Abstract
This paper compares two approaches to modeling (smoothing) aerosol particle size distribution (particle counts for specified diameter intervals): i) the semiparametric approach based on a maximum likelihood fitting of lognormal (LN) mixtures at each time separately, followed by smoothing parameter tracks, ii) the nonparametric approach based on a kernel-like smoothing as an application of the gnostic theory of uncertain data. The specific advantages and disadvantages of both the semiparametric and nonparametric approaches are discussed and illustrated using real data containing a day-long time series of size spectra measurements.
Highlights
The data describing the dynamics of particle size distribution (PSD) are inevitably complex and might be modeled statistically from
This paper presents two methods of modeling atmospheric PSDs: the parametric approach and the nonparametric
The semiparametric method based on lognormal mixtures has these advantages: a) it is more efficient and less computationally demanding; b) it gives excellent results if the model agrees with the data; c) it provides a high data compression ratio; d) it gives concentration of aerosol particles corresponding to each of the modes; and f) it is more programmable since its lognormal components are available as built-in functions in most statistical packages
Summary
The data describing the dynamics of particle size distribution (PSD) are inevitably complex and might be modeled statistically from nonparametric and semiparametric models.The semiparametric models of our interest consist of two parts. The parametric part postulates a mathematical formula to describe PSD feasibly and uses it, together with the measurement error distribution specification, to fit the PSD at each measurement time The time dynamics of parameters are smoothed nonparametrically. Nonparametric models try to escape the danger of possibly incorrect parametric model specifications by making as few assumptions as possible. The resulting solution makes a compromise between the quality of the fit and its smoothness. Such an approach is certainly appealing since it creates the impression that it represents a sort of ideal, fool-proof or automatic tool that does not require any substantial assumption-making and precludes preliminary thinking about model choice. Nothing is for free and the impression is not correct for several reasons
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