The effects of surface roughness on the spectral (300–1400 nm) bidirectional reflectance distribution function (BRDF) of bare sea ice

Abstract. The Bidirectional Reflectance Distribution Function (BRDF) has been calculated for three types of bare sea ice with varying surface roughness (σ = 0.1–10 cm) and ice thicknesses (50–2000 cm) over an incident solar irradiance wavelength range of 300–1400 nm. The comprehensive study of the BRDF of sea ice presented here is paramount for interpreting sea ice measurements from satellite imagery and inter-calibrating spaceborne sensors that derive albedo from multiple multi-angularmeasurements. The calculations performed by a radiative transfer code (PlanarRad) show that the BRDF of sea ice is sensitive to realistic values of surface roughness. The results presented here show that surface roughness cannot be considered indepen- dently of sea ice thickness, solar zenith angle and wavelength. A typical BRDF of sea ice has a quasi-isotropic reflectance over the hemisphere, associated with a strong forward scattering peak of light. Surface roughness is crucial for the location, size and intensity of the forward scattering peak. As the surface roughness increases, a spreading of the BRF peak is observed. The peak remains specular for the smaller surface roughnesses (σ = 0.001 m to σ = 0.01 m), whereas for larger surface roughness features (above σ = 0.05 m), 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 BRF increases by 29.5 % from first-year sea ice to multi-year sea ice at 400 nm and up to 630.7 % at 1100 nm, 31.5 % from melting sea ice to multi-year sea ice at 400 nm and a maximum of 97.7 % at 900 nm, and 11.3 % from melting sea ice to first-year sea ice at 400 nm and up to 86.2 % at 800 nm. As a specific example, for first-year sea ice at λ = 500 nm and θi = 60°, the BRF of an optically thick layer with surface roughness of σ = 0.001 m is 0.543 at nadir. The forward scattering peak is spread over a single quad located at φr = 0°, θr = 60°, that has a BRF of 9.748. For the same configuration with surface roughness of σ = 0.1 m, the nadir has a BRF of 0.549 and the forward scattering peak is spread over 18 quads, located between φr = 345° and φr = 15°, θr = 40° and θr = 87.5° with values between 0.776 and 5.089. The BRDF calculations presented in this study form the first set of complete BRDF values for bare sea ice with a wide range of configurations.