## 1 Introduction  
Remote sensing of coral reefs is an important complementary survey technique for science, monitoring, and management, being able to cover substantially larger areas than in-situ surveys albeit at lower accuracy [1; 2]. A well-established paradigm in coral reef remote sensing is that hyperspectral data offers the best results for discrimination of both benthic habitats and specific benthic types, such as corals, algae, and sand [3; 4]. Applied studies have shown that benthic habitat classification accuracy increases with the number of available spectral bands [3; 5], specifically in the 400-700 nm range since the opacity of water beyond 700 nm limits use of NIR wavelengths to only the shallowest waters(<2 m). Habitats are broad mapping categories, whereas mapping of specific types, e.g., corals vs. algae, is very challenging since their spectral reflectances can be similar. Modelling and sensitivity analyses based on reflectance spectra measured, either in-situ using diver-operated spectroradiometers, or ex-situ in the lab, imply that spectral separation of benthic types by hyperspectral reflectances is possible [4; 6; 7], and there are increasing numbers of applied demonstrations of discriminations of benthic types (e.g., coral, sand, and algae) from airborne hyperspectral imagery [8; 9; 10; 11; 12; 13; 14]. These studies imply that capability for discrimination of coral reef types is reliant on the discrimination of spectral features of the pigments that are present, such as peridinin in the coral symbionts, and accessory pigments of algae [8]. Pigment-based reflectance features are present at the surface of the corals and other benthic types, but the coral reef environment is structurally complex, with multiple benthic types typically present within even the highest spatial resolution imagery (e.g., pixels 1 m). Vertical structure in the reef canopy and the benthic types themselves gives rise to shading, inter-reflections, and a generally complex interaction with the light environment [15; 16]. Most sensitivity analyses to date work with empirically measured reflectances of individual types, at a scale roughly equivalent to their morphology, and use a linear mixing model, which essentially assumes that the individual types can be treated in the same way as a spatially flat Lambertian patchwork [4; 7]. However, even in a carefully defined lab experiment, the linear mixing model does not always work well with structural components [17]. Given the complexity of light interaction with a mixed structural canopy, it is not immediately obvious to what extent a pigment based hyperspectral reflectance feature present at the scale of a coral surface translates to an above water measurement at remote sensing scales. The purpose of the study presented here was to investigate propagation of hyperspectral reflectances from the surfaces of structural bentinos (corals and surrounding substrate) to water leaving reflectance. The study combined a three-dimensional canopy model [18], with a plane parallel water-column model (HydroLight [19]) (Figure 1). The model was parameterized by 3D reconstructions of actual coral shapes and surface reflectances derived from hyperspectral images of the same corals. A variety of investigations were conducted (Table 1), to track the main factors that mitigate the transmission of hyperspectral features, and to justify practical simplifications to provide useful results that can be immediately applied in other contexts. Investigations included the effects of shading, and water attenuation and scattering, both in the region of individual corals and within mixtures of corals and surrounding substrates. The three-dimensional model was used to generate fully populated bi-directional reflectance distribution functions (BRDFs) of mixed canopies, and these were input to HydroLight to model above water reflectance for different depths, water inherent optical properties (IOPs), and solar-view geometries. In summary, specific objectives were:  
1.