Introduction

Some trace gases and pollutants are readily removed from the atmosphere by becoming incorporated into cloudwater and then falling to Earth's surface in precipitation. In cloud-free air, small amounts of condensable species such as sulfates, ammonia, and nitrates coagulate with water vapor to form or nucleate extremely small atmospheric aerosol particles. Through gaseous diffusion and aerosol coagulation, smaller aerosols generally grow in size with time, while continuously maintaining an approximate equilibrium with water vapor and other surrounding condensable trace gases. Some aerosols eventually become large enough to develop an appreciable fall speed that overcomes frictional air drag, and thus slowly settle toward Earth's surface. However, well before particles grow to sizes where gravitational settling becomes important, larger aerosol particles are readily incorporated into clouds when aerosol-laden air cools during lifting, mixing with colder air, or other radiative cooling processes. Cloud drops initially form directly on aerosol particles, immediately incorporating a significant fraction of aerosol-borne trace constituents into the liquid phase. Once clouds form, soluble gases rapidly diffuse toward and dissolve into cloud droplets, contributing to trace chemical concentrations in cloudwater.

Most of the time, cloudwater evaporates, releasing the aerosols and gases that were absorbed during condensation back into the atmosphere. Under some conditions, cloud drops and ice particles grow by vapor diffusion and coalesce with other cloud drops and become large enough to develop appreciable fall speeds, at which point precipitation-sized cloud particles are formed. Within a cloud, falling liquid

Handbook of Weather, Climate, and Water: Atmospheric Chemistry, Hydrology, and Societal Impacts, Edited by Thomas D. Potter and Bradley R. Colman. ISBN 0-471 -21489-2 © 2003 John Wiley & Sons, Inc.

and ice precipitation rapidly scavenges and accretes smaller cloud drops, and precipitation particles grow large enough to leave the cloud and fall to the surface. Outside the cloud, falling precipitation evaporates before reaching the surface, which releases some dissolved constituents back to the atmosphere, and concentrates the remaining dissolved constituents in precipitation before reaching the surface.

Thus there are many pathways through which trace constituents are transferred from the gas phase into precipitation at Earth's surface. Within a cloud there is nucleation scavenging, which takes place as ice and liquid water condenses on condensation and ice nuclei. Impaction scavenging of aerosols and small cloud particles by other cloud drops and other classes of hydrometeors (cloud ice, graupel, snow etc.) involves collisions between hydrometeors and interstitial cloud particles. Gases are also readily absorbed by all categories of hydrometeors through direct gaseous diffusion. Below cloud base, falling precipitation absorbs gases through diffusion, and aerosols are incorporated into falling precipitation by impaction scavenging.

Rudimentary calculations of the physics of these scavenging processes, as well as more sophisticated simulations reveal that the largest fraction of trace constituents in precipitation usually originate from the direct nucleation scavenging of soluble aerosols by cloud drops when they initially condense during cloud formation. Probably the next most important source of trace constituents in precipitation arises from the dissolution of soluble trace gases into cloudwater. Other scavenging mechanisms, such as impaction scavenging of aerosols by cloud or precipitation drops, and diffusion or impaction of gases or aerosols by larger precipitation particles are typically much less efficient. In the following sections, these important scavenging pathways are further discussed and quantified.

2 NUCLEATION SCAVENGING

It is well established that in the atmosphere the phase transition from water vapor to liquid water depends on the presence of cloud condensation nuclei (CCN). CCN are composed of water-soluble substances that bind with water molecules and significantly lower the equilibrium partial pressure of water vapor, allowing water to condense or change phase into these "salty" solutions when water vapor concentrations are well below saturation with respect to pure water.

Raoult's Law. The equilibrium partial pressure of water vapor over a solution containing a dissolved salt is very close to the mole fraction of water molecules in the solution times the saturated partial pressure of water vapor over pure water. This reduction of the equilibrium vapor pressure of water over a "salty" solution is known as "Raoult's law." Thus a droplet composed of 50% water molecules and 50% sodium chloride ions (25% Na+ and 25% Cl~) will be at equilibrium with an environment where the relative humidity is 50%. Therefore, the mole fraction of water molecules in "wetted" aerosols is very close to the ambient relative humidity, and therefore at humidities close to 100%, CCN and the wetted aerosols become nearly "pure" water solutions. Even in the cleanest environments, there are several tens to hundreds of CCN per cubic centimeter of air. Therefore, there are always small amounts of wetted surfaces present in the atmosphere, and the time it takes H20 vapor to diffuse toward these wetted aerosols is sufficiently small so that condensation or evaporation occurs rapidly, maintaining the environment near a saturated equilibrium with respect to these solution droplets at all times.

Clouds form when relative humidities (RH) exceed 100%, and, since the equilibrium partial pressure of water vapor is only a function of temperature, cloud formation is usually induced by the cooling of air. If the total amount of water in an air parcel remains the same, as an air parcel cools, the relative humidity rises, and a small amount of water condenses onto the wetted aerosols, and they swell in size. When air is cooled at humidities below 100%, the wetted aerosol absorbs water vapor, increasing the liquid-phase mole fraction, thus changing the equilibrium pressure of water vapor over the wetted aerosols following Raoult's law. However, when the RH exceeds 100%, the aerosol solutions become essentially "pure water," and additional water added to the droplets does not increase the equilibrium partial pressure of water vapor. Therefore, all vapor in excess of saturation rapidly condenses. Models and measurements in clouds show that the RH in clouds rarely exceeds about 101%, and typical supersaturations in a cloud are on the order of a few tenths of a percent (RH = 100.1 to 100.5%).

Kelvin Effect. For extremely small spherical drops, there is insufficient surface tension to "hold" condensed water in a liquid phase, and thus the equilibrium partial pressure of water vapor over a spherical droplet is higher than the equilibrium partial pressure over a flat liquid surface. For example, a spherical liquid drop with a radius of 0.01 um requires a relative humidity of about 110% to maintain its size without evaporating. A pure water drop with a radius of 1 |im requires RH = 100.1% to maintain its size without growth or evaporation.

Köhler Curves. The increase of the partial pressure over a spherical surface due to the Kelvin effect counters the reduction in vapor pressure due to Raoult's effect. Together, the Raoult and Kelvin effects produce the classical "Köhler curve" (Köhler, 1926) describing the equilibrium partial pressure (eccN) over a spherical droplet of radius r containing a specified amount of dissolved ions relative to pure water:

eCCN

where es is the equilibrium partial pressure of water vapor over a flat pure water surface, and the term involving a/r is a curvature (Kelvin) term, and the b/r3 term is the solution (Raoult) term. Numerically, a 3.3 x 10~5/T (K) (cm), and b ~ 4.3 ims/Ms (cm3) where i is approximately the number of dissolved molecules produced when the soluble CCN dissolves [e. g., sodium chloride (NaCl) produces 2 ions; sulfuric acid (H2S04) produces 3], Ms is the molecular weight and ms is the

100%, water vapor primarily diffuses toward the few CCN containing the largest amounts of dissolved salts, which usually are the largest dry aerosols with the lowest critical supersaturations. Once a few cloud drops are activated, "excess" water vapor can either condense on existing drops or water vapor can diffuse toward and activate new CCN, depending on how rapidly the parcel is cooling. If not enough droplets are activated, the supersaturation increases, and more CCN are activated, incorporating smaller dry soluble aerosols into the cloud water. If sufficient numbers of nucleated drops present, water vapor diffuses toward existing drops, the supersaturation does not increase, and no additional drops are "activated."

The total number of cloud droplets nucleated during cloud formation depends in a very complicated way on the rate of cooling (i.e., lifting rate, or updraft velocity), and the size spectra and composition of soluble aerosols present in the cloud updraft.

Figure 2 shows one example of an explicit simulation of water vapor diffusion in an aerosol-laden cloud updraft. Supersaturations in a cloud updraft increase during the initial few meters above cloud base, and the greatest supersaturations are reached within 20 m or less above cloud base, usually within a few seconds above cloud base. Above the level of highest supersaturation, no additional CCN are activated, and condensing water vapor readily diffuses toward the already activated and growing cloud drops, which provide adequate surface area for condensation.

Numerous measurements show that condensation nuclei concentrations are typically a factor of 3 to 10 higher in continental areas relative to maritime areas, depending on the supersaturation at which CCN concentrations are measured. Figure 2 shows that in maritime environments containing relatively few CCN, supersaturations in a cloud updraft reach considerably higher values since there are so few

0 50 100 150 200 250 300 350 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Cloud drop number concentration (#/cc) Supersaturation (%)

Figure 2 Initial development of cloud properties in air ascending at 1 m/s (a) number of cloud drops and (b) supersaturation. Typical maritime and continental CCN spectra assumed.

0 50 100 150 200 250 300 350 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Cloud drop number concentration (#/cc) Supersaturation (%)

Figure 2 Initial development of cloud properties in air ascending at 1 m/s (a) number of cloud drops and (b) supersaturation. Typical maritime and continental CCN spectra assumed.

condensation nuclei present during cloud formation. Therefore, fewer drops are ultimately nucleated. In contrast, in continental areas where significantly greater numbers of CCN are present, more cloud drops form, and since vapor more efficiently diffuses toward these drops, supersaturations are appreciably lower than maritime clouds.

Figure 3 shows typical droplet number concentrations, maximum supersaturations, and the minimum dry radii of aerosols nucleated in a cloud updraft according to the Köhler theory following the approach of Twomey (1959). The influence of different aerosol size distributions on cloud properties is crudely accounted for here by assigning typical "continental" and "maritime" CCN distributions. Usually maritime conditions have lower numbers of CCN, and the differences between the maritime and continental distributions shown in Figures 2 and 3 qualitatively show the range of the natural variations that occurs in various cloud environments. This figure shows that greater numbers of cloud drops are nucleated at higher updraft velocities, due to increased cooling rate, and therefore condensation rate within the rising cloud parcel. Under continental conditions containing greater numbers of CCN and aerosols, more drops are nucleated and peak supersaturations are lower.

Figure 4 shows the fraction of soluble aerosol mass that is activated or incorporated into cloud drops during cloud formation for several updraft velocities under typical "maritime" or "continental" CCN and aerosol distributions, estimated two ways. One method is to add up the mass of the largest aerosols observed in a typical

" 450

" 450

Updraft velocity (cm/s)

Figure 3 Maximum supersaturation, dry radius of the smallest aerosol activated, and number of cloud drops formed during condensation within a cloud updraft. Ammonium bisulfate aerosol, and typical supersaturation activation for maritime or continental air masses assumed.

Updraft velocity (cm/s)

Figure 3 Maximum supersaturation, dry radius of the smallest aerosol activated, and number of cloud drops formed during condensation within a cloud updraft. Ammonium bisulfate aerosol, and typical supersaturation activation for maritime or continental air masses assumed.

Updraft velocity (cm/s)

Figure 4 Fraction of aerosol mass scavenged during condensation within a cloud updraft. Activation spectra and dry aerosol size distributions typical of continental or maritime for ammonium bisulfate aerosol assumed.

Updraft velocity (cm/s)

Figure 4 Fraction of aerosol mass scavenged during condensation within a cloud updraft. Activation spectra and dry aerosol size distributions typical of continental or maritime for ammonium bisulfate aerosol assumed.

dry aerosol size distribution that were nucleated during condensation. Thus if 300 cloud drops are nucleated, one can calculate the mass of the 300 largest dry aerosols in a measured aerosol size distribution, and compare this mass to the total aerosol mass in all sizes. Another method for estimating nucleation scavenging involves using the Köhler equation. Knowing the maximum supersaturation in a cloud updraft, one can calculate the size of the smallest soluble aerosol particle nucleated. Knowing this size, one can calculate the mass fraction contained in aerosol particles greater than this size from a measured aerosol size distribution. These two methods yield slightly different mass fractions and suggest that there are some inconsistencies and uncertainties in our scientific understanding of the nucleation processes and how it relates to the size distribution of dry aerosols entering a cloud. Despite these uncertainties, Figure 4 shows that a large fraction of the mass of soluble aerosols is activated and incorporated into cloudwater when a cloud forms. Irrespective of these minor uncertainties, the fraction of aerosol mass nucleated is proportional to the updraft velocity and inversely related to the number concentration of aerosol in air. Thus clouds forming under continental conditions typically scavenge a slightly smaller fraction of the aerosol mass.

The concentration of aerosol-laden trace constituents in cloud water can be given by:

£aer10 6Ct

where Q is the liquid-phase concentration (moles per literwater), £aer is the mass scavenging fraction of the aerosol-borne trace constituent, shown in Figure 4, CT is the total concentration (moles per literair) of trace constituent in air from which the cloud forms, and L is the condensed water content of the cloud (grams water per cubic meter of air). As shown in Figure 4, the mass-scavenging fraction is usually large, and nearly all aerosol-borne constituents are incorporated into the aqueous phase within clouds during condensation. Low scavenging efficiencies for soluble aerosols occur under highly polluted, high particle number concentration conditions, or within clouds that form slowly at low cooling rates, such as fogs.

Trace Gas Scavenging

After clouds form, soluble gases rapidly diffuse toward and dissolve into the liquid phase. In the presence of liquid water, gases partition themselves between gas and aqueous phases, and the liquid-phase concentration (moles per liter) divided by the partial pressure (atm) of the dissolved constituent over the liquid at equilibrium is defined as the Henry's law coefficient (Kh moles/liter/atm), a standard measure of trace gas solubility.

For typical clouds, interstitial gases diffuse toward and establish an equilibrium with a condensed phase within a few seconds or less. Therefore, soluble gases are very close to Henry's law equilibrium with cloud drops. Under equilibrium conditions, the liquid-phase concentration of a soluble gas in cloudy air can be written in terms similar to the expression for the concentration of soluble aerosol [Eq. (2)]:

= 106CT

where C; is the liquid-phase concentration (moles per literwater), and as previously defined for aerosols, CT is the total concentration (moles per literair) of trace gas in the cloudy air. The "scavenging efficiency" (£gas) of soluble gases can be calculated from mass conservation and equilibrium constraints as

Here R is the universal gas-law constant (0.082 atm liter/mol K) and T is the temperature (K). For highly soluble gases that partition predominantly into the liquid phase, the term involving Kh in (4) <<C 1, £gas is close to unity, and Ci = 106Ct/L. At the other extreme, for low-solubility gases that remain predominantly in the gas phase, the Kh term in (4)» 1, £gas is small, and therefore C; = CtKhRT, independent of the cloud liquid water content.

Many gases rapidly dissociate into several chemical forms when they dissolve in cloud water. For example, S02 is a weak acid dissociating into three chemical forms: a nonionic hydrated complex (S02H20), bisulfite (HS03~), and sulfite (S03=) ions. Equilibrium expressions are defined to quantify this dissociation as

S02(g) S02H20 (aq) S02H20(aq) HS03" + H+ HSO3- S03= + H+

= [HS0^"][H+]/[S02H20 (aq)] mol/liter K2 = [S03=][H+]/[HS03-] mol/liter

In addition to Henry's law constant for S02, laboratory-measured equilibrium coefficients Kt and K2 are used to quantify the first and second dissociation of S02 in solution. Other gases such as organic acids, C02, NH3, HN03, and HC1 dissociate in a similar manner, and one can define an "effective" Henry's law solubility, which accounts for the concentrations of all dissolved chemical forms of the trace gas, which can generally be expressed as:

This effective solubility must be used in (4) for estimating liquid-phase concentrations in a cloud. This effective Henry's law solubility is therefore usually a function of the concentration of hydrogen ion [H+], or the acidity of the cloudwater, which is proportional to the concentrations of the acids and bases in cloudy air, and strongly influenced by the cloud liquid water content.

Figure 5 shows the mass-scavenging fraction for gases as a function of their effective Henry's law solubility. Also shown on this figure is the approximate solubility and scavenging fraction of several trace gases of interest in atmospheric chemistry. For gases with Henry's law constants less than about 100 mol/liter atm, only an extremely small fraction enters into the liquid phase in a typical cloud. This includes most organic gases, NO, N02, and CO, on the order of a few percent of formaldehyde and S02 dissolve in a cloud. In contrast, 50 to 80% of hydrogen peroxide (H202) dissolves in most clouds, and nearly all ammonia (NH3), nitric acid (HN03), and sulfuric acid (H2S04) are scavenged within cloudy air.

Wet Deposition Fluxes

The rate at which trace chemicals are removed from the atmosphere via wet deposition is intimately related to the life cycle of liquid water in the atmosphere. The flux of dissolved constituents to the surface in precipitation is the product of the precipitation rate Pr (mm/h = kgwater/m~2 h) and the liquid-phase concentration of trace constituents in precipitation (Q moles per liter of solution)

and is proportional to the time constant for the removal of condensed water icw in a cloud; e is the scavenging efficiency for either soluble aerosols (Fig. 4) or trace gases [Eq. (4), Fig. 5]. The time constant for the removal of condensed water in a cloud is the condensed water path in a cloud (mm = L Az/103) divided by the precipitation rate (mm/h) from the cloud. For highly soluble species, the scavenging efficiency shown in Figures 4 and 5 are very high (i: ~ 1), and therefore the wet deposition time scale for liquid water is identical to the time constant for removal of soluble species from the cloudy environment.

Using reasonable estimates for the parameters in Eq. (7), one can quantify the wet deposition time scales for the removal of trace constituents under precipitating conditions. For a convective cloud, Figure 7 shows precipitation rate and the time scale for washout of condensed water as a function of cloud depth at various storm efficiencies. Updraft at cloud base is 1 m/s, and precipitation rates (and washout times) scale linearly with this assumed velocity. Storm efficiency is defined here as the surface precipitation rate divided by the condensation rate in the updraft. Storm efficiencies range from 10%, in relatively dry, high-wind-shear environments to 100% in saturated, low-shear environments (Weisman and Klemp, 1982; Lipps and Hemler, 1986).

Average condensed water contents for calculating the washout lifetime are taken from "typical" water contents shown in Figure 6, or closer to adiabatic (shaded gray region on Fig. lb) conditions. The main point of Figure 7 is to show that time scales for removal of condensed water substance are on the order of an hour or less, and therefore soluble constituents that are completely absorbed into cloudwater are removed rapidly from the atmosphere when precipitation is occurring. For less soluble constituents, such as S02, which partitions only a few percent into the aqueous phase in a cloud, the time constant for wet removal is longer by a factor of 10 to 100, depending on the cloud depth and microphysical storm efficiencies.

Therefore we conclude from these semiqualitative estimates that in the immediate vicinity of precipitation systems, soluble gases and a large fraction of the mass of soluble aerosols are efficiently removed from the atmosphere on a time scale of an hour or less. Chemical species that are rapidly removed by precipitation include gaseous HN03, NH3, and H202. Soluble constituents of CCN including aerosol sulfates, nitrates, and sea salts are also rapidly scavenged from the atmosphere under most precipitating conditions.

From a global perspective, the rate-limiting factor determining how quickly trace constituents are removed from the atmosphere is determined by how often and where precipitation occurs. At any given time, clouds typically cover approximately half of Earth's surface, but only a small fraction of clouds are precipitating. Pruppacher and Klett (1978) suggest that from a global perspective the average residence time of condensed water in the atmosphere is on the order of 7 h, and the residence time of all water substance (vapor + condensed water) is on the order of 9 days. Therefore on a global perspective we expect similar removal time scales for soluble trace chemicals, scaled by the relative partitioning of trace gases in condensed and vapor phases.

Figure 7 {ci} Precipitation rate and (b) condensed water washout time scale within convective clouds as a function of cloud depth at various storm efficiencies. Updraft at cloud base is 1 m/s, and precipitation rates (and washout times) scale linearly with this assumed velocity. Storm efficiency defined as the surface precipitation rate divided by the condensation rate in the updraft Average condensed water contents for calculating lifetime taken from typical water contents shown in Figure 6 or closer to adiabatic (shaded gray region).

3468 10 02468 10

Cloud thickness (km) Cloud thlcknass (km)

Figure 7 {ci} Precipitation rate and (b) condensed water washout time scale within convective clouds as a function of cloud depth at various storm efficiencies. Updraft at cloud base is 1 m/s, and precipitation rates (and washout times) scale linearly with this assumed velocity. Storm efficiency defined as the surface precipitation rate divided by the condensation rate in the updraft Average condensed water contents for calculating lifetime taken from typical water contents shown in Figure 6 or closer to adiabatic (shaded gray region).

3468 10 02468 10

Cloud thickness (km) Cloud thlcknass (km)

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