v where t, is the tropospheric residence time, under dry weather conditions, while H is the scale height (see Subsection 3.6.4).
Equations [5.3] and [5.4] can be applied in the case of relatively simple and sensitive radioactivity measurements. The use of long-lived artificial fission products in intervals without nuclear tests seemed particularly suitable in the past since they have a relatively constant vertical distribution in the troposphere (e.g. Ishii, 1960) which facilitates the determination of H. In this way Small (1960), by using total ^-activity measurements, calculated that the overall dry deposition velocity of aerosol particles over Norway is 0.50 km day-1. On the other hand, Stewart found (see Small, 1960) a much smaller value in England. According to artificials-activity measurements of E. Meszarosand Simon (1967), carried out near
Budapest, Hungary, the corresponding figure is 0.17 km day "l, which is equivalent to 0.2 cm s ~This is a reasonable velocity in light of Fig. 41 if we consider that, in the sixties, 80 % of the artificial ^-radioactivity was found to be on large particles (Gasiev et al., 1966). If H is 10 km, it follows from this latter deposition velocity that without wet removal the residence time of aerosol particles would be as long as several months. Considering that the actual residence time of aerosol particles in the lower troposphere is estimated to be 3-4 days (Martell, 1966; E. Meszaros and Simon, 1967), the role of clouds and precipitation in particle removal is obvious.
We have previously seen that tropospheric background aerosol particles consist mainly of ammonium sulfate (Subsection 4.4.2). Bearing in mind that the radius of the majority of these particles is in the Aitken size range it seems to be reasonable to suppose on the basis of Fig. 41, that their dry deposition velocity cannot be greater than 0.1 cm s-1. This figure is in good agreement with the recent estimate of Garland (1978) which gives the same value for the dry deposition of sulfate particles.
Finally, it is to be noted that in the foregoing discussion of dry removal we considered the total ensemble of particles. If size ranges are taken into account separately, additional sinks have to be mentioned. Thus, thermal coagulation of particles with very small size, as well as the condensation (below a relative humidity of 100 %) of vapours with low saturation vapour pressure provide effective removal for Aitken particles. It is believed (Hidy, 1973) that these processes are dominant in the removal of aerosol particles in the size range below 0.1 pm radius.
In the dry removal of trace gases turbulent diffusion, followed by molecular diffusion in the laminar layer, plays an important role, provided that the soil, vegetation or water surface chemically adsorbs or absorbs the gas considered.
It follows from equation [5.1] that the dry deposition of trace gases (vs = 0) may be calculated by measuring their concentration gradient and the eddy (or molecular) diffusion coefficient This procedure, called the gradient method, is widely used to determine the dry deposition velocity. Thus, Atkins and Garland (1974) studied the dry deposition of S02 in this way. They determined the diffusion coefficient from wind profile observations. Using equation [5.3] these authors were able to calculate
5.2.2 Dry deposition of trace gases
Dry deposition velocity of sulfur dioxide gas for different soil surfaces (Atkins and Garland, 1974)
Short grass •Grass
Bare calcareous soil Pine forest
March-June 0.14-2.0 November-January 0.20-1.3 February-March 0.50-2.2
the deposition velocity. Their results obtained over different surfaces are tabulated in Table 26. Disregarding the data for pine forest, the deposition velocity lies between 0.14-2.2 cm s ~1. As can be seen the highest deposition rates were measured over calcareous soils, which are very effective S02 absorbers.
Recently, Garland (1978) has reviewed the results of measurements carried out to determine the dry deposition velocity of sulfur dioxide gas. He argues that the average removal velocity is around 0.8 cms"1. It is to be noted here that the dry deposition velocity of l3lI gas was also found to be in agreement with the data tabulated in Table 26. Thus, Chamberlain (1960) reports values between 0.3 and 2.6 cms"1 for this radioactive isotope.
Unfortunately, little information is available for other gaseous sulfur and nitrogen species. As we have mentioned in Chapter 3, Judeikis and Wren (1977) published values between 0.015 and 0.28 cms"' for H2S and DMS, on the basis of their model experiments. They also reported indications, however, that observed deposition velocities are due primarily to reversible physical adsorption. This means that real dry removal rate of these compounds may be much smaller.
Laboratory investigations by Botger (1978; personal communication) indicate dry deposition velocity values for N02 of the order of magnitude of 0.01 cms"'. These experiments were carried out by measuring concentration loss in a plexiglass box which contained different water or soil surfaces. The results were corrected for a blank value obtained without any absorbing material. A particularly low velocity was found for ocean water (0.015 cm s "1), while the highest figure was obtained over wet sand: 0.041 cm s "1. It is questionable, however, how to extrapolate these results to natural soils covered by vegetation. Moreover, to the knowledge of the present author, no measured deposition velocities were published for atmospheric ammonia gas. It is obvious that much work remains to be done in this important field.
5.3 Wet deposition 5.3.1 Rain-out of aerosol particles in clouds
The efficiency of wet removal of gases and particles is due to the fact that the falling speed of precipitation elements greatly exceeds the dry deposition velocity of trace constituents. In discussion of removal caused by clouds and precipitation it is reasonable to differentiate processes taking place in the clouds (rain-out) and beneath the cloud base (wash-out).
Rain-out of aerosol particles is begun at the moment of cloud formation, since at the supersatu rations occurring in the atmosphere (< 1 %, which is equivalent to a relative humidity of 101 %) condensation takes place on aerosol particles, called nuclei. To understand the principle of this phenomenon (see Mason, 1957; Fletcher, 1962) let us consider a cooling air parcel. Because of the cooling the relative humidity in the parcel increases. After reaching the saturation level, cloud drops begin to form on aerosol particles in the updraft. Each particle becomes active in the cloud drop formation at a supersaturation (critical supersaturation) which is determined by the physical and chemical properties of the particle. It is obvious that condensation starts on particles having a low critical supersaturation. By further increase of the supersaturation more and more particles are involved in cloud formation by condensation. Owing to water vapour consumption the supersaturation begins to drop after a certain time. Only those particles can participate in the condensation whose critical supersaturation is equal to or less than the maximum supersaturation reached in the cloud.
Results of thermodynamic calculations show (e.g. Dufour and Defay, 1963; E. Meszaros, 1969) that the critical supersaturation of solution droplets formed on water soluble particles (see Subsection 4.5.1) is less than values for insoluble particles of the same size.1 Furthermore, theory indicates that larger particles are more active in condensation processes than smaller nuclei. These theoretical considerations are in good agreement with experimental findings (e.g. Twomey 1971 and 1972) which suggests that the majority of active condensation nuclei are composed of water soluble ammonium sulfate particles with dry radii greater than 0.01 0.05 urn.
It follows from the foregoing discussion that, if the number of particles with low critical supersaturation is significant, a droplet population of high concentration and small average radius will be produced (providing that other factors, e.g. updraft speed, remain the same). In this case the concentration of the substances serving as condensation nuclei will be high in the cloud water. The number of active nuclei depends on the degree of pollution of the air as well as on the age of the aerosol present. Moreover, due to their mixing with the environment, the concentration of nuclei is larger near the edges of a given cloud. Thus, in a cloud parcel near the edge, the concentration of dissolved or suspended material in each drop is higher compared with drops in a parcel near middle of the cloud; this is also promoted by the smaller liquid water content caused by evaporation.
Because the mass of ammonium sulfate and sulfuric acid particles is mainly in the size range of active condensation nuclei, it is believed that this process provides a very effective removal mechanism for the tropospheric background aerosol. However, we have to emphasize that other processes are also operating in the cloud to remove small aerosol particles, of which the most important process is the coagulation of particles and cloud drops. As we have seen (Subsection 4.1.1), thermal coagulation is particularly effective in the range of very small particles inactive in condensation. To estimate this process, let us consider a cloud in which the number concentration of drops with radius rc is Nc. If the number concentration
' The critical supersaturation of solution droplets may be calculated by equations [4.13] and [4.14] by using relative humidities greater than 100 % The curves calculated in this way have a maximum at a certain supersaturation which gives the critical value (Fletcher, 1962). The critical supersaturation of insoluble particles is given by the Thompson formula, obtained by substituting x0 = 1 in equation [4.13].
of aerosol particles with radius rp is designated by Np, then the coagulation loss of particles per unit time may be written as follows (Greenfield, 1957):
where Dp and Dc are the diffusion coefficient (see Subsection 4.1.1) of particles and cloud drops, respectively. Equation [5.5] may be transformed into the simpler form dN„ r,
dt where K is equal to 2n(Dp + Dc)(rp + rc). In a turbulent cloud, coagulation due to the turbulent motion of particles and drops also has to be taken into account. In this case K = K' = KB+ K7, where KB represents the coagulation caused by the Brownian motion of particles, while K1 is the same parameter for turbulent coagulation. The value of this latter coefficient is given by equation [5.7]:
where a> is the gradient of the velocity (shear) perpendicular to the stream trajectories. When these points are taken into account, integration of equation [5.6] yields:
which means that the concentration of particles decreases exponentially with time, owing to their removal by coagulation with cloud elements. It should be mentioned that this removal mechanism is most effective at the cloud edges, where the mixing with the environment provides a constant particle input into the cloud.
By means of equation [5.8] Greenfield (1957) showed that particles with diameters smaller than 0.01 /im are almost entirely removed from cloudy air under normal conditions.
Aerosol particles may also be removed in the clouds by the different phoretic forces, e.g. by diffusiophoresis. This phenomenon involves the motion of particles due to concentration gradient of condensing or evaporating vapour (Goldsmith et al„ 1963). In the case of condensation, particles displace towards the drop surface. According to Goldsmith et al. (1963), velocity caused by diffusiophoresis is
dx where dp/dx is the water vapour gradient expressed in millibar cm ~1 (the dimension of Dp are cms"1). Laboratory experiments and calculations show that the role of the diffusiophoresis in liquid clouds is small compared to the effect of condensation and coagulation. However, in so-called mixed clouds, containing both liquid drops and ice crystals, relatively large numbers of particles can be removed by growing solid cloud elements (Vittori and Prodi, 1967).
The foregoing discussion can be summarized by a simple mathematical expression (Junge, 1963):
w where Cia is the concentration of trace constituents in precipitation due to aerosol particle removal, w is the liquid water content of the cloud, and Ea gives the removed faction of the mass concentration of particles (Ma). Junge (1963) estimated that under tropospheric background conditions £„ is equal to 0.9-1.0, which means that practically all particles are removed from the air during cloud formation.
After cloud formation the sorption of soluble trace gases begins immediately. Rain-out is particularly important in those cases in which an absorbed gas reacts irreversibly in the liquid phase with another constituent. Examples of this type of transformation are provided by S02, NH3, N02 etc. In the following we will deal mostly with S02 removal which is discussed in a considerable body of papers. However, the main points of the rain-out of NH3 and N02 will also be mentioned.
The rain-out of reactive gases is determined by the transport of gas molecules to the droplet surface, their molecular diffusion into the liquid water, and by their rate of chemical transformation. It is shown (Beilke and Gravenhorst, 1978; Hales, 1978) that, in case of sullbr dioxide removal, the rate of this latter process is much smaller than that of diffusion, since the equilibrium between S02 in the gas phase and sulfur(IV) in liquid water is reached within less than 1 s (in this form of notation, a Roman numeral in parentheses means the valence of the elements). For this reason the oxidation of sulfur(IV) in cloud drops is the rate-determining process in S02 removal.
To understand this removal mechanism let us consider a heterogeneous system in which S02 in the gas phase is in equilibrium with sulfur(IV) in liquid water. This equilibrium is represented by the following three equations:
In these equations sulfur (IV) in the aqueous phase is the sum of S02 • H20, HS03 and S03~, while [5.11] describes a simple physical dissolution. Considering the foregoing discussion, the problem is to determine the nature and rate of the sulfur (IV)->sulfur (VI) transformation of bisulfite (HS03) or sulfite (SOf~) ions (unfortunately there is no agreement among different authors as to whether the bisulfite ion, the sulfite ion, or both is the reactive species). It is well documented that the oxidation of sulfur (IV) to form sulfate ions can be proceeded by the following processes:
(a) oxidation by 02 in the absence of catalysts;
(b) oxidation by 02 in the presence of catalysts;
(c) oxidation by strongly oxidizing agents (03, H202).
The overall reaction of sulfite ions with absorbed oxygen is as follows:
Reaction [5.14] was studied in the absence of catalysts by several authors. It was found that the oxidation is zero order with respect to oxygen while the order is unity with respect to bisulfite ions. Unfortunately very different reaction rates (k) were obtained by different research groups, as reviewed by Beilke and Gravenhorst (1978). There is agreement, however, that k depends on the pH of the solution. Thus Beilke et al. (1975) recently found that k = l.2 x 104[H+]"° 16
in a pH range of 3-6 and at a temperature of 25 °C. In this equation, k is expressed in s "while the dimensions of the concentration of hydrogen ions ([H+]) are mol 1" Owing to this pH dependence some authors argued that ammonia gas, by raising the pH, plays an important part in this process. For example, using the model developed by Scott and Hobbs (1967), Georgii (1970) calculated that the rate of formation of sulfate ions in liquid water depends more strongly on the NH3 concentration than on the S02 level, both in the air. However, new investigation by Drews and Hales (mentioned by Scott, 1978) shows that ammonia is much less soluble at atmospheric concentrations than previously thought. Furthermore, it is argued (Beilke and Gravenhorst, 1978) that the effect of acid droplets in the atmospheric particulate matter is not taken into account in the model of Scott and Hobbs (1967) giving generally rather high pH values. Thus, the most prevalent present opinion is that the major function of absorbed NH3 is to transform preexisting sulfuric acid to ammonium sulfate, not to enhance sulfur (IV) oxidation. In any case this process provides an effective NH3 removal mechanism during the lifetime of the clouds.
Much more rapid transformation rates were obtained by using metal catalysts in the aqueous system (e.g. Junge and Ryan, 1958). Manganese and iron were found to be especially effective. Experiments also show (Hegg and Hobbs, 1978) that catalysis by certain "mixed" salts produces larger effects than one metal salt alone. On the basis of this finding Hegg and Hobbs (1978) argue that this process is of importance in clean rural air, while others (Beilke and Gravenhorst, 1978) speculate that this type of sulfur (IV) oxidation is significant only in urban fogs where the concentration of metal catalysts is high.
Sulfate formation by pathways (c) was studied by Penkett (1972) and Penkett and Garland (1974). Their laboratory experiment with bulk water and water drops demonstrated that 03 oxidizes bisulfite ions very rapidly and effectively. These authors found that at 10 C, with an ozone concentration of 0.05 ppm, the sulfate formation rate is given by the following equation:
at where k' is 3.76 x 10~4 s"1. Since bisulfite ion formation is determined by pH and the SO2 concentration in the air, these parameters also influence the sulfate production rate. In a more recent investigation Penkett and his co-workers also showed (see Beilke and Gravenhorst, 1978) that sulfate (IV) oxidation by H202 in water samples is also very fast. However, the concentration of this species in the atmosphere is an open question.
The above discussion is summarized in Fig. 42. In this figure, due to Beilke and Gravenhorst (1978), three curves are represented. The dashed line shows the uncatalyzed sulfate formation rate as a function of pH as reported by Beilke et al. (1975) for 10 °C and for a S02 concentration of 1 ppb. The solid line indicates the
[mgr1 mirij g
- Betz (O2 catalyzed)
''Beilke e/al (1975) (Oouncatalyzed)
Sulfate formation rate in the droplet phase as a function of pH of the liquid for three different S02 oxidation mechanisms (Beilke and Gravenhorst, 1978). Conditions: S02; 1 ppb; 03:40 ppb; 7= 10 C. (By courtesy of Atmospheric Environment)
results of Betz (see Beilke and Gravenhorst, 1978) obtained with natural rainwater containing manganese and iron in concentrations between 10 7-10~6 and 10"6-10"5 molar, respectively. The pH of the rainwater samples ranged from 3.2 to 5.2. Finally, the upper line is based on the experimental results of Penkett (1972) obtained with an ozone concentration of 40 ppb (the other parameters as above). This figure clearly suggests that oxidation by 03 is the dominant pathway for the fixation of sulfur dioxide in clouds. However, further research is certainly needed to confirm the generality of this conclusion2.
The majority of sulfur found in cloud and rainwater is sulfate (see later), while some sulfite (10-30 % of the total) has also been identified. It is believed that the quantity of sulfate ions found in rainwater samples at the surface is practically independent of reduced sulfur species (hydrogen sulfide, organic sulfides) because of their limited solubility. In other words this means that the wet removal of these compounds is expected to be unimportant (Hales, 1978).
It is well known that, after its absorption, N02 forms nitric acid and nitrous acid in water. There is some indication that nitrite produced in this way is oxidized by dissolved 03 (Penkett, 1972). If neutralizing agents (ammonia, calcium carbonate etc.) are present, some nitrate salt is finally formed. It follows from this discussion that both S02 and N02 are oxidized in cloud water by atmospheric ozone. If this speculation is true a correlation should be found between the concentration of sulfate and nitrate ions in precipitation waters. Such a correlation was found in precipitation samples by Gambell and Fisher (1964) among others. However, correlations between any two species in rainwater must be considered with caution because the level of all ions is affected in a similar way by the precipitation intensity or quantity (see Subsection 5.4.1). Nevertheless the identical annual variations of the two ions in precipitation water (see Subsection 5.4.5) suggests that the two species are formed by some similar processes.
For the rain-out of trace gases, equation [5.10] can be applied. According to model experiments and calculations of Beilke and Georgii (1968) Eg (g: gas) ranges from 0.01 to 0.1 in the case of sulfur dioxide. On the other hand, Hales (1978) suggests that about 1 % of the airborne S02 will dissolve in the aqueous phase at a liquid water content of 1 g m" 3; this figure is equivalent to the lower limit proposed by the previous two authors.
5l3l3 Wash-out of trace constituents below the cloud base
Once a cloud is formed there are two possibilities concerning its future fate. One possibility is that the cloud partially or totally evaporates. In this case absorbed trace constituents again become airborne. However, a new aerosol spectrum is produced in this way compared to the size distribution before cloud formation, since
2 It is to be noted that the laboratory experiments of Berry (see Beilke and Gravenhorst, 1978) do not clearly support this conclusion.
one drop generally captures several aerosol particles and some trace gases are transformed irreversibly in cloud water (see the previous paragraph) to acids or salts. Thus, the average size of airborne particles is markedly larger after cloud evaporation than it was before cloud formation, which promotes the further removal of particulate matter.
The other obvious possibility is that materials absorbed are carried by precipitation to the surface of the Earth, that is they are definitively removed from the air. There is no intention here to discuss the formation of precipitation. We only mention that it is believed (Fletcher, 1962) that, in winter layer clouds with small liquid water content, ice crystals play an important role in precipitation formation, while in summer convective clouds the coalescence of large drops with smaller ones is the dominant process. At the same time we have to emphasize that the wet removal of trace constituents is continued by falling precipitation elements (snow crystals, raindrops) below the cloud base. This removal mechanism is called washout.
Aerosol particles below the cloud base are captured by precipitation elements due to gravitational coagulation. This type of coagulation is caused by the difference between falling speeds of the aerosol particles and the raindrops or snow crystals. In other words, this means that precipitation elements "overtake" the particles. The air molecules go around the falling drops (or crystals) while large particles are impacted against the drops due to their inertia. For this reason precipitation elements are considered to be small impactors (see Subsection 4.1.2).
Let us suppose that the radius of raindrops is uniform and equal to R. One raindrop obviously sweeps out an air volume of R2nh between the cloud base and the surface if the height of the cloud base is h. Let this air volume be filled with a monodisperse aerosol containing particles of unit density with radius r at a number concentration N(r\ Then the total mass of aerosol particles in the air volume swept out will be:
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