## 4 Discussion
When vegetation grows on top of a mineral substrate there results a combined spectrum which depends in a highly non-linear fashion on the product of thickness of the vegetation times its backscattering coefficient \(\mathbf{u_{b}}\). The overall effect for the reflectance spectra \(\mathbf{R_{m}}(\lambda)\) of pixels which are partially covered in vegetation is a combination of this non-linear mixing and area coverage factor. \[R_{m}(\lambda)=\ \left[R_{b}(\lambda)\big{(}1-f_{pp}\big{)}+f_{pp}\ R_{t}( \lambda)\right]\,, \tag{41}\]  
\(\mathbf{f_{pp}}\) is the fractional per pixel vegetation cover. Given that the vegetation is generally expected to be of the same type and in substantially the same state of health over areas larger than a pixel it will in many cases be possible to separate the area coverage factor \(\mathbf{f_{pp}}\) from the backscattering thickness factor \(\mathbf{u_{b}}\). This new information has the potential to increase significantly the level of knowledge about the ecologically relevant status and distribution of the near shore underwater vegetation. In summary, the model we proposed here helps limit the number of parameters that need to be fitted for an analysis of the marine environment with hyperspectral irradiance reflectance spectra. This is an important factor because of the restricted wavelength band available when working in the underwater environment. The added complexity of the overlying water column absorption and scattering spectrum renders extremely difficult and unstable any inversion directly based on fitting linear combinations of bottom reflectance spectra. The low reflectance values and the low signal-to-noise ratios as depth increases severely affect the detectable level of spectral variation. The spectral angle is often near or within the noise band so the only hope for reasonable depth and type of bottom estimates and identifications are to use general parameters in low numbers. This is the case with our model. Furthermore, all the parameters in the model have a physical basis and are amenable to being further constrained in their fitting range by any information available from other sources such as the size and shape of chloroplasts, size of mineral grains and size of the spacing for near-surface fragmentation and porosity of rocks and sand. We are currently using as a default reference the specific absorption spectrum of [PERSON] et al. [9]. Given the extensive work in relation to coral reefs on the end member spectra and their variability [21] it may be possible in future to derive reference spectra better suited to modeling vegetation that also include a better balanced and more comprehensive mix of accessory pigments. As we have seen, a substantial part of the vegetation reflectance signature differences and spectral variability may be explained by the chloroplast absorption saturation effect. The remaining differences could, therefore, be less significant than appear at first glance, thus potentially reducing the number of distinct spectral absorption compositions required to model the end member signatures set. The other potential contribution of the approach we have taken of modeling the reflectance signatures by a radiative transfer model is that the variability in the spectral signatures clearly outlined for instance by [PERSON] et al. [21] can be related explicitly to several parameters of interest in the study of coralssuch as the thickness of the thin translucent organic cover \(z_{b}\) over the mineral substrate (Equation (20)), the size of the scattering features of the cells, and their chloroplast pigment concentration. We must remember that bathymetry in unknown waters is one of the main drivers for restricting the number of variables to optimize to obtain an estimate of the water column depth. The standard approach of using a combination of linear mixes is problematic when there is no ground truth or a priori knowledge of the bottom to restrict the space of end members for bottom reflectance.