Page updated: March 13, 2021
Author: Curtis Mobley
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# CDOM Fluorescence

This page tailors the general ﬂuorescence theory seen on the Theory of Fluorescence and Phosphorescence page to the case of ﬂuorescence by colored dissolved organic matter (CDOM). The goal is to develop the quantities needed for prediction of CDOM ﬂuorescence contributions to oceanic light ﬁelds using a radiative transfer model like HydroLight. For convenience of reference, it is recalled from the theory page that the quantities needed are

• the CDOM ﬂuorescence scattering coeﬃcient ${b}_{\text{Y}}\left(z,{\lambda }^{\prime }\right)$, with units of ${m}^{-1}$,
• the CDOM ﬂuorescence wavelength redistribution function ${f}_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$, with units of $n{m}^{-1}$, and
• the CDOM ﬂuorescence scattering phase function ${\stackrel{̃}{\beta }}_{\text{Y}}\left(\psi \right)$, with units of $s{r}^{-1}$.

These quantities are then combined to create the volume inelastic scattering function for CDOM ﬂuorescence

 ${\beta }_{\text{Y}}\left(z,\psi ,{\lambda }^{\prime },\lambda \right)={b}_{\text{Y}}\left(z,{\lambda }^{\prime }\right)\phantom{\rule{0.3em}{0ex}}{f}_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)\phantom{\rule{0.3em}{0ex}}{\stackrel{̃}{\beta }}_{\text{Y}}\left(\psi \right)\phantom{\rule{1em}{0ex}}\left[{m}^{-1}\phantom{\rule{2.6108pt}{0ex}}s{r}^{-1}\phantom{\rule{2.6108pt}{0ex}}n{m}^{-1}\right]\phantom{\rule{0.3em}{0ex}}.$ (1)

The subscript Y indicates yellow matter, i.e. CDOM.

### The CDOM Fluorescence Scattering Coeﬃcient

For CDOM ﬂuorescence, the inelastic “scattering” coeﬃcient in the formalism of treating ﬂuorescence as inelastic scattering is just the absorption coeﬃcient for CDOM. In other words, what matters is how much energy is absorbed by CDOM at the excitation wavelength ${\lambda }^{\prime }$, which is then available for possible re-emission at a longer wavelength $\lambda$. Note that it is only energy absorbed by CDOM molecules that matters for CDOM ﬂuorescence. Energy absorbed by chlorophyll in phytoplankton or pollutants such as oil may (or may not) ﬂuoresce, but that is not CDOM ﬂuorescence. Thus the needed CDOM ﬂuorescence scattering coeﬃcient is commonly modeled as

 ${b}_{\text{Y}}\left(z,{\lambda }^{\prime }\right)={a}_{\text{Y}}\left(z,{\lambda }_{\text{ref}}\right)\phantom{\rule{0.3em}{0ex}}exp\left[-{S}_{\text{Y}}\phantom{\rule{0.3em}{0ex}}\left({\lambda }^{\prime }-{\lambda }_{\text{ref}}\right)\right]\phantom{\rule{1em}{0ex}}\left[{m}^{-1}\right]\phantom{\rule{0.3em}{0ex}},$ (2)

where ${a}_{\text{Y}}\left(z,{\lambda }_{\text{ref}}\right)$ is the absorption by CDOM at a reference wavelength ${\lambda }_{\text{ref}}$, which is usually taken to be 400 or 440 nm, and ${S}_{\text{Y}}$ is a spectral slope parameter. ${S}_{\text{Y}}$ is usually in the range of 0.016 to $0.018\phantom{\rule{2.6108pt}{0ex}}n{m}^{-1}$, but can vary from 0.007 to 0.026. See Fig. 1 of the IOP models page for further discussion. (As noted on the CDOM page, the elastic scattering coeﬃcient for CDOM is usually assumed to be zero.)

### The CDOM Fluorescence Wavelength Redistribution Function

Figure 1 shows a measured spectral ﬂuorescence quantum eﬃciency function for CDOM, ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$, as measured by Hawes (1992) on a sample of water from the Gulf of Mexico on the West Florida Shelf (his station FA7). Other measurements in the Gulf of Mexico, Peru upwelling, and North Atlantic showed similar shapes, although with diﬀerent magnitudes and some variability in the details.

Hawes was able to ﬁt his measurements to a function of the form (his Eq. 10)

 ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)={A}_{0}\left({\lambda }^{\prime }\right)\phantom{\rule{0.3em}{0ex}}exp\left[-{\left(\frac{\frac{1}{\lambda }-\frac{{A}_{1}}{{\lambda }^{\prime }}-{B}_{1}}{0.6\left(\frac{{A}_{2}}{{\lambda }^{\prime }}+{B}_{2}\right)}\right)}^{2}\right]\phantom{\rule{0.3em}{0ex}}.$ (3)

Here ${A}_{0}\left({\lambda }^{\prime }\right)$ has units of $n{m}^{-1}$, ${A}_{1}$ and ${A}_{2}$ are dimensionless, and ${B}_{1}$ and ${B}_{2}$ have units of $n{m}^{-1}$. The values of these model parameters are determined by a best ﬁt of the model to the measured data. For the data of Fig. 1, the best-ﬁt values are shown in Table 1.

 ${\lambda }^{\prime }$ ${A}_{0}$ 310 $5.81×1{0}^{-5}$ 330 6.34 350 8.00 370 9.89 390 9.39 410 10.48 430 12.59 450 13.48 470 13.61 490 $9.24×1{0}^{-5}$ ${A}_{1}$ 0.470 ${B}_{1}$ $8.077×1{0}^{-4}$ ${A}_{2}$ $0.407$ ${B}_{2}$ $-4.57×1{0}^{-4}$

Table 1: Best-ﬁt parameter values of Eq. (3) for the data of Fig. 1. All values of ${A}_{0}$ are times $1{0}^{-5}$. The ${r}^{2}$ value is 0.987. Data from Table 3 of Hawes (1992).

The left panel of Fig. 2 shows the best-ﬁt ${A}_{0}\left({\lambda }^{\prime }\right)$ values of Table 1 as solid dots. The open dots are values extended to other wavelengths for use in the HydroLight radiative transfer software. The corresponding quantum eﬃciencies ${\Phi }_{\text{Y}}\left({\lambda }^{\prime }\right)$ are obtained by integration of ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ over $\lambda$:

 ${\Phi }_{\text{Y}}\left({\lambda }^{\prime }\right)={\int }_{{\lambda }^{\prime }}^{\infty }{\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)\phantom{\rule{0.3em}{0ex}}d\lambda \phantom{\rule{0.3em}{0ex}}.$ (4)

The right panel of Fig. 2 shows the dependence of ${\Phi }_{\text{Y}}$ on the excitation wavelength ${\lambda }^{\prime }$ for the parameter values of Table 1 as extended and used in Eq. (3). Unlike the quantum eﬃciency for chlorophyll ﬂuorescence, the quantum eﬃciency for CDOM ﬂuorescence depends on the excitation wavelength.

Figure 3 shows ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ as computed by Eq. (3) for the parameter values of 1 as extended.

As seen in Fig. 1 of the CDOM page and as modeled by Eq. (2), absorption by CDOM continues to rise rapidly in the ultraviolet (UV). As seen in Fig. 1, CDOM ﬂuorescence is excited by UV wavelengths even below 300 nm, and CDOM emission occurs at wavelengths from the excitation wavelength into the blue and green. Thus CDOM is optically important both because of its strong absorption at blue and UV wavelenghts, and because it can ﬂuoresce at UV to blue and green wavelengths.

As noted on the theory page, the CDOM ﬂuorescence wavelength redistribution function ${f}_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ is obtained from ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ via

 ${f}_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)={\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)\phantom{\rule{0.3em}{0ex}}\frac{{\lambda }^{\prime }}{\lambda }\phantom{\rule{1em}{0ex}}\left[n{m}^{-1}\right]\phantom{\rule{0.3em}{0ex}}.$ (5)

The excellent Master’s Thesis by Hawes remains, three decades later, the one and only publication I can ﬁnd that presents measurements and a model for calibrated spectral ﬂuorescence quantum eﬃciency functions ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ for CDOM (or for any other substance). His functional form (3) is used in HydroLight to model CDOM ﬂuorescence. The parameter values seen above are the defaults in HydroLight. Although the results of his thesis research were presented at the Ocean Optics XI conference (Hawes et al. (1992)), they were never published in the refereed literature. The thesis itself cannot be found online, but a photocopy can be downloaded on the references page.

### The CDOM ﬂuorescence phase function

As previously noted, ﬂuorescence emission is isotropic. Therefore the phase function is simply

 ${\stackrel{̃}{\beta }}_{\text{Y}}\left(\psi \right)=\frac{1}{4\pi }\phantom{\rule{1em}{0ex}}\left[s{r}^{-1}\right]\phantom{\rule{0.3em}{0ex}}.$

The models seen above give everything needed to construct the volume inelastic scattering function of Eq. (1) for CDOM ﬂuoresecence, ${\beta }_{\text{Y}}\left(z,\psi ,{\lambda }^{\prime },\lambda \right)$, which is then ready for use in the radiative transfer equation as seen in Eq. (2) of the theory page.

### Examples of CDOM Fluorescence Eﬀects

The HydroLight radiative transfer model has options to include or omit the inelastic scattering processes of Raman scatter by water and ﬂuorescence by chlorophyll and CDOM.

To see the eﬀect of the CDOM ﬂuorescence on the remote sensing reﬂectance ${R}_{\text{rs}}$, a series of HydroLight runs was done with the following inputs:

• A chlorophyll concentration of $Chl=0.5\phantom{\rule{2.6108pt}{0ex}}mg\phantom{\rule{2.6108pt}{0ex}}Chl\phantom{\rule{2.6108pt}{0ex}}{m}^{-3}$ for Case 1 water (using the new Case 1 IOP model in HydroLight); the water was homogeneous and inﬁnitely deep
• Low and high values of CDOM absorption was included as either
• CDOM absorption at 440 nm was 20% of the chlorophyll absorption at 440 nm, i.e. ${a}_{\text{Y}}\left(440\right)=0.2{a}_{\text{C}}\left(440\right)$. This is a common model for Case 1 water.
• CDOM absorption at 440 nm was 5 times the chlorophyll absorption at 440 nm, i.e. ${a}_{\text{Y}}\left(440\right)=5.0{a}_{\text{C}}\left(440\right)$. This represents a very a high concentration of extra CDOM as could result from river input into coastal water or by the decay of benthos such as sea grass, which gives Case II water.
• CDOM ﬂuorescence was modeled using the parameter values shown above for the Hawes Station FA7
• Sun at a zenith angle of 30 deg in a clear sky, wind speed of $5\phantom{\rule{2.6108pt}{0ex}}m\phantom{\rule{2.6108pt}{0ex}}{s}^{-1}$
• The run was from 300 to 750 nm by 5 nm
• Four sets of inelastic eﬀects were simulated: (1) no inelastic eﬀects at all, (2) Raman scatter only, (3) CDOM ﬂuorescence only, and (4) Raman scatter plus CDOM and chlorophyll ﬂuorescence.

Figure 4 shows the results of these simulations. The top panel is for the Case 1 water with ${a}_{\text{Y}}\left(440\right)=0.2{a}_{\text{C}}\left(440\right)$. The bottom panel is for the high-CDOM Case 2 water with ${a}_{\text{Y}}\left(440\right)=5.0{a}_{\text{C}}\left(440\right)$. For the low-CDOM, Case 1 water, the simulation with CDOM ﬂuorescence increases ${R}_{\text{rs}}$ by less than 2% over the elastic-only case. Raman scatter gives up to an 8% increase over elastic only. For the high-CDOM Case 2 water, Raman gives up to a 7% increase, but CDOM ﬂuorescence gives up to a 27% increase in ${R}_{\text{rs}}$. Thus, it is possible for CDOM ﬂuorescence to have a signiﬁcant eﬀect on ${R}_{\text{rs}}$, but it takes a very high CDOM concentration to do so. In low-to-medium CDOM waters, typical of the open ocean where CDOM covaries with chlorophyll, CDOM ﬂuorescence aﬀects ${R}_{\text{rs}}$ by at most a few percent. If these ${R}_{\text{rs}}$ spectra are used in band-ratio algorithms for retrieval of environmental variables such as the chlorophyll concentration, the CDOM-ﬂuorescence enhancement to ${R}_{\text{rs}}$ should have even less aﬀect on the retrieved values. This conclusion is consistent with the ﬁndings in Hawes et al. 1992). Note also that CDOM ﬂuorescence has a minimal eﬀect in the chlorophyll-ﬂuorescence band near 685 nm.

Figure 5 shows excitation-emission functions as commonly seen in the literature. Such measurements are used to identify the presence (or absence) of various types of ﬂuorescing compounds in the water. The original ﬁgure does not comment on the measurement units, which are often counts per second or something similar. In any case, these excitation-emission plots display relative values and are not the equivalent of the calibrated spectral ﬂuorescence quantum eﬃciency functions ${\eta }_{\text{Y}}\left({\lambda }^{\prime },\lambda \right)$ discussed above and seen in Figs. 1 and 3.

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