The relationship between black carbon concentration and black smoke: A more general approach

The black carbon (BC) component of ambient particulate matter is an important marker for combustion sources and for its impact on human health and radiative forcing. Extensive data archives exist for the black smoke metric, the historic measure of ambient particle darkness. An expression presented in earlier publications (Quincey, 2007; Quincey et al., 2011) for estimating BC concentrations from traditional black smoke measurements is shown to have limitations that can be addressed by using a more systematic approach to the issue of corrections for increasing darkening of the filter. The form of the more general relationship is shown to be an off-axis parabola rather than the on-axis parabola of the earlier work. Existing data from co-located black smoke and aethalometer measurements at 5 UK sites are reanalysed in this context. At very low concentrations of dark particles (British Black Smoke index <~10 ug m-3) a simple linear relationship BC (/ ug m-3) ≈ 0.27.BSI-BRITISH will suffice. A parabolic relationship, [FORMULA HERE], quantitatively similar to the previously published relationship will be more reliable for BSI-BRITISH values up to 20-25 ug m-3. The full set of data available was fitted empirically to the off-axis parabola over the range 0 to 80 ug m-3 as the quadratic:
[BC / ug m-3] = (0.27 +/- 0.03).BSI-BRITISH - (4.0 +/- 0.1)x10-4(BSI-BRITISH)^2, but this curve is highly dependent on the variations between the individual data sets. Adding the extra complexity of the full off-axis parabolic relationship is unlikely to be justified in practical situations. All expressions apply also to the OECD definition of black smoke with the substitution BSIBRITISH =0.85.BSIOECD. However, in common with the previous approach, they apply only to black smoke values obtained from standard black smoke samplers with 25 mm diameter filters and ~2 m3 day-1 volumetric flow rate, and presume a value 16.6 m2 g-1 for the specific absorption of BC in ambient particulate matter measured by aethalometry. Fitting uncertainties correspond to imprecision in estimated BC of +/-5%, +/-12% and +/-18% at BSI-BRITISH of 5, 20 and 80 ug m-3, respectively. Spatial and temporal variation in particle ensemble optical properties contributes to uncertainty in BC quantification.