## 4 Discussion  
It is shown that \(SNR\) can impose significant limitations on the ability to detect benthic cover, bottom depth, and water constituents for all but the shallowest reef conditions considered (\(D=1\) m). The threshold criteria for signal detection, \(\varepsilon=1\), essentially quantifies the average difference between a reference condition and many test conditions relative to sensor noise imposed on the two signals. If \(\varepsilon>(\leq)1\), then the two signals are (are not) detectable as two distinct conditions. Since \(\varepsilon\) expresses the spectrally averaged difference, one should expect that \(\varepsilon>1\) in some parts of the spectrum while in other parts \(\varepsilon<1\). The criteria might, therefore, be viewed as too constraining since there will likely be unique information remaining where \(\varepsilon>1\). However, the amount of retrievable information will diminish as portions of the spectrum become progressively immersed within the envelope of sensor noise. Thus, \(\varepsilon\) may be viewed as a reasonable proxy for the difference between two similar spectra. [PERSON] et al. [26] conducted a sensitivity analysis of sensor and environmental sources of retrieval uncertainty applied to a hypothetical airborne sensor and concluded that \(SNR\) had only a limited influence on the overall uncertainty relative to environmental sources. While many environmental sources, such as atmospheric constituent concentration and glint from a wind-roughened water surface, can easily exceed those associated with \(SNR\), such uncertainty is often spectrally correlated in ways that are well understood and, therefore, can be mitigated. \(SNR\), on the other hand, forms the foundation of irreconcilable uncertainty to which environmental sources of uncertainty are added. It is, therefore, prudent to make sensor development decisions with knowledge of how \(SNR\) impacts the overall uncertainty in the retrieval of key environmental parameters. From an optical remote sensing perspective, one of the strongest indicators of coral health is bleaching; a brightening of the coral host, due to the absence of the microalgal symbiont, zooxanthellae [44]. When present in healthy coral, absorption by photosynthetic pigments contribute largely to the overall reduction in coral reflectance relative to the calcium carbonate foundation secreted by the coral host. During a bleaching event, the zooxanthellae vacate the coral host and the overall reflectance of the coral increases and takes on an appearance more similar to uncolonized calcareous sediment. Remote detection of bleaching is similar to the problem of estimating healthy coral cover when surrounded by uncolonized sand, illustrated in scenarios \(S1\), \(S2\), and \(S3\). For \(SNR=100\), the difference between the maximum and minimum confidence bounds in the detection of uncolonized  
Figure 7: Water constituent uncertainty (\(y\)-axis) for variable depth and benthic cover (\(S1\)) and water depth and benthic cover equal to the reference condition (\(SS_{a}\) and \(SS_{b}\)). Scenario \(SS_{a}\) represents benthic cover of 100% coral and \(SS_{b}\) represents 100% uncolonized sand. The ordinate scale represents the difference between the upper and lower boundaries of parameter uncertainty, within the ranges specified, and the reference condition, indicated as 0 in all graphs. sand at the shallowest depths considered, \(D^{\prime}\) = 1 m, ranged from 0.1 (\(S1\)) with unconstrained water constituent concentration and bottom depth to 0.04 with a priori knowledge water constituent concentration and bottom depth. Increasing \(SNR\) to 1000 decreased detection uncertainty by an order of magnitude. The probability of detecting a bleaching event, assuming that the reflectance of bleached coral is similar to uncolonized sand, and the resulting change in the fraction of healthy coral cover would be reasonably high given these uncertainty limits. However, uncertainty increases with bottom depth for all \(SNR\)s considered, particularly for \(SNR\) = 100.