The relationship between black carbon concentration and black smoke: A more general approach
Highlights
► The aim is to derive black carbon concentrations from ‘black smoke’ measurements. ► Shortcomings in a previous expression at higher blackness values are highlighted. ► New semi-empirical expressions are given, from numerical fitting to aethalometer BC. ► Aspects of the relationship between a reflectance metric and BC are discussed.
Introduction
The black smoke measure of airborne particulate matter (PM) was used throughout Europe for many decades. The method was standardised in the UK in the late 1960s through British Standard BS1747:2:1969 (BSI, 1969) which specified the sample collection method and the quantitative conversion between measured filter reflectance (essentially the inverse of the filter darkness) and a concentration value. This was based on an earlier OECD definition (OECD, 1964), but differed from the OECD version by a simple factor. The metric is useful for PM source apportionment (Heal et al., 2005), and the extensive archives of black smoke data from multiple locations have been invaluable for time-series and cohort epidemiological studies (Hoek et al., 2001, Samoli et al., 2001, Filleul et al., 2005, Cohen et al., in press) many of which show exposure to black smoke to be at least as predictive of negative health outcomes as PM10 or PM2.5 (COMEAP, 2006, Janssen et al., 2011).
The black smoke method is sensitive to the dark particles within PM, a fraction now generally termed black carbon (BC) when measured by optical methods. Recent reviews have discussed using the more general description ‘light-absorbing carbon’ (Andreae and Gelencser, 2006, Bond and Bergström, 2006) but the common usage of BC is retained here. When the black smoke calibration was established it corresponded to the total mass concentration of PM sampled, but the substantial changes in PM composition over time mean black smoke values have long since ceased to equate to total mass concentration (Bailey and Clayton, 1982). However, in principle, it should be possible to derive a relationship between a black smoke value and the concentration of the BC component within the sampled PM. The recent deployment of automated aethalometers alongside traditional black smoke samplers provided an independent measure of BC that can be used in support of this goal. Since BC is a direct marker for combustion sources, this will facilitate a retrospective quantification of historic concentrations from an important source of air pollution.
Quincey (2007) described an algebraic approach to deriving BC from black smoke that the author demonstrated gave good agreement between BC estimates from application of the expression to black smoke values from an automated ETL SX200 instrument and those from a Magee AE21 aethalometer for a few weeks of daily measurements at the Marylebone Road kerbside site in London. The approach and parameters followed directly from an interpretation of a more recent OECD standardised version of black smoke, ISO 9835 (ISO, 1993). In a subsequent paper, Quincey et al. (2011) acknowledged that the original expression for estimating BC relied on an aspect of ISO 9835 that was inconsistent with earlier documents and hence which differed from the procedures used in practice, which followed BS1747. The second approach introduced an empirically determined dimensionless parameter β to account for this inconsistency, but demonstrated that their original expression for deriving BC from black smoke (that is, with β = 1) provided empirical fit (to within 25%) to aethalometer BC concentrations for four other sites in the UK with co-located aethalometers and traditional manual black smoke samplers. The expression did not well fit to new data from the Marylebone Road site, and a plausible explanation for this was provided.
In this paper a more general approach to deriving an empirical relationship is adopted, which clarifies the physical issues and allows better interpretation of data taken in different circumstances. The paper includes extensive discussion on aspects of the relationship between a reflectance metric and BC.
Section snippets
A note on nomenclature
Throughout the rest of this paper the term black smoke index (BSI) is used when referring to a numerical value for black smoke as a reminder that the value does not directly equate to concentration of any physical component of sampled PM. The subscripts ‘BRITISH’ and ‘OECD’ are appended to distinguish between British and OECD definitions of the black smoke index – see next section.
Definitions of black smoke
OECD (1964) defined an unscaled, graphical form of black smoke curve, relating surface concentration to reflectance R, deemed correct over the range R from 40 to 90%. Various different scaling factors were proposed for different combinations of filter material and reflectometer.
British Standard BS1747:2 (BSI, 1969) adopted the curve and gave it a fixed scale (for 25 mm diameter Whatman No. 1 filter paper), again given only graphically but with more precision, as surface concentration (British)
Inconsistency between British Standards 1747:2:1969 and 1747:11:1993 (ISO 9835:1993)
ISO 9835 (1993), adopted as British Standard 1747:11:1993, does not present a curve for surface concentration vs R; instead it has a detailed table (A.1, with a corresponding basic graph) for BSIOECD vs absorption coefficient α. This covers the range 6–370 BSIOECD. Table A.1 in the ISO 9835 standard is fitted by,to better than 1.6% between BSIOECD 6 and 250, and better than 3.2% up to BSIOECD 350.
The expression given in this standard for calculating the
Similarities between black smoke and black carbon expressions
The equations:andprovide a relationship between R and BSIBRITISH (for 25 mm spot size and Whatman No. 1 filter paper) that, for all practical purposes, is equivalent to the conventional quartic curve given in Eqn. (2), and expected to hold well for concentrations up to 350 BSIBRITISH.
Equations (6), (7) can be simply combined as:This equation is very similar in form to that used for black
A more general approach to estimating black carbon from black smoke
The presentation of the situation described above allows a conversion between black smoke and black carbon to be made with much more explicit physical assumptions than were previously possible. In general, the black smoke data can be converted back to raw data (or to ln(R0/R)) and then interpreted as black carbon with appropriate “Black Smoke method” values of “αATN” and “k” in the reflectance equivalent of Eqn. (9):
The term A·106/(VαATN) describes the
Investigation of parameters using existing data
The values of “reflectance αATN” and “reflectance k” were determined empirically using data from the five sites in the UK which had co-located black smoke and aethalometer measurements. These are the same data used by Quincey et al. (2011) and are available at http://uk-air.defra.gov.uk. The sites are Birmingham Tyburn, Edinburgh St. Leonards, Halifax, London North Kensington and London Marylebone Road. Measurement details are provided in Butterfield et al., 2009, Butterfield et al., 2010 but,
Discussion
The method presented here recognises that the reflectance method for particle blackness has an analogous quadratic relationship with filter loading as the aethalometer (transmittance) method (Eqn. (10)); in essence that the particle ensemble absorption coefficient varies with the particle loading. Using all available UK co-located black smoke and aethalometer data, the relationship between BC and ln(R0/R) was determined to bethough the 0.77 coefficient is
Conclusions
A semi-empirical expression presented in earlier publications (Quincey, 2007, Quincey et al., 2011) for estimating black carbon concentrations from traditional black smoke measurements has been shown to be a simple case of a more general relationship between BC and black smoke. The general relationship is shown to be an off-axis parabola, which by fitting with experimental data from 5 different sites across the UK for British black smoke (BSIBRITISH) values up to 80 μg m−3, is empirically
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