## 2 Materials and Methods
### Coral Surface Reflectances and Shape  
The three-dimensional shape and surface reflectance of 16 corals were used as input to the model. Live corals of various species, including _Porites compressa_, _Porites evermani_, and _Montipora capitate_, were sampled from Mahukona Beach Park, Potters, and Pauko Bay Boat Ramp in Big Island, Hawaii, in February 2017. For the purposes of this paper, corals were grouped based on sampling depth, referred to as shallow 'S' (<8 m) or deep 'D' (10 to 20 m) (Table 2). For practical reasons the corals were relatively small (<20 cm diameter). Corals were stored in open buckets filled with natural salt water and kept in a cool water bath that was shaded from the direct sun. Coral samples were imaged in the air, immediately after being removed from the water, using a tripod-mounted 710 hyperspectral imager (Surface Optics Corporation). This instrument records an image cube of 520 \(\times\) 696 pixels with spectral information at 128 spectral bands, and with 5 nm spacing from 380 to 1040 nm. All images were made under natural illumination at noon \(\pm\)2 h, to minimize any shading effects on the coral surfaces. Images were obtained within 24 h of collection, and before any noticeable degradation. A Labsphere Spectralon(tm) Diffuse Reflectance Standard with a reflectance value of 20% was placed in the image frame during each measurement (Figure 1a). Using the reference, for each coral, a single surface reflectance, \(R(\lambda)\), i.e., the reflectance at the scale of the coral surface, assuming the surface is locally flat, was estimated by taking the mean over one or more small areas of the image where the coral surface was relatively horizontal (Figure 1a). While in reality, the reflectance over a coral surface is typically variable, in the scope of this study, we were interested in the effect of coral macro-morphology and canopy structure on reflectance. Hence, each coral was treated as if it had a uniform surface reflectance. The availability of horizontal areas for extracting surface reflectance possibly biased the measured reflectances slightly, but the sample areas where sufficiently large to mitigate small scale influences, such as low pigmented apical polyps (Figure 1a). For the underlying substrate, a spectral reflectance of dead coral rock was used, this data was from a previous study, collected with a GER 1500 spectroradiometer as described in Reference [17]. All spectra were resampled to 168 bands in 2 nm intervals from 400 nm to 736 nm, as this was the spectral resolution of the modelling software. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Modelled Property**} & \multirow{2}{*}{**Res. **} & \multirow{2}{*}{**I. **} & **Derived Reflectance and** & \multirow{2}{*}{**Position**} \\  & & & & **Purpose of Activity** & \\ \hline \multirow{4}{*}{1} & Reflectance averaged over each of the 16 coral shapes, for the coral area only (substrate masked out). Bottom of water & \multirow{4}{*}{high} & \(\pi\,\,\text{${\text{${\text{${\text{${\text{$\text{$\text{$\text{$ $\text{$\text{$}}}$}$}$}}}}}}$}}\,\text{$\text{$\text{$\text{${ \text{${\text{${\text{$0\text{${\text{$1\text{${\text{$2\text{${\text{$3\text{${\text{$4}${\text{$5}}}}}}}}}\,\text{${\text{$6\text  
To capture the shape of each field-sampled coral, they were impressed into silicone rubber putty after imaging and the moulds were allowed to air dry. These moulds were transported back to the University of Connecticut; each mold was filled with plaster to recreate the coral shape (Figure 1b). Digital 3D models of the plaster cast of natural corals were created using Autodesk ReCapTM photogrammetry software (version 5.0.1.30). The process involved taking between 20 and 40 overlapping photographs of the plaster corals and converting them into 3D digital models consisting of a mesh of vertices and triangular surface polygons. Then, the 3D models were edited in Autodesk\({}^{\textregisteredregistered}\)MeshMixerTM (version 3.4.35) to isolate the coral shape from the background.