Department of Mechanical Engineering The Pearlstone Center for Aeronautical Engineering Studies Ben-Gurion University of the Negev P.O.B. 653, Beer Sheva ISRAEL

Remote continental aerosol Background aerosol Maritime aerosol Desert dust Rural aerosol Urban aerosol Polar aerosol Aircraft observation of vertical profiles of Black Carbon (BC) mass concentration over Hyderabad (11 to 21 June 2009) and Bangalore (28 June to3 July 2009) (by P.D. Safai et al., Science of the Total Env. (2012), –331) Ben-Gurion University of the Negev

The set of 152 vertical profiles of aerosol number concentration observed by the airborne optical spectrometer probe in Beijing, China, between February 2005 and September 2006 (by P. Liu et al., Tellus (2009), 61B, 756–767) (see, e.g., Pruppacher and Klett, 1997; Jaenicke, 1993) Ben-Gurion University of the Negev

Scavenging of air pollutions by cloud and rain droplets Cross-sectional area: Mass conservation equation: where j - wet-deposition flux, c (G) - concentration of aerosol in the atmosphere. (1) a – mean droplet radius – water fraction in rain (liquid water content) Wet-deposition flux of aerosol approaching the surface at altitude z = s reads: (2) where U t is droplets’ terminal velocity, I is rain intensity, c (L) is bulk concentration of aerosol in rain droplets. Ben-Gurion University of the Negev

Scavenging of air pollutions by cloud and rain droplets Then using mass balance equation for aerosols we obtain following equation: where  is scavenging coefficient, E (a, R p ) is collision efficiency. (3) (4) After the integration Eq. (4) we obtain the bulk concentration of aerosols in the first falling rain droplet as function of coordinate z: (5) where z the is the distance from the cloud to the ground. Ben-Gurion University of the Negev

Scavenging of air pollutions by cloud and rain droplets Evolution of the vertical distribution of aerosols in a rectangular column with horizontal cross-sectional area can be described as follows: where is the number of aerosol particles in a droplet. (6) Vertical distribution of aerosol concentration in the column after the 1-st droplet fall reads: (7) (8) The vertical distribution of aerosol concentration in the atmosphere can be approximated by the polynomials: Ben-Gurion University of the Negev

Eqs. (7) - (8) yield the following expression for the vertical distribution of concentration of aerosols in the atmosphere after the fall of rain droplets: (9) Sincewe obtain the following expression for : where (10) Ben-Gurion University of the Negev

If the initial distribution of aerosol concentration is uniform, Eq. (9) yields the following formula for the aerosol concentration evolution under the influence of rain: (11) (12) For a ~ 1mm and I ~ 10 mm/h, Thus Eq. (11) recovers equation (see, Pruppacher and Klett, 1997, p.720 or Seinfeld and Pandis, 2006, p. 936): Ben-Gurion University of the Negev

Scavenging of air pollutions by cloud and rain droplets Fig. 1. Evolution of concentration profile of aerosols under the influence of rain. Rain intensity I = 6 mm/h, rain drop diameter d = 1.1 mm, collected particle diameter D p = 20  m Ben-Gurion University of the Negev Initial concentration profile: For the height h = 1 km, L = 730 m, is the distance from the ground to the cloud.

. Fig. 2. Semiempirical correlation for the collision efficiency E (Slinn, 1983) as a function of collected particle size Ben-Gurion University of the Negev

Fig. 3. Evolution of concentration profile of aerosols under the influence of rain (collision efficiency E = 0.1) Fig. 4. Evolution of concentration profile of aerosols under the influence of rain (collision efficiency E = 0.01) Ben-Gurion University of the Negev

Fig. 5. Evolution of concentration profile of aerosols under the influence of rain (R p = 2.5  m) PDF for log-normal size distribution of droplets (Feingold-Levin, 1986) : Fig. 6. Evolution of concentration profile of aerosols under the influence of rain (R p = 1.5  m) Ben-Gurion University of the Negev

Fig. 8. Evolution of scavenging rate for log-normal raindrop size distribution (radii of collected particles R p = 2.5  m) Fig. 7. Evolution of scavenging rate for log-normal raindrop size distribution (radii of collected particles R p = 10  m)

Ben-Gurion University of the Negev  Volcano  Industrial air pollution plume

The simple form of the obtained solution allows analyzing the dependence of the rate of aerosols scavenging on different parameters, e.g. rain intensity, gradient of aerosols concentration in a gaseous phase etc. The obtained solution was analyzed for the exponential initial distribution of aerosols. In the calculations we assumed the log-normal droplet size distribution (DSD) with Feingol-Levin parameterization (Feingold and Levin, 1986). The results of the present study can be useful in an analysis of different meteorology-chemistry models and in particular in various parameterizations of the precipitation scavenging of the atmospheric aerosols. Ben-Gurion University of the Negev