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A 3-mode parameterization of below-cloud scavenging of aerosols for use in atmospheric dispersion models
ARTICLE IN PRESS
Atmospheric Environment 41 (2007) 6808–6822 www.elsevier.com/locate/atmosenv
A 3-mode parameterization of below-cloud scavenging of aerosols for use in atmospheric dispersion models Jian Feng Canadian Meteorological Centre, Meteorological Service of Canada, 2121 Trans-Canada Highway, Dorval, Que., Canada H9P 1J3 Received 20 December 2006; received in revised form 12 April 2007; accepted 20 April 2007
Abstract Atmospheric aerosols are subject to below-cloud scavenging by precipitation. The scavenging coefficient depends on the aerosol size significantly. The traditional bulk parameterization represents the mean wet scavenging coefficient for the whole aerosol size range. This parameterization significantly overestimates the scavenging of aerosol mass by a heavy rain or a long-duration medium rain. In this study, we present a 3-mode parameterization of the mean scavenging coefficient for each aerosol mode instead of representation for the whole aerosol size range. The new parameterization takes into account the aerosol number size distribution, the rain droplet size distribution and the spectral collision efficiency between the aerosol particle and the rain droplet. Comparing the calculation of mass depletion due to below-cloud scavenging, the 3-mode parameterization agrees well with the size-resolved explicit method. The new parameterization can be easily implemented in atmospheric dispersion models. r 2007 Elsevier Ltd. All rights reserved. Keywords: Aerosol; Wet scavenging; Atmospheric dispersion model
1. Introduction Wet scavenging and dry deposition are two important processes of removing airborne aerosols from the atmosphere. Wet scavenging refers to removal of aerosol particles by hydrometeors. The relative importance of these two processes depends on the properties of particles, the amount and intensity of precipitation, the boundary-level turbulence and the surface properties. Wet scavenging can be divided into in-cloud scavenging and belowcloud scavenging. Particles entrained into clouds are subject to in-cloud scavenging, which includes nucleation scavenging and interstitial scavenging. E-mail address: [email protected] 1352-2310/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2007.04.046
Most often, in-cloud scavenging is the main removal mechanism for sub-micron particles, which are usually not removed efficiently from the air by either below-cloud scavenging or dry deposition (Sakashita et al., 2002). Aerosol particles located below the base of a precipitating cloud will be collected by falling hydrometeors and this process is called below-cloud scavenging. Both in-cloud scavenging and below-cloud scavenging are important deposition mechanisms for airborne aerosols, with the relative importance depending on the particle size and the meteorological conditions. In this study, we focus on below-cloud scavenging of aerosols only. In chemical transportation models, below-cloud scavenging is usually described by a first-order mass
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
decay equation. The scavenging efficiency is represented by the mass scavenging coefficient, which depends on both the aerosol size and the properties of falling hydrometers (Gong et al., 2003). The dependence of the wet scavenging coefficient on the aerosol size was recently revisited by Andronache (2003). In his study, the wet scavenging coefficients are calculated for different modeled and observed aerosol size distributions. For the aerosol distribution with a coarse mode, the mean wet scavenging coefficient is parameterized as Sm ¼ aRb, where Sm is the mean wet scavenging coefficient, R is the rain rate in mm h1, b equals 0.7 and a varies from 0.24 to 0.88 for different aerosol size distributions. The dependence of the scavenging coefficient on the aerosol size distribution is implicitly parameterized in the powerlaw expression. However, as also illustrated in Andronache’s study, for different particle diameters, the scavenging coefficient can vary significantly. Below-cloud scavenging is efficient for small particles with diameters o0.01 mm and big particles with diameters larger than about a few micrometers. For particles with diameters between 0.01 mm and a few micrometers, the scavenging coefficient can be smaller by up to a few orders of magnitude. When applying the mean wet scavenging coefficient, the scavenging is assumed equally efficient for aerosols with different sizes. To account for the differences of scavenging efficiency for aerosols with different diameters, one method is to use bin-defined wet scavenging coefficients. A recent example is by Loosmore and Cederwall (2004), who developed a new scavenging model for the National Atmospheric Release Advisory Center (NARAC) system. The system is used at the Lawrence Livermore National Laboratory for both predictions and assessments of depositions of hazardous materials in the atmosphere. In their study, the size-resolved wet scavenging coefficient is approximated as Sðd p Þ ¼ ð3=2Þ ððEðDr ; d p ÞÞ=Dr ÞR, where E is the collision efficiency of a raindrop of diameter of Dr with a particle with diameter of dp; R is the precipitation rate in mm h1; Dr is the representative diameter of rain droplets and is introduced to simplify the integral form of S(dp). This size-resolved wet scavenging coefficient is applied directly to the discrete model particles as the model particles are size-resolved in the NARAC model system. A negative outcome from this method is the simulation anomalies caused by discrete particles. In the study by Loosmore and Cederwall (2004), they had to use a post-processor to smooth the anomalies.
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In this study, we present a new parameterization of below-cloud scavenging for use in atmospheric dispersion models. The new parameterization takes into account the fact that for different aerosol sizes the efficiency of below-cloud scavenging can differ significantly, but the parameterization does not require model particles to be discretized. The new parameterization is an extension of the traditional bulk parameterization, which is widely used in atmospheric dispersion models for the treatment of below-cloud scavenging of aerosols. The paper is presented as (1) the method of calculation of size-resolved wet scavenging coefficients; (2) parameterizations of wet scavenging coefficients; (3) implementation of the new parameterization into an atmospheric dispersion model and results; (4) sensitivity of wet scavenging to aerosol size distributions; and (5) summary.
2. Size-resolved wet scavenging coefficients 2.1. Calculation of size-resolved wet scavenging coefficients The method used to calculate the below-cloud scavenging coefficient is based on the concept of collision of a falling rain droplet with an aerosol particle. This concept was also recently used by Andronache (2003) and Loosmore and Cederwall (2004) in their studies. The detailed description of the method can be found in Seinfeld and Pandis (1998). When rain droplets fall through the air, the total collected mass of particles with diameter of dp by rain droplets during a unit time can be expressed as Z
1
p ðDp þ d p Þ2 ½U t ðDp Þ ut ðd p Þ 4 0 EðDp ; d p ÞNðDp Þ dDp ,
nM ðd p Þdd p
where nM is the aerosol mass size distribution, N is the rain droplet number size distribution, Dp is the diameter of the rain droplet, Ut and ut are the terminal velocities of the rain droplet and the aerosol particle, and E is the collision efficiency. Below-cloud scavenging can be modeled by a firstorder decay equation: dnM ðd p Þ ¼ Sðd p ÞnM ðd p Þ, dt
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where S(dp) is the below-cloud scavenging coefficient and therefore can be given by Z Sðd p Þ ¼
1
p ðDp þ d p Þ2 ½U t ðDp Þ ut ðd p Þ 4 0 EðDp ; d p ÞNðDp Þ dDp .
To calculate S(dp) numerically, we derive an analytical expression for Ut and ut for particles with different diameters. Detail of the derivation is in Appendix 1. Rain droplet number size distributions depend on the type of precipitation. They are generally described with either exponential or gamma functions, and the later ones are usually better to describe the number size distributions for droplets in a small size domain (Dpo1 mm). The scavenging coefficient is affected by the rain droplet size distribution through the total cross-section of the rain droplets. Because this variable is the second moment of the rain droplet diameter, small rain droplets make less contribution to the scavenging coefficient than big ones. In many practical applications, the fit with gamma functions gives little improvement over exponential functions, although the former ones are of greater mathematical complexity (Smith, 2003). In this study, the classical exponential fit of Marshall and Palmer (1948) is used for the rain droplet number size distribution: NðDp Þ ¼ N 0 expðcDp Þ, where N0 ¼ 8 103 m3 mm1, c ¼ 4.1R0.21 mm1 and R is the rain rate in mm h1. The regression values of the Marshall–Palmer fit are usually found to be good for steady rains at continental midlatitudes. Calculation of collision efficiency E is based on Slinn’s (1983) semi-empirical model. The analytical expression of E is E¼
4 ½1 þ 0:4Re1=2 Sc1=3 þ 0:16Re1=2 Sc1=2 Re Sc þ 4f½o
1
where Re ¼
Dp U t ra , 2ma
Sc ¼
ma , ra D
þ ð1 þ 2Re
1=2
Þf þ
!3=2 St S , St S þ 23
St ¼
2tðU t ut Þ , Dp
f¼
dp , Dp
mw , ma 1:2 þ ð1=12 lnð1 þ ReÞ S ¼ 1 þ lnð1 þ ReÞ o¼
and D¼
kTC c , 3pma d p
ut ¼ tg, ðrp ra Þd p C c , 18ma 2l 1:1d p 1:257 þ 0:4 exp Cc ¼ 1 þ l , dp 2l
t¼
l¼
2ma Pð8M=pRTÞ1=2
.
Symbols and constants are listed in Table 1. Slinn’s analytical expression of collision efficiency E has three terms: the first term represents the contribution from the Brownian diffusion; the second term represents interception; and the third term is due to impaction and is included only when the Stokes number is greater than the critical Stokes number S*. Size-resolved collision efficiencies for rain droplets with diameters of 0.1, 0.5, 1.0 and 4.0 mm are shown in Fig. 1, from which we can conclude: (1) the collision efficiency is significantly larger for big particles (dp4a few micrometers) and ultra-fine particles (dpo0.01 mm) than for particles with dp between 0.04 and 2.5 mm; (2) the collision efficiency decreases with the increase of the size of rain droplets. Fig. 2 shows the calculated belowcloud scavenging coefficients, Ss, for different rain rates. S varies significantly with the rain rate and the aerosol size. When the rain rate increases, the corresponding scavenging rate increases. For rain rates from 1 to 10 mm h1, scavenging is efficient for small particles (dpo0.05 mm) due to the Brownian diffusion and for larger particles (dp43 mm) due to the impaction. Scavenging is much less efficient and reaches a minimum in the size range between 0.1 and 1 mm. This range is often referred to as the ‘‘Greenfield gap’’ in the literature after S. Greenfield who first identified it (Seinfeld and Pandis, 1998).
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822 Table 1 List of symbols and constants
100
Sc St T ut Ut ra rp ma mw f o t
l g ¼ 9.807 m s2 k ¼ 1.381 1023 m2 kg s2 K1 ra ¼ 1.292 kg m3 rp ¼ 1. 103 kg m3 ma ¼ 1.720 105 kg m1 s1 8 1:787 > 0 C; > > > > C; 1:519 5 > < C; 1:307 103 kg m1 s1 10 mw ¼ > > > 15 C; 1:139 > > > : 20 C; 1:002
10-1
Collision efficiency
Slip correction factor Diameter of collected particle Particle diffusivity Diameter of rain droplet Acceleration of gravity Boltzmann constant Molecular weight of air Air pressure Molar gas constant Reynolds number of rain droplet Schmidt number of collected particle Stokes number of collected particle Air temperature Terminal velocity of particle Terminal velocity of rain droplet Air density Particle density Viscosity of air Viscosity of water Ratio of diameters Viscosity ratio Characteristic relaxation time of collected particle Mean free path of air
10-2
10-3
10-4
10-5
10-6 10-3
As examples, model aerosol distributions suggested by Jaenicke (1993) are used to calculate wet scavenging of aerosols. Jaenicke’s aerosol number distribution is expressed as the sum of 3 log-normal distributions: nN ðlog Dp Þ ¼
n X
Ni 1=2
ð2pÞ log si ¯ pi Þ2 ðlog Dp log D exp , 2 log2 si i¼1
101
102
101
100
10-1
10-2
10-3
10-4 10-3
2.2. Calculation of wet scavenging
10-2 10-1 100 Aerosol diameter, dp (µm)
Fig. 1. Size-resolved particle collision efficiencies for different rain droplet sizes.
S (h-1)
Cc dp D Dp g k M P R Re
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10-2
10-1 100 101 Aerosol diameter, dp (µm)
102
Fig. 2. Size-resolved wet scavenging coefficients for different rain rates.
¯ p , s are constants for where parameters N, D different types of aerosol, and are listed in Table 2. For aerosols with a unit density, the mass size distribution is equal to the volume size distribution. In the following, we use the volume size distribution for the illustration of wet scavenging of aerosol mass. S(dp) can be applied directly to the volume size distribution to calculate the
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Table 2 Parameters of model aerosol distributions suggested by Jaenicke (1993) N (cm3)
Urban Marine Rural Remote continental Free troposphere Polar Desert
¯ p (mm) D
i¼1
i¼2
i¼3
i¼1
i¼2
i¼3
i¼1
i¼2
i¼3
9.93 104 133 6650 3200 129 21.7 726
1.11 103 66.6 147 2900 59.7 0.186 114
3.64 104 3.1 1990 0.3 63.5 3 104 0.178
0.013 0.008 0.015 0.02 0.007 0.138 0.002
0.014 0.266 0.054 0.116 0.25 0.75 0.038
0.05 0.58 0.084 1.8 0.52 8.6 21.6
0.245 0.657 0.225 0.161 0.645 0.245 0.247
0.666 0.210 0.557 0.217 0.253 0.300 0.770
0.337 0.396 0.266 0.380 0.425 0.291 0.438
40 t=0 t = 0.5 h t=1h t = 10 h
30
dV/d[log(dp)](µm3cm-3)
dV/d[log(dp)](µm3cm-3)
40
20
10
0 10-3
log s
10-2
10-1 100 101 102 Aerosol diameter, dp (µm)
103
t=0 t = 0.5 h t=1h
30
20
10
10-3
10-2
10-1 100 101 102 Aerosol diameter, dp (µm)
103
Fig. 3. Volume size distributions of the remote continental aerosol after a wet scavenging of different times by a rain of (a) R ¼ 1 mm h1 and (b) R ¼ 10 mm h1.
depletion of volume due to wet scavenging. Fig. 3 shows the volume size distribution of the remote continental aerosol 0.5 h and 1 h after a wet scavenging by a 1 and 10 mm h1 rain, and 10 h after a 1 mm h1 rain. For a 1 mm h1 rain, particles with dp 43 mm (coarse mode) are removed from the air efficiently. After 1 h, 73% of the mass in this mode is deposited to the ground. Particles with sizes in the range between 0.04 and 3 mm (accumulation mode) are not sensitive to wet scavenging and only 2% of the mass is scavenged 10 h after the scavenging. A rain of 10 mm h1 can remove 91% of the mass in the coarse mode in just half an hour, while the mass washed out in the accumulation mode is negligible.
3. Parameterization 3.1. Bulk parameterization of wet scavenging Parameterization of wet scavenging is usually in terms of the mean mass scavenging coefficient, and is often referred to as bulk parameterization. The total mass scavenging can be expressed as Z 1 dM p 3 ¼ d r Sðd p Þnðd p Þ dd p ¼ Sm M, dt 6 p p 0 where M is the total aerosol mass, dp is the aerosol diameter, rp is the density of the particle, n is the aerosol number size distribution and SRm is the mean 1 mass scavenging coefficient. M ¼ 0 ðp=6Þd 3p rp n
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
ðd p Þ dd p , therefore R1 Sm ¼
0
d 3p Sðd p Þnðd p Þ dd p . R1 3 0 d p nðd p Þ dd p
When aerosols are subject to wet scavenging, n(dp) changes with time. So Sm is a function of time t even S(dp) does not vary with time. If we assume Sm to be independent of time t, we can have M ¼ M0 exp (Smt), and M0 is the total initial aerosol mass. Fig. 4 shows the relationship between the calculated mean scavenging coefficient and the rain rate. Similar to the results in Andronache (2003), there is a very good linear relationship between log(Sm) and log(R). Therefore, we fit the relationship between Sm and R in terms of Sm ¼ aRb. For the model aerosols by Jaenicke (1993), the corresponding coefficients a and b are listed in Table 3.
Scavenging coefficient (h-1)
102
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Fig. 5 shows the wet scavenging of aerosol mass using the explicit calculation and the bulk parameterization for rain rates of 1 and 5 mm h1. For both rain rates, the wet scavenging is overestimated using the bulk parameterization. For the rain rate of 1 mm h1, the bulk parameterization starts to significantly overestimate the wet depletion of aerosol mass 1 h after the emission. Ten hours after the emission, there is still 23% of the aerosol mass in the air using the explicit calculation, while using the bulk parameterization, all the mass is washed out of the atmosphere. For the rain rate of 5 mm h1, using the explicit calculation, there is still 25% of the aerosol mass in the air 1 h after the scavenging. Using the bulk parameterization, 90% of the aerosol mass is washed out of the air just half an hour after the scavenging and almost all is deposited to the ground 1 h after the scavenging. It is clear that using the bulk parameterization is not good enough for the simulation of below-cloud scavenging of aerosols, especially for a heavy rain of long duration. In the following, we present a 3-mode parameterization of below-cloud scavenging.
101
3.2. 3-mode parameterization 100
10-1 0.1
1
10
100
Rain rate (mm h-1)
Fig. 4. Mean wet scavenging coefficients of the remote continental aerosol vs. rain rate.
Fig. 2 shows that the scavenging coefficients are ‘‘significant’’ for particles in the nucleation and the coarse modes, while the scavenging coefficient is orders of magnitude smaller in the accumulation mode. As the scavenging coefficients are quite different in these three modes, we calculate the mean mass scavenging coefficients for particles in each mode, instead of for the whole aerosol size
Table 3 Regression coefficients of the bulk parameterization Sm ¼ aRb and the 3-mode parameterization Smi ¼ ai Rbi Bulk para Sm (h1) 103 mmodpo100 mm
Mode 1 Sm1 (h1) 103 mmodpo0.04 mm
a
a1
b
b1
Mode 2 Sm2 (h1) 0.04 mmodpo2.5 mm
Mode 3
a2
Sm3 (h1) Sm4 (h1) 2.5 mmodpo16 mm 16 mmodpo100 mm
b2
a3
b3
a4
b4
Urban Remote continental Desert Polar Marine Rural Free troposphere
0.71 1.16 1.76 1.13 0.77 0.76 1.04
0.80 0.80 0.82 0.81 0.80 0.80 0.80
6.4 103 6.1 103 7.4 103 4.3 103 6.2 103 6.5 103 6.3 103
0.62 0.62 0.62 0.62 0.62 0.62 0.62
0.90 103 0.85 103 1.33 103 1.01 103 0.99 103 1.01 103 1.32 103
0.62 0.62 0.61 0.61 0.61 0.61 0.61
0.88 1.11 1.23 0.76 0.80 0.80 0.87
0.79 0.79 0.80 0.79 0.79 0.79 0.79
1.81 1.81 1.77 1.82 1.81 1.81 1.81
0.81 0.81 0.82 0.81 0.80 0.81 0.80
Average
1.05
0.80
6.2 103
0.62
1.06 103
0.61
0.92
0.79
1.81
0.81
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80
100 Explicit cal. Bulk para. Normalized total mass (%)
Normalized total mass (%)
100
60
40
20
Explicit cal. Bulk para.
80
60
40
20
0
0 t = 0.5 h
t=1h
t = 10 h
t = 0.5 h
t=1h
t = 10 h
Fig. 5. Wet depletion of the aerosol mass by a rain of (a) 1 mm h1 and (b) 5 mm h1 using the explicit calculation and the bulk parameterization.
1i
and assume Smi to be independent of time t, then we have Mi ¼ M0i exp(Smit), where Smi, Mi and M0i are the mean mass scavenging coefficient, the total aerosol mass, and the total initial aerosol mass for bin i. d1i and d2i are the low and up bounds of each bin. As an example, Fig. 6 shows the calculated mean scavenging coefficients of the remote continental aerosol vs. rain rate for different bins. As expected, there is a very good linear relationship between log(Si) and log(R) for each bin. Therefore, we fit the relationship between Smi and R in terms of S mi ¼ ai Rbi . The regression coefficients for the model aerosol distributions suggested by Jaenicke (1993) are listed in Table 3. 3.3. Evaluation of the 3-mode parameterization To evaluate the 3-mode parameterization, we use two methods to calculate the aerosol mass depletion. R d 2i For each bin i, the explicit one is V i ðtÞ ¼ d V 0i expðSðd p ÞtÞ dd p , and the 3-mode parame1i
102
Scavenging coefficient
103 (h-1)
range. In the coarse mode, since the scavenging coefficient changes rapidly for the particle size between 10 and 20 mm (Fig. 2), we divide this mode into two bins. For the other two modes, we use one bin for each mode. The four bins are dpo0.04 mm, 0.04 mmpdpo2.5 mm, 2.5 mmpdpo16 mm and dpX 16 mm. Define R d 2i 3 d d p Sðd p Þnðd p Þ dd p Smi ¼ 1iR d 3 2i d d p nðd p Þ dd p
101
Sc_M1 Sc_M2 Sc_M3_1 Sc_M3_2
100 10-1 10-2 10-3 10-4 0.1
1 Rain rate (mm
10
100
h-1)
Fig. 6. Mean wet scavenging coefficients of the remote continental aerosol in each bin vs. rain rate.
terization method is Vi(t) ¼ V0i exp(Smit). Fig. 7a and b shows the normalized aerosol mass (by the initial total mass) using the two methods after 0.5, 1 and 10 h of wet scavenging by a rain of 1 and 5 mm h1, respectively. The results from the 3-mode parameterization generally agree very well with the explicit calculations. The difference in normalized mass is o3% in each bin. Both the explicit method and the 3-mode parameterization show very little mass depletion in the accumulation mode. To see the improvement of the 3-mode parameterization over the bulk parameterization, we compare the total aerosol mass after a wet scavenging using R 1 three methods: (1) the explicit method, V ðtÞ ¼ 0 V 0 expðSðd p ÞtÞ dd p ; (2) the 3-mode
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50 Explicit cal. 3-mode para.
Normalized mass (%)
40
30
20
10
0 -
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
t=0h
t = 0.5 h
t=1h
t = 10 h
6
50 Explicit cal. 3-mode para.
Normalized mass (%)
40
30
20
10
0 -
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
t=0h
t = 0.5 h
t=1h
t = 10 h
6
Fig. 7. Wet depletion of the remote continental aerosol mass using the explicit calculation and the 3-mode parameterization for R ¼ 1 and 5 mm h1.
P method, Vi(t) ¼ V0i exp(Smit) and V ðtÞ ¼ 4i¼1 V i ðtÞ; (3) the bulk parameterization method, V(t) ¼ V0 exp(Smt). Fig. 8 shows the total aerosol mass of the remote continental aerosol after a wet scavenging of 1 mm h1 rain using the three methods. The results from the 3-mode method are very close to those using the explicit calculation. The bulk parameterization method overestimates the wet depletion by 20% of the total initial mass 1 h after the scavenging. After 10 h, using the bulk parameterization, almost all mass is deposited to the ground, while using the other two methods, there
are still significant amounts of aerosol mass in the atmosphere, as the aerosol mass in the ‘‘Greenfield gap’’ is not sensitive to the below-cloud scavenging. Comparing with the explicit calculation, both the 3-mode and the bulk parameterizations overestimate the mass depletion of aerosols. This is because the mean mass scavenging coefficient decreases with time as the particles with higher S(dp) are more efficiently removed from the air. For the wet scavenging by a rain of R ¼ 5 mm h1 presented in Fig. 5b, at t ¼ 0, Sm is weighted by the particles in both the accumulation mode and the coarse mode.
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4.2. Results from the bulk and the 3-mode parameterizations
100 90
Normalized total mass (%)
80
Explicit cal. 3-mode para. Bulk para.
70 60 50 40 30 20 10 0 t = 0.5 h
t=1h
t = 10 h
Fig. 8. Wet depletion of the aerosol mass using the explicit calculation, the 3-mode and the bulk parameterizations.
At t ¼ 1 h, Sm is dominated by the particles in the accumulation mode. The bulk method use Sm determined at t ¼ 0 for the following time, therefore significantly overestimates the mass depletion. The 3-mode method alleviates the overestimation through parameterizing the mean scavenging coefficient for each aerosol mode, for which S(dp) does not change as significantly as it does for the whole size range. As shown in Figs. 7 and 8, the 3-mode method efficiently reduces the overestimation of the wet scavenging. 4. Implementation and results 4.1. Implementation The 3-mode wet scavenging scheme is implemented into a stochastic atmospheric dispersion model MLCD (Flesch et al., 2002). In MLCD, a model particle is assumed to represent an ensemble of a large number of ‘‘real’’ particles. First based on the aerosol mass size distribution, the percentage of aerosol mass in each bin and the regression coefficients of the 3-mode parameterization for each bin are calculated. The total mass of each model particle Pis a sum of the mass in each bin: MðtÞ ¼ 4i¼1 M 0 Pi expðS mi tÞ, where M is the total mass of a model particle; M0 is the initial mass of the model particle; Pi is the percentage of mass in each bin; Smi is the wet scavenging coefficient of bin i and is parameterized as ai Rbi .
To test the newly developed wet scavenging parameterizations, a hypothetical release of aerosols is assumed to have happened in Laval, Quebec, Canada on 1 June 2004. The emission is assumed to last for 6 h and the particles are released evenly from a column with a radius of 50 m and a height of 1000 m. The released particles are assumed to follow the size distribution of the urban aerosol. The wind fields are taken from the Global Environmental Multi-scale (GEM) model simulations. We ran MLCD with two different wet scavenging parameterizations: the bulk parameterization and the 3-mode parameterization. A uniform precipitation field of 1 mm h1 is assumed for the simulation. Fig. 9a and b shows that the wet deposition pattern using the bulk parameterization and the 3-mode parameterization is very similar 6 h after the emission. However, the integrated flux using the bulk parameterization is over two times larger for most of the area around the source site (Fig. 9e). The integrated wet deposition fluxes 12 h after the emission are shown in Fig. 9c and d. As indicated in Fig. 9f, the bulk parameterization predicts the integrated wet deposition over two times larger than the 3-mode parameterization for most of the area around the release source, but for the region far from the source, the bulk parameterization predicts the integrated flux less than half of that by the 3-mode parameterization. Fig. 10a and b shows the mass concentrations in the first model level (from the ground to 250 m above the ground) 6 h after the emission using the bulk parameterization and the 3-mode parameterization. For most of the region affected by the emission, the mass concentration using the bulk parameterization is about 1-order of magnitude smaller than that using the 3-mode parameterization. Fig. 10c and d are the same as Fig. 10a and b, but for 12 h after the emission. Using the 3-mode parameterization, there is still a significant amount of aerosol mass in the air, while using the bulk parameterization, the aerosol mass in the air is about 3 orders of magnitude smaller. Using the 3-mode parameterization, the aerosol mass in the accumulation mode is not sensitive to the wet scavenging, but using the bulk parameterization, it is washed out of the air the same efficiently as the aerosol mass in the coarse mode and the nucleation mode. Therefore, the bulk parameterization
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Fig. 9. Integrated wet depositions (a–d) at the ground 6 h and 12 h after the emission using the bulk parameterization and the 3-mode parameterization respectively. Parts (e) and (f) are the ratios of the wet depositions using the bulk parameterization to that of the 3-mode parameterization 6 and 12 h after the emission.
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Fig. 10. Mass concentrations in the level from the ground to 250 m above the ground 6 and 12 h after the emission using the bulk parameterization and the 3-mode parameterization, respectively.
overestimates the aerosol mass washed out of the air. Fig. 11a–c shows the integrated wet deposition and the low-level concentration for another emission scenario. The emission is assumed to last 2 h and the simulation is for 6 h. The rain rate is assumed to be 5 mm h1. As indicated in Fig. 11d, the bulk parameterization strongly overestimates the wet deposition for the region close to the source site. As most of the mass is washed out from the air near the source, the bulk parameterization predicts o10% of the wet deposition by the 3-mode parameterization for the region away from the source. Fig. 11c shows that there is still a significant amount of aerosol mass in the air using the 3-mode
parameterization 6 h after the emission, while using the bulk parameterization, all aerosol mass is washed out of the air. 5. Sensitivity of wet deposition to aerosol size distributions Aerosol size distributions determine how the total mass of each model particle is distributed to each aerosol mode, and the wet scavenging efficiency for each mode is different, therefore aerosol size distributions affect wet deposition. To test the sensitivity of wet deposition to aerosol size distributions, we ran MLCD for seven different modeled aerosol size
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Fig. 11. Integrated wet depositions (a and b) at the ground and mass concentration (c) in the level from the ground to 250 m above the ground 6 h after the emission for a rain rate of 5 mm h1. (d) The ratio of the wet deposition using the bulk parameterization to that of the 3-mode parameterization.
distributions compiled by Jaenicke (1993). The scenario is the same as the previous one: the emission lasts for 6 h and the rain rate is 1 mm h1. Fig. 12 shows comparisons of the integrated wet deposition flux between the urban aerosol and six other aerosols. Comparing with the urban aerosol, the six types of aerosol all have higher wet deposition for the area close to the source and less wet deposition for the area far away from the source. In particular, the desert aerosol has the largest wet deposition around the source region, and far less deposition away from the source site. This is because for the size distribution of the desert aerosol, only o1% of the total mass is
located in the accumulation mode. For the other types of aerosol, the percentage of the total mass located in the accumulation mode varies from 15% for the free troposphere aerosol to 49% for the urban aerosol. As the wet scavenging coefficient is much higher for the coarse mode than that for the accumulation mode, more mass in the accumulation mode means less mass can be scavenged and more mass can be transported to the region away from the source. This is also consistent with the result that the mass concentration in the first model level is highest for the urban aerosol and lowest for the desert aerosol (figures not shown).
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J. Feng / Atmospheric Environment 41 (2007) 6808–6822
Fig. 12. Ratios of integrated wet depositions at the ground for six types of aerosol to that of the urban aerosol 12 h after the emission.
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
6. Summary Aerosols in the atmosphere are subject to scavenging by precipitation. The below-cloud scavenging efficiency of rain depends strongly on the aerosol size and the rain rate. Bulk parameterization of the wet scavenging coefficient takes into account this dependence implicitly. An inherent drawback of the bulk parameterization is that the scavenging efficiency is assumed to be equal for particles with different sizes. This parameterization works well for a light rain of short duration, but overestimates wet depletion of aerosol mass for a heavy rain or a medium rain of long duration. Using bin-defined wet scavenging coefficients can remove the overestimation, but it requires model particles be size-resolved in a Lagrangian dispersion model, which can cause simulation anomalies; or it requires more aerosol size bins in a Eulerian dispersion model, which takes more computation time. An alternative solution is to use the bulk parameterization for different aerosol modes, as each mode has different wet scavenging characteristics. In this study, we present a 3-mode parameterization. Comparisons of the wet depletion of aerosol mass calculated by the 3-mode parameterization and the explicit method show a very good agreement. The new 3-mode parameterization can be easily implemented into Lagrangian dispersion models. Acknowledgments
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velocity can be given by 4gDp C c rp 1=2 , ut ¼ 3C D ra
(1)
t, g, Dp, Cc, rp, and ra are defined in Table 1. CD is the drag coefficient. CD is a function of Reynolds number Re, and Re is a function of ut. Thus, the above expression is only an implicit one for ut. Based on the idea of Flagan and Seinfeld (1988), here we derive an explicit analytical expression for ut. According to definition, Re ¼
ut Dp ra . ma
(2)
Therefore, C D Re2 ¼
C D u2t D2p r2a . ma
(3)
Substitute Eq. (1) into Eq. (3), we have C D Re2 ¼
4D3p ra rp gC c . 3m2
(4)
The expression for CDRe2 is an explicit one. The analytical expressions of CD for different Reynolds numbers are (Eq. 8.32, Seinfeld and Pandis, 1998)
CD
8 24 Reo0:1; > Re ; > > > 24 3 9 2 < 1 þ 0:1oReo2; Re 16 Re þ 160 Re lnð2ReÞ ; ¼ 24 0:687 ð1 þ 0:15 Re Þ; 2oReo500; > > Re > > : 0:44; 500oReo2 105 :
(5) This study was funded by the Chemical, Biological, Radiological, and Nuclear (CBRN) Research and Technology Initiative (CRTI) of Defence R&D Canada through the CRTI-02-0041RD project. I would like to thank Mr. Nils Ek for reviewing the manuscript. The comments from one of the two reviewers were very helpful in improving the manuscript. Management support from Mr. Richard Hogue and Mr. Michel Jean is gratefully acknowledged. Appendix A. Terminal velocity for particles of any Reynolds number For particles with particles smaller than terminal velocity can particles with larger
Reynolds number o0.1 or about 20 mm in diameter, the be expressed as ut ¼ tg. For Reynolds number, terminal
2
From Eq. (5), we can see that CD Re is a function of only Re. Plot of CD Re2 vs. Re is shown in Fig. 13. According to Eq. (5), when Reo0.1, CDRe2 ¼ 24Re. Therefore, we can have C D Re2 when C D Re2 o2:4. (6) 24 When 500oReo2 105, CDRe2 ¼ 0.44Re2. Therefore, we can have 1=2 C D Re2 when C D Re2 41:1 105 . (7) Re ¼ 0:44
Re ¼
When 0.1oReo500, as shown in Fig. 13, a quadratic regression can excellently fit the relationship between log(CD Re2) and log(Re): logðC D Re2 Þ ¼ a log2 ðReÞ þ b logðReÞ þ c
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References
5
Andronache, C., 2003. Estimated variability of below-cloud aerosol removal by rainfall for observed aerosol size distributions. Atmospheric Chemistry and Physics 3, 131–143. Flagan, R.C., Seinfeld, J.H., 1988. Fundamentals of Air Pollution Engineering. Prentice-Hall, Englewood Cliffs, NJ. Flesch, T., Wilson, J., Crenna, B., 2002. MLCD: A Short-range Atmospheric Dispersion Model for Emergency Response. Contract report, Canadian Meteorological Centre, Dorval, Que., Canada. Gong, S.L., et al., 2003. Canadian aerosol module: a sizesegregated simulation of atmospheric aerosol process for climate and air quality models 1. Module development. Journal of Geophysical Research 108 (D1), 4007. Jaenicke, R., 1993. Tropospheric aerosols. In: Hobbs, P.V. (Ed.), Aerosol–Cloud–Climate Interactions. Academic Press, San Diego, CA, pp. 1–31. Loosmore, G.A., Cederwall, R.T., 2004. Precipitation scavenging of atmospheric aerosols for emergency response applications: testing an updated model with new real-time data. Atmospheric Environment 38, 993–1003. Marshall, J.S., Palmer, W.M., 1948. The distribution of raindrop with size. Journal of Meteorology 5, 165–166. Sakashita, T., Nakamura, Y., Doi, M., 2002. Test of wet scavenging parameterization schemes by simulation of monthly depositions of 7Be using normally available data on environmental monitoring and local meteorology. Journal of Nuclear Science and Technology 39, 180–186. Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics. Wiley, Hoboken, NJ, 1326pp. Slinn, W.G.N., 1983. Precipitation Scavenging, in Atmospheric Sciences and Power Production 1979, Chapter 11. Division of Biomedical Environmental Research, US Department of Energy, Washington, DC. Smith, P.L., 2003. Raindrop size distribution: exponential or gamma—does the difference matter? Journal of Applied Meteorology 42, 1031–1034.
log(CdRe2)
4 3 2 1 0 -2
-1
0
1
2
3
log(Re)
Fig. 13. Relationship between log(Re) and log(CD Re2).
and a ¼ 0:095202;
b ¼ 1:1058;
c ¼ 1:4338.
From the above equation, we can have Re ¼ log
1
b þ ½b2 4ac þ 4a log ðC D Re2 Þ1=2 2a
when 2:4oC D Re2 o1:1 105 .
!
ð8Þ
From Eq. (2), we have ut ¼
ma Re . ra Dp
(9)
Therefore, to calculate ut, we first calculate CD Re2 using Eq. (3); then calculate Re using Eqs. (6)–(8) according to the value of CD Re2; then from Eq. (9), we can calculate ut.
Atmospheric Environment 41 (2007) 6808–6822 www.elsevier.com/locate/atmosenv
A 3-mode parameterization of below-cloud scavenging of aerosols for use in atmospheric dispersion models Jian Feng Canadian Meteorological Centre, Meteorological Service of Canada, 2121 Trans-Canada Highway, Dorval, Que., Canada H9P 1J3 Received 20 December 2006; received in revised form 12 April 2007; accepted 20 April 2007
Abstract Atmospheric aerosols are subject to below-cloud scavenging by precipitation. The scavenging coefficient depends on the aerosol size significantly. The traditional bulk parameterization represents the mean wet scavenging coefficient for the whole aerosol size range. This parameterization significantly overestimates the scavenging of aerosol mass by a heavy rain or a long-duration medium rain. In this study, we present a 3-mode parameterization of the mean scavenging coefficient for each aerosol mode instead of representation for the whole aerosol size range. The new parameterization takes into account the aerosol number size distribution, the rain droplet size distribution and the spectral collision efficiency between the aerosol particle and the rain droplet. Comparing the calculation of mass depletion due to below-cloud scavenging, the 3-mode parameterization agrees well with the size-resolved explicit method. The new parameterization can be easily implemented in atmospheric dispersion models. r 2007 Elsevier Ltd. All rights reserved. Keywords: Aerosol; Wet scavenging; Atmospheric dispersion model
1. Introduction Wet scavenging and dry deposition are two important processes of removing airborne aerosols from the atmosphere. Wet scavenging refers to removal of aerosol particles by hydrometeors. The relative importance of these two processes depends on the properties of particles, the amount and intensity of precipitation, the boundary-level turbulence and the surface properties. Wet scavenging can be divided into in-cloud scavenging and belowcloud scavenging. Particles entrained into clouds are subject to in-cloud scavenging, which includes nucleation scavenging and interstitial scavenging. E-mail address: [email protected] 1352-2310/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2007.04.046
Most often, in-cloud scavenging is the main removal mechanism for sub-micron particles, which are usually not removed efficiently from the air by either below-cloud scavenging or dry deposition (Sakashita et al., 2002). Aerosol particles located below the base of a precipitating cloud will be collected by falling hydrometeors and this process is called below-cloud scavenging. Both in-cloud scavenging and below-cloud scavenging are important deposition mechanisms for airborne aerosols, with the relative importance depending on the particle size and the meteorological conditions. In this study, we focus on below-cloud scavenging of aerosols only. In chemical transportation models, below-cloud scavenging is usually described by a first-order mass
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
decay equation. The scavenging efficiency is represented by the mass scavenging coefficient, which depends on both the aerosol size and the properties of falling hydrometers (Gong et al., 2003). The dependence of the wet scavenging coefficient on the aerosol size was recently revisited by Andronache (2003). In his study, the wet scavenging coefficients are calculated for different modeled and observed aerosol size distributions. For the aerosol distribution with a coarse mode, the mean wet scavenging coefficient is parameterized as Sm ¼ aRb, where Sm is the mean wet scavenging coefficient, R is the rain rate in mm h1, b equals 0.7 and a varies from 0.24 to 0.88 for different aerosol size distributions. The dependence of the scavenging coefficient on the aerosol size distribution is implicitly parameterized in the powerlaw expression. However, as also illustrated in Andronache’s study, for different particle diameters, the scavenging coefficient can vary significantly. Below-cloud scavenging is efficient for small particles with diameters o0.01 mm and big particles with diameters larger than about a few micrometers. For particles with diameters between 0.01 mm and a few micrometers, the scavenging coefficient can be smaller by up to a few orders of magnitude. When applying the mean wet scavenging coefficient, the scavenging is assumed equally efficient for aerosols with different sizes. To account for the differences of scavenging efficiency for aerosols with different diameters, one method is to use bin-defined wet scavenging coefficients. A recent example is by Loosmore and Cederwall (2004), who developed a new scavenging model for the National Atmospheric Release Advisory Center (NARAC) system. The system is used at the Lawrence Livermore National Laboratory for both predictions and assessments of depositions of hazardous materials in the atmosphere. In their study, the size-resolved wet scavenging coefficient is approximated as Sðd p Þ ¼ ð3=2Þ ððEðDr ; d p ÞÞ=Dr ÞR, where E is the collision efficiency of a raindrop of diameter of Dr with a particle with diameter of dp; R is the precipitation rate in mm h1; Dr is the representative diameter of rain droplets and is introduced to simplify the integral form of S(dp). This size-resolved wet scavenging coefficient is applied directly to the discrete model particles as the model particles are size-resolved in the NARAC model system. A negative outcome from this method is the simulation anomalies caused by discrete particles. In the study by Loosmore and Cederwall (2004), they had to use a post-processor to smooth the anomalies.
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In this study, we present a new parameterization of below-cloud scavenging for use in atmospheric dispersion models. The new parameterization takes into account the fact that for different aerosol sizes the efficiency of below-cloud scavenging can differ significantly, but the parameterization does not require model particles to be discretized. The new parameterization is an extension of the traditional bulk parameterization, which is widely used in atmospheric dispersion models for the treatment of below-cloud scavenging of aerosols. The paper is presented as (1) the method of calculation of size-resolved wet scavenging coefficients; (2) parameterizations of wet scavenging coefficients; (3) implementation of the new parameterization into an atmospheric dispersion model and results; (4) sensitivity of wet scavenging to aerosol size distributions; and (5) summary.
2. Size-resolved wet scavenging coefficients 2.1. Calculation of size-resolved wet scavenging coefficients The method used to calculate the below-cloud scavenging coefficient is based on the concept of collision of a falling rain droplet with an aerosol particle. This concept was also recently used by Andronache (2003) and Loosmore and Cederwall (2004) in their studies. The detailed description of the method can be found in Seinfeld and Pandis (1998). When rain droplets fall through the air, the total collected mass of particles with diameter of dp by rain droplets during a unit time can be expressed as Z
1
p ðDp þ d p Þ2 ½U t ðDp Þ ut ðd p Þ 4 0 EðDp ; d p ÞNðDp Þ dDp ,
nM ðd p Þdd p
where nM is the aerosol mass size distribution, N is the rain droplet number size distribution, Dp is the diameter of the rain droplet, Ut and ut are the terminal velocities of the rain droplet and the aerosol particle, and E is the collision efficiency. Below-cloud scavenging can be modeled by a firstorder decay equation: dnM ðd p Þ ¼ Sðd p ÞnM ðd p Þ, dt
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
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where S(dp) is the below-cloud scavenging coefficient and therefore can be given by Z Sðd p Þ ¼
1
p ðDp þ d p Þ2 ½U t ðDp Þ ut ðd p Þ 4 0 EðDp ; d p ÞNðDp Þ dDp .
To calculate S(dp) numerically, we derive an analytical expression for Ut and ut for particles with different diameters. Detail of the derivation is in Appendix 1. Rain droplet number size distributions depend on the type of precipitation. They are generally described with either exponential or gamma functions, and the later ones are usually better to describe the number size distributions for droplets in a small size domain (Dpo1 mm). The scavenging coefficient is affected by the rain droplet size distribution through the total cross-section of the rain droplets. Because this variable is the second moment of the rain droplet diameter, small rain droplets make less contribution to the scavenging coefficient than big ones. In many practical applications, the fit with gamma functions gives little improvement over exponential functions, although the former ones are of greater mathematical complexity (Smith, 2003). In this study, the classical exponential fit of Marshall and Palmer (1948) is used for the rain droplet number size distribution: NðDp Þ ¼ N 0 expðcDp Þ, where N0 ¼ 8 103 m3 mm1, c ¼ 4.1R0.21 mm1 and R is the rain rate in mm h1. The regression values of the Marshall–Palmer fit are usually found to be good for steady rains at continental midlatitudes. Calculation of collision efficiency E is based on Slinn’s (1983) semi-empirical model. The analytical expression of E is E¼
4 ½1 þ 0:4Re1=2 Sc1=3 þ 0:16Re1=2 Sc1=2 Re Sc þ 4f½o
1
where Re ¼
Dp U t ra , 2ma
Sc ¼
ma , ra D
þ ð1 þ 2Re
1=2
Þf þ
!3=2 St S , St S þ 23
St ¼
2tðU t ut Þ , Dp
f¼
dp , Dp
mw , ma 1:2 þ ð1=12 lnð1 þ ReÞ S ¼ 1 þ lnð1 þ ReÞ o¼
and D¼
kTC c , 3pma d p
ut ¼ tg, ðrp ra Þd p C c , 18ma 2l 1:1d p 1:257 þ 0:4 exp Cc ¼ 1 þ l , dp 2l
t¼
l¼
2ma Pð8M=pRTÞ1=2
.
Symbols and constants are listed in Table 1. Slinn’s analytical expression of collision efficiency E has three terms: the first term represents the contribution from the Brownian diffusion; the second term represents interception; and the third term is due to impaction and is included only when the Stokes number is greater than the critical Stokes number S*. Size-resolved collision efficiencies for rain droplets with diameters of 0.1, 0.5, 1.0 and 4.0 mm are shown in Fig. 1, from which we can conclude: (1) the collision efficiency is significantly larger for big particles (dp4a few micrometers) and ultra-fine particles (dpo0.01 mm) than for particles with dp between 0.04 and 2.5 mm; (2) the collision efficiency decreases with the increase of the size of rain droplets. Fig. 2 shows the calculated belowcloud scavenging coefficients, Ss, for different rain rates. S varies significantly with the rain rate and the aerosol size. When the rain rate increases, the corresponding scavenging rate increases. For rain rates from 1 to 10 mm h1, scavenging is efficient for small particles (dpo0.05 mm) due to the Brownian diffusion and for larger particles (dp43 mm) due to the impaction. Scavenging is much less efficient and reaches a minimum in the size range between 0.1 and 1 mm. This range is often referred to as the ‘‘Greenfield gap’’ in the literature after S. Greenfield who first identified it (Seinfeld and Pandis, 1998).
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822 Table 1 List of symbols and constants
100
Sc St T ut Ut ra rp ma mw f o t
l g ¼ 9.807 m s2 k ¼ 1.381 1023 m2 kg s2 K1 ra ¼ 1.292 kg m3 rp ¼ 1. 103 kg m3 ma ¼ 1.720 105 kg m1 s1 8 1:787 > 0 C; > > > > C; 1:519 5 > < C; 1:307 103 kg m1 s1 10 mw ¼ > > > 15 C; 1:139 > > > : 20 C; 1:002
10-1
Collision efficiency
Slip correction factor Diameter of collected particle Particle diffusivity Diameter of rain droplet Acceleration of gravity Boltzmann constant Molecular weight of air Air pressure Molar gas constant Reynolds number of rain droplet Schmidt number of collected particle Stokes number of collected particle Air temperature Terminal velocity of particle Terminal velocity of rain droplet Air density Particle density Viscosity of air Viscosity of water Ratio of diameters Viscosity ratio Characteristic relaxation time of collected particle Mean free path of air
10-2
10-3
10-4
10-5
10-6 10-3
As examples, model aerosol distributions suggested by Jaenicke (1993) are used to calculate wet scavenging of aerosols. Jaenicke’s aerosol number distribution is expressed as the sum of 3 log-normal distributions: nN ðlog Dp Þ ¼
n X
Ni 1=2
ð2pÞ log si ¯ pi Þ2 ðlog Dp log D exp , 2 log2 si i¼1
101
102
101
100
10-1
10-2
10-3
10-4 10-3
2.2. Calculation of wet scavenging
10-2 10-1 100 Aerosol diameter, dp (µm)
Fig. 1. Size-resolved particle collision efficiencies for different rain droplet sizes.
S (h-1)
Cc dp D Dp g k M P R Re
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10-2
10-1 100 101 Aerosol diameter, dp (µm)
102
Fig. 2. Size-resolved wet scavenging coefficients for different rain rates.
¯ p , s are constants for where parameters N, D different types of aerosol, and are listed in Table 2. For aerosols with a unit density, the mass size distribution is equal to the volume size distribution. In the following, we use the volume size distribution for the illustration of wet scavenging of aerosol mass. S(dp) can be applied directly to the volume size distribution to calculate the
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Table 2 Parameters of model aerosol distributions suggested by Jaenicke (1993) N (cm3)
Urban Marine Rural Remote continental Free troposphere Polar Desert
¯ p (mm) D
i¼1
i¼2
i¼3
i¼1
i¼2
i¼3
i¼1
i¼2
i¼3
9.93 104 133 6650 3200 129 21.7 726
1.11 103 66.6 147 2900 59.7 0.186 114
3.64 104 3.1 1990 0.3 63.5 3 104 0.178
0.013 0.008 0.015 0.02 0.007 0.138 0.002
0.014 0.266 0.054 0.116 0.25 0.75 0.038
0.05 0.58 0.084 1.8 0.52 8.6 21.6
0.245 0.657 0.225 0.161 0.645 0.245 0.247
0.666 0.210 0.557 0.217 0.253 0.300 0.770
0.337 0.396 0.266 0.380 0.425 0.291 0.438
40 t=0 t = 0.5 h t=1h t = 10 h
30
dV/d[log(dp)](µm3cm-3)
dV/d[log(dp)](µm3cm-3)
40
20
10
0 10-3
log s
10-2
10-1 100 101 102 Aerosol diameter, dp (µm)
103
t=0 t = 0.5 h t=1h
30
20
10
10-3
10-2
10-1 100 101 102 Aerosol diameter, dp (µm)
103
Fig. 3. Volume size distributions of the remote continental aerosol after a wet scavenging of different times by a rain of (a) R ¼ 1 mm h1 and (b) R ¼ 10 mm h1.
depletion of volume due to wet scavenging. Fig. 3 shows the volume size distribution of the remote continental aerosol 0.5 h and 1 h after a wet scavenging by a 1 and 10 mm h1 rain, and 10 h after a 1 mm h1 rain. For a 1 mm h1 rain, particles with dp 43 mm (coarse mode) are removed from the air efficiently. After 1 h, 73% of the mass in this mode is deposited to the ground. Particles with sizes in the range between 0.04 and 3 mm (accumulation mode) are not sensitive to wet scavenging and only 2% of the mass is scavenged 10 h after the scavenging. A rain of 10 mm h1 can remove 91% of the mass in the coarse mode in just half an hour, while the mass washed out in the accumulation mode is negligible.
3. Parameterization 3.1. Bulk parameterization of wet scavenging Parameterization of wet scavenging is usually in terms of the mean mass scavenging coefficient, and is often referred to as bulk parameterization. The total mass scavenging can be expressed as Z 1 dM p 3 ¼ d r Sðd p Þnðd p Þ dd p ¼ Sm M, dt 6 p p 0 where M is the total aerosol mass, dp is the aerosol diameter, rp is the density of the particle, n is the aerosol number size distribution and SRm is the mean 1 mass scavenging coefficient. M ¼ 0 ðp=6Þd 3p rp n
ARTICLE IN PRESS J. Feng / Atmospheric Environment 41 (2007) 6808–6822
ðd p Þ dd p , therefore R1 Sm ¼
0
d 3p Sðd p Þnðd p Þ dd p . R1 3 0 d p nðd p Þ dd p
When aerosols are subject to wet scavenging, n(dp) changes with time. So Sm is a function of time t even S(dp) does not vary with time. If we assume Sm to be independent of time t, we can have M ¼ M0 exp (Smt), and M0 is the total initial aerosol mass. Fig. 4 shows the relationship between the calculated mean scavenging coefficient and the rain rate. Similar to the results in Andronache (2003), there is a very good linear relationship between log(Sm) and log(R). Therefore, we fit the relationship between Sm and R in terms of Sm ¼ aRb. For the model aerosols by Jaenicke (1993), the corresponding coefficients a and b are listed in Table 3.
Scavenging coefficient (h-1)
102
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Fig. 5 shows the wet scavenging of aerosol mass using the explicit calculation and the bulk parameterization for rain rates of 1 and 5 mm h1. For both rain rates, the wet scavenging is overestimated using the bulk parameterization. For the rain rate of 1 mm h1, the bulk parameterization starts to significantly overestimate the wet depletion of aerosol mass 1 h after the emission. Ten hours after the emission, there is still 23% of the aerosol mass in the air using the explicit calculation, while using the bulk parameterization, all the mass is washed out of the atmosphere. For the rain rate of 5 mm h1, using the explicit calculation, there is still 25% of the aerosol mass in the air 1 h after the scavenging. Using the bulk parameterization, 90% of the aerosol mass is washed out of the air just half an hour after the scavenging and almost all is deposited to the ground 1 h after the scavenging. It is clear that using the bulk parameterization is not good enough for the simulation of below-cloud scavenging of aerosols, especially for a heavy rain of long duration. In the following, we present a 3-mode parameterization of below-cloud scavenging.
101
3.2. 3-mode parameterization 100
10-1 0.1
1
10
100
Rain rate (mm h-1)
Fig. 4. Mean wet scavenging coefficients of the remote continental aerosol vs. rain rate.
Fig. 2 shows that the scavenging coefficients are ‘‘significant’’ for particles in the nucleation and the coarse modes, while the scavenging coefficient is orders of magnitude smaller in the accumulation mode. As the scavenging coefficients are quite different in these three modes, we calculate the mean mass scavenging coefficients for particles in each mode, instead of for the whole aerosol size
Table 3 Regression coefficients of the bulk parameterization Sm ¼ aRb and the 3-mode parameterization Smi ¼ ai Rbi Bulk para Sm (h1) 103 mmodpo100 mm
Mode 1 Sm1 (h1) 103 mmodpo0.04 mm
a
a1
b
b1
Mode 2 Sm2 (h1) 0.04 mmodpo2.5 mm
Mode 3
a2
Sm3 (h1) Sm4 (h1) 2.5 mmodpo16 mm 16 mmodpo100 mm
b2
a3
b3
a4
b4
Urban Remote continental Desert Polar Marine Rural Free troposphere
0.71 1.16 1.76 1.13 0.77 0.76 1.04
0.80 0.80 0.82 0.81 0.80 0.80 0.80
6.4 103 6.1 103 7.4 103 4.3 103 6.2 103 6.5 103 6.3 103
0.62 0.62 0.62 0.62 0.62 0.62 0.62
0.90 103 0.85 103 1.33 103 1.01 103 0.99 103 1.01 103 1.32 103
0.62 0.62 0.61 0.61 0.61 0.61 0.61
0.88 1.11 1.23 0.76 0.80 0.80 0.87
0.79 0.79 0.80 0.79 0.79 0.79 0.79
1.81 1.81 1.77 1.82 1.81 1.81 1.81
0.81 0.81 0.82 0.81 0.80 0.81 0.80
Average
1.05
0.80
6.2 103
0.62
1.06 103
0.61
0.92
0.79
1.81
0.81
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80
100 Explicit cal. Bulk para. Normalized total mass (%)
Normalized total mass (%)
100
60
40
20
Explicit cal. Bulk para.
80
60
40
20
0
0 t = 0.5 h
t=1h
t = 10 h
t = 0.5 h
t=1h
t = 10 h
Fig. 5. Wet depletion of the aerosol mass by a rain of (a) 1 mm h1 and (b) 5 mm h1 using the explicit calculation and the bulk parameterization.
1i
and assume Smi to be independent of time t, then we have Mi ¼ M0i exp(Smit), where Smi, Mi and M0i are the mean mass scavenging coefficient, the total aerosol mass, and the total initial aerosol mass for bin i. d1i and d2i are the low and up bounds of each bin. As an example, Fig. 6 shows the calculated mean scavenging coefficients of the remote continental aerosol vs. rain rate for different bins. As expected, there is a very good linear relationship between log(Si) and log(R) for each bin. Therefore, we fit the relationship between Smi and R in terms of S mi ¼ ai Rbi . The regression coefficients for the model aerosol distributions suggested by Jaenicke (1993) are listed in Table 3. 3.3. Evaluation of the 3-mode parameterization To evaluate the 3-mode parameterization, we use two methods to calculate the aerosol mass depletion. R d 2i For each bin i, the explicit one is V i ðtÞ ¼ d V 0i expðSðd p ÞtÞ dd p , and the 3-mode parame1i
102
Scavenging coefficient
103 (h-1)
range. In the coarse mode, since the scavenging coefficient changes rapidly for the particle size between 10 and 20 mm (Fig. 2), we divide this mode into two bins. For the other two modes, we use one bin for each mode. The four bins are dpo0.04 mm, 0.04 mmpdpo2.5 mm, 2.5 mmpdpo16 mm and dpX 16 mm. Define R d 2i 3 d d p Sðd p Þnðd p Þ dd p Smi ¼ 1iR d 3 2i d d p nðd p Þ dd p
101
Sc_M1 Sc_M2 Sc_M3_1 Sc_M3_2
100 10-1 10-2 10-3 10-4 0.1
1 Rain rate (mm
10
100
h-1)
Fig. 6. Mean wet scavenging coefficients of the remote continental aerosol in each bin vs. rain rate.
terization method is Vi(t) ¼ V0i exp(Smit). Fig. 7a and b shows the normalized aerosol mass (by the initial total mass) using the two methods after 0.5, 1 and 10 h of wet scavenging by a rain of 1 and 5 mm h1, respectively. The results from the 3-mode parameterization generally agree very well with the explicit calculations. The difference in normalized mass is o3% in each bin. Both the explicit method and the 3-mode parameterization show very little mass depletion in the accumulation mode. To see the improvement of the 3-mode parameterization over the bulk parameterization, we compare the total aerosol mass after a wet scavenging using R 1 three methods: (1) the explicit method, V ðtÞ ¼ 0 V 0 expðSðd p ÞtÞ dd p ; (2) the 3-mode
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50 Explicit cal. 3-mode para.
Normalized mass (%)
40
30
20
10
0 -
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
t=0h
t = 0.5 h
t=1h
t = 10 h
6
50 Explicit cal. 3-mode para.
Normalized mass (%)
40
30
20
10
0 -
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
V1 V2 V3 V4
t=0h
t = 0.5 h
t=1h
t = 10 h
6
Fig. 7. Wet depletion of the remote continental aerosol mass using the explicit calculation and the 3-mode parameterization for R ¼ 1 and 5 mm h1.
P method, Vi(t) ¼ V0i exp(Smit) and V ðtÞ ¼ 4i¼1 V i ðtÞ; (3) the bulk parameterization method, V(t) ¼ V0 exp(Smt). Fig. 8 shows the total aerosol mass of the remote continental aerosol after a wet scavenging of 1 mm h1 rain using the three methods. The results from the 3-mode method are very close to those using the explicit calculation. The bulk parameterization method overestimates the wet depletion by 20% of the total initial mass 1 h after the scavenging. After 10 h, using the bulk parameterization, almost all mass is deposited to the ground, while using the other two methods, there
are still significant amounts of aerosol mass in the atmosphere, as the aerosol mass in the ‘‘Greenfield gap’’ is not sensitive to the below-cloud scavenging. Comparing with the explicit calculation, both the 3-mode and the bulk parameterizations overestimate the mass depletion of aerosols. This is because the mean mass scavenging coefficient decreases with time as the particles with higher S(dp) are more efficiently removed from the air. For the wet scavenging by a rain of R ¼ 5 mm h1 presented in Fig. 5b, at t ¼ 0, Sm is weighted by the particles in both the accumulation mode and the coarse mode.
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4.2. Results from the bulk and the 3-mode parameterizations
100 90
Normalized total mass (%)
80
Explicit cal. 3-mode para. Bulk para.
70 60 50 40 30 20 10 0 t = 0.5 h
t=1h
t = 10 h
Fig. 8. Wet depletion of the aerosol mass using the explicit calculation, the 3-mode and the bulk parameterizations.
At t ¼ 1 h, Sm is dominated by the particles in the accumulation mode. The bulk method use Sm determined at t ¼ 0 for the following time, therefore significantly overestimates the mass depletion. The 3-mode method alleviates the overestimation through parameterizing the mean scavenging coefficient for each aerosol mode, for which S(dp) does not change as significantly as it does for the whole size range. As shown in Figs. 7 and 8, the 3-mode method efficiently reduces the overestimation of the wet scavenging. 4. Implementation and results 4.1. Implementation The 3-mode wet scavenging scheme is implemented into a stochastic atmospheric dispersion model MLCD (Flesch et al., 2002). In MLCD, a model particle is assumed to represent an ensemble of a large number of ‘‘real’’ particles. First based on the aerosol mass size distribution, the percentage of aerosol mass in each bin and the regression coefficients of the 3-mode parameterization for each bin are calculated. The total mass of each model particle Pis a sum of the mass in each bin: MðtÞ ¼ 4i¼1 M 0 Pi expðS mi tÞ, where M is the total mass of a model particle; M0 is the initial mass of the model particle; Pi is the percentage of mass in each bin; Smi is the wet scavenging coefficient of bin i and is parameterized as ai Rbi .
To test the newly developed wet scavenging parameterizations, a hypothetical release of aerosols is assumed to have happened in Laval, Quebec, Canada on 1 June 2004. The emission is assumed to last for 6 h and the particles are released evenly from a column with a radius of 50 m and a height of 1000 m. The released particles are assumed to follow the size distribution of the urban aerosol. The wind fields are taken from the Global Environmental Multi-scale (GEM) model simulations. We ran MLCD with two different wet scavenging parameterizations: the bulk parameterization and the 3-mode parameterization. A uniform precipitation field of 1 mm h1 is assumed for the simulation. Fig. 9a and b shows that the wet deposition pattern using the bulk parameterization and the 3-mode parameterization is very similar 6 h after the emission. However, the integrated flux using the bulk parameterization is over two times larger for most of the area around the source site (Fig. 9e). The integrated wet deposition fluxes 12 h after the emission are shown in Fig. 9c and d. As indicated in Fig. 9f, the bulk parameterization predicts the integrated wet deposition over two times larger than the 3-mode parameterization for most of the area around the release source, but for the region far from the source, the bulk parameterization predicts the integrated flux less than half of that by the 3-mode parameterization. Fig. 10a and b shows the mass concentrations in the first model level (from the ground to 250 m above the ground) 6 h after the emission using the bulk parameterization and the 3-mode parameterization. For most of the region affected by the emission, the mass concentration using the bulk parameterization is about 1-order of magnitude smaller than that using the 3-mode parameterization. Fig. 10c and d are the same as Fig. 10a and b, but for 12 h after the emission. Using the 3-mode parameterization, there is still a significant amount of aerosol mass in the air, while using the bulk parameterization, the aerosol mass in the air is about 3 orders of magnitude smaller. Using the 3-mode parameterization, the aerosol mass in the accumulation mode is not sensitive to the wet scavenging, but using the bulk parameterization, it is washed out of the air the same efficiently as the aerosol mass in the coarse mode and the nucleation mode. Therefore, the bulk parameterization
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Fig. 9. Integrated wet depositions (a–d) at the ground 6 h and 12 h after the emission using the bulk parameterization and the 3-mode parameterization respectively. Parts (e) and (f) are the ratios of the wet depositions using the bulk parameterization to that of the 3-mode parameterization 6 and 12 h after the emission.
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Fig. 10. Mass concentrations in the level from the ground to 250 m above the ground 6 and 12 h after the emission using the bulk parameterization and the 3-mode parameterization, respectively.
overestimates the aerosol mass washed out of the air. Fig. 11a–c shows the integrated wet deposition and the low-level concentration for another emission scenario. The emission is assumed to last 2 h and the simulation is for 6 h. The rain rate is assumed to be 5 mm h1. As indicated in Fig. 11d, the bulk parameterization strongly overestimates the wet deposition for the region close to the source site. As most of the mass is washed out from the air near the source, the bulk parameterization predicts o10% of the wet deposition by the 3-mode parameterization for the region away from the source. Fig. 11c shows that there is still a significant amount of aerosol mass in the air using the 3-mode
parameterization 6 h after the emission, while using the bulk parameterization, all aerosol mass is washed out of the air. 5. Sensitivity of wet deposition to aerosol size distributions Aerosol size distributions determine how the total mass of each model particle is distributed to each aerosol mode, and the wet scavenging efficiency for each mode is different, therefore aerosol size distributions affect wet deposition. To test the sensitivity of wet deposition to aerosol size distributions, we ran MLCD for seven different modeled aerosol size
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Fig. 11. Integrated wet depositions (a and b) at the ground and mass concentration (c) in the level from the ground to 250 m above the ground 6 h after the emission for a rain rate of 5 mm h1. (d) The ratio of the wet deposition using the bulk parameterization to that of the 3-mode parameterization.
distributions compiled by Jaenicke (1993). The scenario is the same as the previous one: the emission lasts for 6 h and the rain rate is 1 mm h1. Fig. 12 shows comparisons of the integrated wet deposition flux between the urban aerosol and six other aerosols. Comparing with the urban aerosol, the six types of aerosol all have higher wet deposition for the area close to the source and less wet deposition for the area far away from the source. In particular, the desert aerosol has the largest wet deposition around the source region, and far less deposition away from the source site. This is because for the size distribution of the desert aerosol, only o1% of the total mass is
located in the accumulation mode. For the other types of aerosol, the percentage of the total mass located in the accumulation mode varies from 15% for the free troposphere aerosol to 49% for the urban aerosol. As the wet scavenging coefficient is much higher for the coarse mode than that for the accumulation mode, more mass in the accumulation mode means less mass can be scavenged and more mass can be transported to the region away from the source. This is also consistent with the result that the mass concentration in the first model level is highest for the urban aerosol and lowest for the desert aerosol (figures not shown).
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Fig. 12. Ratios of integrated wet depositions at the ground for six types of aerosol to that of the urban aerosol 12 h after the emission.
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6. Summary Aerosols in the atmosphere are subject to scavenging by precipitation. The below-cloud scavenging efficiency of rain depends strongly on the aerosol size and the rain rate. Bulk parameterization of the wet scavenging coefficient takes into account this dependence implicitly. An inherent drawback of the bulk parameterization is that the scavenging efficiency is assumed to be equal for particles with different sizes. This parameterization works well for a light rain of short duration, but overestimates wet depletion of aerosol mass for a heavy rain or a medium rain of long duration. Using bin-defined wet scavenging coefficients can remove the overestimation, but it requires model particles be size-resolved in a Lagrangian dispersion model, which can cause simulation anomalies; or it requires more aerosol size bins in a Eulerian dispersion model, which takes more computation time. An alternative solution is to use the bulk parameterization for different aerosol modes, as each mode has different wet scavenging characteristics. In this study, we present a 3-mode parameterization. Comparisons of the wet depletion of aerosol mass calculated by the 3-mode parameterization and the explicit method show a very good agreement. The new 3-mode parameterization can be easily implemented into Lagrangian dispersion models. Acknowledgments
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velocity can be given by 4gDp C c rp 1=2 , ut ¼ 3C D ra
(1)
t, g, Dp, Cc, rp, and ra are defined in Table 1. CD is the drag coefficient. CD is a function of Reynolds number Re, and Re is a function of ut. Thus, the above expression is only an implicit one for ut. Based on the idea of Flagan and Seinfeld (1988), here we derive an explicit analytical expression for ut. According to definition, Re ¼
ut Dp ra . ma
(2)
Therefore, C D Re2 ¼
C D u2t D2p r2a . ma
(3)
Substitute Eq. (1) into Eq. (3), we have C D Re2 ¼
4D3p ra rp gC c . 3m2
(4)
The expression for CDRe2 is an explicit one. The analytical expressions of CD for different Reynolds numbers are (Eq. 8.32, Seinfeld and Pandis, 1998)
CD
8 24 Reo0:1; > Re ; > > > 24 3 9 2 < 1 þ 0:1oReo2; Re 16 Re þ 160 Re lnð2ReÞ ; ¼ 24 0:687 ð1 þ 0:15 Re Þ; 2oReo500; > > Re > > : 0:44; 500oReo2 105 :
(5) This study was funded by the Chemical, Biological, Radiological, and Nuclear (CBRN) Research and Technology Initiative (CRTI) of Defence R&D Canada through the CRTI-02-0041RD project. I would like to thank Mr. Nils Ek for reviewing the manuscript. The comments from one of the two reviewers were very helpful in improving the manuscript. Management support from Mr. Richard Hogue and Mr. Michel Jean is gratefully acknowledged. Appendix A. Terminal velocity for particles of any Reynolds number For particles with particles smaller than terminal velocity can particles with larger
Reynolds number o0.1 or about 20 mm in diameter, the be expressed as ut ¼ tg. For Reynolds number, terminal
2
From Eq. (5), we can see that CD Re is a function of only Re. Plot of CD Re2 vs. Re is shown in Fig. 13. According to Eq. (5), when Reo0.1, CDRe2 ¼ 24Re. Therefore, we can have C D Re2 when C D Re2 o2:4. (6) 24 When 500oReo2 105, CDRe2 ¼ 0.44Re2. Therefore, we can have 1=2 C D Re2 when C D Re2 41:1 105 . (7) Re ¼ 0:44
Re ¼
When 0.1oReo500, as shown in Fig. 13, a quadratic regression can excellently fit the relationship between log(CD Re2) and log(Re): logðC D Re2 Þ ¼ a log2 ðReÞ þ b logðReÞ þ c
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References
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Andronache, C., 2003. Estimated variability of below-cloud aerosol removal by rainfall for observed aerosol size distributions. Atmospheric Chemistry and Physics 3, 131–143. Flagan, R.C., Seinfeld, J.H., 1988. Fundamentals of Air Pollution Engineering. Prentice-Hall, Englewood Cliffs, NJ. Flesch, T., Wilson, J., Crenna, B., 2002. MLCD: A Short-range Atmospheric Dispersion Model for Emergency Response. Contract report, Canadian Meteorological Centre, Dorval, Que., Canada. Gong, S.L., et al., 2003. Canadian aerosol module: a sizesegregated simulation of atmospheric aerosol process for climate and air quality models 1. Module development. Journal of Geophysical Research 108 (D1), 4007. Jaenicke, R., 1993. Tropospheric aerosols. In: Hobbs, P.V. (Ed.), Aerosol–Cloud–Climate Interactions. Academic Press, San Diego, CA, pp. 1–31. Loosmore, G.A., Cederwall, R.T., 2004. Precipitation scavenging of atmospheric aerosols for emergency response applications: testing an updated model with new real-time data. Atmospheric Environment 38, 993–1003. Marshall, J.S., Palmer, W.M., 1948. The distribution of raindrop with size. Journal of Meteorology 5, 165–166. Sakashita, T., Nakamura, Y., Doi, M., 2002. Test of wet scavenging parameterization schemes by simulation of monthly depositions of 7Be using normally available data on environmental monitoring and local meteorology. Journal of Nuclear Science and Technology 39, 180–186. Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics. Wiley, Hoboken, NJ, 1326pp. Slinn, W.G.N., 1983. Precipitation Scavenging, in Atmospheric Sciences and Power Production 1979, Chapter 11. Division of Biomedical Environmental Research, US Department of Energy, Washington, DC. Smith, P.L., 2003. Raindrop size distribution: exponential or gamma—does the difference matter? Journal of Applied Meteorology 42, 1031–1034.
log(CdRe2)
4 3 2 1 0 -2
-1
0
1
2
3
log(Re)
Fig. 13. Relationship between log(Re) and log(CD Re2).
and a ¼ 0:095202;
b ¼ 1:1058;
c ¼ 1:4338.
From the above equation, we can have Re ¼ log
1
b þ ½b2 4ac þ 4a log ðC D Re2 Þ1=2 2a
when 2:4oC D Re2 o1:1 105 .
!
ð8Þ
From Eq. (2), we have ut ¼
ma Re . ra Dp
(9)
Therefore, to calculate ut, we first calculate CD Re2 using Eq. (3); then calculate Re using Eqs. (6)–(8) according to the value of CD Re2; then from Eq. (9), we can calculate ut.