3.5 Modeling CDOM absorption spectra in R

Because of it inverse exponential shape, absorption spectra are best modeled using non-linear fittings. In R this is done easy using the nls() function. As we can see from equation (??), the most commonly equation used to model CDOM spectra contains three parameters: a0, s, k.

mod <- nls(spc1 ~ a0 * exp(-s * (wavelength - 250)) + k, # define the formula
           data = spectra, # where the data comes from
           start = list(a0 = 5, s = 0.02, k = 0)) # initial guesses.

# show the summary information
summary(mod)

## 
## Formula: spc1 ~ a0 * exp(-s * (wavelength - 250)) + k
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## a0 1.536e+01  4.778e-01   32.15   <2e-16 ***
## s  4.070e-02  5.989e-04   67.96   <2e-16 ***
## k  4.154e+00  2.871e-01   14.47   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.187 on 308 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.221e-06

The value of \(a0\) is 15.36 represent the absorption coefficient at the reference wavelength of 250 nm (Fig. 3.2). The value of \(S\) is 0.04 means that absorption is decreasing at a rate of 0.04 \(m^{-1}\) for each increase of 1 nm.

• cdom package example

• k parameter (scattering, introduced by C A Stedmon and Markager (2001))

p + geom_line(aes(y = predict(mod)), col = "red") +
  geom_hline(yintercept = coef(mod)[1] + coef(mod)[3], lty = 2) +
  geom_vline(xintercept = 250, lty = 2)

FIGURE 3.2: Predicted values of the exponential model.

3.5.1 Potential drawbacks

When modeling CDOM spectra, there are few things to keep in minds that can have a significant influence on model results.

3.5.1.1 Choice of the reference wavelength

In equation (??), the reference wavelength was set at 350 nm. One question can potentially come to your mind. What is the effect of choosing a different reference wavelengths? What will append to \(S\) if we change the reference wavelength to let’s say 250?

Fig. 3.3 shows that:

• Little effect (computational rounding)

FIGURE 3.3: Effect of varying the reference wavelength on S.

• Plot the calculated curves on a graph

3.5.1.2 Choice of the spectral range

The choice of the spectral range used to model absorption spectra is known to have important consequences on estimated parameters (Massicotte and Markager 2016; Twardowski et al. 2004). I will use the spectrum provided in Fig. 3.1 where absorption has been measured between 190 and 900 nm. For this exercise, I will use four different spectral ranges to show how this is affecting the calculation of \(S\).

1. 275-295 nm
2. 350-450 nm
3. 220-600 nm
4. 250-500 nm

FIGURE 3.4: Effect of wavelength range on modeled absorption.

• Can have important effect on the value of \(S\).

  S	K	a0
  0.0088350	-16.0281500	17.168865
  0.0197242	0.8640024	3.688161
  0.0197387	1.1424607	3.264979
  0.0170917	0.4973948	4.313748

References

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.

Massicotte, Philippe, and Stiig Markager. 2016. “Using a Gaussian decomposition approach to model absorption spectra of chromophoric dissolved organic matter.” Marine Chemistry 180 (March): 24–32. doi:10.1016/j.marchem.2016.01.008.

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.