Reflective properties of melt ponds on sea ice

Melt ponds occupy a large part of the Arctic sea ice in summer and strongly affect the radiative budget of the atmosphere-ice-ocean system. In this study, the melt pond reflectance is considered in the framework of radiative transfer theory. The melt pond is modeled as a plane-parallel layer of pure water upon a layer of sea ice (the pond bottom). We consider pond reflection as comprising Fresnel reflection by the water surface and multiple reflections between the pond surface and its bottom, which is assumed to be Lambertian. In order to give a description of how to find the pond bottom albedo, we investigate the inherent optical properties of sea ice. Using the Wentzel-Kramers-Brillouin approximation approach to light scattering by non-spherical particles (brine inclusions) and Mie solution for spherical particles (air bubbles), we conclude that the transport scattering coefficient in sea ice is a spectrally independent value. Then, within the two-stream approximation of the radiative transfer theory, we show that the under-pond ice spectral albedo is determined by two independent scalar values: the transport scattering coefficient and ice layer thickness. Given the pond depth and bottom albedo values, the bidirectional reflectance factor (BRF) and albedo of a pond can be calculated with analytical formulas. Thus, the main reflective properties of the melt pond, including their spectral dependence, are determined by only three independent parameters: pond depth z, ice layer thickness H, and transport scattering coefficient of ice sigma(t). The effects of the incident conditions and the atmosphere state are examined. It is clearly shown that atmospheric correction is necessary even for in situ measurements. The at-mospheric correction procedure has been used in the model verification. The optical model developed is verified with data from in situ measurements made during three field campaigns performed on landfast and pack ice in the Arctic. The measured pond albedo spectra were fitted with the modeled spectra by varying the pond parameters (z, H, and sigma(t)). The coincidence of the measured and fitted spectra demonstrates good performance of the model: it is able to reproduce the albedo spectrum in the visible range with RMSD that does not exceed 1.5% for a wide variety of melt pond types observed in the Arctic.