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We present our newly developed Cloud optical thickness Retrieval Over Snow (CROS) algorithm, which makes use of the sensitivity of top-of-atmosphere (TOA) reflectance in the oxygen A-band to the cloud optical thickness. The CROS algorithm applies forward simulations for clouds over snow using the radiative transfer model SCIATRAN in order to find the cloud optical thickness (and cloud bottom height and effective underlying surface albedo) representing the measured TOA radiance for a given cloud top height and solar zenith angle. We present results for synthetic retrievals as well as an error analysis with respect to errors in cloud top height. It was demonstrated that the retrievals are most robust for thin high clouds. The retrievals for low-level clouds require an accurate estimation of the cloud altitude ahead of the cloud optical thickness retrieval. Also, it is demonstrated that the retrievals become less accurate for the cases of low Sun.