resulting in gas-to-particle con-version (see Chapters 9 and 13).

Th~ main mechanisms of transfer of particles from the nuclei to accumulation mode iscoagulation (Chapter 12) and growth by condensation of vapors formed by chemical reac-tions (Chapter II) onto existing particles. Coagulation among accumulation mode particlesis a slow process and does not transfer particles to the coarse mode.

Processing of accumulation and coarse mode aerosols by clouds (Chapter 15) can alsomodify the concentration and composition of these modes. Aqueous-phase chemical reac-tions take place in cloud and fog droplets, and in aerosol particles at relative humidities ap-proaching 100%. These reactions can lead to production of sulfate (Chapter 6) and afterevaporation of water, a larger aerosol particle is left in the atmosphere. This transformationcan lead to the formation of two modes in the 0.1 to I jJ.m size range, with the smaller onecalled the condensation mode and the larger one the droplet mode (Hering and Friedlander,1982; John et al., 1990; Meng and Seinfeld, 1994).

Terms often used to describe the aerosol mass concentration include total suspendedparticulate matter (TSP) and PMx (particulate matter with diameter smaller than x jJ.m).TSP refers to the mass concentration of atmospheric particles smaller than 40 to 50 jJ.m,while PM2.s and PM 10 are routinely monitored. For a description of the sampling issuesand problems related to the measurement of TSP, PM2.s, and PM 10 the reader is referred tothe EPA Particulate Matter Criteria document (U.S. EPA, 1996).

7.2.2 Marine Aerosols

In the absence of significant transport of continental aerosols, particles over the remoteoceans are largely of marine origin (Savoie and Prospero, 1989). Marine atmospheric parti-cle concentrations are normally in the range of 100 to 300 cm -3. Their size distribution isusually characterized by three modes (Figure 7.15): the nuclei (Dp < D.l JLm) the accu-mulation (D.l < Dp < D.6JLm), and the coarse (Dp > D.6JLm) (Fitzgerald, 1991).Typically, the coarse particle mode, comprising 95% of the total mass but only 5 to ID% ofthe particle number (Figure 7.16), results from the evaporation of sea spray produced bybursting bubbles or wind-induced wave breaking (Blanchard and Woodcock, 1957;Monahan et al., 1983). Typical sea-salt aerosol concentrations in the marine boundary layer(MBL) are around 5 to 3D cm-3 (Blanchard and Cipriano, 1987; O'Dowd and Smith,

1993).Figures 7.15 and 7.16 show number and volume aerosol distributions in clean maritime

air measured by several investigators (Meszaros and Vissy, 1974; Hoppel et al., 1989; Haafand Jaenicke, 198D; De Leeuw, 1986) and a model marine aerosol size distribution. The dis-

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7.2.3 Rural Continental Aerosols

Aerosols in rural areas are mainly of natural origin but with a moderate influence of an-thropogenic sources (Hobbs et al., 1985). The number distribution is characterized by twomodes at diameters about 0.02 and 0.08 .urn, respectively (Jaenicke, 1993), while the massdistribution is dominated by the coarse mode centered at around 7 .urn (Figure 7.17). Themass distribution of continental aerosol not influenced by local sources has a small accu-mulation mode and no nuclei mode. The PM 10 concentration of rural aerosols is around

20 .ug m -3.

7.2.4 Remote Continental Aerosols

Primary particles (e.g., dust, pollens, plant waxes) and secondary oxidation products arethe main components of remote continental aerosol (Deepak and Gali, 1991). Aerosolnumber concentrations average around 2000 to 10,000 cm -3 and PM 10 concentrations are

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particles in the accumulation mode relative to lower tropospheric spectra, suggesting pre-cipitation scavenging and deposition of smaller and larger particles (Leaitch and Isaac,1991).

7.2.6 Polar Aerosols

Polar aerosols, found close to the surface in the Arctic and Antarctica, reflect their agedcharacter; their concentrations are very low. Collections of data from aerosol measure-ments in the Arctic have been presented by a number of investigators (Rahn, 1981; Shaw,1985; Heintzenberg, 1989; Ottar, 1989). The number distribution appears practicallymonodisperse (Ito and I wai, 1981) with a mean diameter of approximately 0.15 J1.m; twomore modes at 0.75 and 8 J1.m (Shaw, 1986; Jaenicke et aI., 1992) (Figure 7.20) dominatethe mass distribution.

During the winter and early spring (February to April) the Arctic aerosol has been foundto be influenced significantly by anthropogenic sources, and the phenomenon is commonlyreferred to as Arctic Haze (Barrie, 1986). During this period the aerosol number concen-


0.01 0.10 1.00 10.00Diameter. ~

FIGURE 7.19 Typical free tropospheric aerosol number, surface, and volume distributions.

particles in the accumulation mode relative to lower tropospheric spectra, suggesting pre-cipitation scavenging and deposition of smaller and larger particles (Leaitch and Isaac,1991).

7.2.6 Polar Aerosols

Polar aerosols, found close to the surface in the Arctic and Antarctica, reflect their agedcharacter; their concentrations are very low. Collections of data from aerosol measure-ments in the Arctic have been presented by a number of investigators (Rahn, 1981; Shaw,1985; Heintzenberg, 1989; attar, 1989). The number distribution appears practicallymonodisperse (Ito and Iwai, 1981) with a mean diameter of approximately 0.15 ,urn; twomore modes at 0.75 and 8 ,urn (Shaw, 1986; Jaenicke et al., 1992) (Figure 7.20) dominatethe mass distribution.

During the winter and early spring (February to April) the Arctic aerosol has been foundto be influenced significantly by anthropogenic sources, and the phenomenon is commonlyreferred to as Arctic Haze (Barrie. 1986). During this period the aerosol numher cnnc~n-

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AEROSOL CHEMICAL COMPOsmON 441

Aerodynamic Diameter. Dae. JimFIGURE 7.23 Measured size distributions of aerosol sulfate, nitrate, ammonium, chloride,sodium, and hydrogen ion in Claremont, CA (Wall et al., 1988).

fine particles. Crustal materials, including silicon, calcium, magnesium, aluminum, andiron, and biogenic organic particles (pollen, spores, plant fragments) are usually in thecoarse aerosol fraction. Nitrate can be found in both the fine and coarse modes. Fine nitrateis usually the result of the nitric acid/ammonia reaction for the formation of ammonium ni-trate, while coarse nitrate is the product of coarse particle/nitric acid reactions.

A typical urban aerosol size/composition distribution is shown in Figure 7.23 (Wall etal., 1988). These results indicate that sulfate, nitrate, and ammonium have two modes in the0.1 to 1.0 Jl,m size range (the condensation and droplet modes), and a third one over 1 Jl,m(coarse mode) (Figure 7.24). The condensation mode has a peak around 0.2 Jl,m and is theresult of condensation of secondary aerosol components from the gas phase. The dropletmode peaks around 0.7 Jl,m in diameter and its existence is attributed to heterogeneous,aqueous-phase reactions discussed in Chapter 6 (Meng and Seinfeld, 1994). More than halfof the nitrate is found in the coarse mode together with most of the sodium and chloride.This coarse nitrate is the result of reactions of nitric acid with sodium chloride or aerosolcrustal material (see Chapter 9). This is an interesting case where secondary aerosol matter(nitrate) is formed through the reaction of a naturally produced material (sea salt or dust)and an anthropogenic pollutant (nitric acid).

More than 40 trace elements are routinely found in atmospheric particulate matter sam-ples. These elements arise from dozens of different sources including combustion of coal,oil, wood burning, steel furnaces, boilers, smelters, dust, waste incineration, and breakwear. Depending on their sources, these elements can be found in either the fine or the

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AEROSOL CHEMICAL COMPOSITION 443

TABLE 7.7 Comparison of Ambient Fine and Coarse Particles

Formation pathways

Composition Resuspended dustCoal and oil fly ashCrustal element (Si, AI, Ti,Fe) oxidesCaCO3, NaCI

Pollen, mold, sporesPlant, animal debrisTire wear debris

Combustion (coal, oil,gasoline, diesel, wood)Gas-to-particle conversion ofNOx' S03' and VOCsSmelters, mills, etc.

Source: Adapted from Wilson and Shuh (1997) and U.S. EPA (1996).

fonn of oxides (e.g., Fe203, Fe304, AI203), but their chemical fonn is in general un-certain.

A summary of chemical infonnation regarding the coarse and fine modes is presented inTable 7.7.

The composition of sea salt reflects the composition of seawater enriched in organic ma-terial (marine-derived sterols, fatty alcohols, and fatty acids) that exists in the surface layerof the oceans (Schneider and Gagosian, 1985). Seawater contains 3.5% by weight sea saltand when first emitted the sea salt composition is the same as that of seawater (Table 7.8).Reactions on sea salt particles modify its chemical composition; for example, sodium chlo-ride reacts with sulfuric acid vapor to produce sodium sulfate and hydrochloric acid vapor

H2SO4 (g) + 2NaCI ~ Na2S04 + 2 HCI(g)

leading to an apparent "chloride deficit" in the marine aerosol.

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and N B is the number concentration of the background aerosol aloft. For marine aerosolH; varies from -290 to 440 m. Note that if H; is negative n = -I, and (7.60) can berewritten as

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REFERENCES 447

Jaenicke R., Dreiling V., Lehmann E., Koutsenogii, P. K., and Stingl, J. (1992) Condensation nucleiat the German Antarctic Station Vonneymayer, Tellus, 44B, 311-317

John, W., Wall, S. M., Ondo, J. L., and Winklmayr, W. (1990) Modes in the size distributions of at-mospheric inorganic aerosol, Atmos. Environ., 24A,2349-2359.

Koutsenogii, P. K., and Jaenicke, R. (1994) Number concentration and size distribution of atmos-pheric aerosol in Siberia, J. Aerosol Sci., 25,377-383.

Koutsenogii, P. K., Bufetov, N. S., and Drosdova, V. I. (1993) Ion composition of atmosphericaerosol near Lake Baikal, Atmos. Environ, 27A, 1629-1633.

Leaitch, W. R., and Isaac, G. A. (1991) Tropospheric aerosol size distributions from 1982 to 1988over Eastern North America, Atmos. Environ., 25A,601-619.

Li, X., Maring, H., Savoie, D., Voss, K., and Prospero, J. M. (1996) Dominance of mineral dust inaerosol light scattering in the North Atlantic trade winds, Nature, 380,416-419.

Meng, Z., and Seinfeld, J. H. (1994) On the source of the submicrometer droplet mode of urban andregional aerosols, Aerosol Sci. Technol., 20,253-265.

Meszaros, A., and Vissy, K. (1974) Concentration, size distribution and chemical nature of atmos-pheric aerosol particles in remote ocean areas, J. Aerosol Sci., 5, 101-109.

Monahan, E. C., Fairall, C. W., Davidson, K. L., and Jones-Boyle, P. (1983) Observed inter-relation-ships amongst 10-m-elevation winds, oceanic whitecaps, and marine aerosols, Q. J. R. Meteorol.Soc., 109, 379-392.

O'Dowd, C. D., and Smith, M. H. (1993) Physicochemical properties of aerosols over the NortheastAtlantic: evidence for wind-speed related submicron sea-salt aerosol production, J. Geophys.Res., 98, 1137-1149.

Ott, S. T., Ott, A., Martin, D. W., and Young, J. A. (1991) Analysis of trans-Atlantic saharan dust out-break based on satellite and GATE data, Mon. Weather Rev., 119, 1832-1850.

Ottar, B. (1989) Arctic air pollution: a Norwegian perspective, Atmos. Environ., 23,2349-2356.Prospero, J. M. (1995) The atmospheric transport of particles to the ocean, in SCOPE Report: Particle

Flux in the Ocean, Ittekkot, V., Honjo, S., Depetris, P. J. (Eds.), Wiley, New York, NY.Prospero, J. M., Nees, R. T., and Uematsu, M. (1987) Deposition rate of particulate and dissolved alu-

minum derived from sahara dust in precipitation in Miami, Florida, J. Geophys. Res., 92,14723-14731.

Pruppacher, H. R., and Klett, J. D. (1980) Microphysics of Cloud and Precipitation, D. Reidel,Dordrecht, The Netherlands.

Radke, L. F., Lyons, J. H., Hegg, D. A., and Hobbs, P. V. (1984) Airborne observations of Arcticaerosols. I: Characteristics of Arctic haze, Geophys. Res. Lett., 11, 369-372.

Rahn, K. (1981) Relative importance of North America and Eurasia as sources of Arctic aerosol,Atmos. Environ., 15,1447-1456.

Savoie, D. L., and Prospero, J. M. (1989) Comparison of oceanic and continental sources of non-sea-salt sulfate over the Pacific ocean, Nature, 339, 685-687.

Schneider, J. K., and Gagosian, R. B. (1985) Particle size distribution of lipids in aerosols off thecoast of Peru, J. Geophys. Res., 90, 7889-7898.

Schroeder, W. H., Dobson, M., Kane, D. M., and Johnson, N. D. (1987) Toxic trace elements associ-ated with airborne particulate matter: a review, J. Air Pollut. Cont. Assoc., 37,1267-1285.

Shaw, G. E. (1984) Microparticle size spectrum of Arctic haze, Geophys. Res. Lett., 11,409-412.Shaw, G. E. (1985) Aerosol measurements in Central Alaska 1982-1984, Atmos. Environ., 19,

2025-2031.Shaw, G. E. (1986) On physical properties of aerosols at Ross Island, Antarctica, J. Aerosol Sci., 17,

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PROBLEMS 449

7.48 Show that the variance of the size distribution of a log-nonnally distributed aerosol is

7.SA Starting with semilogarithmic graph paper, construct a log-probability coordinateaxis and show that a log-normal distribution plots as a straight line on these coordi-nates.

7.6A The data given below were obtained for a log-normally distributed aerosol size dis-tribution:

Size Interval(,urn)

Geometric Mean ofSize Interval (I/.m)

Number of Particlesin Intervalu

0.1-0.20.2-0.40.4-0.70.7-1.01.0-2.02.0-4.04.0-7.07.0-1010-20

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50460

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U Assume that the particles are spheres with density p = 1.5 g cm -3.

8. Complete the above table by computing the following quantities: ~Ni / ~Dpi.

~Ni/N~Dpi,~Si/~Dpi, ~Si/S~Dpi. ~Mi/~Dpi. ~Mi/M~Dpi,~Ni / ~ log Dpi, ~Ni / N ~ log Dpi, ~ Si / ~ log Dpi. ~ Si / S ~ log Dpi, and~Mi / ~ log Dpi, ~Mi / M ~ log Dpi, where M = particle mass.

b. Plot ~Ni / ~ log Dpi, ~Si / ~ log Dpi, and ~Mi / ~ log Dpi as histograms.

c. Determine the geometric mean diameter and geometric standard deviation of thelog-normal distribution to which these data adhere and plot the continuous distri-butions on the three plots from part (b).

7.78 For a log-normally distributed aerosol different mean diameters can be defined by- - 2DplI = Dpg exp(v In ag)

where v is a parameter that defines the particular mean diameter of interest. Showthat

Diameter v

-Mode (most frequent value)Geometric mean or medianNumber (arithmetic) meanSurface area meanMass meanSurface area medianVolume median

100.511.523

PROBLEMS 449

7.48 Show that the variance of the size distribution of a log-normally distributed aerosol is

7.SA Starting with semilogarithmic graph paper, construct a log-probability coordinateaxis and show that a log-normal distribution plots as a straight line on these coordi-nates.

7.6A The data given below were obtained for a log-normally distributed aerosol size dis-tribution:

Size Interval(,urn)

Geometric Mean ofSize Interval (ILm)

Number of Particlesin Intervalu

0.1-0.20.2-0.40.4-0.70.7-1.01.0-2.02.0-4.04.0-7.07.0-1010-20

0.14140.28280.52920.83671.4142.8285.2928.367

14.14

50460

1055980

1705680102102

U Assume that the particles are spheres with density p = 1.5 g cm -3.

8. Complete the above table by computing the following quantities: ~Ni / ~Dpi,

~Ni/N~Dpi,~Si/~Dpi, ~Si/S~Dpi, ~Mi/~Dpi, ~Mi/M~Dpi,~Ni / ~ log Dpi, ~Ni / N ~ log Dpi, ~ Si / ~ log Dpi, ~ Si / S ~ log Dpi, and~Mi / ~ log Dpi, ~Mi / M ~ log Dpi, where M = particle mass.

b. Plot ~Ni / ~ log Dpi, ~Si / ~ log Dpi, and ~Mi / ~ log Dpi as histograms.

c. Determine the geometric mean diameter and geometric standard deviation of thelog-normal distribution to which these data adhere and plot the continuous distri-butions on the three plots from part (b).

7.78 For a log-normally distributed aerosol different mean diameters can be defined by- - 2DplI = Dpgexp(vln ag)

where v is a parameter that defines the particular mean diameter of interest. Showthat

Diameter v

-Mode (most frequent value)Geometric mean or medianNumber (arithmetic) meanSurface area meanMass meanSurface area medianVolume median

100.511.523

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TEMPERATURE IN THE LOWER ATMOSPHERE 767

is referred to as stable. The stability condition of the atmosphere plays an important role in

determining the rate of dispersal of material.The phenomenon of direct interest in predicting the dispersion of air pollutants is turbu-

lent diffusion. Actually, turbulent diffusion is something of a misnomer. The phrase refersto the observed spreading of a cloud of marked particles in a turbulent fluid at a rate manyorders of magnitude greater than that from molecular diffusion alone. The spreading is re-ally not due to a "diffusion" phenomenon such as results from molecular collisions butrather is a result of the rapid, irregular motion of macroscopic lumps of fluid (called eddies)in turbulence. Thus the scales of length in turbulent diffusion are much greater than in mol-ecular diffusion, with the contribution of the latter to the dispersion of pollutants in turbu-

lence being virtually negligible. The lev~l of turbulence in the planetary boundary layerincreases with increased wind speed, surface roughness, and instability. Turbulence there-fore arises from both mechanical forces (shear, surface friction) and thermal forces (buoy-

ancy).Lower atmospheric temperature profiles determine in part the stability of the atmos-

phere or, in other words, the degree to which turbulence induced by wind, surface rough-ness, or buoyancy will propagate through the layer. Under strongly stable conditions,disturbances are highly damped and mixing of species is strongly suppressed. It is undersuch conditions that the worst air pollution episodes have occurred. The importance ofwinds to the atmospheric aspects of air pollution is clearly evident. Our discussion of windsin this chapter will be largely qualitative; in Chapter 16 we shall treat air motion in the

lower atmosphere from a quantitative standpoint.

14.1 TEMPERATURE IN THE LOWER ATMOSPHERE

The layers of the atmosphere can be classified in a number of ways, such as by tempera-ture, density, and chemical composition. From the standpoint of the dispersion of air pol-lutants, the most important classification is on the basis of temperature.

14.1.1 Pressure and Temperature Relationships in the Lower Atmosphere

We shall utilize the concept of an air parcel, a hypothetical mass of air that may deform asit moves vertically in the atmosphere. The concept of an air parcel is a tenable one as longas the parcel is of such a size that the exchange of air molecules across its boundary is smallwhen compared with the total number of air molecules in the parcel. As such a parcel risesin the atmosphere, it expands to accommodate the lowering pressure; however, it does soin such a way that exchange of heat between the parcel and the surrounding air is negligi-ble. As the parcel expands upon rising, its temperature decreases. The process of verticalmixing in the atmosphere can, for simplicity, be envisioned as one involving a large num-ber of parcels rising and falling. If there is no heat exchange between the parcel and the sur-rounding air, the parcel and the surrounding air may be at different temperatures (but notdifferent pressures). The relation of the parcel's temperature to that of the air determineswhether the parcel will continue rising or falling or whether it will reach a point of equi-librium. Therefore the variation of temperature with altitude in the atmosphere is a keyvariable in determining the degree to which contaminant-bearing air parcels will mix ver-

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TEMPERATURE IN THE LOWER ATMOSPHERE 771

conditions. Integrating (14.14) with respect to z gives

One might ask: Why does not the atmosphere always have an adiabatic lapse rate as itsactual profile? The reason it does not is that other processes such as winds and solar heat-ing of the Earth's surface lead to dynamic temperature behavior in the lowest layers of theatmosphere that is seldom adiabatic. These other processes exert a much stronger influenceon the prevailing temperature profile than does the adiabatic rising and falling of air

parcels.Let us compute the temperature change with z of an isolated parcel of air (or possibly

other gas) as it rises or falls adiabatically through an atmosphere that is not adiabatic. Weassume that conduction or convection of heat across the boundary of the parcel will be slowcompared with the rate of vertical motion. Thus an individual parcel is assumed to rise or

fall adiabatically, even when the surrounding air is nonadiabatic.Let T denote the temperature of the air parcel and T' the temperature of the surround-

ing air. At any height z, the pressure is the same in the parcel as in the atmosphere. The rateof change of T with p in the parcel is given by (14.4), and the rate of change of p with z

is given by (1.3). Combining these two relations, we find that

dT

dz

T=-rr

Therefore the rising air will cool at a greater or lesser rate than the adiabatic, depending onwhether its temperature is higher or lower than that of the adjacent atmosphere.

If A is the actual lapse rate in the atmosphere, then at any height z

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ATMOSPHERIC STABILITY 773

On the other hand, if A < r, a rising air parcel will cool more rapidly with height thanthe surroundings and a point will be reached at which the temperature of the parcel equalsthat of the surroundings. We see that, if A < r, the acceleration will oppose the motion ofa parcel. Thus any fluctuations in the temperature of an air parcel will cause it to rise or fall,but only for a short distance. When A < r, the atmosphere is said to be stable.Summarizing, the conditions are:

A = r, neutral stability

A > r. unstable (vertical motions enhanced)A < r. stable (vertical motions suppressed)

These same arguments may be applied to the case of a moist atmosphere. Because of therelease of the latent heat of vaporization, a saturated parcel cools on rising at a slower ratethan a dry parcel, since

rdry> r wet

Thus a cloudy atmosphere is inherently less stable than a dry atmosphere, and a stable sit-uation with reference to the dry adiabatic lapse rate may actually be unstable for upwarddisplacements of a saturated air parcel.

Figure 14.1 summarizes the types of temperature profiles found in the lower atmos-phere, and Figure 14.2 shows a typical diurnal variation of temperature near the ground.The airmass near the ground is adiabatic only under special circumstances. Adiabatic con-ditions are reached usually when the sky is heavy with clouds and there is a moderate tohigh wind. The clouds prevent radiation from reaching the surface and ensure that the tem-perature of the ground does not differ greatly from the air just above it. The wind serves tomix the air, thereby smoothing out temperature differences. Vertical movement is then a re-

FIGURE 14.1 Temperature profiles in the atmosphere. (1) Adiabatic lapse rate (neutral stability,about 1 °C per 100m) T decreases with height such that any vertical movement imparted to an air par-cel will result in the parcel maintaining the same T or density as the surrounding air. (2) Superadiabatic(unstable): a rising air parcel will be warmer than its environment so it becomes more buoyant and con-tinues rising. (3) Subadiabatic (stable): a rising air parcel is cooler than its surroundings so itbecomes less buoyant and subsides. (4) Isothermal (stable): temperature is constant with height.(5) Inversion (extremely stable): temperature increases with height.

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PROBLEMS 775

Figure 14.3 shows monthly average diurnal and seasonal variations of the vertical ther-mal structure of the planetary boundary layer at rural site near St. Louis, Missouri.

PROBLEMS

14.1A Show that if the atmosphere is isothermal the temperature change of a parcel of airrising adiabatically is

T(z) = Toe-rz/To

Where To and T~ are the temperatures of the parcel at the surface and of the air atthe surface, respectively.

14.2A A rising parcel of air will come to rest when its temperature T equals that of thesurrounding air, T'. Show that the height z where this occurs is given by

. 1;,r 1{(r-A)

0

,~

1z= A

What condition must hold for this result to be valid?

14.3A Show that the condition that the density of the atmosphere does not change withheight is

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Clouds are one of the most significant elements of the atmospheric system, playing several

key roles.

1. Clouds are a major factor in the Earth's radiation budget, reflecting sunlight back tospace or blanketing the lower atmosphere and trapping infrared radiation emittedby the Earth's surface.

2. Clouds deliver water from the atmosphere to the Earth's surface as rain or snow andare thus a key step in the hydrologic cycle.

3. Clouds scavenge gaseous and particulate materials and return them to the surface

(wet deposition).4. Clouds provide a medium for aqueous-phase chemical reactions and production of

secondary species.5. Clouds affect significantly vertical transport in the atmosphere. Updrafts and down-

drafts associated with clouds determine in a major way the vertical redistribution oftrace species in the atmosphere.

Despite their great importance, clouds still remain one of the least understood compo-nents of the weather and climate system. We begin our discussion of clouds by summariz-ing the properties of their basic constituent, water. We then investigate the formation ofdroplets in a cooling air parcel. The microphysics of a droplet population and the dynam-ics of cloud formation are then examined. Finally, we revisit the chemical processes takingplace in clouds and fogs using the material already developed in Chapter 6. A comprehen-sive discussion of cloud physics, beyond the scope of this book, can be found in

Pruppacher and Klett (1980).

15.1 PROPERTIES OF WATER AND WATER SOLUTIONS

Liquid water, H2O, is characterized by the strong hydrogen bonds between its molecules,which give rise to a number of unique properties. Because of the strength of these bonds, arelatively large amount of energy is required to evaporate a unit mass of water. Similarly,the latent heat of freezing is also relatively large, as a result of further strong bonding in icecrystals. The surface tension (surface free energy) is also large. Table 15.1 summarizesthese physical properties of water. In the following sections we discuss the atmospherically

relevant properties of water and and its solutions.

777

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PROPERTIES OF WATER AND WATER SOLUTIONS 779

15.1.3 Water Surface Tension

The surface tension of water decreases with increasing temperature. Pruppacher and Klett(1980) recommend use of the following function:

(Two = 0.0761 - 55 x IO-4(T - 273)

for the temperature range -40 to 40°C, where awo is in J m -2. The surface tension of wa-ter is 76.1 x 10-3 J m-2 at O°C, and decreases by 1.55 x 10-3 J m-2 for every 10°C.Note that these values can be used for supercooled water also, that is, liquid water existingat temp,eratures below O°C.

The dissolution of other compounds in water alters its surface tension. Experimentalvalues of the variation of water solution surface tension with the solution concentration aretabulated in the Handbook of Physics and Chemistry. For salts like NaCI and (NH4)2S04the dependence of the solution surface tension, aw, on the solution molarity is practicallylinear over the range of atmospheric interest:

mNaCIO"w(mNaCI, T) = O"wo(T) + 1.62 x 10-3

O"w(m(N~n so.' T) = O"wo(T) +2.17 x 10-3m(NH.)2S0.

where uwo(T) is the surface tension of pure water and mNaCl and m(N~nS04 are the mo-larities of NaCI and (N~)2 SO4 in M, respectively. I

A last issue is the dependence of the water surface tension on the size of the droplet. Onewould expect that as the droplet surface tension is the result of attractive forces betweenwater molecules near the surface, a change in droplet diameter would change the numberof molecules interacting with the molecules at the surface, thus changing the surface ten-sion. However, because of the small range of molecular interaction, this dependence of Uwoon size is significant only for extremely small drops, consisting merely of a few thousandsof molecules, and the exact dependence is still a subject of debate (Pruppacher and Klett,1980). The change is probably smaller than 1 % for water drops as small as 0.1 JLm and be-comes significant only at drop sizes less than 0.01 JLm. Therefore the dependence of sur-face tension on droplet size can be neglected for atmospheric cloud applications.

]Because solutes alter the surface tension of water, one would expect variations of the concentrations of thesespecies near the droplet-air interface. For example, as nature tries to reach states of lower energies, if a solute in-creases the surface tension of water, this species at equilibrium should have lower concentrations at the interfacethan in the bulk solution. The opposite should happen for a surface-active compound that lowers the surface ten-sion. One would expect higher concentrations of this species near the interface than in the bulk. For a I M NaCIsolution this surface tension effect results in a NaCI deficiency at the interface of less than 1% (Pruppacher andKlett, 1980). The same authors suggested that for drops with diameters larger than 0.2 JLm and NaCI concentra-tions lower than I M, this concentration gradient due to surface tension is less than I % and can safely be ignored.The effect of solution inhomogeneity due to surface tension will therefore be neglected for our discussion of at-mospheric droplet formation.

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WATER EQUILIBRIUM IN THE ATMOSPHERE 781

TABLE 15.2 Saturation Vapor Pressure of Water Vapor Over a Flat PureWater or Ice Surface

pO (mbar) = ao + a) T + a2T2 + a3T3 + a4T4 + asTs + a6T6 (T is in °C)

Ice (-50 to DOC)Water ( -50 to +50°C)

ao = 6.107799961al = 4.436518521 x 10-1a2 = 1.428945805 x 10-2a3 = 2.650648471 x 10-4a4 = 3.031240396 x 10-6as = 2.034080948 x 10-8a6 = 6.136820929 x 10-11

Source: Lowe and Ficke (1974).

where ~Hv is the specific heat for water evaporation, Mw is the molecular weight of wa-ter, and Vv and Vw are the molar volumes of water vapor and liquid water correspondingly.Assuming that Vv » Vw and that water vapor satisfies the ideal gas law (pOvv = RT),then (15.7) becomes (9.68),

dpO

dT

~Hv(T)pOMwRT2

""

Replacing in the above equation a function describing the temperature dependence of thelatent heat of evaporation (e.g., (15.3)), one can integrate and obtain an explicit expressionfor pO(T). A series of such expressions exist in the literature (see Problem 1.1), and thatproposed by Lowe and Ficke (1974) is given in Table 15.2.

15.2.2 Equilibrium of a Pure Water Droplet

In Chapter 9 we showed that the vapor pressure over a curved interface always exceeds thatof the same substance over a flat surface. The dependence of the water vapor pressure onthe droplet diameter is given by the Kelvin equation (9.86) as

E~pO

( 4Mwaw"

exp ~

where Pw(Dp) is the water vapor pressure over the droplet of diameter Dp, po is the watervapor pressure over a flat surface at the same temperature, Mw is the molecular weight ofwater, O"wo is the air-water surface tension, and Pw is the water density. The equilibriumwater vapor concentrations at O°C and 20°C are shown in Figure 15.2 as a function of thedroplet diameter. Note that the effect of curvature for water droplets becomes importantonly for Dp < 0.1 /.Lm.

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15.2.3 Equilibrium of a Flat Water Solution

Let us consider a water solution (flat surface) at constant temperature T and pressure p inequilibrium with the atmosphere. Water equilibrium between the gas and aqueous phasesrequires equality of the corresponding water chemical potentials in the two phases (see

Chapter 9):(15.10),uw(g) = ,uw(aq)

Water vapor behaves in the atmosphere as an ideal gas so its gas-phase chemical potentialis

.uw(g) = .u~(T) + RTlnp~ (15.11)

where p~ is the water vapor partial pressure over the solution. The chemical potential ofliquid water will be given by

(15.12)JLw(aq) = JL~ + RTlnywxw

where Yw is the water activity coefficient and Xw the mole fraction of water in solution.Combining (15.10) to (15.12) we obtain

( /10 * '= exp t"'w - .uw

RT (15.13)~YwXw

The above equation describes the behavior of the system for any solution composition.Note that the right-hand side is a function of temperature only and therefore will be equalto a constant, K, for constant temperature. Considering the case of pure water (no solute)we note that when Xw = I, Yw -+ 1 and p~ = po = K (T), where po is the vapor pressureof water over pure water. Therefore (15.13) can be rewritten as

0 0Ps = Yw Xw P (15.14)

Equation (15.14) is applicable for any solution and does not assume ideal behavior.'.~"'---". -" " Yw,

The mole fraction of water in a solution consisting of nw water moles and ns solutemoles is given by

(15.15)nwXw = nw + ns

and therefore the vapor pressure of water over its solution is given by

p; =. - Yw pO (15.16)n...

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Equations (15.21), (15.24), (15.26), and (15.27) are different forms of the Kohler equa-tions (Kohler, 1921, 1926). These equations express the two effects that determine the va-por pressure over an aqueous solution droplet-the Kelvin effect that tends to increasevapor pressure and the solute effect that tends to decrease vapor pressure. For a pure waterdrop there is no solute effect and the Kelvin effect results in higher vapor pressures com-pared to a flat interface. By contrast, the vapor pressure of an aqueous solution drop can belarger or smaller than the vapor pressure over a pure water surface depending on the mag-nitude of the solute effect term, BI D~, relative to the curvature term, AI Dp. Note thatboth effects increase with decreasing droplet size but the solute effect increases muchfaster. One should also note that a droplet may be in equilibrium in a subsaturated environ-ment if D~A < B.

Figure 15.5 shows the water vapor pressure over NaCl and (NH4)2S04 drops. The Aterm in the Kohler equations can be approximated by

4MwO"w

RTpw

0.66

TA= (in JLm) (15.28):::::

where T is in K, and the solute term,

(in JLm3) (15.29)

where ms is the solute mass (in g) per particle, Ms the solute molecular weight (in gmol-I), and v is the number of ions resulting from the dissociation of one solute molecule.For example, v = 2 for NaCI and NaN°3, while v = 3 for (NH4)2S04.

I'] I I I I I II'I I I I I I I ~ NaCI I I ~ II' ,0.5 - - . (NH4)2S 4

. .,o.

. D =0.05 .urnp

...,..

0.3~

a0

:.j=

~+"=~100~

§'f/)

0.')1

0.1 J.l,mo.

0.0

-0. , 10.5 Ji,m.,.-O.:t

- . ,-,,,,,," ,

- III 'I" "I ilill I; 'I IIIIII I I I IIIIIJ0.3 0 1 10 100

Wet Diameter. p,m

FIGURE 15.5 Kohler curves for NaCl and (NH4)ZSO4 particles with dry diameters 0.05, 0.1, and0.5 ILm at 293 K (assuming spherical dry particles). The supersaturation is defined as the saturationminus one. For example, a supersaturation of 1 % corresponds to a relative humidity of 101 %.

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SJISAHd anolJ 88L


Let us consider first a drop lying on the portion of the Kohler curve for whichDp < Dpc. We assume that the atmospheric saturation is fixed at S. A drop will constantlyexperience small perturbations caused by the gain or loss of a few molecules of water. Saythat the drop grows slightly due to the addition of a few molecules of water. At its momen-tary larger size, its equilibrium vapor pressure is larger than the fixed ambient value and thedrop will evaporate water, eventually returning to its original equilibrium state. The samephenomenon will be observed if the droplet loses a few molecules of water. Its equilibriumvapor pressure will decrease, become less than the ambient, and water will condense on thedroplet returning it to its original size. Therefore drops in the rising part of the Kohler curveare in stable equilibrium with their environment.

Now consider a drop on the portion of the curve for which DIJ > Dpc that experiencesa slight perturbation, causing it to grow by a few molecules of water. At its slightly largersize its equilibrium vapor pressure is lower than the ambient. Thus water molecules willcontinue to condense on the drop and it will grow even larger. Conversely, a slight shrink-age leads to a drop that has a higher equilibrium vapor pressure than the ambient so thedrop continues to evaporate. If it is a drop of pure water, it will evaporate completely. If itcontains a solute, it will diminish in size until it intersects the ascending branch of theKohler curve that corresponds to stable equilibrium. In conclusion, the descendingbranches of the curves describe unstable equilibrium states.

If the ambient saturation ratio S is lower than the critical saturation Sc for a given par-ticle, then the particle will be in equilibrium described by the ascending part of the curve.If 1 < S < Sc, then there are two equilibrium states (two diameters corresponding to S).One of them is a stable state and the other is unstable. The particle can reach stable equi-librium only at the state corresponding to the smaller diameter.

If the ambient saturation ratio S happens to exceed the particle critical saturation Sc,there is no feasible equilibrium size for the particle. For any particle diameter the ambientsaturation will exceed the saturation at the particle surface (equilibrium saturation), and theparticle will grow indefinitely. In such a way a droplet can grow to a size much larger thanthe original size of the dry particle. It is, in fact, through this process that particles as smallas 0.01 JLm in diameter can grow one billion times in mass to become 10 JLm cloud or fogdroplets. Moreover, in cloud physics a particle is not considered to be a cloud droplet un-less its diameter exceeds its critical diameter Dpc.

The critical saturation Sc of a particle is an important property. If the environment hasreached a saturation larger than Sc, the particle is said to be activated and starts growingrapidly, becoming a cloud droplet. For a spherical aerosol particle of diameter ds (dry di-ameter), density Ps, and molecular weight Ms, the number of moles (after complete disso-ciation) in the particle is given by

V7rd; Ps

6Ms(15.33)ns =

and combining this result with (15.32) we find that

1/2In Sc = (15.34)

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(NH4)2S04, T= 20°C

- No dissociation- - -. Complete dissociation

.01

1.009

1.007

s.005 I

III

0.02 ~m---

~II1.003

'?,,

1.001 0.04 ~m - - --,I . ; . ~O.l ~m0.999 I I I I .10.2 10.1 1 10

Wet Radius, Ilffi

FIGURE 15.7 Kohler curves for (NH4)2S04 assuming complete dissociation and no dissociation

of the salt in solution for dry radii of 0.02, 0.04, and 0.1 IL m.ts, allat theacti-

Our analysis follows exactly Section 15.2.4, until the derivation of the mole fraction ofwater Xw in (15.19) and (15.20). The existence of the insoluble material needs to be in-cluded in these equations. If the insoluble particle fraction is equivalent to a sphere of di-ameter duo then the droplet volume will be

ODOr

v and

1 and~ (thee ab-

1 D3 - - 1 d36" 7r p = nwvw + nsvs + 6" 7r u (15.35)

and the mole fraction of water Xw in the solution will be given by

ns

nw(15.36)+-- =

dig-wa.

Xw

Substituting this expression into (15.18) we find

4MwC1w

RTp:D;not (15.37)+ In Yw - InIn =

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CLOUD AND FOG FORMATION 793

~

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'"'",,-"

of the in-It the in-allowing

0 -.'- - - 0.10 1.0

Dry Diameter, ,u,m

FIGURE 15.9 Critical supersaturation as a function of the particle dry diameter for different con-tents of insoluble material. The soluble material is (NH4)2S04.

01

(15.39)

and (15.38) can be rewritten as a function of the particle soluble fraction and the initial par-ticle diameter provided that the densities of soluble and insoluble material are known. Thenumber of moles of solute are in this case given not by (15.33) but by the following

expression:

(15.40)

Kohler curves for a particle consisting of various combinations of (NH4)2 SO4 and in-soluble material are given in Figure 15.8. We see that the smaller the water-soluble fractionthe higher the supersaturation needed for activation of the same particle, and the lower thecritical diameter. Critical supersaturation as a function of the dry particle diameter is givenin Figure 15.9.

15.3 CLOUD AND FOG FORMATION

The ability of a given particle to become activated depends on its size and chemical com-position and on the maximum supersaturation experienced by the particle. If, for example,the ambient RH does not exceed 100%, no particle will be activated and a cloud cannot beformed 2. In this section we will examine the mechanisms by which clouds are created in

ontainingIble mass

2The classic Kohler formulation does not consider the cases of solutes that are not completely soluble or solublegases, both of which influence the solute effect term in (15.27). In such cases cloud droplets can exists at S < 1

since B/D~ > A/Dp.

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S;)ISAHd GnO.1;) t'6J.


For an air parcel initially at 283 K with a relative humidity of 80% (RH = 0.8), a tem-perature reduction of 3.3 K is required to bring the parcel to saturation. The dew point of asubsaturated air parcel is always lower than its actual temperature (Figure 15.10). The twobecome equal only when the relative humidity reaches 100%.

15.3.2 Adiabatic Cooling

The thennodynamic behavior of a rising moist air parcel can be examined in two steps: thecooling of the air parcel from its initial condition to saturation followed by the cooling of

the saturated air.Let us consider first a moist unsaturated air parcel. Assuming that the rise is adiabatic

(no heat exchange with its surroundings) and reversible, then it will also be isentropic.Recall that for a reversible process d Q = T dS and therefore when d Q = 0, dS = 0 also.Under these conditions we have shown in Chapter 14 that if the air parcel is dry (no watervapor), its temperature will vary linearly with height according to (14.6),

dT

dz(15.44)=-r

where r = g/cp = 9.76°C km-1 is the dry adiabatic lapse rate. If the air is moist, then,as we saw in Chapter 14, the heat capacity of the air parcel cp must be corrected. Thechanges are small as the water vapor mass fraction is usually less than 3%. Even at thisrather extreme condition, the lapse rate of the moist parcel is 9.71 °C km -I, an essentially

(6v'~I)- = '1;)'111 . T

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S;)ISAHd Gno!;) 96L


The lifting condensation level hLcL is shown in Figure 15.11 as a function of the initialtemperature and relative humidity of the air parcel.

If the air parcel is lifted beyond the LCL, water will start condensing on the availableparticles, and latent heat of condensation ( - ~ H v) will be released. The lapse rate r s in this

case can be calculated by an energy balance, assuming that the air parcel remains saturated.The cooling rate of the air parcel is balanced by the work necessary for the expansion of theair parcel and the condensation latent heat released. If the air parcel contains a water vapormass mixing ratio Wvs (the subscript s is used to denote saturation of the atmosphere withwater), where Wvs = Mwpo / MaPa, then the energy change due to cooling will be cp dT(c p is the heat capacity of air, which will be almost equal to the heat capacity of the air par-cel including the water), the latent heat released will be ~Hv dwvs, and the expansion workis vdp = RTdpa/PaMa. Therefore the energy balance is

A dpaCp dT + .1.Hv dwvs - RT - = 0 (15.50)PaMa

and dividing by dz leads to the expression

r - (-~ )=~~--~~ S- A A

dz Cp dz MaPacp dz(15.51)

4000 I I I I ' I I I ' I I

E 3500

~ 3000>Q)

~

c: 25000

:0=C1/1 2000c:Q)

"0

§ 1500

u

~ 1000:0=

:J500

RH=O.2

0 I I I I I I I I I I I .0 5 10 15 20 25 30

Temperature. °cFIGURE 15.11 Lifting condensation level as a function of initial temperature and relative humid-ity of the air parcel assuming that the air parcel starts initially at the ground at p = I atm.

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S:)ISAHd GnOl:) 861..


15.3.4 A Simplified Mathematical Description of Cloud Formation

Let us revisit the rising moist air parcel assuming that we are in a Lagrangian referenceframe, moving with the air parcel. The air parcel is characterized by its temperature T, wa-ter vapor mixing ratio wv, liquid water mixing ratio w L, and velocity W. At the same timewe need to know the temperature T', pressure p, and water vapor saturation w~ of the airaround it (Figure 15.12). The pressure of the air parcel is assumed to be equal to its envi-ronment.

Let us assume that the air parcel has mass m and air density p (without including theliquid water). The velocity of the air parcel will be the result of buoyancy forces and thegravitational force due to liquid water. The buoyancy force is proportional to the volume ofthe air parcel, m / p, and the density difference between the air parcel and its surroundings,pi - p. The liquid water mass is mWL and the corresponding gravitational force gmwL.The equation for conservation of momentum is

p'-pp

(15.56)-WLd- (mW) = gmdt

where p' is the density of the surrounding air.As the air parcel is moving, it causes the acceleration of surrounding airmasses, result-

ing in a decelerating force on the air parcel. The deceleration force is proportional to themass of the displaced air, m', and the corresponding deceleration, -dW/dt. Pruppacherand Klett (1980) show that this effect is actually equivalent to an acceleration of an "in-duced" mass m/2 and therefore a term -!m dW /dt should be added on the right-handside of (15.56). Using the ideal gas law (p' - p)/ p = (T - T')/T' and the modified

(15.56) can be rewritten as

T-T'T' (15.57)

3dW Wdm--+--=g2 dt m dt

-WL

Zp

,.LP'

tp

,.LP(Z9.~I)111=

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S:>ISAHd ana']:> 008

GROWTH RATE OF INDIVIDUAL CLOUD DROPLETS 801

and

~

15.4 GROWTH RATE OF INDIVWUAL CLOUD DROPLETS

When cloud and fog droplets have diameters significantly larger than 1 ,um, mass transferof water to a droplet can be expressed by the mass transfer equation for the continuum

regime (see Chapter 11)

(15.64)dm~ = 21f DpDv(cw.oo - c~)

by.94

-~ (.!.-)Dv - p 273 (15.65)

(15.66)D' - Dvv-- ,7:0

. 2D., '~) 1/2

RT

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S:)ISAHd anal:) ZO8

GROWTH RATE OF INDIVIDUAL CLOUD DROPLETS 803

droplet surface is then

(15.68)

where we have used the mass balance

dm

dt(15.69)

and we have defined

(15.70)

For atmospheric cloud droplet growth 8 « I; however, let us continue the dervation with-out assuming that Ta = T~. Combining (15.64) and (15.69) and using the ideal gas law, wefind that

Pw(Dp. Ta)

pO (Too)

dDp -DP-"dt - 4D~M~)Sv.oo (15.71)

PwRT

where Sv.oo = Pwoo/ po (Too) is the environmental saturation ratio. Recall that for a relativehumidity equal to I ()()% the partial pressure of water in the atmosphere Pwoo is equal to the

saturation vapor pressure pO (Too) and Sv,oo is equal to unity. The ratio of the water satura-

tion pressures at T a and Too is given by the Clausius-Clapeyron equation as

pO(Ta)

pO(Too)(15.72)

Combining (15.68), (15.71), (15.38), and (15.72) we finally get

4D~Mwp~dDp -DP&- Sv,oo

PwRToo

4MwO"w(15.73)

+RTpwDp(l + <5)

The above result can be simplified since 11 « and

exp [~Hv Mw8/ RToo(l + 8)] ~ 1 + ~Hv Mw8/ RToo

After some algebra the implicit dependence on 8 can be resolved to obtain

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S:)ISAHd ano'1;) f'O8

GROWTH OF A DROPLET POPULATION 805

For a cloud droplet larger than 10 JLffi, using ac = aT = I, at 283 K,

and defining Sv,eq as the equilibrium saturatiQn of the droplet, (15.74) can be rewritten as

- SV,eq)

where Dp is in cm and tin s. The growth of an aerosol size distribution under constant su-persaturation of 1% is shown in Figure 15.14. The rate of growth of droplets is inverselyproportional to their diameters so smaller droplets grow faster than larger ones. As a result,small droplets catch up in size with larger ones during the growth stage of the cloud.

15.5 GROWTH OF A DROPLET POPULATION

. The growth of an aerosol population to cloud droplets can be investigated using the growthequation derived in the previous section. In general, one would need to integrate simulta-neously the differential equations derived in Section 15.3.4 for the air parcel updraft ve-locity, temperature, water vapor mixing ratio, and environmental temperature and watervapor mixing ratio, coupled with a set of droplet growth equations, one for each dropletsize class. The liquid water mixing ratio of the population consisting of Ni droplets pervolume of air of diameters Dpi will then be

n

WL =~.:!:. L N;D:;Pa 6 ;=1

(15.77)

where we have assumed that there are n groups of droplets.It is instructive, before examining the interactions between cloud dynamics and micro-

physics, to focus our attention on the microphysics. Figure 15.15 presents the results of theintegration of these equations for a polluted urban aerosol population (Pandis et al., 1990a)for an aerosol distribution consisting of seven size sections. At time zero the relative hu-midity is assumed to be 100%. At this time the particles have grown several times fromtheir dry size as a result of water absorption and are assumed to be in equilibrium with thesurrounding environment. The temperature of the air parcel is assumed to decrease with aconstant rate of 2 K h -1. As the temperature decreases, the saturation of the air parcel in-creases. The particles absorb water vapor, but the cooling rate is too rapid compared tomass transfer and the air parcel becomes supersaturated. After a few minutes the particlesstart becoming activated. The larger particles become activated first (Section 15.2) and thesmaller soon follow. As particles become activated, they are able to grow much faster. Notethat based on the Kohler curves as a particle grows the driving force for growth

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GROWTH OF A DROPLET POPULATION 807

(cw.oo - c~q) becomes larger for almost constant Cw.oo, because c~ decreases rapidly withsize. Therefore, as more and more particles get activated, the rate of transport of water fromthe vapor to the particulate phase increases, while the rate of supersaturation increase dueto the cooling remains approximately constant. The result is that the supersaturation in-crease slows down and after 6 min reaches a maximum value of 0.1 %.

Let us describe the above situation quantitatively, by deriving the equation for the rateof change of the supersaturation sv.The water vapor mixing ratio Wv is related to the wa-ter vapor partial pressure Pw by (15.46), while by definition

Pw

pO+sv =

Therefore combining these two relationships one gets

MaPa

Mwpo(15.78)S -v- Wv -

Differentiating this expression with respect to time and rearranging the terms we obtain

(15.79)~ = ~~ - (1 +sv)(~~ - ~~ )dt Mwpo dt po dt Pa dt

The change of the air pressure with time can be calculated assuming that the environmentis in hydrostatic equilibrium so that

~ = -~wdt RT

~

where we have assumed that T' ~ T. The change of the parcel saturation pressure withtime can be calculated using the chain rule and the Clausius-Clapeyron equation,

. ° dpo dT-=--tt dT dt

~HvMwpO dTRT2 dt

do(15.81)=

Substituting (15.80) and (15.81) into (15.79) one gets

dsvdt

MaPa dwv--Mwpo dt

=

If we assume that there is no entrainment (e = 0) and substitute (15.60) and (15.61) into(15.82), we obtain

~H2Mv w

cpRT2

PaMa

poMw

dWL

dtdsvdt

~HvMwg

cpRT2

gMaRT

w- (15.83)+=

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S:>ISAHd anol:> 808

CLOUD CONDENSATION NUCLEI 809

TABLE 15.3 Updraft Velocities and Maximum Supersaturations for Clouds and Fogs

0.25--0.70.3--0.8

Pruppacher and Klett (1980)Pruppacher and Klett (1980)Mason (1971)Pruppacher and Klett (1980)Pandis and Seinfe1d (1989)

~O.O5~O.l

'" 0-StratiformFog

15.6 CLOUD CONDENSATION NUCLEI

Supersaturations of several hundred percent are necessary for the fonnation of waterdroplets in particle free air (see Chapter 10). The need for such high supersaturations indi-cates the necessity of particles for cloud fonnation in the ambient atmosphere. The abilityof a given particle to serve as a nucleus for water droplet fonnation, as we have seen in theprevious sections, will depend on its size, chemical composition, and the local supersatu-

ration.Particles that can activate at a given supersaturation are defined as cloud condensation

nuclei (CCN) for this supersaturation. In the cloud physics literature one often defines ascondensation nuclei (CN) those particles that fOnD droplets at supersaturations of ~400%and therefore CN include all the available particles. One can therefore assume that the CNconcentration is equal to the total aerosol number concentration. This CN definition shouldbe contrasted with the CCN definition where supersaturations often well less than 2% areused. Therefore CCN represent the particles that can fonD cloud droplets under reasonableatmospheric supersaturations. We caution the reader that CCN concentrations always referto a specific supersaturation, for example, CCN(I%) or CCN(0.5%) and one should becareful when comparing CCN concentrations measured or estimated at different supersat-

urations.The CCN concentration of a given supersaturation corresponds under ideal cloud for-

mation conditions (e.g., spatial unifonnity) to the number concentrations of droplets if thecloud had the same supersaturation. We will use the symbol CCN(s) for CCN at s% super-

saturation.For a given aerosol population CCN(s) depends on both the size and composition of the

particles. In the simple case of an aerosol population that has unifonn size-independent

composition, by definition,

CCN(s) = rooJDs

n(Dp) dDp(15.85)

where n(Dp) is the number distribution of the aerosol population, and Ds the activation di-ameter for s% supersaturation of these particles. Note that CN = CCN(oo) according tothe above notation. Therefore, if all particles had the same composition, one ne~ds to knowonly the activation diameter and the size distribution of these particles to estimate the cor-

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CLOUD CONDENSATION NUCLEI 811

c = 600 and k = for continental air. Hegg and Hobbs (1992) reviewed more recent mea-surements of marine CCN and suggested values of c = 200 and k = 4. Other values for cand k based on ambient measurements are given in Table 15.4.

As expected, because of the variability of the aerosol size/composition both spatiallyand with time, the parameters c and k vary significantly, making the use of such empiricalrelationships rather questionable. Generally, CCN(1 %) concentrations in maritime andmodified maritime airmasses are around 100 cm-3, while concentrations in excess of 1000cm-3 are found in air that has been over land for several days.

The fraction of aerosol particles that are CCN(I%) is also quite variable. Over theoceans this fraction is roughly 0.5 (Hegg and Hobbs, 1992), but it does vary from 0.2 to0.6. For polluted conditions the fraction is much lower, usually less than 1 %. This is mainlydue to the existence of thousands of ultrafine particles (less than 50 nm) that cannot get ac-tivated at this supersaturation regardless of their chemical composition.

Since ambient supersaturations rarely exceed 1 %, the above CCN measurements indi-cate that cloud droplet concentrations should range from 200 to 1000 cm-3 over continentsand from 10 to 200 cm-3 over oceans. These values agree well with the drop concenti:a-lions found in continental and maritime clouds.

The link between aerosol chemical composition and CCN behavior is still not com-pletely understood. Whereas behavior of soluble inorganic aerosols is relatively well es-tablished, much less is known about the ability of organic aerosols (alone or mixed withinorganic components) to serve as CCN.

A series of studies have reported the activation efficiency of particles generated duringfuel combustion. These results were summarized by Lammel and Novakov (1995) and are

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TABLE 15.4 Empirical Parameters for the CCN ConcentrationDependence on the Supersaturation s

0.30.5-0.6

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0.4,-0.61.00.30.40.50.40.9

Maritime (Australia)Maui (Hawaii)Atlantic, Pacific OceansPacificNorth AtlanticNorth AtlanticArcticCape Grim (Australia)North AtlanticNorth PacificNorth PacificPolluted North PacificEquatorial PacificContinentalContinental (Australia)Continental (Buffalo, NY)

Source: Hegg and Hobbs (1992).

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CLOUD PROCESSING OF AEROSOLS 813

Finally, there are other processes that cwoccur around clouds that may lead to the forma-tion of new particles.

15.7.1 Nucleation Scavenging of Aerosols by Clouds

Nucleation scavenging of aerosols in clouds refers to activation and subsequent growth ofa fraction of the aerosol population to cloud droplets. This process is described by (15.74)and has been discussed in Section 15.5.

If Ci,o is the concentration (in mass per volume of air) of an aerosol species in clear airbefore cloud formation (e.g., at the cloud base), and Ci,cloud and Ci.int are its concentra-tions again in mass per volume of air in the aqueous phase and in the interstitial aerosol, re-spectively, one can define the cloud mass scavenging ratio for species i, Fi' as

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CO OI.Fi = (15.88)

Note that if there is no production or removal of i in the cloud then Ci,o = Ci,int + Ci,cloud'

The mass scavenging ratio defined above may vary from zero to unity. The number scav-enging ratio F N can be defined as

No - NiDI

No(15.89)FN=

where No is the aerosol number concentration before cloud formation and NiDI is the num-ber concentration of interstitial aerosol.

Theoretically, as particles larger than 0.5 .urn or so become cloud droplets in a typicalcloud and these particles represent most of the aerosol mass, one would expect mass acti-vation efficiencies close to unity. Junge (1963) predicted sulfate scavenging ratios from nu-cleation scavenging alone to range from 0.5 to 1.0. Since then all theoretical studies havepredicted high mass nucleation scavenging efficiencies for all aerosol species. For exam-ple, Flossmann et al. (1985, 1987) reported calculated aerosol scavenging efficiencies ex-ceeding 0.9 in typical cloud environments. Pandis et al. (1990a) estimated scavengingefficiencies of 0.7 for sulfate and 0.8 for nitrate and ammonia in polluted clouds. In othernumerical studies, Flossmann (1991) reported mass scavenging efficiencies of 0.9 orhigher for warm clouds over the Atlantic.

These theoretical estimates are in good agreement with the high mass scavenging effi-ciencies measured in the atmosphere. Ten Brink et al. (1987) observed nearly completescavenging of aerosol sulfate in clouds. The data of Daum et al. (1984) also showed that thebulk of the sulfate mass is incorporated into cloud droplets. Hegg and Hobbs (1988) re-ported scavenging ratios for sulfate of 0.5 :i: 0.2.

On the contrary, low number scavenging efficiencies are expected in clouds influencedby anthropogenic sources because of the prevalence of fine aerosol particles; number scav-enging efficiencies of a few percent or less are expected in most such situations. Only inclouds in the remote marine atmosphere does the total number scavenging efficiency ex-ceed 0.1.

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The above predictions agree with measured concentration/size dependencies measuredin clouds that are not heavily influenced by anthropogenic sources. Noone et al. (1988)sampled droplets from a marine stratus cloud and calculated that the volumetric meansolute concentration of the 9 to 18 J.Lm droplets was a factor of 2.7 smaller than in the 18to 23 J.Lm droplets. Ogren et al. (1989) reported similar results for a cloud in Sweden. Onthe other hand, similar measurements for cloud and fog droplets in heavily polluted envi-ronments suggest that solute concentrations decrease with increasing droplet size (Mungeret al., 1989; Ogren et al., 1992). No satisfactory explanation exists for such behavior.

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During cloud formation, aerosols that serve as cloud condensation nuclei (CCN) be-come activated and grow freely by vapor diffusion. Soluble gases such as nitric acid, am-monia, and sulfur dioxide dissolve into the droplets. The cloudwater serves as the reactingmedium for a series of aqueous-phase reactions, most importantly the transformation ofdissolved SO2, S(IV), to sulfate, S(VI). The sulfate formed is not volatile and remains inthe particulate phase. Other reactions, for example, the oxidation of formaldehyde toformic acid, result in volatile products that return to the gas phase (Figure 15.20). Duringthe cloud evaporation stage, several species that were dissolved in the cloudwater evapo-rate. Others, like sulfate, remain in the aerosol phase. Ammonia often accompanies the sul-fate formed as the neutralizing cation. Species like nitrate or chloride that may have existedin the original particle can be displaced by the sulfate produced and forced to return to thegas phase. The result of these aqueous-phase processes is usually an overall increase in par-ticle mass and size. Chemical composition of the particles may also change, with sulfateand ammonium concentrations generally increasing and nitrate and chloride decreasing(Pandis et al., 1990b).

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FIGURE 15.21 Measurements of the gas-phase partial pressures of H202 versus the S02 partialpressure for interstitial cloud air (Daum et aI., 1984). Arrows signify that the mixing ratio was below

the detection limit.

during a 3 day springtime period, chemical reactions in clouds occupying I to 2% of thetropospheric volume were responsible for sulfate production comparable to the gas-phasereactions throughout the entire tropospheric volume under consideration. McHenry andDennis (1994) proposed that annually more than 60% of the ambient sulfate in central andeastern United States is produced in mostly nonprecipitating clouds. Similar conclusionswere reached by Dennis et al. (1993) and Karamachandani and Venkatram (1992).Aqueous-phase SO2 oxidation in clouds is predicted to be the most important pathway forthe conversion of SO2 to sulfate on a global scale (Hegg, 1985; Langner and Rodhe, 1991).

Effect of cloud processing of aerosols in the remote marine atmosphere has beendemonstrated in a series of field studies (Hoppel et al., 1986; Frick and Hoppel, 1993).Figure 15.22 shows the formation of a second peak in the accumulation mode as an air-mass is advected off North America to the Atlantic and the Pacific Oceans. Note that thetwo modes observed in the number distribution should not be confused with modes of themass distribution. Hoppel et al. (1986) proposed that cloud processing of aerosol is anefficient mechanism for accumulating mass in the 0.08 to 0.5 j),m size range in the marine

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Radius, ~mFIGURE 15.23 Typical remote marine aerosol size distributions. Reprinted from Atmos. Environ.,24A, Hoppel, W. A. and Frick, G. M., 645-649, Copyright 199O, with kind permission from ElsevierScience Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK.

(aerodynamic diameter around 0.7 J1,m). These two submicrometer mass distributionmodes have also been observed in nonurban continental locations (McMurry and Wilson,1983; Hobbs et al., 1985; Radke et al., 1989). Hering and Friedlander (1982) and John etal. (1990) proposed that the larger mode could be the result of aqueous-phase chemical re-actions. Meng and Seinfeld (1994) showed that growth of condensation mode particles byaccretion of water vapor or by gas-phase or aerosol-phase sulfate production cannot ex-plain existence of the droplet mode. Activation of condensation mode particles, formationof cloud/fog drops, followed by aqueous-phase chemistry, and droplet evaporation wereshown to be a plausible mechanism for formation of the aerosol droplet mode.

Simulations of the aerosol-cloud-aerosol cycle have shown that sulfate formed duringcloud/fog processing of an airmass favors aerosol particles that have access to most of thecloud liquid water content, which are those with diameters in the 0.5 to 1.0 J1,m range(Pandis et al., 1 990a). Figure 15.24 depicts simulation of fog processing of an urbanaerosol population. Note that the shape of the aerosol distribution changes with the creationof an extra mode, resulting mainly from the formation of (NH4)2S04. Note also that thereare significant changes in the aerosol chemical composition before and after the fog withsulfates replacing nitrate and chloride salts.

15.7.4 Interstitial Aerosol Scavenging by Cloud Droplets

Interstitial aerosol particles collide with cloud droplets and are removed from cloud inter-stitial air. The coagulation theory of Chapter 12 can be used to quantify the rate and effectsof such removal. If n(Dp, t) is the aerosol number distribution and nd(Dp, t) the droplet

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OTHER FORMS OF WATER IN THE ATMOSPHERE 823

TABLE 15.6 Estimated Lifetimes of Aerosols in a Nonraining Cloud(N = 955 cm-3, Dp = 10 J.Im, WL = 0.5 g cm-3) at Standard Conditions

4x1.6 x1.1 x2.2 x

1.03 x3x

and K(Dp, 10 ,urn) can be calculated from (12.57) (see also Figure 12.5 and Table 12.3).Corresponding particle collision efficiencies and lifetimes are shown in Table 15.6. Nucleismaller than 10 nm will be scavenged in a few minutes by such a cloud whereas particleslarger than 0.1 ,urn will not be collected by droplets during the cloud lifetime.

The above results indicate that for average residence times of air parcels in clouds (onthe order of an hour) only the very fine aerosol particles will be collected by cloud droplets.These particles often represent a significant fraction of the aerosol number, so the totalnumber may be reduced significantly, and the shape of the aerosol number distribution maychange drastically. However, these particles contain little of the mass and therefore themass distribution effectively will not change. These qualitative conclusions are in agree-ment with detailed simulations of aerosol processing by clouds (Flossmann and

Pruppacher, 1988; Flossmann, 1991).

15.7.5 Aerosol Nucleation Near Clouds

Clouds remove individual fine aerosol particles by scavenging. Even so, enhanced aerosolnumber concentrations in the vicinity of clouds have been observed (Saxena and Hendler,1983; Hegg et al., 1990, 1991; Radke and Hobbs, 1991). Saxena and Hendler (1983) sug-gested that observed high aerosol number concentrations near clouds could be a result ofshattering of rapidly evaporating droplets. Hudson and Frisbie (1991) suggested that thesehigh particle concentrations may actually be an artifact due to droplet splashing. Hegg et al.(1991) proposed that the high actinic flux near cloud tops resulting from upward scatteringof solar radiation could lead to high OH concentrations, rapid H2SO4 formation, and sub-sequent nucleation of new H2SO4-H2O particles. Kerminen and Wexler (1994) estimateda high nucleation probability associated with high relative humidity areas around clouds inrelatively clean environments. Note that such a nucleation process in the vicinity of theclouds produces very little aerosol mass but a large number of particles and may influencesignificantly the shape of the aerosol number distribution, especially in remote regions.

15.8 OTHER FORMS OF WATER IN THE ATMOSPHERE

Our discussion in the preceding sections has focused on "wann" nonraining troposphericclouds. Water in the atmosphere can also exist as ice, rain, snow, and so on. We summarizehere aspects of the formation and removal of these water forms that are most associated

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where Pm is the melting pressure of ice, ~Hm the molar enthalpy of melting, and Vw themolar volume of water. Equations (9.66), (15.98), and (15.99) can be integrated and plot-ted to produce the p-T phase diagram for pure water shown in Figure 15.26. Note thatthere is only one point (T = QoC, p = 6.1 mbar), the water triple point for which allphases coexist. Another interesting observation is that for temperatures below QoC the wa-ter vapor pressure over liquid water is higher than water vapor pressure over ice,

(T <DOC)Psat,w > Psat,i

So if air is saturated with respect to ice, it is subsaturated with respect to water. As a result,supercooled water droplets cannot coexist in equilibrium with ice crystals. Note that Figure15.26 refers to the equilibrium of bulk water (curvature is neglected), without any impuri-ties (zero solute concentration). Curvature and solute effects cause the behavior of water in

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tain the estimate

RT~Mw m~Tf = 1000 ~Hm (15.105)

where m is the solution molarity. For ideal solutions this results in a depression of 1.86°CM-1 of solute, and for a salt that dissociates into two ions this results in a depression of3.72°C M-1 of the salt. Due to the nonideality of real salts actual depression at I M con-centration is 3.35 °C for NaCI.

Curvature Effects Ice crystals in the atmosphere have a variety of shapes, withhexagonal prismatic being the basic one (Pruppacher and Klett, 1980). For instructivepurposes let us ignore this complexity and concentrate on the behavior of a spherical iceparticle of diameter Dp. Our analysis for water droplets and the Kelvin effect is directlyapplicable here and the vapor pressure of water over the ice particle surface, Pi. will be

(15.106)

where Psat.i is the vapor pressure over a flat ice surface, O'ia the surface energy of ice in air,and Pi the ice density. Pruppacher and Klett (1980) reviewed theoretical and experimentalvalues for O'ia and suggested that it varies from 100 to 110 ergs cm -2. This surface tensionthat is higher than the water/air value results in relative vapor increases (p / PsaJ higherthan those for a water droplet of the same size.

Pruppacher and Klett (1980) show that the freezing temperature decreases with de-creasing size of the ice particle. This decrease becomes particularly pronounced for crystaldiameters smaller than 20 nm and is further enhanced by the solute effect for solute con-centrations larger than 0.1 M.

Ice Nuclei Ice particles can be formed through a variety of mechanisms. All of theserequire the presence of a particle, which is called an ice nucleus (IN). These mechanismsare (1) water vapor adsorption onto the IN surface and transformation to ice (depositionmode), (2) transformation of a supercooled droplet to an ice particle (freezing mode), and(3) collision of a supercooled droplet with an IN and initiation of ice formation (contact

mode).Formation of ice particles in the absence of IN is possible only at very low temperatures,

below -40°C (Hobbs, 1995). The presence of IN allows ice formation at higher tempera-tures. Aerosols that can serve as IN are rather different from those that serve as CCN.Ice-forming nuclei are usually insoluble in water and have chemical bonding and crystal-lographic structures similar to ice. Larger particles are more efficient than smaller ones.While our understanding of the ice nucleating abilities of aerosols remains incomplete, par-ticles that are known to serve as IN include dust particles (especially clay particles such as

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""0OTHER FORMS OF WATER IN THE ATMOSPHERE

~ "' ' .a b

FIGURE 15.27 Schematic of the flow around a falling drop. The dashed lines are the trajectoriesof small drops considered as mass points. Trajectory a is a grazing trajectory, while b is a collision

trajectory.

The collision process is illustrated in Figure 15.27 for viscous flow around a sphere ofdiameter Dp. As the large droplet approaches small drops of diameter dp, the viscousforces exerted by the flow field around the large droplet push the droplets away from thecenter of flow, modifying their trajectories. In Figure 15.27 droplet b is collected by theraindrop while droplet a is not. Therefore the falling raindrop will in general collect fewerdrops than those existing in the cylinder of diameter Dp below it. Droplets in the cylinderof diameter y will be collected. The distance y is defined by the grazing trajectory a andis a function of the raindrop size Dp and drop size dp. One defines the collision efficiencyE as the ratio of the actual collision cross section to the geometric cross section, or

(IS.IO8)y2

E=(Dp + dp)2

Note that all drops of diameter dp in the cylinder with diameter y, below the falling dropwith diameter Dp, will be collected by it. Because small drops tend to move away from thefalling raindrop, E is expected to be smaller than unity for most cases.

Figure 15.28 shows theoretically estimated collision efficiencies among drops as func-tions of the radii of the small and large drops. There is a rapid increase in collision effi-ciency as the two drops approach equal size. This is due to fluid mechanical interactionsthat accelerate the upper drop more than the lower one but have little importance for theatmosphere where the probability of collision of equal-sized drops is extremely small.

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The growth of a falling drop of mass m as a result of accretion of drops can be described

by

dm

dt

1T 2= 4Et(Dp + dp) WL(VD - Vd) (I5.IID)

where Et is the overall accretion efficiency (collision efficiency times coalescence effi-ciency, Et = EEc), WL is the liquid water content of the small drops, and VD and Vd are,respectively, the fall speeds of the larger and smaller particles. Equation (15.110) is calledthe continuous accretion equation and assumes that the smaller drops are uniformly dis-tributed in space. The description of the size change of droplets falling through a cloud by(15.110) implicitly assumes that all droplets of the same size will grow in the same way.According to the continuous equation, if several drops with the same initial diameter fallthrough a cloud, they would maintain the same size at all times. In reality, each droplet-droplet collision is a discrete event. Droplets that collide first with others grow faster thandroplets that had initially the same size. As a result, the simple continuous equation can se-riously underestimate the collision frequency and the growth rate of falling drops, espe-cially when the collector and collected drops have the same size. The coagulation equation(see (12.80)) is a better mathematical description of these discrete collisions. Equation(12.80) (often called the stochastic accretion equation in cloud microphysics) describes im-plicitly individual collisions and predicts that even if all falling droplets had initially thesame size some will grow more than others.

The role of ice in rain formation was first proposed by Bergeron in 1933, based on thecalculations of Wegener. Using thermodynamics, Wegener showed in 1911 that at temper-atures below O°C supercooled water drops and ice crystals cannot exist in equilibrium.Using this result, Bergeron proposed that in cold clouds the ice crystals grow by vapor dif-fusion at the expense of the water droplets until either all drops have been consumed or allice crystals have fallen out of the cloud as precipitation. Findeisen later produced addi-tional observations supporting the above mechanism, which is often called theWegener-Bergeron-Findeisen mechanism. Mathematically the description of the mecha-nism requires solution of the growth equations by vapor diffusion for both ice crystals andwater drops in a supersaturated environment (Pruppacher and Klett, 1980).

Raindrop Distributions A number of empirical formulas have been proposed for theraindrop spectrum. The distribution proposed by Best is often used to describe the fractionof rainwater comprised of raindrops smaller than Do, F{Do):

F(Dp) = 1 - exp [ -2.25

(15.111)

where Po is the rainfall intensity in (mm h-l) and Dp is in mm.Probably the most widely used is the Marshall-Palmer (MP) distribution, where

n(Dp) = no exp (-1{1 Dp) (15.112)

where n(Dp) = dnjdDp is the number distribution in drops m -3 mm -I, no = 8000 m-3mm-l, and 1/1 = 4.1PoO.21 mm-l. The MP distribution is often not sufficiently general to

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CLOUD CLIMATOLOGY 833

TABLE 15.7 Microphysical Cloud Characteristics

< 19<500312350500

100-250 0.1-0.9 12 (base)19 (top)

117

18

200-350200-70025-125

0.3

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302200

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300100

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St (marine)St (continental)Sc (California)Sc (California)Sc (U.K.)Sc (Washington State)Sc (North Sea)Sc (England)As-Ac (Russia)As-Ac (Alaska)As-Ac(Wisconsin)As-Ac(Wisconsin)As-Ac(Washington State)As-Ac (U.S.) 35-75 <0.2 14-19

Source: Heymsfield (1993).

4. It is less than the liquid water content calculated assuming adiabatic ascent of an airparcel due to entrainment of dry air. This deviation is on the order of 10% or so forthe lower half of stratiform clouds and it increases with height.

Average droplet diameters are usually in the 10 to 20 ,urn range. Marine clouds are char-acterized by relatively smaller droplet concentration and larger diameters, where continen-tal clouds tend to have smaller droplets (Table 15.7).

Minimum droplet diameters are a few micrometers, where large droplets exceed 100 ,urn.In general, droplet spectra are wider for orographic clouds, less wide for stratus, and rathernarrow for cumulus cloud types. Continental cumuli drop sizes range only from a few mi-crometers to around 20 ,urn in diameter. Frequency distributions of the mean cloud dropletsize for various cloud types are shown in Figure 15.30.

Squires' (1958) observations suggested that high drop concentrations are associatedwith narrow size spectra and small drop sizes for continental clouds. Bimodal droplet spec-tra are often encountered in the upper half of clouds. Lee and Pruppacher (1977) explainedthis bimodality by entrainment of fresh CCN into the cloud.

CLOUD CLIMATOLOGY 833

TABLE 15.7 Microphysical Cloud Characteristics

0.09-0.63

0.1-0.9

< 19<500312350500

100-250

-12 (base)19 (top)

117

18

10

12-208-149-117-10<9

200-350200-70025-125

200-500302200

200-400

300100

0.3

0.1<0.10.15

< 0.7<0.5

0.09-0.170.03-0.09

<0.01

25 <0. 15-20

70-1000

St (marine)St (continental)Sc (California)Sc (California)Sc (U.K.)Sc (Washington State)Sc (North Sea)Sc (England)As-Ac (Russia)As-Ac (Alaska)As-Ac(Wisconsin)As-Ac(Wisconsin)As-Ac(Washington State)As-Ac (U.S.) 35-75 <0.2 14-19

Source: Heymsfield (1993).

4. It is less than the liquid water content calculated assuming adiabatic ascent of an airparcel due to entrainment of dry air. This deviation is on the order of 10% or so forthe lower half of stratiform clouds and it increases with height.

Average droplet diameters are usually in the 10 to 20 JLm range. Marine clouds are char-acterized by relatively smaller droplet concentration and larger diameters, where continen-tal clouds tend to have smaller droplets (Table 15.7).

Minimum droplet diameters are a few micrometers, where large droplets exceed 100 JLm.In general, droplet spectra are wider for orographic clouds, less wide for stratus, and rathernarrow for cumulus cloud types. Continental cumuli drop sizes range only from a few mi-crometers to around 20 JLm in diameter. Frequency distributions of the mean cloud dropletsize for various cloud types are shown in Figure 15.30.

Squires' (1958) observations suggested that high drop concentrations are associatedwith narrow size spectra and small drop sizes for continental clouds. Bimodal droplet spec-tra are often encountered in the upper half of clouds. Lee and Pruppacher (1977) explainedthis bimodality by entrainment of fresh CCN into the cloud.

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REFERENCES 837

Hegg, D. A., and Hobbs, P. V. (1992) Cloud condensation nuclei in the marine atmosphere: a review,in Nucleation and Atmospheric Aerosols, edited by N. Fukuta and P. E. Wagner. DeepakPublishing, Hampton, VA, pp. 181-192.

Hering, S. V., and Friedlander, S. K. (1982) Origins of aerosol sulfur distributions in the Los Angelesbasin, Atmos. Environ., 16,2647-2656.

Heymsfield, A. J. (1993) Microphysical structures of stratiform and cirrus clouds, inAerosol-Cloud-Climate Interactions, edited by P. V. Hobbs, Academic Press, San Diego,

pp.97-121.Hobbs, P. V., Bowdle, D. A., and Radke, L. F. (1985) Particles in the lower troposphere over the high

plains of the United States, 1. Size distributions, elemental compositions and morphologies, J.

Climat. Appl. Meteorol., 24, 1344-1356.Hobbs, P. V. (1995) Aeroso1-c1oud interactions, in Aerosol-Cloud-Climate Interactions, edited by P.

V. Hobbs. Academic Press, San Diego, CA, pp. 33-73.Hoppel, W. A., Frick, G. M., and Larson, R.E. (1986) Effects of non-precipitating clouds on the

aerosol size distribution in the marine boundary layer, Geophys. Res. Lett., 13, 125-128.Hoppel, W. A., and Frick, G. M. (1990) Submicron aerosol size distributions measured over the trop-

ical and south Pacific, Atmos. Environ., 24A, 645-659.Houghton H. G. (1985) Physical Meterology, MIT Press, Cambridge, MA.Hudson, J. G., and Clark, A. D. (1992) Aerosol and cloud condensation nuclei measurements in the

Kuwait plume, J. Geophys. Res., 97, 14533-14536.Hudson, J. G., and Frisbie, P. R. (1991) Cloud condensation nuclei near marine stratus, J. Geophys.

Res., 96, 20795-20808.Husain, L., Dutkiewicz, V. A., Hussain, M. M., Khwaja, H. A., Burkhard, E. G., Mehmood, G.,

Parekh, P. P., and Canelli, E. (1991) A study of heterogeneous oxidation of SO 2 in summer clouds,

J. Geophys. Res., 96, 8789-8805.John, W., Wall, S. M., Ondo, J. L., and Winklmayr, W. (1990) Modes in the size distributions of at-

mospheric inorganic aerosol, Atmos. Environ., 24A,2349-2359.Junge, C. E. (1963) Air Chemistry and Radioactivity. Academic Press, New York.Karamachandani, P., and Venkatram, A. (1992) The role of non-precipitating clouds in producing

ambient sulfate during summer-results from simulation with the Acid Deposition and OxidantModel (ADOM), Atmos. Environ., 26, 1041-1052.

Kelly, T. J., Schwartz, S. E., and Daum, P. H. (1989) Detection of acid producing reactions in natural

clouds, Atmos. Environ., 23,569-583.Kerrninen, V. M., and Wexler, A. S. (1994) Post-fog nucleation of H2SO4-H2O particles in smog,

Atmos. Environ., 28, 2399-2406.Kohler, H. (1921) Zur Kondensation des Wasserdampfe in der Atmosphiire, Geofys. Publ., 2,3-15.Kohler, H. (1926) Zur Thermodynamic der Kondensation an hygroskopischen Kernen und

Bemerkungen iiber das Zusammenfliessen der Tropfen, Medd. Met. Hyd1: Anst. Stockholm, 3 (8).Lamme1, G., and Novakov, T. (1995) Water nucleation properties of carbon black and diesel soot par-

ticles, Atmos. Environ., 29,817-823.Langner, J., and Rodhe, H. (1991) A global three-dimensional model of the tropospheric sulfur cy-

cle, J. Atmos. Chem., 13,225-263.Leaitch, W. R., Strapp, J. W., Isaac, G. A., and Hudson, J. G. (1986) Cloud droplet nucleation and

scavenging of aerosol sulphate in polluted atmospheres, Tellus, 38B, 328-344.Lee, I. Y., and Pruppacher, H. R. (1977) A comparative study of the growth of cloud drops by con-

densation using an air parcel model with and without entrainment Pure Appl. Geophys., 115,

523-545.

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PROBLEMS 839

Saxena, V. K., and Hendler, A. H. (1983) In-cloud scavenging and resuspension of cloud activeaerosols during winter storms over Lake Michigan, in Precipitation Scavenging, Dry Depositionand Resuspension, edited by H. R. Pruppacher, R. G. Semonin, and W. G. N. Slinn. Elsevier, NewYork, pp. 91-102.

Sekhon, R. S., and Srivastava, R. C. (1971) Doppler observations of drop size distributions in a thun-derstorm, J. Atmos. Sci, 28, 983-994.

Squires, P. (1958) The microstructure and colloidal stability of warm clouds, Tel/us, 10, 256-261.Swozdziak, J. W., and Swozdziak, A. B. (1992) Sulfate aerosol production in the Sudety Range,

Poland, J. Aerosol Sci., S369-S372.Ten Brink, H. M., Schwartz, S. E., and Daum, P. H. (1987) Efficient scavenging of aerosol sulfate by

liquid water clouds, Atmos. Environ, 21, 2035-2052.Twomey, S. (1959) The nuclei of natural clouds formation. Part II: The supersaturation in natural

clouds and the variation of cloud droplet concentration, Geofis. Pura Appl., 43,243-249.

Twomey, S., and Wojciechowski, T. A. (1969) Observations of the geographical variation of cloudnuclei, J. Atmos. Sci., 26, 684-688.

United States National Acid Precipitation Assessment Program (1991) Acidic Deposition: State ofScience and Technology, Vol. I Emissions, Atmospheric Processes and Deposition, edited by P. M.Irving. U.S. Government Printing Office, Washington, DC.

Walcek, C. J., Stockwell, W. R., and Chang, J. S. (1990) Theoretical estimates of the dynamic radia-tive and chemical effects of clouds on tropospheric gases, Atmos. Res, 25,53-69.

Wall, S. M., John, W., and Ondo, J. L. (1988) Measurements of aerosol size distributions for nitrateand major ionic species, Atmos. Environ, 22, 1649-1659.

Warner, J. (1968) The supersaturation in natural clouds, J. Appl. Meteorol., 7, 233-237.Whelpdale, D. M., and List, R. (1971) The coalescence process in droplet growth, J. Geophys. Res,

76,2836-2856.

PROBLEMS

ls.lA Show equations (15.39) and (15.40).

15.28 Derive equation (15.53).

ls.3A You dissolve 5 g of NaCI in a glass containing 200 cm3 of water. The glass is in aroom with constant temperature equal to 20°C and relative humidity 80%. Calculatethe volume of water that will be left in the glass after several days of residence inthis environment. Repeat the calculation for a relative humidity of 95%.

ls.4A Your grandmother and grandfather are upset, because it has just started raining.After listening to the weather prediction for a cloudy day but without rain, theyplanned to spend the day working in the garden. They have started criticizing the lo-cal weather forecaster who, despite the impressive gadgets (radar maps, 3D ani-mated maps), still cannot reliably predict if it will rain tomorrow. They turn to youand ask why if we can send people to the Moon we still cannot tell if it is going torain or not. Explain, avoiding scientific terminology.

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