3.4 Mathematical formulation of absorption spectra

As observed in figure 3.1, absorption decrease exponentially with increasing wavelengths. As wavelengths increase, light absorbed by CDOM decrease exponentially 3.1.

library(cdom)
data(spectra)

spectra <- spectra %>% filter(wavelength <= 500)

p <- ggplot(spectra, aes(x = wavelength, y = spc1)) +
  geom_line() +
  xlab("Wavelength (nm.)") +
  ylab(bquote(Absorption~(nm^{-1})))

p
Example of an absorption spectrum of CDOM.

FIGURE 3.1: Example of an absorption spectrum of CDOM.

Jerlov (1968) and Bricaud, Morel, and Prieur (1981) first proposed to use a simple exponential formulation to model absorption (equation (??)).

\[\begin{equation} a_{\text{CDOM}}(\lambda) = a_{\text{CDOM}}(\lambda0)e^{-S(\lambda - \lambda0)} \label{eq:cdom1} \end{equation}\]

Where \(a_{\text{CDOM}}(\lambda)\) is the absorption coefficient (m\(^{-1}\)), \(\lambda\) is the wavelength (nm), \(\lambda0\) is a reference wavelength (nm) and \(S\) is the spectral slope (nm\(^{-1}\)) that describes the approximate exponential rate of decrease of absorption with increasing wavelength. Higher slopes indicate a more rapid decrease in absorption with increasing wavelength. The \(S\) parameter is frequently used as a proxy for tracing photochemical and microbial-induced changes of CDOM (Moran, Sheldon, and Zepp 2000; Twardowski et al. 2004; Helms et al. 2013) or to determine its origin (C A Stedmon and Markager 2001).

In 2001, equation (??) was modified by C A Stedmon and Markager (2001) which introduced \(k\), a background constant (m\(^{-1}\)) accounting for scatter in the cuvette and drift of the instrument (equation (??)).

\[\begin{equation} a_{\text{CDOM}}(\lambda) = a_{\text{CDOM}}(\lambda0)e^{-S(\lambda - \lambda0)} + \mathbf{k} \label{eq:cdom2} \end{equation}\]
  • The \(K\) parameter…
  • Graph showing \(K\)

There are other mathematical formulations that can be used to model CDOM spectra. These are reviewed in Twardowski et al. (2004).

References

Jerlov, N.G. 1968. Optical oceanography. New York: Elsevier Publishing Company.

Bricaud, Annick, André Morel, and Louis Prieur. 1981. “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains.” Limnology and Oceanography 26 (1): 43–53. doi:10.4319/lo.1981.26.1.0043.

Moran, Mary Ann, Wade M. Sheldon, and Richard G. Zepp. 2000. “Carbon loss and optical property changes during long-term photochemical and biological degradation of estuarine dissolved organic matter.” Limnology and Oceanography 45 (6): 1254–64. doi:10.4319/lo.2000.45.6.1254.

Twardowski, Michael S., Emmanuel Boss, James M. Sullivan, and Percy L. Donaghay. 2004. “Modeling the spectral shape of absorption by chromophoric dissolved organic matter.” Marine Chemistry 89 (1-4): 69–88. doi:10.1016/j.marchem.2004.02.008.

Helms, John R., Aron Stubbins, E. Michael Perdue, Nelson W. Green, Hongmei Chen, and Kenneth Mopper. 2013. “Photochemical bleaching of oceanic dissolved organic matter and its effect on absorption spectral slope and fluorescence.” Marine Chemistry 155. Elsevier B.V.: 81–91. doi:10.1016/j.marchem.2013.05.015.

Stedmon, C A, and S Markager. 2001. “The optics of chromophoric dissolved organic matter (CDOM) in the Greenland Sea: An algorithm for differentiation between marine and terrestrially derived organic matter.” Limnology and Oceanography 46 (8): 2087–93. doi:10.4319/lo.2001.46.8.2087.