ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-6-2927-2006 An inverse modeling procedure to determine particle growth and nucleation rates from measured aerosol size distributions Verheggen B. 1 2 Mozurkewich M. 1 Department of Chemistry and Centre for Atmospheric Chemistry, York University, Toronto ON M3J 1P3, Canada now at: Laboratory for Atmospheric Chemistry, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland 17 07 2006 6 10 2927 2942 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/6/2927/2006/acp-6-2927-2006.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/6/2927/2006/acp-6-2927-2006.pdf

Classical nucleation theory is unable to explain the ubiquity of nucleation events observed in the atmosphere. This shows a need for an empirical determination of the nucleation rate. Here we present a novel inverse modeling procedure to determine particle nucleation and growth rates based on consecutive measurements of the aerosol size distribution. The particle growth rate is determined by regression analysis of the measured change in the aerosol size distribution over time, taking into account the effects of processes such as coagulation, deposition and/or dilution. This allows the growth rate to be determined with a higher time-resolution than can be deduced from inspecting contour plots ("banana-plots''). Knowing the growth rate as a function of time enables the evaluation of the time of nucleation of measured particles of a certain size. The nucleation rate is then obtained by integrating the particle losses from time of measurement to time of nucleation. The regression analysis can also be used to determine or verify the optimum value of other parameters of interest, such as the wall loss or coagulation rate constants. As an example, the method is applied to smog chamber measurements. This program offers a powerful interpretive tool to study empirical aerosol population dynamics in general, and nucleation and growth in particular.

 References Andronache, C., Chameides, W. L., Davis, D. D., Anderson, B. E., Pueschel, R. F., Bandy, A. R., Thornton, D. C., Talbot, R. W., Kasibhatla, P., and Kiang, C. S.: Gas-to-particle conversion of tropospheric sulfur as estimated from observations in the western North Pacific during PEM-West B, J. Geophys. Res., 102, 28 511–28 538, 1997. Bienenstock, Y.: Smog chamber studies of toluene photo-oxidation by OH radicals, M. Sc. thesis, York University, Canada, 2000. Chan, T. W. and Mozurkewich, M.: Measurement of the coagulation rate constant for sulfuric acid particles as a function of particle size using tandem differential mobility analysis, J. Aerosol Sci., 32, 321–339, 2001. Clarke, A. D., Kapustin, V. N., Eisele, F. L., Weber, R. J., and McMurry, P. H.: Particle production near marine clouds: Sulfuric acid and predictions from classical binary nucleation, Geophys. Res. Lett., 26, 2425–2428, 1999. Crump, J. G. and Seinfeld, J. H.: Turbulent deposition and gravitational sedimentation of an aerosol in a vessel of arbitrary shape, J. Aerosol Sci., 12, 405–415, 1981. Easter, R. C. and Peters, L. K.: Binary homogeneous nucleation: Temperature and relative humidity fluctuations, non-linearity, and aspects of new particle production in the atmosphere, J. Appl. Meteor., 33, 775–784, 1994. Friedlander, S. K.: Smoke, dust, and haze, Oxford Unversity Press, Oxford, 2000. Fuchs, N. A. and Sutugin, A. G.: Highly dispersed aerosols, Ann Arbor Sci., Ann Arbor, Michigan, p. 49–60, 1970. Gmitro, J. I. and Vermeulen, T.: Vapor-liquid equilibria for aqueous sulfuric acid, Amer. Inst. Chem. Eng. J., 10, 740–746, 1964. Hoppel, W., Fitzgerald, J., Frick, G., Caffrey, P., Pasternack, L., Hegg, D., Gao, S., Leaitch, R., Shantz, N., Cantrell, C., Albrechcinski, T., Ambrusko, J., and Sullivan, W.: Particle formation and growth from ozonolysis of alpha-pinene, J. Geophys. Res., 106, 27 603–27 618, 2001. Jacobson, M. Z., Turco, R. P., Jensen, E. J., and Toon, O. B.: Modeling coagulation among particles of different composition and size, Atmos. Environ., 28, 1327–1338, 1994. Jefferson, A., Eisele, F. L., Ziemann, P. J., Weber, R. J., Marti, J. J., and McMurry, P. H.: Measurements of the H$_2$SO$_4$ mass accommodation coefficient onto polydisperse aerosol, J. Geophys. Res., 102, 19 021–19 028, 1997. Kerminen, V. M. and Wexler, A. S.: The occurrence of sulfuric acid-water nucleation in plumes: Urban environment, Tellus B, 48, 65–82, 1996. Kerminen, V. M. and Kulmala, M.: Analytical formulae connecting the "real" and the "apparent" nucleation rate and the nuclei number concentration for atmospheric nucleation events, J. Aerosol Sci., 33, 609–622, 2002. Kulmala, M. and Laaksonen, A.: Binary nucleation of the water sulfuric acid system – comparison of classical theories with different H$_2$SO$_4$ saturation vapor pressures, J. Chem. Phys., 93, 696–701, 1990. Kulmala, M., Laaksonen, A., and Pirjola, L.: Parameterizations for sulfuric acid/water nucleation rates, J. Geophys. Res., 103, 8301–8307, 1998a. Kulmala, M., Toivonen, A., Makela, J. M., and Laaksonen, A.: Analysis of the growth of nucleation mode particles observed in Boreal forest, Tellus B, 50, 449–462, 1998b. Kulmala, M., Pirjola, U., and Makela, J. M.: Stable sulphate clusters as a source of new atmospheric particles, Nature, 404, 66–69, 2000. Kulmala, M., Dal Maso, M., Makela, J. M., Pirjola, L., Vakeva, M., Aalto, P., Miikkulainen, P., Hameri, K., and O'Dowd, C. D.: On the formation, growth and composition of nucleation mode particles, Tellus B, 53, 479–490, 2001. Kulmala, M., Vehkamaki, H., Petajda, T., Dal Maso, M., Lauri, A., Kerminen, V. M., Birmili, W., and McMurry, P. H.: Formation and growth rates of ultrafine atmospheric particles: a review of observations, J. Aerosol Sci., 35, 143–176, 2004. Lehtinen, K. E. J., Rannik, U., Petaja, T., Kulmala, M., and Hari, P.: Nucleation rate and vapor concentration estimations using a least squares aerosol dynamics method, J. Geophys. Res., 109, D21209, doi:10.1029/2004JD004893, 2004. Lohmann, U. and Feichter, J.: Global indirect aerosol effects: a review, Atmos. Chem. Phys., 5, 715–737, 2005. Mäkelä, J. M., Aalto, P., Jokinen, V., Pohja, T., Nissinen, A., Palmroth, S., Markkanen, T., Seitsonen, K., Lihavainen, H., and Kulmala, M.: Observations of ultrafine aerosol particle formation and growth in boreal forest, Geophys. Res. Lett., 24, 1219–1222, 1997. McMurry, P. H. and Wilson, J. C.: Growth laws for the formation of secondary ambient aerosols – implications for chemical conversion mechanisms, Atmos. Environ, 16, 121–134, 1982. McMurry, P. H. and Rader, D. J.: Aerosol wall losses in electrically charged chambers, Aerosol Sci. Tech., 4, 249–268, 1985. Molina, M. J., Molina, L. T., and Kolb, C. E.: Gas-phase and heterogeneous chemical kinetics of the troposphere and stratosphere, Ann. Rev. Phys. Chem., 47, 327–367, 1996. O'Dowd, C., McFiggans, G., Creasey, D. J., Pirjola, L., Hoell, C., Smith, M. H., Allan, B. J., Plane, J. M. C., Heard, D. E., Lee, J. D., Pilling, M. J., and Kulmala, M.: On the photochemical production of new particles in the coastal boundary layer, Geophys. Res. Lett., 26, 1707–1710, 1999. O'Dowd, C. D., Geever, M., and Hill, M. K.: New particle formation: Nucleation rates and spatial scales in the clean marine coastal environment, Geophys. Res. Lett., 25, 1661–1664, 1998. Oberdorster, G.: Pulmonary effects of inhaled ultrafine particles, Int. Arch. Occup. Environ. Health, 74, 1–8, 2001. Pöschl, U., Canagaratna, M., Jayne, J. T., Molina, L. T., Worsnop, D. R., Kolb, C. E., and Molina, M. J.: Mass accommodation coefficient of H$_2$SO$_4$ vapor on aqueous sulfuric acid surfaces and gaseous diffusion coefficient of H$_2$SO$_4$ in N$_2$/H$_2$O, J. Phys. Chem. A, 102, 10 082–10 089, 1998. Preining, O.: The physical nature of very, very small particles and its impact on their behaviour, J. Aerosol Sci., 29, 481–495, 1998. Press, W. H., Teukolsy, S. A., Vettering, W. T., and Flannery, B. P.: Numerical recipes in C++, Cambridge University Press, Cambridge, 2002. Sandu, A., Liao, W., Carmichael, G. R., Henze, D. K., and Seinfeld, J. H.: Inverse modeling of aerosol dynamics using adjoints: Theoretical and numerical considerations, Aerosol Sci. Technol., 39, 677–694, 2005. Sceats, M. G.: Brownian coagulation in aerosols – the role of long-range forces, J. Colloid Inter. Sci., 129, 105–112, 1989. Schwartz, S. E.: The Whitehouse effect – Shortwave radiative forcing of climate by anthropogenic aerosols: An overview, J. Aerosol Sci., 27, 359–382, 1996. Toon, O. B., Turco, R. P., Westphal, D., Malone, R., and Liu, M. S.: A multidimensional model for aerosols - description of computational analogs, J. Atmos. Sci., 45, 2123–2143, 1988. Verheggen, B. and Mozurkewich, M.: Determination of nucleation and growth rates from observation of a SO$_2$ induced atmospheric nucleation event, J. Geophys. Res., 107, 4123–4134, doi:10.1029/2001JD000683, 2002. Verheggen, B.: Determination of particle nucleation and growth rates from measured aerosol size distributions, Ph.D. thesis, York University, Canada, 2004. Viisanen, Y., Kulmala, M., and Laaksonen, A.: Experiments on gas-liquid nucleation of sulfuric acid and wafer, J. Chem. Phys., 107, 920–926, 1997. Weber, R. J., McMurry, P. H., Eisele, F. L., and Tanner, D. J.: Measurement of expected nucleation precursor species and 3–500-nm diameter particles at Mauna-Loa observatory, Hawaii, J. Atmos. Sci., 52, 2242–2257, 1995. Weber, R. J., Marti, J. J., McMurry, P. H., Eisele, F. L., Tanner, D. J., and Jefferson, A.: Measurements of new particle formation and ultrafine particle growth rates at a clean continental site, J. Geophys. Res., 102, 4375–4385, 1997. Weber, R. J., McMurry, P. H., Mauldin, L., Tanner, D. J., Eisele, F. L., Brechtel, F. J., Kreidenweis, S. M., Kok, G. L., Schillawski, R. D., and Baumgardner, D.: A study of new particle formation and growth involving biogenic and trace gas species measured during ACE 1, J. Geophys. Res., 103, 16 385–16 396, 1998. Williams, M. M. R. and Loyalka, S. K.: Aerosol science: theory and practice, with special applications to the nuclear industry, Elsevier Science, 116–117, 1991. Wyslouzil, B. E., Seinfeld, J. H., Flagan, R. C., and Okuyama, K.: Binary nucleation in acid water systems 2: Sulfuric acid water and a comparison with methanesulfonic acid water, J. Chem. Phys., 94, 6842–6850, 1991.