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widely applied to excitation-emission matrices (EEMs) and enables qualitative and
quantitative characterization of CDOM samples (Ishii and Boyer 2012 ).
The PARAFAC model is similar to a principal component analysis (PCA), but
decomposes the data matrix into a set of trilinear terms and a residual array:
X
F
x ijk ¼
b if c jf d kf þ e ijk ;
ð
4
Þ
f ¼1
i ¼
1
; ... ; I ;
j ¼
1
; ... ; J ;
k ¼
1
; ... ; K
According to Stedmon et al. ( 2003 ), when applying the PARAFAC model to
EEMs, x ijk
fluorescence for the ith sample at emission wavelength
j and excitation wavelength k; bif if is directly proportional to the concentration of the
fth component in sample i; c jf
is the intensity of
fl
is linearly related to the
fl
uorescence quantum
ef
ciency of the fth component at emission wavelength j, d kf
is linearly proportional
to the speci
nes the
number of components in the model, and a residual e ijk represents the variability not
accounted for by the model. The parameters of the PARAFAC model are found by
the process of minimizing the sum of squared residuals.
For our study we used the data from a paper by J
c absorption coef
cient at excitation wavelength k. F de
ø
rgensen et al. ( 2011 ), who
conducted a broad analysis of CDOM
ed
seven components with the PARAFAC model, using split half analysis for vali-
dation (introduction to the PARAFAC technique and description of its application
to CDOM fluorescence are presented in more detail in Stedmon and Bro ( 2008 )).
J
fl
fluorescence on a global scale and identi
rgensen et al. ( 2011 ) characterized these components by comparing their spectral
characteristics to components identi
ø
uorophores.
Spectral characteristics (product of matrices c and d) of seven PARAFAC com-
ponents are shown in Fig. 2 .J
ed in earlier studies and pure
fl
ed components 1 and 4
as humic-like DOM. Components 2, 3, 5 and 7 were characterized as amino acid-
like DOM, which had spectra similar to phenylalanine, tryptophan and tyrosine.
Component 6 had characteristics similar to both groups.
ø
rgensen et al. ( 2011 ) identi
Fig. 2 Fluorescence characteristics of the seven components identi ed by the PARAFAC analysis
and included into radiative transport model SCIATRAN. Redrawn from J ø rgensen et al. ( 2011 )
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