Atmospheric particulate absorption and black carbon measurement

It is convenient to measure the optical attenuation A of the combination of a layer of atmospheric particulate matter and the quartz fiber filter on which it has been collected. The problem of relating A to the absorption and scattering coefficients k and s of the particulate matter itself is treated as a problem in diffuse reflectance spectroscopy using the Kubelka-Munk theory. The results show that although, in general, A is a nonlinear function strongly dependent on both a and k, for a limited range of s and sample thickness d, A can be a practically linear function of k. Fortunately, this range includes that common to atmospheric particulate samples. Furthermore, it is shown that if the filter's reflectance is sufficiently high, A can be nearly independent of s. This is in agreement with experimental and, for the limiting case when the substrate filter reflectance is unity, theoretical results obtained by other researchers. Use of such measurements of A as a means of determining the black carbon mass loading C on a filter is also investigated. It is shown that when the black carbon mass fraction f(c) is high, as it is for samples collected in large urban areas, A is a predictable and practically linear function of C. However, when f(c) is low, as it is for many rural locations, then the slope of the function A(C) is strongly dependent on f(c), leading to possible overestimates of C. This problem can be alleviated by making the measurement of A at near-infrared wavelengths rather than in the visible spectrum.