## 5 Conclusions  
There are three primary conclusions of this research.  
(1) \(SNR\) was found to have significant and non-linear impacts on the uncertainty in detecting change in key environmental parameters associated with shallow coral reef systems (bottom depth, benthic cover, and the concentration of particulate and dissolved materials within the water column). In general, uncertainty decreased with increasing \(SNR\) and the rate of change in uncertainty per incremental change in \(SNR\) was greatest for \(SNR<500\). Increasing \(SNR\) from 100 to 500 resulted in significant decreases in parameter uncertainty, but increasing \(SNR\) further to 1000 resulted in only modest improvements in uncertainty.  
(2) Regardless of \(SNR\), benthic cover uncertainty increased with bottom depth as reported by previous researchers. However, uncertainty in water constituent concentration increased with decreasing water depth, particularly when the geometric depth was less than 1 optical depth. For \(D_{o}>1\), uncertainty associated with \(a_{g,450}\) and \(C_{cal}\) was relatively small for \(SNR\geq 500\). Uncertainty in the \(C_{chl}\) was high regardless of \(SNR\) for all scenarios except when the benthic cover was 100% uncolonized sand and \(SNR\geq 500\). Regardless, retrieval of water constituent concentration in shallow water is problematic.  
The sensitivity of uncertainties in water constituent concentrations to benthic cover is unrelated to \(SNR\), but nonetheless is impacted by sensor noise. The results suggest that it may be possible to retrieve water constituent concentration in shallow water environments by parsing the imagery based on benthic brightness, where algorithms developed for absorbing matter, such as chlorophyll and dissolved organic matter, might be better retrieved over areas of high benthic reflectance, such as uncolonized sand, while the concentration of highly scattering suspended particulate matter, such as calcite sediment, may be better retrieved in areas of dark benthic cover, such as healthy coral and algae.  
(3) Lastly, given the change in parameter uncertainty with sensor noise and the likely trade-offs that will be required for the development of future spaceborne imaging systems with application to coastal ecosystems, we conclude that \(SNR\) = 500 is a reasonable sensor design goal in order to optimize the utility of such a sensor for application to shallow coral reef environments. Uncertainty in submerged feature detection and retrieval increases significantly as \(SNR\) approaches a value of 100. While this may result in significant immediate savings in sensor development and launch costs, the potential loss of environmental information may have larger societal costs in the long run. On the other hand, increasing \(SNR\) above 500 will likely result in much higher sensor development costs that will be hard to justify based on expected scientific benefits.  
All authors contributed significantly to the writing and/or final editing of the manuscript. [PERSON] was the lead author and was responsible for model development and analysis and writing the manuscript. [PERSON] was responsible for developing concepts of \(SNR\). [PERSON] was responsible for defining a clear maritime atmosphere, running the Tafkaa atmospheric model.  
Financial support for this project is provided by the National Aeronautic and Space Administration HyspIRI Program through grants NNH15 AB471 and NNX16 AB05G and the research funds provided by the U.S. Naval Research Laboratory.  
There are no conflicts of interest on the part of any of the authors.  
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