Solar SW radiative transfer in bubbled ice: spectral considerations, subsurface enhancement, and inclusions

Abstract. We describe and validate a Monte Carlo model to track photons over the full range of solar wavelengths as they travel into optically thick bubbled ice. The model considers surface effects, scattering by bubbles and spectral absorption due to the ice. Using representative Antarctic ice bubble radii and number concentrations we calculate spectral albedos and spectrally-integrated downwelling and upwelling radiative fluxes as a function of depth and find there is a marked subsurface enhancement in both the downwelling and upwelling fluxes relative to the incidence irradiance. This is due to the interaction between the refractive air-ice interface and the highly scattering interior and is particularly notable at blue and UV wavelengths which correspond to the minimum of the absorption spectrum of ice. A subsurface peak is also observed in the available radiative flux at depths of ~ 1 cm, and consequently the attenuation is more complex than can be described by a simple Lambert-Beer style exponential decay law. We find a moderate dependence on the solar zenith angle and surface conditions such as altitude and cloud optical depth. For macroscopic absorbing inclusions we observe geometry- and size- dependent self-shadowing that reduces the fractional irradiance incident on the inclusion's surface. Despite this the inclusions are subject to fluxes that are several times the magnitude of the single scattering contribution and act as local photon sinks. Such enhancement may have consequences for the energy budget in regions of the cryosphere where particulates are present near the surface. These results also have particular relevance to measurements of the internal radiation field: account must be taken of both self-shadowing and the optical effect of introducing the detector.