## 3 Results
### Modeling Algae  
We are now in a position to analyse the spectral signature of algae and other marine vegetation. The spectra we will be using were collected on the shores of Janvrin Island in Nova Scotia. These calibrated reflectance spectra range from 0.35 to 2.5 microns. This range extends beyond the wavelength band over which chlorophyll-a absorption has a significant amplitude. This is fortunate in as much as we can use the reflectance measured in the wavelength range over 0.90 micron to obtain a measurement of \(<\)\(d\)\(>\). This is because the components which dominate absorption in that wavelength range are water and cellulose and their absolute values and relative abundances are well known. In that spectral band, therefore, we have:  
\[<\)\(d\)\(>\;=\left(\frac{1-x(\lambda)}{x(\lambda)}\right)\,\frac{\omega_{b}(n_{cp}/n_ {w})}{[a_{w}(\lambda)(1-f_{cl})+f_{cl}\;a_{cl}(\lambda)]}\;, \tag{38}\]  
\(f_{cl}\) is the mass fraction of cellulose in the cell and \(n_{cw}\) is the index of refraction of the walls of the cell and its subcomponents and \(n_{w}\) is the index of refraction of water. This cell wall index has been estimated for both the mesophyll and antidermal cell walls by [PERSON] [12]. Since both are quite close to one another we use their average value as an estimate for \(n_{cw}\). We can use the fact that the mean spacing between backscattering layers \(<\)\(d\)\(>\) should be independent of wavelength to estimate \(f_{cl}\). To do this, we vary \(f_{cl}\) to minimize the variance in the estimate of \(<\)\(d\)\(>\) as a function of wavelength computed with Equation (39). We use the wavelength range from 0.90 to 1.35 micron. We need to be above 0.90 microns to ensure that we are completely out of the zone where there could be remaining absorption by chlorophyll-a and other pigments in the algae. We also must stay below 1.35 micron to remain below the large water absorption band which reduces the irradiance signal to levels where instrument noise totally dominates. Figure 5 and Table 5 show the result of such a fit to the reflectance spectra of wet _Fucus_ sp. and a drying mixture of _Fucus_ sp. and _F. serratus_ from Janvrin Island in Nova Scotia. These samples were chosen because they represent the extreme values of the reflectance spectra we measured. The results show the potential of this approach to estimate the status of the vegetation. In this case the _Fucus_ sp. is much more saturated with water than the drying mixture sample while the mean backscattering feature size of the mixture is larger. The ratio of the standard deviation to the mean value of \(<\)\(d\)\(>\) is of the order of 5% in both cases which shows that a constant mean value \(<\)\(d\)\(>\) is a good model for the data. Once we have obtained the value of \(<\)\(d\)\(>\) we can use it in the wavelength range where the absorption of chlorophyll is dominant. \[a_{v}(\lambda)=\rho_{chl}a_{v}^{*}(\lambda)=\bigg{(}\frac{1}{<\!\!d\!\!>} \bigg{)}\bigg{(}\frac{1-x(\lambda)}{x(\lambda)}\bigg{)}\;\omega_{b}(n_{cw}/n_{ w})-\;[a_{w}(\lambda)(1-f_{cl})+f_{cl}\;a_{cl}(\lambda)]\;, \tag{39}\]  
As a final step we can now estimate the absorption saturation parameter \(u_{cp}\) and the bulk chlorophyll concentration \(\rho_{chl}\) by using Equation (39) and performing a non-linear least squares fit on the ratio of the experimental absorption obtained with the procedure described above to the low chlorophyll-a concentration limit \(a_{o}^{*}(\lambda)\). \[\Big{(}\frac{\rho_{chl}}{2\;u_{cp}}\Big{)}\Big{(}1-e^{-a_{o}^{*}(\lambda)2\;u _{cp}}\Big{)}\Big{(}\frac{1}{<\!\!d\!\!>}\Big{)}\Big{(}\frac{1-x(\lambda)}{x( \lambda)}\Big{)}\;\omega_{b}(n_{cl}/n_{w})-\;[a_{w}(\lambda)(1-f_{cl})+f_{cl} \;a_{cl}(\lambda)]\;, \tag{40}\]  
Figure 6 shows the result of such a fit for a reflectance spectrum of wet _Fucus_ sp. and a drying mixture of _Fucus_ sp. and _F. serratus_. Note the significant noise increase in the short wavelength region. Figure 5: Fit of the mean backscatter distance derived from the irradiance reflectance of wet _Fucus_ sp.