## 3 Results and Discussion  
### Effect of Coral Shape on Nadir View Reflectance  
Pseudo-color renderings of the 512 \(\times\) 512 pixel images used to derive the upward radiance over the corals are shown in Figure 3. These model outputs are for high resolution 3D models, for one of the 32 bottom of water column illumination treatments. The RGB images were derived from the 168 band model output by forming the product of the spectrum in each pixel with red, green, and blue visual tristimulus functions [24]. The surface reflectance for some corals was darker than the substrate reflectance, e.g., coral 03 (Figure 3), but for most, the coral surface reflectance was lighter. The necessity of obtaining the reflectance from a horizontal surface area in the hyperspectral image (Figure 1a) may bias the reflectance compared to the true total surface average, but this is of minor consequence in this study, since the overall brightness of the reflectance is of secondary importance to the spectral shape. With respect to the modelled reflectance over the coral area (Figure 1g), for all corals, the spectra averaged over the coral area had a very similar shape to the coral surface reflectance but was darker due to shading within the coral structure (Figure 4). The different illumination conditions introduced some variability in the reflectance but in general, this variability was small and certainly smaller than the shading effect. Coral 16 had the highest variability in reflectance under different illuminations, as this coral was a relatively vertical structure with an overall irregular shape when viewed from above; therefore the level of shading was quite dependent on azimuth angle of the incident light. Regarding corals shapes that were flatter (e.g., coral 39), or with numerous protrusions (coral 35), different lighting conditions produced little variation in the average reflectance (Figure 4).The first useful observation from these results was that in general, the average reflectance over the coral shape up to 690 nm can be represented by a scaled version of the surface reflectance, where the scaling factor \(<1\) effectively introduces shading as a black endmember in a linear mixing model, i.e., the transformation of surface reflectance \(R(\lambda)\) is of the form \(R^{\prime}(\lambda)=R(\lambda)\times f\), where \(0\leq\)\(f\)\(\leq\) 1 and for a flat Lambertian surface \(f\) = 1. Shading endmembers have been used in mineral applications [26]. For each coral, a single scaling factor was deduced as the median value of the fit from 400 to 690 nm to each of the 32 treatments (Table 3, Figure 4). These scaling factors varied from 0.50 (coral 16) to 0.84 (coral 39),  
Figure 3: High resolution model outputs, as a nadir-view orthogonal projected rendering above each coral, converted to RGB using the tristimulus functions [24]. Illumination conditions are solar zenith \(\theta_{\mathrm{s}}\) = 50\({}^{\circ}\), forereef IOPs, depth 1 m. These are the high-resolution models without interstitial IOPs (activity 1, Table 1). Note: Corals are not shown in the same relative scale, bar is 5 cm. and for flatter coral shapes, the scaling factor was higher since less shading was introduced. Corals 18 and 31, which were also relatively vertical structures, had scaling factors of 0.59 and 0.54, respectively. Above 690 nm, the fit to the simple shadow model was not as good, as reflectances over the coral area tended to be higher (Figure 4). It is likely the reason for this is the very high coral surface reflectance above 690 nm (Figure 4). A part of the coral surface that is shaded will \"see\" in its hemispherical field of view other parts of the coral surface. In wavelengths where the coral surface is highly reflective, those surrounding surfaces will reflect light to the point in question, and so the shading effect will be less overall. In each coral, most of the reflectances under different illumination conditions were within \(\pm\)20% of the surface reflectance scaled by the mean shade factor (Figure 4).