The effects of surface roughness on the calculated, spectral, conical–conical reflectance factor as an alternative to the bidirectional reflectance distribution function of bare sea ice

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Abstract. The conical–conical reflectance factor (CCRF) has been calculated as an alternative to the bidirectional reflectance distribution function (BRDF) for three types of bare sea ice with varying surface roughness (σ= 0.1–10) and ice thicknesses (50–2000 cm) over an incident solar irradiance wavelength range of 300–1400 nm. The comprehensive study of the CCRF of sea ice presented here is paramount for interpreting sea ice measurements from satellite imagery and inter-calibrating space-borne sensors that derive albedo from multiple multi-angular measurements. The calculations performed by a radiative-transfer code (PlanarRad) show that the CCRF of sea ice is sensitive to realistic values of surface roughness. The results presented here show that surface roughness cannot be considered independently of sea ice thickness, solar zenith angle and wavelength. A typical CCRF of sea ice has a quasi-isotropic reflectance over the hemisphere, associated with a strong forward-scattering peak of photons. Surface roughness is crucial for the location, size and intensity of the forward-scattering peak. As the surface roughness increases, a spreading of the CCRF peak is observed. The hemisphere was split in to 216 quadrangular regions or quads. The peak remains specular for the smaller surface roughnesses (σ=0.001 to σ=0.01), whereas for larger surface roughness features (above σ=0.05), the peak spreads out over multiple quads with a lower intensity than for smaller roughness features, and the highest value is displaced further out on the solar principal plane. Different types of sea ice have a similar pattern with wavelength: the CCRF increases by 30 % from first-year sea ice to multi-year sea ice at 400 nm and up to 631 % at 1100 nm, 32 % from melting sea ice to multi-year sea ice at 400 nm and a maximum of 98 % at 900 nm, and 11 % from melting sea ice to first-year sea ice at 400 nm and up to 86 % at 800 nm. The CCRF calculations presented in this study form the first set of complete CCRF values as an approximation of the BRDF for bare sea ice with a wide range of configurations.