Atmospheric Chemistry and Physics

Preface xxv 1 The Atmosphere 1 1.1 1.2 1.3 1.4 1.5 History and Evolution of the Earth'sAtmosphere 1 Climate 4 The L...

Author: John H. Seinfeld | Spyros N. Pandis

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Preface

xxv

1 The Atmosphere

1

1.1 1.2 1.3 1.4 1.5

History and Evolution of the Earth'sAtmosphere 1 Climate 4 The Layersof theAtmosphere 6 Variationof Pressurewith Height in the Atmosphere 9 Large-ScaleMotion of the Atmosphere 10 1.5.1 The GeneralCirculation 10 1.5.2 Troposphere-Stratosphere Transport 14 1.6 TemperatureandWaterVapor 16 1.7 ExpressingtheAmount of a Substancein the Atmosphere 18 1.8 Compositionof theAtmosphere 21 1.9 Radiation 23 1.9.1 SolarandTerrestrialRadiation 26 1.9.2 Absorptionof Radiationby Gases 29 1.10 EnergyBalancefor Earth andAtmosphere 33 1.10.1 SolarVariability 37 1.10.2 Earth'sEnergyBalance 38 1.11 SpatialandTemporalScalesof AtmosphericProcesses 40 Appendix 1 Derivation of the GeostrophicWind Speed 43 References 47 Problems 47 2 Atmospheric Composition, Global Cycles,and Lifetimes 2.1 2.2

2.3

AtmosphericResidenceTimes 50 2.1.1 ResidenceTime 51 Sulfur-ContainingCompounds 55 2.2.1 Dimethyl Sulfide (CH3SCH3) 2.2.2 CarbonylSulfide (OCS) 62 2.2.3 Sulfur Dioxide (SO2) 63 2.2.4 The AtmosphericSulfur Cycle Nitrogen-ContainingCompounds 67 2.3.1 Nitrous Oxide (N2O) 67 2.3.2 Nitrogen Oxides(NOx = NO + 2.3.3 ReactiveOdd Nitrogen (NOy)

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4 Chemistry of the Stratosphere 4.1 4.2 4.3

ChapmanMechanism 164 HO x Cycles 171 NO x Cycles 173 4.3.1 N2O StratosphericSourceof NO x 173 4.3.2 NOx Cycles 175 4.4 ClOx Cycles 177 4.5 ReservoirSpeciesand Coupling of the Cycles 180 4.6 StratosphericSpeciesObservationsand Predictions 184 4.6.1 Upper Stratosphere 184 4.6.2 Lower Stratosphere 186 4.7 OzoneHole 189 4.7.1 Polar StratosphericClouds 192 4.7.2 PSCsand the OzoneHole 194 4.7.3 Antarctic OzoneHole Measurements 198 4.7.4 Arctic OzoneHole 199 4.7.5 Summary 202 4.8 Heterogeneous (Nonpolar)StratosphericChemistry 203 4.8.1 Heterogeneous Hydrolysis ofN2Os 203 4.8.2 Effect of Volcanoeson StratosphericOzone 207 4.8.3 Summaryof Midlatitude andTropical Stratospheric OzoneChemistry 210 4.9 TransportBetweenthe Tropical andMidlatitude Stratosphere 210 4.10 Ozone-DepletingPotentialof Halocarbons 212 4.11 Effect of Aircraft Emissionson StratosphericOzone 215 4.12 CarbonylSulfide (OCS)and the Stratospheric Aerosol Layer 216 4.12.1 AtmosphericChemistryofOCS and OCSLifetime 217 4.12.2 StratosphericAerosol Layer 217 4.13 Projectionsof FutureOzoneChange 218 Appendix 4 Sensitivity/UncertaintyAnalysis of Atmospheric ChemicalMechanisms 219 4.A.l SensitivityCoefficients 222 4.A.2 The Direct DecoupledMethod 223 4.A.3 Adjoint Methods 224 4.A.4 Green'sFunctionMethods 224 References 226 Problems 230 5 Chemistry of the Troposphere 5.1 5.2 5.3

Basic PhotochemicalCycle of N02, NO, and03 235 AtmosphericChemistryof CarbonMonoxide andNOx 239 AtmosphericChemistryof FonnaldehydeandNOx 244

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5.15 AtmosphericChemistry(GasPhase)of Sulfur Compounds 314 5.15.1 Sulfur Oxides 314 5.15.2 ReducedSulfur Compounds(Dimethyl Sulfide) 315 5.16 TroposphericChemistryof HalogenCompounds 317 5.16.1 ChemicalCyclesof HalogenSpecies 318 5.16.2 TroposphericChemistryofCFC Replacements: Hydrofluorocarbons(HFCs)and Hydrochlorofluorocarbons (HCFCs) 319 References 323 Problems 331 6 Chemistry of the Atmospheric Aqueous Phase 6.1 6.2 .6.3

6.4 6.5

6.6

Liquid Waterin the Atmosphere 337 6.1.1 Cloud Typesand Liquid WaterContent 338 AbsorptionEquilibria and Henry's Law 340 6.2.1 Gas/Aqueous-Phase Distribution Factor 343 Aqueous-Phase ChemicalEquilibria 344 6.3.1 Water 344 6.3.2 CarbonDioxide/WaterEquilibrium 345 6.3.3 Sulfur Dioxide 348 6.3.4 Ammonia/WaterEquilibrium 353 6.3.5 Nitric Acid/Water Equilibrium 355 6.3.6 Equilibrium of OtherImportantAtmosphericGases 356 Aqueous-Phase ReactionRates 361 S(IV) to S(VI) Transformationand Sulfur Chemistry 363 6.5.1 Oxidation of S(IV) by Dissolved03 363 6.5.2 Oxidation of S(IV) by HydrogenPeroxide 366 6.5.3 Oxidation of S(IV) by OrganicPeroxides 367 6.5.4 UncatalyzedOxidation of S(IV) by O2 368 6.5.5 Oxidationof S(IV) by 02 Catalyzedby Iron andManganese 369 6.5.6 S(IV) Oxidationby the OH Radical 372 6.5.7 Oxidation ofS(IV) by Oxidesof Nitrogen 374 6.5.8 Reactionof DissolvedS02 with HCHO 376 6.5.9 Comparisonof Aqueous-Phase S(IV) Oxidation Paths 378 Aqueous-Phase Nitrite andNitrate Chemistry 380

6.6.1 NOx Oxidation 380 6.7 6.8 6.9

6.6.2 Nitrogen Radicals 381 Aqueous-Phase OrganicChemistry 381 Oxygenand HydrogenChemistry 383 Dynamic Behaviorof Solutionswith Aqueous-Phase ChemicalReactions 384 6.9.1 ClosedSystem 385

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8.5.2 Aerosol Mobility andDrift Velocity 475 8.5.3 MeanFreePathof an Aerosol Particle 478 8.6 PhoreticEffects 480 8.6.1 Thermophoresis 480 8.6.2 Diffusiophoresis 483 8.6.3 Photophoresis 483 8.7 Aerosol andFluid Motion 484 8.7.1 Motion of a Particlein an IdealizedFlow (900 Corner) 485 8.7.2 StopDistanceand StokesNumber 486 8.8 Diametersof NonsphericalParticles 488 References 488 Problems 489 9 Thermodynamics of Aerosols

491

9.1

ThermodynamicPrinciples 491 9.1.1 Internal Energyand ChemicalPotential 491 9.1.2 The GibbsFreeEnergy,G 493 9.1.3 Conditionsfor ChemicalEquilibrium 495 9.1.4 ChemicalPotentialsof Ideal Gasesand Ideal GasMixtures 499 9.1.5 ChemicalPotentialof Solutions 501 9.1.6 The Equilibrium Constant 506 9.2 Aerosol Liquid WaterContent 507 9.2.1 ChemicalPotentialof Waterin AtmosphericParticles 508 9.2.2 TemperatureDependenceof the DRH 510 9.2.3 Deliquescenceof Mu1ticomponent Aerosols 514 9.2.4 Crystallizationof Single andMulticomponentSalts 519 9.3 Equilibrium VaporPressureOver a CurvedSurface: The Kelvin Effect 519 9.4 Thermodynamicsof AtmosphericAerosol Systems 523 9.4.1 The H2SO4-H2OSystem 523 9.4.2 The Sulfuric Acid-Ammonia-Water System 529 9.4.3 The Ammonia-Nitric Acid-Water System 531 9.4.4 The Ammonia-Nitric Acid-Sulfuric Acid-Water System 537 9.4.5 OtherInorganicAerosol Species 539 References 541 Problem 543

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10 Nucleation 10.1

ClassicalTheory of HomogeneousNucleation: KineticApproach 547 10.1.1 The ForwardRateConstant.Bi 550 10.1.2 The ReverseRateConstantYi 551

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11.2.5 CharacteristicTime for Aqueous-Phase ChemicalReactions 617 11.3 MassTransportandAqueous-Phase Chemistry 617 11.3.1 Gas-Phase Diffusion andAqueous-Phase Reactions 618 11.3.2 Aqueous-Phase Diffusion and Reaction 620 11.3.3 Interfacial MassTransportandAqueous-Phase Reactions 621 11.3.4 Application to the S(IV)-Ozone Reaction 623 11.3.5 Application to the S(IV)-Hydrogen Peroxide Reaction 626 11.3.6 Calculationof Aqueous-Phase ReactionRates 627 11.3.7 An Aqueous-Phase Chemistry/Mass TransportModel 634 11.4 MassTransferto Falling Drops 635 11.5 CharacteristicTime for AtmosphericAerosol Equilibrium 636 11.5.1 Solid Aerosol Particles 636 11.5.2 AqueousAerosol Particles 638 Appendix 11 Solution of the TransientGas-Phase Diffusion ProblemEquations(11.4)to (11.7) 641 References 643 Problems 645 12 Dynamics of Aerosol Populations 12.1

12.2 12.3

12.4 12.5 12.6

MathematicalRepresentations of the Aerosol SizeDistributions 648 12.1.1 DiscreteDistribution 648 12.1.2 ContinuousDistribution 649 Condensation 649 12.2.1 Solutionof the CondensationEquation 652 Coagulation 656 12.3.1 Brownian Coagulation 656 12.3.2 Coagulationin Laminar ShearFlow 664 12.3.3 Coagulationin TurbulentFlow 665 12.3.4 Coagulationfrom GravitationalSettling 665 12.3.5 Brownian Coagulationand ExternalForceFields 666 12.3.6 The CoagulationEquation 672 12.3.7 Solutionof the CoagulationEquation 676 The DiscreteGeneralDynamic Equation 680 The ContinuousGeneralDynamic Equation 682 Evolution of an Aerosol SizeDistribution During Gas-to-ParticleConversion 684 12.6.1 Diffusion-ControlledGrowth 685 12.6.2 SurfaceReaction-ControlledGrowth 686 12.6.3 VolumeReaction-ControlledGrowth 688 12.6.4 DimensionlessSizeSpectraEvolution 689

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14.1.2 TemperatureChangesof a Rising (or Falling) Parcelof Air 770 14.2 AtmosphericStability 772 Problems 775 15 Cloud Physics

777

15.1

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18.3 18.4

Summaryof GaussianPoint SourceDiffusion Fonnulas 923 DispersionParametersin GaussianModels 926 18.4.1 Correlationsfor uyand UzBasedon Similarity Theory 926 18.4.2 Correlationsfor uyand UzBasedon PasquillStability Classes 929 18.5 PlumeRise 931 18.6 Analytical Propertiesof the GaussianPlumeEquation 933 18.7 FunctionalFonns of MeanWind SpeedandEddy Diffusivities 938 18.7.1 MeanWindSpeed 938 18.7.2 Vertical Eddy Diffusion Coefficient Kzz 938 18.7.3 Horizontal Eddy Diffusion Coefficients Kxx and K yy 942 18.8 Solutionsof the Steady-State AtmosphericDiffusion Equation 943 18.8.1 Diffusion from a Point Source 943 18.8.2 Diffusion from a Line Source 944 References 947 Problems 949 19 Dry Deposition

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GeneralRepresentation of Atmospheric Wet RemovalProcesses 997

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22 Radiative Effects of Atmospheric Aerosols: Visibility and Climate 22.1

ScatteringandAbsorptionof Light by Small Particles 1114 22.1.1 RayleighScatteringRegime 1120 22.1.2 GeometricScatteringRegime 1122 22.1.3 ScatteringPhaseFunction 1123 22.1.4 Extinction by an Ensembleof Particles 1123 22.2 Visibility 1126 22.3 Scattering,Absorption,and Extinction Coefficientsfrom Mie Theory 1131 22.4 CalculatedVisibility ReductionBasedon AtmosphericData 1135 22.5 Direct Effect of Aerosolson Climate 1139 22.5.1 Optical Depth 1143 22.5.2 UpscatterFraction 1146 22.5.3 ScatteringModel of an Aerosol Layer 1147 22.5.4 Cooling VersusHeatingof anAerosol Layer 1152 22.5.5 ScatteringModel of anAerosol Layer for a NonabsorbingAerosol 1154 22.5.6 Direct AerosolForcing of Climateby SulfateAerosols 1156 22.5.7 Effect of Mineral Dust on RadiativeForcing of Climate 1160 22.5.8 Effect of Carbonaceous Aerosolson Radiative Forcingof Climate 1166 22.5.9 Internaland ExternalMixtures 1166 22.6 Indirect Effect of Aerosolson Climate 1170 22.6.1 RadiativeModel for a Cloudy Atmosphere 1173 22.6.2 Sensitivityof Cloud Albedo to Cloud Drop NumberConcentration 1175 22.6.3 Relationof Cloud Drop NumberConcentrationto Aerosol Concentrations 1177 22.6.4 Estimatesof Indirect RadiativeForcing of Aerosols 1179 22.7 Summary:Estimatesof Contributionsto RadiativeForcing ~ 1180 22.8 Climate Responseto AnthropogenicAerosol Forcing 1182 Appendix 22 Calculationof ScatteringandExtinction Coefficients by Mie Theory 1184 References 1185 Problems 1190 23 Atmospheric Chemical Transport Models 23.1

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24.6

Alternative Formsof Air Quality Standards 1277 24.6.1 Evaluationof Alternative Formsof the OzoneAir Quality Standardwith 1971Pasadena, California, Data 1279 24.6.2 Selectionof the AveragingTime 1281 24.7 RelatingCurrentandFutureAir Pollutant StatisticalDistributions 1281 References 1283 Problems 1285 Appendix A

Units and Physical Constants

1289

A.l SI BaseUnits 1289 A.2 SI Derived Units 1289 A.3 FundamentalPhysicalConstants 1292 A.4 Propertiesof theAtmosphereandWater 1293 A.5 Units for RepresentingChemicalReactions 1294 A.6 Concentrationsin the AqueousPhase 1295 A.7 Symbolsfor Concentration 1295 References 1295 Appendix B

Rate Constantsof Atmospheric Chemical Reactions

1297

References 1307 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 atmosphere, nitrogen, oxygen, water, carbon dioxide, and the noble gases. In the late 19th and early 20th centuries attention turned to the so-called trace gases,speciespresent at less than 1 part per million parts of air by volume (1 JLmol per mole). We now know that the atmosphere contains a myriad of trace species, some at levels as low as 1 part per trillion parts of air. The role of trace species is disproportionate to their atmospheric abundance; they are responsible for phenomena ranging from urban photochemical smog, to acid deposition, to stratospheric ozone depletion, to potential climate change. Moreover, the composition of the atmosphere is changing; analysis of air trapped in ice cores reveals a record of striking increases in the long-lived so-called greenhouse gases, carbon dioxide (CO2), methane (CH4), and nitrous oxide (N 20). Within the last century, concentrations of tropospheric ozone (03), sulfate (SO~-), and carbonaceous aerosols in the Northern Hemisphere have increased significantly. There is evidence that all these changes are altering the basic chemistry of the atmosphere. Atmospheric chemistry occurs within a fabric of profoundly complicated atmospheric dynamics. 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 vortex over Antarctica, with the concomitant formation of polar stratospheric clouds that serve as sites for heterogeneous chemical reactions involving chlorine compounds resulting from anthropogenic chlorofluorocarbons-all leading to the near total depletion of stratospheric ozone over the South Pole each spring; witness the nonlinear, and counterintuitive, dependence of the amount of ozone generated by reactions involving hydrocarbons and oxides of

nitrogen(NOx) at the urbanandregionalscale-although both hydrocarbonsandNOx are ozoneprecursors,situationsexist wherecontinuing to emit more and more NO x actually leads to less ozone. The chemical constituents of the atmosphere do not go through their life cycles independently; the cycles of the various species are linked together in a complex way. Thus a perturbation of one component can lead to significant, and nonlinear, changes to other components 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 in the atmosphere is ozone (03). High in the stratosphere ozone screens living organisms from biologically harmful solar ultraviolet radiation; ozone at the surface, in the troposphere, can produce adverse effects on human health and plants when present at levels elevated above natural. At the urban and regional scale, significant policy issues concern how to decreaseozone levels by controlling the ozone precursors-hydrocarbons and oxides of nitrogen. At the global scale, understanding both the natural ozone chemistry of the troposphere and the causes of continually increasing background tropospheric ozone levels is a major goal.

xxv

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JAxx

PREFACE xxvii

for the benefit of the studentand the instructor.The designation(A) indicatesa problem that involves a straightforwardapplicationof materialin the text. Thoseproblemsdenoted (B) requiresomeextensionof the ideasin the text. Problemsdesignated(C) encouragethe readerto apply conceptsfrom the book to currentproblemsin atmosphericscienceandgo somewhatbeyondthe level of (B) problems.Finally, thoseproblemsdenoted(D) are of a degreeof difficulty correspondingto (C) but generallyrequiredevelopmentof a computer programfor their solution. This book isa successorto John H. Seinfeld'sAtmosphericChemistryand Physicsof Air Pollution (Wiley, 1986),which has been widely usedfor a decade.Substantialadditions havebeenmadein virtually all areascoveredby the earlier book, reflectingthe significant increasein our understandingof atmosphericprocessesthat hasemergedover the last decadeand reflecting the truly global scopeof the scienceof atmosphericchemistry and physics. We extendsincereappreciationto Marta GoodmanandLaura Shaheenwho providedso much valuableassistancein making this book a reality and to Cecilia Lin who draftedthe figuresso skillfully. JOHN H. SEINFELD SPYROSN. 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 gas and dust, referred to as the "primordial solar nebula," about 4.6 billion years ago. The atmospheres of the Earth and the other terrestrial planets, Venus and Mars, are thought to have 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), a mixture similar to that emitted by present day volcanoes. The composition of the present atmosphere bears little resemblance to the composition of the early atmosphere. Most of the water vapor that outgassed from the Earth's interior condensed out of the atmosphere to form the oceans. The predominance of the CO2 that outgassed formed sedimentary carbonate rocks after dissolution in the ocean. It is estimated that for each molecule of COz presently in the atmosphere, there are about 105 COz molecules 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 atmosphere over geologic time to become the atmosphere's most abundant constituent. The early atmosphere of the Earth was a mildly reducing chemical mixture, whereas the present atmosphere is strongly oxidizing. The dramatic rise of oxygen (Oz) as an atmospheric constituent over time was the result of the production of Oz as a by-product of photosynthetic activity. It has been estimated that the current level of Oz in the atmosphere was achieved approximately 400 million years ago (Cloud, 1983). The present level of Oz is maintained by a balance between production from photosynthesis and removal through respiration and decay of organic carbon. If Oz were not replenished by photosynthesis, the reservoir of surface organic carbon would be completely oxidized in about 20 years, at which time the amount of Oz in the atmosphere would have decreased by less than 1% (Walker, 1977). In the absenceof surface organic carbon to be oxidized, weathering of sedimentary rocks would consume the remaining O2 in the atmosphere, but it would take approximately 4 million years to do so. The Earth's atmosphere is composed primarily of the gases Nz (78%), Oz (21%), and Ar (1 %), whose abundancesare controlled over geologic time scales by the biosphere, uptake and release from crustal material, and degassing of the interior. Water vapor is the next most abundant constituent; it is found mainly in the lower atmosphere and its concentration is highly variable, reaching concentrations as high as 3%. Evaporation and precipitation control its abundance. The remaining gaseous constituents, the trace gases, comprise less than 1% of the atmosphere. These trace gases playa crucial role in the Earth's radiative

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OF THE EARTH'S ATMOSPHERE

3

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 of new synthetic chemicals. Historically these emissions can lead to unforeseen consequences in the atmosphere. Classical examples include the realization in the 1950s that motor vehicle emissions could lead to urban smog and the realization in the 1970s that emissions of chlorofluorocarbons from aerosol spray cans and refrigerators could cause the depletion of stratospheric ozone. The chemical fates of trace atmospheric species are often intertwined. The life cycles of the trace species are inextricably coupled through the complex array of chemical and physical processesin the atmosphere. As a result of these couplings, a perturbation in the concentration of one species can lead to significant changes in the concentrations and lifetimes of other trace species and to feedbacks that can either amplify or damp the original perturbation. An example of this coupling is provided by methane. Methane is the predominant organic molecule in the troposphere and it is the sec.ondmost important greenhouse gas after CO2. Methane sources such as rice paddies and cattle can be estimated and are increasing. 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 concentration dependson the amount of carbon monoxide (CO), which itself is a product of C~ oxidation as well as a result of fossil fuel combustion and biomass burning. The hydroxyl concentration also depends on the concentration of ozone and oxides of nitrogen. Change in C~ can affect the total amount of ozone in the troposphere, so methane itself affects the concentration of the species, OR, that governs its removal. Depending on their atmospheric lifetime, trace species can exhibit an enormous range of spatial and temporal variability. Relatively long-lived species have a spatial uniformity such that a handful of strategically located sampling sites around the globe are adequate to characterize their spatial distribution and temporal trend. As species lifetimes become shorter, their spatial and temporal distributions become more variable. Urban areas,for example, can require tens of monitoring stations over an area of hundreds of square kilometers 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 be made for CO2 and C~, whose histories can be reconstructed from their concentrations in bubbles of air trapped in ice in such perpetually cold places as Antarctica and Greenland. With gasesthat are long-lived in the atmosphere and therefore distributed rather uniformly over the globe, such as CO2 and C~, polar ice core samples reveal global average concentrations of previous eras. Analyses of bubbles in ice cores show that CO2 and C~ concentrations remained essentially unchanged from the end of the last ice age some 10,000 years ago until roughly 300 years ago, at mixing ratios close to 260 ppm by volume and 0.7 ppm by volume, respectively. (See Section 1.4 for discussion of units.) About 300 years ago methane levels began to climb, and about 100 years ago levels of both gases began to increase markedly. Before the large-scale production of chlorofluorocarbons the natural level of chlorine in the stratosphere was 0.6 part per billion (ppb) by volume; now it is 3 ppb, a factor of 5 increase. Activities of humans account for most of the rapid changes in the trace gases over the past 200 years-combustion of fossil fuels (coal and oil) for energy and transportation, in-

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century. It has been estimated that a doubling of CO2 from its pre-Industrial Revolution mixing ratio of 280 ppm by volume could lead to a rise in average global temperature of 1.5 to 4.5°C. A 2°C warming would produce the warmest climate seen on Earth in 6000 years. A 4.5°C rise would place the world in a temperature regime last experienced in the Mesozoic Era-the age of dinosaurs. Although an average global ~arming of a few degrees does not sound like much, it could 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 days or more exceeding 35°C (95°F) in the Com Belt of the United States would increase threefold. Such conditions at critical stages of the growing season are known to harm com and lead 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 many major American cities. Changes in the timing and amount of precipitation would almost certainly occur with a warmer climate. Soil moisture, critical during planting and early growth periods, will change. Some regions would probably become more productive, others less so. The North American Grain Belt, according to at least one climate model, will shift northward into Canada as warming produces hotter, drier conditions in the American Midwest. Of all the effects of a global warming, perhaps none has captured more attention than the prospect of rising sea levels. This would result from the melting of land-based glaciers and volume expansion of ocean water as it warms. Prevailing opinion is that a sea level rise of about 0.5 m could occur by 2100. In the most dramatic scenario, the West Antarctic ice sheet, which rests on land that is below sea level, could slide into the sea if the buttress of floating ice separating it from the ocean were to melt. This would raise the average sea level 5 to 6 m (Bentley, 1997). Even a 0.3 m (1 foot) rise would have major effects on the erosion of coastlines, salt water intrusion into the water supply of coastal areas, flooding of marshes, and inland extent of surges from large storms. To systematically approach the complex subject of climate, the scientific community has 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 example of a forcing is a change in energy output from the sun. Responsesare the meteorological results of these forcings, reflected in temperatures, rainfall, extremes of weather, sea level height, and so on. Much of the variation in the predicted magnitude of potential climate effects resulting from the increase in greenhouse gas levels hinges on estimates of the size and direction of various 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 reinforce the initial warming. One example of a greenhouse warming feedback mechanism involves water vapor. As air warms, each cubic meter of air can hold more water vapor. Since water vapor is a greenhouse gas, this increased concentration of water vapor further enhances greenhouse warming. In turn, the warmer air can hold more water, and so on. This is an example of a positive feedback, providing a physical mechanism for multiplying the original impetus for change beyond its initial amount. Some mechanisms provide a negative feedback, which decreasesthe initial impetus. For example, 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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9

'HE LAYERS OF THE ATMOSPHERE

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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 is slow. Mesosphere. Extends from the stratopause to the mesopause (-80 to 90 kIn altitude); temperature decreaseswith altitude to the mesopause, which is the coldest point in the atmosphere; rapid vertical mixing. Thermosphere. The region above the mesopause; characterized by high temperatures as a result of absorption of short wavelength radiation by N2 and O2; rapid vertical mixing. The ionosphere is a region of the upper mesosphereand lower thermosphere where ions are produced by photoionization. Exosphere. The outermost region of the atmosphere (>500 kIn altitude) where gas molecules with sufficient energy can escape from the Earth's gravitational attraction.

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3'M3HdSOW.LV 3ffi

8

VARIATION OF PRESSURE WITH HEIGHT IN THE ATMOSPHERE

9

Absorption of solar ultraviolet radiation by 03 causesthe temperature in the stratosphereto be much higher than expected, based on simply extending the troposphere's lapse rate into the stratosphere.

1.4 VARIATION OF PRESSUREWITH HEIGHT IN THE ATMOSPHERE The variation of pressurewith height in the atmospherecan be addressedwith the hydrostaticequation,! dp(z)

dz

=

.p(z)g

(1.1)

where p(z) is the massdensityof air at height z and g is the accelerationdue to gravity. From the ideal gaslaw,

p(z)=

MairP(Z) RT(z)

(1.2)

where Mairis the averagemolecularweight of air (28.97g mol-I). Thus dp(z)

dz

-

Mairgp(z) RT(z)

(1.3)

which we can rewrite as d lnp(z) - -~

dz

where H(z)

= RT(z)/

-

H(z)

(1.4)

Mairg is a characteristic length scale for decrease of pressure with

height. The temperaturein the atmospherevariesby lessthan a factor of 2, while the pressure changesby six ordersof magnitude(seeTableA.8). If the temperaturecan be takento be approximatelyconstant,just to obtain a simple approximateexpressionfor 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 gas pressure can support. The unit mm Hg is often called the Torr in honor of the scientist, Evangelista Torricelli. A related 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 is called the pascal (Pa). In terms of pascals, the standard atmosphere is 1.01325 x 10s Pa. Another commonly used unit of pressure in atmospheric science is the millibar (mbar), which is equivalent to the hPa (see Tables A.5 and AR) Thp .t"nti"rti "tmn.nhprP i. 101, ?~ mh"r

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to the tropics must pass through more atmosphere and intercept a larger surface area. The uneven distribution of energy resulting from latitudinal variations in insolation and from differences in absorptivity of the Earth's surface leads to the large-scale air motions of the Earth. In particular, the tendency to transport energy from the tropics toward the pola( regions, thereby redistributing energy inequalities on the Earth, is the overall factor governing the general circulation of the atmosphere. In order to visualize the nature of the general circulation of the atmosphere, we can think of the atmosphere over either hemisphere as a fluid enclosed within a long, shallow container, 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 be neglected, and the container can be considered to be rectangular. If such a container were constructed in the laboratory and the ends differentially heated as described above, one would observe a circulation of the fluid, consisting of rising motion along the heated wall and descending motion along the cooled wall, flow in the direction of warm to cold at the top of the box, and flow in the direction of cold to warm along the bottom of the box. In the atmosphere, 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's surface an object at the equator has a greater tangential velocity than one in the temperate zones. Air moving toward the south cannot acquire an increased eastward (the Earth rotates from west to east) tangential velocity as it moves south and thus, to an observer on the Earth, appears to acquire a velocity component in the westward direction. Thus air moving south in the Northern Hemisphere appears to lag behind the Earth. To an observer on the Earth it appears that the air has been influenced by a force in the westward direction. To an observer in space, it would be clear that the air is merely trying to maintain straight-line motion while the Earth turns below it. Friction between the wind and the ground diminishes this effect in the lower atmosphere. From the standpoint of air motion, the atmosphere can be segmented vertically into two layers. Extending from the ground up to about 1000 m is the planetary boundary laye!; the zone in which the effect of the surface is felt and in which the wind speed and direction are governed by horizontal pressure gradients, shear stresses, and Coriolis forces. Above the planetary boundary layer is the geostrophic laye!; in which only horizontal pressure gradients and Coriolis forces influence the flow. . To predict the general pattern of macroscale air circulation on the Earth we must consider both the tendency for thermal circulation and the influence of Coriolis forces. Figure 1.2 shows the nature of the general circulation of the atmosphere. At either side of the equator is a thermal circulation, in which warm tropical air rises and cool northern air flows toward the equator. The circulation does not extend all the way to the poles becauseradiative cooling of the upper northward flow causesit to subside (fall) at about 30° Nand S latitude. The Coriolis force acting on these cells leads to easterly winds, called the trade winds. The same situation occurs in the polar regions, in which warm air from the temperate zones moves northward in the upper levels, eventually cooling by radiation and subsiding at the poles. The result is the polar easterlies. In the temperate regions, between 40° and 55° latitude, influences of both tropical and polar regions are felt. The major feature of the temperate regions is large-scale weather systems, which results in the circulation shown in Figure 1.2. The surface winds in the Northern Hemisphere are westerlies because of the Coriolis force.

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Latitude FIGURE 1.4 Meanatmospherictemperatureover the period 1980to 1989between1000mbarand 50 mbar averagedarounda latitude band(Salstein.1995).Data not availablein blackenedareas.

the averagetemperatureexceeds295 K. The annualmeantemperaturestructureis largely symmetricabout the equator(although the highest temperatureoccursat about 10° N), with the differencein meansurfacetemperaturebetweenthe tropics and the poles about 35°C.At the top of the troposphere,aboutthe 200 mbar level, the meridionaltemperature gradientbeginsto reverse;at 100 mbar, for example,temperatureincreasespolewardby about20°C. Watervapor is distributedthroughoutthe lower troposphere,at highly variablelevels. The watervaporcontentof the atmospherecanbe expressedin a variety of ways: 1. Mole (or volume) mixing ratio--moles of water vaporper mole of air (seeSection 1.7). 2. Amount of water vaporto dry air by mass[g H2O (kg dry air)-']. 3. Specifichumidity-proportion of watervapor to total air [g H2O (kg air)-']. 4. Relativehumidity-ratio of the specifichumidity to the maximumspecifichumidity possibleat a given temperatureandpressure(dimensionless).(SeeSection1.7.) 5. Massconcentrationg H2O (m3air)-'. 6. Massmixing ratio g H2O (g air)-'. Figure 1.5showsthe zonalmeanspecifichumidity for the period 1980to 1989.Maximum specifichumidities are reachedin the tropics, about 16 g kg-I. By the 500 mbar altitude, the valueover the tropics hasdecreasedto 2 g kg-I. This value of 2 g kg-I also holdsin the northernand southernpolar regions.

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EXPRESSING THE AMOUNT OF SUBSTANCE IN THE ATMOSPHERE

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OF THE ATMOSPHERE

The atmosphere is composed primarily of nitrogen, oxygen, and several noble gases, the concentrations of which have remained remarkably fixed over time. Also present are a number of trace gases that occur in relatively small and sometimes highly variable amounts. In spite of its apparent unchanging nature, the atmosphere is in reality a dynamic system, with its gaseous constituents continuously being exchanged with vegetation, the oceans, and biological organisms. The so-called cycles of the atmospheric gasesinvolve a number of physical and chemical processes. Gases are produced by chemical processes within the atmosphere itself, by biological activity, volcanic exhalation, radioactive decay, and human industrial activities. Gases are removed from the atmosphere by chemical reactions 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 average lifetime of a gas molecule introduced into the atmosphere can range from secondsto millions of years, depending on the effectiveness of the removal processes. Most of the species considered air pollutants (in a region in which their concentrations exceed substantially the normal background levels) have natural as well as man-made sources. Therefore, in order to assessthe 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 and anthropogenic sources as well as predominant removal mechanisms. The important atmospheric gasesare listed in Table 1.1 arranged according to the nature of their global cycles. The total quantity of a species both in the atmosphere and dissolved

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23

erals at the Earth's surface. Thus the oxygen concentration in the atmosphere is probably a result of both accumulation and geochemical cycles. While in the air, a substancecan be chemically altered in one of two ways. First, the sunlight itself may contain sufficient energy to break the molecule apart, a so-called photochemical reaction. The more frequently occurring chemical alteration, however, takes place when two molecules interact and undergo a chemical reaction to produce new species. Atmospheric chemical transformations can occur homogeneously or heterogeneously. Homogeneous reactions occur entirely in one phase; heterogeneous reactions involve 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 substancesare likely to participate in some form of chemical reaction. This process can transform a chemical from its original state, the physical (gas, liquid, or solid) and chemical form in which it first enters the atmosphere, to another state that may have either similar or very different characteristics. Transformation products can differ from their parent substance in their chemical properties, toxicity, and other characteristics. These products may be removed from the atmosphere in a manner very different from that of their precursors. For example, when a substancethat was originally emitted as a gas is transformed into a particle, the overall removal 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 reason for the atmosphere's oxidizing capacity arises because the atmosphere contains minute amounts of very reactive molecular fragments, called free radicals. The most important free radical in the chemistry of the troposphere is the hydroxyl (OH) radical, which reacts with nearly every molecular species in the atmosphere. In addition, the atmosphere contains trace amounts of species less reactive than free radicals but nonetheless reactive enough 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 characterized by higher chemical oxidation statesthan their parent substances.Frequently this oxidative transformation is accompanied by an increase in polarity (and hence water solubility) or other physical and chemical changes from the precursor molecule. An example is the conversion of sulfur dioxide (SOz) into sulfuric acid (HzS04). Sulfur dioxide is moderately water soluble, but its oxidation product, sulfuric acid, is so water soluble that even single molecules of sulfuric acid in air immediately become associated with water molecules. The demise of one substance through a chemical transformation can become another species in situ source. In general, then, a species emitted into the air can be transformed by a chemical process to a product that may have markedly different physicochemical properties and a unique fate of its own.

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because the electric field of the wave causes oppositely directed forces and therefore accelerations 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 thus are not strongly affected by radiation above 400 nm. The CO2 molecule is linear but can easily be bent, leading to an induced dipole moment. A transverse vibrational mode exists for 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 7 to 13 JLmis also a window region; nearly 80% of the radiation emitted by the Earth in this region escapesto space. Most of the non-CO2 greenhouse gases, including 03, CH4, N2O, and the chlorofluorocarbons, all have strong absorption bands in this window region. For this reason, relatively small changes in the concentrations of these gasescan produce a significant change in the net radiative flux. As the concentration of a greenhouse gas continues to increase, it can absorb more of the radiation in its energy bands. Once an absorption wavelength becomes saturated, further increases in the concentration of the gas have less and less effect on radiative flux. This is called the band saturation effect. For CO2, for example, the 15 JLmband is already close to saturated. In addition, if a gas absorbs at wavelengths that are also absorbed by other gases, then the effect of increasing concentrations on radiative flux is less than in the absence of band overlap. For example, there is significant overlap between some of the absorption bands of CH4 and N2O; this overlap must be carefully 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 already so much CO2 in the atmosphere, more CO2 can have no additional effect on absorption of outgoing radiation. When gases are present in small concentrations, doubling the concentration of the gas will approximately double its absorption. When an absorbing gas is present in high concentration the effect of further addition is not one-to-one but it is not

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Reflected Emitted

For Rp = 0.30, this equation gives Te = 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 equilibrium temperature Te = 268 K. This simple equation predicts that Te varies about 0.5 K for a 10 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

= Fs -

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 longwave components by

= ~Fs - ~FL

(1.20)

To reestablish equilibrium, a temperature change ~T eresults, which can be related to ~F net by a parameter }.O,

whereAo,having units K (W m-1-1 is called the climate sensitivityfactor. If we neglect any feedbacksin the climate system,Aocanbe estimatedas (8Fe/8Te)-I,

~=,

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(1.22)

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Global climate changeis inducedby a forcing that disturbsthe equilibrium andleadsto a nonzeroaveragedownwardnet flux at the top of the atmosphere(TOA), -Foe!

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So -(1

-

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4

It is customary to write (1.23) in terms of downward flux, -Fnet, at the TOA; an increase of - F net corresponds to heating of the planet. Primary forcing can occur as a result of changes of So,Rp, or FL, Changes in incoming solar radiation have resulted from changes in the Earth's orbit and fromyariations in the Sun's output of energy. Changes in the planetary albedo Rp can result from changes in surface reflectance from human activity (agriculture, deforestation), from changes in the aerosol content of the atmosphere from both natural (volcanoes) and anthropogenic (industrial emissions, biomass burning) causes,and to 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 gasesin the atmosphere and to a lesser extent from changes in aerosols. As we have seen, in the long-wave portion of the spectrum gasesand aerosols absorb much of the radiation 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 Sun have been the major causes for climatic change throughout its history. If the Sun's radiation intensity declined 5 to 10% and there were no other compensating factors, ice would engulf the planet in less than a century. Although no theory exists to predict future changes in solar output, the effect of changes in Earth's orbit as it travels around the Sun is beginning to be understood. During the past million years, Earth has experienced 10 major and 40 minor episodes of glaciation. All appear to have been controlled by three so-called orbital 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 24,000 years. Currently, Earth is closest to the Sun in January. This month-of-closest-approach factor can make a difference of 10% in the amount of solar radiation reaching a particular location in a given season. Last, the shape of Earth's orbit varies from being nearly circular to being more elliptical with a period of 100,000 years. The climatic cycles caused by these orbital factors are called Milankovitch cycles after the Serbian mathematician Milutin Milankovitch, who first described them in 1920. Superimposed on the Milankovitch 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 principal determinant of the times of glaciation, the exact mechanisms by which Earth responds to the orbital changes have not been established. Orbital changes alone appear not to 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 orbital changes to enhance global warming and cooling. The levels of carbon dioxide and

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43

atmosphere's scales of motion. Much of this book will be devoted to understanding the exquisite interactions between chemical and transport processes in the atmosphere. In anticipation of much of the remainder of this book, Table 1.4 summarizes atmospheric effects of trace gases.

APPENDIXl

DERIVATION OF THE GEOSTROPffiC WIND SPEED

The direction of winds in the geostrophic layer is determined by horizontal pressure gradients and Coriolis forces. As we have discussed, an air parcel moving southward in the Northern Hemisphere as a result of pressure gradients is accelerated toward the west by the Coriolis force. We can actually compute the wind speed and direction at any latitude as a function of the prevailing pressure gradient if we assume that only pressure and Coriolis forces influence the flow. It can be shown that the acceleration experienced by an object on the surface of the Earth (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 is simply the centrifugal force, in a direction that acts normal to the Earth's surface and is counterbalanced by gravity. The second term, 0 x u, is the Coriolis force. This force

arisesonly when an object, suchas an air parcel,is moving; that is U :;t: O. Even though the Coriolis force is of much smaller magnitude than the centrifugal force, only the Coriolis force 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, 2uGQ sin cf>,where Q is the rate of rotation of the Earth and cf> is the latitude.The direction 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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Low p

~ Parcel initially at rest here FIGURE 1.A.2 Approachto geostrophicequilibrium.

Weusuallydenote20 sin r/> by f, calledthe Coriolis parameter.From the continuity equation (I.A.I), we seethat au/ax = 0, since v = w = O.Thusfrom (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 seethat the componentof the Coriolis force, -ju,

is exactly balancedby the

pressuregradient, (1/ p) op/oy. Therefore the geostrophic wind speed UGis given by

Ua=

apjay 2pQ sin 4>

(I.A.7)

The approach to the geostrophic equilibrium for an air parcel starting from rest, accelerated by 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 friction of the Earth's surface. The presence of the surface induces a shear in the wind profile, as in a turbulent boundary layer over a flat plate generated in a laboratory wind tunnel. In analyzing the geostrophic wind speed we found that for steady flow a balance exists between the pressure force and the Coriolis force. Consequently, steady flow of air at levels near the ground leads to a balance of three forces: pressure force, Coriolis force, and friction force due to the Earth's surface. Thus, as shown in Figure 1.A.3, the net result of these three

forcesmust be zero for a nonacceleratingair parcel. Sincethe pressuregradientforce Fp must be directed from high to low pressure, and the frictional force Ff must be directed opposite to the velocity u, a balance can be achieved only if the wind is directed at some angle toward the region of low pressure. This angle between the wind direction and the isobars increases as the ground is approached since the frictional force increases. At the ground, over open terrain, the angle of the wind to the isobars is usually between 10° and 20°. Because of the relatively smooth boundary existing over this type of terrain, the wind speedat a 10 m height (the height at which the so-called surface wind is usually measured)

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REFERENCES Bentley,C. R. (1997)Rapidsea-levelrise soonfrom WestAntarctic Ice Sheetcollapse?Science,275, 1077-1078. Boering,K. A. et al. (1995) Measurements of stratosphericcarbondioxide andwater vapor at northern midlatitudes:implications for troposphere-to-stratosphere transport,Geophys.Res.Lett., 22, 2737-2740. Brasseur,G., and Solomon,S. (1984)Aeronomyof the Middle Atmosphere.Reidel, Dordrecht,The Netherlands. Cloud,P.(1983).The biosphere.Sci.Am., 249, 176-189. Graedel,T. E., and Crutzen,P.J. (1989)The changingatmosphere,Sci.Am., 261,58-68. Hickey,J. R., Alton, B. M., Kyle, H. L., andHoyt, D. (1988)Total solarirradiancemeasurements by ERB/Nimbus-7:a review of nine years,SpaceSci. 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. IntergovernmentalPanel on Climate Change (IPCC) (1995) Climate Change 1994: Radiative Forcing of ClimateChangeand an Evaluationof the 1PCCIS92 EmissionScenarios.Cambridge University Press,Cambridge,UK. Iqb~l, M. (1983)An Introduction to Solar Radiation.AcademicPress,Toronto. Liou, K. N. (1992) Radiation and Cloud Processesin the Atmosphere.Oxford University Press, Oxford, UK. Mecherikunnel,A. T., Lee, R. B., Kyle, H. L., andMajor, E. R. (1988)Intercomparisonof solartotal irradiancedatafrom recentspacecraftmeasurements, J. Geophys.Res.,93,9503-9509. Prather,M., McElroy, M., Wofsy, S., Russell,G., and Rind, D. (1987) Chemistryof the global troposphere:fluorocarbonsastracersof air motion, J. Geophys.Res.,92,6579-6613. Ramanathan, V. (1987)The role of earthradiationbudgetstudiesin climate and generalcirculation research,J. Geophys.Res.,92,4075-4095. Ramanathan, V., Cess,R. D., Harrison,E. F., Minnis, P.,Barkstrom,B. R.,Ahmad,E., andHartmann, D. (1989)Cloud-radiativeforcing andclimate:resultsfrom the earthradiationbudgetexperiment, Science,243,57-63. Salstein,D. A. (1995) Mean propertiesof the atmosphere,in Composition,Chemistry,and Climate of theAtmosphere,editedby H. B. Singh.VanNostrandReinhold,New York, pp. 19-49. Trenberth,K. E., andGuillemot, C. J. (1994)The total massof the atmosphere,J. Geophys.Res.,99, 23079-23088. Walker,J. C. G. (1977)Evolution of theAtmosphere.Macmillan, New York. Willson, R. C., and Hudson,H. S. (1988) Solar luminosity variationsin solarcycle 21, Nature,332, 810-812.

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2 Virtually every element in the periodic table is found in the atmosphere; however, when classifying atmospheric species according to chemical composition it proves to be convenient 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, for example, also include atoms of carbon. And virtually all the atmospheric halogens involve a carbon atom backbone. We do not include in the above list species of the general formula HxOy; with the exception of water and hydrogen peroxide (H2O2), these are all radical species (e.g., hydroxyl, OH) that play key roles in atmospheric chemistry but do not necessarily require a separate category. Every substance emitted into the atmosphere is eventually removed so that a cycle of the elements in that substanceis established. This is called the biogeochemical cycle of the element. The biogeochemical cycle of an element or a compound refers to the transport of that substance among atmospheric, oceanic, biospheric, and land compartments, the amounts contained in the different reservoirs, and the rate of exchange among them. The circulation of water among oceans, atmosphere, and continents is a prime example of a biogeochemical cycle. The term biogeochemical cycle is often used to describe the global or regional cycles of the "life elements," C, 0, N, S, and P, 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 substancesthat result from anthropogenic activities are present at concentrations sufficiently high above their normal ambient levels to produce a measurable effect on humans, animals, vegetation, or materials. This definition could include any substance, whether noxious or benign; however, the implication is that the effects are undesirable. Traditionally, air pollution has been viewed as a phenomenon characteristic only of large urban centers and industrialized regions. It is now clear that dense urban centers are just "hotspots" in a continuum of trace speciesconcentrations over the entire Earth. Both urban smogs and stratospheric ozone depletion by chlorofluorocarbons are manifestations of what might be termed in the broadest senseas air pollution. The first recognized type of air pollution was that typified by high concentrations of sulfur compounds (S02 and sulfates) and particles, resulting from combustion of coal and high-sulfur-containing fuels. Cities with this characteristic type of air pollution are often in cold climates where electric power generation and domestic heating are major sources of emissions. 49

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from direct emissionsof particlesbut also from emissionsof certaingasesthat either condenseas particlesdirectly or undergochemicaltransformationto a speciesthat condenses as a particle.A full descriptionof atmosphericparticlesrequiresspecificationof not only their concentrationbut also their size,chemicalcomposition,phase(i.e., liquid or solid), andmotphology. Onceparticlesare in the atmo~phere, their size,number,and chemicalcompositionare changedby severalmechanismsuntil ultimately they are removedby natural processes. Someof the physicaland chemicalprocessesthat affect the "aging" of atmosphericparticles are more effective in one regimeof particle size than another.In spite of the specific processesthat affect particulateaging,the usualresidencetime of particlesin the lower atmospheredoesnot exceedseveralweeks.Very closeto the ground,the main mechanisms for particle removalaresettling anddry depositionon surfaces;whereasat altitudesabove about 100m, precipitationscavengingis the predominantremovalmechanism. As air risesthrougha cloud andbecomesslightly supersaturated with water vapor (i.e., asits relative humidity exceeds100%),cloud dropletsform on condensationnuclei-usually solubleaerosolparticles(e.g., microscopicparticlesof various salts)that exist in the atmosphereat concentrationsof 100 to .1000cm-3-and grow by condensationof water vapor.As the droplets grow and collide with each other they becomeraindrops,which grow rapidly asthey fall and accretecloud droplets. 2.1.1

Residence Time

The fundamental physical principle governing the behavior of a chemical in the atmosphere is conservation of mass. In any imaginary cube of air the following balance must hold:

Rateof the species flowing in

Rateof the Rateof introduction (emisspecies + flowing out sion) of the species

-

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Rateof accumulation of the speciesin the imaginaryvolume

This balance must hold from the smallest cube of air all the way up to the entire atmosphere. If we let Q denotethe total massof the substancein the volume of air, Fin and Foulthe massflow ratesof the substancein and out of the air volume,respectively,P the rateof introductionof the speciesfrom sources,andR the rate of removalof the species,thenconservationof masscanbe expressedmathematicallyas dQ dt

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(2.1)

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= O. In

order for Q to be unchanging,

all the sources of the

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+ P = Foul+ R

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

(2.2)

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The stratosphere can be considered well mixed vertically only for atmospheric species with residence times greatly exceeding 50 years. In fact, one of the only examples of such a long-lived species is He, which has its source at the Earth's surface and its sink as escape through the very top of the atmosphere into space. Thus the stratosphere is poorly mixed vertically for essentially all atmospheric trace constituents. Frequently the rate at which a chemical is removed from the atmosphere is proportional to its concentration (first-order loss)-the more that is present, the faster its rate of removal. This is generally the case for both dry deposition at the Earth's surface and scavenging by cloud droplets. Consider a species for which steady-state conditions hold and which is removed at a rate proportional to its concentration with a proportionality constant A. Such a species is 85Kr,the only significant removal process for which is radioactive decay. For 85Kr,then

Q -)..Q

1 -)..

Thus to estimate the residence time of 85Kr does not even require knowledge of its atmospheric abundance Q, but only of the radioactive decay constant. Consequently, it does not matter whether 85Kris uniformly mixed throughout the entire atmosphere or not to estimate its lifetime. In a case where the removal process is first order, then even for a poorly mixed species a simple and accurate estimate for its residence time can be obtained provided that its removal rate constant can be accurately estimated. Now consider a species with mass Q in the atmosphere that is removed by two independent processes,the first at a rate kl Q and the second at a rate k2 Q, where kl and k2 are the first-order removal coefficients. Its overall residence time is given by

or ~ = kl + k2 1:

Process1. for example.could be dry depositionand process2 cloud scavenging.We can actually associatetime constantswith the two individual removalprocesses,

.. = kl

T2= k2

where ., canbe thoughtof asthe residencetime of the speciesif the only removalprocess is process1, which is alsotrue for .2. From (2.8) and (2.9) we canexpressthe overall residencetime. in termsof the two individual removaltimes ., and .2 by

..:.=..:.+..:. . .1 .2

(2.10)

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SULFUR-CONTAINING

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55

The loss processesare usually representedas first order; for example, Rt = kt Qi' wherethe first-orderrate constants,which we will denoteby k's, must be specified.Thus (2.13)becomes dQi dt

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

(2.14)

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

p.n+ p.a+ p.C,

,

,

( kd

+ ,

k!1'

+ ,

k':

+ ,

k~

)

Q,

'

=

0

I

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-

.,.,=

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

or

t";=

Qi

p!'I + p.a I + p.C I

(2.17)

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 be derived 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 by mass 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 atmosphere and, likely, on climate. The main questions that we will seek to answer with respect to 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 anthropogenic sources? 2. What chemical reactions do they undergo in the atmosphere? How fast are these reactions? 3. What are the products of atmospheric transformations? 4. What effect does the presence of the compound and its chemical transformation products have on the atmosphere? In this chapter we focus on the first question.

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The meanresidencetime of SO"is 7:S02

= P;02QS02 + PS02 a k~o, + k~O2+ kso,

whereas that for sulfate is QSO4

1'SO. =

kSO,QSO2

kSO4d+ kSO4

The meanresidencetime of a sulfur atom is t's =

QSO2

+ QSO4

P;O2+ P:~

which canbe expressedin termsof the two previousmeanresidencetimes as 1:S

= 1:S02 + b1:s04

(2.23)

where

b=

ksozQs~

(2.24)

PSOz + Ps~

the fraction of S convertedto SO~- beforebeingremoved. We can alsodefineindividual characteristictimes suchas

'so, d = (kso, d'

.502= (ks02)

t'SO4 d

= (kSO4, d'

sothat

1"S04

~ 1"S04

w TSO,

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

cipitation scavengingby d,w -TS

Qs~ + QS04 Q + kd.w kd,w SO, S02 SO.QS04

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NITROGEN-CONTAINING

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2.3 NITROGEN-CONTAINING COMPOUNDS Aside from N2, which is extremely stable chemically and is not involved in the chemistry of the troposphere or stratosphere, the important nitrogen-containing trace species in the atmosphere 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 that is emitted almost totally by natural sources, principally by bacterial action in the soil. The gas is employed as an anesthetic and is commonly referred to as "laughing gas." The second, nitric oxide (NO), is emitted by both natural and anthropogenic sources. Nitrogen dioxide (NOJ is emitted in small quantities from combustion processesalong with NO and is also formed in the atmosphere by oxidation of NO. The sum of NO and NO2 is usually designated as NOx' Nitric oxide is the major oxide of nitrogen formed during high-temperature combustion, resulting from both the interaction of nitrogen in the fuel with oxygen present in the air and the chemical conversion of atmospheric nitrogen and oxygen at the high temperatures of combustion. Other oxides of nitrogen, such as NO3 and N20S, exist in the atmosphere in relatively low concentrations but nonetheless participate importantly in atmospheric chemistry. Nitric acid is an oxidation product of NO2 in the atmosphere. Ammonia (NH3) is emitted primarily by natural sources. Finally, nitrate and ammonium salts are not emitted in any significant quantities but result from the atmospheric conversion of NO, NO2, and NH3' Nitrogen is an essential nutrient for all living organisms. The primary source of this nitrogen is the atmosphere. However, N2 is not useful to most organisms until it is "fixed" or converted to a form that can be chemically utilized by the organisms. (Nitrogen fixation refers to the chemical conversion ofN2 to any other nitrogen compound.) The "natural" fixation of N2 occurs by two types of processes.One is the action of a comparatively few microorganisms that are capable of converting N2 to ammonia, ammonium ion (NHt), and organic nitrogen compounds. The other natural nitrogen fixation process occurs in the atmosphere by the action of ionizing phenomena, such as cosmic radiation or lightning, on N2. This process leads to the formation of nitrogen oxides in the atmosphere, which are ultimately deposited on the Earth's surface as biologically useful nitrates. In addition to natural nitrogen fixation, human activities have led to biological and industrial fixation and fixation by combustion. Humans have increased the cultivation of legumes, which have a symbiotic relationship with certain microorganisms capable of nitrogen fixation. Legumes provide an increase in the soil nitrogen and serve as a valuable food crop. Industrial nitrogen fixation consists primarily of the production of ammonia for fertilizer use. Combustion can also lead to the fixation of nitrogen as NOx' In the process of nitrification, ammonium is oxidized to N°"i and NO3 by microbial action. N2O and NO are 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 accomplished by a number of bacteria and is the process that continually replenishes the atmosphere'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 biological sources in soils and water. Although by comparison to CO2 and H2O, N2O has a far lower concentration, it is an extremely influential greenhousegas. This is a result of its long

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TABLE 2.4 Estimated Sourcesand Sinks of N2OTypical of the Last Decade Sources

Range(Tg(N) yr-l)

Likely (Tg(N) yi

NATURAL

Oceans Tropical soils Wet forests Dry savannas Temperate soils Forests Grasslands

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Total natural sources ANTHROPOGENIC

Cultivated soils Biomassburning Industrial sources Cattle and feedlots

1.8-5.3 0.2-1.0 0.7-1.8 0.2-0.5

3.5 0.5 1.3 0.4

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).

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Moleculeswith two doublebondsarecalled alkadienes,an exampleof which is CH2=CH-CH=CH2 1,3-Butadiene

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

Individual Estimate

Total

NATURAL

Wetlands Termites Oceans Other Total identified natural sources

115(55-150) 20 (10-50) 10 (5-50) 15 (10-40) 160 (110-210)D

ANTHROPOGENIC

Fossil-fuelrelatedsources Natural gas Coal mines Petroleumindustry Coal combustion Total fossil-fuel related Biosphericcarbon Enteric fermentation Rice paddies Biomassburning Landfills Animal waste Domesticsewage Total biospheric

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)"

Total identified anthropogenic sources Total identified sources

Sinks TroposphericOH Stratosphere Soils Total sinks

445 (360-530) 40 (32-48) 30 (15-45) 515 (430-600)

Total global burden:4850Tg (C~) aA preindustrial level of 700 ppb would have required a source of2l0 Tg(CH.) yr-1 if the lifetime has remained constant, 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 Emissionsof NonmethaneVolatile Organic Compounds

FUEL PRODUCTION/DISTRIBUTION Petroleum

Natural gas Oil refining Gasoline distribution

8 2 5 2.5

FUEL CONSUMPTION

Coal Wood Crop residues(including waste) Charcoal Dung cakes Roadtransport Chemicalindustry Solventuse Uncontrolledwasteburning

3.5 25 14.5 2.5 3 36 2 20 8

OTHER

10

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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 incomplete combustion of fuel or from its vaporization. These contributions are generally categorized and reported as exhaust and evaporative emissions. Within the exhaust emissions category are included the unburned and partially burned fuel and lubricating oil in the exhaust and gases that leak from the engine. The evaporative emissions category includes fuel 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 the heat of the engine after it has been turned off (hot-soak emissions), vaporization of fuel from the (uel system while the vehicle is operating (running losses), fuel losses due to leaks and diffusion through containment materials (resting losses), and fuel vapor displacement as 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 global anthropogenic VOC emissions. As seen in Table 2.10, transportation is the largest source ofVOC emissions worldwide, with solvent use following as the second largest source. As an illustration of the large number of organic compounds identified in the atmosphere, Table 2.11 lists the median concentrations of the 25 most abundant nonmethane organic species measured in the 1987 Southern California Air Quality Study.

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biogenic hydrocarbon emissions in the southeastern United States is predicted to be as large as that in the tropics. An estimate of global biogenic VOC emissions appears in Table 2.13. On a global basis, biogenic hydrocarbon emissions far exceed those of anthropogenic hydrocarbons. 2.4.5

Carbon Monoxide

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TABLE 2.14 Estimated Sourcesand Sinks of CO Typical of the Last Decade

Technological Biomassburning Biogenics Oceans Methaneoxidation NMHC oxidation

Sinks

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As a group of atmospheric chemicals, halogen-containing compounds have a wide variety of anthropogenic and natural sources. They are produced by biological processesin the oceans, from sea salt, from biomass burning, and from industrial synthesis. Their atmospheric lifetimes vary considerably depending on their mechanism of removal, ranging from a few days to several centuries. Table 2.15 lists atmospheric halogenated organic species with global average concentrations, atmospheric burdens, lifetimes, sources, and sinks.4 Of the exclusively man-made organic halogenated species, the chlorofluorocarbons are used as refrigerants (CFC-12, HCFC-22), blowing agents (CFC-ll, HCFC-22), and cleaning agents (CFC-113). Methyl chloroform (CH3CCI3), methylene chloride (CHzClz), and tetrachloroethene (CzCI4) are used as degreasersand as dry cleaning and industrial solvents. Methyl bromide (CH3Br) is a widely used agricultural and space fumigant. All the monomethyl halides in Table 2.15 have 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 capture detector. In landmark work in atmospheric chemistry for which they received the 1995 Nobel Prize in Chemistry, Molina and Rowland (1974) showed that CFCs that are immune to removal in the troposphere could decompose photolytically in the stratosphere to release Cl atoms capable of catalytic destruction of stratospheric ozone. The very lack of chemical reactivity that makes chlorofluorocarbon molecules so intrinsically useful also allows them to survive unchanged in most commercial applications and eventually to be released to the atmosphere in their original gaseous form. The usual tropospheric sinks of oxidation, photodissociation, and wet and dry deposition are ineffective with the chlorofluorocarbons. The only important sink for CFC13and CFzClz is photodissociation in the midstratosphere (25 to 40 kill) by solar ultraviolet radiation with wavelengths shorter than 230 nm. These same CFCs that lead to stratospheric ozone depletion are efficient absorbers of infrared radiation and potentially important greenhouse gases. There is a sharp demarcation in atmospheric behavior between fully halogenated halocarbons and those containing one or more atoms of hydrogen. Halocarbons containing at least one hydrogen atom, such as CFzHCl, CHCI3, and CH3CCI3, are effectively broken down in the troposphere by reaction with the hydroxyl radical before they can reach the stratosphere. Atmospheric lifetimes of these species range from months to decades. Some of these gases also react with seawater; it is estimated that 5 to 10% of the removal of CH3CCl3 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 of carbon, hydrogen, chlorine, and fluorine atoms. The somewhat arcane system of numbering these compounds was proposed by the American Society of Heating and Refrigeration Engineers in 1957. For the simpler hydrochlorofluorocarbons, 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 this digit 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 and hydrogen atoms from the total number of atoms that can be connected to the carbon atoms.

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methyl chloroform (CH3CCI3) and the HCFCs are also significant infrared absorbers but their shorter atmospheric lifetimes reduce their radiative impact relative to the fully halogenated CFCs. Discovery of the stratospheric ozone-depleting potential of CFCs in the mid-1970s led to a ban in the United States (announced in 1976 and effective in 1978) on the use ofCFCs as aerosol propellants and to similar restrictions in Canada and Scandinavia. When the Antarctic ozone hole was discovered, subsequently, an international protocol outlining proposed actions to protect the stratospheric ozone layer was signed in Montreal in September 1987. The so-called Montreal Protocol specifies a 20% reduction from 1986 emissions of fully halogenated CFCs by 1994 and a further 30% reduction by 1999. Global emissions of CFCI3, CF2CI2, C2F3C13,CF2HC1, and CH3CC13up to 1992 are shown in Figure 2.9. The turn-down in emission rates reflects the results of the Montreal Protocol. Atmospheric levels of CF2CI2, CFCI3, and CH3CC13from 1978 to 1992 are shown in Figure 2.10. Mixing ratios increased steadily until about 1990. Methyl chloride (CH3Cl), at an atmospheric abundance of about 600 ppt, is the dominant halogen compound in the atmosphere. To maintain the steady-state CH3Cl concentration, with an atmospheric lifetime of order 2 years, requires a source strength of about 3.5 Tg yr-1 , most of which comes from the ocean. Southern Hemisphere (SH) CFC concentrations lag behind those in the Northern Hemisphere (NH) by about 1 year, reflecting the predominant source of CFCs in the NH and the approximate 1 year mixing time between the NH troposphere and the SH troposphere. 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 atmosphere, arising from both man-made and natural sources.A calculated atmospheric lifetime of 1.7 to 1.9 years, based solely on removal by reaction with OH radicals, is consistent with a global source of 90 to 110 Gg (109 g) yr-l (Singh and Kanakidou, 1993). A shorter lifetime of about 1.3 years (see Table 2.15) results if deposition/hydrolysis losses are also considered. 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 with CH3Br 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,ound 1992 were about 14 ppt, with a ratio of NH to SH mixing ratios varying between 1.2 and 1.4 depending on season.The seasonalvariation is a result of source strength and OH variations. CH3Br levels have been increasing at a rate of 0.1 to 0.2 ppt yr-i. Despite the fact that CH3Br is largely removed in the troposphere by OH reaction, enough survives to enter the stratosphere and contribute to halogen-induced stratospheric ozone depletion.

2.6 ATMOSPHERIC OZONE Ozone(03) is a reactiveoxidant gasproducednaturally in traceamountsin the Earth's atmosphere.Ozonewas discoveredby C. F. Schonbeinin the middle of the last century;he alsowas first to detectozonein air (Schonbein,1840,1854).Schonbein(1840) suggested the presenceof an atmosphericgashaving a peculiarodor (the Greekword for "to smell" is ozein).Spectroscopicstudiesin the late 19th century showedthat ozoneis presentat a higher mixing ratio in the upper atmosphericlayersthan closeto the ground.Attemptsto explainthe chemicalbasisof existenceof ozonein the upperatmospherebegannearly 70 yearsago.Within the last 30 years,however,while increasedunderstandingof the role of other trace atmosphericspeciesin stratosphericozonewas unfolding, it becameapparent that anthropogenicallyemitted substanceshave the potential to seriouslydepletethe natural levels of ozonein the stratosphere. At aboutthe sameperiod, ironically, it was realized that anthropogenicemissionscould lead to ozone increasesin the troposphere. Whereasstratosphericozoneis essentialfor screeningof solar ultraviolet radiation,ozone at groundlevel can,at elevatedconcentrations,lead to respiratoryeffectsin humans.This paradoxicaldual role of ozonein the atmospherehas, on occasion,led to the dubbing of stratosphericozoneas "good" ozoneandtroposphericozoneas "bad" ozone. Most of the Earth's atmosphericozone(about90%) is found in the stratospherewhere it plays a critical role in absorbingultraviolet radiation emitted by the Sun. Figure 2.11

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from 1979to 1991have shownthat broadly similar midlatitudelosseshavealso occurred at equivalentlatitudesin the SouthernHemisphere(IPCC, 1995).Figure 2.12 showsthe annual,latitudinal variation of the total ozonetrendscalculatedfrom the Dobsongroundbasedmeasurementrecord and satellite observations.The effect of the Antarctic ozone hole is seenin the data from 60° S to 90° S. Analysis of the total ozonemappingspectrometer(TOMS) dataover the period 1979to 1989between69° S and69° N revealsa total global averageozonedecreaseof 3.5% over that 11year period (Hermanet al., 1991). Statisticaily significant decreasesin total ozoneare now being observedin all seasonsin both the Northernand SouthernHemispheresat middle andhigh latitudes(Stolarskiet 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-called tropopause folding events (Danielson, 1968) in which tongues of stratospheric air intrude into the troposphere, usually at extratropicallatitudes (recall Figure 1.3 and associated discussion). Estimates of the amount of 03 transported from the stratosphere to the troposphere on an annual basis rely on measurements of conserved tracers or on general circulation models but are quite uncertain. In the NH ozone fluxes seem to maximize in spring, being as much as five times the value in the fall. The NH stratosphere-totroposphere ozone flux has been estimated to fall in the range of (3 to 8) X 1010molecules cm-2 S-l (Crutzen, 1995). The SH flux may be about half as large. An estimate for the total 03 production in the stratosphere is about 5 X 1013molecules cm-2 S-I; only about 0.1 % 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 1010molecules cm-2 S-I, which generously exceeds the amount of 03 from stratosphere-to-troposphere exchange.

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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 an aerosol is technically defined as a suspension of fine solid or liquid particles in a gas, common usage refers to the aerosol as the particulate component only (Table 2.17). Emitted directly as particles (primary aerosol) or formed in the atmosphere by gas-to-particle conversion processes (secondary aerosol), atmospheric aerosols are generally considered to 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, aerodispersesystems Dusts Fog

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Suspensions of solid particlesproducedby mechanicaldisintegrationof materialsuchascrushing,grinding, andblasting.Dp > I JLm. A looseterm appliedto visible aerosolsin which the dispersedphaseis liquid. Usually,a dispersionof water or ice, closeto the ground. The solid particlesgeneratedby condensationfrom the vapor state,generally after volatilization from meltedsubstances, and often accompanied by a chemicalreactionsuchas oxidation.Often the material involved is noxious.Dp < I JLm. An aerosolthat impedesvision and may consistof a combinationof water droplets,pollutants,and dust.Dp < 1 JLm. Liquid, usually water in the form of particlessuspendedin the atmosphereat or nearthe surfaceof the Earth; small water dropletsfloating or falling, approachingthe form of rain, and sometimesdistinguished from fog asbeing more transparentor as havingparticlesperceptibly moving downward.Dp > I JLm. An aerosolparticle may consistof a single continuousunit of solid or liquid containingmany moleculesheld togetherby intermolecular forcesandprimarily largerthan moleculardimensions(> 0.001 JLm). A particle may alsobe consideredto consistof two or more suchunit structuresheld togetherby interparticleadhesiveforcessuchthat it behavesas a singleunit in suspensionor upondeposit. A term derivedfrom smokeand fog, appliedto extensivecontamination by aerosols.Now sometimesusedloosely for any contaminationof the air. Small gas-borneparticlesresultingfrom incompletecombustion,consistingpredominantlyof carbonandother combustiblematerial,and presentin sufficientquantity to be observableindependentlyof the presenceof other solids.Dp 2: 0.01 JLm. Agglomerationsof particlesof carbonimpregnatedwith "tar," formed in the incompletecombustionof carbonaceous material.

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to atmospheric aerosol have increased dramatically over the past century and have been implicated in human health effects (Dockery et al., 1993), in visibility reduction in urban and regional areas (see Chapter 22), in acid deposition (see Chapter 20), and in perturbing the 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. It is interesting to note that average total fine particle mass (that associated with particles of diameter less than about 2 .urn) in nonurban continental, (i.e., regional) aerosols is only a factor of 2 lower than urban values. This reflects the relatively long residence time of particles. Correspondingly, the average compositions of nonurban continental and urban aerosols are roughly the same. The average mass concentration of remote aerosols is a factor 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 remote aerosols, but sulfate is still a major component. This is attributable to a global average concentration of non-sea-salt sulfate of about 0.5 .ugm-3. Rubidoux, California, located about 100 km east of downtown Los Angeles, routinely experiences some of the highest particulate matter concentrations in the United States.

2.7.3 Cloud CondensationNuclei (CCN) Aerosols are essential to the atmosphere as we know it; if the Earth's atmosphere were totally devoid of particles, clouds could not form. Particles that can become activated to grow to fog or cloud droplets in the presence of a supersaturation of water vapor are termed cloud condensation nuclei (CCN). At a given mass of soluble material in the particle there is a critical value of the ambient water vapor supersaturation below which the particle exists in a stable state and above which it spontaneously grows to become a cloud droplet of 10 JLmor more diameter. The number of particles from a given aerosol population that can act as CCN is thus a function of the water supersaturation. For marine stratiform clouds, for which supersaturations are in the range of 0.1 to 0.5%, the minimum CCN particle diameter is 0.05 to 0.14 tLm. CCN number concentrations vary from fewer than 100 cm-3 in re-

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Atmospheric particulate matter samples can be analyzed routinely for more than 50 trace elements. Trace element emissions arise from a large number of different source types in urban areas.For example, motor vehicles burning leaded fuel, electric arc steel furnaces, Kraft recovery boilers, and secondary lead smelters contribute to atmospheric lead concentrations. The wide spectrum of sources, together with the fact that trace metals often are only a minor fraction of the mass emissions from each source, obscure the relative importance of the contributors to atmospheric trace element levels. As with all atmospheric species, trace metal emissions undergo atmospheric transport and dilution before they reach a particular receptor site. Mathematical models can be constructed based on the fundamentals of atmospheric chemistry and physics that will track the contributions from many emission sources as they undergo atmospheric transport. Indeed, the development of such models will receive considerable attention in this book. In the case of particulate emissions, an alternative is available. It is possible to attack the source contribution identification problem in reverse order, proceeding from measured particulate concentrations at a receptor site backward to the responsible emission sources (see Chapter 24). The unique metals content of the emissions from each source type is viewed as 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 or black carbon (sometimes referred to as elemental or free carbon) and organic material. The latter can be directly emitted from sources or produced from atmospheric reactions involving gaseous organic precursors. Elemental carbon can be produced only in a combustion process and is therefore solely primary. Graphitic carbon particles are the most abundant light-absorbing aerosol species in the atmosphere. Particulate organic matter is a complex mixture of many classes of compounds (Daisey, 1980). A major reason for the study of particulate organic matter has been the possibility that such compounds pose a health hazard. Specifically, certain fractions of particulate organic matter, especially those containing polycyclic 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 function of activity level (e.g., amount of annual production at an industrial facility) with regard to each source. For example, suppose one wants to sample a power plant's emissions of SO2 or NOx at the stack. The plant's boiler design and its BTU (British thermal unit) consumption rate are known. The sulfur and nitrogen content of fuel burned can be used to calculate 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 results since 1972 in "AP-42 Compilation of Air Pollutant Emission Factors," for which supolements are issued regularly. Emission factors currently in use are developed from only a

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lationship that requires the U.S. Environmental Protection Agency (EPA) to develop National AmbientAir-Quality Standards(NAAQS) andempowersthe statesto implement and enforceregulationsto attain them. The act also requiresthe EPA to set NAAQS for commonand widespreadpollutantsafter preparingcriteria documentssummarizingscientific knowledgeof their detrimentaleffects.The EPAhasestablishedNAAQS for eachof six criteria pollutants:sulfur dioxide, particulatematter,nitrogendioxide, carbonmonoxide, ozone,and lead.At certainconcentrationsand length of exposurethesepollutantsare anticipatedto endangerpublic healthor welfare.The NAAQS arethresholdconcentrations basedon a detailedreview of the scientific information relatedto effects.Concentrations below the NAAQS are expectedto have no adverseeffects for humansand the environment. Table 2.20 presentsthe U.S. national primary and secondaryambient air-quality standardsfor ozone,carbonmonoxide,nitrogendioxide, sulfur dioxide, suspendedparticulate matter,and lead. In the CleanAir Act Amendmentsof 1970,Congressset 1975asthe deadlinefor meeting the NAAQS. By 1977,2 yearsafter this deadline,many areaswere still in violation of the ozoneNAAQS. The 1977amendmentsto the CleanAir Act delayedcompliancewith the ozone and carbon monoxide NAAQS until 1982, and areasthat demonstratedthey could not meetthe 1982deadlineweregiven extensionsuntil 1987.The 1990amendments classify nonattainmentareasaccordingto degreeof noncompliancewith the NAAQS. The classificationsareextreme,severe,serious,moderate,or marginal,dependingon the area's ozone design value and the percentageby which the value is greaterthan the NAAQS. Ozonedesign valuesare ozoneconcentrationsthat are statistically determinedfrom airquality measurements for eachnonattainmentarea.If monitoring datafor an areaarecomplete,the designvalue is the fourth highestmonitor readingover the past 3 years.Design valuesareusedto determinethe extentof control neededfor an areato reachattainment. The 1990amendmentsof the CleanAir Act establishan interstateozonetransportregion extendingfrom the Washington,DC metropolitanareato Maine. In this denselypopulated region, ozone violations in one area are caused,at least in part, by emissionsin upwind areas.A transportcommissionis authorizedto coordinatecontrol measureswithin the interstatetransportregion and to recommendto the EPAwhen additionalcontrol measuresshouldbe appliedin all or part of the region in order to bring any areain the region into attainment.Henceareaswithin the transportregion that arein attainmentof the ozone NAAQS might becomesubjectto the controlsrequiredfor nonattainmentareasin that region. The CleanAir Act requireseachstateto adopta plan, a so-calledStateImplementation Plan (SIP), that provides for the implementation,maintenance,and enforcementof the NAAQS. It is, of course,emissionreductionsthat will abateair pollution. Thus the states' plansmust containlegally enforceableemissionlimitations, schedules,and timetablesfor compliancewith suchlimitations. The control strategymust consistof a combinationof measuresdesignedto achievethe total reductionof emissionsnecessaryfor the attainment of the air-quality standards.The control strategymay include,for example,suchmeasures asemissionlimitations, emissionchargesor taxes,closing or relocationof commercialor industrial facilities, periodic inspectionandtestingof motor vehicle emissioncontrol systems,mandatoryinstallationof control deviceson motor vehicles,meansto reducemotor vehicle traffic, including suchmeasuresas parking restrictionsand carpool laneson freeways,and expansionandpromotionof the useof masstransportationfacilities.

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2.11 HAZARDOUS AIR POLLUTANTS (AIR TOXICS) Hazardousair pollutantsor toxic air contaminants("air toxics") refer to any substances that may causeor contributeto an increasein mortality or in seriousillness,or that may posea presentor potentialhazardto humanhealth.Title III of the CleanAir Act Amendmentsof 1990completelyoverhauledthe existing hazardousair emissionprogram.Section 112of theAmendmentsdefinesa new processfor controlling air toxics that includesthe listing of 189 substances,the developmentand promulgation of Maximum Achievable Control Technology(MACT) standards,and the assessment of residualrisk after the implementation of MACT. Any stationary sourceemitting in excessof 10 tons yr-1 of any listed hazardoussubstance,or 25 tonsyr-1 or moreof any combinationof hazardousair contaminants,is a major sourcefor the purposeof Title III and is subjectto regulation.Congress establisheda list of 189 hazardousair pollutants in the CAA itself. It includes organic chemicals,pesticides,metals,coke-ovenemissions,fine mineral fibers, and radionuclides (including radon).This initial list may be revisedby the EPAto either add or removesubstances.The EPA is required to add pollutants to the list if they are shown to present, throughinhalationor other routesof exposure,a threatof adversehumanhealtheffectsor adverseenvironmentaleffects,whetherthroughambientconcentrations,bioaccumulation, deposition,or otherwise. Congressdirectedthe EPA to list by 15 November 1995,the categoriesand subcategoriesof sourcesthat represent90% of the aggregateemissionsof:

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Alkylatedleadcompounds Polycylicorganicmatter Hexachlorobenzene Mercury

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Congress further directed the EPA to establish and promulgate emissions standards for such sources by 15 November 2000. The emissions standards must effect the maximum degree of reduction in the listed substance, including the potential for a prohibition on such emissions, taking into consideration costs, any non-air-quality health and environmental impacts, and energy requirements. In establishing these emissions standards, the EPA may also consider health threshold levels, which may be established for particular hazardous air pollutants. Each state may develop and submit to the EPA for approval a program for the implementation and enforcement of emission standards and other requirements for hazardous air pollutants or requirements for the prevention and mitigation of accidental releases of hazardous substances. The California Air Resources Board (ARB) (1989) has developed a list of substancesof concern in California, called "Status of Toxic Air Contaminant Identification." This list and the organization of substances within it are subject to periodic revision, as needed. The February 1989 Status List groups substances into three categories. Category I includes identified toxic air contaminants: asbestos,benzene, cadmium, carbon tetrachloride, chlorinated dioxins and dibenzofurans (15 species), chromium (VI), ethylene dlbromide and

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COMPARTMENTALMODELS OF GLOBAL BIOGEOCHEMICAL CYCLES

113

Comparablebalanceson the two stratospherecompartmentsyield 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.5) (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 +

(2.A.8)

0 = -CX7Q3

+ CXSQ4+

0 = -aloQ4 where QI

+ all

Q3

P2

CX9QI

(2.A.9)

+ al2Q2

(2.A.IO)

= Q~H' Qz = Q~H'Q3= Q~H'Q4= Q~H'PI = PNH,andPz= PsH.Also, at a4

+ kTIS NH + kT NH SH + k SH + kTIS T

a5

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as

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all-

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SIT

TIS

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= .81 Qz + .8ZQI

(2.A.II)

Q4

= .83QZ+ .84QI

(2.A.I2)

where

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0 = (a~ + a"BJJ.)01

+ (a2 + a3.8t)Q2 + PI + (a"B~ - aJJ.)O, + P,

(2.A.I3) (2.A.14)

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COMPARTMENTALMODELS OF GLOBAL BIOGEOCHEMICAL CYCLES

115

It can be assumedthat thesemassesdivide equally betweenthe NH and SH. With the averagemolecularweight of air, Mair= 28.9 g mol-I, the troposphericmassof a substanceof molecularweight M that hasa troposphericmixing ratio of ~ T is

(2.A.19) Similarly, for the stratosphere, s QS= ~~sM Mair

(2.A.20)

(2.A.21) If the troposphericmassis divided into Q~Hand QIH' (2.A.22)

-

Q SH T -

-Wa{r/2t:T SSHM

(2.A.23)

Mair

As an example,the averagemixing ratios of OCS in the troposphereand stratosphere are (Chin andDavis, 1995) ~Jcs = 490 ppt = 490 x 10-12 ~JcS = 380 ppt = 380 X 10-12

The total atmosphericmassofOCS is (Mocs = 60 g mol-I) 4.56 X 1021

Q

(490

x 10-11+

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

0.72 X

1021

28.9

= 4.63Tg + 0.57Tg 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 atmosphere are reasonably well known. Its atmospheric degradation occurs almost entirely by hydroxyl radical reaction. The CH3CCl3 mixing ratio in the atmosphere is well established;

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PROBLEMS 121 Went,F.W. (1960)Organicmatterin the atmosphereandits possiblerelationto petroleumformation, Proc. Natl. Acad. Sci. (USA),46,212-221. Whitby, K. T., and Cantrell, B. (1976) Fine particles,in InternationalConferenceon Environmental SensingandAssessment,Las Vegas,NV, Institute of Electrical and ElectronicEngineers. Winer, A. M., Arey, J., Aschmann,S. M., Atkinson, R., Long, W. D., Morrison, L. C., and Olszyk, D. M. (1989)Hydrocarbonemissionsfrom vegetationfound in California's CentralValley.Final Report.ContractNo. A 732-155.California Air ResourcesBoard, Sacramento,CA. World Meteorological Organization (WMO) (1986) Atmospheric Ozone 1985. Global Ozone ResearchandMonitoring Project:ReportNo. 16, Geneva. World MeteorologicalOrganization(WMO) (1990)Reportof the InternationalOzoneTrendsPanel: 1988.Global OzoneResearchand Monitoring Project:ReportNo. 18,Geneva. Yokouchi,Y. (1994) Seasonaland diurnal variation of isopreneand its reactionproductsin a semirural area.Atmos.Environ.,28,2651-2658. Yvon, S. A., Saltzman,E. S., Cooper,D. J., Bates,T. S., and Thompson,A. M. (1996)Atmosphere sulfur cycling in the tropical Pacificmarineboundarylayer (120S, 1350W): a comparisonoffield dataand modelresults I. Dimethylsulfide,J. Geophys.Res.,101,6899-6909. Zimmerman,P.(1979) Testingof hydrocarbonemissionsfrom vegetation,leaf litter andaquaticsurfaces, and development of a method for compiling biogenic emission inventories. U.S. EnvironmentalProtectionAgency Report,EPA-450-4-70-004,ResearchTrianglePark,NC. Zimmerman,P.,Greenberg,J., andWestberg,C. (1988) Measurements of atmospherichydrocarbons and biogenicemissionfluxes in the Amazonboundarylayer,J. Geophys.Res.,93, 1407-1416.

PROBLEMS 2.1A In the simplified calculationof the atmosphericsulfur cycle in Section2.2.4, if the valueof c, the S02 fraction of the total sulfur, is takenas0.5, a sulfur atomresidence time of 50 hoursis estimated.What is the value of b, the fraction of sulfur converted to SO~- beforebeing removed,that is consistentwith this choiceof c? 2.2A

Preparea plot of ozonemixing ratio versusaltitudefrom groundlevel to 50 km. Total molecularnumberdensity of air can be obtainedfrom TableA.8, and 03 molecular numberdensity is given in Figure 2.11. Why do the molecularnumberdensity and mixing ratio peakat different altitudes?

2.3A One Dobsonunit correspondsto 2.69 X 1016molecules03 cm-2 integratedover a vertical column to the top of the atmosphere.Show how vertical ozonecolumn data canbe convertedto Dobsonunits. 2.4A Calculatethe changein total ozonecolumn, as measuredin Dobsonunits, between 1969and 1988for the ozoneprofiles in Figure 2.13. 2.5A Confirm the calculationspresentedin Section2.A.2 on the concentrationandlifetime of methyl chloroform. 2.6B Derive the balanceequationsfor a substancethat is completelyremovedin the troposphere,but for which two tropospheric reservoirs should be considered(see Appendix 2). Apply the balanceto CO using the sourceand sink data from Table 2.14.As a first approximation,assumethat anthropogenicsourcesaretotally concentratedin the NorthernHemisphereandthat biomassburning sourcesaretotally in the

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PROBLEMS 123

atmosphericresidencetime. = p-l. Given valuesof land r,p canbe calculated from 1= rf(r + p) sincethesespecieshave beenemitted long enoughso that rt» 1. Plot/versusp (and .) for r = 0.15 yr-1 showingpoints corresponding to the threecompounds. c. Let us now assumethat the tropospherecan be divided into Northern and SouthernHemisphereswith an interhemisphericfractionalmixing rateof m yr-i. The rate of removal from the atmosphere,p yr-l, is assumedto be the samein both hemispheres.If all the manufactureand releaseof the compoundare assumedto occur in the NorthernHemisphere,then let us find the ratio of concentrations,R, betweenthe Northernand SouthernHemispheresat any time t. Let

= massof speciesin NorthernHemisphere Ms = mass of species in Southern Hemisphere

MN

Showthat the hemisphericmaterialbalancesare

dMN= Poert - pMN + m(Ms - MN) dt dMs = m(MN- Ms)- pMs dt MN(O)= Ms(O)

0

Po MN + Ms = _(err r+p

- e-pt)

show that e-pt

R=

MN(t) Ms(t)

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

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3

Atmospheric Photochemistry and Chemical Kinetics

3.1 RADIATIVE FLUX IN THE ATMOSPHERE The essentialenergyflux in atmosphericchemistryis the flux of solarradiation.The radiantflux densityF is the radiantenergyflux acrossany surfaceelement,without consideration of the direction; F is measuredin watts per squaremeter (W m-1. The radiant flux densityis called the irradiance E when the radiation is receivedon a surface.Thus F and E are often usedinterchangeably.We will use F in generaland E when we are referring specificallyto the radiantflux densityon a surface.The radianceL is the radiantflux as a function of the solid angled{J)crossinga surfaceperpendicularto the axis of the radiation beam;L is measuredin wattsper squaremeterper steradian(W m-2 sr-I). The radianceas a function of direction gives a completedescriptionof the radiativefield. Considera beamof radiation of radianceL crossinga surfacedS with the beamaxis making an angle e to the normal to dS (Figure 3.1). dS projectsasdS cos e perpendicular to the beamaxis of the radiation,and the radiantflux densitydF on dS is

dF

= Lcos(J dw

The radiant flux density,or irradiance,on the surfacedS is obtainedby integratingthe radianceover all angles,

E

=

f L case dw

When the radianceL is independentof direction, the radiative field is called isotropic. In this case,(3.2) canbe integratedover the half space,n = 271; andthe relation betweenthe irradianceandthe radianceis

E = JrL

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RADIATIVE FLUX IN THE ATMOSPHERE 127

Sometimesthe spectralradiant flux density is expressedas a function of frequency v, that is, F(v). Becausethe frequency v of radiation is relatedto its wavelengthby (1.13), v = ciA, F(A) andF( v) can be interrelated.Sincethe flux of energyin a small interval of wavelengthdA mustbe equalto that in a small interval of correspondingfrequencyd v,

F()')

Since dv

d)'

= F(v)

dv

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=

~)F(V) -;;)F(v) V2

Generally we will deal with wavelengthas the variable rather than frequency,although they can easily be interrelatedasindicatedin (3.6).

3.1.1

Solar Radiation Received on Earth

Light absorption and scattering by atmospheric constituents attenuate the solar radiation as it passes through the atmosphere. The amount of attenuation depends on the nature and concentration of gases and particles and on the pathlength through which the solar beam passes.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 processesthat lead to the progressive attenuation of radiation was given in Chapter 1 in association with Figure 1.9.) Usually radiative transfer through the atmosphere is calculated by radiative transfer models that divide the atmosphere into layers and the radiative spectrum into wavelength intervals (Goody and Yung, 1989; Liou, 1992; Lenoble, 1993). The vertical distribution of trace gasesand particles and the surface albedo serve as inputs to such models. Near the Earth's surface the spectral distribution shows a steep cutoff, when moving from longer to shorter wavelengths, beginning at about 320 nm. Radiation below 290 nm does not reach the Earth's surface; as noted in Chapter 1, this cutoff is the result of absorption of solar radiation by stratospheric ozone. There is no overlap between the absorption cross section of the major atmospheric gases,Nz, Oz, COz, and HzO, and the solar spectrum at 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(A)

A (nm)

(W m -2

om

-I,

0.438 0.387 0.353 0.323 0.296 0.273 0.247 0.234 0.217 0.187 0.169 0.148 0.133 0.126 0.116 0.093 0.075

J;F(X)dX (W m-1 1120 1140 1159 1176 1191 1205 1218 1230 1241 1251 1260 1267 1274 1281 1287 1298 1307

A (nm)

F(A) (W m-2 nm-1 0.066 0.054 0.047 0.041 0.036 0.031 0.024 0.019 0.015 0.012 0.010 0.008 0.005 0.003 0.002 0.001 0.000

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

1313 1319 1325 1329 1332 1336 1342 1346 1349 1353 1355 1357 1360 1362 1364 1366 1367

Source: Frohlich and London (1986).

important in troposphericchemistry.In spite of its stratosphericabsorption,a sufficient overlap exists betweenthe solar UV spectrumat the Earth's surfaceand the absorption crosssectionof ozonethat 03 photolysisis also importantin troposphericchemistry.

3.1.2

Earth Geometry for Solar Radiation

Because of the rotation of the Earth around the Sun and its daily rotation around itself, the solar irradiance actually received at a given location on Earth depends on the location on the Earth, the date of the year, and the time of day. The Earth describes an ellipse around the Sun. The shortest distance between the Earth and Sun, occurring around January 3, is 1.471 X 108kIn, and the largest distance, around July 4, is 1.521 X 108kIn. The mean distance, the average of the two extremes, is 1.496 X 108kIn. 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 the center of the Sun makes an angle 11with the equatorial plane, which is called the Sun declination with the equatorial plane. 11reaches its maximum value of + 23 °27' at the summer solstice 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. 11can be computed at any day of the year by 11(in radians) = -0.4cos[27r(dn + 10)/365], where dn = 1 for January

1,2 for January2, andsoon.

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RADIATIVE FLUX IN mE ATMOSPHERE 131

FIGURE 3.4 Definition of latitudeand longitudeof a point M on the Earth. Oz is the local vertical.

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

FIGURE 3.5 Horizontal coordinatesof the Sun:

eo= solar zenith

angle;

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ABSORPTION COEFFICIENT AND ABSORPTION CROSS SECTION

133

3.2 ABSORPTION COEFFICIENT AND ABSORPTION CROSSSECTION Considerthe propagationof radiationthrougha mediumand selecta layer of thicknessdx perpendicularto a beamof intensity F (Figure 3.7). The lossof intensity F over the infinitesimalslice dx as a result of light absorptionis dF

= -baF dx

(3.10)

where ba is the absorption coefficient (m-l) of the medium. For a finite path between Xl and X2,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,independentof X, and

F(xV

I

= F(XI)eXp[-ba(X2

-XI)]

(3.13)

This resultis known asthe Beer-Lambertlaw of extinction.Whenx is measuredvertically in the atmospherethe optical thicknessis called the optical depth. The transmittanceof the layer betweenXI and X2along the direction of propagationis definedby F(xV = exp( -b'a) 'f=~

Ildx

.

..

F(x.;

F(~

FIGURE 3.7 Propagationof radiationthrougha medium.

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ACTINICFLUX 137

As indicated,the quantity on the R.H.S. multiplying nA is jA. The spectralactinic flux is then the radiative quantity that drives the photodissociation,that is, the quantity that multiplies rPA(A)aA(A)to producea product that when integratedover all wavelengthsproducesthe photodissociationrate coefficient. The spectralactinic flux I (A) is then I(J..)

= !L(J..,(},

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()")

=

ff

L()", e, 4» cose sine de d4>

(3.24)

"'9 The factor cos () reflects the change in the projected area of the surface as the angle of incidence is varied. This factor does not appear in the expression for the actinic flux because the projected area and the pathlengths offset exactly. As the angle of incidence is changed from overhead «() = 0°) to nearly glancing «() -+ 90°), the energy (irradiance) incident upon the layer decreases,but the actinic flux remains unchanged because the lower intensity is exactly compensated for by the longer pathlength of light through the layer. Two special casesexist, collimated and isotropic light, in which simple relationships exist between actinic flux and irradiance (Madronich, 1987). These two limiting cases often can be used to approximate atmospheric situations. Collimated light can be considered to be parallel, having originated from a very small solid angle Ll(JJ(j.An example is the direct solar beam, which subtends Ll(JJ(j~ 7 X 10-5 sr at the Earth. Over this small solid angle the 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(jcentered about «(}o,CPo).In this case (3.23) and (3.24) become

=

10

= Lo~~

(3.25)

Eo= Locas(Jo~~ Thus, if

(3.26)

Lois 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

= 21TLI

(3.27)

E = 1TL.

(3.28)

I

Equation(3.28)is identicalto (3.3).

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ACTINICFLUX 139 TABLE 3.2 Relation Betweenthe Slant Path Optical Depth m and sec 80for a Standard Rayleigh Atmosphere

SOUIre: Kasten and Young (1989).

If Foo(A)is the spectralradiantflux densityat the top of the atmosphere(TOA), that at groundlevel on a planeperpendicularto the solarbeamcanbe determinedfrom an extension 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 between the slant path optical depth for the actual solar zenith angle (Joand the overhead Sun optical depth (Figure 3.8). When the Sun is directly overhead «(Jo= 0°), m = 1.0andatmospheric attenuation is at its minimum. As the Sun approaches the horizon, (Joincreases toward 90°, m increases and the attenuation of sunlight increases as a result of the increased pathlength. When the sphericity of the Earth can be neglected,

m=

-

1

= secf}o

(3.38)

coseo

This relation holds for eo less than about 75°. For larger values of eo, m has to be computed, taking into account the path through the spherical atmospheric layers, the vertical profile of absorbing and scattering species, and the curvature of the optical rays as a result of 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 zenith angles

(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

producesthe solarconstantSo'

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ATMOSPHERICPHOTOCHEMISTRY 141

of radiation can only occur if an upper energy level of the molecule exists that is separated from the lower level by an energy equal to that of the incident photon. Small molecules generally exhibit intense electronic absorption at wavelengths shorter than do larger molecules. For example, N2 and H2 absorb significantly at wavelengths less than 100 nm, while O2 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 progressively removed (recall Figure 1.10; also Figure 3.3). Photochemistry in the troposphere is confined 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: I

Dissociation A*--+-B1 + B2 2 Direct Reaction A* + B--+-CI + 3 Fluorescence A*--+-A+hv 4 Collisional deactivation A* +M--+-A+M 5 Ionization A*--+-A+ +e

C2

The quantumyield for a specificprocessinvolving A * is definedasthe ratio of the number of molecules of A * undergoing that process to the number of photons absorbed. Since the total number of A * molecules formed equals the number of photons absorbed, the quantum yield cf>ifor 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 possible processesmust equal 1. The rate of formation of A * is equal to the rate of photon absorption and is written4

d[A *] = ;A [A]

dt

(3.41)

where jA, having units S-I, is the first-order rate constantfor photolysisor the so-called specificabsorptionrate; jA is normally takento be independentof [A]. The rateof formation of B 1 in step I is

~

dt

=cf>tjA [A]

(3.42)

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where the overbar denotes an average over a wavelength interval ~>"i centered at >"i.The width of the wavelength intervals ~>"i is usually dictated by the available resolution for the actinic flux /(>"). A typical size of ~>"i is 5 nm from 290 nm to over 400 nm, and 10 nm beyond 400 nm.5 Values of (1(>..)and 4>(>")may not be available on precisely the same intervals as for /(>..),so some interpolation may be necessary. Table 3.3 summarizes important light-absorbing molecules in atmospheric chemistry. Photodissociation of molecular oxygen is key to stratospheric chemistry and will be adTABLE 3.3 SomePhotochemicalReactionsof Importance in Atmospheric Chemistry" Comments

Reaction O2 +hv ~O

+ O('D) > 50km

~O+O

I

03 + hV--02 2

--

+ 0

O2+ 0(10)

Photodissociationof molecularoxygenresultsprimarily from absorptionof solar radiationin the 200-220 nm wavelengthregion.The 185-200nm region, the O2Schumann-Rungebandspectral range,is also importantsincesolarradiationpenetratesefficiently into the stratosphereat those wavelengths.Recommendedabsorptioncrosssections are given by DeMoreet al. (1994). 03 absorptioncrosssectionsare given in WMO ReportNo. 16 (1986) and DeMoreet al. (1994). DeMore et al. (1994) presenta polynomialexpressionfor the quantumyield forO(ID) production, cP(OID),as a function of Ii and T in the range 305-320 nm. The upperlimiting value of cP(OID) is takenas 0.95 at 305 nm. Discrepanciesexist betweenpublishedO(ID) quantumyields, which can be separated into two groups: those that show

cf>

to

drop to zero at about315 nm (DeMoreet al., 1994)andthosethat exhibit a "tail" extendingbeyond 320 nm (Michelsenet al., 1994).In evaluating ambientdataagainstboth groupsof quantum yields, Hofzumahauset al. (1995) found that the cf> dataexhibiting a tail above315 nm betterrepresent observed data. As noted in the text, the implication of this finding is that solar photolysis of 03 at wavelengths longer than 310 nm contributes significantly more to tropospheric O(ID) formation than that based on the recommended correlation of DeMore et al. (1994).

h = 10-3 S-I h = 10-5s-t

at 40 kID at 10 kID continued

SMadronich and Weller (1990) calculated tropospheric photolysis rate constants for N02, 03, HONO, HCHO, and CH3CHO 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) Comments

Reaction I

Formaldehydephotolysisis a significantsourceof free radicalsin the troposphere.Absorptioncross sectionsfor HCHO aregiven by DeMore et al. (1994). DeMore et al. (1994) give quantumyields,

HCHO + hv--+- H + HCO 2 --+- H, + CO

cf>1

andcf>20from301to 356nm.Channellpre-

dominatesat shorterwavelengthsand channel2 at longer wavelengths. CH3OOH+ hv--products

Absorptioncrosssectionsfor CH3OOHfrom 210 to 360 nm aregiven by DeMore et al. (1994).

Cl2+ hv~CI

Absorption cross sections for Clz from 260 to 470 nm are given by DeMore et al. (1994).

+ CI

ClOG + hv-+CIO OCIO + hv--'O HOCI + hv

+ 0

Absorption cross sections for ciao from 220 to 280 nm aregiven by DeMore et aI. (1994).

+ CIO

Absorption cross sections for OCIO from 272 to 475 nm aregiven by DeMore et al. (1994).

OH + CI

1 CIONO2 + hv-+CI

Absorptioncrosssectionsfor HOCI from 200 to 380 nm are given by DeMore et aI. (1994).

+NO3

2 -+CIO

Absorptioncrosssectionsfor CIONOzfrom 196to 414 nm are given by DeMoreet aI. (1994).The

+ NO2

preferred quantum yieldvaIuesarecf>1 = 0.6(). < 308nm), cf>.= 1.0(). > 364nm), and cf>z= I - cf>1'

CCl3F + hv--+products

Absorptioncrosssectionsfor CCI3Ffrom 170to 260 nm are given by DeMore et al. (1994).

CCl2F2 + hjl~products

Absorptioncrosssectionsfor CClzFzfrom 170to 240 nm aregiven by DeMore et aI. (1994).

OCS + hv~CO

Absorptioncrosssectionsfor OCS from 186to 296 nm are given by DeMore et al. (1994).The recommendedquantumyield for photodissociation is 0.72.

+ S

I

CH3CHO+ hv--+CH4 + CO 2 --+CH3 + HCO

CH3C(O)CH3 + hv-CH3

+ CH3CO

Absorptioncrosssectionsfor acetaldehydehave beenmeasuredby Martinez et al. (1992)at 300 :t 2 K over the wavelengthregion 200-366 nm. Recommended quantumyields for channelsI and 2 havebeentabulatedby Atkinson et al. (1992). Absorptioncrosssectionsandquantumyields for acetonehavebeensummarizedby Atkinson et al. (1992).An averagephotodissociationquantum yield for CH3COformation is about0.33 over the wavelengthregion 280-330 nm.

"Many of the rateconstantsfor reactionsimportantin atmosphericchemistryaresurveyedperiodicallyby a group organized 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 sections, and quantum yields appear in these reports.

145

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Photolysis Wavelength, nm -0 '-' 0

-

320 I

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Photolysis Energy, cm-l FIGURE 3.10 Primaryquantumyield for 0(10) formationfrom 03 photolysisat 298 K. Summary of datapresentedby Michelsenet al. (1994).

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FIGURE 3.12 Primaryquantumyield for 0 formationfrom NO2photolysis,ascorrelatedby Demerjian et al. (1980).

wavelengths, there is insufficient energy to promote bond cleavage. The point at which dissociation fails to occur is not sharp becausethe individual molecules of NO2 do not possess a 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 temperature and therefore increasing the ground-state energy of the system. Table 3.5 gives tabulated 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, at 40oN.

Example 3.2 Atmospheric Heating Rates: The Chapman Function The natureof the attenuationthat occursasradiationpenetratesthe atmospherecan be seenby considering the Beer-Lambertlaw of light absorptionfor a singleabsorbingcomponent, dF(A)

= -a(A)NF(A)

dx

(3.47)

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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

1.22 1.43 1.74 2.02 2.33 2.65 2.97 3.28 3.61 3.91 4.18 4.51 4.75 5.00 5.23 5.41 5.57 5.69 5.84 5.86 5.93 5.86 5.89 5.78 5.73 5.78

0.9976 0.9966 0.9954 0.9944 0.9934 0.9924 0.9914 0.9904 0.9894 0.9884 0.9874 0.9864 0.9848 0.9834 0.9818 0.9798 0.9762 0.9711 0.9636 0.9360 0.7850 0.4925 0.2258 0.0914 0.0354 0.0188 Total jNO2

jNO2 a

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

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CHEMICALKINETICS 153 where Nj is the number concentration of species i (cm-3), (8kT /;rmij)1/2 is the rootmean-square relative speed of the i and j molecules, k is the Boltzmann constant, mij mimj/(mi + mj) is the reducedmass,and ;rUi} is the so-calledcollision crosssection of molecules i andj. The characteristic time during which molecules in thermal motion in a gas are close enough to interact is brief, on the order of 10-12 to 10-13 s. At ambient temperature 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 the time between collisions. Whereas the collision of two molecules is a necessary condition for reaction, sufficient energy must be available to break chemical bonds. Theory indicates that the fraction of collisions involving energy greater than a required energy E is given by exp (- E / kT). In this form E has units of energy per molecule. More commonly, E is expressed in terms of energy per mole, and we use exp( -E/ RT), where R is the universal gas constant. The rate of reaction is expressed in a form that accounts for both the frequency of collisions and the fraction that exceed the required energy,

=

(3.54) The preexponentialfactor A(T) may dependon temperaturesincethe translationalkinetic energyand internal degreesof freedomof the moleculesinfluencethe probability of reaction in any collision event. The rate of reactionis usually written as r = kcjcj, wherethe parameterk is calledthe rate constant,6

k

= A(T)

exp( - E'

(3.55)

RT

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 molecular collision between molecules of i and j results in reaction. This is called the gas-kinetic collision rate, and the corresponding value of the second-order rate constant k at room temperature is about 2 X 10-10 cm3 molecule S-I. Most reactions have rate constants less than this. First, the activation energy E must be overcome for the reaction to proceed. Second, molecules that are geometrically complex may have to be aligned properly at the point of collision for reaction to take place and perfect alignment is not achieved in every collision. Consider the potential energy surface for the bimolecular reaction (most elementary reactions can be considered to be reversible) f

A+BC~AB b

+C

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

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S;)I.L3NI)f 'Y;)IW3H;) aNY J..~.LSIW3H;)o.LOHd;)I~3HdSOW.LY J-SI

CHEMICAL KINETICS

155

moleculedenotedby A *, followed by decompositionof 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

equationsfor this mechanismare d[A]

dt

=

-k(f[A][M]

+ k1b[A*][M]

The reactive intennediate in this mechanism is A *. The PSSA states that the rate of generation of A * is equal to its rate of disappearance; physically, what this means is that A * is so reactive 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 concentrationof A * in terms of the concentrationsof the stable moleculesA and M,

[A*] =

k1f[A][M]

k1b[M] + k2

This expressioncan be usedin (3.57) to give d[A] -- - klfk2[M][A] k1b[M]+ k2 dt

(3.61)

We see that the single overall reaction A -+ B + C with a rate given by (3.61) depends on the concentration of M. If the background species M is in such excess that its concentration 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 formation and disappearanceof a reactive intermediate are equal. A consequenceof this statement is that d[A*]/dt = 0 from (3.58). This should not, however, be interpreted to mean that [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*] -- ~ k)f[A][M] dt k)b[M] + k2 dt

(3.62)

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:HEMICAL

The time behaviorof 0 following irradiation beginningat t

[0]

Rl k3[O2]

KINETICS

1-"7

0 is

[Mj (1 exp(-k3[OZ] [M]t))

(3.64)

At 80 km, T = 200 K, at which k3 = 1.4 X 10-33cm6molecule-2S-I. The exponential term in (3.64) is ~Iow pJ!q~ B f.q f.~J~U~ ss~:>x~ ~q~ Jo IBAOW~J IBUO!S!II°:> ~Bq~~B~J~OS'.1qUB:>~W!~~J!I ~qt '~In:>~Iow ~:>npoJd~~mI f.I~U~!:>YJnsB q~!A\. 'u~){OJq S! puoq

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CHEMICAL KINETICS

159

Actual experimental data on the pressure variation of the pseudo-second-order rate constant k do not conform with (3.71). The reason is that the elementary rate constants ka, kr, and k.,should have been defined for each individual quantized vibrational level of ABt, and the individual rates summed to give the total rate. Also, vibrations and rotations can interconvert in the newly formed molecule. A widely used modification of the treatment of pressure-dependent reactions is due to Troe (1983). In the Troe theory, the right-hand side of (3.71) is multiplied by a broadening factor F that is itself a function of ko/ koo'

(3.72) Third-order reactionsoften exhibit decreasingrate with increasingtemperature.The higher the temperature,the larger the thermalkinetic energypossessed by the reactantsA and B, andthe largerthe internal vibrationalenergystoredin theABt molecule.The larger this energy,the higher the chanceof recombinationand the largerthe value of kr. The rate constantskaand ksdo not dependstrongly on temperature,so in the low-pressureregime sincekr increasesas T increases,the overall rate constantdecreases. This temperaturedependenceof kois frequentlyrepresentedempirically by a factor Tn in the overall rateconstant(seeAppendix B).

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PROBLEMS 161 Hofzumahaus,A., Kraus, A., and Milller, M. (1995) Comparisonof troposphericphotolysis frequency data J(O'D) measuredsimultaneouslyby chemical actinometryand spectroradiometry: test of laboratoryO(ID) quantumyield data,in TroposphericOxidation Mechanisms,edited by K. H. Becker.EuropeanCommission,ReportEUR 16171EN,Luxembourg,pp. 71-76. Kasten,F., andYoung,A. T. (1989)Revisedoptical air masstablesandapproximationformula,Appl. Opt. 28,4735-4738. Lenoble,J. (1993)AtmosphericRadiativeTransfer:A. DeepakPublishing,Hampton,VA. Liou, K. N. (1992) Radiation and Cloud Processesin the Atmosphere.Oxford University Press, Oxford, UK. Madronich, S. (1987) Photodissociationin the atmosphereI. Actinic flux and the effectsof ground reflectionsand clouds,J. Geophys.Res.,92,9740-9752. Madronjch, S., and Weller, G. (1990) Numerical integrationerrors in calculatedtroposphericphotodissociationrate coefficients,J. Atmos.Chem.,10, 283-300. Martinez, R. D., Buitrago,A. A., Howell, N. W., Hearn,C. H., andJoens,J. A. (1992)The nearUV absorption-spectra of severalaliphatic aldehydesand ketones,Atmos.Environ., 26, 785-792. Merienne,M. F., Jenouvrier,A., andCoquart,B. (1995)The N02 absorptionspectrum.I. Absorption cross-sections at ambienttemperaturesin the 300-500 nm region,J. Atmos.Chem.,20, 281-297. Michelsen,H. A., Salawitch,R. J., Wennberg,P.O., andAnderson,J. G. (1994)ProductionofO(ID) from photolysisof 03, Geophys.Res.Left., 21,2227-2230. Troe, J. (1983) Specific rate constantsk(E, 1) for unimolecularbond fissions,J. Chem.Phys.,79, 6017-6029. Wayne,R. P.(1991) Chemistryof Atmospheres,2nd ed. Oxford University Press,Oxford, UK. World Meteorological Organization (WMO) (1986) Atmospheric Ozone 1985. Global Ozone ResearchandMonitoring Project,ReportNo. 16,Geneva.

PROBLEMS 3.1B Considerthe following reactionsystem

A~B B+M~C AssumeM is presentin great excess,so that [M] ~ constant.The concentrationsof B and C arezero at t = O. 8. Derive analyticalexpressionsfor the exactdynamicbehaviorof this systemover time. Show mathematicallyunder what conditions the pseudo-steady-state approximation (PSSA)can be madefor [B]. b. Use the PSSAto derive a simpler setof equationsfor the concentrationsof A, B, andC. 3.28

The most importantoxidizing speciesfor troposphericcompoundsis usuallythe hydroxyl (OH) radical. A standard way of determining the OH rate constant of a compound is to measure its decay in a reactor in the presence of OH relative to the decay of a second compound, the OH rate constant of which is known. Consider two compounds A and B, A being the one for which the OH rate constant is to be determined and B the reference compound for which its OH rate constant is known. Show that the

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BASIC PHOTOCHEMICAL

5.1

CYCLE OF N02, NO, AND 0,

235

BASIC PHOTOCHEMICAL CYCLE OF N02, NO, AND 03

When NO and NOz are presentin sunlight,ozoneformation occursas a result of the photolysis of NOz at wavelengths< 424 nm, NO2+hv

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NO+O

O+O2+M~O3+M

(5.1) (5.2)

whereM representsN2 or O2or anotherthird moleculethat absorbsthe excessvibrational energyand therebystabilizesthe 03 moleculeformed.Thereare no significantsourcesof ozonein the atmosphereother than reaction5.2. Once formed, 03 reactswith NO to regenerateN02,

03 + NO --

N02 + O2

Let us consider for a moment the dynamics of a system in which only these three reactions 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 temperature and 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 speciesin the system:N02, NO, 0, and 03, We could write the dynamicequationsfor NO, 0, and03 just aswe havedonefor N02. For example,the equationfor [0] is d[O] dt

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

However,if we were to evaluatethe right-handside numerically we would find that it is very closeto zero.Physically,this meansthat the oxygenatom is so reactivethat it disappearsby reaction5.2 virtually asfast asit is formedby reaction5.1. In dealingwith highly reactivespeciessuchasthe oxygenatom,it is customary,as notedin Chapter3, to invoke the pseudo-steady-state approximation(PSSA)and therebyassumethat the rate of formation is exactly equalto the rateof disappearance, for example, jS.1

[NO2]

= kS.2[O][O2][M]

The steady-stateoxygenatomconcentrationin this systemis then given by

[0]88=

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BASIC PHOTOCHEMICAL CYCLE OF N02. NO. AND 0,

237

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

100 1000 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 maximum steady-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 greater than those in the sample calculation. Since most of the NOx emitted is in the form of NO and 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 concluded that reactions other than 5.1 to 5.3 are important in tropospheric air in which relatively 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 is a key atmospheric reaction. Its photodissociation rate can be calculated if the actinic flux I (A)-is known. However, such measurementsrequire specialized apparatus that is complex and expensive. A method that allows one to determine the NOz photodissociation rate, j5.1, directly circumvents the need for elaborate measurementsof the radiation intensity. By exposing a mixture of NOz and Nz to sunlight one can determine the value of j5.1 by comparing the measured NOz decay as a function of time with that obtained by integration of the 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 predicted 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'

0 + N02 -+ NO + 02 0+N02 +M

-+

(5. 11)

N03 +M

(5. 12)

NO+ N03 -+ 2N02

(5. 13)

0 + NO + M -+ N02 + M

(5. 14)

N02 + N03 + M -+

N20S

+M

(5. 15)

N20S+ M -+ N02 + N03 + M

I

(5. 16)

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.

31I3HdSOdO~.L3H.L dO J..~SIW3HJ

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~

ATMOSPHERIC CHEMISTRY OF CARBON MONOXIDE

6.0.

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AND NO,

239

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AND NO,

241

The atmosphericoxidation of CO can be summarizedasfollows: ~

CO+OH.

~

CO2+ HO2'

HO2.+NO

~

NO2+0H.

NO2+hv

~

NO+O

O+O2+M~O3+M Net

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

Note that neitherOH nor H02 is consumedin this reactioncycle, which can be viewed as a catalytic oxidation of CO to CO2-Net formation of 03 occursbecausethe conversionof NO to N02 is accomplishedby the H02 radicalratherthanby 03 itself. This setof reactions can occur repeatedlyuntil one of the moleculesis removedin a terminationreaction. Terminationof the chain can occur when OH and N02 reactto form nitric acid, OH. +NO2+M

-+ HNO3 +M

(5.26)

Again, we have already encountered this reaction in the stratosphere. (Termination can also occur when HO2 reacts with itself, but at this point we assumethat 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]88

=

Rs.I - RS.2+ RS.22 0

jS.1[N02] - kS.2[0] [02] [M] + kS.22 [M] [0(10)] = 0 [O(IO)]SS

RS.21b- RS.22+ RS.23= 0

kS.21b [03] - kS.22[M][0(10)] - kS.23 [H2O] [0(10)] = 0 2Rs.23- RS.24 + RS.2S - RS.26 =0

[OH]ss [HO2]ss

2kS.23[H2O] [O( 1D)]

[03]88

- Rs.2s=

RS.24

RS.2

-

0

kS.26[OH] [N02]

= 0

- RS.3- RS.21= 0

kS.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 appropriate formula, 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 appropriate formula.

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AND NO.

243

The qualitative featuresof the set of CO/NOxreactionscan be describedas follows. PhotolysisofN02 producesNO ando. The 0 atomimmediatelycombineswith an oxygen moleculeto form 03, Ozonethen reactsmainly with NO to regenerateN02oThe cycle of thesethreereactionscan be representedconciselyas (whereO2is not indicated) hv

NO2 ~ NO+O3 The characteristictime of this cycle is usually shortenoughrelativeto the competingreactions so that a steadystateis achievedquickly. The concentrationof 03 at sucha steadystatecondition is given by the photostation~ staterelation (5.8). If we now considerthe reactionsresulting when CO is present,we seethat the simple reversiblecycle aboveis modified to be3 hv

NOz~ NO+03 r HOz I The HO2radical that convertsNO back to NO2is convertedin the processto OH, which then is availableto react with anothermoleculeof CO. Thus we obtain two interwoven cycles,a "fast" cycle and a "slow" cycle, hv NOz .

~

NO + 01

CO+ qH-E~ .

NO

.

The CO/NOxreaction mechanismis a chain reaction with OH as the chain carrier. The chain length Lc of sucha reactionis definedas the numberof propagationstepsoccurring for eachterminationstep,

Lr =

RS.2S

RS.26

= RS.24

kS.Z4[CO]

RS.26

kS.z6[NOz]

(5.31)

Since the steady-state 03 concentration achieved in the fast cycle is proportional to the ratio of [N02] to [NO], the effect of the slow CO cycle is to slowly convert NO to N02 and therefore to increase the steady-state 03 concentration. Thus, because of the rapidity of the N02/O3 cycle, an independent path that changes the ratio of [N02] to [NO] indirectly controls the ozone concentration. It is common to refer to such oxidation chains that are driven by sunlight as photooxidations. The basic reaction mechanism of the CO/NOx system exhibits many of the key features of 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]

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f'f'Z

CHEMISTRY OF THE BACKGROUND TROPOSPHERE 245

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

[HCHO] The chain length of the HCHO photooxidationis given by

Lc=

R5.25 RS.Z6 2jS.32a

+ RS.33

RS.z6 1 +

kS.33[HCHO]

kS.Z6[NOz] We seethat Lc is alwaysgreaterthan one as long asHCHO is presentin the system.Each moleculeof HCHO that photolyzesvia reaction5.32aleadsto the conversionof two moleculesof NO to N02 and at the sametime generatestwo OH radicals.The HCHO-OH reaction,on the other hand,leadsto one NO to N02 conversionand producesa singleOH radical. The reactivity of the systemis controlled by the amountof HCHO. Upon photolysis, HCHO providestwo H02 radicalson one pathandnoneon the other.Sincethesepathsare roughly comparablein rate, we can sayapproximatelythat eachHCHO moleculeleadsto one H02 molecule.(It leadsto exactly one in the OH reaction.)The conversionof NO to N02 andthe formation of 03 arethereforedriven by HCHO throughits productionof H02. Thus the theoreticalmaximumamountof 03 that could be producedin this systemis [03]

= [HCHO]o +

[N02]o

When all the NOx is converted to HNO3, the system ceasesreacting.

5.4 CHEMISTRY OF THE BACKGROUND TROPOSPHERE We have begun a systematic development of the chemistry of the troposphere. We began with carbon monoxide since its atmospheric chemistry is the simplest, while exhibiting some of the essential elements of hydroxyl radical attack, formation of the hydroperoxyl radical, and conversion of NO to NO2. We then proceeded to formaldehyde, the atmospheric chemistry of which is slightly more complex than that of carbon monoxide. The next logical 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 hydrocarbon species in the chemistry of the background troposphere. Thus, in studying the atmospheric chemistry of methane, we are led naturally to the chemistry of the background troposphere.

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Methyl peroxynitrate,CH3OONObthermally dissociatesback to the reactantswith a lifetime with respectto thermaldecompositionof 1 secondat room temperatureand atmosphericpressure,which increasesto ~2 daysfor the temperatureandpressureconditionsin the upper troposphere(Atkinson et aI., 1989;Atkinson, 1990).Methyl peroxynitratecan act asa temporaryreservoirof NO2andCH3O2radicalsin the uppertroposphere. The reactionof CH3O2with the HO2radicaIleadsto the formation of methyl hydroperoxide, CH302' + H02' ~ CH300H + 02 (5.42) ~

which can photolyzeor reactwith the OH radical CH300H + hv --+- CH30, + OH.

(5.43)

CH300H+ OH, ~ H2O + CH3O2'

~

(5.44a)

H2O+ CH200H -!-

(5.44b)

fast

HCHO + OH.

wherethe fractional splits indicatedare thoseat 298 K. The lifetime of methyl hydroperoxide in the troposphereresultingfrom photolysisandreactionwith the OH radical is calculatedto be - 2 days.Methyl hydroperoxideis thena temporarysink of radicals,with its wet or dry depositionbeing a troposphericloss processfor radicals. The only important reactionfor the methoxy radical under troposphericconditionsis with O2to form formaldehydeandthe H02 radical,

CH30.+ 02 ~ HCHO+ H02'

(5.45)

Formaldehydeis a "first-generation"productthat reactsfurther, by photolysisby reactions 5.32aand5.32bandwith the OH radical,reaction5.33.Formaldehydeis the first major product of C~ oxidation with a lifetime longer than a few seconds.The lifetimes of HCHO resulting from photolysisand OH radical reactionare -4 hours and 1.5 days,respectively,leadingto an overall lifetime of -3 hoursfor overheadsunconditions. Major chain-terminatingstepsin C~ oxidationincludenitric acid andhydrogenperoxide formation,4

OH. + N02 + M -+ HN03+ M H02. + H02. 4

-+ H202 + 02

(5.26) (5.46)

The recommendedrateconstantfor reaction5.46 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-dependent term, andfw is a water-vapor-dependent factor. Stockwell (1995) has shown that the contribution of the water-dependent term can be very important; at the surface the value of kS46in air saturated with water vapor is over twice the value of kS46in dry air. Above about 15 km the water-dependent contribution is negligible and above 25 km the reaction is almost completely bimolecular.

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dation and assumingthat the photostationarystateholds at any instant, the local rate of formation of 03 as a result of the abovecycle is po]

= {kS.2s[HO2]+

kS.4o[CH302]} [NO]

As a result of peroxy radical-NO reactions,the photostationarystaterelation must be adjustedto (Parrishet 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 peroxy radical mixing ratios of 60 ppt or so were required to account for observations of this ratio (Ridley et al., 1992). Production of 03 in the CH4 oxidation chain is interrupted if the peroxy radicals H02 and CH3O2react 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 H02 radical, besides reaction 5.46, another important reaction is

H02' + 03 -+- OH. + 202

(5.47)

Reaction 5.46 is the principal gas-phasesource of H2O2in 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 variations of the H2O2concentration. H2O21evelshave been found to be higher in the afternoon, during the summer, and in the southern latitudes (Sakugawa et al., 1990). The major gas-phase destruction pathways for H2O2are its reaction with OH and its photolysis,

H202+ OR. ~ H2O+ H02

(5.48)

H202 +hv ~ 2 OR.

(5.49)

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 United States in June 1987. The range of H2O2mixing ratios was < 0.2 to 37 ppb, with an average of 2 to 4 ppb. H2O2 concentrations are typically low near the surface, rise to a maximum at the top of the boundary layer, then slowly decrease with height. 'Photochemical model predictions indicate the H2O2levels depend on whether the atmosphere is in a high or low NOx regime, according to whether radical production is greater or less than the NOx emission rate (Kleinman, 1991). In the low NOx regime, more radicals are formed that can react with NOx, and the "excess" radicals are removed by radical-radical reactions that are the source of peroxides (e.g., reaction 5.46). In this regime, peroxide formation is nearly proportional to the difference between radical source strength and NOx emission rate. In the high NOx regime, peroxide formation is suppressed.

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3'M3HdSOdOll.L3ill dO J..1I.LSIW3H:> OSZ

THE HYDROXYL RADICAL

251

Because the temperature dependences of these two rate constants are quite close, the atmospheric oxidation rate ofCH4 can be scaled to that ofCH3CCI3. An atmospheric CH4 destruction rate' of 440 :t 50 Tg yr-1 can be inferred in this way. From the current atmospheric 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 in soils are also considered, the lifetime shortens to about 10 years. Only in the past few years have reliable direct measurementsbeen made of lower tropospheric 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 exhibit a diurnal profile, with daytime maximum concentrations of several 106molecules cm-3. Ehhalt et al. (1991) have evaluated the extent of agreement between calculated and measured OH concentrations on May 20, 1983, 0908 to 1130 hours, at Deuselbach, a rural area in 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

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FIGURE 5.3 Concentrationsand fluxes betweenOH and HO2(Ehhalt et al., 1991).The calculation simulatesan airmassobservedbetween0908 and 1130hours, May 20, 1983 at Deuselbach, Germany.Numbersin boxesarecalculatedconcentrations(moleculescm-3); numberson arrowsare conversionratesofOH and HO" (moleculescm-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 (see Atkinson, 1991, Wayne et al., 1991, and Platt and Heintz, 1994, for comprehensive reviews of the nitrate radical),

N02 + 03 -+ N03 + 02 M N02 + N03 ~ N20S

(5.52) (5.15,5.16)

with N2Os being in a relatively rapid (characteristic time to reach equilibrium -1 minute at 298 K) equilibrium with N02 and the N03 radical. Nitrate radicals were first detected in the troposphere in 1980. N03 is a strong oxidizing agent and reacts with a number of other atmospheric species. The prerequisite for N03 radical production is the simultaneous presence ofN02 and 03 in the same airmass, as reaction 5.52 is the only primary source ofN03 in the troposphere. The equilibrium with N2Os,reactions 5.15 and 5.16, is an important feature ofN03 chemistry. During daytime N03 radicals photolyze rapidly via two paths (see Table 3.3),

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

(5.53a)

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

(5.53b)

with a noontimelifetime of -5 seconds,andreactwith NO,

NO3+ NO

~

2NO2

(5.13)

sufficiently rapidly that NO andN03 cannotcoexistat mixing ratiosof a few partsper trillion (ppt) or higher. For typical daytime conditionsof [N02] = 40 ppb, [03] = 50 ppb, and [NO] = 40 ppb, the maximumN03 mixing ratio will be 0.6 ppt. At nighttime,however,when NO concentrationsdrop nearzero,dueto reactionwith 03, the N03 mixing ratio can reach 100 ppt. Under conditionstypical of rural areasin industrializedcountries (N02 mixing ratio of -1 ppb), N03 andN2Osconcentrationsareroughly the sameorderof magnitude.Whereashomogeneousreactionsof N2Oswith water vapor and other trace

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

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] ...r fo Q) x

Latitude FIGURE 5.4 Meridianal crosssectionof 03 (in ppb) obtainedduring March and April 1987via ozonesondes releasedfrom the researchvesselPolarsternon a northerncruisein theAtlantic, mostly along 30° W. Approximate location of the tropopauseis shown with crosses.(Figure presentedin Monthly Update,Departmentof EnergyAtmosphericChemistry Program,originally presentedby Smit et al., in Ozonein the Atmosphere,edited by R. D. Bojkov and P. Fabian,DeepakPublishing, 1989.)

5.7.1 Tropospheric Sinks of Ozone The principal photochemicalsink of 03 in the troposphereis reactions5.21b, 5.22, and 5.23.Becausethis removalpath dependson the concentrationof watervapor,it is mosteffective in low latitudesat low altitudes,wherethe radiationis intenseand the humidity is high. An estimateof the magnitudeof the local rate of 03 destructionby reactions5.21b, 5.22,and5.23 canbe obtainedby assumingthat [O(ID)] is in a pseudo-steady stateasa result of thesethreereactions.The pseudo-steady-state concentrationof O(ID) is given by

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The fractional 03 photochemical loss in Figure 5.5 can be converted into absolute 24hour averages of the normalized 03 destruction rate (in S-I) by multiplying the fractions in Figure 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 contrast, the lifetime of 03 resulting from dry deposition to the surface of the ocean can be estimated 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 to photochemical 03 loss, such as reaction 5.47, one concludes that photochemistry is likely the 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 is estimated 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 by the lack of observed 03 decreaseat night, which would occur if dry deposition to the ocean were having a noticeable effect on 03, since photochemical destruction occurs only during daytime and dry deposition operates both day and night. (Over land the 03 dry deposition velocity may be as much as an order of magnitude larger than that over the ocean, and with a nighttime boundary layer generally shallower than that over the ocean, dry deposition of ozone may compete effectively with chemical removal.)

5.7.2 Tropospheric Sourceof Ozone The principal in situ chemical sourceof ozone in the troposphereis photochemicalproduction through the methaneoxidation chain. The level of NO is critical in this chain in dictating the fate of the HO2radical. Reaction5.25, +NO~

NO2+0H.

(5.25)

OH-+202

(5.47)

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~

destroys ozone. The break-even concentration of NO, below which 03 is destroyed and above which it is produced, depends on the local 03 concentration. Tropospheric air may be called NOx rich when NO mixing ratios exceed those of 03 by more than the ratio of the rate constants of reactions 5.47 and 5.25. The ratio of the rates of these two reactions is RS.47

= --kS.47[03]

RS.2S

kS.2S[NO]

The rate constant ratio, k5.47/k5.25~ 2.5 x 10-4. The 03 mixing ratio near the Earth's surface in the remote continental troposphere is about 20 ppb. Then R5.25> R5.47for NO mixing ratios exceeding about 5 ppt. This amount of NO is roughly equivalent to 15 to 20 ppt NOx. A competition also exists between NO and the H02 radical for reaction with the CH3O2 radical, and the preferred route depends on the concentrations of H02 radicals and NO. The rate constants for the reaction of the CH3O2radicals with NO (reaction 5.40) and H02 radicals (reaction 5.42) are of comparable magnitude (see Table B.l). Based on expected H02 radical concentrations in the troposphere, Logan et al. (1981) calculated that the reaction of the CH3O2radical with NO dominates over that with H02 for NO mixing ra-

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NOx, ppt FIGURE 5.6 Calculated24 hour average03 production and loss rates for the free troposphere aboveHawaii during the MLOPEX as a function of the NOxmixing ratio (Liu et al., 1992).

of the reduced solar intensity. At 20° N, for example, it is estimated that 03 lifetimes at the surface are about 5 days in summer and 17 days in winter, whereas at 40° N these increase to 8 days in summer and 100 days in winter. At 20° N, at 10 kIn altitude, estimated summer and winter 03 lifetimes are 30 days and 90 days, respectively, increasing by about a factor of 6 from those at the surface. The key to understanding background tropospheric ozone is to determine whether a region is in a local 03-producing or 03-destroying condition. Because of the critical role played by NOx, assessing the effect of anthropogenic NOx emissions on background tropospheric NOx is one of the major issues in tropospheric chemistry. Increasing NOx weakens the net photochemical sink of 03 in the background troposphere, leading to an overall increase of 0,.

5.7.3 Fate of NO., At first glanceit might appearthat NOx releasedin urban and regional areaswill have a lifetime too shortto permit its transportto the remotetroposphereto influencebackground 03. For typical OH levels,reaction5.26,

N02 + OH. + M -+ HN03+ M

(5.26)

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moval is indeed occurring, predicted HNO3 concentrations and the HNO3/ NOx ratio can be reduced to a value close to those measured. The heterogeneous hydrolysis of N2Os,reaction 5.54, has been suggestedto play an important role in tropospheric chemistry (Dentener and Crutzen, 1993). Particles on which HNO3 has formed can be transported to the dry upper troposphere, where it is expected that most water and HNO3 would evaporate. From the point of view of explaining the reason for 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 the original NO2 were simply converted to HNO3 by OH. Understanding the relationship between HNO3 and NOx in the upper troposphere remains as an outstanding problem in atmospheric chemistry.

5.7.4 OzoneBudget 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 estimated downward flux of 03 from the stratosphere is (3-8) X 1010molecules cm-2 S-I. Loss of 03 by dry deposition on the Earth's surface is estimated at about 8 X 1010molecules cm-2 S-I (Galbally and Roy, 1980). The principal mechanism for in situ chemical destruction of 03 is photolysis and subsequent reaction of 0(10) with H2O, estimated also to be about 8 X 1010molecules cm-2 S-I (Lelieveld et al., 1993). The most difficult term to estimate, of the four, is the average rate of in situ chemical production. We know that in situ production of 03 on the global scale is driven by the oxidation of CO and CH4. Thus a good starting point is to estimate the amount of 03 that can be produced globally from the oxidation of CO and C~. Average destruction rates of CO and CH4 by OH reaction are 3 X 1011molecules cm-2 S-I and 1 X lOll molecules cm-2 S-I, respectively (Lelieveld et al., 1993). If all the CO and CH4 oxidation were to occur in NOx-rich environments, yielding one 03 molecule per each CO and 2.7 03 molecules for each C~ (this number accounts for oxidation of the formaldehyde formed as a product of C~ oxidation), the average global production rate6 of 03 would be 3 X 1011+ 2.7 X lOll ~ 6 X 1011molecules cm-2 S-I. This production rate exceeds substantially the amount of 03 that can be destroyed by reactions 5.21b and 5.23 and that which can be removed by deposition at the Earth's surface. The conclusion one reaches is that large portions of the troposphere must contain so little NOx that these regions 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 of such calculations must be assessedby careful comparisons with field data that provide all inportant components of production and loss. Nonetheless, there is little doubt that production and loss of tropospheric ozone are dominated by in situ chemistry and not by downward transport of 03 from the stratosphere. Manzerall et al. (1996) have quantified the ozone budget over remote high northern latitudes 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 molecules of OH for every CH. molecule destroyed (Tie et aI., 1992). The associated average annual yield of CO from methane oxidation is about 0.82 molecule of CO per molecule of CH. destroyed. The global methane oxidation chain is estimated to produce, as a result, about 1.15 molecules of ozone for each molecule of CH. destroyed.

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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 60 minutes. These multicell storms can last for several hours and vertically redistribute large quantities 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 pollutants into the upper troposphere (Dickerson et aI., 1987; Pickering et aI., 1989). Not all cases 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 increase in the production rate of ozone averaged through the troposphere (Pickering et aI., 1990).

Example 5.3 The Troposphere/StratosphereTransition The transitionfrom troposphereto stratosphereis traditionally definedbasedon the reversalof the atmospherictemperatureprofile. That transitionis also dramaticallyreflectedin how the concentrationsof tracespeciesvary with altitude below andabovethe tropopause.Of tracespecies.H02 and OH exhibit perhapsthe mostprofounddifferencesacrossthe tropopause(Wennberget al., 1995).In the lower stratosphereH02 andOH participatein HOxCycle 4, which is the predominant cycle involved in 03 removal in that portion of the stratosphere.We saw in Chapter4 that in the lower stratospherethe H02/0H ratio is describedby [HO2]

k4.ll [03]

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

The presenceof NO short-circuitsHO" Cycle 4 by reconvertingH02 backto OH beforeit hasa chanceto reactwith 03, This ratio variesfrom about4 to 7 anddecreases as [NO] increases.[OH] itself is essentiaIlyindependentof [NO] and dependsalmostentirely on solar zenith angle.This independence of OH on NO is a resultof the fact that the increaseof OH that resultsfrom reaction4.36 is offset almostexactly by a decreaseof the ratesof reactionsthat generateOH, reactions4.14, 4.40, and4.41.This occursbecausethe HO2that participatesin reaction4.36 is not otherwiseavailablefor reactions4.14 and4.40. The behaviorof HO2and OH in the uppertroposphereis dominatedby CO chemistry. (Becauseof its I to 3 month lifetime, CO is more or less uniformly mixed up to the tropopause.Above the tropopause,CO faIls off with increasingaltitude. Becauseof the much slower vertical transportrate in the stratosphere,the rate of the CO-OH reaction competeswith the rateof vertical mixing.) TroposphericCO oxidationproceedsaccording to reactions5.24 and 5.25,coupledto reactions5.1 to 5.3. (Note that 4.36 and5.25 arethe samereaction.)From Section5.2 we canobtainan expressionfor the HO2/OH ratio in the uppertroposphere.Basedon the steady-staterelation for HO2,we obtain [HOz] [OH]

k5.24[CO] k .5.25,

[

NO .

]

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

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~3HdSOdO~

3H.L dO A~SIW3HJ

t9Z

CHEMISTRY OF NONMETHANE ORGANIC COMPOUNDSIN THE TROPOSPHERE 265

These alkyl peroxy radicals can be classed as primary, secondary, or tertiary depending on the 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 occurring such as those that form R in the first place. Henceforth, the formation of an alkyl radical 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,

RO2' + NO

-M

--

RO.+ NO2

(S.S9a)

RONO?

(5.59b)

For alkyl peroxy radicals,reaction5.59acanform the correspondingalkoxy (RO.) radical togetherwith NO2,or the correspondingalkyl nitrate,reaction5.59b,with the yield of the alkyl nitrate increasingwith increasingpressureand with decreasingtemperature.For secondaryalkyl peroxy radicals at 298 K and 760 Torr total pressure,the alkyl nitrate yields increasemonotonically from QJd}o I.t:}!Jl!A ~ ~!A suof\!puo:) :)!l:}qdsodoI! J:}pun t:)~:}J sI~:)!P~J I.xO){IV 'sJOA

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:}q1 wOl} ~U!tIns:}J st:)npoJd

3'H3HdSOdO~l. 3Hl. dO J..&SIW3H:>

99Z


The 2-pentoxyradical canthen reactwith 020decompose,or isomerize:

o.

"

Decomposition

Isomerization

/ CH3CHO+ CH3CHzCHz or CH3. + CH3CH2CH2CHO CH3CH(OH)CH2CH2CH2' CH3C(0)CH2CH2CH3 + H02 . Rate constants for alkoxy radical isomerizations can be combined with rate constants for alkoxy radical decomposition and reaction with O2 to predict the relative importance of the three pathways (Atkinson. 1994). Alkoxy radicals can also react with NO and N02. but under ambient tropospheric conditions these reactions are generally of negligible importance.

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CH3CH2CH (~.) NOI

r

CH3CH2CH2CH202'

CH3

Nol r

CH3CH2CH(ON02)CH3

CH3CH2CH (0.) CH 3 °2 ICH,CH.C(O)

I

CH, I

+

-

CH3CH2CH2CH20NO2

CH3CH2CH2CH20.

,,-

V2!

I

;onm

~

irH ,rH.rH.rHOI

CHJCH2O2° + ICH3CHOI

! NO

CH2(02.) CH2CH2CH2OH

+

H02"

102

! NO

HO" 2

CH3CH20"

CH2(0.) CH2CH2CH20H

i

02

fsom.

@~

CH2(OH) CH2CH2CHOH

+ H02. + H02"

FIGURE 5.7 Atmosphericphotooxidationmechanismfor n-butane.The only significantreaction of n-butaneis with the hydroxyl radical. Approximately 85% of that reactioninvolves H-atom abstractionfrom an internalcarbonatomand 15%from a terminalcarbonatom.In the terminalH-atom abstractionpath,the CH3CH2CH2CH2O. alkoxy radical is estimatedto reactwith O225% of the time and isomerize75% of the time. The secondisomerizationis estimatedto be a factor of 5 fasterthan the first isomerizationof the CH3CH2CH2CH2 O. radical, so that competitionwith O2reactionis not consideredat this step.The predominantfate of a-hydroxy radicalsis reactionwith O2,For example,

.CHzOH+Oz-+ HCHO+HOz', and CH3CHOH+Oz-+ CH3CHO+HOz', In the n-butane mechanism,the a-hydroxy radical, CHz(OH)CHzCHzCHOHreactsrapidly with O2to form 4-hydroxy-l-butanal, CHz(OH)CHzCHzCHO.In the internal H-atom abstractionpath,the alkoxy radical CH3CH2CH(0.)CH3reactswith O2to yield methyl ethyl ketone(MEK), CH3CH2C(0)CH3,and decomposesto form CH3CHOand CH3CH2.,which, after reactionwith O2 and NO and O2 again, yields anothermoleculeof CH3CHOand H02.

The HOCH2CH20.radicalthen decomposesand reactswith O2: HOCH2CH2O. ~

HCHO+ .CH20H

HOCH2CH20. +02 ~ HOCH2CHO+ H02' The numbers over the arrows indicate the fraction of the reactions that lead to the indicated products at 298 K. Finally, the .CH2OH radical reacts with O2 to give formaldehyde and a hydroperoxyl radical,

.CH20H + 02

--+

fast

HCHO+ H02

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'HO + OHJlHJOH 8Z"O+ OHJH vv'r + lONZ

+-

ONZ +, HO + ~lJ

~A!g O:J'ON Q:I!M AI~IOS S:J~~~J~OH ~wnss~ un~ ~M '~undoJd Q:I!M P!P ~M sy .lOH

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s~ UO!!:)~~J II~J~AO u~ ~!!lM UR:) ~M 'suo!:! s! ZOZH:JZH:JOH !~q! ~u~wnss~ ',\IJUU!.o:{

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followed by rapid addition of O2to yield the corresponding{3-hydroxyalkylperoxy radicals, OH

RJ, "

R~

.

c-c

R/2

OH 00. R)",I I /R3

:c-c

M + °2 -=--

\R 4

R1 2

"R4

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

:c-c

+ NO

\R 4

RI2

-

(5.69)

,c-c

NO2+ R/2

R4

Rate constants for the reactions of f3-hydroxyalkyl peroxy radicals with NO are essentially identical 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. radical with O2 and decomposition are competitive, the f3-hydroxyalkoxy radicals formed subsequent to OH addition to ~C3 alkenes undergo decomposition and the reaction with O2 is negligible. The decomposition reaction is

08 O. Rl~

I

1/ R1

,C-C" RI2

R4

OH 0 RI" I II ,C. + R3CR4 R1 2

Carbonylyields from alkene-OH reactionsare summarizedin Table5.1. The yields of HCHO and RCHO arising from cleavage of the -C = C- bond of l-alkenes RCH = CHz decreasemonotonically from ~0.90 for propeneand I-butene to 0.21 to 0.39 for l-octene.H-atom abstractionfrom the CHzgroupsin the l-alkenesis expectedto accountfor an increasingfraction of the overall OH radical reactionasthe carbonnumber of the l-alkenes increases,with about 15% of the I-heptenereactionbeing estimatedto proceedby H-atom abstractionfrom the secondaryCHzgroups.The propene-OHreaction mechanismis shownin Figure 5.8.

"The {3-hydroxynitrate formation pathway accounts for only -I to 1.5% of the overall NO reaction pathway at 298 K for propene (Shepson et aI., 1985). The yields of {3-hydroxynitrates from the propene-OH and 1butene-OH reactions are about a factor of 2 lower than those of alkyl nitrates from the propane-OH and n-butane-OH reactions. These observations suggest that the formation yields of {3-hydroxynitrates from the OH reaction with higher l-alkenes could also be a factor of 2 lower than those from the reactions with the corresDondinl! n-alkanes.


followed by rapid addition of O2to yield the corresponding{3-hydroxyalkylperoxy radicals, R OR 00

OH RJ

" c-c

R~

.

I",

M

+ °2 -=--

.C-C.

R4

R{

I

R'l

II

R4

R1 2

In the presenceof NO, the f'-hydroxyalkyl peroxyradicalreactswith NO to form eitherthe f'-hydroxylalkoxy radical plus NO2or the f'-hydroxynitrate:9 OH 00. RI",! I/R3

:c-c

RI2

+ NO

\R 4

-

(5.69)

:c-c

NO2+ R/2

R4

Rate constants for the reactions of f3-hydroxyalkyl peroxy radicals with NO are essentially identical 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. radical with O2 and decomposition are competitive, the f3-hydroxyalkoxy radicals formed subsequent 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 / R1 ,C-C" RI2 R4

-

08 RI", I

C. +

0 II R'tCR,i

R1 2

Carbonylyields from alkene-OH reactionsare summarizedin Table5.1. The yields of HCHO and RCHO arising from cleavage of the -C = C- bond of 1-alkenes RCH = CHz decreasemonotonically from ~0.90 for propeneand I-butene to 0.21 to 0.39 for l-octene.H-atom abstractionfrom the CHzgroupsin the 1-alkenesis expectedto accountfor an increasingfraction of the overall OH radical reactionasthe carbonnumber of the 1-alkenesincreases,with about 15% of the 1-heptenereactionbeing estimatedto proceedby H-atom abstractionfrom the secondaryCHzgroups.The propene-OHreaction mechanismis shownin Figure 5.8.

"The {3-hydroxynitrate formation pathway accounts for only -I to 1.5% of the overall NO reaction pathway at 298 K for propene (Shepson et aI., 1985). The yields of {3-hydroxynitrates from the propene-OH and 1butene-OH reactions are about a factor of 2 lower than those of alkyl nitrates from the propane-OH and n-butane-OH reactions. These observations suggest that the formation yields of {3-hydroxynitrates from the OH reaction with higher l-alkenes could also be a factor of 2 lower than those from the reactions with the corresponding n-alkanes.

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This is followed by rapid O2addition: ONO2 I /R3 C-C R/ o""R

R"", 2

ONOz RI" I /R3 C-C R/ I "R4 Z 00.

+°24

to producethe {3-nitratoalkylperoxy radical, subsequentreactionsof which are

+NO -

+ NO2

(5.73) R},

ONO2 R

I / "c -C,

/

I

R2

3

"R4

ONO2

The latter reactionis expectedto be minor. Furtherreactionsof {3-nitratoalkoxyradicalsinclude R

+°2-

ONOz R

I" I

/

4

C-C R /

z

+

HO.

II

2

0 if R3 = H

0 II

0 II

R)CR2 + R3CR4 + NO2

ONO2 RI~ I /R3 C-C R/ - I~R 2 0. 4

+NOZ -

of which the last reactionis expecedto be minor. Figure 5.9 showsthe mechanismof the orooene-NO,reaction.

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Atkinson, 1994;Horie et al., 1994a, b; Neebet al., 1995;Thomaset al., 1995;Neebet al., 1996)and are reasonablywell understoodfor a large numberof the smalleralkenes.The major mechanisticissueconcernsthe fate, under atmosphericconditions,of the initially energy-richCriegeebiradical, which can be collisionally stabilized or can undergounimoleculardecomposition, [RI CH2t(R2)O6]~

-+- RI CH2C(R2)O6

(stabilization)

-+- RICH2C(O)R2 + 0 -+- [RICH2C(O)OR2]'" -+- [RICH

(5.76a) (5.76b)

-+- decomposition

= C(OOH)R2]'"

-+-

RICHC(O)R2 + OH.

(5.76c) (5.76d)

At atmosphericpressure,0 atomsarenot formedin any appreciableamount,sopath5.76b can generallybe neglected. Hydroxyl radicalshave beenobservedto be formed from alkene-O3reactions,sometimes with close to a unit yield (1 molecule of OH per 1 molecule of alkene reacted) (Atkinson andAschmann,1993).Atkinson et al. (1995a)reported.OH radical yields from a seriesof alkene-O3reactions: Alkene

OH Yield

I-Pentene I-Hexene I-Heptene l-Octene 2,3-Dimethyl-l-butene Cyclopentene I-Methylcyclohexene

0.37 0.32 0.27 0.18 0.50 0.61 0.90

(Estimateduncertaintiesin theseyields area factor of -1.5.) At I atm, fractional yields of stabilizedbiradicalsareestimatedas (Atkinson, 1994): Ethene Propene trans-2-Butene 2-Methylpropene 2,- 3-Dimethy 1-2-butene

0.37 0.275 0.18 0.174 0.30

The reactionpathwaysof Criegeebiradicalsare generallywell establishedfor the first two compoundsin the seriesalthoughthe exactfractionsthat proceedvia eachindividual pathare still opento question(Horie and Moortgat, 1991): M --+-

CH200. (stabilization) CO2+ H2 CO + H2O

0,

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(5.77)

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5.8.3 Aromatics Aromatic compounds are of great interest in the chemistry of the urban atmosphere because of their abundance in motor vehicle emissions and becauseof their reactivity with respect to ozone and organic aerosol formation. Understanding the atmospheric oxidation mechanisms of aromatics has long been cited as the most critical need in further development of reaction mechanisms for the urban and regional atmosphere (National Research Council, 1991). The major atmospheric sink for aromatics is reaction with the hydroxyl radical. Whereas rate constants for the OR reaction with aromatics have been well characterized (Atkinson, 1994), mechanisms of aromatic oxidation following the initial OR attack have been highly uncertain. Aromatic compounds of concern in urban atmospheric chemistry are given in Figure 5.10.

CH~

~

CH3

A

~

~

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CH3

CH3

A

A ~

~

Benzene

C2Hs

X

Toluene

0

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y

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-

m Xylene

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CH3

A

A

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y

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, CH3

~

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CH3

Ethyl benzene

0

- Ethyl

toluene

,2,4 Trimethyl benzene

m - Ethyl toluene

,3,5 Trimethyl benzene

p - Ethyl toluene

FIGURE S.10 Aromatic compoundsof interestin troposphericchemistry.

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Peroxyacetylnitrate, the first compoundin the seriesof PANs, which itself is usually called PAN. is formedfrom the OH reactionwith acetaldehyde,

CH3CHO+ OH, -+- CH3CO+ H2O

(5.92)

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(5.93)

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(5.97)

Peroxyacetyl nitrate does not absorb radiation above 290 nm so this class of compounds is not expected to photodissociate in the troposphere. Peroxyacetyl nitrate is not highly water soluble; it is more soluble than NO and NO2 but considerably less soluble, for example, than nitric acid. Thus aqueous-phasescavenging is not expected to be an important tropospheric 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 principal loss mechanism is thermal decomposition by reaction 5.91 or 5.95 back to the peroxyacyl radical and NO2. The thermal decomposition is highly temperature dependent; at temperatures 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 atmospheric pressure. Using the Troe falloff expression, over the temperature range 280 to 330K,

k=

ko[M] F{I

ko[M]

1+-

'gJoko[M]/koof}"

(5.98)

koo

the specificvaluesfor PAN are ko = 4.9 X 10-3exp(-12100/ T) cm3molecule-I S-I koo

= 4.0 X 1016exp( -13600/

T) S-I

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with 5.99abeing the major reactionpathway.Subsequentreactionof this particularradical with NO leadsto

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 conditions, ground-level background mixing ratios of 550 ppt have been found throughout the NH troposphere. In the free troposphere, acetone mixing ratios on the order of 500 ppt are present at northern midlatitudes, declining to about 200 ppt at southern latitudes (Singh et al., 1995). From atmospheric data and three-dimensional photochemical models, a global acetone source of 40 to 60 T g yr-1 has been estimated, comprised of 51 % secondary formation from the atmospheric oxidation of precursor hydrocarbons (principally propane, isobutane, and isobutene), 26% direct emission from biomass burning, 21 % direct biogenic emissions, and 3% primary anthropogenic emissions (Singh et al., 1994). Atmospheric removal of acetone is estimated to result from photolysis (64%), OH reaction (24%), and deposition (12%). Acetone photolysis, which produces the PAN-precursor CH3CO radical, is estimated to contribute 40 to 50 ppt of PAN in the middle and upper troposphere of the Northern Hemisphere. Based on tropospheric models, up to 50% of observed PAN may be formed by this mechanism. The average lifetime of acetone in the atmosphere is estimated to be 16 days (Singh et al., 1995). By virtue of its photooxidation chemistry (Figure 5.11), acetone is a source of HOx radicals in the upper troposphere. Under the dry conditions of the upper troposphere, where 0(10) + H2O is relatively slow, acetone makes an important additional contribution to

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5.8.10

Acids

The atmospheric sources of formic and acetic acid are still open to question. In the Shenandoah Cloud and Photochemistry Experiment conducted during 1990 in the rural continental atmosphere at a mountaintop (1014 m) in Virginia, median mixing ratios for HCOOH and CH3COOH were 5.4 and 2.1 ppb, respectively (Talbot et al., 1995). Formic acid mixing ratios often approached or exceeded 10 ppb. An observed lack of correlation between HCOOH and CH3COOH with peroxide speciesargued against a significant source from permutation reactions of peroxy radicals (e.g., reaction 5.61). A strong correlation between the mixing ratios of both acids was suggestive of a common source, although combustion emissions could be ruled out. Correlation between the seasonalvariation of the two acids and ambient temperature is consistent with a soil microbial source. Together, the two acids contribute between 16 and 35% of the free acidity in North American precipitation and between 25 and 98% of the free acidity in precipitation in remote areas. Photochemical production of organic acids occurs in the gas phase from ozone-alkene reactions and in cloud water by the hydrolysis of aldehydes followed by aQueous-phasereaction with OH radicals (see Chapter 6). These routes can explain, in part,

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409

TABLE 7.1 Example of SegregatedAerosol Size Information

11111 20000 3000 2000 1000 750 1250 563 117 160 80 2

100 300 330 350 390 450 650 830 890 910 915 916

100 200 30 20 40 60 200 180 60 20 5 1

0.001-0.01 0.01-0.02 0.02-0.03 0.03-0.04 0.04-0.08 0.08-0.16 0.16-0.32 0.32-0.64 0.64-1.25 1.25-2.5 2.5-5.0 5.0-10.0

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large-andsmall-particleregionsare depicted,but it now erroneouslyappearsthat the distribution consistsalmostexclusivelyof particlessmallerthan0.1 j.Lm. Using a numberof sizebins to describean aerosolsizedistribution generallyresultsin lossof information aboutthe distribution structureinside eachbin. While this may be acceptablefor someapplications,our goal in this chapteris to developa rigorousmathematical frameworkfor the descriptionof the aerosolsizedistribution.The issuesdiscussedin the precedingexampleprovide valuableinsights into how we shouldexpressand present ambientaerosolsizedistributions.

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Example 7.1

. ') exist.

For the distribution of Figure 7.4, how many particles of diameter 0.1 j),m

According to the inset of Figure 7.4, nN(O.1 fLm)

= 13,000 fLm-l

cm-3. However, this

is not the numberof particlesof diameter0.1 fLm (it evenhasthe wrong units). To calculate the numberof particleswe needto 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 and

thereforethereare zeroparticlesof diameterexactly equalto 0.1 fLm. Let us try to rephrasethe abovequestion. Example 7.2. For the distribution of Figure7.4, how manyparticleswith diameterin the range 0.1 to 0.11 .urn exist? The size distribution is practically constant over this narrow range with n N(0.1 JLm) cm -3. The width of the region is 0.11 - 0.1 = 0.01 JLm and there are 0.0 I X 13,000 = 130 particles cm -3 with diameters between 0.1 and 0.11 JLm for this

= 13,000JLm -I

size distribution.

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415

The total aerosolvolume per cm3 of air, V, is

andis equalto the areabelow the nv(Dp) curve in Figure 7.4. If the particlesall havedepsity Pp (g cm-3) then the distribution of particle masswith respectto particle size, nM(Dp), is

)

Pp nv(Dp) ,1"66

=

Pp .106

)("6, D~nN(Dp) 7r

(,ug ,um-l cm-3)

(7.7)

where the factor 106is 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. Becauseparticle diameters in an aerosol population typically vary over several orders of magnitude, use of the distribution functions, nN(Dp), ns(Dp), nv(Dp), and nM(Dp), is often inconvenient. For example, all the structure of the number distribution depicted in Figure 7.4 occurs in the region from a few nanometers to 0.3 ILm diameter, a small part of the 0 to 10 ILm range of interest. To circumvent this scale problem the horizontal axis can be scaled in logarithmic intervals so that several orders of magnitude in Dp can be clearly seen (Figure 7.5). Plotting nN(Dp) on semilog axes gives, however, a somewhat dis-

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417

Theunits of n~ (In Dp) arecm-3 sinceInDp is dimensionless.The total numberconcentrationof particles N is

N =

{(X}

n~(In Dp) d In Dp

(7.8)

(cm-3)

J -(X}

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 thosewith respectto Dp,

n~(lnDp) = 11"D;nN(ln

Dp)

(,um2cm-3) (.um3cm-3)

(7.9) (7.10)

with

The aboveaerosoldistributionscan alsobe expressedas functionsof the base10 logarithm log Dp, defining nN(log Dp), ns(log Dp), and ny(log Dp). Note that nN, nN' and nN aredifferent mathematicalfunctions,and,for the samediameter Dp, they havedifferent arguments,namely Dp,ln Dp, and log Dp. The expressionsrelating thesefunctions will be derivedin the next section. Using the notation dNjdSjdV

= the differential

number/surface/volume of particles

in the sizerange Dp to Dp + dDp we have dN

= nN(Dp)

dDp

= n~(ln

dS

= ns(Dp)

dDp

= ns(lnDp)

dV

= ny(Dp) dDp = nt(ln

Dp) d In Dp d InDp

Dp) d In Dp

= n~(log

= ns(log

= ny(log

Dp) d log Dp

(7.13)

Dp) d log Dp

(7.14)

Dp) d log Dp

(7.15)

(LI'U

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419

This procedurecanbe generalizedto relateany two sizedistributionfunctions n(u) and n(v), whereboth u and v arerelatedto Dp. The generalizationof (7.17) is n(u) du = n(v) dv

(7.24)

and dividing both sides by dDp

(dvfdDp) = n(v)(d~)

n(u)

7.1.5

(7.25)

Properties of Size Distributions

It is often convenient to summarize the features of an aerosol distribution using one or two of its properties (mean particle size, spread of distribution) than by using the full function n N (D p) . Growth of particles corresponds to a shifting of parts of the distribution to larger sizes or simply an increase of the mean particle size. These properties are called the moments 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 concentration of aerosols is therefore M

N = L Nk k=l

(7.26)

The meanparticle diameter,Dp, of the populationis M

Dp = ~~1 =;--.--NkDk = ~ L N

NkDk

k=1

(7.27)

The variance,0'2, a measureof the spreadof the distribution aroundthe meandiameter Dp, is definedby 1

M

NL -D Pr k=l Nk(Dk

(7.28)

A value of a2 equalto zero would meanthat every one of the particlesin the distribution haspreciselydiameterDp. An increasinga2 indicatesthat the spreadof the distribution aroundthe meandiameterDp is increasing. We will usually deal with aerosoldistributionsin continuousform. Given the number distribution nN(Dp), (7.27) and (7.28) can be written in continuousform to define the

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9,..

THE SIZE DISTRIBUTION FUNCfION

427

1 It) I

E U ~

10.2

Q.

Q

C) .p. '-"

10

o~ c:

10.6

10.80.1

1.0 Diameter.

FIGURE 7.9 Power-lawdistributionsfor C

10.0 ~

= 0.001,anddifferent valuesof a

1000.0

106

c = 91.658 a = 3.746 10' '" I

c=

91.658 a = 3.746

,

/"

',/

,,

100.0

Q. ~ Q;

10Z

E u

~

01 2-

0 CO

10.0

11

~ ~ "0

3c.. () 3

\~ 4 1.0

I c..

10

0.1

10.6

.

I I I "",1

0.1

'"

"".!

1.0 Diameter.

FIGURE

t:J

~

'\

10

..,

7.10

I I I I ",,1

1",,1

100.0

10.0

"

I '" ,,1

0.1

IJtT1

volume distributions

pears to match the number distribution,

I ",,1

1.0

10.0

Diameter.

IJtT1

Fitting of an urban aerosol number distribution

comparison of the corresponding

'"

(right).

I'

with a power-law

I I "i11 100.0

distribution

Even if the power-law

it fails to reproduce the volume distribution.

(left) and

distribution

ap-

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'OSOll3V :>11I3HdSOmV am dO S3I.L1I3dOlld St"

AMBIENT AEROSOL SIZE DISTRIBUTIONS 429

The Modified Gamma Distribution The modified gammadistribution (Deirrnendjian, 1969) has been proposedas another function that approximatesambient aerosol size distributions, nN(Dp)

= AD;

exp(-BD~)

(7.55)

whereA, b, B, and c are all positive parameters.This distribution form providessignificant flexibility (Figure 7.11). but its use is often cumbersome.The total aerosolnumber concentrationN is equalto

N=

AB-(b+l)/c

r(~

c

wherer is the gammafunction. The maximumof the distribution occursat diameter Dm. )

Dm=

I/c

!!.Bc

7.2

AMBIENT

AEROSOL SIZE DISTRIBUTIONS

Atmosphericaerosolsizedistributionsareoften describedasthe sumof n log-normaldistributions, ( exp

(log Dp -log -

-Dpj) 2

2 1 2 og aj

where Ni is the number concentration, Dpi is the mean diameter, and O"iis the standard deviation of the jib log-normal mode. In this case 3n parameters are necessary for the description of the full aerosol distribution. Characteristics of model aerosol distributions are presentedin Table 7.3 following the suggestions of Jaenicke (1993).

7.2.1 Urban Aerosols Urban aerosols are mixtures of primary particulate emissions from industries, transportation, power generation, and natural sources and secondary material formed by gas-to-particle conversion mechanisms. The number distribution is dominated by particles smaller than 0.1 ILm, while most of the surface area is in the 0.1 to 0.5 ILm size range. On the contrary, the aerosol mass distribution has usually two distinct modes, one in the submicron regime (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 concentrations of fine particles (less than 0.1 ILm in diameter) are found close to sources (e.g., highways), but their concentration decreasesrapidly with distance from the source (Figure

Off'

~

~

~ 8~ ==

AMBIENT AEROSOLSIZE DISTRIBUTIONS 431

0.01

0.10 1.00 10.00 Diameter, IJIn FIGURE 7.12 Typical urbanaerosolnumber,surface,and volumedistributions.

7.13). Figure 7.13 describes the number of particles as a function of their diameter (both in logarithmic scales) for a variety of environments. There are roughly an order of magnitude more particles close to the freeway compared to the average urban concentration. Figure 7.14 illustrates the corresponding volume distributions. These distributions show that most of 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 character. Mass distributions, measured in urban centers, are characterized by three modes with a 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 nuclei mode (particles below 0.1 JLm),accumulation mode (0.1 < Dp tqg!~qjO uo!t:>unj U su UO!tuIJu~:>uo:>ssuw IOSOJ~U~q.L '(1661 'SUJo) ~pmrlIu tuqt ~AOqU ~IyoJd tUUtSUO:>J~qtUJ U puu dB tqg!~q U Ot dn ~pmrlIu qt!M ~SU~J:> -~p JU!tu~uodx~ UU SMoqS AIJU:>!dAtUO!tuIJU~:>uo:>ssuw IOSOJ~UjO u°rlnq!J:js!p JU:>!tJ~A~Q.L

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VERTICAL VARIATION

445

and N B is the numberconcentrationof the backgroundaerosolaloft. For marine aerosol H; varies from -290 to 440 m. Note that if H; is negative n = -I, and (7.60) can be rewrittenas -1

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(7.62)

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REFERENCES447 JaenickeR., Dreiling V., LehmannE., Koutsenogii,P. K., and Stingl, J. (1992) Condensationnuclei at the GermanAntarctic StationVonneymayer,Tellus,44B, 311-317 John,W., Wall, S. M., Ondo,J. L., and Winklmayr, W. (1990) Modes in the size distributionsof atmosphericinorganicaerosol,Atmos.Environ., 24A,2349-2359. Koutsenogii,P. K., and Jaenicke,R. (1994) Number concentrationand size distribution of atmospheric aerosolin Siberia,J. AerosolSci., 25,377-383. Koutsenogii, P. K., Bufetov, N. S., and Drosdova,V. I. (1993) Ion composition of atmospheric aerosolnearLake Baikal, Atmos.Environ, 27A, 1629-1633. Leaitch, W. R., and Isaac,G. A. (1991) Troposphericaerosolsize distributions from 1982to 1988 over EasternNorth America,Atmos.Environ., 25A,601-619. Li, X., Maring, H., Savoie,D., Voss,K., and Prospero,J. M. (1996) Dominanceof mineral dust in aerosollight scatteringin the North Atlantic tradewinds, Nature,380,416-419. Meng, Z., and Seinfeld,J. H. (1994) On the sourceof the submicrometerdroplet modeof urbanand regionalaerosols,AerosolSci. Technol.,20,253-265. Meszaros,A., and Vissy, K. (1974) Concentration,size distribution and chemical natureof atmospheric aerosolparticlesin remoteoceanareas,J. AerosolSci., 5, 101-109. Monahan,E. C., Fairall, C. W., Davidson,K. L., andJones-Boyle,P.(1983)Observedinter-relationshipsamongst10-m-elevationwinds, oceanicwhitecaps,andmarineaerosols,Q. J. R. Meteorol. Soc.,109, 379-392. O'Dowd, C. D., andSmith, M. H. (1993)Physicochemicalpropertiesof aerosolsover the Northeast Atlantic: evidencefor wind-speedrelated submicron sea-saltaerosolproduction, J. Geophys. Res.,98, 1137-1149. Ott, S. T., Ott, A., Martin, D. W., andYoung,J. A. (1991)Analysisof trans-Atlanticsaharandustoutbreakbasedon satelliteandGATE data,Mon. WeatherRev.,119, 1832-1850. Ottar, B. (1989)Arctic air pollution: a Norwegianperspective,Atmos.Environ.,23,2349-2356. Prospero,J. M. (1995)The atmospherictransportof particlesto the ocean,in SCOPEReport:Particle Flux in the Ocean,Ittekkot, V., Honjo, S., Depetris,P.J. (Eds.),Wiley, New York, NY. Prospero,J. M., Nees,R.T., andUematsu,M. (1987)Depositionrateof particulateanddissolvedaluminum derived from saharadust 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 observationsof Arctic aerosols.I: Characteristicsof Arctic haze, Geophys.Res.Lett., 11, 369-372. Rahn, K. (1981) Relative importanceof North America and Eurasiaas sourcesof Arctic aerosol, Atmos.Environ., 15,1447-1456. Savoie,D. L., andProspero,J. M. (1989)Comparisonof oceanicandcontinental sourcesof non-seasalt sulfateover the Pacific ocean,Nature, 339, 685-687. Schneider,J. K., and Gagosian,R. B. (1985) Particle size distribution of lipids in aerosolsoff the coastof Peru,J. Geophys.Res.,90, 7889-7898. Schroeder,W. H., Dobson,M., Kane,D. M., andJohnson,N. D. (1987)Toxic traceelementsassociatedwith airborneparticulatematter:a review,J. Air Pollut. Cont.Assoc.,37,1267-1285. Shaw,G. E. (1984) Microparticle sizespectrumof Arctic haze, Geophys.Res.Lett., 11,409-412. Shaw, G. E. (1985) Aerosol measurementsin Central Alaska 1982-1984,Atmos. Environ., 19, 2025-2031. Shaw,G. E. (1986) On physicalpropertiesof aerosolsat RossIsland,Antarctica,J. Aerosol Sci., 17, 937-945.

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PROBLEMS 449

Showthatthe varianceof the sizedistributionof a log-nonnallydistributedaerosolis

7.48

7.SA Starting with semilogarithmicgraph paper,constructa log-probability coordinate axis and showthat a log-normaldistribution plots as a straightline on thesecoordinates. 7.6A The datagiven below were obtainedfor a log-normally distributedaerosolsizedistribution: SizeInterval (,urn) 0.1-0.2 0.2-0.4 0.4-0.7 0.7-1.0 1.0-2.0 2.0-4.0 4.0-7.0 7.0-10 10-20 U

GeometricMean of SizeInterval (I/.m)

Numberof Particles in Intervalu

0.1414 0.2828 0.5292 0.8367 1.414 2.828 5.292 8.367 14.14

50 460 1055 980 1705 680 102 10 2

Assume that the particles are spheres with density p = 1.5 g cm -3.

8. Completethe abovetable 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. Determinethe geometricmeandiameterand geometricstandarddeviationof the log-normaldistribution to which thesedataadhereandplot the continuousdistributionson the threeplots from part (b). 7.78 For a log-normally distributedaerosoldifferent meandiameterscan be definedby

-

-

2

DplI = Dpgexp(v In ag)

where v is a parameterthat definesthe particular meandiameterof interest.Show that Diameter Mode (mostfrequentvalue) Geometricmeanor median Number(arithmetic)mean Surfaceareamean Massmean Surfaceareamedian Volumemedian

v

-1 0 0.5 1 1.5 2 3

PROBLEMS 449

7.48 Showthatthe varianceof the sizedistributionof a log-normallydistributedaerosolis

7.SA Starting with semilogarithmicgraph paper,constructa log-probability coordinate axis and showthat a log-normaldistribution plots asa straightline on thesecoordinates. 7.6A The datagiven below were obtainedfor a log-normally distributedaerosolsizedistribution: SizeInterval (,urn) 0.1-0.2 0.2-0.4 0.4-0.7 0.7-1.0 1.0-2.0 2.0-4.0 4.0-7.0 7.0-10 10-20 U

GeometricMean of SizeInterval (ILm)

Numberof Particles in Intervalu

0.1414 0.2828 0.5292 0.8367 1.414 2.828 5.292 8.367 14.14

50 460 1055 980 1705 680 102 10 2

Assume that the particles are spheres with density p = 1.5 g cm -3.

8. Completethe abovetable 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. Determinethe geometricmeandiameterand geometricstandarddeviationof the log-normaldistribution to which thesedataadhereandplot the continuousdistributionson the threeplots from part (b). 7.78 For a log-normally distributedaerosoldifferent meandiameterscan be definedby

-

-

DplI = Dpgexp(vln

2

ag)

where v is a parameterthat definesthe particular meandiameterof interest.Show that Diameter Mode (mostfrequentvalue) Geometricmeanor median Number(arithmetic)mean Surfaceareamean Massmean Surfaceareamedian Volumemedian

v

-1 0 0.5 1 1.5 2 3

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TEMPERATUREIN 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 turbulent diffusion. Actually, turbulent diffusion is something of a misnomer. The phrase refers to the observed spreading of a cloud of marked particles in a turbulent fluid at a rate many ordersof magnitude greater than that from molecular diffusion alone. The spreading is really not due to a "diffusion" phenomenon such as results from molecular collisions but ratheris 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 moleculardiffusion, with the contribution of the latter to the dispersion of pollutants in turbulence being virtually negligible. The lev~l of turbulence in the planetary boundary layer increaseswith increased wind speed, surface roughness, and instability. Turbulence therefore arises from both mechanical forces (shear, surface friction) and thermal forces (buoyancy). Lower atmospheric temperature profiles determine in part the stability of the atmosphereor, in other words, the degree to which turbulence induced by wind, surface roughness,or buoyancy will propagate through the layer. Under strongly stable conditions, disturbancesare highly damped and mixing of species is strongly suppressed. It is under such conditions that the worst air pollution episodes have occurred. The importance of winds to the atmospheric aspectsof air pollution is clearly evident. Our discussion of winds in 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 Thelayersof the atmospherecan be classifiedin a numberof ways, suchas by temperature,density,and chemicalcomposition.From the standpointof the dispersionof air pollutants,the most importantclassificationis on the basisof 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 as it moves vertically in the atmosphere. The concept of an air parcel is a tenable one as long asthe parcel is of such a size that the exchange of air molecules across its boundary is small when compared with the total number of air molecules in the parcel. As such a parcel rises in the atmosphere, it expands to accommodate the lowering pressure; however, it does so in such a way that exchange of heat between the parcel and the surrounding air is negligible. As the parcel expands upon rising, its temperature decreases.The process of vertical mixing in the atmosphere can, for simplicity, be envisioned as one involving a large number of parcels rising and falling. If there is no heat exchange between the parcel and the surrounding air, the parcel and the surrounding air may be at different temperatures (but not different pressures). The relation of the parcel's temperature to that of the air determines whether the parcel will continue rising or falling or whether it will reach a point of equilibrium. Therefore the variation of temperature with altitude in the atmosphere is a key variable in determining the degree to which contaminant-bearing air parcels will mix vertically.

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conditions.Integrating(14.14)with respectto z gives

One might ask: Why does not the atmosphere always have an adiabatic lapse rate as its actual profile? The reason it does not is that other processes such as winds and solar heating of the Earth's surface lead to dynamic temperature behavior in the lowest layers of the atmospherethat is seldom adiabatic. These other processesexert a much stronger influence on 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. We assumethat conduction or convection of heat across the boundary of the parcel will be slow compared 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 surrounding air. At any height z, the pressure is the same in the parcel as in the atmosphere. The rate of 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

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On the other hand, if A < r, a rising air parcel will cool more rapidly with height than the surroundings and a point will be reached at which the temperature of the parcel equals that of the surroundings. We see that, if A < r, the acceleration will oppose the motion of a 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, neutralstability A > r. unstable(vertical motionsenhanced) A < r. stable(vertical motionssuppressed) These same arguments may be applied to the case of a moist atmosphere. Because of the releaseof the latent heat of vaporization, a saturated parcel cools on rising at a slower rate than a dry parcel, since

rdry> r wet Thus a cloudy atmosphere is inherently less stable than a dry atmosphere, and a stable situation with reference to the dry adiabatic lapse rate may actually be unstable for upward displacements of a saturated air parcel. Figure 14.1 summarizes the types of temperature profiles found in the lower atmosphere, 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 conditions are reached usually when the sky is heavy with clouds and there is a moderate to high wind. The clouds prevent radiation from reaching the surface and ensure that the temperatureof the ground does not differ greatly from the air just above it. The wind serves to mix 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 decreaseswith height such that any vertical movement imparted to an air parcel 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 continues rising. (3) Subadiabatic (stable): a rising air parcel is cooler than its surroundings so it becomes 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 14.3showsmonthly averagediurnal and seasonalvariationsof the vertical thermalstructureof the planetaryboundarylayer at rural site nearSt. Louis, Missouri.

PROBLEMS 14.1A Showthat if the atmosphereis isothermalthetemperaturechangeof a parcelof air rising adiabaticallyis T(z)

= Toe-rz/To

Where Toand T~are the temperaturesof the parcelat the surfaceand of the air at the surface,respectively. 14.2A A rising parcel of air will cometo rest when its temperatureT equalsthat of the surroundingair, T'. Showthat the height z wherethis occursis given by 1

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0

z= A ,~

What condition musthold for this result to be valid? 14.3A Show that the condition that the density of the atmospheredoesnot changewith height is

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Clouds are one of the most significant elements of the atmospheric system, playing several key roles.

1. Cloudsarea major factor in the Earth'sradiationbudget,reflectingsunlightbackto spaceor blanketing the lower atmosphereand trapping infrared radiation emitted by the Earth's surface. 2. Cloudsdeliver waterfrom the atmosphereto the Earth'ssurfaceasrain or snowand arethus a key stepin the hydrologic cycle. 3. Clouds scavengegaseousand particulatematerialsand return them to the surface (wet deposition). 4. Cloudsprovide a mediumfor aqueous-phase chemicalreactionsandproductionof secondaryspecies. 5. Cloudsaffect significantlyvertical transportin the atmosphere.Updraftsanddowndraftsassociatedwith cloudsdeterminein a major way the vertical redistributionof tracespeciesin the atmosphere. Despite their great importance, clouds still remain one of the least understood components of the weather and climate system. We begin our discussion of clouds by summarizing the properties of their basic constituent, water. We then investigate the formation of droplets in a cooling air parcel. The microphysics of a droplet population and the dynamics of cloud formation are then examined. Finally, we revisit the chemical processestaking place in clouds and fogs using the material already developed in Chapter 6. A comprehensive 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, a relatively 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 ice crystals. The surface tension (surface free energy) is also large. Table 15.1 summarizes thesephysical properties of water. In the following sections we discuss the atmospherically relevant properties of water and and its solutions.

777

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PROPERTIESOF WATERAND WATERSOLUTIONS 779

15.1.3 Water Surface Tension Thesurfacetensionof water decreaseswith increasingtemperature.Pruppacherand Klett (1980)recommenduseof 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 water 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 existing at temp,eraturesbelow O°C. The dissolution of other compounds in water alters its surface tension. Experimental valuesof the variation of water solution surface tension with the solution concentration are tabulatedin the Handbook of Physics and Chemistry. For salts like NaCI and (NH4)2S04 the dependence of the solution surface tension, aw, on the solution molarity is practically linear over the range of atmospheric interest:

O"w(mNaCI,

T)

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O"w(m(N~n so.' T) = O"wo(T)+2.17 x 10-3 m(NH.)2S0. where uwo(T) is the surface tension of pure water and mNaCland m(N~nS04 are the molarities of NaCI and (N~)2 SO4 in M, respectively. I A last issue is the dependenceof the water surface tension on the size of the droplet. One would expect that as the droplet surface tension is the result of attractive forces between water molecules near the surface, a change in droplet diameter would change the number of molecules interacting with the molecules at the surface, thus changing the surface tension.However, becauseof the small range of molecular interaction, this dependenceof Uwo on size is significant only for extremely small drops, consisting merely of a few thousands of 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 JLmand becomessignificant only at drop sizes less than 0.01 JLm. Therefore the dependence of surfacetension 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 these speciesnear the droplet-air interface. For example, as nature tries to reach states of lower energies, if a solute increasesthe surface tension of water, this species at equilibrium should have lower concentrations at the interface than in the bulk solution. The opposite should happen for a surface-active compound that lowers the surface tension. One would expect higher concentrations of this species near the interface than in the bulk. For a I M NaCI solution this surface tension effect results in a NaCI deficiency at the interface of less than 1% (Pruppacher and Klett, 1980). The same authors suggested that for drops with diameters larger than 0.2 JLm and NaCI concentrations 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 atmospheric droplet formation.

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WATEREQUILIBRIUM IN THE ATMOSPHERE 781

TABLE 15.2 Saturation Vapor Pressureof Water Vapor Over a Flat Pure Water 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 = 6.107799961

= = a3 = a4 = as = a6 = al

a2

4.436518521 1.428945805 2.650648471 3.031240396 2.034080948 6.136820929

x x x x x x

10-1 10-2 10-4 10-6 10-8 10-11

Source: Lowe and Ficke (1974).

where ~Hv is the specific heat for water evaporation, Mw is the molecular weight of water, 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)pOMw RT2

Replacing in the above equation a function describing the temperature dependence of the latent heat of evaporation (e.g., (15.3)), one can integrate and obtain an explicit expression for pO(T). A series of such expressions exist in the literature (see Problem 1.1), and that proposedby 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 exceedsthat of the same substance over a flat surface. The dependence of the water vapor pressure on the droplet diameter is given by the Kelvin equation (9.86) as

E~

( exp

4Mwaw" ~

pO wherePw(Dp) is the water vaporpressureover the dropletof diameterDp, po is the water vaporpressureover a flat surfaceat the sametemperature,Mw is the molecularweight of water,O"wo is the air-water surfacetension,and Pwis the water density.The equilibrium watervaporconcentrationsat O°C and 20°C are shownin Figure 15.2asa function of the dropletdiameter.Note that the effect of curvaturefor water dropletsbecomesimportant only for Dp < 0.1 /.Lm.

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15.2.3 Equilibrium of a Flat Water Solution Let us considera water solution (flat surface)at constanttemperatureT andpressurep in equilibriumwith the atmosphere.Waterequilibrium betweenthe gasand aqueousphases requiresequality of the correspondingwater chemical potentialsin the two phases(see Chapter9): ,uw(g) = ,uw(aq)

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Water vapor behaves in the atmosphere as an ideal gas so its gas-phasechemical potential is .uw(g)

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(15.12)

whereYwis the water activity coefficient and Xw the mole fraction of water in solution. Combining(15.10)to (15.12)we obtain

~

=

(

exp

/10 t"'w

-

* ' .uw

(15.13)

RT

YwXw

Theaboveequationdescribesthe behavior of the systemfor any solution composition. Notethat the right-handside is a function of temperatureonly and thereforewill be equal to a constant,K, for constanttemperature.Consideringthe caseof pure water (no solute) wenotethat when Xw= I, Yw-+ 1 and p~ = po = K (T), wherepo is the vaporpressure of waterover pure water.Therefore(15.13)canbe rewritten as

0

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0

(15.14)

Equation(15.14) is applicablefor any solution and does not assumeideal behavior. '.~"'---".

-"

" Yw,

The mole fraction of water in a solution consistingof nw water moles and ns solute molesis given by Xw

= nwnw + ns

(15.15)

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p; =.

n... -

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(15.16)

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Equations (15.21), (15.24), (15.26), and (15.27) are different forms of the Kohler equations (Kohler, 1921, 1926). These equations express the two effects that determine the vapor pressure over an aqueous solution droplet-the Kelvin effect that tends to increase vapor pressure and the solute effect that tends to decreasevapor pressure. For a pure water drop there is no solute effect and the Kelvin effect results in higher vapor pressurescompared to a flat interface. By contrast, the vapor pressure of an aqueous solution drop can be larger or smaller than the vapor pressure over a pure water surface depending on the magnitude of the solute effect term, BI D~, relative to the curvature term, AI Dp. Note that both effects increase with decreasing droplet size but the solute effect increases much faster. One should also note that a droplet may be in equilibrium in a subsaturatedenvironment if D~A < B. Figure 15.5 shows the water vapor pressure over NaCl and (NH4)2S04 drops. The A term in the Kohler equations can be approximated by

A=

4MwO"w RTpw

0.66 ::::: T

(15.28)

(in JLm)

where T is in K, and the soluteterm, (15.29)

(in JLm3)

where ms is the solute mass (in g) per particle, Ms the solute molecular weight (in g mol-I), and v is the numberof ions resultingfrom the dissociationof one solutemolecule. For example,v = 2 for NaCI and NaN°3, while v = 3 for (NH4)2S04.

0.5I']

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a

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o. 0.0

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, 10.5

.,

Ji,m

,

"I ilill 1

I;

'I IIIIII 10

Wet Diameter.

I

I I IIIIIJ100

p,m

FIGURE 15.5 Kohler curves for NaCl and (NH4)ZSO4 particles with dry diameters 0.05, 0.1, and 0.5 ILm at 293 K (assuming spherical dry particles). The supersaturation is defined as the saturation minus one. For example, a supersaturation of 1% corresponds to a relative humidity of 101%.

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Let us consider first a drop lying on the portion of the Kohler curve for which Dp < Dpc. We assume that the atmospheric saturation is fixed at S. A drop will constantly experience small perturbations caused by the gain or loss of a few molecules of water. Say that the drop grows slightly due to the addition of a few molecules of water. At its momentary larger size, its equilibrium vapor pressure is larger than the fixed ambient value and the drop will evaporate water, eventually returning to its original equilibrium state. The same phenomenon will be observed if the droplet loses a few molecules of water. Its equilibrium vapor pressure will decrease,become less than the ambient, and water will condense on the droplet returning it to its original size. Therefore drops in the rising part of the Kohler curve are in stable equilibrium with their environment. Now consider a drop on the portion of the curve for which DIJ > Dpc that experiences a slight perturbation, causing it to grow by a few molecules of water. At its slightly larger size its equilibrium vapor pressure is lower than the ambient. Thus water molecules will continue to condense on the drop and it will grow even larger. Conversely, a slight shrinkage leads to a drop that has a higher equilibrium vapor pressure than the ambient so the drop continues to evaporate. If it is a drop of pure water, it will evaporate completely. If it contains a solute, it will diminish in size until it intersects the ascending branch of the Kohler curve that corresponds to stable equilibrium. In conclusion, the descending branchesof the curves describe unstable equilibrium states. If the ambient saturation ratio S is lower than the critical saturation Sc for a given particle, 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 equilibrium 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 ambient saturation will exceed the saturation at the particle surface (equilibrium saturation), and the particle will grow indefinitely. In such a way a droplet can grow to a size much larger than the original size of the dry particle. It is, in fact, through this process that particles as small as0.01 JLm in diameter can grow one billion times in mass to become 10 JLmcloud or fog droplets. Moreover, in cloud physics a particle is not considered to be a cloud droplet unless its diameter exceeds its critical diameter Dpc. The critical saturation Sc of a particle is an important property. If the environment has reached a saturation larger than Sc, the particle is said to be activated and starts growing rapidly, becoming a cloud droplet. For a spherical aerosol particle of diameter ds (dry diameter), density Ps, and molecular weight Ms, the number of moles (after complete dissociation) in the particle is given by

ns=

V7rd; Ps

(15.33)

6Ms

andcombiningthis result with (15.32)we find that

1/2

In Sc=

(15.34)

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(NH4)2S04, T= 20°C

-

.01

- - -.

No dissociation Complete dissociation

1.009

1.007

s .005

I

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I

~I

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10.1 Wet

FIGURE 15.7

,

,

~m

1 Radius,

. 10

Ilffi

Kohler curves for (NH4)2S04 assuming complete dissociation and no dissociation

of the salt in solution for dry radii of 0.02, 0.04, and0.1 ILm.

ts, all at the actiODOr

v and

Our analysisfollows exactly Section15.2.4,until the derivationof the mole fraction of water Xw in (15.19) and (15.20).The existenceof the insoluble material needsto be includedin theseequations.If the insoluble particle fraction is equivalentto a sphereof diameterduothen the droplet volume will be

1 and ~(the e ab-

1 7r 6"

D3 p

- 1 = nwvw+ nsvs+ 6"7rdu3

(15.35)

andthe mole fraction of water Xwin the solution will be given by

--

digwa.

Xw

+

ns

=

(15.36)

nw

Substitutingthis expressioninto (15.18)we find not

In

=

4MwC1w

RTp:D;

+ In Yw- In

(15.37)

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CLOUD AND FOG FORMATION 793

ns analothis case

£

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FIGURE 15.9 Critical supersaturationas a function of the particle dry diameterfor different contentsof insolublematerial.The solublematerialis (NH4)2S04.

(15.39)

ontaining Ible mass

~

and (15.38) can be rewritten as a function of the particle soluble fraction and the initial particle diameter provided that the densities of soluble and insoluble material are known. The number 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 insoluble material are given in Figure 15.8. We see that the smaller the water-soluble fraction the higher the supersaturation needed for activation of the same particle, and the lower the critical diameter. Critical supersaturation as a function of the dry particle diameter is given in Figure 15.9.

15.3 CLOUD AND FOG FORMATION The ability of a given particle to becomeactivateddependson its size and chemicalcomposition andon the maximumsupersaturation experiencedby the particle.If, for example, the ambientRH doesnot exceed100%,no particle will be activatedanda cloud cannotbe formed2. In this sectionwe will examinethe mechanismsby which cloudsare createdin 2The classic Kohler formulation does not consider the cases of solutes that are not completely soluble or soluble gases, 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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For an air parcelinitially at 283 K with a relative humidity of 80% (RH = 0.8),a temperaturereductionof 3.3 K is requiredto bring the parcelto saturation.The dew point of a subsaturated air parcelis alwayslower than its actualtemperature(Figure 15.10).The two becomeequalonly whenthe relative humidity reaches100%. 15.3.2 Adiabatic Cooling Thethennodynamicbehaviorof a rising moist air parcelcanbe examinedin two steps:the coolingof the air parcel from its initial condition to saturationfollowed by the cooling of thesaturatedair. Let us considerfirst a moist unsaturatedair parcel.Assumingthat the rise is adiabatic (no heat exchangewith its surroundings)and reversible,then it will also be isentropic. Recallthat for a reversibleprocessd Q = T dS andthereforewhen d Q = 0, dS = 0 also. Undertheseconditionswe haveshownin Chapter14 that if the air parcelis dry (no water vapor),its temperaturewill vary linearly with height accordingto (14.6), dT dz

=-r

(15.44)

wherer = g/cp = 9.76°C km-1 is the dry adiabaticlapserate. If the air is moist, then, as we saw in Chapter 14, the heat capacity of the air parcel cp must be corrected.The changesare small as the water vapor massfraction is usually less than 3%. Even at this ratherextremecondition, the lapserate of the moist parcelis 9.71°C km -I, an essentially

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The lifting condensation level hLcL is shown in Figure 15.11 as a function of the initial temperature and relative humidity of the air parcel. If the air parcel is lifted beyond the LCL, water will start condensing on the available particles, and latent heat of condensation ( - ~ H v) will be released. The lapse rate r s in this casecan 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 the air parcel and the condensation latent heat released. If the air parcel contains a water vapor mass mixing ratio Wvs(the subscript s is used to denote saturation of the atmosphere with water), where Wvs= Mwpo/ MaPa, then the energychangedue to cooling will be cpdT (c p is the heat capacity of air, which will be almost equal to the heat capacity of the air parcel including the water), the latent heat released will be ~Hv dwvs, and the expansion work is vdp = RTdpa/PaMa. Therefore the energy balance is

+ .1.Hvdwvs - RT - dpa = 0

A Cp dT

(15.50)

PaMa

anddividing by dz leadsto the expression

r S--

( dz ) =~~--~~ dz -~

A

Cp

4000

E

I

I

I

I

'

(15.51)

A

MaPacp dz

I

I

I

'

I

I

3500

RH=O.2 ~ >

3000

Q) ~

c: 0 :0= C

1/1

2500

2000

c: Q) "0 §

1500

u

~ :0=

1000

:J 500

0

I

0

I

5

I

I

I

I

I

I

10 15 20 Temperature. °c

I

I

25

I

.

30

FIGURE 15.11 Lifting condensationlevel as a function of initial temperatureand relative humidity of the air parcelassumingthat the air parcelstartsinitially at the groundat p = I atm.

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15.3.4 A Simplified Mathematical Description of Cloud Formation Let us revisit the rising moist air parcel assumingthat we are in a Lagrangianreference frame,moving with the air parcel.The air parcelis characterizedby its temperatureT, watervapormixing ratio wv, liquid water mixing ratio wL, andvelocity W.At the sametime weneedto know the temperatureT', pressurep, and water vapor saturationw~of the air aroundit (Figure 15.12).The pressureof the air parcel is assumedto be equalto its environment. Let us assumethat the air parcel has massm and air density p (without including the liquid water).The velocity of the air parcel will be the result of buoyancyforces and the gravitationalforce dueto liquid water.The buoyancyforce is proportionalto the volumeof theair parcel,m/ p, and the densitydifferencebetweenthe air parceland its surroundings, pi - p. The liquid water massis mWLand the correspondinggravitationalforce gmwL. Theequationfor conservationof momentumis -d (mW) = gm p'-p

p

dt

-WL

(15.56)

wherep' is the densityof the surroundingair. As the air parcel is moving, it causesthe accelerationof surroundingairmasses,resulting in a deceleratingforce on the air parcel.The decelerationforce is proportionalto the massof the displacedair, m', and the correspondingdeceleration,-dW/dt. Pruppacher andKlett (1980) show that this effect is actually equivalentto an accelerationof an "induced"mass m/2 and thereforea term -!m dW /dt shouldbe addedon the right-hand sideof (15.56). Using the ideal gas law (p' - p)/ p = (T - T')/T' and the modified (15.56)canbe rewritten as

3dW

Wdm

--+--=g 2 dt

m dt

T-T' T'

-WL

(15.57)

(Z9.~I)

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(Ulp + UI)(7mp + 7m + limp + 11m)= Ulp ~m + (7m + IIm)UI

-UM P!nb!I

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~

GROWTH RATE OF INDIVIDUAL CLOUD DROPLETS 801

and

15.4 GROWTH RATE OF INDIVWUAL CLOUD DROPLETS Whencloud and fog dropletshavediameterssignificantly larger than 1,um,masstransfer of water to a droplet can be expressedby the masstransfer equationfor the continuum regime(seeChapter11) dm ~

= 21fDpDv(cw.oo-

c~)

(15.64)

by

Dv--~ p

(.!.273 )

D'v---

.94

(15.65)

Dv 2D.,.

.

)

'~

+acDp

RT

,7:0 1/2

(15.66)

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{UUll~q}

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GROWTH RATE OF INDIVIDUAL CLOUD DROPLETS 803

droplet surface is then

(15.68) where we have used the mass balance dm

(15.69)

dt and we have defined

(15.70) For atmosphericcloud dropletgrowth 8 « I; however,let us continuethe dervationwithout assumingthat Ta = T~.Combining(15.64)and(15.69)andusingthe ideal gaslaw, we find that Pw(Dp. Ta)

dDp -- 4D~M~) DP-"dt

PwRT

Sv.oo

pO(Too)

(15.71)

whereSv.oo = Pwoo/po (Too) is the environmental saturation ratio. Recall that for a relative humidity 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 Ta and Toois given by the Clausius-Clapeyron equation as pO(Ta)

(15.72)

pO(Too)

Combining(15.68),(15.71),(15.38),and (15.72)we finally get dDp

DP&-

-

4D~Mwp~

Sv,oo

PwRToo

(15.73)

4MwO"w

+ RTpwDp(l

+ ~qt qt!M f.t!:>OI~A tJelpdn ~qt u°!1gnb~ ~AOqg ~qt U! ~:>gId~l PIno:> ~uO 'UO!tgSU~puo:>l~tgM f.q P~Sg~l:>~PS! pug f.t!:>OI -~A tJglpdn ~qt qt!M f.Im~u!I S~!l11AUO!tglmgS ~qt 'UO!tgSU~pUO:> JO ~:>U~sqg~qt U! tgqt SIg~A -~l uo!1gnb~ ~AOqg ~ql. 'spnoI:> U! 10'0;;::; liS Sg '1 ;;::;liS + 1 tgqt p~wnssg ~Agq ~M ~l~qM

S:>ISAHd anol:>

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CLOUD CONDENSATIONNUCLEI

809

TABLE 15.3 Updraft Velocities and Maximum Supersaturations for Clouds and Fogs

0.25--0.7 0.3--0.8 Stratiform Fog

'" 0-

~O.O5 ~O.l

Pruppacher and Klett (1980) Pruppacher and Klett (1980) Mason (1971) Pruppacher and Klett (1980) Pandis and Seinfe1d (1989)

15.6 CLOUD CONDENSATION NUCLEI Supersaturations of several hundred percent are necessary for the fonnation of water droplets in particle free air (see Chapter 10). The need for such high supersaturations indicatesthe necessity of particles for cloud fonnation in the ambient atmosphere. The ability of a given particle to serve as a nucleus for water droplet fonnation, as we have seen in the previous sections, will depend on its size, chemical composition, and the local supersaturation. 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 as condensation 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 CN concentration is equal to the total aerosol number concentration. This CN definition should be contrasted with the CCN definition where supersaturations often well less than 2% are used.Therefore CCN represent the particles that can fonD cloud droplets under reasonable atmospheric supersaturations. We caution the reader that CCN concentrations always refer to a specific supersaturation, for example, CCN(I%) or CCN(0.5%) and one should be careful when comparing CCN concentrations measured or estimated at different supersaturations. The CCN concentration of a given supersaturation corresponds under ideal cloud formation conditions (e.g., spatial unifonnity) to the number concentrations of droplets if the cloud had the same supersaturation. We will use the symbol CCN(s) for CCN at s% supersaturation. 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) = roo JDs

n(Dp) dDp

(15.85)

where n(Dp) is the number distribution of the aerosol population, and Ds the activation diameter for s% supersaturation of these particles. Note that CN = CCN(oo) according to the above notation. Therefore, if all particles had the same composition, one ne~dsto know only the activation diameter and the size distribution of these particles to estimate the cor-

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c = 600 and k = for continental air. Hegg and Hobbs (1992) reviewed more recent measurements of marine CCN and suggested values of c = 200 and k = 4. Other values for c and k based on ambient measurements are given in Table 15.4. As expected, because of the variability of the aerosol size/composition both spatially and with time, the parameters c and k vary significantly, making the use of such empirical relationships rather questionable. Generally, CCN(1 %) concentrations in maritime and modified maritime airmasses are around 100 cm-3, while concentrations in excessof 1000 cm-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 the oceansthis fraction is roughly 0.5 (Hegg and Hobbs, 1992), but it does vary from 0.2 to 0.6. For polluted conditions the fraction is much lower, usually less than 1%. This is mainly due to the existence of thousands of ultrafine particles (less than 50 nm) that cannot get activated at this supersaturation regardless of their chemical composition. Since ambient supersaturations rarely exceed 1%, the above CCN measurementsindicate that cloud droplet concentrations should range from 200 to 1000 cm-3 over continents and from 10 to 200 cm-3 over oceans. These values agree well with the drop concenti:alions found in continental and maritime clouds. The link between aerosol chemical composition and CCN behavior is still not completely understood. Whereas behavior of soluble inorganic aerosols is relatively well established, much less is known about the ability of organic aerosols (alone or mixed with inorganic components) to serve as CCN. A series of studies have reported the activation efficiency of particles generated during fuel combustion. These results were summarized by Lammel and Novakov (1995) and are

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TABLE 15.4 Empirical Parameters for the CCN Concentration Dependenceon the Supersaturation s

0.3 0.5-0.6 0.5 0.8 1.3-1.4 0.4-0.9 0.4 0.5 0.4,-0.6 1.0 0.3 0.4 0.5 0.4 0.9 Source: Hegg and Hobbs(1992).

Maritime (Australia) Maui (Hawaii) Atlantic, Pacific Oceans Pacific North Atlantic North Atlantic Arctic Cape Grim (Australia) North Atlantic North Pacific North Pacific Polluted North Pacific Equatorial Pacific Continental Continental (Australia) Continental (Buffalo, NY)

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Finally,thereare other processesthat cwoccur aroundcloudsthat may leadto the formationof new particles. 15.7.1 Nucleation Scavengingof Aerosolsby Clouds Nucleationscavengingof aerosolsin cloudsrefersto activationand subsequentgrowth of a fractionof the aerosolpopulationto cloud droplets.This processis describedby (15.74) andhasbeendiscussedin Section15.5. If Ci,ois the concentration(in massper volume of air) of an aerosolspeciesin clearair beforecloud formation (e.g., at the cloud base),and Ci,cloudand Ci.intare its concentrationsagainin massper volumeof air in the aqueousphaseandin the interstitial aerosol,respectively,one can definethe cloud massscavengingratio for speciesi, Fi' as

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where No is the aerosol number concentration before cloud formation and NiDIis the number concentration of interstitial aerosol. Theoretically, as particles larger than 0.5 .urn or so become cloud droplets in a typical cloud and these particles represent most of the aerosol mass, one would expect mass activation efficiencies close to unity. Junge (1963) predicted sulfate scavenging ratios from nucleation scavenging alone to range from 0.5 to 1.0. Since then all theoretical studies have predicted high mass nucleation scavenging efficiencies for all aerosol species. For example, Flossmann et al. (1985, 1987) reported calculated aerosol scavenging efficiencies exceeding 0.9 in typical cloud environments. Pandis et al. (1990a) estimated scavenging efficiencies of 0.7 for sulfate and 0.8 for nitrate and ammonia in polluted clouds. In other numerical studies, Flossmann (1991) reported mass scavenging efficiencies of 0.9 or higher for warm clouds over the Atlantic. These theoretical estimates are in good agreement with the high mass scavenging efficiencies measured in the atmosphere. Ten Brink et al. (1987) observed nearly complete scavenging of aerosol sulfate in clouds. The data of Daum et al. (1984) also showed that the bulk of the sulfate mass is incorporated into cloud droplets. Hegg and Hobbs (1988) reported scavenging ratios for sulfate of 0.5 :i: 0.2. On the contrary, low number scavenging efficiencies are expected in clouds influenced by anthropogenic sources becauseof the prevalence of fine aerosol particles; number scavenging efficiencies of a few percent or less are expected in most such situations. Only in clouds in the remote marine atmosphere does the total number scavenging efficiency exceed 0.1.

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During cloud formation, aerosols that serve as cloud condensation nuclei (CCN) become activated and grow freely by vapor diffusion. Soluble gases such as nitric acid, ammonia, and sulfur dioxide dissolve into the droplets. The cloudwater serves as the reacting medium for a series of aqueous-phase reactions, most importantly the transformation of dissolved SO2, S(IV), to sulfate, S(VI). The sulfate formed is not volatile and remains in the particulate phase. Other reactions, for example, the oxidation of formaldehyde to formic acid, result in volatile products that return to the gas phase (Figure 15.20). During the cloud evaporation stage, several species that were dissolved in the cloudwater evaporate.Others, like sulfate, remain in the aerosol phase. Ammonia often accompanies the sulfate formed as the neutralizing cation. Species like nitrate or chloride that may have existed in the original particle can be displaced by the sulfate produced and forced to return to the gasphase.The result of these aqueous-phaseprocessesis usually an overall increase in particle mass and size. Chemical composition of the particles may also change, with sulfate and ammonium concentrations generally increasing and nitrate and chloride decreasing (Pandiset al., 1990b). Available evidence suggeststhat the single most important reaction during aerosol processingby clouds is the oxidation ofHSOj"" by H202. This reaction, as we saw in Chapter

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during a 3 day springtime period, chemical reactions in clouds occupying I to 2% of the tropospheric volume were responsible for sulfate production comparable to the gas-phase reactions throughout the entire tropospheric volume under consideration. McHenry and Dennis (1994) proposed that annually more than 60% of the ambient sulfate in central and eastern United States is produced in mostly nonprecipitating clouds. Similar conclusions were 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 for the 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 been demonstrated 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 airmass is advected off North America to the Atlantic and the Pacific Oceans. Note that the two modes observed in the number distribution should not be confused with modes of the mass distribution. Hoppel et al. (1986) proposed that cloud processing of aerosol is an efficient mechanism for accumulating mass in the 0.08 to 0.5 j),m size range in the marine

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Radius, ~m FIGURE 15.23 Typical remotemarineaerosolsizedistributions.Reprintedfrom Atmos.Environ., 24A, Hoppel,W. A. andFrick, G. M., 645-649, Copyright 199O,with kind permissionfrom Elsevier ScienceLtd., The Boulevard,Langford Lane, Kidlington OX5 1GB, UK.

(aerodynamic diameter around 0.7 J1,m).These two submicrometer mass distribution modes 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 et al. (1990) proposed that the larger mode could be the result of aqueous-phasechemical reactions. Meng and Seinfeld (1994) showed that growth of condensation mode particles by accretion of water vapor or by gas-phase or aerosol-phase sulfate production cannot explain existence of the droplet mode. Activation of condensation mode particles, formation of cloud/fog drops, followed by aqueous-phase chemistry, and droplet evaporation were shown to be a plausible mechanism for formation of the aerosol droplet mode. Simulations of the aerosol-cloud-aerosol cycle have shown that sulfate formed during cloud/fog processing of an airmass favors aerosol particles that have accessto most of the cloud liquid water content, which are those with diameters in the 0.5 to 1.0 J1,mrange (Pandis et al., 1990a). Figure 15.24 depicts simulation of fog processing of an urban aerosolpopulation. Note that the shape of the aerosol distribution changes with the creation of an extra mode, resulting mainly from the formation of (NH4)2S04. Note also that there are significant changes in the aerosol chemical composition before and after the fog with sulfates 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 interstitial air. The coagulation theory of Chapter 12 can be used to quantify the rate and effects of such removal. If n(Dp, t) is the aerosol number distribution and nd(Dp, t) the droplet

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OTHER FORMS OF WATERIN 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

4x 1.6 x 1.1 x 2.2 x 1.03 x 3x

0-5 0-6 0-7 0-8 0-9 0-10

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. Nuclei smaller than 10 nm will be scavenged in a few minutes by such a cloud whereas particles larger 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 (on the 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 total number may be reduced significantly, and the shape of the aerosol number distribution may change drastically. However, these particles contain little of the mass and therefore the mass distribution effectively will not change. These qualitative conclusions are in agreement 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 aerosol number 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) suggested that observed high aerosol number concentrations near clouds could be a result of shattering of rapidly evaporating droplets. Hudson and Frisbie (1991) suggestedthat these high 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 scattering of solar radiation could lead to high OH concentrations, rapid H2SO4 formation, and subsequentnucleation of new H2SO4-H2O particles. Kerminen and Wexler (1994) estimated a high nucleation probability associated with high relative humidity areas around clouds in relatively clean environments. Note that such a nucleation process in the vicinity of the clouds produces very little aerosol mass but a large number of particles and may influence significantly 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 tropospheric clouds. Water in the atmosphere can also exist as ice, rain, snow, and so on. We summarize here aspects of the formation and removal of these water forms that are most associated

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~Hm

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FIGURE 15.27 Schematicof the flow arounda falling drop. The dashedlines are the trajectories of small dropsconsideredas masspoints.Trajectory a is a grazingtrajectory,while b is a collision trajectory.

The collision processis illustratedin Figure 15.27for viscousflow arounda sphereof diameterDp. As the large droplet approachessmall drops of diameter dp, the viscous forcesexertedby the flow field aroundthe large droplet push the dropletsaway from the centerof flow, modifying their trajectories.In Figure 15.27droplet b is collectedby the raindropwhile droplet a is not. Thereforethe falling raindropwill in generalcollect fewer dropsthan thoseexisting in the cylinder of diameter Dp below it. Dropletsin the cylinder of diametery will be collected.The distancey is definedby the grazingtrajectory a and is a function of the raindrop size Dp and drop size dp. One definesthe collision efficiency E asthe ratio of the actualcollision crosssectionto the geometriccrosssection,or

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=

Raindrop Distributions A number of empirical formulas have been proposedfor the raindropspectrum.The distribution proposedby Best is often usedto describethe fraction of rainwatercomprisedof raindropssmallerthan Do, F{Do):

F(Dp) = 1 - exp[ -

2.25

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where n(Dp) mm-l, and

1/1

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REFERENCES837 Hegg,D. A., and Hobbs,P.V. (1992)Cloud condensationnuclei in the marineatmosphere:a review, in Nucleation and Atmospheric Aerosols, edited by N. Fukuta and P. E. Wagner. Deepak Publishing,Hampton,VA, pp. 181-192. Hering,S. V., andFriedlander,S. K. (1982)Origins of aerosolsulfur distributionsin the Los Angeles basin,Atmos.Environ., 16,2647-2656. Heymsfield, A. J. (1993) Microphysical structures of stratiform and cirrus clouds, in Aerosol-Cloud-Climate Interactions, edited by P. V. Hobbs, Academic Press, San Diego, pp.97-121. Hobbs,P.V., Bowdle, D. A., andRadke,L. F. (1985)Particlesin the lower troposphereover the high plains of the United States,1. Size distributions,elementalcompositionsand morphologies,J. Climat.Appl. Meteorol.,24, 1344-1356. Hobbs,P.V. (1995)Aeroso1-c1oud interactions,in Aerosol-Cloud-ClimateInteractions,editedby P. V. Hobbs.AcademicPress,SanDiego, CA, pp. 33-73. Hoppel,W. A., Frick, G. M., and Larson, R.E. (1986) Effects of non-precipitatingclouds on the aerosolsizedistribution in the marineboundarylayer, Geophys.Res.Lett., 13, 125-128. Hoppel,W. A., andFrick, G. M. (1990) Submicronaerosolsizedistributionsmeasuredover the tropical and southPacific,Atmos.Environ.,24A, 645-659. HoughtonH. G. (1985)PhysicalMeterology,MIT Press,Cambridge,MA. Hudson,J. G., and Clark, A. D. (1992)Aerosol and cloud condensationnuclei measurements in the Kuwait plume,J. Geophys.Res.,97, 14533-14536. Hudson,J. G., and Frisbie, P. R. (1991) Cloud condensationnuclei nearmarinestratus,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.,andCanelli, E. (1991)A studyof heterogeneous oxidationof SO2 in summerclouds, J. Geophys.Res.,96, 8789-8805. John,W., Wall, S. M., Ondo, J. L., andWinklmayr, W. (1990) Modes in the size distributionsof atmosphericinorganicaerosol,Atmos.Environ., 24A,2349-2359. Junge,C. E. (1963)Air Chemistryand Radioactivity.AcademicPress,New York. Karamachandani, P., and Venkatram,A. (1992) The role of non-precipitating clouds in producing ambientsulfateduring summer-results from simulationwith the Acid Depositionand Oxidant Model (ADOM), Atmos.Environ.,26, 1041-1052. Kelly, T. J., Schwartz,S. E., and Daum,P.H. (1989)Detectionof acid producingreactionsin natural clouds,Atmos.Environ., 23,569-583. Kerrninen,V. M., and Wexler,A. S. (1994) Post-fog nucleationof H2SO4-H2O particlesin smog, Atmos.Environ., 28, 2399-2406. Kohler, H. (1921)Zur KondensationdesWasserdampfe in der Atmosphiire,Geofys.Publ., 2,3-15. Kohler, H. (1926) Zur Thermodynamic der Kondensation an hygroskopischenKernen und Bemerkungeniiber dasZusammenfliessen der Tropfen,Medd.Met. Hyd1:Anst. Stockholm,3 (8). Lamme1,G., andNovakov,T. (1995)Waternucleationpropertiesof carbonblack anddieselsootparticles,Atmos.Environ., 29,817-823. Langner,J., and Rodhe,H. (1991)A global three-dimensionalmodel of the troposphericsulfur cycle, J. Atmos.Chem.,13,225-263. Leaitch,W. R., Strapp,J. W., Isaac,G. A., and Hudson,J. G. (1986) Cloud droplet nucleationand scavengingof aerosolsulphatein polluted atmospheres, Tellus,38B, 328-344. Lee, I. Y., and Pruppacher,H. R. (1977)A comparativestudy of the growth of cloud dropsby condensationusing an air parcel model with and without entrainmentPure Appl. Geophys.,115, 523-545.

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PROBLEMS 839 Saxena,V. K., and Hendler,A. H. (1983) In-cloud scavengingand resuspensionof cloud active aerosolsduring winter stormsover Lake Michigan, in Precipitation Scavenging,Dry Deposition andResuspension, editedby H. R. Pruppacher,R. G. Semonin,andW. G. N. Slinn. Elsevier,New York, pp. 91-102. Sekhon,R. S., andSrivastava,R. C. (1971)Dopplerobservationsof drop sizedistributionsin a thunderstorm,J. Atmos.Sci, 28, 983-994. Squires,P.(1958)The microstructureand colloidal stability of warm clouds,Tel/us,10, 256-261. Swozdziak,J. W., and Swozdziak,A. B. (1992) Sulfate aerosolproduction in the SudetyRange, Poland,J. AerosolSci., S369-S372. TenBrink, H. M., Schwartz,S. E., and Daum,P.H. (1987) Efficient scavengingof aerosolsulfateby liquid water clouds,Atmos.Environ, 21, 2035-2052. Twomey,S. (1959) The nuclei of natural clouds formation. Part II: The supersaturationin natural cloudsand the variation of cloud droplet concentration,Geofis.Pura Appl., 43,243-249. Twomey,S., and Wojciechowski,T. A. (1969) Observationsof the geographicalvariation of cloud nuclei,J. Atmos.Sci., 26, 684-688. UnitedStatesNational Acid PrecipitationAssessmentProgram(1991) Acidic Deposition: Stateof Scienceand Technology,Vol.I Emissions,AtmosphericProcessesand Deposition,editedby P.M. Irving. U.S. GovernmentPrinting Office, Washington,DC. Walcek,C. J., Stockwell,W. R., and Chang,J. S. (1990)Theoreticalestimatesof the dynamicradiative andchemicaleffectsof cloudson troposphericgases,Atmos.Res,25,53-69. Wall,S. M., John,W., and Ondo,J. L. (1988) Measurementsof aerosolsize distributionsfor nitrate andmajor ionic species,Atmos.Environ, 22, 1649-1659. Warner,J. (1968)The supersaturationin naturalclouds,J. Appl. Meteorol.,7, 233-237. Whelpdale,D. M., and List, R. (1971)The coalescenceprocessin droplet growth, J. Geophys.Res, 76,2836-2856.

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Atmospheric Chemistry and Physics

Atmospheric thermodynamics: elementary physics and chemistry

Atmospheric Thermodynamics: Elementary Physics and Chemistry

Atmospheric Thermodynamics: Elementary Physics and Chemistry

ATMOSPHERIC THERMODYNAMICS - Elementary Physics and Chemistry