4.2 PARAFAC

The seminal paper of (Colin A. Stedmon, Markager, and Bro 2003) put at the forefront the use of parallel factor analysis (PARAFAC) to aid the characterization of fluorescent DOM. Briefly, this three-way technique allows the decomposition of complex DOM fluorescence signals contained in the excitation-emission matrix (EEM, Fig. 1) into a set of individual chemical components and provides estimations of their relative contribution to the total fluorescence (Bro 1997; Jason B Fellman, Hood, and Spencer 2010; Colin A. Stedmon, Markager, and Bro 2003).

The PARAFAC model is described as (Bro 1997; Harshman 1970):

\[\begin{equation} x_{ijk} = \sum_{f=1}^{F} a_{ij}b_{jf}c_{kf} + e_{ijk} \end{equation}\]

where \(i = 1, ..., I\); \(j = 1, ..., J\); \(k = 1, ..., K\), \(x_{ijk}\) is the intensity of fluorescence of the the \(i^{th}\) sample at the \(j^{th}\) emission wavelength at the \(k^{th}\) excitation wavelength. \(a_{ij}\) is directly proportional to the concentration of the \(f^{th}\) component in the sample \(i\). Although PARAFAC gained a lot of attention in environmental sciences, it is also widely used in other research fields such as medical, pharmaceutical, food, social and information sciences (Murphy et al. 2013). Until today, more than 1850 published scientific papers relying on PARAFAC have been identified on Web of Science.

Although PARAFAC was made easier using the drEEM MATLAB toolbox (Murphy et al. 2013), preprocessing of EEMs prior to the analysis is still not straightforward. EEM preprocessing is an important part of PARAFAC since it aims to correct any systematic bias in the measurements and to remove signal unrelated to DOM fluorescence (Murphy et al. 2013). Biased models can be produced if these steps are not conducted carefully (see Hiriart-Baer, Diep, and Smith (2008) where scattering fluorescence signals have been modeled and wrongly interpreted). Such data processing is cumbersome as it involves many steps (Colin A Stedmon and Bro 2008; Murphy et al. 2013) which are usually executed by hand or within in-house scripting and therefore prone to introduce errors. Another important drawback limiting effective preprocessing of EEMs arise from the wide variety of file formats provided by the different manufacturers of spectrofluorometers that makes data importation difficult to generalize.

Possibly reflecting these difficulties, it was recently pointed out that characterization of DOM using fluorescence spectroscopy is still not routinely included in ecological studies (Jason B Fellman, Hood, and Spencer 2010). Given the increasing interest for fluorescence spectroscopy in ecology, tools are needed to unify the main preprocessing steps needed for further analyzes such as PARAFAC or metric calculations. The purpose of the eemR R package is to provide a rapid and an elegant interface to perform preprocessing of EEMs as well as to extract common fluorescence-based metrics proposed in the literature to obtain quantitative information about the DOM pool. This paper presents theoretical and mathematical background of the main PARAFAC preprocessing steps and metric calculations with concrete code examples.

References

Stedmon, Colin A., Stiig Markager, and Rasmus Bro. 2003. “Tracing dissolved organic matter in aquatic environments using a new approach to fluorescence spectroscopy.” Marine Chemistry 82 (3-4): 239–54. doi:10.1016/S0304-4203(03)00072-0.

Bro, Rasmus. 1997. “PARAFAC. Tutorial and applications.” Chemometrics and Intelligent Laboratory Systems 38 (2): 149–71. doi:10.1016/S0169-7439(97)00032-4.

Fellman, Jason B, Eran Hood, and Robert G M Spencer. 2010. “Fluorescence spectroscopy opens new windows into dissolved organic matter dynamics in freshwater ecosystems: A review.” Limnology and Oceanography 55 (6): 2452–62. doi:10.4319/lo.2010.55.6.2452.

Harshman, Richard a. 1970. “Foundations of the PARAFAC procedure: Models and conditions for an ‘explanatory’ multimodal factor analysis.” UCLA Working Papers in Phonetics 16 (10): 1–84.

Murphy, Kathleen R., Colin a. Stedmon, Daniel Graeber, and Rasmus Bro. 2013. “Fluorescence spectroscopy and multi-way techniques. PARAFAC.” Analytical Methods 5 (23): 6557. doi:10.1039/c3ay41160e.

Hiriart-Baer, Véronique P., Ngan Diep, and Ralph E. H. Smith. 2008. “Dissolved Organic Matter in the Great Lakes: Role and Nature of Allochthonous Material.” Journal of Great Lakes Research 34 (3): 383–94. doi:10.3394/0380-1330(2008)34[383:DOMITG]2.0.CO;2.

Stedmon, Colin A, and Rasmus Bro. 2008. “Characterizing dissolved organic matter fluorescence with parallel factor analysis: a tutorial.” Limnology and Oceanography: Methods 6 (11): 572–79. doi:10.4319/lom.2008.6.572.