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Below-cloud scavenging by rain of atmospheric gases and particulates Nora Duhanyan*, Yelva Roustan CEREA, Joint Laboratory École des Ponts ParisTech - EDF R&D, Université Paris-Est, 77455 Marne la Vallée Cedex 2, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 September 2010 Received in revised form 19 August 2011 Accepted 1 September 2011

Below-cloud scavenging (BCS) by rain is one of the phenomena that control the removal of atmospheric pollutants from air. The present work introduces a detailed review of the most literature referred theories and parameterisations to describe the below-cloud scavenging by rain in air quality modelling. The theories and parameterisations in question concern the raindrop size distribution (RSD), the terminal velocity of raindrops, and the below-cloud scavenging coefﬁcient for gaseous and particulate pollutants. 0D computations are run to calculate the latter coefﬁcient with the help of the current theories and parameterisations thus extracted from the literature. As a result to improve the atmospheric modelling studies, it can be mentioned that the choice of the raindrop terminal velocity among the available parameterisations does not matter much and therefore, the practice of the most simple formulae is advised. On the other hand, a great dispersion on the scavenging coefﬁcient (several orders of magnitude) is observed related to the variations of the RSD. Therefore, a great care is recommended in the choice of the RSD with respect to the type of rain and sampling duration involved (e.g. thunderstorm, widespread, shower, etc.; long or instantaneous sampling duration). Many uncertainties do remain due to the lack of precision in the experimental records after which the RSD parameterisations are established or to the poor level of accuracy of the theoretical models. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Scavenging coefﬁcient Model Below-cloud scavenging by rain Raindrop size distributions Raindrop terminal velocities Gas Particulate matter

1. Introduction In air quality modelling, below-cloud wet scavenging (BCS) refers to the physical processes leading to the removal of pollutants, gases and particulate matters (PMs), from the atmosphere by precipitating hydrometeors (raindrops, snowﬂakes, hailstones). The present review focuses on the cleaning of the atmosphere by rain. In-cloud and fog scavenging, which are other wet scavenging processes, are not considered. The BCS is an essential mechanism to describe the concentration of pollutants both in the atmosphere and on the Earth surface. It is a sink of pollution for the atmosphere and a source for the ground ecosystem. It is involved in long term air quality issues such as acidiﬁcation, eutrophication, contamination by heavy metals or persistent organic pollutants, as well as, in short term events such as accidental release of radionuclides. In the transport equation describing the evolution of the atmospheric concentrations, BCS is usually modelled using the simple relation (1), where C is the atmospheric concentration (for instance in mg m3) and l, the scavenging coefﬁcient (in s1).

* Corresponding author. E-mail address: [email protected] (N. Duhanyan). 1352-2310/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2011.09.002

dC ¼ lC dt BCS

(1)

The mechanisms of wet scavenging and their implementation in the transport equation are investigated for many years (see for instance Hales (1972) and Hales (1978)). Established theories state a dependence of the BCS coefﬁcient, among other things, on the raindrop size distributions (RSDs) and on the raindrops terminal velocities. Here are shortly recalled the theoretical formulae of the scavenging coefﬁcient for gases, lg and for PMs, lp. The derivation of these formulae are detailed, for instance, in Seinfeld and Pandis (1998).

lg ¼

Z

2p Ddif Sh R NðRÞ e

Ddif Sh 3 2 v ðRÞ R2 HRu T t

z

dR

(2)

R

lp ¼

Z

pR2 vt ðRÞ EðR; rÞ NðRÞ dR

(3)

R

In the equations above, R and r (in m) are the raindrop and the PM radii, respectively. Ddif (in m2 s1) is the molecular diffusion coefﬁcient of the considered gaseous pollutant in the air. Sh is the Sherwood number to take the transfer of gases from air towards

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a moving raindrop into account (see the “Electronic Supplementary Material” later referred to as “ESM”). H (in M atm1) is the Henry’s constant for the considered gaseous species, Ru (0.0831 atm M1 K1), the universal constant for ideal gases, T (in K), the air temperature and ﬁnally, z (in m), the distance of the falling raindrop to the bottom of the cloud. E(R,r) is the collision efﬁciency of a PM with a raindrop. This is the probability for a PM of radius r to collide with a raindrop of radius R. In both Equations (2) and (3), N(R) (in m4) is the raindrops size distribution and vt(R) (in m s1), the raindrops terminal velocity. Lots of interesting papers address the topic of BCS. The different aspects involved in them, such as, the raindrop size distribution, are useful for many atmospheric study ﬁelds including, for instance, air quality or cloud modelling. However, to keep the present review within sensible limits, this paper is restricted to the air quality models, which do not address explicitly the fate and transport of the atmospheric aqueous phases. Yet, the development of the air quality models which will be presented here, remain of interest as they will continue to be requested for academic and operational purposes in the coming years. Recent reviews were published, for instance, by Sportisse (2007) (dealing with the parameterisations involved in both dry and wet scavenging but focusing on radionuclides) and by Wang et al. (2010) (an interesting work on the uncertainty assessment of the BCS models of atmospheric PMs). However, none to our knowledge shows such a thorough analysis as it is put forward in the present paper as regards the RSDs and the raindrops terminal velocities. This paper aims to explore comprehensively the BCS processes for gases and PMs. It also aims to discuss the relevance of the parameterisations to be used in atmospheric modelling. The available theories and a wide range of literature extracted parameterisations are reviewed and compared to assess the BCS coefﬁcient, l. This review aims to gather knowledge and provide recommendations for the development of 3D air quality models, though, the use of 0D parameterisations appears sufﬁcient to highlight the most important points. In all this paper, the SI units are assumed unless other ones are speciﬁed. In Section 2, the most often referred RSDs are sorted out with respect to the type of precipitation. The Section 3 is devoted to the experimental measurements and analytical parameterisations of the raindrops terminal velocities. The Sections 4 and 5 deal with the below-cloud scavenging coefﬁcients of gases and PMs, respectively. Finally, 0D computations of the scavenging coefﬁcient according to the theories are presented and compared to the literature extracted parameterisations. 2. Raindrop size distributions 2.1. Mathematical representation Rain can be described as a large number of falling droplets of water of different diameters. Mathematical representations of the raindrop populations in the air, called raindrop size distributions (RSDs), are used in order to assess modelling parameters such as the BCS coefﬁcient. Reviewing many years of published experimental investigations, it can be seen that several RSD functions were successfully ﬁtted to rainfall observations. These RSD functions are of four main kinds, exponential, gamma, log-normal (or Gaussian) and Weibull. They will be introduced in the present section. In what will follow, let’s identify by D the diameter of raindrops. The number concentration of raindrops with a diameter between D and D þ dD (let’s say a raindrop with diameter D) is then

dCðDÞ ¼ NðDÞdD where, N(D) is the raindrop size distribution.

(4)

In Table 1, are summarised the parameters to be provided (experimentally or analytically) to determine the different kinds of RSDs. 2.1.1. Gamma and exponential distributions In the early meteorological studies, four parameter gamma functions were often used to ﬁt the observed RSDs.

NðDÞjGamma ¼ ADa expðbD

g

Þ

(5)

Thus, the four parameters A, a, b and g in the equation just above are chosen to ﬁt the rainfall observations. Some of them can be even deduced from the meteorological conditions (e.g. the type of precipitation). In particular, when a and g are settled to 0 and 1, respectively, the distribution described by equation (5) is called exponential. 2.1.2. Log-normal distribution The Gaussian or normal probability density function is deﬁned as follows, where x is the arithmetic mean value of x and s, its standard deviation.

1

rðxÞ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e 2ps2

ðxxÞ2 2s2

(6)

Assuming that x ¼ ln D, the following log-normal distribution can be found, where Dg is the geometric mean for the diameters and sg, their geometric standard deviation.

NðDÞjLog-normal

ðlnDlnDg Þ2 2

Ctot e 2ðlnsg Þ ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 D 2p lnsg

(7)

Ctot is the total number concentration of raindrops regardless their diameter. 2.1.3. Weibull distribution The following three parameter probability density function was introduced in 1939 by the Swedish engineer and mathematician Dr. E.H. Waloddi Weibull.

rðxÞ ¼

c1 xac b c xa e b b

(8)

In this relation, a is called the location parameter, b, the scale parameter and c, the shape parameter or slope. For RSD purposes, the below presented distribution can be deduced from a two parameter Weibull distribution, that is, equation (8) with a ¼ 0.

NðDÞjWeibull ¼ Ctot

c1 Dc b c D e b b

(9)

Table 1 Summary of the needed parameters to fully determine the different size distributions. Name

Size distribution N(D)

Needed parameters

Exponential Gamma

AebD g ADa ebD ðlnDlnDg Þ2 Ctot qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e 2ðlnsg Þ2 2 D 2pðlnsg Þ c D c1 Db c Ctot e b b

A and b A, a, b and g

Log-normal

Weibull

Ctot, Dg and sg

Ctot, b and c

N. Duhanyan, Y. Roustan / Atmospheric Environment 45 (2011) 7201e7217

2.1.4. Monodispersed raindrops To ease the computations, very often a single diameter is assumed to be representative of a whole range of raindrop diameters. Here are introduced some of the most often used representative diameters in wet scavenging studies. Dmean: The arithmetic mean value of diameters. Dmedian: The median value of diameters. Dmode: The mode value which is deﬁned as being the most often observed diameter value. All these deﬁnitions can also apply to the mass or volume distributions of droplets. Thus, instead of the arithmetic mean diameter, the diameter corresponding to the arithmetic mean value volume of the observed masses ðDmass mean Þ or volumes ðDmean Þ can be considered. As a matter of fact, for spherical droplets, the two last diameters are found to be identical. In a similar way, the median

mass or the median volume diameters ðDmass ; Dvolume Þ and the median median mode mass or the mode volume diameters ðDmass ; Dvolume Þ can be mode mode considered. 2.2. Type of rain and sampling duration Fujiwara (1965) studied many rain events from Miami (Florida, USA), Champaign (Illinois, USA) and Tokyo (Japan). He noticed that the proﬁles of drop size distributions were varying with the type of rain, with the measurement sampling duration and even with the rain event itself. He stored rain in three main categories: thunderstorm, shower and continue. Ever since, similar nomenclatures were suggested by many authors, such as, Waldvogel (1974, thunderstorm, shower, widespread), Joss et al. (1967, thunderstorm, widespread, drizzle), Ulbrich (1983, orographic, thunderstorm, shower and widespread), Mircea and Stefan (1998, heavy, moderate, light), Campos et al. (2006, convective, transition, stratiform) and Saikia et al. (2009, thunderstorm, shower, drizzle). Thunderstorms are characterised by wind, lightnings and high intensity rains. They are associated to convective thick cumulonimbus clouds. Shower rains or warm rains are related to thinner clouds with lower convective activities (cumulus congestus). Widespread or continuous rains are due to stratiform clouds (nimbostratus) without wind and convective motion. Drizzle is a very light rain with very small droplets and is also associated to stratiform clouds (stratus). Finally, orographic rains are due to the elevation of humid air along a mountain. The air is thus cooled and the water in it condensated into rain. In below-cloud scavenging by rain, the diameter of raindrops generally ranges between 100 mm (drizzle) and 6 mm (thunderstorm) (Michaelides, 2008). Raindrops for drizzle type of precipitation have diameters ranging between 50 and 500 mm (Pujol et al., 2007). Raindrops of higher than 6 mm diameter are unstable and break into smaller raindrops (Pruppacher and Klett, 1998; Willis, 1984). In all the literature which was reviewed for the present study, no mention was made of smaller or bigger raindrops which precipitate to the ground surface. This does not mean there is no smaller drops reaching the ground. Their concentration is just too low to interfere in BCS. Interesting attempts were made to connect to the different types of rain, some physical or statistical parameters such as the total number concentration of raindrops, the parameters related to the gamma functions, the standard deviation, the intensity of rain, the water content of the air, etc. Please see the joined “ESM” for more information. The classiﬁcation proposed by Mircea and Stefan (1998) can be mentioned as a representative example (Table 2). The raindrop size distribution measuring devices and facilities most often referred to in the papers are the laser spectrometer

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Table 2 Categories of rain proposed by Mircea and Stefan (1998). uL (in m3water m3 air ) is the precipitating water content of the atmosphere, Ctot (in # m3) is the total concentration of raindrops in the atmosphere regardless their size and I (in mm h1) is the rain intensity.

Light Moderate Heavy

uL 106

Ctot

I

0e1 1e5 5e15

107 5000 500

1e5 5e100 100e500

(ﬁt to airborn measurements), the vertical incidence Doppler radar (can scan the air from ground level up to several hundreds or even thousands of metres) and, mainly, the mechanical or optical disdrometer (can provide only ground based information). These apparatus measure the size of raindrops, their velocity and the number of them per size interval which are distributed in a given volume of air. A gauge is associated to those facilities to measure the intensity of rain. The sampling duration is also an important parameter to take into account when monitoring rainfall events. The measurements are said “instantaneous” when their duration is less than or equal to 1 min. The other measurements are said “long” (several minutes to hours). The accuracy of the raindrops size and velocity measuring devices is generally dependent on the sampling duration, on the minimum and maximum values of the diameters which can be measured and on the intensity of rain (Sheppard and Joe, 1994). The experimental facilities can not report the natural ﬂuctuations (both in time and space) of the number of drops for each drop size interval. However, the instantaneous measurements display these ﬂuctuations with a ﬁner temporal scale than the long sampling ones. The minimum and maximum diameters which can be measured induce truncation errors on the RSDs mainly for small and big size intervals. Finally, higher is the intensity of rain and lower is the accuracy of the size, shape and terminal velocity of raindrops that can be measured by the facilities. 2.3. Literature extracted parameterisations In Tables 3e6 are reported the literature extracted parameters for different types of raindrop size distributions (exponential, gamma, log-normal, Weibull and monodispersed). As a general comment, it can be said that there is not any deﬁnite agreement between the authors as to the RSD proﬁles to be used for a given type of rain. The authors suggest that the parameterisations they introduce should be used preferably in the same circumstances than those described in their paper (geographic location, type of rain, sampling duration for the measurements). However, to summarise the 60 last years of research on the matter, the following points can be highlighted. The exponential RSD of Marshall and Palmer (1948) is still nowadays one of the simplest and probably the most often used parameterisation in BCS studies. Best (1950a) was the ﬁrst to notice that a gamma function instead of an exponential one could ﬁt correctly widespread rain observations but was not convinced that this was also suitable for other types of rain. However, Ulbrich (1983) suggested that the gamma RSD functions provided a good enough description for most rain types. Fujiwara (1965) concluded that exponential RSD proﬁles ﬁtted well instantaneous measurements of thunderstorms but they were not that good for other kinds of rain. According to Waldvogel (1974), exponential RSDs were also sufﬁcient to parameterise instantaneous orographic rains. In opposition to this, Joss and Gori (1978) showed that the RSD proﬁles could be ﬁtted by exponential functions for long sampling durations only. Whatever the type of

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Table 3 Literature extracted parameters for gamma and exponential raindrop size distributions. The intensity of rain (I) is in mm h1. For sampling, “long” means several hours. A (m3 m(1

Reference Marshall and Palmer (1948) Best (1950a) Joss et al. (1967) e e Sekhon and Srivastava (1971) Wickerts (1982) Ulbrich (1983)a Ulbrich (1983)b e e Ihara et al. (1984) Willis and Tattelman (1989) Massambani and Morales (1991) Coutinho and Tomas (1995) Delrieu et al. (1996) Cerro et al. (1997) De Wolf (2001)a Chapon et al. (2008) a b

þ

a)

)

6

8 10 0.9I0.324 1.4 106 7 106 30 106 7 106I0.37 6 106I0.15 5.1 106I0.03 4.45 107 1.37 1012 4.49 107 1.73 107I0.16 1.06 1014I0.0295 2.91 1011I0.0524 390 103e1150 103 5.43 106I0.107 2.32 106I0.22 1.22 1016I0.384 7.506 1018I0.001

a

b (mg)

g

Type of rain

Sampling

0 1.75 0 0 0 0 0 0 0.4 1.63 0.18 0 2.16 2 0 0 0 2.93 3.47

4100I0.21 3.12 106I0.522 3000I0.21 4100I0.21 5700I0.21 3800I0.14 3800I0.21 3800I0.2 3449I0.2 5000I0.16 4695I0.21 5110I0.253 5679I0.153 1.41 106I0.287 3720I0.221 for I > 4 mm h1 3990I0.195 4000I0.1065 5380I0.186 7640I0.214

1 2.25 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1

Widespread Widespread Thunderstorm Widespread Drizzle Thunderstorm Widespread, shower, drizzle Widespread Thunderstorm Shower Widespread Widespread Hurricane / Widespread Widespread Widespread Widespread Widespread

Long Long Long e e Instant. Instant. Long Instant. e e Long Instant.

(1 min) (30 s) (1 min)

(1 min) / Instant. (1 min) Several minutes Instant. (30 s) Long Instant. (1 min)

After the measurements of Laws and Parsons (1943). After the measurements of Fujiwara (1965).

rain, according to them, instantaneous measurements could be better described by monodispersed RSDs. Chapon et al. (2008) suggested that gamma distributions were more ﬁt to instantaneous measurements than exponential distributions, when Sekine and Lind (1982) thought that a Weibull function was certainly much better than both gamma and exponential. Finally, after having studied the differences between the exponential and gamma functions for the RSDs, Smith (2003) concluded that the beneﬁts brought by one or the other of these proﬁles were falling within the observational uncertainties. Therefore, he recommended to use the most simple possible formulae. Joss et al. (1967) were one of the ﬁrsts to suggest that the RSD proﬁles were dependent on the sampling duration of the rainfall measurements. This point of view was later contradicted by Chapon et al. (2008) who, like Cerro et al. (1997) and later Harikumar et al. (2010), was more inclined to think that the RSD proﬁles were rather dependent on the intensity of rain. As a matter of fact, Feingold and Levin (1986), Cerro et al. (1997), Ochou et al. (2007) and Harikumar et al. (2010) suggested lognormal RSDs for instantaneously sampled rain events. In the Figs. 2e6 from the “ESM” are plotted the literature extracted RSDs. As can be seen, the parameterisations obtained are in good agreement for each type of rain and also for each type of RSD function, granted that the diameters are between 1 and 3 mm. Indeed, for thunderstorms, the discrepancy between the suggested RSDs are less than one order of magnitude. The same observation goes for widespread type of rains (instantaneous sampling) when using gamma RSDs. For log-normal and Weibull RSDs, as well as, for widespread rains (long sampling duration), the discrepancies observed are even less than a half order of magnitude. This is quite good, keeping in mind that the scatter of the measured rainfall data can be about one or two orders of magnitude for similar rain events

Table 4 Literature extracted parameters for Weibull raindrop size distributions. The intensity of rain (I) is in mm h1. Reference

Ctot (m3)

b (m)

c

Sekine and Lind (1982)

1000

2.6 104I0.44

0.95I0.14

Type of rain

Sampling

/

/

(for instance, see Fig. 3 of Sekhon and Srivastava (1971)). On Fig. 1 are reported together all the literature extracted parameterisations. It can be concluded that for most of the RSD functions used, the distributions are in quit good agreement for raindrop diameters between 1 and 3 mm (the maximum scatter observed is about one order of magnitude), provided that the comparisons are made for suitable intensities of rain. The differences become important for low and high values of the raindrop diameters. However, their impact on the scavenging coefﬁcient is not obvious and is presented in the following sections. In Fig. 3, are presented the intensities of rain, I, computed using the relation (6) from the “ESM”. Thus, the different RSDs were integrated with the Kessler’s terminal velocity (please see Table 7) all over the raindrop diameters (0.1 < D < 6 mm). First, an intensity of rain was assumed. Second, the intensity of rain was computed and compared to its assumed value. In Fig. 3, it can be seen that most of the RSDs (which are empirical interpolations of rainfall observations) ensure the conservation of the rain rate at more or less 30%. However, some parameterisations (Chapon et al., 2008; Coutinho and Tomas, 1995; Cerro et al., 1997) show a deviation much more important. As the theoretical relation for the intensity of rain (see relation (6) from the “ESM”) involves an empirical formula for the RSD, as well as, for the terminal velocity of raindrops, it is difﬁcult to draw out deﬁnite conclusions as to the validity of the above cited parameterisations. Indeed, the conservation of I depends on the quality of the interpolations performed to establish the parameterisations for, both, the RSD and the terminal velocity of raindrops. For instance, the latter is expected to deviate from reality because of the atmospheric conditions which are not taken into account in the empirical formulae (please see Section 3). In air quality modelling the use of detailed RSDs to determine BCS coefﬁcients is usually avoided to limit computational burden. In Fig. 2 are displayed several parameterisations found in the literature for a monodispersed representation of rain. The inﬂuence of the use of such parameterisations is discussed in Section 6. 3. Terminal or settling velocity of raindrops For below-cloud modelling purposes, it is generally assumed that the raindrops fall at their terminal speed (or settling velocity), whatever their position (their height) in the atmosphere. The transient period to reach that speed is then totally neglected.

N. Duhanyan, Y. Roustan / Atmospheric Environment 45 (2011) 7201e7217

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Table 5 Literature extracted representative raindrop diameters. For sampling, “long” means several hours. The intensity of rain (I) is in mm h1. Reference

D (m)

Laws and Parsons (1943) Best (1950a) Atlas (1953)a Blanchard (1953) Jones (1956) Sekhon and Srivastava (1971) Slinn (1977) Ulbrich (1983)b e e Willis (1984) Coutinho and Tomas (1995)

1.238 7.88 0.9 3.97 8 1.3 7 1.18 1.06 0.82 9.7 1.16

a b

103I0.182 104I0.3 103I0.21 104I0.37 104I0.34 103I0.14 104I0.25 103I0.2 103I0.16 103I0.21 104I0.158 103I0.227 for I > 4 mm h1

Deﬁnition

Type of rain

Sampling

Median volume Median volume Median volume Median volume Median volume Median volume Mean volume Median volume e e Median volume Median volume

Widespread Widespread Widespread Orographic Shower Thunderstorm Steady frontal Thunderstorm Shower Widespread Hurricane Widespread

Long Long Long / / Instant. (1 / Instant. (1 e e Instant. (1 Instant. (1

min) min)

min) min)

After the works of Marshall and Palmer (1948). After the works of Fujiwara (1965).

If the raindrop is assumed to behave as a solid sphere (which is certainly not true for big size droplets, please see Pruppacher and Klett, 1998), its terminal speed is calculated using the second law of Newton. Many parameterisations of the raindrops terminal speed do also exist. Most of them are based on laboratory performed experimental observations (the effects of atmospheric conditions are not taken into account). They are usually given under a handy form depending on the raindrop’s diameter and are based on ﬁve main series of measurements carried out by Davies in 1939 (cited by Best (1950b)), by Laws (1941), by Gunn and Kinzer (1949), by List in 1958 (cited by Liu and Orville (1969)) and by Wang and Pruppacher (1977). All these measurements, concerning raindrops from 0.25 to 7 mm diameter, are in very good agreement (please see Fig. 1 in the “ESM”). In Table 7 and Fig. 4 are presented the parameterisations most often referred to, especially for below-cloud scavenging purposes. The analytical formulations of the terminal velocity established by Beard (1976), also reported in Fig. 4, are split in three different ﬂow regimes. The ﬁrst regime is for the very small raindrops needing sleeplaw correction (Re << 1; 0.5 mm < D < 19 mm), the second one is for Stokes to moderate ﬂow regimes (Re up to 300; 19 mm < D < 1.07 mm) and the third one for high Reynolds number regimes where the raindrops are deformed such that the spherical shape assumption can no more apply (300 < Re < 4000; 1.07 mm < D < 7 mm). Though being in very good agreement with Gunn and Kinzer’s measurements (please see Fig. 4) and widely referred to by Wang and Pruppacher (1977) and by Pruppacher and Klett (1998), the form in which these relations are presented is less convenient for air quality modelling studies. Indeed, their implementation in a numerical model tends to increase the number of basic operations without notably improving the computed results (please see Section 6). All the measurements and parameterisations presented in this section are related to observations and studies made at ground level, in standard atmospheric pressure and temperature (1013 hPa and 20 C). In case the studies concern higher atmospheric levels (lower pressure and temperature), as suggested by Foote and Du Toit (1969), a correction should be applied to the ground level parameterisations:

vt ¼

vground t

rground air rair

!0:4 (10)

This correction was made out using Davies measurements of 1939 which were carried out not only for standard but also for different atmospheric conditions. Moreover, as explained by Foote and Du Toit (1969), if the drag coefﬁcient (CD, please see the “ESM”) of the droplet does not depend on the atmospheric pressure, then the power law in relation (10) is changed from 0.4 to 0.5. Once all these parameterisations plotted on a same graph (see Fig. 4), it can be seen that three of them provide a very satisfactory match with the experimental data (displayed on the same graph by Gunn and Kinzer (1949)). Indeed, the parameterisations of Best (1950b), Beard (1976) and of Atlas et al. (1973) follow very closely the experimental curve from 0.1 to 6 mm diameter which is the range of raindrop diameters typically involved in BCS. However, the other parameterisations, such as Kessler’s, have a very simple analytical expression. As to the discontinuity of the solid sphere plot, as speciﬁed by Sportisse (2007), it corresponds to a change in the correlation used to determine the settling velocity, for Reynolds numbers greater than 450e500 (please see the “ESM”). 4. Scavenging of gases The polluting chemical species in the air which happen to be in the vicinity of the falling raindrops diffuse towards or from them (as long as there is a difference of concentration between the raindrop and its vicinity). The concentration of species in the air at the raindrop surface is controlled by this diffusive ﬂux and also by the Henry’s law that makes the concentration of species in the air, at the surface of the raindrop, to be at any time linked to the concentration of the species inside the raindrop (assumed homogeneous). As soon as, the concentration induced by the diffusive ﬂux is different from the concentration commanded by the Henry’s equilibrium, a ﬂow of species inters

Table 6 Literature extracted parameters for log-normal raindrop size distributions. The intensity of rain (I) is in mm h1. Reference

Ctot (m3)

Dg (m)

Feingold and Levin (1986) Cerro et al. (1997) Ochou et al. (2007) Harikumar et al. (2010)

1.72 102I0.22 1.94 102I0.3 77.45I0.44 268.06I0.308

7.2 6.3 1 5.96

104I0.23 104I0.23 103I0.16 104I0.216

sg

Type of rain

Sampling

1.43 3 104I for I > 5 mm h1 1=2 2 expð0:1911:110 lnIÞ 1=2 ð8:48 Þ exp 0.0217lnI þ 1.55

Widespread Widespread Shower Monsoon

Instant. Instant. Instant. Instant.

(1 min) (30 s) (1 min) (1 min)

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N. Duhanyan, Y. Roustan / Atmospheric Environment 45 (2011) 7201e7217

Fig. 1. Literature extracted RSD parameterisations (please see Tables 3, 4 and 6).

or exits the raindrop in order to establish a new Henry’s equilibrium. In order to put the above described phenomenon into equation, it is assumed that the raindrop’s size is very big compared to the mean free path of the air molecules and that the volume of the supposedly spherical raindrop is not affected by the dissolution or evaporation of species, nor by the condensation or evaporation of water. The concentration inside the raindrop at the beginning of the fall is also neglected with respect to the concentration that would be in equilibrium with the concentration in the surrounding air. The latter concentration is still supposed not to vary with height. Moreover, when it is assumed that the Henry’s constant remains unchanged, the expression (2) is found for the below-cloud scavenging coefﬁcient.

Fig. 2. Literature extracted parameterisations for representative diameters (please see Table 5). The sampling durations are instantaneous (less than or equal to 1 min) or long (several hours or days).

Fig. 3. Rain rate computed from the literature extracted RSDs for different rain types. The sampling durations are instantaneous (less than or equal to 1 min) or long (several hours or days).

N. Duhanyan, Y. Roustan / Atmospheric Environment 45 (2011) 7201e7217 Table 7 Literature extracted parameterisations for the terminal velocity of raindrops (vt). The diameter (D) of raindrops is given in m. vt in (m s1)

Reference Spilhaus (1948) Best (1950b)

a

142D1/2 1:147 i h 1000 D 9:43 1 e 1:77

b

Liu and Orville (1969)e 842D0.8 Kessler (1969)a Atlas et al. (1973)

130D1/2 9.65 10.3e(600D) for D > 104

f

Beard (1976)f

f1 ðDÞ f2 ðDÞ f3 ðDÞ

for

0:5 106 < D < 19 106 19 106 < D < 1:07 103 1:07 103 < D < 7 103

Atlas and Ulbrich 386.577D0.67 (1977) Sekhon and Srivastava 267.85D0.6 (1971) Uplinger (1981)c 4854.1De195D Zhao and Zheng (2006) Campos et al. (2006)d Abel and Shipway (2007)d

f

3:075 107 D2 3:8 103 D 133:046D1=2

for

D < 104 104 < D < 103 103 < D

0.193 þ 4.96 103D 9.04 105D2 þ 5.66 107D3 4854.1De(195D) þ 446.01D0.782e(4085.35D)

The parameterisations of Atlas et al. (1973) and Campos et al. (2006) give negative values for D less than 0.1 mm and 40 mm, respectively. a After the measurements of Laws (1941). b After the measurements of Davies (unpublished, 1939). c After the measurements of Mason (1971). d After the measurements of Gunn and Kinzer (1949). e After List’s meteorological tables (1958). f The Beard (1976) formulae are detailed in the “ESM”.

It is also interesting to notice that if a unique representative radius R is assumed for all the raindrop population, then equation (2) leads to the following expression,

lRg ¼

3 Ddif Sh u e 2 L R2

3 Ddif Sh z 2 v R2 HRu T t

7207

It is important to keep in mind that aqueous chemistry potentially inﬂuences the scavenging of gases through the production/ destruction of the scavenged species in the raindrop. The mass transfer rate from the air to the droplet can be enhanced or limited. An interesting discussion on this topic is lead in Hales (1972) or more recently in Zhang et al. (2006). The current analysis will be restricted to the extreme cases (highly soluble and scarcely soluble gases) and to the intermediate ones without considering the chemical context. Here, it will be mainly question of checking the sensitivity of the scavenging coefﬁcient to the apparent solubility. Please do take notice that the approach introduced here, which takes only the diffusion driven kinetics into account, is not the only possible approach to quantify the scavenging coefﬁcient. More detailed kinetic aspects can be introduced, for instance, when it comes to considere a detailed aqueous chemistry (Seinfeld and Pandis (1998)). On the other hand, simpliﬁed parameterisations or empirical formulations are often proposed (see Table 8). A simpliﬁed approach assuming an instantaneous Henry’s equilibrium to partition the pollutant mass between the gaseous and aqueous phases, can also be used. 4.1. The particular case of highly soluble gases For a very soluble gaseous species, Henry’s constant is high enough to lead the exponential term of equation (2) towards unity. Therefore, whatever the initial concentration of the raindrop and its distance to the bottom of the cloud, the considered very soluble gaseous species is scavenged anyway from the atmosphere. The scavenging coefﬁcient is then constant and given by

lg;soluble ¼

Z

2p Ddif Sh R NðRÞ dR

(12)

R

(11)

where, uL is the precipitating water content of the air (in m3water m3 air , please see the joined “ESM”).

and, in the case of monodispersed raindrops of radius R, by

lRg;soluble ¼

3 Ddif Sh u 2 L R2

Fig. 4. The most often used parameterisations of raindrop terminal velocities versus the raindrop diameter.

(13)

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Table 8 Literature extracted parameterisations for the below-cloud scavenging coefﬁcient of atmospheric gases. The intensity of rain (I) is in mm h1. Reference

lg (s1)

Pollutant

Type of rain

According to

Chang (1984)

0.33 104I0.42 þ 104I0.58

HNO3 highly soluble

Theory and computations

e

0.34 104I0.65 þ 1.1 104I0.76

e

Asman (1995)

aIb

Mizak et al. (2005) Calderon et al. (2008)

8.94 105I0.66 2.277 105I0.0787

Highly soluble (e.g. HNO3, NH3, HCl, H2O2) NH3 highly soluble HNO3 highly soluble

Widespread (RSD from MarshallePalmer) Widespread (RSD from SekhoneSrivastava) Convective

Field experiments and computations Field experiments and computations

e

4.43 105I0.7338

e

e

6.655 105I0.6194

e

Convective summer thunderstorm Convective thunderstorm (RSD from SekhoneSrivastava) Convective thunderstorm (RSD from MassambanieMorales) Convective thunderstorm (RSD from FeingoldeLevin)

e Theory and computations

e e

For Asman (1995), a ¼ 4.476 105 1.347 107T0 þ (3.004 107 þ 1.498 109T0)RH0 þ (8.717 2.787 102T0 þ (5.074 102 þ 2.894 104T0)RH0)Ddif and b ¼ 9.016 102 þ 2.315 103T0 þ (4.458 103 2.115 105T0)RH0. I is the intensity of rain (in mm h1), T0 and RH0 are respectively the temperature (in K) and the relative humidity (between 40 and 90%) at ground level. Ddif is the molecular diffusion coefﬁcient (in m2 s1) of the pollutant in the atmosphere at ordinary atmospheric conditions (1 atm and 25 C).

4.2. The particular case of scarcely soluble gases The cloud droplets (before the precipitation begins) are already in equilibrium with their environment and few or no more species can be scavenged from the atmosphere by the falling raindrops. Even when assuming the raindrops are totally free of pollutant, a ﬂow of species enters the droplets which get saturated almost immediately. The concentration in the raindrops is then directly given by the equation relating Henry’s equilibrium.

C liq ðz; tÞ ¼ HRu TCN ðtÞ

(14)

In other respects, it can be seen that the concentration in the raindrops does not depend any more on the distance z to the bottom of the cloud, neither on the size of the raindrop. Therefore, it is sensible to assume

lg;nonsoluble x0

(15)

It can be tricky to deﬁne a boundary to shift from one to the other of the above introduced formulations of the scavenging coefﬁcient. The general formula (2) is always valid but would cost too much computational time. According to Seinfeld and Pandis (1998), for a Henry’s constant less than 100 M atm1, the pollutant is scarcely soluble and for a Henry’s constant more than 10,000 M atm1, it is highly soluble. 5. Below-cloud scavenging of particulate matters PMs are captured by raindrops essentially by collision. Collision becomes possible when the PMs are located in a cylinder of radius (R þ r) centred around the falling raindrop (R and r being the raindrop and PM diameters, respectively). However, even though PMs are located in that volume, collision does not necessarily occur. Indeed, PMs are pushed aside by the streamlines induced by the

falling raindrop itself. Let’s call E(R,r), the collision efﬁciency (please see the joined “ESM”). This is the probability for a PM of radius r to collide with a raindrop of radius R. For convenience, it is also assumed that any collision leads to the capture of the particle by the raindrop. Moreover, the PM fall speed is neglected with respect to the raindrop terminal velocity. Following these assumptions, equation (3) is established for the scavenging coefﬁcient of PMs of radius r. Now, if it is assumed that a single representative radius R can account for all the raindrops (monodispersion), the following easy to use relation is obtained for the scavenging coefﬁcient.

lRp ¼

u 3 vt EðR; rÞ L 4 R

(16)

In this paper, collisions only due to interception, inertia and Brownian motion are taken into account. This is achieved with the help of the formula for the collision efﬁciency given in Slinn (1983) (please see the “ESM”). A comprehensive discussion on the collision efﬁciency can be found in Wang et al. (2010). In the latter are discussed the parts played in the scavenging coefﬁcient by the different processes leading to the capture of a particle by a falling raindrop. A discussion on the sensitivity of the collection efﬁciency (thus, of the scavenging coefﬁcient) to the different parameterisations can also be found. It is clear that the collection efﬁciency is strongly sensitive to the size of the scavenged PMs. However, as the current study focuses on the inﬂuence of the RSD and of the terminal raindrop velocity, the scavenging coefﬁcient for the PMs are rather displayed as a function of the rain intensity. 5.1. Particle size distributions (PSDs) Usually, this is a class of different size particles which is characteristic of the pollution due to the PMs. Some of the works of reference on the matter were achieved by Jaenicke (1988) and

Table 9 PM in m3, d in m and sPM dimensionless). The PM size distribution (PSD) are Literature extracted parameters for one, two or three modes log-normal PM size distributions (Ctot gi gi i U: urban, R: rural, M: marine, RC: remote continental and A: alpine. Reference

PSD

PM Ctot 1

Jaenicke (1993) e e e Raes et al. (1997) Covert et al. (1996) Weingartner et al. (1999)

U R M RC M M A

993 665 133 32 329 235 4134

PM Ctot 2

108 107 106 108 106 106 105

111 147 666 29 2825 129 2738

107 106 105 108 105 106 105

PM Ctot 3

dg1

364 108 199 107 3.1 106 3 105 / / /

1.3 1.5 0.8 2 5.9 5 3.9

dg2

108 108 108 108 108 108 108

1.4 5.4 2.66 1.16 1.81 1.9 1.34

108 108 107 107 107 107 107

dg3

sPM g1

sPM g2

sPM g3

5 108 8.4 108 5.8 107 1.8 106 / / /

1.75 1.67 4.53 1.45 1.415 1.43 1.79

4.64 3.6 1.62 1.65 1.52 1.35 1.73

2.17 1.84 2.48 2.39 / / /

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Table 10 Literature extracted parameterisations for the below-cloud scavenging coefﬁcient of atmospheric PMs. The intensity of rain (I) is in mm h1 and the PMs diameter (dp) in m. Reference

lp (s1)

PM diameter

Type of rain

According to

ApSimon et al. (1988) Sparmacher et al. (1993) e e e Baklanov and Sorensen (2001)

104I0.8 2.34 107I0.588 3.14 107I0.604 2.56 107I0.942 1.72 106I0.611 8.4 105I0.79

137

Cs 0.23 mm 0.46 mm 0.98 mm 2.16 mm dp < 2.8 mm

Intense Any e e e Widespread

e e Brandt et al. (2002) Laakso et al. (2003)

f1(dp) f2(I) a 2.7 104I 3.62 106I2 8.4 105I0.79 10f3 ðdp ;IÞ b

dp > 137

2.8 < dp < 20 mm 20 mm Cs and 134Cs UFP (0.01 < dp < 0.5 mm)

Loosmore and Cederwall (2004) Andronache (2004) Chate (2005) Henzing et al. (2006) e e e e

4.29 104EI0.842 c f4(dp,I) d 7.5774 106expI/28.83 3 0:682 1Þ 1:45 104 ðexp1:1810 I 4 0:682 1Þ 6:75 105 ðexp6:7710 I 4 0:676 1Þ 5:66 105 ðexp5:8410 I 4 0:655 1Þ 6:11 105 ðexp6:3410 I 3 0:63 1 104 ðexp1:02610 I 1Þ

1 < dp < 10 mm UFP (dp < 0.1 mm) 0.02e1 mm 0.05 mm 0.23 mm 0.46 mm 0.98 mm 2.16 mm

e e Any Widespread, for I < 20 mm h1 Intense Thunderstorm Thunderstorm Widespread e e e e

Theory Field experiments e e e Theory from Naslund and Holmstrom (1993) e e Model from Maryon et al. (1996) Measurements Theory Theory Theory and ﬁeld measurements Computations e e e e

2 3 dp dp dp $106 0:03 $106 $106 þ 9:345 104 and f2 ðIÞ ¼ 2:7 104 I 3:62 106 I 2 . 2 2 2 4 b 1=2 f3 ðdp ; IÞ ¼ 274:36 þ 0:245I þ 332; 839:59½log10 ðdp Þ þ 226; 656:57½log10 ðdp Þ3 þ 58; 005:91½log10 ðdp Þ2 þ 6588:39½log10 ðdp Þ1 . c The collection efﬁciency E is calculated for the raindrop diameter (in m) Dr ¼ 9.7 104I0.158. 2=3 1=2 d f4 ðdp ; IÞ ¼ 2:809Ddif I 0:43 þ 0:163Ddif I 0:61 þ 0:01Ddif I 0:61 þ 0:097CC dp a2 I 0:64 , Ddif is the brownian diffusion coefﬁcient of the considered PM in air (in m2 s1), a is a parameter related to the electrical charge of the raindrop and PM (its value lies between 0 (for neutral particulates) and 7) and CC is the Cunningham slip correction factor (see “ESM” for more details). a

f1 ðdp Þ ¼ 0:15 þ 0:322

Jaenicke (1993). The latter named the different classes he observed after the area where the considered type of pollution was occurring (for instance, Urban, Rural, Marine, Continental, etc.). Each class was identiﬁed by a PM size-range and a one or several-modes lognormal distributions (please see equation (4) and Table 2 in Jaenicke, 1993). Directly inspired from these works, other measurements of particulate matters were reported later in the literature among which, can be mentioned Raes et al. (1997) for PMs related to marine environments in Northern Atlantic, Covert et al. (1996) for also marine PMs recorded in mid-paciﬁc and Weingartner et al. (1999) for Alpine PMs measured at Jungfraujoch (Switzerland). As did Jaenicke, all these authors suggested severalmodes PM log-normal distributions for the pollution classes they studied. The PM size distributions were then calculated according PM (the total to equation (17), just below, where the parameters Ctot i PMs concentration regardless their size in m3), dgi (the mean

geometric diameter of PMs in m) and sPM gi (the geometric standard deviation), i being the mode, are given in Table 9. As usual, N(dPM) is the PMs number size distribution given in (m4).

dCðdPM Þ ¼ NðdPM ÞddPM 0 B i¼n PM BP Ctot i e ¼B p ﬃﬃﬃﬃﬃﬃ ﬃ B @ i¼1 2p ln sPM gi

gi Þ ½lnðdPM Þlnðd

2ln2

sPM gi

2

1 C C 1 C C d ddPM A PM

(17)

Andronache (2003) introduced then an average below-cloud scavenging coefﬁcient to quantify the cleaning of the atmosphere in a given pollution class. He called it the mean mass scavenging coefﬁcient and deﬁned it as follows, where rPM (in kg m3) is the density of the particulates (supposed spherical) in the considered PM class and N(r) (in m4), their number size distribution.

Table 11 Literature extracted parameterisations for the average below-cloud scavenging coefﬁcient of atmospheric PMs. The intensity of rain (I) is in mm h1 and the PMs diameter (dp) in m. The PM size distribution (PSD) are U: urban, R: rural, M: marine, RC: remote continental and A: alpine. Reference

lm (s1)

PSD

Type of rain

According to

Mircea et al. (2000) e e e Andronache (2003) e e e e e e Calderon et al. (2008) e e

1.98 þ 0.319I 8.9 102 þ 1.47 102I 1.58 102 þ 2.17 103I 2.32 102 þ 3.68 103I 6.67 105I0.7 1.25 104I0.7 1.39 104I0.7 1.28 104I0.7 8.33 107I0.6 3.3 108I0.59 2.39 107I0.59 2.68 106Iln(I) þ 2.054 105I 3.312 105I0.8409 4.024 105I0.7976

Ua Ra Ma RCa Ua Ra Ma RCa Mb Mc Ad NO 3 e e

Widespread e e e Widespread and thunderstorm e e e e e e Thunderstorm e e

Theory and computations e e e Theory and computations e e e e e e Field experiments and computations e e

a b c d

Jaenicke (1993). Raes et al. (1997). Covert et al. (1996). Weingartner et al. (1999).

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Z

4

pr3 rPM lðrÞNðrÞdr

rZ3

lm ¼ Z

r

4 3 pr rPM NðrÞdr 3

Z

¼

r

R

(18)

r pR vt EðR; rÞNðRÞNðrÞdRdr Z r 3 NðrÞdr 3

2

r

5.2. Literature extracted parameterisations In the literature, can be found the parameterisations of the scavenging coefﬁcient versus the rain intensity. Usually, these ones were established analytically or according to experimental observations and even to numerical computations. In Tables 8, 10 and 11, some of them are presented. For highly soluble gases, most of the different parameterisations found in the literature are in good agreement (please see Fig. 5). The results Calderon SS (extracted from Calderon et al. (2008)) can seem surprising because they are very low with respect to the others. They correspond to an empirical parameterisation of the scavenging coefﬁcient ﬁtted over different rain events and implicitly taking an exponential raindrop size distribution into account (exponential RSD of Sekhon and Srivastava (1971)). One can notice a lack of consistency between the characteristic time scale of the measurements (hourly rain events) and the characteristic time scale used for the determination of the RSD (1 min or less for the work of Sekhon and Srivastava, 1971). However, this inconsistency alone does not explain the large difference observed. Indeed, the same theoretical issue occurs when the distribution proposed in Feingold and Levin (1986) is used (plot Calderon FL) without showing such a large difference with the other reported parameterisations. For the PMs, many differences can be observed and this, even for comparable size PMs (please see Fig. 6). The differences between the proﬁles can be due to the size of the scavenged particles, to the rain conditions, as well as, to the theoretical or experimental methods used. However, the few parameterisations found in the literature are not sufﬁcient to draw out more deﬁnite conclusions. For instance, the difference between Laakso et al. (2003) and Andronache (2004), the size of scavenged particles being the same, can be due to the rain type (widespread for the ﬁrst one and thunderstorm for the second) and also to the method involved (experimental for the ﬁrst one and theoretical for the second). ApSimon et al. (1988) and Brandt et al. (2002) give similar results but they are both devoted to the same PMs and were derived from theoretical considerations. Even the rain type in this case is not a determinant point. The big difference between Sparmacher et al. (1993) and Baklanov and Sorensen (2001) can not be explained just by the method used to derive the parameterisations (ﬁeld experiments for the ﬁrst one and theory for the second). In Fig. 7, the differences observed between the average scavenging coefﬁcients introduced by a same author are due to the different aerosol classes (PSDs). The differences observed between different authors can be due to the PMs size distributions, as well as, to the RSDs used in the computations. However, one set of parameterisations remains surprisingly high with respect to the others. The average belowcloud scavenging parameterisations from Mircea et al. (2000) are several orders of magnitude too high when compared with all the other parameterisations extracted from the literature. These results seem highly doubtful, all the more so a lack of consistency can be noticed between the formula the authors use to calculate the below-cloud scavenging coefﬁcient (equation (2) in their paper) and the units which are exhibited for it on their ﬁgures (s1).

Fig. 5. Some literature extracted parameterisations of the scavenging coefﬁcient of highly soluble gases versus the rain intensity.

6. Discussion The different parameterisations extracted from the literature and presented in the previous sections for the RSDs, as well as, the raindrop terminal velocities, are used to calculate the below-cloud scavenging coefﬁcient for gaseous and particulate pollutants, according to the introduced theoretical expressions. A simple Riemann method is used in order to compute the integrals. The consideration of a more efﬁcient numerical method would have been relevant in case of a 3D model. The range of diameters over

Fig. 6. Some literature extracted parameterisations of the size dependent scavenging coefﬁcient for the PMs versus the rain intensity.

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7211

which the integrations are performed is 0.1 < D < 6 mm. No signiﬁcant changes were observed in the results when decreasing the lower or increasing the upper limits. The computation results are presented in the ﬁgures below and compared to the reviewed parameterisations. As regards the parameterisations for the terminal velocities (of raindrops, Section 3), only two of those extracted from the literature were selected for the present computations. Indeed, as shown in Fig. 4, two kinds of parameterisations do exist for the velocities: the ones which are very close to the measurements but induce higher computational costs and the ones which are rough approximations but are very simply formulated. Therefore, it was decided to take a parameterisation representative of each of those two categories. For the ﬁrst one, Best (1950b)’s parameterisation was selected and for the second one, Kessler (1969)’s (please see Table 7). No noticeable differences were seen in the calculated scavenging coefﬁcients. In the present section, only the results of the computations run with the Kessler’s terminal velocity are displayed.

6.1. Gaseous pollutants

Fig. 7. Some literature extracted parameterisations of the mean (average) scavenging coefﬁcient for the PMs versus the rain intensity.

For gaseous pollutants and polydispersed raindrop size distributions, the computed equations are (2), in the most general case and (12), for the highly soluble gases. Are displayed, in the following ﬁgures, the computation results for a very soluble gaseous pollutant (HNO3, Heffective ¼ 1011 M atm1,

Fig. 8. Calculated below-cloud scavenging coefﬁcients for a highly soluble gaseous species (HHNO3 ¼ 1:02 1011 M atm1 , the effective Henry’s constant), versus the rain intensity. The computation results, using all the RSD parameterisations, are presented for comparison. The parameterisation used for the raindrops terminal velocity is the one given by Kessler (1969).

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Fig. 9. Calculated below-cloud scavenging coefﬁcients for a moderately soluble gaseous species (HHCHO ¼ 3.23 103 M atm1, the effective Henry’s constant), versus the rain intensity, near the ground (the distance from the cloud bottom is 1000 m). The computation results, using all the RSD parameterisations, are presented for comparison. The parameterisation used for the raindrops terminal velocity is the one given by Kessler (1969).

Fig. 10. Calculated below-cloud scavenging coefﬁcients for a 0.46 mm diameter PM, versus the rain intensity. The computation results, using all the RSD parameterisations, are presented for comparison. The parameterisation used for the raindrops terminal velocity is the one given by Kessler (1969).

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Fig. 11. Calculated below-cloud scavenging coefﬁcients for 0.05, 0.46 and 2.16 mm diameter PMs, versus the rain intensity. The computation results are presented for all the RSD parameterisations. The parameterisation used for the raindrops terminal velocity is the one given by Kessler (1969).

Ddif ¼ 1.2 105 m2 s1) and for a moderately soluble one (HCHO, Heffective ¼ 3.23 103 M atm1, Ddif ¼ 1.7 103 m2 s1). For a moderately soluble gas, the scavenging coefﬁcient depends on the distance of the raindrops to the bottom of the precipitating cloud, though, this is totally negligible for a highly soluble gas.

In Figs. 8 and 9 can be seen the scavenging coefﬁcients calculated with all the RSD parameterisations given in Section 2.3. The variations in the computed results are more important for the parameterisations established after experimental records made with instantaneous sampling durations (less or equal to 1 min)

Fig. 12. Calculated mass-averaged below-cloud scavenging coefﬁcient for “RC” class PMs (Jaenicke, 1993) versus the rain intensity, for all the literature extracted RSDs. The parameterisation for the raindrops terminal velocity is the one given by Kessler (1969).

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Fig. 13. Calculated and literature extracted mass-averaged below-cloud scavenging coefﬁcients versus the rain intensity, for different PSDs. The parameterisation for the raindrops terminal velocity is the one given by Kessler (1969) and the one for the RSD is given by Marshall and Palmer (1948).

rather than with long sampling ones. As mentioned in Section 2, the instantaneous measurements display more accurately the natural ﬂuctuations of the precipitations. The variations seem also more important for widespread type of rain than for drizzle, shower and thunderstorm. However, this last point can not be deﬁnitely stated as most of the parameterisations reported on these ﬁgures happen to be widespread (there is not enough parameterisation for the other types of rain to conclude). In the Figs. 7 and 8 from the “ESM”, it can be seen that the scavenging coefﬁcient for HNO3 varies between 1 104 and 4 103 s1 for an intensity of rain of 20 mm h1, according to the different raindrop size distributions, for a widespread type of rain (instantaneous sampling). It varies between 3.5 104 and 7.5 104 s1 for widespread type of rains when the latter are recorded on a long duration. According to equation (12), the scavenging coefﬁcient for highly soluble gases is dependent on the size of the raindrops, as well as, on their number distribution. As regards the BCS, a small drop is less efﬁcient than a bigger one. This explains the plots of Figs. 7 and 8 of the “ESM” where the RSDs with low number of small size raindrops and high total number of raindrops (for instance Chapon et al. (2008)) involve a bigger scavenging coefﬁcient. On the other hand, according to the Fig. 3, some RSD parameterisations (Chapon et al., 2008; Coutinho and Tomas, 1995; Cerro et al., 1997) involve intensities of rain probably too high to be relevant. However, as explained in Section 2.3, no deﬁnite conclusions as to the validity of the above cited parameterisations can be drawn out. In the Fig. 9 from the “ESM”, the computation results for various rain types are presented set together for convenience. In order to read these ﬁgures suitably, it should be kept in mind that shower rains seldom exceed 25 mm h1 in intensity and that the thunderstorm type of rains are connected to 50e100 mm h1 rain intensities. Therefore, it can be seen that the scavenging coefﬁcient for HNO3 and thunderstorm type of precipitation is between 4.5 104 and 2.5 103 s1 for a rain intensity of 50 mm h1. It is between 3.5 104 and 6 104 s1 for shower rains, for an intensity of 20 mm h1.

These results are of the same order of magnitude than the ones given by the parameterisations found in the literature for the scavenging coefﬁcients of highly soluble gaseous pollutants. Indeed, in Fig. 5, it can be seen that for widespread rains, the scavenging coefﬁcient, according to most raindrop size distributions, varies between 7 104 and 1.5 103 s1 for intensities of rain of 20 mm h1. It varies between 6 104 and 1 103 s1 for convective (thunderstorm) type of precipitations at about 50 mm h1. These results show that there are important differences between the parameterisations used for the raindrops size distribution. For instance, in 10 min time, at 20 mm h1 and with a widespread rain (instantaneous sampling), about 20% of the HNO3 pollutant would be scavenged from the atmosphere when using the Feingold and Levin’s log-normal raindrops size distribution in the computations. Now, this is almost the double which would be scavenged from the atmosphere when using the Ulbrich’s gamma distribution. Some computations were also run for “monodispersed” scavenging coefﬁcients using the representative diameters extracted from the literature (please see Table 5). In that respect, equation (13) was used. The connection between the intensity of rain (I) and the precipitating water content of the atmosphere (uL) is given in the joined “ESM”. For the HNO3 highly soluble gas, the results shown in Fig. 14 are close to the literature extracted parameterisations (Fig. 5). Indeed, the computed scavenging coefﬁcient, any rain type included, varies between 3 104 and 9 104 s1 at a rain intensity of 20 mm h1 and between 5.5 104 and 103 s1 at 50 mm h1. Most of the literature extracted parameterisations for highly soluble gases give a scavenging coefﬁcient of 3 104e1.3 103 s1 for 20 mm h1 and 6.5 104e2.5 103 s1 for 50 mm h1. 6.2. Particulate matters In Figs. 10 and 11, can be seen the scavenging coefﬁcient of given-size particulate matters (computed according to equation

Fig. 14. Calculated monodispersed below-cloud scavenging coefﬁcients for the HNO3 highly soluble gas versus the rain intensity, for all the literature extracted representative diameters. The parameterisation for the raindrops terminal velocity is the one given by Kessler (1969).

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Fig. 15. Calculated monodispersed below-cloud scavenging coefﬁcients for 0.05, 0.46 and 2.16 mm diameter PMs versus the rain intensity, for all the literature extracted representative diameters. The parameterisation for the raindrops terminal velocity is the one given by Kessler (1969).

(3)). Different PM sizes are considered, 0.05 mm diameter particles to represent Ultra Fine Particles (UFP) and also 0.46 mm and 2.16 mm diameter PMs. The collection efﬁciency used for the computations is the one extracted from Slinn (1983) (please see the ESM for more information). As often stated in the literature (Sparmacher et al. (1993)) and also displayed in the ﬁgures, there is a great dispersion in the parameterisations of the scavenging coefﬁcient for the particulate matters. However, as this is the case for the gases, the choice of the parameterisation for the terminal velocity of raindrops does not matter much for the scavenging coefﬁcient. Our results on this point are consistent with those of Wang et al. (2010). In particular, it can be seen that, as for the gaseous pollutants, there is a great dispersion in the calculated scavenging coefﬁcients for the RSDs related to rain recorded with instantaneous sampling duration. For UFP (0.05 mm diameter) and widespread rains (instantaneous sampling), at 20 mm h1, the scavenging coefﬁcient varies between 7 107 and 3 105 s1. For widespread rains recorded on a long sampling duration, the scavenging coefﬁcient varies between 3 106 and 5 106 s1. For thunderstorm type of precipitations, at 50 mm h1, it ranges between 4 106 and 2 105 s1. Finally, for shower rains, at 20 mm h1, it ranges between 3 106 and 4.5 106 s1. In the computational results for PMs of 0.46 mm diameter, it can be seen that for widespread rains (instantaneous sampling), at 20 mm h1, the scavenging coefﬁcient varies between 1.5 107 and 6 106 s1, when it varies between 5 107 and 106 s1 for long sampling durations. In case of thunderstorms (50 mm h1), it varies between 7 107 and 3.5 106 s1 and ﬁnally, for shower rains, between 5.5 107 and 8.5 107 s1. The same kind of computations were run also for particles of 2.16 mm diameter. For widespread rains (instantaneous sampling of the raindrop size distributions), the scavenging coefﬁcient is included between 4 107 and 2 105 s1 at 20 mm h1. It is between 1.5 106 and 3 106 s1 for widespread rains (long sampling duration), between 2 106 and 1.5 105 s1 at 50 mm h1 for thunderstorms and ﬁnally, between 1.5 106 and 2.5 106 s1 at 20 mm h1 for shower rains. The parameterisations found in the literature for the same PM sizes are not in very good agreement between each other. Indeed,

for widespread rains and UFPs, at 20 mm h1, Baklanov and Sorensen (2001) (Fig. 6) suggest a scavenging coefﬁcient of 103 s1 when Laakso et al. (2003) suggest 104 s1 and Henzing et al. (2006), 1.5 106 s1 (for PMs of 0.05 mm diameter). For thunderstorms or intense rain events and UFPs, at about 50 mm h1, ApSimon et al. (1988) suggest a scavenging coefﬁcient of 2 103 s1 when Andronache (2004) suggests 105 s1 and Chate (2005), 4 105 s1 (for PMs of 0.05 mm diameter). Brandt et al. (2002), for UFPs and any kind of rain, suggest scavenging coefﬁcients of 2 103 s1 for 50 mm h1 and of 103 s1 for 20 mm h1. Sparmacher et al. (1993) give relations which at 20 mm h1 induce scavenging coefﬁcients of 2 106 s1 for 0.46 mm diameter PMs and of 105 s1 for 2.16 mm. For the same sizes and rain intensity, Henzing et al. (2006) suggest 3 107 s1 and 7 107 s1. As can be noticed, there are already one to three orders of magnitude differences in the published parameterisations. The computed theoretical results presented in the Figs. 10 and 11, can be compared to the literature extracted results of Fig. 6. In particular, the results of Fig. 11 for a PM diameter of 0.05 micron, can be compared to the plots from Laakso et al. (2003), Andronache (2004) and Henzing et al. (2006). The results corresponding to the PM diameters of 0.46 and 2.16 micron can be compared to the plots from Sparmacher et al. (1993) and Henzing et al. (2006). What can be observed in those ﬁgures is that the published data are located inside the bunch of the calculated results and show the same level of dispersion. They are perfectly consistent with the computations. Computations have also been performed to calculate an average below-cloud scavenging coefﬁcient according to equation (18). In that respect, the “Rural”, “Urban”, “Marine” and “Remote Continental” classes of Jaenicke (1993) (please see Table 9) were used in connection with Kessler (1969)’s raindrop terminal velocity. The results are shown in the Figs. 10e12 from the “ESM” and in the Fig. 12. For the “Urban”, “Rural” and “Marine” classes, the results are almost identical. The mass-averaged scavenging coefﬁcient ranges between 2.5 103 and 102 s1 for thunderstorm type of precipitations and for an intensity of rain of 50 mm h1. It ranges between 2 103 and 3 103 s1 for shower rains (at about 20 mm h1), between 5 104 and 2 102 s1 for widespread rains (instantaneous sampling, at about 20 mm h1) and ﬁnally between 2 103 and 3 103 s1 for widespread rains recorded

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on a long sampling duration (at about 20 mm h1). As regards the “Remote Continental” class, the computed mass-averaged scavenging coefﬁcients are between 4.5 103 and 2 102 s1 for thunderstorm type of precipitations and for an intensity of rain of 50 mm h1, between 3.5 103 and 4 103 s1 for shower rains (20 mm h1), between 7 104 and 3 102 s1 for widespread instantaneous-sampling rains (20 mm h1) and ﬁnally between 2.5 103 and 5 103 s1 for widespread rains (long sampling duration at 20 mm h1). The same as for the gases, some computations were run for “monodispersed” scavenging coefﬁcients using the representative diameters extracted from the literature (see Table 5). In that respect, equation (16) was used. For an UFP of 0.05 mm diameter, the results shown in Fig. 15 are in very good agreement with the parameterisation given by Andronache (2004) (Fig. 6). Indeed, the computed scavenging coefﬁcient, all rain types merged, for 0.05 mm diameter PMs, varies between 2 106 and 7 106 s1 for 20 mm h1 and between 3.5 106 and 9 106 s1 for 50 mm h1. Most of the literature extracted results show a scavenging coefﬁcient varying between 5 106 and 1 103 s1 for 20 mm h1 and between 9 106 and 2.3 103 s1 for 50 mm h1. In particular, the scavenging coefﬁcient according to Andronache (2004) is 5 106 s1 at 20 mm h1 and 9 106 s1 at 50 mm h1. The results obtained for 0.46 and 2.16 mm diameter PMs (please see the Fig. 15 and also the Fig. 13 from the “ESM”) are also in quite good agreement with the parameterisations (according to experiments) given by Sparmacher et al. (1993). The computed scavenging coefﬁcient for 0.46 mm diameter PMs is between 4 107 and 1.3 106 s1 for 20 mm h1 and between 6 107 and 1.7 106 s1 for 50 mm h1. According to Sparmacher et al. (1993), it is of 2 106 s1 at 20 mm h1 and of 3 106 s1 at 50 mm h1. For 2.16 mm diameter PMs, the computed results are one order of magnitude lower that the ones given by Sparmacher et al. (1993). However, no clear improvement can be seen when using “polydispersed” RSDs. Indeed, the computed scavenging coefﬁcient varies between 1 106 and 3.7 106 s1 for 20 mm h1 and between 1.5 106 and 4.5 106 s1 for 50 mm h1. Sparmacher et al. (1993) suggest 1 105 s1 at 20 mm h1 and 2 105 s1 at 50 mm h1. 7. Conclusion As a ﬁrst conclusion on the modelling of the scavenging of gases and PMs, no noticeable differences are observed with the choice of the terminal raindrop velocity. In consequence, the simplest formulation of the terminal velocity is recommended to avoid additional computational burden. It can also be noticed that the experiments from which the parameterisations of the terminal velocity are derived, are carried out in laboratories. Therefore, it would be interesting to investigate how the real atmospheric conditions would impact the apparent terminal velocity and if it is worth to take them into account in air quality models. A higher dispersion in the results for both the gases and PMs is observed for the rains which were monitored with short sampling durations (less than 1 min). Indeed, the experimental facilities providing instantaneous measurements can catch the natural ﬂuctuations of rainfalls more accurately than those providing long measurements. That dispersion could also be explained by the difﬁculties encountered to make precise instantaneous measurements. The physical models in order to establish the theoretical formulae to be used for the computations, are not comprehensive either. For instance, Zhang et al. (2004) developed a one dimensional numerical model including the “below”, as well as, the “in” cloud scavenging of condensation nuclei. As regards the below-

cloud scavenging, a warm continental cloud was assumed with very light precipitations (lots of small raindrops) and with weak vertical ascending motions. During the simulation, a given amount of “cloud nuclei” (particulates) was injected in the numerical model, below the cloud, after the beginning of the precipitation. From the computed concentrations, a more comprehensive scavenging coefﬁcient was calculated and linked to the intensity of rain. The results thus computed (please see also Fig. 13) remain comparable to the ones found in the literature (Sparmacher et al., 1993; Laakso et al., 2003; Andronache, 2003, 2004; Chate, 2005), although probably even more physical phenomenon should have been taken into account to enable a better comparison with experimental measurements. For the selected highly soluble gas HNO3, as well as, the 0.05, 0.46 and 2.16 mm diameter PMs, the scavenging coefﬁcients calculated assuming a single representative diameter have shown similar results (same level of dispersion) than the ones computed using RSDs, at least, for the theoretical models which are used in the present study. However, in case accurate RSDs would be available, them would be worth using them for more comprehensive theoretical models of atmospheric phenomena. Appendix. Supplementary material The Supplementary material associated with this article can be found online, at doi:10.1016/j.atmosenv.2011.09.002. References Abel, S.J., Shipway, B.J., 2007. A comparison of cloud-resolving model simulations of trade wind cumulus with aircraft observations taken during RICO. Q. J. Roy. Meteorol. Soc. 133, 781e794. Andronache, C., 2003. Estimated variability of below-cloud aerosol removal by rainfall for observed aerosol size distributions. Atmos. Chem. Phys. 3, 131e143. Andronache, C., 2004. Diffusion and electric charge contributions to below-cloud wet removal of atmospheric ultra-ﬁne aerosol particles. J. Aerosol Sci. 35, 1467e1482. ApSimon, H.M., Simms, K.L., Collier, C.G., 1988. The use of weather radar in assessing deposition of radioactivity from chernobyl across England and Wales. Atmos. Environ. 22, 1895e1900. Asman, W.A.H., 1995. Parameterization of below-cloud scavenging of highly soluble gases under convective conditions. Atmos. Environ. 29, 1359e1368. Atlas, D., 1953. Optical extinction by rainfall. J. Meteorol. 10, 486e488. Atlas, D., Srivastava, R.C., Sekhon, R.S., 1973. Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys. Space Phys. 11, 1e35. Atlas, D., Ulbrich, C.W., 1977. Path and area integrated rainfall measurement by microwave attenuation in the 1e3 cm band. J. Appl. Meteorol. 16, 1322e1331. Baklanov, A., Sorensen, J.H., 2001. Parameterisation of radionuclide deposition in atmospheric long-range transport modelling. Phys. Chem. Earth (B) 26, 787e799. Beard, K.V., 1976. The terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci. 33, 851e863. Best, A.C., 1950a. The size distribution of raindrops. Q. J. Roy. Meteorol. Soc. 76, 16e36. Best, A.C., 1950b. Empirical formulae for the terminal velocity of water drops falling through the atmosphere. Q. J. Roy. Meteorol. Soc. 76, 302e311. Blanchard, D.C., 1953. Raindrop size distribution in Hawaiian rains. J. Meteorol. 10, 457e473. Brandt, J., Christensen, J.H., Frohn, L.M., 2002. Modelling transport and deposition of caesium and iodine from the Chernobyl accident using the DREAM model. Atmos. Chem. Phys. 2, 397e417. Calderon, S.M., Poor, N.D., Campbell, S.W., Tate, P., Hartsell, B., 2008. Rainfall scavenging coefﬁcient for atmospheric nitric acid and nitrate in a subtropical coastal environment. Atmos. Environ. 42, 7757e7767. Campos, E.F., Zawadzki, I., Petitdidier, M., Fernandez, W., 2006. Measurement of raindrop size distributions in tropical rain at Costa Rica. J. Hydrol. 328, 98e109. Cerro, C., Codina, B., Bech, J., Lorente, J., 1997. Modelling raindrop size distribution and Z(R) relations in the western Mediterranean area. J. Appl. Meteorol. 36, 1470e1479. Chang, T., 1984. Rain and snow scavenging of hno3 vapor in the atmosphere. Atmos. Environ. 18, 191e197. Chapon, B., Delrieu, G., Gosset, M., Boudevillain, B., 2008. Variability of rain drop size distribution and its effect on the z-r relationship: a case study for intense Mediterranean rainfall. Atmos. Res. 87, 52e65. Chate, D., 2005. Study of scavenging of submicron-sized aerosol particles by thunderstorm rain events. Atmos. Environ. 39, 6608e6619.

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