## 3 Results
### Modeling Algae
and a drying mixture of _Fucus_ sp. and _F. serratus_ from Janvrin Island in Nova Scotia. In the zone below 0.90 microns the absorption of the chlorophyll-a and various pigments starts to dominate while in the zone above 1.35 microns the absorption of water becomes large enough that the resulting irradiance reflectance signal is dominated by noise. The full parameters of the fit are given in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Substance** & \(f_{cl}\) & \(<\!\!d\!\!>\) (_microns_) & \(\sigma_{<\!\!d\!\!>}\) & \(\sigma_{<\!\!d\!\!>}/n_{<\!\!d\!>}\) \\ \hline _Fucus_ sp. & 0.043 & 3.29 & 0.15 & 0.048 \\ _Fucus_ sp. \& _F. serratus_ & 0.164 & 4.07 & 0.21 & 0.054 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Functional fits to the mean spacing of backscatter layers \(<\!\!d\!\!>\). This is due to the signal to noise of the reflectance measuring instrument in the blue and near UV. This significant spectral variation of the signal to noise forces us to use of an appropriate weighing function in performing the fit. Once this weighing is applied we can see that the resulting modeled absorption spectrum approaches the experimental results. In order to further verify the accuracy of the predictions of the model we have used the parameters of the fit to compute directly the predicted irradiance reflectance spectra and compare them to the original measured spectra. The results are shown in Figure 7 below. Figure 6: Fit of the absorption spectrum of wet _Fucus_ sp. and a drying mixture of _Fucus_ sp. and _F. Serratus_ with the extended Bricaud model. Note the noise due to the instrumental signal to noise degradation in the blue wavelength range. This effect was compensated by weighing the fit function inversely proportional to the S/N. The blue and yellow curves are the derived spectrum from the reflectance measurements and Equation (29). The green and red curves are the fit using Equation (37). Figure 7: Comparison of modeled irradiance reflectance spectrum of wet _Fucus_ sp. and a drying mixture of _Fucus_ sp. and _F. Serratus_ (yellow curves) with the experimental measurements (blue curves). Note the noise degradation of the instrumental signal in the blue wavelength range. This reduced sensitivity may explain part of the incipient discrepancy in that spectral region. The error between the modeled and measured reflectance signatures is of the same relative magnitude as the corresponding error in the absorption fit shown in Figure 6. Given the simplicity and generality of the model the overall precision of the fit is sufficient to satisfy our original purpose of hyperspectral bathymetry in uncharted waters. One should note that the present model does not explicitely involve accessory pigments such as fucoxanthin which is known to be present in _Fucus_. It is based on the transformation due to absorption saturation in the chloroplasts (package effect) of the spectrum of phytoplankton. This phytoplankton spectrum is taken here as an archetype of a naturally occuring assemblage of various pigments dominated by chlorophyll-a. The absorption saturation effect shifts the resulting reflectance spectrum to the yellow and red which accounts for the relative closeness of the fit even without specific contributions from the accessory pigments. In the bathymetry application which most concerns us, the overall spectral shift and absolute level of the absorption are the key parameters needed to obtain reliable estimates of the depth. Given the exact pigment composition one could obviously improve the fit to the reflectance spectrum. However, this would defeat the purpose of obtaining the depth and the bottom spectrum without any a priori information other than the reflectance spectrum of the shoreline. This approach can, however, be improved by an iterative technique as we shall see in the discussion.