T. Elperin , A. Fominykh and B . Krasovitov

1. Effect of Rain on the Evolution of Aerosol Concentration Distribution in the Atmosphere T. Elperin, A. Fominykh and B. Krasovitov Department of Mechanical Engineering The Pearlstone Center for Aeronautical Engineering Studies Ben-Gurion University of the Negev P.O.B. 653, Beer Sheva 84105 ISRAEL

2. Vertical distribution of aerosol concentration • 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), 431 323–331) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

3. Vertical distribution of aerosol concentration (see, e.g., Pruppacher and Klett, 1997; Jaenicke, 1993) 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) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

4. Description of the model Scavenging of air pollutions by cloud and rain droplets a–mean droplet radius – water fraction in rain (liquid water content) Cross-sectional area: Mass conservation equation: (1) where j- wet-deposition flux, c (G) - concentration of aerosol in the atmosphere . Wet-deposition flux of aerosol approaching the surface at altitude z = s reads: (2) where Ut is droplets’ terminal velocity, I is rain intensity, c(L) is bulk concentration of aerosol in rain droplets. IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

5. Description of the model Scavenging of air pollutions by cloud and rain droplets Then using mass balance equation for aerosols (3) we obtain following equation: (4) where is scavenging coefficient, E (a, Rp) is collision efficiency. 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. IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

6. Description of the model 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: (6) where is the number of aerosol particles in a droplet. Vertical distribution of aerosol concentration in the column after the 1-st droplet fall reads: (7) The vertical distribution of aerosol concentration in the atmosphere can be approximated by the polynomials: (8) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

7. Description of the model 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) Since we obtain the following expression for : (10) where IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

8. Description of the model 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) 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): (12) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

9. Results and discussion Scavenging of air pollutions by cloud and rain droplets Initial concentration profile: For the height h = 1 km, L = 730 m, is the distance from the ground to the cloud. 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 Dp = 20 mm IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

10. Results and discussion . Fig. 2. Semiempirical correlation for the collision efficiency E (Slinn, 1983) as a function of collected particle size IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

11. Results and discussion Fig. 4. Evolution of concentration profile of aerosols under the influence of rain (collision efficiency E = 0.01) Fig. 3. Evolution of concentration profile of aerosols under the influence of rain (collision efficiency E = 0.1) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

12. Results and discussion PDF for log-normal size distribution of droplets (Feingold-Levin, 1986) : Fig. 5. Evolution of concentration profile of aerosols under the influence of rain (Rp = 2.5 mm) Fig. 6. Evolution of concentration profile of aerosols under the influence of rain (Rp = 1.5 mm) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

13. Results and discussion Fig. 7. Evolution of scavenging rate for log-normal raindrop size distribution (radii of collected particles Rp = 10 mm) Fig. 8. Evolution of scavenging rate for log-normal raindrop size distribution (radii of collected particles Rp = 2.5 mm) IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

14. Research in progress • Volcano • Industrial air pollution plume IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev

15. Conclusions 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. IAAR 26th Annual Meeting May 21, 2013, Tel-Aviv University, Israel Ben-Gurion University of the Negev