CRC Report No. A-34 - Coordinating Research Council

April 2005
This assumption is a mathematical requirement of the CMB methodology. In practice, the
number of resolvable source categories is limited by profile co-linearity rather than available
degrees of freedom. In this study, CMB resolved about 7 source categories with typically
available profile information and about 13 source categories with complete source profile
information. The number of categories identified (7-13) was substantially smaller than the
theoretical maximum (55).
5. The source profiles are sufficiently different one from another.
Receptor models rely upon sources having uniquely identifiable fingerprints. Two consequences
of profile co-linearity were observed in this study. First, CMB could not separate different
categories of gasoline exhaust emissions that had similar speciation profiles; e.g., catalyst and
non-catalyst vehicles, start and stabilized emissions, on-road and off-road vehicles.
A second co-linearity problem was observed for diesel exhaust. CMB was able to apportion
diesel exhaust with some skill; i.e., correctly ranking high and low contributions. The accuracy
of the diesel apportionments depended upon whether several heavy hydrocarbons (nonane,
decane and undecane) were used as fitting species. Excluding these heavy hydrocarbons resulted
in partial co-linearity between diesel and gasoline and a bias toward over-estimating diesel.
The conclusion from these findings is that severe profile co-linearity will likely be detected and
accounted for by combining source categories, but less severe co-linearity may go undetected
and lead to biased source contribution estimates.
6. Measurement errors are random, uncorrelated and normally distributed.
Several experiments investigated the impact of random sampling errors and confirmed that CMB
is robust against realistic levels of random measurement noise. This did not mean that random
sampling errors had no impact on CMB apportionments for individual samples. CMB performed
better for larger groups of samples because of improved signal/noise ratio.
This study did not investigate the effects of non-random errors, such as measurement bias for
specific species, on CMB performance. Because CMB relies upon ratios of species
concentrations, it is evident that non-random errors could bias CMB results. For example, the
CMB developers have shown that CMB apportionments are sensitive to ethylene/acetylene
ratios, so biasing the ethylene or acetylene measurements is likely to bias CMB source
apportionments.
Other Factors that Influence CMB
The CMB assumptions discussed above apply to source apportionment of air samples, which is a
zero-dimensional (non-spatial) analysis. Other assumptions come into play when receptor
models are used to analyze 4-D spatial/temporal source-receptor relationships. Issues that might
affect the accuracy or interpretation of CMB receptor model results in real world (4-D)
applications are source overlap, chemical degradation, heterogeneity in the spatial distribution of
emissions sources, and accounting for different measures of total organic compounds.
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