Abstract. The degree of surface roughness of ice particles within thick, cold ice clouds is inferred from multi-directional, multi-spectral satellite polarimetric observations over oceans, assuming a column-aggregate particle habit. An improved roughness inference scheme is employed that provides a more noise-resilient roughness estimate than the conventional best-fit approach. The improvements include the introduction of a quantitative roughness parameter based on empirical orthogonal function analysis and proper treatment of polarization due to atmospheric scattering above clouds. A global 1-month data sample supports the use of a severely roughened ice habit to simulate the polarized reflectivity associated with ice clouds over ocean. The density distribution of the roughness parameter inferred from the global 1-month data sample and further analyses of a few case studies demonstrate the significant variability of ice cloud single-scattering properties. However, the present theoretical results do not agree with observations in the tropics. In the extratropics, the roughness parameter is inferred but 74% of the sample is out of the expected parameter range. Potential improvements are discussed to enhance the depiction of the natural variability on a global scale.