3.7: Atmospheric deposition

Heterogeneous chemical reactions are normally defined as ones which occur at the interface between two phases, e.g., gas-liquid, gas-solid, or liquid-solid. In the atmosphere processes are considered to be heterogeneous as long as the overall reaction involves two phases even though specific steps in the reaction may be homogeneous. An example of this is the oxidation of \(\mathrm{SO}_2\) in cloudwater, i.e. the dissolution of gaseous \(\mathrm{SO}_2\) into a cloud droplet followed by the oxidation of aquated \(\mathrm{SO}_2\) by homogeneous aqueousphase reactions. Because \(\mathrm{SO}_2\) is transferred from the gas to the aqueous phase, this process is considered to be heterogeneous even though the actual oxidative reaction is homogeneous.

Interactions with Aerosols and Particulates

The presence of particles in the atmosphere raises the possibility that atmospheric gaseous species interact with these particles heterogeneously. In most cases this interaction results in a gas-to-particle conversion; i.e. the transfer of a chemical species from the gas phase to an aerosol or liquid droplet or the formation of a new particle from a gaseous species. Typically gas-to-particle conversion processes are classified into three categories (Kiang et al., 1973; Schryer, 1982):
1) Homogeneous, homomolecular nucleation (the formation of a new stable liquid or solid ultrafine particle from a gas involving one gaseous species only);
2) Homogeneous, heteromolecular nucleation (the formation of a new particle from two or more gaseous species);
3) Heterogeneous, hetermolecular condensation (the growth of pre-existing particles due to deposition of molecules from the gas phase).

Of the above processes, the third, sometimes referred to as "aerosol scavenging", probably has the greatest impact upon the gas-phase levels of nitrogen oxides and hydrogen oxides and thus on the atmospheric abundances of ozone and HO (Turco et al., 1982). Scavenging reactions that are most relevant in this regard are those involving \(\mathrm{HNO}_3, \mathrm{NO}_3, \mathrm{~N}_2 \mathrm{O}_5\), organic nitrates \(\left(\mathrm{RONO}_2\right), \mathrm{H}_2 \mathrm{O}_2, \mathrm{HO}_2\), and organic peroxides \((\mathrm{ROOH})\). These reactions can be represented by

(Rla) \(\mathrm{HNO}_3 \rightarrow\) aerosol
(Rlb) \(\mathrm{NO}_3 \rightarrow\) aerosol
(R1c) \(\mathrm{N}_2 \mathrm{O}_5 \rightarrow\) aerosol
(R1d) \(\mathrm{RONO}_2 \rightarrow\) aerosol
(Rle) \(\mathrm{H}_2 \mathrm{O}_2 \rightarrow\) aerosol
(R1f) \(\mathrm{HO}_2 \rightarrow\) aerosol
(R1g) \(\mathrm{ROOH} \rightarrow\) aerosol

A complete understanding of scavenging reactions such as those listed above requires a thorough description of all the processes occurring at the surface interface and thus a knowledge of the aerosol surface structure and composition and its interaction with the relevant reactants and products. At the present time we have not yet developed this understanding; to do so will require the continued design and application of sophisticated experimental techniques used in conjunction with advanced theoretical studies of surface interactions. As a result present-day descriptions of heterogeneous reactions such as aerosol scavenging are quite rudimentary and involve the use of simple parameterizations to treat many of the complex molecular processes that occur but are not yet understood. One such simple description is described below.
The rate of scavenging of a gaseous species \(\mathrm{J}\) is normally assumed to be proportional to the species ambient concentration, \(\mathrm{n}_{\mathrm{J}}\), so that

\[ \text{Rate of aerosol scavenging} =\mathrm{n}_{\mathrm{J}} \mathrm{k}_{\text {part }\]

where the proportionality constant, \(\mathrm{k}_{\text {part }}\), has units of \(\mathrm{s}^{-1}\). The parameter \(\mathrm{k}_{\text {part }}\) can be represented by (Chameides and Davis, 1982; Heikes and Thompson, 1983),
\[
\mathrm{k}_{\mathrm{part}}=\int \phi_{\mathrm{J}}(\mathrm{r}) \mathrm{n}_{\mathrm{p}}(\mathrm{r}) \mathrm{dr}
\]
where \(n_p(r)\) is the concentration of aerosol particles having radii between \(r\) and \(r+d r\) and \(\phi_J(r)\) is the rate at which species \(\mathbf{J}\) diffuses and sticks to an aerosol particle of radius \(\mathrm{r} . \phi_{\mathrm{J}}(\mathrm{r})\) can be represented by (Schwartz, 1983)
\[
\phi_{\mathrm{J}}(\mathrm{r})=\frac{4}{3} \pi \ell \mathrm{r} \mathrm{V}_{\mathrm{j}}\left(1+\frac{4 \ell}{3 \mathrm{r} \alpha}\right) \frac{\left[\mathrm{n}_{\mathrm{J}}-\mathrm{n}_{\mathrm{J}}{ }^{\mathrm{o}}\right]}{\mathrm{n}_{\mathrm{J}}}
\]
where \(\ell\) is the mean free path, \(\mathrm{V}_{\mathbf{J}}\) is the species thermal velocity, \(\alpha\) is the appropriate sticking or accommodation coefficient for species \(\mathrm{J}\) impinging upon the aerosol surface, and \(\mathrm{n}_{\mathrm{J}}{ }^{\mathrm{o}}\) is the species' concentration at the surface of the aerosol. Typically, \(\mathrm{n}_{\mathrm{J}}{ }^{\mathrm{o}}\) is assumed to be zero for solid particles and \(\left(\mathrm{a}_{\mathrm{J}} / \mathrm{H}_{\mathrm{J}} \mathrm{RT}\right)\) for wet particles, where \(a_J\) is the activity of \(J\) in solution, \(H_J\) is the species solubility constant in the appropriate aerosol solution, \(\mathrm{R}\) is the gas constant, and \(\mathrm{T}\) is the temperature.

While appearing to be quite straightforward, the application of Equations (1), (2), (3) to determine the rate of aerosol scavenging of a given species \(\mathrm{J}\) is quite difficult. For one the value of \(\alpha\) is highly uncertain. The little data that does exist suggest that \(\alpha\) can vary widely depending upon the aerosol composition (i.e. basic or acidic), relative humidity (i.e. for hygroscopic aerosols, solid particles at low humidity and solution droplets at high humidity), and the nature of the impinging gas. For instance while sticking coefficients for species such as \(\mathrm{HO}_2, \mathrm{H}_2 \mathrm{O}_2, \mathrm{NO}_3\) impinging upon water solutions with \(\mathrm{pH}\) 's above about 5 may approach unity, the \(\alpha\) for these species impinging upon \(\mathrm{H}_2 \mathrm{SO}_4\) particles or similar highly acidic dry particles are likely of the order of \(10^{-6}\) to \(10^{-4}\) (cf. Chameides and Davis, 1982).

Another complication arises for hygroscopic aerosol particles which, provided the humidity is high enough, exist as small suspended solution droplets of relatively high ionic strength (i.e. \(\mu>1\) ). At these ionic strengths, the particle can no longer be treated as an ideal solution as one does for lower ionic strengths. The appropriate values for \(\mathrm{a}_{\mathrm{J}}\) and \(\mathrm{H}_{\mathrm{J}}\) are generally not known and can only be accurately determined by detailed experimental studies such as those carried out by Pytkowicz (1984) for seawater.

In spite of these uncertainties, Equation (1), (2), and (3) can be used to obtain a preliminary indication of how important these scavenging reactions may be for a range of possible values for uncertain parameters such as \(\alpha\). As an example, values for \(\mathrm{k}_{\text {part }}\) for \(\mathrm{NO}_3\) and \(\mathrm{N}_2 \mathrm{O}_5\) as a function of \(\alpha\) and the total number density of aerosol particles (assuming a log-normal distribution) are illustrated in Figure 4-3 for the case when \(\mathrm{n}_{\mathrm{J}}{ }^{\mathrm{O}}=0\). (Very similar scavenging coefficients would be obtained for other species such as \(\mathrm{HNO}_3\), \(\mathrm{HO}_2\), and \(\mathrm{H}_2 \mathrm{O}_2\) ). The results of Figure 4-3 suggest that for species with sufficiently long lifetimes (i.e. of the order of days or more), aerosol scavenging would represent a significant sink in regions of modestto-large aerosol loadings if \(\alpha \geq 10^{-2}\). Indeed the large levels of \(\mathrm{NO}_3^{-}\)found in aerosols in the marine boundary layer would appear to confirm that scavenging of gaseous \(\mathrm{HNO}_3\) by sea salt aerosol represents a major sink for this species in the marine atmosphere (Huebert and Lazrus, 1980; Liu et al., 1983). At night when \(\mathrm{NO}_3\) photochemical lifetimes become large, scavenging by aerosols could also be a significant sink for \(\mathrm{NO}_3\); in fact this mechanism has been proposed to explain the low levels of \(\mathrm{NO}_3\) observed at night (Noxon et al., 1978; Platt et al., 1980b; Heickes and Thompson, 1983). It is also interesting to note that in urban locations where aerosol number densities of \(10^4-10^5 \mathrm{~cm}^{-3}\) are not uncommon, aerosol scavenging could also be an important sink for \(\mathrm{HO}_2\), whose photochemical lifetime is about 100 s, if \(\alpha=\) values near 1 are appropriate.

Thus these calculations imply that aerosol scavenging can be an important sink for \(\mathrm{HNO}_3\) and \(\mathrm{NO}_3\), as well as \(\mathrm{H}_2 \mathrm{O}_2\) and possibly \(\mathrm{HO}_2\). As such this process would represent a major heterogeneous sink for nitrogen oxides and hydrogen oxides. However, many uncertainties are associated with this assessment. Before a more definitive assessment of aerosol scavenging can be made, experimental studies establishing accurate values for \(\alpha\) as well as field measurements characterizing the chemical composition and structure of aerosol surfaces will be needed.

In addition to aerosol scavenging another potentially important heterogeneous sink of nitrogen oxides that needs to be considered is the formation of \(\mathrm{NH}_4 \mathrm{NO}_3\) from gaseous \(\mathrm{NH}_3\) and \(\mathrm{HNO}_3\), i.e.
\[
\text { (R2) }\left(\mathrm{NH}_3\right)_{\mathrm{g}}+\left(\mathrm{HNO}_3\right)_{\mathrm{g}}-\left(\mathrm{NH}_4 \mathrm{NO}_3\right)_{\mathrm{g}}
\]
In regions of high \(\mathrm{NH}_3\) levels this process can represent a significant heterogeneous sink for nitrogen oxides. Studies by Stelson and Seinfeld (1982) have indicated that the levels of \(\mathrm{NH}_4 \mathrm{NO}_3\) in the particulate phase relative to that of gas-phase \(\mathrm{NH}_3\) and \(\mathrm{HNO}_3\) can be accurately described in terms of the thermodynamic equilibrium between the phases. While the condensation of \(\mathrm{NH}_4 \mathrm{NO}_3\) can occur via heteromolecular, homogeneous condensation as well as hetermolecular, heterogeneous condensation, observations indicate that the later process is the dominant one in the atmosphere.

Scavenging

Similar to the interactions of gases with aerosol particles, scavenging or heterogeneous removal is probably the most common process by which hydrometeors affect gas-phase species. This can occur via rainout (removal of gases by cloud droplets) as well as washout (removal of gases by raindrops). Of these two it is generally believed that rainout is more important than washout simply because of the longer lifetime and greater surface area afforded by cloud drops when compared to that of raindrops. With regard to nitrogen oxides and hydrogen oxides, removal of \(\mathrm{HNO}_3, \mathrm{NO}_3, \mathrm{H}_2 \mathrm{O}_2\), and \(\mathrm{HO}_2\) are most relevant because of their high solubility or reactivity in clouds.

The rate of incorporation of a gaseous species \(\mathrm{J}\) into a cloud droplet can be treated in much the same manner as that for aerosol particles described in the previous section. Thus
Rate of cloud droplet scavenging \(=\mathrm{n}_{\mathrm{J}} \mathrm{k}_{\mathrm{cloud}}\)
where
\[
\mathrm{k}_{\text {cloud }}=\int \phi_{\mathrm{J}}(\mathrm{r}) \mathrm{n}_{\mathrm{d}}(\mathrm{r}) \mathrm{dr}
\]
and \(n_d\) is the number of cloud droplets with radii between \(r\) and \(r+d r . \phi_J j(r)\) in Equation (5) is essentially the same as that given by Equation (3), except that now \(n_J{ }^{\circ}=[J] / H R T\), where \([J]\) is the concentration of \(\mathrm{J}\) in solution in units of moles (liter) \()^{-1}\). (Because ionic strengths in cloudwater are small, the solution can be treated as ideal so that \(\mathrm{a}_{\mathrm{J}}=[\mathrm{J}]\) and \(\mathrm{H}_{\mathrm{J}}\) is given by the Henry Law constant for \(\mathrm{J}\) in a pure water solution.) Values for \(\alpha\) for cloud drops, while not accurately known, are probably not nearly as uncertain or variable as those for aerosol particles since the water droplet surface is better defined. (On the other hand, the reader should note that the presence of organic films on droplets could further complicate the issue as discussed by Gill et al., 1983). Sticking coefficients for most species of interest impinging on water are probably of the order of \(10^{-2}\) or higher although values as low as \(10^{-4}\) cannot be ruled out at this time (cf., Chameides and Davis, 1982).

Within a cloud, gaseous species are transferred to droplets until equilibrium is attained. Calculations simulating the transfer of gases to droplets indicates that, for reasonable values of \(\alpha\), equilibrium between the two phases is rapidly attained. This fact is illustrated in Table 4-2 where equilibration times, \(\tau_{\mathrm{eq}}\), are listed for several species of interest as a function of \(\alpha\) and \(r\). Because equilibrium does apply the concentration of a species \(\mathrm{J}\) in solution can be related to its ambient gas-phase concentration in cloud-free regions via
\[
[\mathrm{J}] \cong[\mathrm{J}]^{\mathrm{eq}}=\mathrm{n}_{\mathrm{J}} /\left(\mathrm{A} \mathrm{Lx10^{-9 }}+(\mathrm{HRT})^{-1}\right)
\]
where \([\mathrm{J}]^{\mathrm{eq}}\) is the concentration of \(\mathrm{J}\) in the cloudwater at equilibrium, A is Avogadro's number, and \(\mathrm{L}\) is the liquid water content in units of \(\mathrm{gm}^{-3}\).

Given Equation (6) as well as statistics for the average cloudiness of the atmosphere, the rate of precipitation from clouds, and the liquid water content of clouds, an expression for the rate of removal of a species via rainout can be obtained. The results of such an analysis are found in Figure 4-4a, where the rainout

lifetimes, \(\tau_{\mathrm{J}}\), are illustrated as a function of \(\mathrm{z}\) for different values of \(\mathrm{H}\) and varying types of storm cycles. For species of low solubility, \(\tau_{\mathrm{J}}\) is linearly related to \(\mathrm{H}\) but independent of the length of time between storms. For species of high solubility which are virtually completely removed from the atmosphere during each storm, \(\tau_{\mathrm{J}}\) is independent of \(\mathrm{H}\) but linearly related to the time between storms; in this case \(\tau_{\mathrm{J}}=\mathrm{T}\) where \(\mathrm{T}\) is the storm period.

Thus in regions of long dry periods between storms, the rainout lifetimes for highly soluble species can become significantly longer than the average 10 day lifetime for water vapor that has been previously assumed to be representative of the lifetime of highly soluble species. It can be seen in Figure 4-4b that for nitrogen oxide species strikingly different profiles can be obtained in model calculations using this parameter for different assumed storm periods even though identical source strengths were assumed in each case. Thus, given the large seasonal and latitudinal variations in the water vapor-cycle, this result would seem to imply that in addition to \(\mathrm{NO}_{\mathrm{y}}\) sources, \(\mathrm{NO}_{\mathrm{y}}\) removal rates can also lead to large temporal and spatial variations in \(\mathrm{NO}_{\mathrm{y}}\) concentrations.

In addition to providing a liquid phase where soluble gases can be dissolved, clouds also offer an active chemical medium where aqueous-phase chemical reactions can occur which affect the removal rate of atmospheric species in general and nitrogen oxide and hydrogen oxide species in particular. For instance while the distribution of gaseous \(\mathrm{HNO}_3\)
\[
\text { (R3) }\left(\mathrm{HNO}_3\right)_{\mathrm{g}}-\left(\mathrm{H}^{+}\right)_{\mathrm{aq}}+\left(\mathrm{NO}_3^{-}\right)_{\mathrm{aq}}
\]
provides a major rainout sink for atmospheric nitrogen oxides and source of dissolved \(\mathrm{NO}_3-\) in rainwater, another important sink can arise in regions where \(\mathrm{NO}_{\mathrm{x}}\left(=\mathrm{NO}+\mathrm{NO}_2\right)\) is large. This sink occurs via the production of gaseous \(\mathrm{NO}_3\) radicals in clouds at night. Because \(\mathrm{NO}_3\) radicals have long chemical lifetimes at night and can be rapidly scavenged by cloud droplets, their night time production in a cloud is followed by their incorporation into cloudwater. Once in the aqueous-phase, \(\mathrm{NO}_3\) is rapidly converted to \(\mathrm{NO}_3{ }^{-}\). A typical reaction sequence leading to \(\mathrm{NO}_3^{-}\)production in cloudwater is
\[
\text { (R4) }\left(\mathrm{NO}_2\right)_{\mathrm{g}}+\left(\mathrm{O}_3\right)_{\mathrm{g}} \rightarrow\left(\mathrm{NO}_3\right)_{\mathrm{g}}+\left(\mathrm{O}_2\right)_{\mathrm{g}}
\]
(R5) \(\left(\mathrm{NO}_3\right)_{\mathrm{g}} \rightarrow\left(\mathrm{NO}_3\right)_{\mathrm{aq}}\)
\[
\text { (R6) }\left(\mathrm{NO}_3\right)_{\mathrm{aq}}+\left(\mathrm{Cl}^{-}\right)_{\mathrm{aq}} \rightarrow\left(\mathrm{NO}_3^{-}\right)_{\mathrm{aq}}+(\mathrm{Cl})_{\mathrm{aq}}
\]
Figure 4-5 taken from a numerical simulation of the coupled gas- and aqueous-phase chemistry of a cloud, illustrates the enhanced levels of \(\mathrm{NO}_3{ }^{-}\)that can result from this process at night.

SURFACE EXCHANGE AND VERTICAL REDISTRIBUTION

Surface Exchange

Vertical transport in the boundary layer (i.e., the layer of air that is coupled directly to the surface by turbulent exchange processes on a time scale of about an hour or less), and between the boundary layer and the overlying free atmosphere, plays an important role in determining the fate of trace atmospheric species. At the surface, trace species may be both deposited and emitted, so that the flux at the surface is a net balance between the two processes. Deposition at the surface requires transport of the trace species to the surface by turbulent eddies.

Redistribution between the boundary layer and the overlying free atmosphere is mostly a result of highly intermittent cloud processes. Cycling of trace species through clouds can result in chemical transformations and loss through wet deposition (see section 4). The latent heat released by clouds can result in several kilometer ascents of boundary layer air into the free atmosphere within a few minutes. Compensating downward motions can transport air from the free atmosphere into the boundary layer. Eddy diffusivity models are not adequate for describing mixing of trace species over such large vertical displacements. Although some progress has been made in parameterizing these processes, much still remains to be done.
The subsequent sections discuss our current understanding of surface exchange of trace species important in estimating the tropospheric ozone budget, including both dry deposition and surface emission, as well as the exchange of trace species between the boundary layer and the overlying free atmosphere. Both are important in estimating the ozone budget throughout the troposphere.

Dry deposition is the transfer of an atmospheric constituent from the air directly to the earth's surface, regardless of whether the surface is wet or dry, or whether the loss is at the ground or in elements that are attached to, or touching the ground, such as a forest canopy or a snow cover. Because of the complexity of the earth's surface, and the variety of mechanisms for capturing species, precise physical descriptions of how this process takes place are difficult. Instead, the rate of dry deposition is commonly specified with a gross parameter such as a deposition velocity. The deposition velocity is defined as the ratio of the downward flux \(\mathrm{F}_{\mathrm{S}}\) of a species \(\mathrm{s}\) to its mean concentration at some reference level \(\mathrm{s}\)
\[
\mathrm{v}_{\mathrm{d}}=\mathrm{F}_{\mathrm{s}} / \overline{\mathrm{s}}
\]
Trace constituents are transferred from the atmospheric boundary layer to within a centimeter of the surface (or surface protrusions) by turbulent eddies. Below this, the transfer is predominantly by molecular diffusion. We can, therefore, define the downward flux through a particular level as the averaged product of instantaneous departures of the constituent concentration \(\mathrm{s}^{\prime}\) and vertical velocity \(\mathrm{w}^{\prime}\) from their means, measured at that level; i.e., \(\mathrm{F}_{\mathrm{s}}=-\overline{\mathrm{w}^{\prime} \mathrm{s}^{\prime}}\), where the overbar denotes an average over a distance or time long enough to ensure a statistically reliable result.

Dry deposition is determined by the efficiency of the turbulence transport process, and the properties of both the constituent and the surface. The constituent may be either adsorbed or absorbed at the surface; that is, the constituent may either be stored on the surface without changing its identity, or it may combine chemically with the surface material. The deposition rate for constituents which are efficiently absorbed at the surface is controlled mainly by the ability of the turbulent eddies to transport the constituents to impinging constituents stick to the surface. As discussed by Wesely (1983) and Wesely and Hicks (1977), a convenient way to express this mathematically is to separate the effects of turbulence transport from constituent and surface properties by considering the reciprocal of the deposition velocity as a "resistance" to deposition, and equating it to the sum of the individual resistances contributed by (1) the turbulence transport process, commonly called the aerodynamic resistance \(r_a\); (2) that contributed by molecular transport through the quasilaminar layer within about a centimeter of the surface and surface elements \(r_{\mathrm{s}}\); and (3) that contributed by how well the constituent sticks to the particular surface \(r_c\) :
\[
v_d^{-1}=r_a+r_s+r_c
\]
In this way, properties of the constituent and surface can, in principle, be separated from aerodynamic properties.

Many species are not only deposited, but are also emitted at the surface. Therefore, in these cases, the surface flux is the net result of both deposition and emission, and the concept of a surface resistance is no longer applicable for estimating surface flux, except when emission is negligible compared to deposition. Nitrogen oxides \(\left(\mathrm{NO}_{\mathrm{x}}=\mathrm{NO}+\mathrm{NO}_2\right)\) for example, are emitted from vegetated surfaces. Depending upon the situation, either deposition or emission may dominate; thus the surface flux may be either positive or negative. Their emissions are mostly the result of the activity of various soil microbes, whose rates of production are governed mainly by soil composition, temperature, moisture and \(\mathrm{pH}\), available oxygen, and fertilization practices. Over water, nitrite photolysis is believed to be a source of NO emission (Zafiriou and McFarland, 1981). Surface emissions of \(\mathrm{O}_3\) and \(\mathrm{HNO}_3\) are considered to be negligible, so that the resistance concept can be used to estimate their surface flux.

The actual process of deposition depends upon many factors. Over vegetated surfaces, the condition of the vegetation can be important, particularly for reactive gas species. Ozone deposition, for example, is much larger when the leaf stomata are open than when they are closed. Thus, ozone deposition is maximized over vegetated areas in the daytime when plants are actively growing. Observations over the ocean indicate a deposition rate several times that predicted on the basis of laboratory studies over pure water. This indicates that trace constituents in the water and on the water surface are important in determining the actual deposition rate.

Excerpted from:

V.A. Mohnen, W. Chameides K.L. Demerjian D. H. Lenschow J.A. Logan R.J. McNeal, S.A. Penkett, U. Platt, U. Schurath, P. da Silva Dias. Tropospheric Chemistry, in Atmospheric Ozone 1985: Assessment of Our Understanding of the Processes Controlling Its Present Distribution and Change, World Meteodrological Organization. Accessed November 2023 at https://csl.noaa.gov/assessments/ozone/1985/report.html