## 4 Discussion  
The simple model presented in the previous sections leads to several important insights into the behavior of the irradiance reflectance spectra of minerals and vegetation in the underwater environment. The first significant result is that we are now able to estimate the ratio of the reflectance of materials immersed in water to their dry state. Figure 9 shows the ratio of irradiance reflectance for limestone and for beach sand that can be computed using Equations (14) and (17) from our model. The ability to transfer reflectance spectra measured in air to their in-water equivalent is of great importance in practice as there are many comprehensive sources of spectral signatures measured in air while very few data are available under water due to the obvious difficulties in measurement. These underwater reflectance spectra are the backbone of all near shore shallow water hyperspectral surveys and the accuracy of any depth or bottom cover composition depends directly on their estimates. Using the algebraic radiative transfer model, we have shown that we can estimate directly from reflectance measurement the relative absorption spectrum <_d_> _a_(\(\lambda\)). Using these spectra, we have managed to obtain a simple and accurate fitting function whose structure is nevertheless based on fundamental physical considerations in far wing line broadening of the absorption from the lowest energy electronic transition in the material. Note that, strictly speaking, this fitting function is only appropriate for dielectric materials since the presence of the conduction bands in metals is not accounted for. The existence of this simple function valid over the range of wavelength of relevance to underwater hyperspectral measurements opens the possibility of identifying the material by a direct fit to the absorption parameters obtained from an inversion of the irradiance reflectance measurements of the water column using the algebraic radiative transfer model. The variance of the \(\
u\) and \(\lambda_{o}\) parameters seen in Table 4 which control the spectral shape of the material may be indicative of a fundamental difficulty in obtaining directly bottom-type identification from the measured airborne  
Figure 9: Computed irradiance reflectance for wet limestone and beach sand. The spectral signature for dry limestone comes from the shore of Lake Ontario. The signature of dry sand comes from a beach in Santa Barbara. hyperspectral reflectance. Addressing the scope and precise nature of this problem will be the subject of a further study. We have also obtained a similarly simple four-parameter fitting function to the reflectance spectra of vegetation. The first parameter is the mean size of the vegetative cells \(<\)_d_\(>\), the second parameter is the chlorophyll-a absorption saturation factor \(\mathbf{u_{cp}}\), the third parameter is the mass fraction of cellulose contained in a cell \(f_{c\!t}\), and the fourth parameter is the bulk chlorophyll-a mass concentration \(\mathbf{\rho_{c\!t}}\). The backscattering term is controlled by the relative index of cellulose in water and the mean size of the cells while the absorption is the weighed sum of the absorption of water, cellulose and chlorophyll-a. The cell absorption is composed the absorption of pure water, cellulose and chlorophyll-a. The shape of the absorption of chlorophyll-a is controlled by the package effect through the absorption saturation parameter \(\mathbf{u_{cp}}\) and its magnitude is controlled by the chlorophyll-a bulk density \(\mathbf{\rho_{c\!t}}\). The parameters of the model are interrelated. Relationships such as the one given in Equation (27) open up the possibility of obtaining estimates of parameters such as the ratio of the total volume of the chloroplasts to the total cell volume which could be used as an indicator of cell health. We have shown that the reflectance of a mix of vegetation and minerals is not just a simple relative area coverage problem.