CRC Report No. A-34 - Coordinating Research Council

April 2005
composition derived from the virtual tunnel study for gasoline exhaust was similar to that used in
Round 1. The major changes to apportionments occurred for solvents and diesel due to profile
co-linearity and choice of fitting species. When nonane, decane and undecane were excluded as
fitting species in Round 2 the gasoline and diesel profiles became somewhat co-linear and the
apportionment for diesel was degraded.
Round 4 provided the receptor modelers with complete knowledge of the sources present and
their source profiles, which is not a realistic scenario for the real world. The CMB results for
Round 4 show that receptor model apportionments become increasingly accurate as assumption 3
is better satisfied (finding 2). This conclusion was confirmed by Round 3 (findings 17-19 and
21) where the experiment design provided CMB with accurate source profiles. With complete
source profile information CMB performance was limited by other assumptions such as the
absence of profile co-linearity (findings 5 and 18).
4. The number of source categories is less than the number of species, i.e., there are degrees of
freedom available in the analysis.
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 in Round 2 with
typically available profile information and about 13 source categories in Round 4 with complete
source profile information.
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 different speciation profiles: catalyst and noncatalyst
vehicles, start and stabilized emissions, on-road and off-road vehicles. This result is
expected because these categories all have very similar source profiles.
A second co-linearity problem was observed for diesel exhaust. CMB was able to apportion
diesel exhaust with some skill (correctly ranking high and low contributions) in all of the
experiments from Rounds 1 to 4. Exclusion of the heavy hydrocarbons nonane, decane and
undecane from the fit resulted in co-linearity with gasoline and a bias toward over-estimating
diesel. This bias is particularly noticeable at the downwind sites.
The conclusion from these findings is that severe profile co-linearity will likely be detected and
be 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 (findings 21, 7 and 6). 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 (findings 14 and 15).
H:\crca34-receptor\report\Final\sec5.doc 5-6