Abstract
Aerosol particles play an important role in many physical and chemical processes in the atmosphere1. Physical and chemical behaviour of aerosol particles is strongly dependent on particle size and thus the size cannot be ignored in the evaluation and theoretical prediction of the effects caused by airborne particles. Since the particle diameter d p can range from few nanometers to about 100 micrometers, a size distribution function is used to describe how certain property, e.g. number, surface area or mass, of particles per unit gas volume is distributed on different particle sizes. The determination of the size distribution function is a very important fundamental task in aerosol research. However, the size distribution cannot be measured directly but it has to be reconstructed on the basis of indirect observations using computational methods. From the mathematical point of view the determination of the size distribution function is an ill-posed problem since the problem does not have a unique solution. The purpose of this chapter is to describe the problem and give a brief review on some computational methods proposed for the reconstruction of particle size distributions.
Keywords
- Markov Chain Monte Carlo
- Posterior Density
- Tikhonov Regularization
- Observation Error
- Markov Chain Monte Carlo Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.H. Seinfeld and S.N. Pendis, Atmospheric Physics and Chemistry. From Air Pollution to Climate Change (John Wiley & Sons, 1998).
M. Kandlikar and G. Ramachandran, Inverse methods for analysing aerosol spectrometer measurements: a critical review, J Aerosol Sci. 30, 413–437 (1999).
T.G. Dzubay and H. Hasan, Fitting multimodal lognormal size distributions to cascade impactor data, Aerosol Sci. Tech. 13, 144–150 (1990).
O.G. Raabe, A general method for fitting size distributions to multicomponent aerosol data using weighted least-squares, Env. Sci. Tech. 12, 1162–1167 (1978).
A. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996 ).
U. Amato, D. Di Bello, F. Esposito, C. Serio, G. Pavese, and F. Romano, Intercomparing the Twomey method with a multimodal lognormal approach to retrieve the aerosol size distribution, J. Geophys. Res. D 101, 19267–19275 (1996).
J.K. Wolfenbarger and J.H. Seinfeld, Inversion of aerosol size distribution data, J. Aerosol Sci. 21, 227–247 (1990).
V.S. Bashurova, K.P. Koutzenogil, A.Y. Pusep, and N.V. Shokhirev, Determination of atmospheric aerosol size distribution functions from screen diffusion battery data: mathematical aspects, J. Aerosol Sci. 22, 373–388 (1991).
U. Amato, M.R. Carfora, V. Cuomo, and C. Serio, Objective algorithms for the aerosol problem, Appl. Opt. 34, 5442–5452 (1995).
S. Twomey, Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions, J. Comput. Phys. 18, 188–200 (1975).
M.T. Chahine, Determination of the temperature profile in an atmosphere form its outgoing radiance, J. Opt. Soc. Am. 58, 1634–1637 (1968).
G. Ramachandran and M. Kandlikar, Bayesian analysis for inversion of aerosol size distribution data, J. Aerosol Sci. 27, 1099–1112 (1996).
E.F. Maher and N.M. Laird, EM algorithm reconstruction of particle size distributions from diffusion battery data, J. Aerosol Sci. 16, 557–570 (1985).
P. Paatero, The Extreme Value Estimation Deconvolution Method with Applications in Aerosol Research, Technical Report No. HU-P-250, University of Helsinki, Department of Physics (1990).
A.Voutilainen, V. Kolehmainen, and J.P. Kaipio, Statistical inversion of aerosol size measurement data, Inv. Probl. Eng. (2001), in press.
A. Voutilainen, F. Stratmann, and J.P. Kaipio, A non-homogeneous regularization method for the estimation of narrow aerosol size distributions, J. Aerosol Sci. 31, 1433–1445 (2000).
A. Voutilainen and J.P. Kaipio, Estimation of non-stationary aerosol size distributions using the state-space approach, J. Aerosol Sci. (2001), in press.
W. Winklmayr, G.P. Reischl, A.O. Lindner, and A. Berner, A new electromobility spectrometer for the measurement of aerosol size distributions in the size range from 1 to 1000 nm, J. Aerosol Sci. 22, 289–296 (1991).
TSI Inc. (St. Paul, MN, USA, January 10, 2001 ); http://www.tsi.com
A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques (SIAM, 1990 ).
W.R. Gilks, S. Rickhardson, and D.J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice (Chapman & Hall, 1996 ).
C.K. Chui and G. Chen, Kalman Filtering (Springer-Verlag, 1987 ).
B.D.O Anderson and J.B. Moore, Optimal Filtering (Prentice-Hall, 1979 ).
J. Kaipio and E. Somersalo, Nonstationary inverse problems and state estimation, J. Inv. Ill-Posed Problems 7, 273–282 (1999).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Voutilainen, A., Kolehmainen, V., Stratmann, F., Kaipio, J.P. (2001). Computational Methods for the Estimation of the Aerosol Size Distributions. In: Uvarova, L.A., Latyshev, A.V. (eds) Mathematical Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3397-6_22
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3397-6_22
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-3371-3
Online ISBN: 978-1-4757-3397-6
eBook Packages: Springer Book Archive