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Mathematical models for the variation of air-pollutant concentrations

Published online by Cambridge University Press:  01 July 2016

Jan Grandell
Jan Grandell*
Affiliation:
The Royal Institute of Technology
*
∗Postal address: Department of Mathematics, The Royal Institute of Technology, S-100 44 Stockholm, Sweden.
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Abstract

The purpose of this paper is to study simple mathematical models for the variation of the concentration of atmospheric pollutants. The particles are assumed to be emitted into the atmosphere with constant intensity and removed from the atmosphere with an intensity proportional to the precipitation intensity. The precipitation intensity is assumed to be a stationary stochastic process with no spatial variation. The mean, variance and covariance function of the concentration are calculated for some precipitation models. Under certain general assumptions it is shown that the concentration of ‘long-lived' particles is approximately described by an Ornstein–Uhlenbeck process. Finally, the different models are compared by means of Swedish precipitation data.

Keywords

PRECIPITATION SCAVENGINGCONCENTRATION OF ATMOSPHERIC POLLUTANTS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982, pp. 240 - 256
Copyright
Copyright © Applied Probability Trust 1982 

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References

Baker, M. ?, Harrison, H. Vinelli, J. and Ericksson, K. B. (1979) Simple stochastic models for the sources and sinks of two aerosol types. Tellus 31, 39–51.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Grandell, J. (1976) Doubly Stochastic Poisson Processes. Lecture Notes in Mathematics 529, Springer-Verlag, Berlin.Google Scholar
Grandell, J. (1980a) Approximate waiting times in thinned point processes. Liet. matem. rink. XX, No. 4, 29–47.Google Scholar
Grandell, J. (1980b) Mathematical models for the variation of air pollutant concentrations. Technical Report, Department of Mathematics, Royal Institute of Technology, Stockholm.Google Scholar
Grandell, J. and Rodhe, H. (1978) A mathematical model for the residence time of aerosol particles removed by precipitation scavenging. Trans. 8th Prague Conf. A, 247–261.Google Scholar
Hamrud, M., Rodhe, H. and Grandell, J. (1981) A numerical comparison between Lagrangian and Eulerian rainfall statistics. Tellus 33, 235–241.Google Scholar
Junge, C. E. and Gustafson, P. E. (1957) On the distribution of sea salt over the US and its removal by precipitation. Tellus 9, 164–173.Google Scholar
Lindvall, T. (1973) Weak convergence of probability measures and random functions in the function space D[0, 8). J. Appl. Prob. 10, 109–121.CrossRefGoogle Scholar
Rodhe, H. and Grandell, J. (1972) On the removal time of aerosol particles from the atmosphere by precipitation scavenging. Tellus 24, 442–454.CrossRefGoogle Scholar
Rodhe, H. and Grandell, J. (1981) Estimates of characteristic times for precipitation scavenging. J. Atmospheric Sci. 38, 370–386.Google Scholar