## 2 Approach
### Shallow Water Light Model  
Light propagation within a shallow reef environment was modeled following the original two-flow irradiance propagation concepts of [PERSON] [27] and adapted for a shallow ocean [28; 29; 30]. While all of the terms are spectrally dependent, wavelength notation \(\lambda\) is generally omitted for brevity and inserted as necessary for clarity. Water remote sensing reflectance measured just above the water surface is expressed as  
\[R_{rs}=\frac{0.52\ r_{rs}}{1-1.7\ r_{rs}}, \tag{5}\]  
\[r_{rs}=r_{rs,\infty}+\Big{[}\frac{\rho_{b}}{\pi}-r_{rs,\infty}\Big{]}e^{-(K_{d }+K_{u})\ D}, \tag{5a}\] \[r_{rs,\infty}=\sum_{i=1}^{2}g_{i}\bigg{(}\frac{b_{b}}{a+b_{b}} \bigg{)}^{i},\] (5b) \[K=\frac{a}{\mu}\ \bigg{[}1+(0.425\ \mu-0.19)\frac{b}{a}\bigg{]}^{ \frac{1}{2}}, \tag{5c}\]  
where \(r_{rs}\) sr\({}^{-1}\) is the radiance reflectance measured just below the water surface, \(\rho_{b}\) is the irradiance reflectance of the shallow bottom, \(K\) m\({}^{-1}\) is the attenuation coefficient for diffuse light, the subscripts \(d\) and \(u\) refer to the downwelling and upwelling irradiance streams, respectively, and \(D\) m is bottom depth. Equation (5) propagates underwater reflectance through the air/water interface assuming a flat surface [31]. The reflectance from infinitely deep water (Equation (5b)) is approximated as a polynomial [32], where \(b_{b}\) m\({}^{-1}\) is the backscatter coefficient of the water mixture (pure water plus suspended particles) and \(a\) m\({}^{-1}\) is the absorption coefficient of the water mixture (pure water plus all absorbing dissolved and particulate matter). The factors \(g_{1}\) = 0.084 and \(g_{2}\) = 0.125 were derived by [PERSON] et al. [32] through extensive Monte Carlo simulations. Diffuse attenuation (Equation (5c)) was expressed as a function of \(a\), the total scatter coefficient of the water mixture (\(b\) m\({}^{-1}\)), and the average cosine of the irradiance stream (\(\mu\)), according to [PERSON] [33]. For \(K_{d}\), the attenuation of downwelling irradiance, \(\mu=cos(\theta_{w})\), where \(\theta_{w}\) is the in-water solar zenith angle. For upwelling irradiance attenuation, \(K_{u}\), \(\mu\) = 0.7. The inherent optical properties of the water column (\(a\), \(b\), and \(b_{b}\)) are defined as linear combinations of pure water (subscript \(w\)) and three primary constituents: Phytoplankton (subscript \(p\)), colored dissolved organic matter (subscript \(g\)), and suspended non-algal particulate matter (subscript \(d\)), assumed to be non-absorbing calcite;  
\[a=a_{w}+a_{p}+a_{g}, \tag{6a}\] \[b=b_{w}+b_{p}+b_{d},\text{ and}\] (6b) \[b_{b}=b_{bw}+b_{bp}+b_{bd}. \tag{6c}\]  
Pure water optical properties [34] were considered constant. Phytoplankton optical properties were spectrally dependent and defined as the product of chlorophyll concentration (\(C_{chl}\) mg m\({}^{-3}\)) and the chlorophyll-specific coefficients for absorption (\(a^{*}_{chl}\) m\({}^{2}\) mg\({}^{-1}\)) and scatter (\(b^{*}_{chl}\) m\({}^{2}\) mg\({}^{-1}\)). The spectral shapes for \(a^{*}_{chl}\) and \(b^{*}_{chl}\) were defined as the average of spectra reported by [PERSON] et al. [35] for laboratory cultures of phytoplankton. Absorption due to dissolved organic matter was computed as \(a_{g,\lambda}=a_{g,450}\ e^{0.014\ (450-\lambda)}\), where \(a_{g,450}\) is the absorption at the reference wavelength \(\lambda\) = 450 nm [36]. Light scatter from suspended calcite particles was computed as \(b_{d}=C_{cal}b^{*}_{cal}\big{[}\frac{660}{\lambda}\big{]}^{-1.45}\), where \(C_{cal}\) g m\({}^{-3}\) is calcite concentration and \(b^{*}_{cal}\) m\({}^{2}\) g\({}^{-1}\) is the calcite-specific scattering coefficient. For this study, \(b^{*}_{cal}=1.034\) and is based on light scatter measurements reported for calcite-dominated water within intense coccolithophore blooms [37]. Backscatter from pure water, \(b_{bw}\) m\({}^{-1}\), was computed according to [PERSON] and [PERSON] [38] as \(b_{bw}=0.002\left[\frac{450}{\lambda}\right]^{4.3}\).