4.3 Fluorescence of DOM: theoretical and mathematical background

Let us define \(X\), an EEM of fluorescence intensities measured along a vector of excitation wavelengths (\(ex\)) at emission wavelengths (\(em\)). Usually, \(ex\) and \(em\) vary, respectively, between 200-500 nm and 220-600 nm (Fig. 1). \(X_{ex, em}\) denotes the fluorescence intensity measured at excitation \(ex\) and emission \(em\) (ex.: \(X_{250, 400}\)).

The following sections present the main correction steps for fluorescence data aiming to correct any systematic bias in the measurements and remove signal unrelated to fluorescence prior to any analysis.

Correction	Description
Blank subtraction	Subtract a pure water sample blank from the fluorescence data to help the removal of Raman and Rayleigh scattering peaks.
Scattering removal	Remove the the so-called scattering bands caused by first and second order of Raman and Rayleigh scattering.
Inner-filter effect correction	Correct for reabsorption of light occurring at both the excitation and emission wavelengths during measurement.
Raman normalization	Remove the dependency of fluorescence intensities from the measuring equipments thus allowing cross-study comparisons.

4.3.1 Scattering correction

Rayleigh and Raman scattering are optical processes by which some of the incident energy can be absorbed and converted into vibrational and rotational energy (Lakowicz 2006). The resulting scattered energy produce the so-called scattering bands which are visually easily identifiable (Figs. 1 and 2). Given that both types of scattering are repeated across EEMs, it is important to remove such artifacts prior to analysis (Bahram et al. 2006; R. G. Zepp, Sheldon, and Moran 2004).

FIGURE 4.2: Emission fluorescence emitted at excitation \(ex = 350\). First order of Rayleigh and Raman scattering regions are identified in blue and red.

First order of Rayleigh scattering is defined as the region where emission is equal to excitation (\(em = ex\)) causing a diagonal band in the EEM (Fig. 1) whereas the second order of Rayleigh scattering occurs at two times the emission wavelength of the primary peak (\(em = 2ex\)). For water, Raman scattering occurs at a wavenumber 3 600 \(cm^{-1}\) (or \(3.6 \times 10^{10} nm^{-1}\)) lower than the incident excitation wavenumber (Lakowicz 2006). Mathematically, first order Raman scattering is defined as follow:

\[\begin{equation} \text{Raman}_{\text{1st}} = -\frac{ex}{0.00036 ex - 1} \label{eq:raman1} \end{equation}\]

where \(ex\) is the incident excitation wavelength (nm). Second order Raman scattering is then simply defined as:

\[\begin{equation} \text{Raman}_{\text{2nd}} = -\frac{2ex}{0.00036 ex - 1} \label{eq:raman2} \end{equation}\]

Different interpolation techniques have been proposed to eliminate scattering (R. G. Zepp, Sheldon, and Moran 2004; Bahram et al. 2006). However, it is a common practice to simply remove the scattering-bands by inserting missing values (Fig. 3) at the corresponding positions (Murphy et al. 2013; Colin A Stedmon and Bro 2008).

4.3.2 Inner-filter effect correction

The inner-filter effect (IFE) is an optical phenomenon of reabsorption of emitted light and occurs particularly in highly concentrated samples (Fig. 4). IFE is known to cause underestimation of fluorescence intensities especially at shorter wavelengths and even to alter the shape and the positioning of fluorescence spectra by shifting peak positions toward lower wavelengths (Fig. 4) with increasing concentration (Mobed et al. 1996; Kothawala et al. 2013). However, it was shown that the loss of fluorescence due to IFE could be estimated from absorbance spectra measured on the same sample using Equation (??) (Ohno 2002; Parker and Barnes 1957):

\[\begin{equation} X_0 = \frac{X}{10^{-b(A_{ex} + A_{em})}} \label{eq:ife} \end{equation}\]

where \(X_0\) is the fluorescence in the absence of IFE, \(X\) is the measured fluorescence intensity, \(b\) is half the cuvette pathlength (usually 0.5 cm) for excitation and emission absorbance, \(A_{ex}\) is the absorbance at the excitation wavelength \(ex\) and \(A_{em}\) the absorbance at the emission wavelength \(em\) (Fig. 4B).

It was recently shown that IFE corrected algebraically was not appropriate when total absorbance, defined as \(A_{\text{total}} = A_{\text{ex}} + A_{\text{em}}\) (see Equation (??)), is greater than 1.5 (Kothawala et al. 2013). Under this circumstance, a two-fold dilution of the sample has been recommended. If this happen, a warning message will be displayed by the package during the correction process.

4.3.3 Raman calibration

The same DOM sample measured on different spectrofluorometers (or even the same but with different settings) can give important differences in fluorescence intensities (Lawaetz and Stedmon 2009; Paula G. Coble, Schultz, and Mopper 1993). The purpose of the Raman calibration is to remove the dependency of fluorescence intensities on the measuring equipment, thus allowing cross-study comparisons. Given that the Raman peak position of a water sample is located at a fixed position, (Lawaetz and Stedmon 2009) proposed to use the Raman integral of a blank-water sample measured the same day as the EEM to perform calibration. Moreover, the area of the Raman peak (\(A_{\text{rp}}\), Fig. 5) is defined as the area of the emission profile between 371 and 428 nm at a fixed excitation of 350 nm (Lawaetz and Stedmon 2009).

Mathematically, the value of \(A_{\text{rp}}\) is calculated using the following integral (Equation(??)):

\[\begin{equation} A_{\text{rp}} = \int\limits_{\lambda_{\text{em}371}}^{\lambda_{\text{em}428}} W_{350, \lambda} d\lambda \label{eq:arp} \end{equation}\]

where \(W_{350, \lambda}\) is the fluorescence intensity of a pure water sample (preferably deionized and ultraviolet exposed, Lawaetz and Stedmon (2009)) at excitation \(ex = 350\) nm and at emission \(em = \lambda\) nm. Each values of the EEM \(X\) are then normalized using the scalar value of \(A_{\text{rp}}\) accordingly to Equation @ref(eq:raman_normalisation):

\[\begin{equation} X_0 = \frac{X}{A_{\text{rp}}} \label{eq:raman_normalisation} \end{equation}\]

where \(X_0\) is the normalized EEM with fluorescence intensities now expressed as Raman Units (R.U.), \(X\) are the unnormalized measured fluorescence intensities and \(A_{\text{rp}}\) is the Raman peak area.

4.3.4 Metrics

A wide range of different metrics obtained from EEMs have been proposed to characterize the DOM pool in aquatic ecosystems. These metrics extract quantitative information in specific regions (wavelengths) in EEMs. The following sections present an overview of the principal metrics supported by the package.

4.3.4.1 Coble’s peaks

The following table presents the five major fluorescent components identified by (Paula G Coble 1996) in marine EEMs. Peaks B and T represent protein-like compounds (tyrosine and tryptophane), peaks A and C are indicators of humic-like components whereas peak M was associated to marine humic-like fluorescence.

Peak	Ex (nm)	Em (nm)
B	275	310
T	275	340
A	260	380-460
M	312	380-420
C	350	420-480

4.3.4.2 Fluorescence, humification and biological indices

Three main indices have been proposed to trace the diagnostic state of the DOM pool in aquatic ecosystems. The fluorescence index (FI) was shown to be a good indicator of the general source and aromaticity of DOM in lakes, streams and rivers (McKnight et al. 2001). This index is calculated as the ratio of fluorescence at emission 450 nm and 500 nm, at fixed excitation of 370 nm (Equation (??)).

\[\begin{equation} \text{FI} = \frac{X_{370, 450}}{X_{370, 500}} \label{eq:fi} \end{equation}\]

The humification index (HIX) is a measure of the complexity and the aromatic nature of DOM (Ohno 2002). HIX calculated as the ratio of the sum of the fluorescence between 435 and 480 nm and between 300 and 345 nm at a fixed excitation of 254 nm (Equation (??)).

\[\begin{equation} \text{HIX} = \frac{\sum\limits_{em = 435}^{480} X_{254, em}}{\sum\limits_{em = 300}^{345} X_{254, em}} \label{eq:hix} \end{equation}\]

The biological index (BIX) is a measure to characterize biological production of DOM (Huguet et al. 2009). BIX is calculated at excitation 310 nm, by dividing the fluorescence intensity emitted at emission 380 nm and at 430 nm (Equation ((??))).

\[\begin{equation} \text{BIX} = \frac{X_{310, 380}}{X_{310, 430}} \label{eq:bix} \end{equation}\]

References

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