## 2 Materials and Methods
### Radiative Transfer Modelling
HydroLight was used to generate a bottom of water column radiance distribution, and this was used to illuminate the individual coral structures, standing on flat dead coral substrate, by being used as the input radiance boundary condition (Figure 1e,f). From these model runs, the reflectance over the coral structure was determined under different illumination conditions to deduce the average reflectance and its variability due to shading and other effects, across a range of illumination conditions (Figure 1g,h). Treatments were applied corresponding to the range limits of interest: Depths of 1 m and 10 m; solar zenith angles of 10\({}^{\circ}\) and 50\({}^{\circ}\), azimuth angles of 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), 270\({}^{\circ}\), and two sets of Inherent Optical Properties (IOPs) denoted \"forereef\" and \"lagoon\" (described below). Water surface roughness was set to correspond to a wind speed of 5 ms\({}^{-1}\) but note that only water leaving radiance was used in the results, so surface reflectance was excluded. This method was used for tests 1 to 4, listed in Table 1.
2. Mixtures of 3D living coral structures were assembled on flat dead coral rock substrate, in areal cover densities from 39% to 75%. The 3D model was used with horizontal periodic boundaries to generate a canopy BRDF function, which was then used as a bottom boundary condition in HydroLight (Figure 1i,j). By this method, spectral water-leaving reflectances derived as water-leaving radiance at a given wavelength (\(\lambda\)) normalized to downwelling planar irradiance (\(L_{\mathrm{w}}(\theta,\,\Delta\varphi,\,\lambda)/E_{\mathrm{d}}(\lambda)\)), could be derived above the water for different view directions under different solar zenith angles and water column conditions (Figure 1l). Incorporating the water column this way spatially averages the results, and scope of the results corresponds to pixels larger than the coral structures, i.e., pixels \(\geq\) 1 m, since the coral structures were less than 20 cm across. This modelling covered the same range of depths, solar zenith angles, and the two IOP treatments mentioned above. This aspect of the work corresponds to activities 5 and 6 in Table 1.  
One important test was to determine if water attenuation and scattering within the canopy, i.e., at the scale of, and in between, coral shapes was at all important with respect to the derived reflectances. The 3D model can incorporate volumetric absorption and scattering but it is computationally slow, especially for computations in 168 bands. The \"interstitial\" IOPs were incorporated by embedding the shape in a mesh of 16 \(\times\) 16 \(\times\) 16 voxels in activity 4 (Table 1), with IOPs consistent with the corresponding HydroLight modelling (see below). In the other modelling activities, interstitial IOPs were not included. Since the coral shapes were small, within the canopy path lengths of only a few centimeters through the water were achieved. Scattering is predominantly in the forward direction so on short path lengths it has very little effect; the primary issue was absorption on the paths between surface patches. An absorption coefficient of 0.4 (approximately as at 700 nm) gives losses of just 4% on a 10 cm path, so whilst it was not expected that excluding interstitial IOPs would have a substantial effect, a specific test was conducted, and this is evaluated in the results section.