Radiative transfer model for contaminated slabs : experimental validations

Abstract

This article presents a set of spectro-goniometric measurements of different water ice samples and the comparison with an approximated radiative transfer model. The experiments were done using the spectro-radiogoniometer described in Brissaud et al. (2004). The radiative transfer model assumes an isotropization of the flux after the second interface and is fully described in Andrieu et al. (2015). Two kind of experiments were conducted. First, the specular spot was closely investigated, at high angular resolution, at the wavelength of $1.5\,\mbox{\mu m}$, where ice behaves as a very absorbing media. Second, the bidirectional reflectance was sampled at various geometries, including low phase angles on 61 wavelengths ranging from $0.8\,\mbox{\mu m}$ to $2.0\,\mbox{\mu m}$. In order to validate the model, we made a qualitative test to demonstrate the relative isotropization of the flux. We also conducted quantitative assessments by using a bayesian inversion method in order to estimate the parameters (e.g. sample thickness, surface roughness) from the radiative measurements only. A simple comparison between the retrieved parameters and the direct independent measurements allowed us to validate the model. We developed an innovative bayesian inversion approach to quantitatively estimate the uncertainties on the parameters avoiding the usual slow Monte Carlo approach. First we built lookup tables, and then searched the best fits and calculated a posteriori density probability functions. The results show that the model is able to reproduce the spectral behavior of water ice slabs, as well as the specular spot. In addition, the different parameters of the model are compatible with independent measurements.