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In-Depth Information
and McKnight,
2010
). In many such studies, judgments of model suitability have been
based on the magnitude of error residuals relative to the measured fluorescence signals. A
problem with this approach is that the fit of an existing PARAFAC model to a new data set
increases
trivially
with the number of components in the model, because irrelevant com-
ponents can be used to model noise and compensate for poor fit. In fact, a range of outlier
diagnostics are needed to verify that existing models provide unbiased representations of
new data before using them in a predictive capacity (Rinnan et al.,
2007
). It should further
be noted that the assumptions of PARAFAC may not be sufficiently met by all data sets,
depending, for example, on sample concentration (Stedmon and Bro,
2008
), stoichiometry
(Bro et al.,
2009
), and interactions between fluorophores (Boyle et al.,
2009
) or with metal
ions, among other factors. For all of these reasons, the interpretation of PARAFAC models
of organic matter fluorescence, and particularly their application in a predictive capacity, is
at present a developing science necessitating a cautious investigative approach.
10.8.2 PARAFAC Example
PARAFAC modeling of the Horsens catchment data set was performed after normalizing
concentrations to unit norm in the first mode and imposing non-negativity constraints on
model scores and loadings. The model resolves five components (
Figure 10.6
) that describe
99.6% of the variability in the EEMs. The model has low core consistency - in fact, core
consistency diagnostics alone would indicate that a two component model is most appro-
priate. However, the five component model is confirmed by modeling independent halves
of the data set in a split-half validation (
Figure 10.6
) and the spectra obtained are regu-
larly shaped and consistent with other published PARAFAC spectra for DOM samples
(
Figure 10.7
). The loadings of the Horsens catchment PARAFAC model, and correlations
with similar spectra in previous studies, are provided in the appendices to this chapter.
Identifying the sources of PARAFAC components is also not straightforward, even when
aided by comparisons with earlier studies. A difficulty is that the presence of high concen-
trations of a component near terrestrial sources does not in itself ensure that the component
has allochthonous origins. Also, it is generally not possible to distinguish between produc-
tion and removal of components except in carefully designed experiments (e.g., Stedmon
and Markager,
2005b
; Stedmon et al.,
2007
).
In our example, there are 5!/3!2! = 10 pairs of components that can be plotted in order
to explore the relationships between the five PARAFAC components from the Horsens
catchment model. Four of these are shown in
Figure 10.8
(note log-log scales). Similar
to the PCA in
Figure 10.4
, the PARAFAC analysis detects three clusters of samples.
However, due to the additional information provided by the PARAFAC spectra, it is pos-
sible to obtain a more direct chemical interpretation of the differences between sites than
previously. Component 3 appears to represent a terrestrially derived fraction that is more or
less absent in the WTP organic matter (
Figure 10.8
, first and last panels). Closer analysis
shows that this signal was present in the water in conjunction with periods of intensive rain
where soil organic matter is also expected to be a more significant fraction of the municipal
