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The unambiguous retrieval of cloud phase from polarimetric lidar observations is dependent on the assumption that only cloud scattering processes affect polarization measurements. A systematic bias of the traditional lidar depolarization ratio can occur due to a lidar system's inability to accurately measure the entire backscattered signal dynamic range, and these biases are not always identifiable in traditional polarimetric lidar systems. This results in a misidentification of liquid water in clouds as ice, which has broad implications on evaluating surface energy budgets. The Clouds Aerosol Polarization and Backscatter Lidar at Summit, Greenland employs multiple planes of linear polarization, and photon counting and analog detection schemes, to self evaluate, correct, and optimize signal combinations to improve cloud classification. Using novel measurements of diattenuation that are sensitive to both horizontally oriented ice crystals and counting system nonlinear effects, unambiguous measurements are possible by over constraining polarization measurements. This overdetermined capability for cloud-phase determination allows for system errors to be identified and quantified in terms of their impact on cloud properties. It is shown that lidar system dynamic range effects can cause errors in cloud-phase fractional occurrence estimates on the order of 30% causing errors in attribution of cloud radiative effects on the order of 10-30 %. This paper presents a method to identify and remove lidar system effects from atmospheric polarization measurements and uses colocated sensors at Summit to evaluate this method. Enhanced measurements are achieved in this work with non-orthogonal polarization retrievals as well as analog and photon counting detection facilitating a more complete attribution of radiative effects linked to cloud properties. [ABSTRACT FROM AUTHOR]