Geoscience Reference
In-Depth Information
concentrations that are perfectly correlated (an example could be a set of diluted samples);
(2) trilinearity: emission spectra do not vary across excitation wavelengths, excitation spec-
tra do not vary across emission wavelengths, and fluorescence increases approximately
linearly with concentration; (3) additivity: fluorescence is due to the linear superposition of
a fixed number of components (Bro,
1997
). In the case where data consists of a three-way
array of EEMs (samples × emission × excitation), PARAFAC has been shown to be capa-
ble of recovering accurate spectra and concentrations of known fluorescent materials in
mixtures, even in the presence of uncalibrated spectral interferents (Bro,
1997
).
Practical issues associated with DOM measurements that can challenge or violate these
assumptions include the presence of strongly correlated components with similar spectral
properties, inner filter effects at high concentrations, spectral changes due to e.g. varying
pH, charge transfer and intersystem crossing, quenching, changes in instrumental set up
affecting spectral resolution between samples, Rayleigh and Raman scatter bands and other
non-trilinear systematic error structures. The presence of highly correlated fluorophores
in a data set is problematic for PARAFAC because it violates the variability assumption.
Recently, a new class of factor models (PARALIND) were designed to deal with complica-
tions arising from linearly dependent factors (Bro et al., 2009).
10.7.1 Determining the Number of Components
The chemical interpretation of a PARAFAC model relies on the right number of components
being specified by the user. When models are underspecified, fewer components are used in
the model than there are independently varying fluorescent moieties present at detectable
levels. When this occurs, the model may hybridize the spectra of chemically distinct com-
ponents and produce scores that model fluorescence from multiple unrelated fluorophores.
When models are overspecified, more components are present in the model than there are
independently varying fluorescent moieties. In this case, two or more PARAFAC compo-
nents may be used to represent a single fluorophore often in combination with noise, or
components may be included that are not chemically meaningful. The presence of highly
correlated components in a model can indicate that it is overspecified.
Whether distinct chemical moieties can be separated by PARAFAC depends on a range
of factors, including the relative concentrations of the various fluorophores in the sample
and the degree of overlap between their spectra, as well as the number of samples and the
degree of environmental variability encompassed in the data set. In natural systems where
the number of detectable fluorophores is unknown, visualization and diagnostic tools are
needed to assess the validity of PARAFAC models and determine the correct number of
components (Andersen and Bro,
2003
). Most simply, visualization of the model spectra can
be used to assess whether its components appear to be reasonable. The spectra of organic
matter fluorophores are typically smoothly shaped, with single, often broad emission peaks
and either single or multiple excitation peaks. Spectra that look highly irregular, strange or
noisy may be distorted - possibly due to the incomplete removal of scatter or other artefacts
during preprocessing. Alternatively, the model may be overfitted and such components
