Aviation-Produced Aerosols and ContrailsBerndKaercher/SG20_113-167_1999.pdf · AVIATION-PRODUCED...

AVIATION-PRODUCED AEROSOLS AND CONTRAILS

B. KÄRCHERDeutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, D-82 234

Wessling, Germany

Abstract. Liquid and solid particles in the plumes of jet aircraft cruising in the upper troposphere andlower stratosphere lead to the formation of ice clouds (contrails), modify the microphysical propertiesof existing cirrus clouds, and provide sites for heterogeneous chemical reactions. Characterization ofaviation-produced particles in terms of physico-chemical properties is an important step in assess-ing the global impact of aircraft emissions upon atmospheric chemistry and climate parameters.Chemistry and microphysics of the gas-aerosol system in aircraft plumes and its evolution in theatmosphere is a field of intense research. This paper reviews the current knowledge (mid-1998) andoutlines possible atmospheric implications.

Key words: Aircraft wake, binary nucleation, chemical conversion, cirrus, coating, contrails,freezing, mixing, soot

Abbreviations: CI – chemi-ion; CN – condensation nuclei; EI – emission index; FSC – fuel sulfurcontent; IN – ice forming nuclei; VNM – volatile nucleation mode

1. Introduction

Environmental concerns about the impact of aviation on the atmosphere were ini-tially raised by the predictions of possible reductions in stratospheric ozone thatwould result from the emissions of nitrogen oxides (NOx) from a future fleet ofsupersonic aircraft (Crutzen, 1971; Johnston, 1971). The impact of stratosphericaircraft emissions on global ozone was assessed in the Climatic Impact AssessmentProgram (CIAP), funded by the US Department of Transportation (CIAP, 1975).With aviation among the fastest growing economic sectors, a renewed interest hasarisen in the development of a larger fleet of commercial supersonic aircraft. Be-cause environmental impacts are still of concern, this interest has lead to severalinternational research and assessment programs in this decade (World Meteorolo-gical Organization, 1995; Albritton et al., 1997; Fabian and Kärcher, 1997; Chaninet al., 1997; Brasseur et al., 1998; Kawa et al., 1998). A comprehensive assessmentof the effects of both supersonic and subsonic aviation is currently being preparedunder the auspices of the Intergovernmental Panel on Climate Change (IPCC).

Cruise altitudes of present as well as future supersonic aircraft are in the lowerstratosphere in the altitude range of 16–22 km. Subsonic aircraft fly both in theupper troposphere and in the lower stratosphere at altitudes near the tropopausebetween 9 and 14 km. Aircraft flight altitudes, emissions, and the atmospheric

Surveys in Geophysics20: 113–167, 1999.© 1999Kluwer Academic Publishers. Printed in the Netherlands.

114 B. KÄRCHER

Troposphere

Stratosphere 16-22 kmOzone Depletion

Ozone ProductionCirrus Cloud Formation

Tropopause

Region

Aircraft EmissionsCO2,H2O,CO,UHC,NOx,SOx,soot,chemi-ions

Contrail and 9-14 km

Figure 1.Schematic portraying the region of the Earth’s atmosphere which is influenced by aviationemissions. Cruise altitudes of today’s commercial aircraft fleet (9–14 km) and of planned supersonicaircraft (16–22 km) are indicated. The thick line marks the tropopause, separating the tropospherefrom the stratosphere. Aircraft pollutants can be mixed by small-scale exchange (round arrow) orare transported in folding events (indicated by the gap between the thick lines) across the tropo-pause. Aircraft constitute a direct emission source of chemically and radiatively active gases andparticulates, causing changes of radiative properties and chemical composition. Emissions of thegreenhouse gas CO2 directly contribute to global warming. Emissions of nitrogen oxides (NOx), inconcert with carbon monoxide (CO) and unburned hydrocarbons (UHC), lead to ozone productionin the troposphere and ozone destruction in the lower stratosphere. Together with emitted watervapor (H2O) and chemi-ions (CIs) produced during fuel combustion, oxidation of reactive sulfur(S) species (SOx) in the plume near-field leads to the formation of new liquid particles, which mayincrease the background aerosol surface area and thereby affect heterogeneous chemistry, especiallyabove the tropopause. Particulate emissions lead to contrails, which, like cirrus clouds, affect theEarth’s radiative balance. Aerosol processing in contrails may facilitate subsequent ice formation.Even without contrail formation, exhaust particles, especially soot, may produce artificial cirrus (ice)clouds in the tropopause region and upper troposphere.

effects of emissions are shown together in Figure 1. The contribution of aircraftemissions to the budgets of nitrogen or sulfur (S) species is small in comparisonto global surface emissions from human activities and natural sources. Aircraftemissions are in general more effective than surface emissions because aircraftemissions occur directly in the upper atmosphere, bypassing the lower atmospherewhere a variety of processes remove emissions from the atmosphere. As a result,the residence times of gases and particles at flight altitudes are much longer (bya factor>10) than in the planetary boundary layer. Except for the production ofNOx by lightning and decomposition of nitrous oxide (N2O), aircraft are the onlyin situ emission source of the species noted in Figure 1 in the upper troposphereand lower stratosphere. Thus, the accumulation of aircraft emissions in regionssuch as the midlatitude upper troposphere and lower stratosphere in the Northern

AVIATION-PRODUCED AEROSOLS AND CONTRAILS 115

Hemisphere, may lead to abundances of aircraft NOx and induced aerosol particlesurface areas which may exceed background values.

The potential effects of aircraft emissions include ozone depletion in the stra-tosphere, ozone production in the troposphere, contrail formation, and changesin cirrus cloud formation (Figure 1). The emissions of NOx, water vapor (H2O),and aerosol particles all participate in the photochemistry of ozone in both theupper troposphere and lower stratosphere. In the decades since CIAP, atmosphericand laboratory research has shown that the chemical effects of aircraft emissionsare more complex than initially thought. Specifically, knowledge of the reactionkinetics involving the NOx, hydrogen (HOx), chlorine (ClOx), and bromine (BrOx)families has grown substantially to include heterogeneous reactions on sulfate aer-osols and polar stratospheric cloud particles. Heterogeneous reactions underly thelate winter ozone depletion in the stratosphere of the Antarctic and Arctic regions(e.g., Portmann et al., 1996; Müller et al., 1997), and the declining ozone levels inthe lower stratosphere at northern midlatitudes (e.g., Bojkov and Fioletov, 1997).Together with emitted water vapor and chemi-ions (CIs) produced during fuelcombustion, oxidation of reactive sulfur species in the plume near-field leads tothe formation of new liquid particles, which may increase the background aerosolsurface area. Modeled changes in global ozone from a supersonic aircraft fleetare sensitive to the number of sulfate aerosol particles produced in the jet regionof the plume and their accumulation in the background atmosphere (Weisensteinet al., 1996). In addition, laboratory and modeling studies indicated that exhaustsoot particles may affect air composition (Lary et al., 1997) and be important inproviding nuclei for liquid or ice particles.

The emission of water vapor leads to the formation of contrails in certain airmasses. These contrails often persist and evolve into larger cirrus cloud clusters.In addition, aviation-induced aerosols also accumulate in the background atmo-sphere. Cirrus clouds and aerosols are important players in the climate systembecause they change the radiative balance of the atmosphere (e.g., Crutzen andRamanathan, 1996; Cox et al., 1997). Particles emitted by aircraft jet engines orproduced in the exhaust plumes may act as additional cloud condensation nuclei(CCN) or ice forming nuclei (IN) some time after passage of the aircraft. Thus,clouds may form where they otherwise would not have because more CCN arepresent (Jensen and Toon, 1997). The resulting perturbations of the occurrencefrequency and microphysical and optical properties of natural cirrus clouds likelycause changes in regional and global radiative forcing and the chemical processingof cloud particles.

Before the chemical and radiative impact of aircraft-indued aerosols can beaddressed adequately, a more complete understanding of their formation, chemicalcomposition, chemical activation of their surfaces, and their nucleation and freez-ing properties is required. Since the formation of new aerosols evolves on temporaland spatial scales too small to be resolved in global models of the atmosphere,properly assessing aerosol effects requires models describing the strongly interde-

116 B. KÄRCHER

pendent microphysical, chemical, and dynamic wake processes which form andmodify aviation aerosols. This work addresses the emission, formation, and evolu-tion of particles in the plumes of subsonic and supersonic jet aircraft under cruisingconditions, with an emphasis on presenting an overview about basic concepts andresults.

The remainder of this paper is divided into sections. Section 2 provides anoverview of the fluid-dynamical, chemical, and microphysical processes in thenear-field of an aircraft exhaust plume and wake; introduces the mathematical toolsnecessary to describe these processes; and includes a brief tutorial covering the mi-crophysical processes relevant to this work. Section 3 outlines the evolution of theflow field properties relevant for exhaust plume chemistry and particle formation.Section 4 discusses the formation of aerosol precursors in the young jet plume.Section 5 presents an overview of the different aerosol types present in wakesof cruising aircraft and discusses the physico-chemical processes involving theseparticles. Section 6 explains how new liquid particles are formed in the plume.Section 7 describes the emissions of non-volatile combustion aerosols (black car-bon soot) and metal particles. Section 8 reviews how contrails form and describestheir microphysical properties. Section 9 addresses how aviation-induced particlesmay perturb chemistry and cloud formation. Section 10 concludes this article. Ap-pendices A to E give useful background information and contain mathematicalderivations not included in the main text.

2. Description of Dynamical, Chemical, and Microphysical Processes

2.1. JET FLOW FIELD MODELS

Exhaust gases from aircraft are introduced into the atmosphere in the form of co-flowing jets. The turbulent expansion of a sub- or supersonic jet of hot exhaustgases is characterized by a symmetrical growth of its width along the jet axis, ac-companied by a rapid relaxation of the axial velocityu and (static) temperatureT .Especially for subsonic jets, the mixing with the background air evolves at nearlyconstant atmospheric pressurep.

In a frame of reference moving with the aircraft, the hydrodynamic conservationlaws of mean momentum, energy, and mixing ratioχ of any trace species in theexhaust for the two-dimensional turbulent jet mixing problem take the general form(e.g., Pai, 1954):

∂ϕu = ∂ψ(F · ∂ψu

)+ E F

%∂ψρ · ∂ψu (1)

∂ϕT = 1

Pr∂ψ(F · ∂ψT

)+ 1

cpF(∂ψu

)2(2)


∂ϕχ = Le

P r∂ψ(F · ∂ψχ

) + 1

εu

[(∂tχ)chm+ (∂tχ)mic

]. (3)

In these equations,cp is the specific heat of air at constant pressure,% ∝ 1/T isthe mass density of air,ε is a (semi-empirical) exchange coefficient for momentumat the given axial location andE ≥ 1 is a constant parameter,Pr andLe arethe turbulent Prandtl and Lewis numbers, andF = F (%, y, u). The independentvariablesϕ andψ (the stream function) are linked to the axial directionx of thejet and the radial coordinatey of the jet perpendicular tox, respectively. Theirdefinition contains information about the jet geometry.

The first terms on the right sides of Equations(1)–(3) describe the jet mixingprocess by the parabolic operator∂ψ(F ∂ψ ·), essentially similar to a nonlineardiffusion problem. The second terms are source terms stemming from correlationsbetween turbulent fluctuations of density and velocity (Equation (1)), heating dueto turbulent dissipation of momentum (Equation (2)), and chemical and microphys-ical production or losses (Equation (3)). Each chemical species or aerosol particleconsidered requires an equation of the form of Equation (3) to be solved. The localchemical and microphysical terms do not feed back into the dynamical equationsin this approach. Solutions are discussed in Section 3.

2.2. TRAJECTORY BOX MODELS

The application of box models, often referred to as zero-dimensional, implies thatinformation about the spatial distribution of the dependent variables is lost. Onthe other hand, they are computationally efficient and thus well-suited for processstudies.

Any spatial average of Equation (3) can be shown to lead to an equation of theform (keeping the same notation)

dχ

dt= −ω(t)(χ − χa)+ (∂tχ)chm+ (∂tχ)mic , (4)

whereω represents an entrainment rate carrying the information of the turbulentexchange coefficientε. The subscripta denotes the value ofχ outside the boxin the background atmosphere. The species mixing ratioχ and the chemical andmicrophysical source terms are now interpreted as suitable averages over their re-spective spatial (radial) distributions. The entrainment rate represents the averagemixing history of this region in the flow field, that is, it follows from averaging themomentum balance Equation (1). The evolution of the axial velocity is applied todefine the aget (x) of the plume. Equation 4 must be accompanied by an equationdescribing the evolution of the temperature in the box, substituting the energy bal-ance Equation (2). In Section 3 (Figure 4), a specific definition of a trajectory isexplained in more detail.

118 B. KÄRCHER

2.3. GAS PHASE CHEMICAL MECHANISMS

The term(∂tχ)chm in Equations (3) and (4) describes changes of the species mixingratios due to chemical reactions. It can be cast into the form

M (∂tχ)chm= ∂tn = P − nL, (5)

with the total number density of air moleculesM, the number densities of thespeciesn = Mχ , and the net chemical production and loss ratesP andL inunits cm−3 s−1 and s−1, respectively. For a given number of chemically reactingspecies, Equation (5) describes a set of nonlinear, first-order, stiff ordinary differ-ential equations. The reciprocal of the loss terms are the characteristic chemicalrelaxation times describing how quickly the concentrations approach equilibriumand are a measure for the stiffness of the equations.

The production and loss termsP andL in Equation (5) lead to nonlinear coup-ling among the species. Several groups have developed reaction mechanisms thatlink high temperature chemistry in the nascent exhaust with atmospheric chemistry(Miake-Lye et al., 1993; Kärcher et al., 1996a; Anderson et al., 1996; Wang andChen, 1997; Tremmel et al., 1998). Most of them are mean-field approaches, i.e.,they do not consider that certain chemical reactions can be limited due to finitemixing rates, possibly leading to an overestimation of reaction rates.

Typical applications involve∼ 20 reactants and consider more than 50 indi-vidual kinetic reactions in the gas phase, mainly oxidation reactions of the primaryexhaust species (nitrogen oxides, NOx = NO + NO2, and sulfur oxides, SOx = SO2

+ SO3) mediated by hydrogen oxide (HOx = OH + HO2) radicals and O-atomscreated during fuel combustion.

2.4. AEROSOL MICROPHYSICAL PROCESSES: A BRIEF TUTORIAL

Microphysical production and loss terms add to the chemical changes in Equations(3) and (4):

(∂tχ)mic = (∂tχ)nuc+ (∂tχ)con+ (∂tχ)cog+ (∂tχ)frz , (6)

where the subscripts indicate nucleation (new particle formation), condensation(molecular mass transfer from the vapor phase to the particles), coagulation(particles collide and attach to each other), and freezing (formation of the ice phase)processes.

Atmospheric aerosols are often described in terms of size distributions, givingthe differential number of particles in a given size bin. Therefore, the individualprocesses listed in Equation (6) are formulated for each size bin of each particletype separately. With 3 particle types and sizes discretized into 50 bins, Equation(6) comprises 150 individual equations to be solved.

New particle formation in aircraft plumes is believed to occurvia binary ho-mogeneous nucleation, where liquid phase droplets form by condensation of two


distinct types of molecules from the gas phase in the absence of surfaces thatcould assist the phase transition (McDonald, 1962, 1963). It is generally recognizedthat binary nucleation of sulfuric acid (H2SO4) and H2O is an especially efficientparticle formation process in the atmosphere (Mirabel and Katz, 1974), due mainlyto the extremely low saturation vapor pressure of H2SO4. This holds as well underaircraft plume conditions, where the nucleation process is facilitated by ionizedmolecular clusters emitted by jet engines. Eventually, homogeneous gas-to-particleconversion leads to the formation of ultrafine, volatile particles, or condensationnuclei (CN), by subsequent growth processes.

If the surface of a foreign particle (e.g., soot) does participate in the gas-to-particle conversion process, the nucleation is referred to as heterogeneous. Thefirst elemental step in heterogeneous nucleation involves molecular adsorption,characterized by either weak (physisorption) or strong (chemisorption) bonding.In the presence of H2O, adsorbed molecules can lead to a liquid coating around theparticles. Therefore, heterogeneous nucleation can potentially alter the chemicalsurface reactivity of the soot particles.

Condensation denotes the diffusion and uptake of molecules from the gas phaseby any liquid or solid particle, leading to an increase of the particle mass. It is abasic growth mechanism for atmospheric particles, and is referred to as hetero-molecular if more than one type of molecule is involved. The reverse process iscalled evaporation. Gas phase transport may entirely take place in the free molecu-lar regime (Knudsen limit) described by the kinetic theory of gases, if the size ofthe particle is much smaller than the mean free path` of the vapor molecules. Inthe tropopause region,̀' 0.1–0.3µm, that is, the mass transport is controlledby diffusion for particles larger than this value. Because the typical mean size ofatmospheric aerosols is of the order`, both kinetic and diffusive transport must beconsidered in the treatment of condensation and evaporation.

Coagulation occurs when particles collide and attach to each other, therebyforming larger particles (Fuchs, 1964). The total mass is conserved in a co-agulating aerosol ensemble, but particle numbers are not. Collisions betweenatmospheric particles can be initiated by gravitational settling, turbulence, andthermal (Brownian) motion. Whereas the two former processes are important forlarger (diameterD > 1µm) particles, the latter is mainly responsible for collisionsbetween smaller particles and is especially relevant for aircraft-induced aerosols.Scavenging by coagulation occurs when a small particle collides with a larger one,indicating that this is a true loss for the small particle, that is, it is removed fromits size category and its mass serves to slightly increase the mass of its largercounterpart.

The formation of the ice phase occursvia freezing nucleation (Pruppacher andKlett, 1997). Freezing may take place within a liquid aerosol droplet either homo-geneously, or is initiated by inclusions of insoluble particles (immersion freezing).There also exists a direct gas-to-solid path by H2O vapor deposition onto nuc-leating ice crystals, especially in the presence of particle surfaces that exhibit a

120 B. KÄRCHER

similar crystallographic arrangement of molecules than the H2O molecules in ice.These alternative ways indicate that distinct modes exist to form ice crystals fromatmospheric ice nuclei (IN). In the upper troposphere and lower stratosphere aswell as in aircraft contrails, freezing of dilute solution droplets appears to be ofdominating importance. Ice nucleation occurs in solution droplets containing acidiccomponents that cause a substantial freezing point depression (up to 40 K), that is,the liquid aerosols rest in a highly supercooled state prior to freezing. If coolingrates are sufficiently high, the droplets may become water-rich before they freezewhich acts to reduce the freezing point depression.

Explicit expressions used to describe these microphysical processes in plumeaerosol modeling and the various approaches to derive them are given in the liter-ature (Brown et al., 1996a; Kärcher et al., 1998a; Yu and Turco, 1998a; Gleitsmannand Zellner, 1998). Further general remarks about the formation and the dynam-ics of nanoparticles are given in Appendix B, and Appendix C introduces basicrelations describing condensation in a simplified, single particle approach.

3. Aircraft Plume and Wake Dynamics

The principal features of the plume and wake evolution behind a twin-jet aircraftare delineated in Figure 2 (left side). The exhaust jets emanating from the nozzleexit planes (black) are trapped in the wingtip vortices (grey). During the firstseconds after emission (jet regime), the jet plumes spread up but remain isolated.This stage is characterized by rapid cooling of the exhaust from 400–600 K toatmospheric temperatures (<230 K), and by a concomitant dilution of the exhaustproducts due to isobaric turbulent mixing with background air. The followingvortex regime lasts 2–3 minutes and is terminated by turbulent dissipation. It ischaracterized by slower dilution at nearly constant temperatures (Miake-Lye et al.,1993; Lewellen and Lewellen, 1996; Gerz et al., 1998). Figure 2 (right side) showsa video picture of a contrail taken aboard the DLR research aircraftFALCON andvisualizes the wake structure in the vortex regime.

Wake inhomogeneities induced by turbulence directly translate into pronouncedvariabilities of meteorological parameters and species abundances on temporalscales∼1 s and spatial scales∼1 m (Petzold et al., 1997; Baumgardner et al.,1998). Also, because temperature and mixing evolves differently along the in-dividual streamlines of the flow field, the results of chemical and microphysicalprocesses (which sensitively depend upon these parameters) can differ dependingon the location in the wake (e.g., Lesniewski and Friedlander, 1995). Often, thiscomplicates the evaluation of measured data and comparisons with model results.

Several model approaches exist to simulate the dynamics of aircraft exhaustplumes in the jet regime under atmospheric conditions (e.g., Kärcher, 1994; An-derson et al., 1996; Garnier et al., 1997). Taking a closer look to the (mean-field)dynamical evolution of the jet regime, encompassing a time span of approximately


Figure 2.Schematic of the near-field plume and wake dynamics behind a twin-jet aircraft, coveringthe evolution in the first few minutes after emission (jet and vortex regime, shown on the left handside). The jets (black, only one is drawn) are exhausted by the turbine nozzles and are captured by thedeveloping wingtip vortices (grey). The rotating vortices perform a downward motion (see arrows).The right hand side is a video picture of a contrail visualizing the complex dynamical structure ofthe turbulent wake. Its dynamical microstructure can be resolved in numerical calculations usinglarge-eddy simulation techniques. From Gerz et al. (1998).

10 s after emission, Figure 3 depicts the spatial distribution of the temperature (leftside) and the number density of emitted soot particles (right side) behind the jetengine of a wide-body aircraft. Two-dimensional profiles are shown as a functionof the jet radius and the axial distance past exit, which can be related to the age ofthe jet plume.

Near the nozzle exit plane, the temperature profile is characterized by highvalues in the jet core, and values only slightly higher than in the ambient air inthe bypass region. Turbulent mixing starts cooling the bypass first and reaches thecore region∼10 m past exit. Hereafter, the jet cools very rapidly to atmospherictemperatures, as indicated by the steep decrease of the core profile.

The impact of plume mixing on the distribution of soot particles (as well as ofany other chemically passive tracer) in the flow field reveals similar features. Dilu-tion due to the entrainment of background air starts reducing the number densities10–100 m behind the engine, and the radial gradients are rapidly smoothed out.Because in the simulation, soot is not present in the ambient air drawn into the jetengines, no initial concentration enhancement is seen in the bypass region.

The description of the wake dynamics in the vortex regime is more complexand requires the application of sophisticated simulation tools (e.g., large eddysimulation techniques). In these cases, the numerical studies of chemical andmicrophysical phenomena in two- or three-dimensional flow fields require a con-siderable amount of simulation time and computer resources, especially when theeffects of turbulence on chemical reaction rates are taken into account. The applic-ation of trajectory box models is a viable alternative to perform parametric studiesdue to relatively modest computational efforts.

122 B. KÄRCHER

0.01.0

2.0radial distance (m)

−1.0

0.0

1.0

2.0

log 10 axial dista

nce (m)

300

400

500

tem

pera

ture

(K

)

0.0

2.0

4.0log 10

axial distance (m)

0.01.0

2.03.0

radial distance (m)

10 1

10 2

10 3

10 4

10 5

10 6

soot

num

ber

dens

ity (

cm-3)

Figure 3.Evolution of temperature and number density of emitted soot particles in the jet plume ofa wide-body aircraft (Kärcher et al., 1996a). The variables are plotted as a function of jet radius anddistance after the jet engine’s nozzle exit plane. Background temperature and pressure are set equalto 220 K and 240 hPa.

Figure 4.Simulated entrainment rateω of the plume and wake of a commercial airliner versus timet

after passage of the aircraft without (solid line) and with (dashed line) weak atmospheric turbulence,adapted from Gerz et al. (1998). The rate is based on the maximum value of the concentration of atracer in the flow field. The different flow regimes and the fitα/t (dot-dashed line) are indicated.

Box models contain no information about the spatial distribution of the vari-ables, but allow the inclusion of detailed reaction kinetics. Many results obtainedin the context of aircraft-generated aerosols have been obtained using trajectoriesthat start at the center of the exit plane of a single nozzle and stream along the axisof an isolated jet, thereby increasing the box cross sections by entraining ambientair. The time evolution of the rateω of entrainment of background air into such abox (cf., Section 2.2) is shown in Figure 4.


The trajectory initially follows the evolution of the jet core and takes the rapidcooling and mixing there into account, as indicated by the pronounced maximumof ω at t ' 10 ms. At∼10 s, the box becomes immersed in the developing vortexfield (see also Figure 2, left). Here, further mixing is suppressed, as a consequenceof decreasingω-values shown in Figure 4 between 10–100 s. The reduced mixingresults in a much slower increase of the box dimensions. The action of atmosphericturbulence is mainly to shorten the duration of the vortex regime, compare solid anddashed line. Up to this point, the dynamical evolution of the wake is dominated bythe aircraft. After break up of the organized vortex structure (t ' 130 s), mixing ofambient air with the exhaust is governed by atmospheric diffusion and wind shearat progressively increasing length scales. In Appendix A the entrainment rate isrelated to the overall dilution ratio of the wake.

4. Gaseous Aerosol Precursors

Chemical reactions that take place in the near-field wake set the stage for the sub-sequent chemical evolution up to the global scale. They determine which fractionsof the primary emissions (NOx, SOx) are transformed into higher oxides. Sincesome of these secondary species are potential aerosol-forming species (precursors),they affect ozone indirectlyvia heterogeneous chemical reactions involving theparticles they have formed.

Since this work deals with aviation-produced aerosols, special emphasis is puton gas phase reactions in young jet plumes responsible for the build-up of speciesthat may either lead to new particle formation (such as sulfuric acid, H2SO4, andionized molecular clusters) or may dissolve into liquid particles (such as nitricacid, HNO3). The conversion chemistry is discussed here for subsonic aircraft, butthere is yet no evidence for principle differences between subsonic and supersonicaircraft emissions.

4.1. CHEMISTRY OF HYDROGEN AND OXYGEN RADICALS

The oxidation potential of young aircraft plumes is largely controlled by exhausthydroxyl radicals (OH). The chemical lifetime of OH past emission is determinedby reactions with emitted NOx for exit plane mixing ratios[OH]0 < 10 ppmv, andby OH self-reactions for higher concentrations. Exhaust OH molecules reactingwith emitted CO and SO2 are reformed. The self-reactions lead to the formationof the highly water-soluble species hydrogen peroxide (H2O2). The OH lifetimeranges between 1–5 ms when the[OH]0 is varied between 0.1–100 ppmv fortypical NOx emission indices.In situ observations support OH emissions around1–10 ppmv (Hanisco et al., 1997; Tremmel et al., 1998).

Figure 5 (left) shows the simulated evolution of hydrogen and oxygen radicalspecies in the jet plume center of a commercial airliner versus distancex past exit.

124 B. KÄRCHER

0.0

1.0

2.0radial distance (m)

0.0

2.0

4.0log 10

axial

distan

ce (m

)10 −16

10 −11

10 −6

10 −1

OH

mix

ing

ratio

(pp

mv)

Figure 5. Chemistry of hydrogen and oxygen radicals in the jet plume center of an commercialairliner versus distance past nozzle exit plane (left). Oxidation of primary exhaust products such asNOx and SO2 are mainly driven by the OH and O radicals. The two-dimensional plot of OH (right)visualizes the simultaneous action of plume mixing and chemical depletion. (From Kärcher et al.,1996a).

Forx > 1 m, OH becomes chemically depleted, before entrainment of backgroundair becomes important atx ' 10 m (see Figure 4). Except OH, all other initialspecies concentrations are set equal to zero in the calculation. Radicals directlyproduced by OH (H, O(3P)) are quenched as soon as OH is depleted. The levels oflonger-lived products such as O3 and H2 tend to assume constant values at the endof the jet regime because they are readily governed by entrainment. Forx > 20 m aquasi steady-state between OH and the hydroperoxy radical HO2 develops, whichis determined by the abundance ratio of NO2 and NO in the plume. Compared totypical background levels, high concentrations of H2O2 are built up, indicated bydecreasing values caused by mixing after its formation ceased. On longer times-cales, H2O2 may act as a net HOx sink through heterogeneous removal or slowlyreform OH by photolysis.

Figure 5 (right) depicts the two-dimensional evolution of the OH radical in thejet, similar to Figure 3. In the bulk of the plume, OH mixing ratios are reduced wellbelow the background level. Because turbulent mixing and chemical depletion acton comparable time scales, OH is mixed into the outer jet layers. The particularshape of the radial profile indicates that OH is far from equilibrium at this stage.

It is justified to assume only OH emissions, because simultaneous emission ofother hydrogen or oxygen radicals hardly change the above picture (Kärcher et al.,1996a). There is evidence that part of the described radical chemistry may occurwithin the jet engines, especially in the turbine flow downstream of the combustor.It may happen that OH is already largely depleted at the nozzle exit. However, theprincipal issues as outlined above and the key features of the conversion chemistrydescribed below remain similar.


4.2. CHEMICAL CONVERSION OF NITROGEN AND SULFUR EMISSIONS

The oxidation of (mainly) NO and NO2 leads to the production of nitrous acid(HNO2) and HNO3. Under daylight conditions, HNO2 decomposes within minutesdue to photolysis, but HNO3 represents a photochemically stable reservoir gassequestering part of the primary NOx emissions (Miake-Lye et al., 1993; Kärcheret al., 1996a). Arnold et al. (1992) measured both HNO2 and HNO3 in situ, demon-strating that concentration levels in young plumes can exceed background levels byat least one order of magnitude.

Figure 6 (left) shows the conversion rates of exhaust NOx and SO2 versusemitted OH as a result of the following gas phase reactions that occur in the firsttenths of seconds after emission (M denotes the number density of O2 and/or N2

molecules):

NO+OHM−→ HNO2

NO2+OHM−→ HNO3

OH+OH −→ H2O+O

OH+OHM−→ H2O2

SO2+OHM−→ HSO3

HSO3+O2 −→ HO2+ SO3

SO3+ n · H2OM−→ H2SO4 · (H2O)n−1.

The underlying simulations assume an average NOx emission index; especially theNO2 conversion increases for decreasing EI(NOx). The conversion efficienciesη inFigure 6 are defined as the maximum concentrations the secondary species acquirein the young plume relative to the concentrations of their precursors at emission.Therefore, they also depend on the mixing history of the jet plume. Possible hetero-geneous losses on soot particles are not considered (see Section 7.2 and AppendixD).

As expected, allη-values increase with increasing OH emissions, but do notexceed a few percent for [OH]0 < 10 ppmv, in general agreement with valuesinferred fromin situ observations. The absolute amount of HNO3 produced in theplume also depends on the emission ratio of NO2 to NO, which appears to bevariable in the range from values near zero up to 0.22, according to observations(Schulte et al., 1997). However, HNO3 can also be produced in the absence ofdirect NO2 emissionsvia reactions of NO with O3 and HO2 that yield NO2, withsomewhat less efficiency. Typical conversion efficiencies from OH to H2O2 rangebetween 1–4% (not shown in Figure 6).

Formation of H2SO4 via SO2 and OH is relatively inefficient (η < 1%). Suchlow conversion fractions proved to be insufficient to explain most of the measured

126 B. KÄRCHER

SO2 H2SO4

NO HNO2NO2 HNO3

[OH]0 (ppmv)

η (%

)

104

103

102

101

100

s

102

101

100

101

102

η (%

)

[OH]0=10 ppmv[OH]0= 1 ppmv[OH]0=0.1 ppmv

Figure 6. Simulated conversion efficienciesη of the primary species NO, NO2, and SO2versus emitted OH in the young plume of a commercial airliner (left). The sulfur conver-sion efficiency into H2SO4 when S is emitted in the form of SO2 and SO3 is shown versuss = [SO3]0/([SO2]0 + [SO3]0) on the right side for three values of emitted OH. Simulations areperformed using average S and NOx emissions. (Adapted from Kärcher et al., 1996a; 1998b).

number densities of volatile particles in aircraft wakes (see Section 6.3), revealing abasic discrepancy between models and observations. This picture changes if directemissions of SO3 are allowed (Brown et al., 1996b). The amount[SO3]0 present atthe nozzle exit plane is generated within the jet engines and is intimately linked todetails of the combustion kinetics. Since formation of SO3 is reduced by quench-ing of the reactive flow after the combustion chamber, SO3 emissions depend ondetails of the engine design (Lukachko et al., 1998). Precise knowledge ofs is ofcrucial importance since aerosol formation and growth rates are extremely sensitivefunctions ofη (Brown et al., 1996c; Kärcher and Fahey, 1997).

In Figure 6 (right), sulfur conversion fractions are plotted as a function ofs = [SO3]0/[SOx]0, since direct measurements of SO3 at the engine exit arenot available. For low levels of SO3 (s < 10−2), η shows a pronounced [OH]0

dependence, because SO3 levels produced in the plumevia SO2 + OH are greaterthan, or at least similar to, [SO3]0. Direct emissions of H2SO4 could enhanceη inthis limit. The rate of the SO2 + OH reaction causesη to be bound between 0.1%and 2% for low (dashed line) to very high (dotted line) [OH]0 levels, see Figure 6(left). With increasing amounts of directly emitted SO3 (s > 10−2), η increasesbecause the fast SO3 hydrolysis reaction produces H2SO4 directly, bypassing theslower SO2 + OH reaction and eliminating the dependence on OH.

Sulfur dioxide and oxidized S species including H2SO4 have been detected injet plumes of commercial aircraft (e.g., Arnold et al., 1992; Miake-Lye et al., 1998;Curtius et al., 1998). Simulations of sulfur chemistry inside jet engines suggestthats-values in the range 5–9% may occur in advanced subsonic engines, possiblyenhanced by a factor two due to blade cooling and other effects not considered inthe calculations (Lukachko et al., 1998). Near-field volatile particle measurementspoint to a distinct variability of SO3 emissions, sometimes outside the range ofthese model predictions, when the liquid plume aerosols are assumed to consist ofH2SO4/H2O (Section 6.3).


4.3. EMISSIONS OF CHEMI-IONS AND HYDROCARBONS

A large number of CIs are present in aircraft exhaust since ion productionviachemi-ionization is known to occur in the combustion of carbon-containing fuels(e.g., Burtscher, 1992). Ion formation due to chemi-ionization reactions is a well-known phenomenon and has been observed for example in premixed hydrocarbonflames. Positive ions are mainly light organic molecules, whereas free electronsrapidly attach to O2 which in turn reacts with nitrogen and sulfur species to formthe stable ions NO−3 and HSO−4 . These negative ions further attract polar moleculessuch as HNO3 and H2SO4 to form larger molecular clusters.

Substantial ion emissions from aircraft combustors can be expected due to thesimilarity to the thermochemistry of flames. Chemi-ions have been detected onthe ground by Arnold et al. (1998) who report a lower limit concentration of 5×107 cm−3 in the nascent plume of a small jet engine. Calculations indicate that CIspromote the formation and growth of molecular clusters containing H2SO4 andH2O into electrically charged H2SO4/H2O droplets (Yu and Turco, 1997).

In general, the combustion process creates a charge distribution on particles inyoung aircraft exhaust plumes which differs greatly from an equilibrium chargedistribution, thereby enhancing nucleation rates and contributing to the activationof exhaust soot. Comparisons with particle measurements in plumes and calcula-tions based on ion-ion recombination kinetics suggest the presence of 109 cm−3 ormore CIs at the engine exit planes (Yu and Turco, 1997). There is no indicationthat the production of CIs is linked to the sulfur content in the kerosene.

Under flight conditions, methane is the most abundant hydrocarbon in theexhaust, as demonstrated by several measurements (see compilation by Fabianand Kärcher, 1997). Few measurements of unburned (non-methane) hydrocarbons(UHC) indicate plume concentration enhancements of alkenes (mostly ethene),aldehydes (mostly formaldehyde), alkines (mostly ethine), carbonyl compounds,and a few aromates. Typically, only few (8–10) species account for most of theUHC emissions.

It is well-known that the presence of trace amounts of certain organic speciescan facilitate nucleation and may alter the hygroscopic behavior and growth ratesof atmospheric aerosols (e.g., Saxena et al., 1995). Many of the organic exhaustcompounds do not act as aerosol-forming agents, pointing to a limited, if any,role in aerosol formation in nascent jet plumes. However, some of them may beadsorbed and/or dissolved by plume aerosols and thereby contribute to particlegrowth (see also Section 6.3). Thus, it cannot be ruled out that organic speciesinteract with plume aerosols (Kärcher et al., 1998b), thereby increasing the totalmass and influencing condensation properties of the latter.

128 B. KÄRCHER

Figure 7.Schematic of the various aerosol types present in a young jet plume. Shown are approximatenumber size distributions versus aerosol radius for volatile aerosols (neutral and ionized modes),black carbon soot (primary and secondary modes), and primary contrail ice particles (dashed line).Exhaust metal particles are not shown. Horizontal and vertical bars indicate the estimated ranges ofvariability of both number and sizes due to variations of key parameters (e.g., fuel S content, engineemission parameters, ambient conditions). In the presence of contrail crystals, the spectra of the othercomponents may be subject to changes (not shown).

5. Aerosol Types and Interactions

The following aerosol types have been identified byin situ observations in aircraftexhaust plumes: (1) Liquid aerosols that mainly consist of H2SO4 and H2O, res-ulting from binary homogeneous nucleation. Part of these aerosols originate fromemitted CIs and carry an electrical charge. (2) Non-volatile combustion aerosolsthat are mainly composed of black carbon soot, and to a lesser extent, of metallicparticles. The soot particles very likely acquire a liquid surface coating in the jetplume by interaction with sulfur gases and H2SO4/H2O droplets. (3) Ice particlesformedvia freezing nucleation in contrails that rapidly take up the emitted H2O inan initial growth stage.

Figure 7 depicts the approximate sizes and abundances of the plume aerosols ata plume age around 1 s, or typically 250 m behind an aircraft. The overall spectrumof plume aerosols covers a wide range of sizes from below 1 nm up to∼10µm.

At the smallest sizes, Figure 7 displays the liquid, ultrafine particles formed inyoung plumes, hereafter referred to as volatile nucleation mode (VNM).In situobservations clearly demonstrate their existence and point towards the key role ofexhaust sulfur in producing these particles. Experimental information about theVNM spectrum (e.g., from CN counter measurements) is scarce. Model simula-tions provide strong evidence that the spectrum is bimodal. Since nucleation andgrowth preferably occurs among the charged particle fraction due to lower energybarriers, charged particles are predicted to rapidly occupy larger (>1 nm) sizes.


SOx, NOx,chemi-ionemissions

charged, hydratedH2SO4-clusters

H2SO4H2O, HNO3

soot, metalparticleemissions

volatileplumeaerosols

coated,involatileaerosols

contrailiceparticles

OH H2O

chemicalactivation

(binary)hetero-geneousnucleation

H2O

binaryhomo-geneousnucleation

coagu-lation

homo-geneousfreezing

hetero-geneousfreezing

sca-ven-ging

sca-ven-ging

coagulation

re- subli-mation

condensation

Figure 8.Aerosol transformation processes in aircraft wakes.

The primary soot mode is typically characterized by number-averaged sizes inthe range 10–30 nm. Occasionally, a second mode has been observed at larger sizes,which may compare well with the primary mode in terms of mass, but containsmuch fewer particles. The formation of a bimodal soot distribution is unlikelyto occur in the plume and must be related to interaction processes (coagulation,surface oxidation) within the jet engines. The soot particles coagulate with theliquid exhaust particles, leading to an internal aerosol mixture and to changes ofthe soot spectra not shown in Figure 7.

The dashed line shows the typical initial size distribution of new contrail iceparticles after they have taken up the emitted H2O. Given the jet plume dimensions,µm-sized crystals present at concentrations in the indicated range are required tomake the contrail visible at a very early stage after emission of the exhaust, asfrequently observed. The ice particles nucleate mainly on exhaust aerosols, butentrained background aerosol may also participate in contrail formation.

Figure 8 summarizes the physico-chemical processes that have been outlinedbriefly in Section 2.4 and Appendix B. Key issues of the gas phase chemistryin the young plume have been reviewed in Section 4. Hydrated H2SO4 clustersand emitted chemi-ions are mainly responsible for the formation of new particles(Section 6) and for the activation of soot particles (Section 7). The gas-aerosolsystem strongly interacts by coagulation and condensation processes. Freezing ofwater ice involving volatile and non-volatile exhaust particles leads to contrails; the

130 B. KÄRCHER

ice particles return the aerosol cores upon which they nucleated into the atmospherewhen the contrail evaporates (Section 8).

6. New Particle Formation

Atmospheric mixing processes causing gradients in relative humidity (RH) andtemperatureT may lead to enhancements of particle formation rates. This alsoholds for binary nucleation of H2SO4 and H2O due mainly to the pronounced non-linear dependence of the nucleation rates on RH andT (e.g., Nilsson and Kulmala,1998). Mixing can be triggered by large-scale motions (e.g., gravity waves), byturbulence (e.g., in spreading jets), and by mixing of two air parcels with differentthermodynamic states. A combination of the two latter phenomena is responsiblefor new particle formation in aircraft wakes.

6.1. NUCLEATION AND GROWTH OF VOLATILE AEROSOLS

The balloon-borne observations of Hofmann and Rosen (1978) suggested theformation of new aerosols behind aircraft, presumably resulting from binary ho-mogeneous nucleation of H2SO4 and H2O. The possibility that new particles mightform in jet plumes involving oxidized S gases through gas-to-particle conversion,and that these aerosols can contribute to contrail formation, has been demonstratedby models that couple nucleation, condensation, and coagulation processes (e.g.,Kärcher et al., 1995; Zhao and Turco, 1995; Brown et al., 1996a; Yu and Turco,1997; Taleb et al., 1997). The calculations demonstrate that the greatest particleformation probability has to be expected in the nascent jet plume. Only at thisstage of plume evolution are the gas concentrations and mixing/cooling rates largeenough to trigger the phase transition in the turbulent jet flow (cf., Figure 3).

As indicated in Figure 7, neutral particles typically dominate the volatile aerosolfraction numerically in the young plume. The concentration of these molecular-sized, hydrated H2SO4 clusters is controlled by the fuel sulfur content (FSC) anddirect emissions of SO3. Previous particle measurements in the plume of the Con-corde using a single CN counter (Fahey et al., 1995) have been explained with amodel using the ‘classical’ approach (see Appendix B) to simulate particle forma-tion (Kärcher and Fahey, 1997; Danilin et al., 1997). In these models the build-up ofthe VNM is calculated with the theory of binary homogeneous nucleation. Recentin situ observations of ultrafine aerosol particles during the SULFUR 5 field mis-sion reported by Schröder et al. (1998a) have been analyzed in detail by Kärcheret al. (1998b) and Yu et al. (1998). It was demonstrated that ‘classical’ modelsneglecting CI emissions fail to explain these measurements. In this case, measureddata from two CN counters were used to constrain the simulations.

In a model that takes into account the effect of CIs on particle formation (Yuand Turco, 1997), binary nucleation still leads to the neutral mode (with a mean


0.1 1 10t [s]

0.1

1

10

N x

1016

[#/k

g fu

el]

D > 5nm

D > 14nm

H

0.1 1 10t [s]

0.1

1

10

N x 10

16 [#/kg fuel]D > 5nm

D > 14nm

L

Figure 9.Measured total (mostly volatile) particle abundances vs plume aget (open symbols: dia-meterD > 5 nm; filled symbols:D > 14 nm) for high (2.7 g S/kg, H) (left) and low (0.02 g S/kg,L) FSC (right) in theATTAS plume without contrail (Schröder et al., 1998a). Dashed lines give therange of dry (nonvolatile) soot emissions. The solid curves are simulation results including chemi-ionemissions (Yu et al., 1998). From Kärcher et al. (1998b).

diameterD < 1 nm) – calculated with reduced collision kernels due to an assumedimperfect sticking between the clusters – but the emission of CIs leads to the for-mation of electrically charged H2SO4/H2O droplets (ion mode atD > 1 nm, seeFigure 7). Emitted CIs recombine on a timescale of milliseconds after emissionand are turned into macroscopic droplets by coagulation, which can be viewedas prompt nucleation. In such a bipolar aerosol system, the net collisional ratesare enhanced due to charge effects (Twomey, 1977). Only particles from the ionmode grow beyond the smallest detectable size (∼ 3 nm with CN counters) due toenhanced growth rates, whereby scavenging of the neutral mode clusters is the keygrowth path in the decaying wake.

Figure 9 depicts CN data measured during SULFUR 5 in theATTAS plume asa function of the plume age. Two sets of observations with high (2.7 g S/kg, caseH) and low (0.02 g S/kg, case L) S emissions are shown. The solid lines representresults from a numerical model including CI emissions of 2.6× 1017/kg fuel. Incase H (L), initial emissions of SO3 of 1.8% (55%) have been prescribed.

In case H (left side in Figure 9), the observed abundance of particles>5 nm isachieved within 0.3 s after emission, while it takes considerably longer (∼1 s) forthese particles to grow to diameters>14 nm. Att = 9 s, the ion mode is centeredatD = 9.5 nm. In case L (right side in Figure 9), most of the volatile particles aresmaller (D = 4 nm) and just approach 5 nm within 10 s of plume age, so that thenumber appears to increase continually over this time interval.

In-flight measurements of the number of CIs at emission required to explain theCN data are pending, but the prescribed value does not contradict the lower bound3×1015/kg reported by Arnold et al. (1998) (Yu et al., 1998). The value assumed forthe S to H2SO4 conversion efficiency,η = 1.8% in case H, agrees with independentATTAS measurements (η > 0.34%, Curtius et al., 1998). The remarkable agreementbetween simulations and measurements in Figure 9 suggests that models including

132 B. KÄRCHER

Figure 10.Apparent number emission indices of volatile particles measuredin situ in plumes ofvarious subsonic aircraft and the supersonic Concorde. The aircraft were examined as part of severalmissions: European SULFUR 5:ATTAS; NASA SASS, SUCCESS and SNIF III: B737, B757, DC-8,T-38, F-16; European POLINAT: B747, DC-10, A310. Particles were measured with diametersD

greater than 4–6 nm at plumes ages less than 20 s (ATTAS, B737, DC-8, B757, T-38), withD > 9 nmat ages of 0.25–1 h (Concorde), and withD > 12 nm at ages of 1–2 min (B747, DC-10, A310). FSCvalues were determined by chemical analysis of the fuel or inferred fromin situSO2 measurements(for B747 and DC-10). During the observations a contrail either did (filled symbols) or did not form(open symbols). Typical average FSCs range between 0.2 and 0.5 g S/kg.

CIs, in concert with moderately elevated SO3 emissions (relative to SO3 levelsachievedvia OH-induced oxidation of emitted SO2 alone, see Figure 6), providean accurate description of the plume microphysics. However, the prescribed valueη = 55% in case L contradicts the measurements of Curtius et al. (1998) (η <

2.5% would be consistent with their observations) and is well outside the range (1–6%) of that predicted for theATTAS jet engines (Brown et al., 1996b). This raisesthe possibility that species other than H2SO4 may contribute to, or even dominate,the growth of volatile droplets for low FSCs, see Section 6.3.

Figure 10 summarizes apparent emission indices of ultrafine volatile particlesobserved in the plumes of commercial aircraft as a function of the FSC. The scatterin the data may be at least partly explained by different ambient conditions, plumeages, aircraft types, and different CN detection limits.

For average S emissions (0.2–0.5 g S/kg), a typical number of 1016 particlesper kg fuel consumed are measured in the near-field. The Concorde data point foran average fuel sulfur content lies above the others because it was taken in an oldplume where the particles had much longer time to grow beyond the lower sizedetection limit of the CN counter. The apparent number EI rises by about a factor10 with increasing S emissions (see B 757,ATTAS, and F-16), revealing the basicimpact of oxidized S species on the growth of these particles, as discussed above.Decreasing S emissions causes a reduction of the EIs, but the ATTAS data suggest


a saturation to values 1015–1016/kg. In near-field contrails, volatile EIs are typicallyreduced by a factor 2–5, see Section 8.4 and Appendix D.

If the sulfur conversion fractions were similar in all cases, the trend of thevolatile EI with increasing FSC would solely be caused by enhanced growth ofion mode particles due to larger levels of available H2SO4. However, a detailedanalysis of the data shown in Figure 10 similar to those discussed in Figure 9 is notyet available.

6.2. COMPOSITION OF VOLATILE AEROSOLS

To facilitate the discussion of VNM particle composition, Figure 11a depicts asimulated phase diagram (left) and the condensational growth history (right) ofsingle particles (initial radii indicated by thin lines) in the plume of a commercialairliner, similar to that discussed in Figure 3.

The simulations are based on the growth equations presented in Appendix C,taking into account plume mixing effects, and assume the background upper tro-posphere (240 hPa, 224 K) to be ice-saturated. Although these conditions are closeto those for contrail formation, one does not form. The EI of NOx is 20 g/kg fuel,with 10% of the emissions assumed to be in the form of NO2. The resulting overallconversion efficiency from NOx to HNO3 is 0.4%. The ambient mixing ratio ofHNO3 is set equal to 1 ppbv.

New particles are created by homogeneous nucleation (see arrow) of H2SO4 andH2O at plume ages below 0.1 s. The evolution of composition and radius is shownfor initial particle radii 2 nm (black), 4 nm (red), 40 nm (blue). Figure 11a (left)shows that, depending on their size, the particles first (<1–2 s) take up H2O andHNO3 forced by cooling (Kärcher, 1996). This leads to a decrease of the H2SO4

mass fractions (solid lines) and an increase of the HNO3 mass fractions (dashedlines). Hereafter, decreasing humidity at nearly constant temperature leads to evap-oration of the droplets, which eventually adjust to ambient conditions. Uptake andevaporation is hampered by the Kelvin barrier for the smallest (<4 nm) particles,as seen by the moderate size variations (Figure 11a right). The H2SO4 moleculesenter the droplets during nucleation and are then nonvolatile due to their very lowsaturation vapor pressure. The predicted, coupled uptake of HNO3 and H2O insupercooled, diluted H2SO4 aerosols under plume conditions is thermodynamic-ally possible, and essentially similar to stratospheric ternary aerosol formation, butexperimental confirmation is lacking.

The uptake kinetics changes when the plume relative humidity surpasses liquidwater saturation (as necessary for contrail formation). The discussion of this case iscontinued in Section 8.4. The above discussion describes the composition of volat-ile plume aerosols for average and high FSCs. In such cases, oxidized S species areobserved to control both particle formation and growth. There are first indicationsthat the volatile particles are not mainly composed of H2SO4 when the FSC is aslow as 0.02 g/kg. This issue will be addressed in the next section.

134 B. KÄRCHER

0.0 0.1 0.2 0.3 0.4 0.5 0.6acid weight fraction

0.1

1

10

100

plum

e ag

e (s

)

binarynucleation

sulfuricacid

nitricacid

(a)

1 10 100particle radius (nm)

224

248

260

240

231

226

228

235

280

plume tem

perature (K)

0.0 0.1 0.2 0.3 0.4 0.5 0.6acid weight fraction

0.1

1

10

100

plum

e ag

e (s

)

sulfuricacid

nitricacid

contrailformation

(b)

1 10 100 1000particle radius (nm)

218

236

250

230

220

225

222

219

270

plume tem

perature (K)

Figure 11.(a) Simulated acid composition (left panel) and sizes (right panel) of single, liquid particlesfrom the nucleation mode with initial radii of 2 nm, (black), 4 nm (red), and 20 nm (blue) in asubsonic plume under upper tropospheric conditions (240 hPa, 224 K, 1 ppbv HNO3) when a contraildoes not form. New H2SO4/H2O particles nucleate early at plume ages below 0.1 s (see arrow). Acidweight fractions of the particles are shown as solid (H2SO4) and dashed (HNO3) lines. (b) Same as(a) but at 218 K, including the formation of a contrail (see double arrow) which persists throughoutthe simulation. Freezing and the evolution of ice particles are not shown. The evolution of liquiddroplets from this single particle calculation reflects the results from more detailed microphysicalmodels that additionally include coagulation and is explained in the text. (Coagulation processes donot alter the discussion of this figure.) The equations employed to produce this figure are explainedin Appendix C (plume mixing has been included). Panels (b) are discussed in Section 8.4.


6.3. CONVERSION OFFUEL SULFUR TO SULFURIC ACID

Table I summarizes sulfur conversion fractionsη (the molecular ratio of fully oxid-ized versus total sulfur) inferred indirectly from recent field measurements (exceptthe direct measurements of H2SO4 by Curtius et al., 1998) and computed by chem-ical and microphysical simulation models. Some field observations are explainedby model studies of plume chemistry and aerosol formation only when assuminglarge initial SO3/S ratios (>10–20% by number) at the engine exit. However, suchSO3 emission values are larger than computed by current combustion models (seeSection 4.2), which predict a range between 1–10% forη due to oxidation of SO2mediated by atomic oxygen.

Part of the volatile aerosol may possibly result from uptake of HNO2 (Kärcher,1997), unknown S oxidation reactions (Miake-Lye et al., 1998) or other unknowncondensable gases such as NMHCs (Kärcher et al., 1998b). For the Concorde, thepossibility that yet unknown chemical reactions could have contributed to aerosolformation (Danilin et al., 1997) through the uptake of gaseous SO2 and subsequentheterogeneous oxidation is considered inefficient (Kärcher, 1997). However, thepossible role of additional, condensational or aqueous-phase growth mechanismshas not yet been fully explored.

The SUCCESS B 757 plume data were used to infer an increase ofη from6% for low to 31% for high S content (Miake-Lye et al., 1998). These numbersrepresent averages over many measurements within contrails and were found tobe consistent with simultaneous SO2 measurements. On the other hand, it may beimportant to focus on plumes without contrails to infer S conversion fractions, sincecontrails modify the small aerosols and favor the uptake of HNO3 (cf., Section 3.4).

In agreement with chemistry simulations (Brown et al., 1996b; Lukachko et al.,1998), the analysis of the SULFUR 5 observations (cf., Figure 9) suggests that SO3

emissions, if at all, must increase with decreasing FSC (Schröder et al., 1998a).However, the conversion fraction of 55% prescribed in the model in order to matchthe CN data for low fuel S levels would lead to an H2SO4 mixing ratio of 1.2 ppbvwhich was not observed by Curtius et al. (1998). It is therefore conceivable thatorganic compounds (possibly formaldehyde and/or ethene) may have been takenup by the volatile plume aerosols (Kärcher et al., 1998b). Incorporating emissionsof only 4 mg/kg of these organics into plume models might remove the necessityof prescribing very highη-values for low FSCs. For sufficiently high S emissions,the abundance of H2SO4 is adequate to dominate particle growth, thus renderingunimportant the comparatively low organic mass in the exhaust.

7. Characterization of Soot and Metal Particle Emissions

Solid soot particles result from incomplete fuel combustion and are directly emittedby the jet engines (see Appendix B). Metal particles are formed either by burning

136 B. KÄRCHER

TABLE I

Overview on S to H2SO4 near-field conversion fractions inferred from field measure-ments and computed by simulation models.

Reference Conversion fraction Remarks

Fahey et al. (1995) >12% Concorde CN data

Schumann et al. (1996) 0.4–2% SULFUR 4ATTAS CN data

Brown et al. (1996b) 1–8% 1D simulations of S

chemistry in jet engines

Kärcher and Fahey (1997) 25–60% simulation of Concorde data

Yu and Turco (1997) 20–30% simulation of Concorde data

based on CI emissions

Curtius et al. (1998) >0.34% (<2.5%) SULFUR 5ATTAS total

H2SO4 data

Hagen et al. (1998), SUCCESS B757 SOx and

Anderson et al. (1998a,b), CN data; low to high fuel

Miake-Lye et al. (1998) 6–13% S contents

Kärcher et al. (1998a) 2–4% simulation ofATTAS data

with/without ion effects

Lukachko et al. (1998) 6–10% 1D and 2D simulations of

S chemistry in jet engines

Schröder et al. (1998a), ATTAS CN data and simula-

Kärcher et al. (1998b), tions based on CI emissions;

Yu et al. (1998) 1.8% SULFUR 5ATTAS CN data;

high fuel S content

traces of metal compounds contained in the fuel or metal particles enter the exhaustdue to engine erosion.

7.1. OBSERVATIONS

Figure 12 presents electron microspcope photographs of soot (left) and metal(right) particles sampled in the wake of a cruising aircraft. The soot particle iscomposed of primary spheres with diameters below 0.1µm which is beyond thesize resolution of the microscope. Main components of the metallic particles areFe, Cr, and Ni (stainless steel), suggesting mechanical generation within the jetengines.

Soot emissions depend on engine types, power settings, flight levels, and pos-sibly on the state of engine maintenance. Available smoke numbers as derived fromoptical absorption or filter measurements permit the derivation of a crude estimate(at a given power setting) for the total soot mass EI of 0.04 g soot/kg fuel for


Figure 12.Electron microscope photographs of a large soot particle (left, scale 500 nm) and a coarsemetallic particle (right, scale 2µm) measured as contrail residuals in the wake of a commercialairliner. (From Petzold et al., 1998a).

the present subsonic fleet (Döpelheuer, 1997). Older jet engines may emit higherlevels up to 0.5–1 g/kg. Detailed size distributions and microphysical properties foruse in nucleation calculations cannot be derived from smoke number data, therebyseverely limiting their use in microphysical calculations.

Only few direct measurements of aircraft soot size distributions (as sketchedin Figure 7) exist. Hagen et al. (1992) measured and extracted soot from exhaustplumes 2 m behind the exit planes of various aircraft. They found general agree-ment between measurements of laboratory-generated soot from jet fuel and sootsampled behind actual engines. Soot particles emitted by theATTAS have beencharacterized in both ground tests and at cruising levels, in terms of chemicalcomposition and size distribution (Petzold et al., 1998b). No significant, if any,dependence exists between soot EI and FSC, as can be read off the collection ofsoot measurements shown in Figure 13.

Whitefield et al. (1993) extracted spectra from the post combustion region oflaboratory burners using jet fuel, showing that a rich combustion stoichiometryleads to a larger (radius 100 nm) and broader soot mode than lean combustion,containing fewer particles. Systematic soot measurements behind a turbojet engineat different simulated altitude conditions were reported by Rickey (1995), showingexit plane abundances near 107 cm−3 and particle diameters 15–20 nm.

Most measured near-field soot EIs and sizes are consistent with a large range of0.01–0.5 g/kg fuel, or about 1014–1015/kg fuel, depending on the size distribution(Figure 13). The 30 year old-technology Concorde and T-38 engines show excep-tionally high number EIs. Some very low soot particle number densities that havebeen reported (Pueschel et al., 1997) are very likely the result of undersamplingof the small size fraction, which by far dominates the number distribution. Typ-ical values reported for the specific surface area of emitted soot are 5000–25,000µm2 cm−3 (Rickey, 1995) and 105 µm2 cm−3 (Petzold et al., 1998b). The fractal

138 B. KÄRCHER

Figure 13.As Figure 10, but for soot particles.

geometry of soot renders an accurate determination of the specific surface areadifficult.

7.2. SOOT HYDRATION PROPERTIES

Only little information is available concerning the chemical reactivity and surfacemorphology of exhaust soot, although this information is essential to evaluate theimpact of the combustion aerosols on heterogeneous plume chemistry, cirrus form-ation, and interactions with the stratospheric aerosol layer. In the initial stages offormation, the graphite-like soot particles are hydrophobic. However, observationshave shown that n-hexhane soot and other black carbons are partially hydrated(Chughtai et al., 1996 and references therein). Soot particles fresh from jet enginesvery likely become hydrophilic due to activation by deposition of H2O and water-soluble species present in the exhaust. Irregular surface features can also increasethe chemical reactivity and amplify nucleation processes.

In contrast to the EI, soot hydration properties are enhanced with increasingFSC (Hagen et al., 1992). Wyslouzil et al. (1994) observed hydration of carbonaerosols under water-subsaturated conditions after treatment with gaseous H2SO4.This increase of H2O adsorption after treatment with H2SO4 is in qualitative agree-ment with an analysis of the wetting behavior of graphitic carbon under plumeconditions (Kärcher et al., 1996b). The latter authors performed laboratory exper-iments to determine the contact angle (64◦) of a H2SO4/H2O droplet (50 wt-%H2SO4) on a model soot particle. The contact angle was found to increase byabout 10◦ after the graphite surface became more hydrophilic due to exposurewith OH radicals at doses expected to be present in nascent jet plumes. Hetero-geneous nucleation of H2SO4 hydrates on soot was found to be unlikely underplume conditions.


Whitefield et al. (1993) reported a clear correlation between soluble mass frac-tions found on fresh soot taken a few meters behind jet engines with the FSC,suggesting that H2SO4 is the primary soluble constituent on soot surfaces. Themeasured soluble mass fractions typically scatter around 8%. Ground-based meas-urements behind theATTAS engines revealed a decrease of the S mass fraction persoot particle from 70% at very low (10%) to 10% at high (70%) power settings (Pet-zold and Schröder, 1998). This S mass could stem from S-containing hydrocarbonspossibly involved in soot formation.

Production of soluble material by soot and SO2 interaction is only possibleby assuming efficient adsorption of SO2 molecules and rapid heterogeneous con-version to sulfate on the carbon surfaces (Andronache and Chameides, 1997).However, the sticking probability of gaseous SO2 on amorphous carbon (Rogaskiet al., 1997) is too small to lead to significant surface coverages in the young plume.Timescales in young exhaust plumes seem too short to allow heterogeneous H2SO4

production, even under optimum adsorption conditions.On the contrary, SO3 and H2SO4 might easily adsorb on soot. Direct emissions

of SO3 as suggested by recent observations (see Section 6.3) can lead to S(VI)(=SO3 + H2SO4) mass fractions in the range 0.7–14%via adsorption from the gasphase, depending on jet mixing properties and soot surface parameters (Kärcher,1998b). If no SO3 is emitted, the total adsorbed S(VI) mass fraction is only 0.1–1%. Andronache and Chameides (1997) came to a similar conclusion and presentedarguments in favor of S being incorporated into soot or being efficiently convertedto H2SO4 within the engines. Kärcher (1998b) has also estimated that only a minorfraction of the emitted gaseous SO3 (<8%) and H2SO4 (<30%) can be removedby adsorption on soot prior to binary homogeneous nucleation.

Scavenging of small VNM droplets constitutes another soot activation pathway(Brown et al., 1996a; Schumann et al., 1996) after oxidized S species are depletedfrom the gas phase. The resulting liquid H2SO4/H2O coating increases with timeand likely increases the ice forming ability of soot (Kärcher et al., 1998a,b). Theimplications for the role of exhaust soot in contrail formation are discussed inSection 8.3.

7.3. METAL PARTICLES

Metal particle emissions from commercial airliners have been found as residuals incirrus and contrail ice particles (Petzold et al., 1998a; Twohy and Gandrud, 1998).Nearly pure metal particles were observed with volume equivalent radii of about1µm and a morphology and composition that suggests mechanical generation (cf.,Figure 12, right). A second mode of this particle type appeared with radii less than0.5 µm with a higher carbon fraction. Small metal particles (approximate radii0.18µm) have been detected as inclusions in large (>2–3 µm) ice particles inyoung contrails by Twohy and Gandrud (1998).

140 B. KÄRCHER

Based on the available data, the greatest contribution by number to the non-volatile particle mass is most likely to be from carbon-containing soot. Thecomparatively low metal particle emissions limit the role of metals as contrailforming agents.

8. Contrail Formation and Freezing Mechanisms

8.1. FORMATION CONDITIONS AND VISIBILITY THRESHOLD

Contrails consist of ice particles that nucleate primarily on aerosol particles thatare emitted or are formed in the plume, as predicted by models (e.g., Kärcher etal., 1995, 1996b; Brown et al., 1996a, 1997; Yu and Turco, 1998b; Gleitsmann andZellner, 1998) and inferred byin situ contrail observations (e.g., Schumann et al.,1996; Petzold et al., 1997; Anderson et al., 1998). Simulations strongly suggestthat contrails would also form without soot and sulfur emissions by activation andfreezing of background particles (Kärcher et al., 1998a).

The formation of contrails is due to the increase in relative humidity that occursduring the isobaric mixing of the hot and humid exhaust gases with the colderand less humid ambient air. A contrail will form when saturation with respect toliquid water is reached within roughly a wingspan distance behind the aircraft. Theexistence of this liquid saturation threshold has been demonstrated experimentally.Thus, threshold temperatures and humidities for contrail formation at a given flightlevel are directly specified by thermodynamic relations (e.g., Schumann, 1996).Figure 14 summarizes observed formation temperatures (symbols), plotted as dif-ferences to calculated threshold temperatures, that were taken during recent fieldmissions under a variety of altitude and humidity conditions and types of aircraft.Appendix E presents a brief derivation of the threshold conditions.

Simple estimates show that a lower limit concentration of 104 cm−3 particlesis necessary for a contrail to have an optical depth above the visibility threshold(Kärcher et al., 1996b). Figure 15 depicts optical depths of theATTAS contrail(observed by Busen and Schumann, 1995) versus time after freezing for differentice particle number densitiesn and for two initial ice particle radiir0, as indicated.The vertical and horizontal dashed lines mark the time past exit (0.3 s) when thecontrail first became visible and the minimum optical depth (0.03) approximatelyrequired for visibility, respectively.

In their initial growth stage, the ice particles particles grow by deposition of ex-haust H2O, so that mass conservation yields a simple relationn ∝ 1/r3

max betweenn and the maximum radius of the particles. For small values ofn, the crystals needa relatively long time to grow to sizes large enough to impact the optical depth, theevolution of which reflects the oscillating behavior of the Mie scattering functionwith increasing particle radius. The maximum optical depths increase in proportionto n, althoughrmax becomes smaller. This behavior is reversed forn > 105 cm−3,


Figure 14.Contrail formation temperaturesT observed during several flight missions taken fromBusen and Schumann (1995), Schumann et al. (1996), Petzold et al. (1997), Jensen et al. (1998), andKärcher et al. (1998a). The plot shows (T − Tth) versusT . How the calculated threshold valuesTthcome about is discussed in Appendix E. Individual symbols represent different aircraft engine types,and background pressures and humidities. Note that the threshold observations (triangles) clusteraround the liquid saturation temperature (long-dashed line). Data compilation and figure courtesy ofU. Schumann.

optic

al d

epth

τ at

0.5

5 µm

100

10-1

107

106105

104

n=103cm-3

10-2

10-3

10-2

r0=0.02 µmr0=0.20 µm

10-1 101100

time after freezing (s)

Figure 15.Optical depths of anATTAS contrail versus time after freezing for various ice particlenumber densities with initial radius 0.02µm (solid lines) and 0.2µm (dashed lines). For the contrailto become visible as observed, the optical depth has to pass the visibility threshold (horizontal dashedline) within 0.3 s or 35 m distance past freezing (vertical dashed line). (From Kärcher et al., 1996b.)

142 B. KÄRCHER

when the particle radius becomes too small (rmax < 0.6 µm) and scattering is lesseffective.

According to Figure 15, around 104 cm−3 or more particles with initial radii of∼20 nm must grow to a visible contrail within the time window given by theATTAS

observations. Typical mean ice crystal radii after deposition of the exhaust H2O are∼1 µm. These values are consistent with the thermodynamic theory outlined inAppendix E. They are consistent with contrail depolarization data inferred fromlidar measurements and agree with near fieldin situ measurements (see below).

8.2. CONTRAIL OBSERVATIONS AND CONTRAIL PERSISTENCE

Besidesin situ measurements, remote sensing methods are employed to detectcirrus clouds and contrails. These can be ground-based lidar observations (e.g.,Freudenthaler et al., 1996) or analyses of infrared brightness temperatures meas-ured on satellites. Contrails can be distinguished from cirrus clouds visually bytheir linear shape, but spreading due mainly to wind shear and accompanyinggrowth of the crystals in a persistent contrail renders this distinction impossible asthe contrail ages. Observations from space (e.g., Minnis et al., 1998; Mannstein etal., 1998) and fromin situmeasurements (e.g., Schröder et al., 1998b) clearly showthat persistent contrails may develop into cirrus clouds (Gierens, 1996), therebyapproaching size distributions as typically observed in young cirrus clouds (meanice crystal size∼10–20µm) on timescales of up to a few hours.

Contrail persistence is linked to synoptic conditions that support vertical mo-tions of air, such as frontal zones connected with the warm sector of lows, jetstreams that carry moist air across stable highs, and flows induced by mountainwaves. These conditions ensure that the relative humidity exceeds ice saturation,promoting depositional growth of the contrail crystals. Recentin situ observationshave revealed that often large regions exist in the upper troposphere which arecharacterized by very large ice relative humidities (up to 160%), but void of iceclouds (Heymsfield et al., 1998).

Contrail ice particle size distributions observedin situ, such as those shownin Figure 16, exhibit strong variations from the plume center to the diluted plumeedge (Petzold et al., 1997). The variations diminish with increasing plume age. Thespectra have been measured with a Forward Scattering Spectrometer Probe (FSSP)in theATTAS contrail at a plume age of 11 s. The lower size detection limit of thisinstrument is∼0.3µm. Two size distributions are shown for very low (0.006 g/kg,closed circles) and very high (3 g/kg, open circles) FSCs. According to these andother measurements (e.g., Anderson et al., 1998a), the formation of contrails isonly weakly linked to the sulfur content in the fuel. In agreement with the visibilityanalysis (Figure 15), the bulk of the contrail crystals areµm-sized, as indicated bythe rapid fall-off of the spectrum with increasing diameter.

Also plotted are results from a microphysical simulation model that takes intoaccount freezing processes of both volatile and soot exhaust aerosols. These curves


Figure 16.Aerosol number size distributions as a function of crystal diameterD measured with theFSSP in the wake of theATTAS at a plume aget = 11 s (symbols) for two different FSCs (closedcircles: low, open circles: high). The corresponding lines without symbols are model results andrepresent the sum of soot particles coated with liquid H2SO4/H2O (mostly left of the FSSP detectionlimit of 0.3 µm) and ice particles. (From Kärcher et al., 1998a.)

are in fair agreement with the observations, increasing confidence about the abilityof current models to simulate details of contrail formation. The simulations indic-ate a slight decrease of the mean ice particle size, accompanied by an increase inthe number of ice particles, with increasing FSC. The simulations also predict theformation of coated soot particles below the lower size limit of the measurements.

Contrail properties do not strongly depend on the level of sulfur in the plume(Figure 16) because ice formation and growth is a self-limiting process and deple-tion of H2O from the gas phase prevents further nucleation when the concentrationof ice particles exceeds∼105 cm−3. Besides the variations related to sulfur, initialice particle number densities increase from 104 cm−3 to 105 cm−3 and mean radiidecrease from 1µm to 0.3µm when the ambient temperature is lowered by 10 Kfrom a typical threshold value 222 K according to the simulations (Kärcher et al.,1998a).

Although the crystals in the central contrail region mainly nucleate on exhaustparticles, as further discussed below, ambient aerosols may play a larger role incontrail regions that formed at the plume edges or in upwelling limbs of the vorticesand could contribute to the contrail ice mass. This especially holds when the air isice-supersaturated and secondary nucleation involving ambient particles can occur.Residual particles containing mineral components have been sampledin situ inlarge (radius>2–3µm) contrail crystals (Twohy and Gandrud, 1998), indicating acontribution of ambient particles in ice formation in contrails.

8.3. FREEZING MECHANISMS

Soot is expected to play an important role in the formation of contrails at and downto a few K below the threshold formation temperatures (e.g., Kärcher et al., 1995,

144 B. KÄRCHER

1996a; Schumann et al., 1996; Brown et al., 1997). Contrails observed under suchconditions are explained to result from freezing of ice within water-activated sootparticles. This result is supported by laboratory experiments which provide evid-ence that soot may induce ice formation by heterogeneous (immersion) freezing attemperatures as warm as about 250 K (Diehl and Mitra, 1998). Volatile dropletsare then prevented from freezing because the freezing of soot-containing particlesis too rapid.

Fresh soot particles do not act as efficient ice deposition nuclei in the exhaustbecause their surfaces are not well suited to initiate the direct gas-to-solid (ice)phase transition. This is consistent with the absence of contrails at temperaturesabove the liquid water saturation threshold, as documented in Figure 14. Water ac-tivation of soot may result from the formation of at least a partial coating of the sootsurfaces with H2SO4/H2O droplets (cf., Section 7.2). Prior to contrail formation,this surface coverage increases with the FSC and leads to a greater number of iceparticles. Due to the low volatility of H2SO4/H2O solutions, the acid coating willpersist at the soot particle surfaces. In Appendix D, the formation of the coatingby molecular adsorption and droplet scavenging is analyzed quantitatively (cases Iand II in Table III). Figure 17 sketches the heterogeneous freezing pathway leadingto contrails.

Contrails at threshold conditions are also observed when very low (0.002 g/kg)fuel sulfur is used (Busen and Schumann, 1995). This amount of S only leads tosurface coverages of∼0.02% (Kärcher et al., 1996b, 1998a), which raises the ques-tion whether the soot activation by sulfur gases supports heterogeneous freezing insuch cases. This may point towards the formation of a pure water coating (dashedarrow in Figure 17) that is enhanced when the FSC is increased to average valuesor higher. Such a process could explain the observed insensitivity of contrail form-ation and visibility to changes of the FSC for very low sulfur levels. The formationof a (partial) liquid H2O coating may be facilitated by both physical (adsorptiondue to an inverse Kelvin law effect in concave surface features) and chemical (hy-drolyzable, oxygen-containing functional groups and other polar adsorption sitesto which H2O molecules are bonded) mechanisms.

The proposed mechanism of (sulfur-enhanced) heterogeneous ice formationvialiquid coatings on soot is mainly inferred indirectly from the observations andneeds experimental confirmation. Unique evidence that soot is involved in iceformation is difficult to obtain fromin situ measurements, because it is difficult todistinguish whether a soot particle caused freezing or whether it was scavenged byan ice particle that formed from homogeneous freezing. A first direct indication thatpart of the exhaust soot is transformed to ice in a contrail is discussed by Schröderet al. (1998a). There is also strong experimental evidence for scavenging of sootparticles in persistent contrails (Ström and Ohlsson, 1998a), which is supported bythe simple estimates in Appendix D (case IV in Table III).

Metal particles have been detected as inclusions in contrail ice crystals (Petzoldet al., 1998a; Twohy and Gandrud, 1998). Simulations indicate that metal particles


dry exhaust soot

sulfur-freepath

activationinto waterdroplets

immersionfreezing

sulfur-enhancedsoot activation(liquid coating)

Figure 17.Schematic showing the soot-induced freezing pathway leading to contrails. Soot particlesacquire a (partial) liquid coating of H2SO4/H2O due to adsorption of oxidized sulfur gases andscavenging of volatile droplets (cf., Figure 8). They also trigger freezing if the FSC is very low (afew ppm by mass), suggesting an additional sulfur-free heterogeneous freezing mode (dashed arrow).Few ice particles may also nucleate without water activation (dot-dashed arrow). Soot dominates iceformation at and slightly below threshold formation temperatures. Homogeneous freezing may alsooccur and enhance the ice mass for lower temperatures and/or higher FSCs (not shown). Ice crystalshapes are close to spherical in young contrails, but may vary in aging contrails as indicated by thehexagon. Soot cores may reside inside the crystals, or are attached at their surface. (From Kärcher,1998a.)

may contribute to the formation of larger (radius>1–2 µm) ice crystals dependingon their assumed ice nucleation ability (Kärcher et al., 1998a). However, comparedto the other exhaust aerosol components they are numerically unimportant and playonly a minor role in contrail formation, despite the fact that they may well act asefficient IN (e.g., in the formation of cirrus clouds).

8.4. AEROSOL PROCESSING INCONTRAILS

The activation of volatile particles is not possible when the plume does not reach li-quid saturation. Well below threshold formation temperatures, contrail ice particlesare predicted to result from (mainly) homogeneous and heterogeneous freezingof solution droplets (Kärcher, 1996), depending on the FSC, the SO3/SOx ratioat emission, ambient temperature and humidity, and the assumed ice nucleationproperties of soot. In a contrail, particles have to grow to sizes>0.1µm by H2Ouptake and have undergone freezing to form water ice (Kärcher et al., 1995, 1996b;Schumann, 1996; Brown et al., 1997). This general view of freezing processesis supported by observations of contrails and their microphysical properties for

146 B. KÄRCHER

different sulfur emissions (Petzold et al., 1997) and environmental temperatures(Freudenthaler et al., 1996).

Compared to volatile aerosol growth under conditions where no contrail forms(recall the discussion in Section 6.2), aerosol growth markedly differs when theplume becomes water supersaturated. The dramatic changes that occur in a con-trail are shown in Figure 11b. Liquid VNM particles with radii>2–5 nm prior tofreezing can be activated into water droplets in the contrail with radii of several100 nm. The threshold activation size and, hence, freezing probability, depends onthe maximum supercooling reached in the expanding plume. Decreasing ambienttemperature and increasing ambient humidity both lower the threshold size andincrease the homogeneous freezing rates. In this regard, volatile particles from theion mode are more easily activated than those from the neutral mode (cf., Figure 7),and, hence, can play an important role in contrail formation (Yu and Turco, 1998b).

The fraction of activated VNM droplets that freeze depends on the dropletcomposition which affects the homogeneous freezing rate, the evolution of H2O su-persaturation, and the possible competition with heterogeneous freezing processesinvolving soot. (The particles in Figure 11b stay liquid.) Such a competition is sug-gested by plume models and is consistent with observations, although the freezingprobability of soot remains poorly defined (see above). The freezing behavior ofVNM droplets is also affected by the evolution of the acid mass fraction, which isclearly enhanced for HNO3 in the contrail formation stage (Figure 11b).

The growth of nucleated ice particles (plume age 0.7–0.9 s) causes the humidityin the plume to decrease rapidly and forces remaining liquid droplets to shrinkin size by evaporation of H2O. This may explain why the abundance of ultrafinevolatile particles in contrails is somewhat lower than in plumes without contrails.Also, this particle mode diminishes with increasing plume age due to scavengingby ice crystals (Anderson et al., 1998a; Schröder et al., 1998a; see also Figure 10).Evaporation of HNO3 from droplets is slower (<1 min) than of H2O due to thesmaller saturation vapor pressure, and can last for tens of seconds at 218 K for thelarger droplets (red and blue curves). By this mechanism, a nearly pure HNO3/H2Ointerstitial aerosol forms in the contrail. In the upper troposphere, the lifetime ofthese particles is short, and they quickly transform back into smaller H2SO4/H2Odroplets (Kärcher, 1996). These calculations suggest that measurements of liquidaerosol particles in young contrails must be analyzed with care regarding theirsoluble mass fractions.

It is well-known that processing of aerosols in non-precipitating clouds maylead to selective growth among the aerosol particles (e.g., Ayers and Larson, 1990).Condensation-evaporation cycles cause an initially monodisperse aerosol size dis-tribution to split up into two or more distinct modes. CCNs larger than a criticalsize become activated and chemically processed by uptake of soluble gases, addingdissolved mass to the droplets. Upon evaporation, only part of the dissolved massmay leave the droplets, returning particles to the atmosphere that are larger thanthose present prior to the cloud processing event.


Yu and Turco (1998b) proposed that a similar aerosol processing may occurin aircraft contrails. According to their simulations, short-lived contrails wouldsignificantly contribute to the production of CCN or IN in the aircraft wake, ori-ginating from volatile and soot exhaust aerosols that are processed by rapid uptakeof H2O and (nonvolatile) H2SO4 during the lifetime of the contrail. Evaporatingice particles that scavenged smaller H2SO4/H2O-droplets during their lifetime (anefficient process, see Appendix D, case III in Table III) return large H2SO4/H2Odroplets (compared to their initial sizes). This source of CCN/IN becomes ampli-fied with increasing S emissions. Unfortunately, no experimental data are availableto validate these predictions.

9. Atmospheric Implications

Two issues emerge from the research on aviation-produced aerosols that are be-lieved to have a great potential to affect the state of the atmosphere on largerscales. Aerosol emissions primarily from subsonic aircraft might alter the forma-tion and optical properties of cirrus clouds (Jensen and Toon, 1997). Heterogeneouschemical processing on exhaust aerosols and contrail ice particles might alter thechemical state of the exhaust air and lead to enhanced ozone depletion (Kärcherand Peter, 1995).

9.1. AIRCRAFT-INDUCED CIRRUS FORMATION

Cirrus clouds originating from persistent contrails have been discussed in Section8.2. Aircraft-produced particles may also trigger cirrus without contrails, or afterthe disappearence of short-lived contrails.

Soot particles acting as freezing nuclei have the potential to alter cirrus cloudproperties, as demonstrated by model simulations (Jensen and Toon, 1997; DeMottet al., 1997). Although fresh soot particles seem to be poor IN, the present obser-vations do not rule out that aircraft soot particles can act as freezing nuclei withregard to cirrus formation, even without a H2SO4/H2O coating (cf., Section 8.3).Information is completely lacking on how the freezing properties of soot changein aging plumes due to interaction with background gases and particles. On theother hand, aerosol processing in contrails likely increases the ice forming abilityof exhaust aerosols (cf., Section 8.4).

In situ measurements of upper tropospheric cirrus clouds in regions with denseair traffic have clearly shown an enhancement of the ratio between ice crystal andaerosol number densities in regions of cirrus where the crystals contain relativelyhigh amounts of absorbing material, presumably aircraft-derived soot (Ström andOhlsson, 1998b). This result suggests that the enhanced crystal concentrationsare linked to aircraft soot emissions, but the detailed mechanism causing thisenhancement cannot be inferred from the observations.

148 B. KÄRCHER

0.01 0.1 1r (µm)

104

103

102

101

100

101

102

103

dn/d

log(

r) (

#/cm

3 )sulfateaerosols

soot-sulfateparticles

10 100r (µm)

103

102

101

100

101

dn/dlog(r) (#/cm3)

t=30 minpuresulfate

cirrusicecrystals

withsoot

Figure 18.Initial stage of the formation of a cirrus cloud in a rising air parcel containing pure sulfateaerosols (case 1) and additionally sulfate-coated soot particles (case 2). Left panel: Size distributionsof sulfate and mixed soot/sulfate particles (solid lines: initial distributions; dot-dashed line (case 1)and dashed lines (case 2): after 30 minutes). Right panel: Ice crystal spectra after 30 minutes forcases 1 and 2. The data to initialize the model are taken from Jensen and Toon (1997).

If exhaust particles act as heterogenous IN, cirrus formation can take place atrelative humidities less than those required for homogeneous freezing (<150% inthe upper troposphere) (Kärcher et al., 1996b). Heterogeneous freezing due to sootparticles immersed in a solution droplet may start at lower supersaturations thanhomogeneous freezing (see also Section 2.4). To illustrate the strong effect sootparticles may have on cirrus formation, Figure 18 shows results from a box modelsimulating ice crystal nucleation and growth in a rising air parcel. Two cases arediscussed: case 1 assumes homogeneous freezing of H2SO4/H2O droplets. Case 2additionally includes heterogeneous freezing of H2SO4/H2O-coated soot particles.

The left panel in Figure 18 depicts the initial size distribution of the solutiondroplets with and without soot inclusions as solid lines. The dot-dashed line showsthe H2SO4/H2O droplet spectrum after 30 minutes in case 1. Hygroscopic growthand subsequent homogeneous freezing reduced the number of large droplets. Thedashed lines represent the spectra for droplets with (lower line) and without (upperline) soot inclusions after 30 minutes (case 2). In case 2, almost all soot particlesfroze heterogeneously and depleted the available H2O, and thus prevented thedroplets without soot inclusions from ever freezing.

The right panel in Figure 18 depicts the resulting ice crystal spectra in theyoung cirrus cloud after 30 minutes. In case 2, the number of crystals is lowersince the number of soot particles is less than the number of droplets that wouldhave nucleated in case 1, i.e., in the absence of the soot mode. Consistent withthe lower number density, the mean crystal radius increases from 18µm (withoutsoot) to 26µm (with soot) in this simulation. Depending, among others, on therelative droplet concentrations with and without soot inclusions and whether soot isinternally or externally mixed with the liquid particles, the crystal number density


TABLE II

Mean size and changes (zonal mean values) ofH2SO4/H2O aerosol and soot particle properties due tothe present subsonic aircraft fleet in the lowermost stra-tosphere. The estimated changes at cruise altitudes haveto be compared with background values of 200 cm−3,1 µm2 cm−3 (sulfate) and 0.1 cm−3, 0.01µm2 cm−3

(soot). From Kärcher et al. (1998a).

Perturbed quantity, unit Sulfate Soot

Diameter of mean mass (nm) 25 65

Number concentration (# cm−3) 105 2

Surface area density (µm2 cm−3) 0.2 0.03

may decrease, increase, or remain unchanged, as investigated by Jensen and Toon(1997), who also discuss possible implications for the optical properties and thelife cycle of the resulting cirrus clouds.

9.2. HETEROGENEOUS CHEMICAL PLUME PROCESSING

Liquid aerosols and ice particles play an important role in atmospheric chemistryby providing the heterogeneous surfaces for chemical reactions that activate halo-gen species (Solomon et al., 1986). Activation of chlorine- and bromine-containinggases in catalytic cycles lead to efficient chemical losses of ozone in the stra-tosphere. The observed continual reduction of lower stratospheric ozone in thenorthern hemisphere at mid-latitudes (Section 1) is at least partly caused by het-erogeneous chemistry on the surface and in the bulk of aerosol and ice particles.The mechanism of cirrus-induced ozone losses in the tropopause region, as re-cently proposed by Borrmann et al. (1996) and Solomon et al. (1997), places newemphasis on this issue.

Aircraft plumes constitute anin situ source of liquid aerosols, soot, and iceparticles in this region. The estimated perturbations noted in Table II show thataircraft emissions cause significant changes of background aerosol number concen-trations and surface area densities, even though the contribution of (current) aircraftemissions to the sulfur mass budget at cruising levels remains limited (Kjellströmet al., 1998). Thus aviation may contribute to the observed ozone losses, or atleast lessen the net ozone production potential of the aircraft NOx emissions. Thesimple estimates for sulfates in Table II are supported by a statistical analysis ofballoon-borne CN data (Hofmann et al., 1998) and by calculations of the averageperturbation of the background aerosol layer in flight corridors, based on a properdescription of particle coagulation processes in the decaying wakes (Kärcher andMeilinger, 1998).

150 B. KÄRCHER

Figure 19.Timescales of heterogeneous chemical reactions on volatile plume particles versus the re-active uptake coefficient for low (left panel) and high (right panel) soot emissions, assuming averagewake mixing properties. The dashed arrows denote the transition from low to high volatile surfaceareas assumed in the underlying calculation. From Kärcher (1997).

The global chemical effects of enhanced aerosol concentrations caused by aplanned fleet of supersonic aircraft have been assessed using two-dimensionalmodels (Weisenstein et al., 1996). However, no model exists to date that permitsa proper investigation of subsonic or supersonic plume processing effects, that is,of possible chemical perturbations as they become relevant when the aged exhaustgases enter regional and global scales. On the other hand, the precise knowledgeof the partitioning of gas phase concentrations between active and inactive formsin aged wakes (especially for NOx and ClOx species) is a prerequisite to assess theglobal aviation impact on ozone with large-scale models. For example, model cal-culations show that mesoscale polar stratospheric clouds in the Antarctic can causean almost complete conversion of inactive chlorine to ozone-destroying forms onthe timescales of minutes (Carslaw et al., 1998). Large increases in ClO and HO2

have also been observed in a volcanically perturbed sulfate aerosol layer in thetropopause region at midlatitudes (Keim et al., 1996). Particles in exhaust plumesand contrails may act in a similar way.

The surface areas of plume particles are high enough for a sufficiently long timeso that heterogeneous chemistry can become potentially important during the life-time of single aircraft plumes (Kärcher, 1997). This result is based on calculationsof the reaction timescales (defined ase-folding decay times of gas phase speciesdue to heterogeneous reactions on the plume aerosols) as a function of a prescribedreactive uptake coefficientγ (cf., Appendix C), as shown in Figure 19. The dif-ferent curves bracket the range from low to high volatile surface areas (dashedarrows), including low (high) soot emissions on the left (right) side. Reactionswith γ > 0.003–0.007 over the entire plume lifetime proceed efficiently in aircraftplumes.


Chemical processing on ice crystals in persistent contrails (not shown) will berapid if γ > 0.01. (For reactions of ClONO2 and HOCl with HCl on water ice,γ= 0.1–0.3.) The model also indicates that soot plays a less important role in ozone-related plume chemistry. Thein situ observations discussed by Gao et al. (1998)revealed thatγ values for reactions of O3 and NO2 on soot under atmosphericconditions are considerably smaller than found in the laboratory using dry carbonsurfaces. These authors argue that the presence of H2SO4/H2O coatings (see Sec-tion 8.3) may well affect the efficiency of chemical reactions on the soot surfaceand care must be taken when using reaction rates derived in the laboratory usingdry soot.

10. Summary and Research Needs

Binary homogeneous nucleation of sulfuric acid and water vapor mainly controlsthe formation of short-lived nuclei mode particles (sizes<1 nm) in young exhaustplumes. Emitted chemi-ions of the order 1017 per kg fuel consumed play a decisiverole in the production of longer-lived aerosol droplets detectable by particle coun-ters (sizes>3 nm). A clear impact of sulfuric acid on particle growth has beenobserved for average and high fuel sulfur contents and can be accurately simulatedwith models that include coagulation of charged ultrafine aerosols. An impact ofother exhaust species, presumably unburned hydrocarbons, is likely for low fuelsulfur contents (<0.02 g/kg fuel). As far as these basic processes are concerned,no principal differences between different aircraft/engine types are known or havebeen observed to date, but the exact emission levels of oxidized sulfur gases andchemi-ions remain relatively poorly defined.

Observed emission levels of exhaust soot at cruise range between 1014 to 1015

particles per kg fuel, that is at least two orders of magnitude less than for thenew volatile particles. This range is consistent with a mass-based emission indexof 0.04 g soot per kg, with an uncertainty of at least a factor 2. The few sootsize distributions observed exhibit a main maximum at diameters between 10–30 nm. Exit plane specific surface areas are of the order 5000–105 µm2/cm3. Sootemissions vary with power setting, but the spectra do not change significantly. Nosignificant effects of fuel sulfur on soot emissions have been reported, in contrastto the volatile aerosols. Soot particles become chemically activated by adsorptionof fully oxidized sulfur gases and scavenging of the small sulfate droplets in theexhaust, leading to a thin film (liquid coating) around their surfaces.

The thermodynamic relationship to predict contrail formation and occurrenceis well established. Contrails consist of ice particles that mainly nucleate on sootand volatile plume particles, which grow to sizes>0.1µm by water uptake prior tofreezing (except at threshold formation conditions, where the largest soot particlesfreeze without being activated into water droplets). Thus soot particles initiatecontrail formation, but volatile aerosols do also freeze with a contribution that in-

152 B. KÄRCHER

creases with increasing fuel sulfur content and/or decreasing temperatures. Youngcontrails contain around 104 cm−3 ice particles with mean diameters between1–2 µm. Observations and models show that contrail microphysical propertiesdepend only weakly on the fuel sulfur level. Contrails would also form withoutsoot and sulfur emissions by freezing of background aerosols. Aerosol processingin evaporating contrails may lead to enhanced production of cloud condensationnuclei from the exhaust.

The investigations of near-field processes have effectively increased our un-derstanding of basic plume aerosol physics and need to be continued. To confirmand improve the simulations of particle formation and evolution, additional fieldexperiments should be carried out with simultaneous measurements of chemi-ionsand sulfur emissions. A better understanding of the processes that control particlegrowth and composition in cases with low sulfur emissions and of the absoluteamount and apparent variability of SO3 emissions is also needed. More field stud-ies detailing the chemical composition and size distribution of ultrafine exhaustparticles and soot are required.

Observations of the microphysical evolution of exhaust particles from the waketo the global scale, of their ice-forming properties, and of gaseous species parti-cipating in ozone-related, heterogeneous chemistry (e.g., chlorine and hydrogenoxide radicals, and nitric acid) in aged plumes and contrails are not available.Together, this lack of knowledge causes important uncertainties in assessing therole of aviation-produced aerosols in cloud formation and atmospheric chemistry.

Acknowledgements

I wish to thank the University of Munich, the German Secretary of Education andResearch (BMBF), the Federal Authority of the Environment (UBA), and the Ger-man Science Foundation (DFG) for partial financial support. Special thanks go toPeter Fabian (Universität München), David Fahey (NOAA), and Ulrich Schumann(DLR) for their continuing interest and support.

Appendix A: Emission Indices and Wake Dilution Rates

The emission index EI(X) is defined as the mass of an exhaust effluent X perunit mass of fuel consumed, usually given in units of gX/kg fuel. Alternatively,a number emission indexN(X) can be derived from EI(X) if the total mass of X,m(X), is known. This quantity has the units # X/kg fuel. Strictly speaking, an emis-sion index can only be defined for emitted (primary) exhaust products, i.e., thoseproduced by the jet engines. However, throughout this work, the same terminologyis also applied to gases and aerosol particles that are formed in the exhaust plume(secondary species). It must be kept in mind in such cases that secondary species


result from chemical and/or microphysical processes that occur outside the enginesand often cannot be unambiguously related to the primary exhaust species or thethermodynamic conditions inside the engines.

To describe the average mixing history of a spreading aircraft plume, it is use-ful to define an overall dilution rateD(t) as a function of the plume aget . Asused in this work, this quantity describes the dilution representative for the bulkof the plume (see Section 3). Often,D can be parameterized byD = (t0/t)

α,where t0 is a reference plume age andα = 0.8–1 is a parameter describing theintensity of turbulent mixing of exhaust air with background air (entrainment)that causes the dilution. The dilution rate is linked to the entrainment rateω viaD = exp[− ∫ t

t0ω(t)dt], which implies thatω takes the formω(t ≥ t0) = α/t , see

Figure 4. It can be shown that the plume and wake cross sectionA(t) follows fromd ln(A)/dt = ω, or A(t) = A(t0)/D(t). The corresponding equation governingthe dilution history of a tracer in the bulk of the aircraft wake reads

(∂tχ)mix = −ω(t)(χ − χa) (7)

(see also Equation (4)) with the solution

χ(t) = χa +D(t)(χ0− χa), (8)

where the subscripts 0 anda denote initial conditions (at a reference plume aget0, usually the nozzle exit planes of the jet engines) and ambient conditions (out-side the wake). Here, both are assumed to be constant parameters. Equation (7) iswritten in terms of mixing ratios, because turbulent diffusion essentially leads toequalχ-values inside and outside the wake rather than equaln-values. (At constanttemperature, Equation (8) also holds for number densities.)

Discussions of chemistry and aerosol microphysics are facilitated by usingN-values instead of volume mixing ratiosχ or number densitiesn (as # /cm3 air),becauseN does not depend on plume dilution. Any observed changes ofN withthe plume aget directly reflect chemical changes and processes like particle growthdue to condensation or coagulation. In many cases, the dilution rate can be inferredfrom in situmeasurements of a chemical tracer (often CO2) or can be derived fromnumerical simulations of the flow field. IfD is known, the trivial dependence ofmeasured quantities on plume spreading (see Equation (8)) can be eliminated byemployingN = λ/ρ · (n− na)/D (Schumann et al., 1998), whereλ is the air/fuelratio at the engine’s exit plane andρ is the local mass density of air. Under typicalcruising conditions,λ ' 70 kg air/kg fuel andρ [kg/m3] = 0.35 · p [hPa]/T [K],wherep andT denote air pressure and temperature, respectively.

154 B. KÄRCHER

Appendix B: Formation and Dynamics of Ultrafine Particles

Atmospheric aerosols exist in different size categories. Particles with diametersD > 1µm constitute the coarse mode, whereas smaller particles make up the fineaerosol fraction, or accumulation mode. Very small particles (D < 10 nm) aretermed ultrafine particles, nanoparticles, Aitken mode, or nuclei mode particles.Whereas coarse mode aerosol is usually generated mechanically, ultrafine particlesare formed by homogeneous nucleation of supersaturated vapors. The intermedi-ate fine mode fraction can either be created by coagulation and/or condensationalgrowth of smaller ones, or when larger particles disintegrate (Whitby, 1978). Icecrystals are defined as a special class of hydrometeors and are not categorized asaerosol particles.

Since new volatile H2SO4/H2O particles nucleate in aircraft plumes and arecreated during fuel combustion processes (soot), the proper characterization ofnanoparticles is essential to understand the impact of aviation-produced aerosolson chemistry and cloud formation.

To describe the formation of atmospheric nuclei particles by gas-to-particleconversion, macroscopic approaches based on the ‘classical’ droplet model arefrequently applied. In these nucleation models, the nanoparticles are character-ized in terms of macroscopic (bulk) quantities such as mass density and surfacetension. This thermodynamic description breaks down in the nanometer size re-gion, because surface effects become important and macroscopic concepts becomequestionable. Despite this well-known deficiency, the ‘classical’ approach oftenprovides a fair description of nucleation rates in homomolecular (unary) vapors.However, in binary systems the ‘classical’ description does usually fail in predict-ing energy barriers to nucleation, and therefore also nucleation rates. This failuremay be related to principle problems arising from the proper statistical-mechanicaldefinition of a cluster, missing information about intermolecular potentials, and theinability to mathematically describe the internal structure of clusters containingtens or hundreds of molecules (Preining, 1998).

Apart from these basic issues, non-equilibrium effects and turbulence furthercomplicate nucleation calculations under aircraft plume conditions. Due to the verylarge (>10–100) supersaturation of the binary H2SO4/H2O system that is reachedunder typical conditions, energetic barriers hampering the phase transition becomesmall and the nucleation rates can be expected to be close to the kinetic limit (givenby the thermal collision rate of two hydrated H2SO4 clusters), justifying the kineticapproach used by Yu and Turco (1998a).

The collisional dynamics of aerosol particles is governed by the transport in thegaseous medium, which can be described by continuum processes (diffusion). Foraccumulation mode and Aitken particles, gas kinetic effects become important andmust be included in the description of coagulation. Phenomenological models tocalculate coagulation rates are available that account for this effect (Fuchs, 1964).In the case of ultrafine particles, surface properties become increasingly important


for the description of collisional interactions. They determine the effectiveness ofcollisions expressed by sticking probabilities and collection efficiencies. AttractiveVan der Waals interaction forces or electrostatic (Coulomb) forces enhance the(net) coagulation rates.

The term soot encompasses all primary, carbon-containing products from in-complete combustion processes. Besides the pure (black) carbon fraction, theseproducts may also contain primary organic compounds that are involved in sootformation (Goldberg, 1985). Soot forms in hot regions in the combustor in patchesof low O2, where paraffins and polycyclic aromatic radicals in the kerosene arenot completely broken down to CO2. Such patches exist because the liquid fuel issprayed into the heated air and mixesvia turbulent diffusion, resulting in spatialinhomogeneities. Soot production depends on the ratio of carbon to hydrogen,among many other details. The production of soot precursors is followed by surfacegrowth of a graphite-like, layered structure which eventually develops into a blackcarbon particle.

Substantial progress in soot-related research has been reported by the combus-tion community for relatively simple or idealized sooting systems (e.g., Bockhorn,1994). However, the knowledge of soot particle properties from higher hydrocar-bon mixtures (especially from kerosene) is still very poor owing to the complexityof such multiphase systems.

Appendix C: Heteromolecular Condensation and Uptake Coefficients

Condensation of H2O, H2SO4, and HNO3 vapors, either emitted by the engines,produced chemically in the plumevia oxidation of the primary exhaust gases, orentrained from the ambient air, can occur on liquid particles in aircraft plumes.When the plume temperature drops below∼300 K, the saturation vapor pressure ofH2SO4 over the ternary (H2O/HNO3/H2SO4) solution becomes so small that con-densed H2SO4 molecules never return into the gas phase. In contrast, droplets maytake up or evaporate H2O and HNO3, depending on the evolution of temperatureand partial pressures in the plume.

The coupled uptake of H2O, HNO3, and H2SO4 onto ternary aerosol particlesis described here in a single particle approximation. Saturation vapor pressures (interms of number densities) of H2O (subscriptk = 1), HNO3 (k = 2), and H2SO4

(k = 3) are denoted byek. Theyek-values depend on the temperatureT and themass fractionsWk of all components present in the particle.

The numberNk of type k-molecules condensing on or evaporating from aparticle with radiusr per unit time is central for this discussion. The correspondingrate per unit time and per particle reads

dNkdt= 4πDkrGk (nk −Kkek) = 4πDkrGkek (Sk −Kk) , (9)

156 B. KÄRCHER

In Equation (9),nk denotes the number density of gas molecules far away fromthe droplet surface,Dk(p, T ) is the diffusivity of the vapor molecules in air, andSk is their saturation ratio over the droplet. The functionGk takes account of thetransition of the uptake from the gas kinetic to the diffusional regime. It is given by(Sedunov, 1974):

Gk(r) =( 1

1+ `k/r +4`k3αr

)−1, (10)

with the mass accomodation coefficientα and the molecular mean free path inair, `k(p, T ). It takes the limiting valuesGk → 1 for `k � r (diffusion limit)andGk → 3αr/(4`k) for `k � r (free molecular regime). For condensation ofmolecules onto macrospcopic liquid surfaces,α = 1 (Clement et al., 1996).

The Kelvin correctionKk accounts for the increase of the saturation vaporpressuree(T ,Wk) over a curved surface and is given by

K(r, T ,Wk) = exp[2σkυk/ (r kBT )

], (11)

with the Boltzmann constantkB, the surface tension of the solutionσ (T ,Wk), andthe specific molecular volumesυ(T ,Wk). The supersaturationsk = Sk−Kk drivesthe condensation/evaporation kinetics of the gas-aerosol system. For a given partialpressurenk, small droplets may be undersaturated (sk < 0) and tend to evaporate,although larger ones are supersaturated (sk > 0) and tend to grow.

Corrections of the flux Equation (9) due to heat conduction are small comparedto the correction term Equation (10) due primarily to the low temperatures in theupper troposphere and lower stratosphere and are neglected. The mass fraction oftype-k molecules in the droplet follows from

Wk(r, T ) = MkNk/(M1N1+M2N2+M3N3), (12)

whereMk denotes the molecular mass. Finally, the time history of condensation isobtained by integrating the mass growth rate

dm

dt= M1

dN1

dt+M2

dN2

dt+M3

dN3

dt(13)

together with the fluxes Equation (9) that determine the droplet compositionEquation (12).

The described coupled condensation kinetics is essentially similar to that ofliquid stratospheric aerosol particles under cold (T < 200 K) conditions, where thedroplets become sufficiently water-rich to dissolve HNO3 (Carslaw et al., 1997).In the stratosphere, H2SO4 can often be treated as a passive component. Coupleduptake of HNO3 and H2O may also occur in the relatively more humid tropopauseregion where it could facilitate cirrus nucleation (Laaksonen et al., 1997). Nitricacid may dissolve in aircraft-produced liquid aerosols at higher temperatures due


to the markedly higher partial pressures or H2O and HNO3 in young aircraft plumesas compared to background values (Kärcher, 1996). A representative example ofcondensation involving plume aerosols is discussed in Sections 6.3 and 8.4.

The saturation number densitiesek introduced in Equation (9) can be expressedin terms of effective Henry’s law constantsHk (in units of mol (kg bar)−1) via

ek = nlk(r)/(H RT ), (14)

with the universal gas constantR and the concentrationnlk of k-molecules inthe liquid particle. According to their definition, the Henry’s law constants yieldthe gas/liquid partitioning that would be established at equilibrium (Henry’s law).Their temperature dependences at a given liquid phase composition can usually beapproximated by ln(H/H0) = A+ B/T . The equilibrium fraction ofk-moleculesthat reside in the aerosol phase, characterized by a specific volume densityV (inunits of cm3 liquid per cm3 air), reads

fl = H RT V

1+H RT V. (15)

The threshold solubility for which 50% of a gas will be partitioned into the aerosolphase (fl = 0.5) reads:Hth = 1/(RT V).

The uptake coefficient is defined as the ratio between the rate at which themolecules enter the droplet versus the rate at which they strike its surface. Ignoringthe Kelvin effect, it can be written as

γk = α(

1− nlk(r)

nk(r)H RT

). (16)

If a chemical reaction occurs in the bulk of the liquid that consumes the enteringmolecules, the concentrationnlk will be reduced and the uptake is referred to asreactive. Valuesγk > 0 point to a disequilibrium at the droplet surface, broughtabout by diffusion in the gas phase and by chemical reactions in the aerosol. Atequilibrium and for negligible loss rates in the liquid phase,γk → 0. For very rapidchemical reactions, the maximum gas-to-liquid flux is established,γk → α. Ingeneral,γk is a function of the droplet composition and the gas/liquid partitioning.The reader is referred to Schwartz and Freiberg (1981) for a detailed solution ofthe reaction-diffusion equation for spherical droplets.

Appendix D: Scavenging and Adsorption in Expanding Wakes

Molecules and small H2SO4/H2O clusters that nucleate early in the plume can beadsorbed and scavenged by exhaust soot particles and by ice particles producedin contrails. Adsorption and scavenging rates depend on sticking probabilities,

158 B. KÄRCHER

collection efficiencies, temperature, and particle sizes and mobilities. A simple re-lationship derived below permits a fair estimate of the depletion of exhaust specieswith number emission indexN1 in the near-field due to the presence of adsorbingor scavenging material (number densityn2).

Assuming constant temperature, the equation governing the loss rate of 1 interms of number densities reads

dn1

dt= −K12n2 · n1, n2(t) = n20D(t),

whereK12 denotes the rate of adsorption or the scavenging kernel (in units ofcm3/s). This approach neglects entrainment of species 1 into the plume, whichis usually a good approximation in the near-field. Eliminating plume dilution byintroducing the number emission indexN1 and recalling that dD/dt = −ωD andthatn = const. ·ND (cf., Appendix A) leads to

dN1

dt= −K12n20D(t) ·N1, ω12 = K12n20t0, (17)

with the normalized, inverse time scaleω12. Integrating Equation (17) fromt0 to tgives the solution

N1(t)/N10 ≡ 1− f (t) = exp[−ω12φ(t)] (18)

with the auxiliary functionφ(t) = ∫ tt0

D(t)dt/t0:

φ(t) ={ [(t/t0)1−α − 1]/(1− α) : t > t0 andα < 1

ln(t/t0) : t > t0 andα = 1.(19)

In Equation (18),f (t) defines the fraction ofN1 lost by adsorption (scavenging) inthe near-field at plume aget .

Table III illustrates the results for four cases of interest. In case (I) emittedmolecules are adsorbed by the surfaces of exhaust soot particles, assuming perfectsticking. With t0 = 10 ms andα = 0.9, a mean soot radius ofrs = 20 nm andnumber density ofns0 = 5× 106 cm−3 at emission, it followsKI = 4πr2

s v̄/4, orωI = 0.05 using a molecular thermal speedv̄ ' 2×104 cm/s. (KI is derived in theframework of gas kinetic theory.) Case (II) is similar, but instead of gas moleculesthe soot particles now scavenge freshly nucleated H2SO4/H2O droplets of radius1 nm. It is assumed that the droplets have acquired this size att0 = 0.1s̃. Accordingto Fuchs (1964),KII = 3× 10−8 cm3/s, assuming perfect collection efficiency,yieldingωII = 0.02. In case (III) the same H2SO4/H2O droplets are scavenged bycontrail ice particles (formation finished att0 = 0.3 s) with a typical mean radiusof 0.5µm. Here, the coagulation kernel isKIII = 8×10−6 cm3/s, again assumingperfect collection efficiency. The representative choice ofni0 = 5 × 104 cm−3


TABLE III

FractionfI of emitted molecules lost by adsorption on the surfaces of emit-ted soot particles (starting 10 ms after emission); fractionfII of smallH2SO4/H2O droplets (formation finished at 0.1 s) scavenged by soot particles;fractionfIII of small H2SO4/H2O droplets lost by Brownian scavenging bycontrail ice particles (starting after the contrail has formed at 0.3 s); and frac-tion fIV of soot scavenged by ice particles in a growing contrail as a functionof plume aget . Results from the analytical solution Equation (18) are given,assuming typical initial concentrations and constant average sizes of soot andcontrail particles. Dilution of gases and particles due to mixing is taken intoaccount.

t (s) 0.05 0.1 0.5 1 5 10 50 100 500

fI 0.08 0.12 0.21 0.25 0.35 0.39 0.49 0.53 0.62

fII – 0 0.03 0.05 0.09 0.11 0.16 0.18 0.24

fIII – – 0.06 0.14 0.32 0.4 0.55 0.61 0.73

fIV – – ∼ 0 ∼ 0 ∼ 0 ∼ 0 ∼ 0 0.01 0.02

ice particles yieldsωIII = 0.12. Case (IV) is similar to case (III), except that thecontrail particles scavenge soot particles that did not participate in the formationof the contrail. Whereas in case (III) it is assumed that the contrail crystals stay attheir initial size, the ice particles in case (IV) have a larger size. (Persistent contrailsgrow in ice supersaturated air.) For scavenging of 20 nm soot particles by crystalswith 2µm radius (assumed constant, for illustration),KIV = 1.2×10−7 cm3/s andωIV = 0.002.

The results given in Table III generally indicate that losses increase when thesize of the scavenging particle increases (due to a larger geometrical cross section)and/or when the size of the molecule adsorbed or particle scavenged decreases(due to a higher mobility). They also strongly suggest that processes (I) and (III)are important near-field loss pathways for gaseous exhaust products and molecularclusters created in the plume. Case (II) leads to the formation of an aqueous H2SO4

coating at the surfaces of the soot particles as the plume ages, supported by case (I)if the adsorbed molecules are (hydrated) SO3 and H2O. Case (IV) becomes relevantin persistent contrails on time scales exceeding several minutes.

Through collisions with smaller exhaust particles, the contrail ice crystals willincrease the number of soot inclusions and acquire oxidized sulfur, which leadsto mixed H2SO4/H2O particles after contrail evaporation. Due to the soluble ma-terial they have acquired, these contrail residuals can probably act as CCN. Theadsorption losses on soot will be less than indicated for molecules with a stickingprobability< 1 for comparable soot emission properties. Adsorption and possiblebonding to the surface or scavenging of liquid H2SO4/H2O droplets is a potential

160 B. KÄRCHER

pathway to chemically activate exhaust soot particles and to transform them intoCCN, even when soot does not go through a contrail cycle.

A similar methodology as used above has been employed to investigate thepotential for heterogeneous chemical reactions of exhaust species involving thesurfaces of aircraft-produced particles (Kärcher, 1997). Turco and Yu (1997,1998) have presented more general analytical solutions for the problem of aero-sol coagulation in an expanding plume, both in terms of concentrations and sizedistributions.

Appendix E: Contrail Threshold Formation Conditions

The thermodynamic relation for contrail formation is derived with the help of thediagram shown in Figure 20 (left). The saturation vapor pressure curves separatesaturated (contrail forming) from unsaturated (contrail dissipating) regions. Ac-cording to what has been discussed in Section 8.1, an air parcel starting at theexit plane may pass point A of the mixing line during cooling and mixing. Theparcel then crosses theliquid saturation curve (solid line) at a certain plume age,where a contrail forms. The state of the atmosphere is represented by the point B,where the mixing line ends some time after emission. If the atmosphere at B is(super-)saturated with respect to ice, a persistent contrail may develop, otherwisethe contrail starts evaporating when the mixing line again crosses theicesaturationcurve (dashed line).

Threshold conditions are derived with the help of the mixing line tangent to theliquid saturation curve in the left panel of Figure 20. (Pressures are discussed interms of mass mixing ratios and denoted byq for the following discussion.) Itsslope atT = T+ is denoted byσ (T+). A contrail forms whenever the condition

dqsat

dT= σ (T ) ≤ σ (T+) (20)

is fulfilled, wherebyqsat(T ) is the liquid H2O saturation mixing ratio. The upper(lower) black square in Figure 20 (left), where the threshold relative humidity is100% (0%), yields the maximum (minimum) threshold temperaturesT+ (T−) fora contrail to form at a given pressure altitudep. Threshold temperaturesTth ∈{T−, T+} are uniquely related to corresponding relative humidities RHth ∈ {0%,100%}.

The T -derivative ofqsat in Equation (20) is given by the Clausius–Clapeyronequation and reads

σ (T ) = 0.622L(T )

RT 2qsat(T ), (21)


102

102

102

102

102

102

102

102

102

102

102

temperature 0

100

101

H2O

va

po

r p

ressu

re

T T+

saturated unsaturated

A

B

contrailthresholdtemperatures

Figure 20.Left panel: Schematic diagram of the H2O saturation vapor pressures over liquid water(thick solid line) and over ice (thick dashed line) versus temperature. The line AB illustrates howan air parcel mixes isobarically in a jet plume, assuming that heat and water vapor mix similarly.The age of a contrail increases from A to B. The line tangent to the liquid saturation curve (endpoints denoted by black squares) is used to derive the threshold temperatures for contrail formation,which lie betweenT+ (water saturated air) andT− (dry air). Right panel: Diagonal lines representthe critical pressure altitudes where contrails form at a given ambient temperature, parameterizedby the ambient H2O saturation ratioSa . Subsonic and supersonic flight levels are indicated. (FromKärcher, 1994.)

whereL denotes the latent heat of evaporation andR is the specific gas constantfor dry air. Along the mixing line, changes of the H2O partial pressureqw and theplume temperature combine such that

σ (T+) = cpEI

Q(1− ε) H⇒ T+, (22)

(e.g., Schumann, 1996), where the specific heat capacity of dry aircp, the emissionindex of H2O EI, and the specific combustion heat of the jet fuelQ are well-knownquantities. The overall aircraft propulsion efficiencyε is defined as the fraction ofcombustion heat that is used up to propel the aircraft and thus is not available toheat the plume.

Equation (22) directly yields the maximum possible threshold formation tem-peratureT+ (corresponding to RHth = 100%) by iteration. The minimum thresholdT− (corresponding to RHth = 0%) simply follows by extrapolating the tangentmixing line toT−, whereqw = 0:

T− = T+ − qsat(T+)/σ (T+). (23)

162 B. KÄRCHER

The relative humidity is RH/100%= q/qsat. Combined with the equation for thetangent mixing lineq(T ) = σ (T+)(T − T−), any pair of threshold conditions{Tth,RHth} can be calculated iteratively from

Tth− T−T+ − T− ·

qsat(T+)qsat(Tth)

= RHth

100%(24)

where Equation (23) has been inserted.The derivation of Equation (22) assumed that water vapor and heat mix similarly

in the plume. For engines with a bypass this does not hold, because the bypassair temperature is enhanced but does only contain background H2O levels (seeFigure 3). This additional warm air causes a shift of the threshold temperaturescalculated by Equation (24) to slightly lower values. Valuesε ' 0.3 in Equation(22) are typical for the present aircraft fleet. Increasingε leads to contrail formationat higher ambient temperatures under otherwise unchanged conditions.

The right panel in Figure 20 depicts the critical pressure altitudespcr for contrailformation versus background temperature as diagonal lines. These lines are para-meterized by the background relative humidity, expressed in terms of the saturationratioSa = RH/100%. In the zone labeled ‘always contrails’, contrails will alwaysform, regardless of the ambient humidity. In the region ‘never contrails’, contrailformation is very unlikely since supersaturations with respect to water are not ob-served in the atmosphere. In the intermediate region, the formation of contrails, ortheir absence, depends on RH: the curvespcr(T ) define the minimum value of RHat a given temperature and pressure.

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