## 2 Approach
### Model Scenarios
In the first scenario, \(S1\), the objective was to compute the uncertainty in the signal representing 100% coral imposed by variability in water constituents, bottom depth, and benthic cover type. Since all parameters were allowed to vary without constraints, this scenario might in practice represent the application of remote sensing to an environment where the user has no a priori knowledge other than assumptions regarding parameter value ranges. The resulting uncertainties, therefore, represented the combined variability in all parameters. The reference bentnos was defined as 100% coral cover having a reflectance equal to the average coral endmember, \(B^{\prime}_{c}\)= 1.0, and test conditions included random mixtures of \(B_{c}\), \(B_{a}\), and \(B_{s}\). In scenario \(S2\), uncertainties associated with endmember benthic cover and bottom depth retrieval were investigated with the assumption that the water constituent concentrations were known. This scenario is perhaps analogous to a situation where the coral reef is rather remote with typically clear water conditions and no direct influence of degraded water quality imposed by a nearby population center. The reference conditions were identical to \(S1\), test water conditions were set equal to the reference condition, and bottom depth and benthic cover were varied randomly across the prescribed ranges. In scenario \(S3\), uncertainty in benthic cover was investigated with the assumption that water clarity and bottom depth are known. This scenario is analogous to a coral reef monitoring program where water quality is measured on a frequent basis, detailed bathymetric data are available, and the objective is to detect changes in benthic cover type. The reference conditions were identical to \(S1\), water conditions and depth were set equal to the reference conditions, and only the benthic cover was allowed to vary randomly. In scenario \(S4\), the impact of \(SNR\) on coral species discrimination was investigated. The reference benthic cover was assumed to be 100% coral and represented by the average coral reflectance spectra, \(B^{\prime}_{c}\). The test benthic conditions consisted of random mixes of the coral species _Porites astroeides_ (\(B_{c,p}\)) and the benthic algae endmember (\(B_{a}\)). Water constituent concentration and depth were constant and equivalent to the reference conditions specified in \(S1\). Finally, in scenario \(S5\), we investigated the impact of \(SNR\) on water property retrieval with knowledge of endmember benthic cover and bottom depth. As in \(S3\), this scenario is analogous to the situation in a coral reef monitoring program where benthic cover and bottom depth have been previously mapped and the objective is to quantify changes in water quality. In addition to changes in bottom depth, this scenario was devised to test the potential impact of benthic cover on water constituent uncertainty. Two separate reference conditions were considered: 100% coral cover and 100% uncolonized sand. In both cases, benthic cover and bottom depth were held constant and equal to the reference condition and only water constituent concentrations were allowed to change independently.