Geoscience Reference
In-Depth Information
10000
1000
100
10
2
4 6 8
Number of PARAFAC components
10
12
14
Figure 10.5. The relationship between number of samples and number of components determined
by the analysts in 33 PARAFAC models of natural organic matter fluorescence EEMs, published
between 2003 and 2010.
components that correspond with the protein-like (T and B), humic-like (A and C) and
autochthonous humic (M) peaks described by Coble (
1996
).
Figure 10.5
suggests there is a relatively low cap on the number of PARAFAC compo-
nents able to be identified in organic matter data sets. Undoubtedly, the number of fluoro-
phores and spectra in natural samples is much greater. It is not at present clear to what
extent the small number of components typically identified is a reflection of undetectably
low concentrations of many organic matter fluorophores (i.e., low signal-to-noise ratios),
or of combinations of very similar fluorophores being modeled by PARAFAC as if they are
single components, or if the low number of components reflect that there are significant
deviations from Beer-Lambert's law.
Providing that the assumptions of trilinearity, additivity and variability are met, the
chemical interpretation of PARAFAC models is clear; specifically, the equivalence of the
PARAFAC loadings and the chemical spectra of the individual underlying fluorophores.
However, the chemical interpretation of PARAFAC components in decompositions of
DOM data sets is not straightforward, in part because the degree to which these assump-
tions are reasonable is difficult to assess (e.g., the presence of collinearity in a data set)
or else a point of debate (e.g., additivity and trilinearity) (Del Vecchio and Blough,
2004
;
Boyle et al.,
2009
). Studies have shown that PARAFAC can provide interpretable if imper-
fect models, even in the presence of known violations of the assumptions of variability or
trilinearity (Bro,
1997
; Bro et al.,
2009
; Murphy et al.,
2011
), and that the imposition of
appropriate model constraints can ameliorate these in some cases. Even so, in natural sys-
tems it is difficult to assess the severity of departures from model assumptions, particularly
in cases where data sets are large or diverse.
A number of recent studies have projected new data sets on to existing models in order
to extract concentrations of “known” PARAFAC components (e.g., Mladenov et al.,
2008
;
Fellman et al.,
2009c
; Macalady and Walton-Day,
2009
; Miller et al.,
2009a
,
2009b
; Miller
