## 3 Results and Discussion
### Above-Water BRDF Effects  
Canopy BRDFs contributed to the directional pattern in water leaving radiance under naturalistic sky illumination primarily for dense canopies in shallow, clear water (Figure 10). For the 46% cover canopy, S46, a slight BRDF effect of increased retro-reflection in the incident plane, leading to effective propagation of the hotspot effect, was evident for depths less than 5 m with a low sun position, \(\theta_{\rm s}=50^{\circ}\) (Figure 10a). In deeper waters and at 90\({}^{\circ}\) to the incident plane \(L_{\rm w}\), it decreased with increased view angle (Figure 10b,d,f). In deeper waters over sparser canopies, the water column itself becomes a contributor to the above water BRDF, where at 10 m depth the BRDF response in the solar plane (Figure 10a) resembles the response at 90\({}^{\circ}\) to the solar plane (Figure 10b). Figure 9: Bidirectional reflectance functions (BRDFs) at 550 nm, of three of the composite coral canopies for shallow (S, 0–10 m) and deep (D, 10–20 m) corals with areal cover: (**a,b**) 46%; (**c,d**) 75%; and (**e,f**) 74%, in the incident plane (a, c, e, \(\Delta\varphi=0^{\circ}\)) and at 90\({}^{\circ}\) to the incident plane (**b,d,f,**\(\Delta\varphi=90^{\circ}\)). Arrows show direction of incident light, each plot shows \(\vartheta\)i of 10\({}^{\circ}\), 30\({}^{\circ}\) and 50\({}^{\circ}\). Negative view zenith angle for \(\Delta\varphi=0^{\circ}\) (**a,c,e**) means backward reflection (source and view point in the same hemisphere). Error bars are \(\pm 1\) standard error on 12 values from assumed reciprocity, rotational and mirror symmetries. Regarding the dense 74% coral cover canopy D74, water-leaving BRDF effects in the incident plane were quite prominent for both the forereef IOP treatment and the higher scattering lagoon waters (Figure 10c,e). For example, when the water depth was 1 m, the difference in \(L_{\mathrm{w}}\)(550) between a view zenith angle of 50\({}^{\circ}\) toward and away from a sun at \(\theta_{\mathrm{s}}\) = 50\({}^{\circ}\) was about a factor of 1.5 (\(\sim\)0.06 vs. \(\sim\)0.04, Figure 10c,e); whereas this factor was \(\sim\)1.2 for view zenith angles at \(\pm\) 20\({}^{\circ}\). At 90\({}^{\circ}\) to the incident plane, even for dense canopies, BRDF effects are less apparent (Figure 10d,f). It is clear that for these modelled canopies, the assumption of a Lambertian bottom is primarily violated close to the retro-reflected (hotspot) direction for large zenith angles (>30\({}^{\circ}\)) but could be a more reasonable assumption under other solar-view geometries. The difference in nadir view water-leaving reflectance at 550 nm for canopy D74 at 1 m, for solar zenith angle of 50\({}^{\circ}\) vs. 10\({}^{\circ}\), was 18% (Figure 10c,d, \(\sim\)0.047 vs. \(\sim\)0.057). This is equivalent to the variation previously shown in reflectance over individual corals under different  
Figure 10: Modelled influence of three-dimensional coral BRDF effects (from Figure 9) on water-leaving reflectance (\(\pi\) Lw/Ed) at 550 nm for: (**a,b**) Composite canopies S46 (46% shallow coral cover) and; (**c,d,e,f**) D74 (74% deep coral cover), in the incident plane (**a,c,e**, \(\Delta\varphi\) = 0\({}^{\circ}\)) and at 90\({}^{\circ}\) to the incident plane (**b,d,f**, \(\Delta\varphi\) = 90\({}^{\circ}\)). Each plot shows results of incident solar zenith angles of 10\({}^{\circ}\) (dotted lines) and 50\({}^{\circ}\) (solid lines), and depths 1, 2, 5, and 10 m. Negative view zenith angle for \(\Delta\varphi\) = 0\({}^{\circ}\) (**a,c,e**) means backward reflection (source and view point in the same hemisphere). illumination conditions (Figures 4 and 6), which for some corals was as much as \(\pm\)20%, but here the variation was reduced by the water column, to effectively \(\pm\)9%. [PERSON] et al. [31] estimated ignoring non-Lambertian bottom effects would in general, cause errors of less than 10% in remote sensing reflectance.