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In the recent years, there has been increased interest in using synthetic aperture radar (SAR) to study and monitor glaciers and ice sheets for glaciological and climate change research. This paper describes the estimation of ice extinctions through the modeling of polarimetric interferometric SAR (Pol-InSAR) coherences as a combination of a surface contribution (from the snow-firn interface and wind-induced sastrugi features) and a volume response. Ground-to-volume scattering ratios derived from a novel polarimetric decomposition are used in conjunction with Pol-InSAR coherence magnitudes to invert the extinction of the ice layer. The inversion is performed for experimental airborne Pol-InSAR data at L-band and P-band acquired by the German Aerospace Center's (DLR) E-SAR system over the Austfonna ice cap in Svalbard, Norway, as part of the 2007 IceSAR campaign. Extinction dependences on frequency and glacier facie are investigated, and validation is performed comparing ground-penetrating radar data to SAR backscatter and extinction values. Best extinction results are obtained at shallow incidence angles with small wavenumbers and for low ground-to-volume scattering ratios. For swath areas in mid range to far range, accuracies of 25% in extinction are anticipated when averaging over 100 effective looks for a four-baseline inversion constraining solutions to vertical wavenumbers of 0.01 ≤ kz ≤ 0.1. To allow inversion using single-baseline Pol-InSAR, the proposed model is of limited complexity. Suggested extensions for a more realistic scattering scenario include incorporating multiple englacial ice scattering layers and improving the way multiple baselines are combined.