## 2 Approach
### Model Scenarios  
Several scenarios were considered to investigate the effects of environmental conditions on the detection uncertainty for benthic and water column properties as a function of sensor _SNR_ (Table 2). In each scenario three reference _SNR_ values were considered; 100, 500, and 1000. The benthic cover was defined as fractional contributions from the three primary coral reef endmembers; average brown hermatypic coral (\(B_{c}\)), green fleshy algae (\(B_{a}\)), and uncolonized calcareous sand (\(B_{s}\)). In addition, the average coral spectrum was compared with that of a specific coral species, _Porites astroeides_ (\(B_{c,p}\)), in order to test the impact of _SNR_ on coral species discrimination. Total benthic reflectance was computed as linear combinations of the reflectance spectra representing the specified bottom types (Figure 2) using data reported by [PERSON] et al. [43] and collected using methods reported in [PERSON] [44]. Water constituent concentrations for all reference conditions were set low to represent a relatively clear water column; \(C^{\prime}_{chl}\) = 0.1 mg m\({}^{-3}\), \(a^{\prime}_{g,450}\) = 0.2 m\({}^{-1}\), and \(C^{\prime}_{cal}=0.3\) g m\({}^{-3}\). The conditions are \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{3}{c}{**Global Scenario Reference Conditions**} \\  & \multicolumn{2}{c}{SNR = **100, 500, 1000**} \\  & \multicolumn{2}{c}{1 m \(\leq\)\(D^{\prime}\)\(\leq\)10 m; \(\Delta\)\(D^{\prime}\)=1 m} \\  & \multicolumn{2}{c}{\(C^{\prime}_{chl}\)=0.1 mg m\({}^{-3}\); \(a^{\prime}_{g,450}\)=0.2 m\({}^{-1}\); \(C^{\prime}_{cal}\)=0.3 g m\({}^{-3}\)} \\ \hline
**Scenario** & **Benthic Cover** & **Bottom Depth** & **Water Constituents** \\ \hline S1 & & 0 \(\leq C_{chl}\leq\) 1 mg m\({}^{-3}\) \\  & \(B^{\prime}_{c}=1\); \(B^{\prime}_{a}=B^{\prime}_{s}=0\) & 0.1 \(m\leq D\leq OD^{*}\) & 0 \(\leq a_{g,450}\leq\) 1 m\({}^{-1}\) \\  & \(0\leq B_{c}\), \(B_{a}\), \(B_{s}\leq 1\) & 0 \(\leq C_{cal}\leq\) 1 g m\({}^{-3}\) \\ \hline S2 & & *OD = Optically Deep & \(C_{chl}=C^{\prime}_{chl}\) mg m\({}^{-3}\) \\  & & & \(a_{g,450}=a^{\prime}_{g,450}\) m\({}^{-1}\) \\  & \(B^{\prime}_{c}=1\); \(B^{\prime}_{c,p}=B^{\prime}_{s}=0\) & \(C_{cal}=C^{\prime}_{cal}\) g m\({}^{-3}\) \\  & \(0\leq B_{c}\), \(B_{c,p}\), \(B_{s}\leq 1\) & \(D=D^{\prime}\) & 0 \(\leq C_{chl}\leq\) 1 mg m\({}^{-3}\) \\ \hline S5a & S5b & 0 \(\leq C_{chl}\leq\) 1 mg m\({}^{-3}\) \\  & \(B_{c}=B^{\prime}_{c}=1\) & \(B_{c}=B^{\prime}_{c}=0\) & 0 \(\leq a_{g,450}\leq\) 1 m\({}^{-1}\) \\  & \(B_{a}=B^{\prime}_{a}=0\) & \(B_{a}=B^{\prime}_{a}=0\) & 0 \(\leq C_{cal}\leq\) 1 g m\({}^{-3}\) \\  & \(B_{s}=B^{\prime}_{s}=0\) & \(B_{s}=B^{\prime}_{s}=1\) & 0 \(\leq C_{cal}\leq\) 1 g m\({}^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of Scenario Conditions. Figure 2: Benthic reflectance spectra used in model computations. similar to the least clear waters examined by [PERSON] and others [26]. Diffuse attenuation for this condition, expressed as the spectrally weighted \(K_{d}\),  
\[\overline{K}_{d}=\frac{\sum_{i=400}^{750}E_{si}K_{di}}{\sum_{i=400}^{750}E_{si}}, \tag{11}\]  
where \(E_{s}\) is the solar and sky irradiance at the water surface, was 0.409 m\({}^{-1}\). Test constituent concentrations were varied randomly between zero and maximum values judged to be reasonable representations of most coral reef environments; \(C_{chl}\) = 1.0 mg m\({}^{-3}\), \(a_{g,450}\) = 1.0 m\({}^{-1}\), and \(C_{cal}\) = 1.0 g m\({}^{-3}\). These conditions span the clearest waters to be encountered within coral reef environments and episodic turbid conditions that might be encountered in close proximity to population centers. The reference bottom depth for each scenario ranged from 1 to 10 m in increments of 1 m. For test conditions \(D\) was varied randomly between 0.1 m and the maximum depth at which the test condition could be distinguished from optically deep water.