## 2 Materials and Methods
### Coral Model Outputs and Processing  
For activities 1 to 4 (Table 1), the main output of interest was reflectance just above the canopy under naturalistic illumination conditions, for a typical range of situations, i.e., the kind of reflectance that could be used as a simple bottom reflectance boundary condition in a remote sensing model (Figure 1g,h). The key questions were if this reflectance was consistent under different illumination conditions (hence robust), and the extent of the effect of shading and other spectral mixing processes due to structure. Toward this aim, for each coral shape and illumination treatment, the model  
Figure 2: Total absorption, \(a(\lambda)\), and attenuation, \(c(\lambda)\), as used in the two water column inherent optical property (IOP) treatments, forereef and lagoon (includes the contribution of pure water itself).  
generated a 512 \(\times\) 512 pixel hyperspectral nadir-view image of the coral in orthographic projection (no perspective) (Figure 1g,h). For activities 1 to 3, the upward radiance directly above the coral shape only (no substrate) was extracted from this image and averaged to give an average nadir view upward radiance, \(L_{\text{u}}(\lambda)\), over the coral shape. Reflectance was calculated as \(L_{\text{u}}(\lambda)/E_{\text{d}}(\lambda)\) and multiplied by \(\pi\), for the purpose of comparing to the surface scale diffuse reflectance. For activity 4, which was concerned with spectral mixing with the substrate reflectance (Table 1), the upward radiance was averaged over the shape plus enough surrounding substrate to make a 50% areal cover mix between the coral shape and substrate (Figure 1h). The extent of this area was manually determined as a roughly consistent border around the shape. Activities 1 to 4 illuminated corals with azimuth angles of 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\), so shadows and other effects would be variable between these repeats, corresponding to the same shape illuminated from different directions.  
The evaluation of BRDFs required that the full BRDF function be tabulated in a form suitable to use as input to HydroLight. HydroLight requires azimuthally averaged BRDFs, i.e., as a function of relative azimuth only, so the form of the function is BRDF (\(\theta_{\text{i}}\), \(\theta_{\text{e}}\), \(\Delta\varphi\)) (units sr\({}^{-1}\)) in terms of quad-averaged radiance in the HydroLight directional discretization (directional segments of 10\({}^{\circ}\)\(\times\) 15\({}^{\circ}\), [19]). The incident and exitant zenith angles are denoted by \(\theta_{\text{i}}\) and \(\theta_{\text{e}}\), and only the relative azimuth angle, \(\Delta\varphi\), is relevant. The 3D model can work directly with the input and output quad-averaged radiances, where a single run of the model illuminates the canopy with radiance from a single directional quad, and the full hemisphere of exitant quad-averaged radiances is averaged over a 5 \(\times\) 5 grid of points over the canopy (Figure 1k), see Reference [21] for more details. A minimum of 10 model runs can populate the azimuthally averaged function, one run for each incident zenith angle quad position, \(\theta_{\text{i}}\) (Figure 1i). Here, three runs per zenith angle were conducted with the canopy rotated by 120\({}^{\circ}\) each time. Mirror image symmetry was assumed BRDF (\(\theta_{\text{i}}\), \(\theta_{\text{e}}\), \(\Delta\varphi\)) = BRDF (\(\theta_{\text{i}}\), \(\theta_{\text{e}}\), \(-\Delta\varphi\)), and the reciprocity condition BRDF (\(\theta_{\text{i}}\), \(\theta_{\text{e}}\), \(\Delta\varphi\)) = BRDF (\(\theta_{\text{e}}\), \(\theta_{\text{i}}\), \(-\Delta\varphi\)) was checked to ensure there were no major errors and then enforced. Each value in the final function was the average of 12 values in general, although not all values were independent.