Environmental Engineering Reference
In-Depth Information
the quantum efficiency of fluorescence of the analyte
f
at the emission wavelength
j
. Similarly,
c
kf
is linearly related to the specific absorption coefficient at excitation
wavelength
k
.
F
is the number of components in the model and
ε
ijk
is the residual
matrix that indicates the variability not accounted for by the model.
Three steps are followed before running EEM data in the PARAFAC model
(Bro
1997
; Stedmon et al.
2003
). First, the Milli-Q water blank is subtracted
from every sample. Second, all values of the Raleigh light scattering are properly
eliminated from the data of sample's EEMs to avoid any effect on the component
numbers. Third, non-negative constraints are applied in the PARAFAC modeling
to avoid negative values of excitation, emission and concentration in any model
component.
By applying bilinear models to the EEM data (Bro
1999
), it is possible
to judge the residuals of the fit. If systematic variation is left in, the residuals
that indicate more components can be extracted. If a plot of the residual sum
of squares versus the number of components sharply flattens out for a certain
number of components, this indicates the true number of components. To cal-
culate variance-like estimators, the degrees of freedom are expressed as follows
(Eq.
2.9
):
DOF
(
F
) =
IJK
−
F
(
I
+
J
+
K
−
2
)
(2.9)
for a trilinear PARAFAC model where
I
,
J
and
K
are the dimensions of the first,
second and third mode, respectively, and
F
is the number of components in the
model (Bro
1997
). In the PARAFAC model, it is important to select the true
number of components, ranging from 1 until the proper components are identi-
fied. The true number (Bro
1997
) of components is determined on the basis of
the residuals, the core consistency (that must be 100 %), the number of iterations
(which should be near zero) and the findings of the EEM spectra for the respec-
tive samples, with reference to the various standard substances. The loadings of
the emission and excitation wavelengths are often used to check the variability
of the selected components (Stedmon et al.
2003
). The three key ways of deter-
mining the true number of components are (Bro
1997
): (i) Spilt-half experiments,
(ii) judging residuals, and (iii) comparison with the external knowledge of the
original EEM images and data being modeled. The other most important fac-
tors that one needs to know before PARAFAC modeling are: (i) Selection of the
proper excitation-emission wavelength ranges for the measured samples. Such
ranges significantly affect the shape and images of the isolated components, as
well as the reproducibility of fluorescence intensity. Depending on the nature of
FDOM components in natural waters, the most chosen wavelength ranges could
be 220-400 nm for excitation and 280-550 nm for emission. (ii) Similar types of
samples must be modeled individually. For example, individual modeling should
be made of upstream rivers with merely natural sources of DOM, downstream
rivers with a variety of DOM sources, and lake waters with both autochthonous
and allochthonous sources of DOM. PARAFAC can identify the key fluorescent
components in DOM, but it cannot isolate the minor ones that remain as a residue
(Stedmon et al.
2003
).
