A model for calculation of radiative transfer in a layer of particles on a fiber filter that takes into account multiple scattering has been developed. It was shown that the model describes calibration curves for the black smoke method. Multiple scattering and variations in the black carbon fraction are the main factors that control complex relationships between substrate loading and optical response. It was obtianed that on average for the UK the fraction of the black carbon decreased from about 23 in the 1960s to about 10 in the 1990s. An approach has been suggested to convert black smoke data into PM_(10). A new method of measuring PM_(10) based on measuring light reflectance of two filters containing the same aerosol but different surface mass concentrations is suggested. The model can be applied to the integrating plate and other optical methods.
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