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New evidence from collocated measurements, with support from theory and numerical simulations, that multidirectional measurements in the oxygen A band from the third Polarization and Directionality of the Earth’s Reflectances (POLDER-3) instrument on the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL) satellite platform within the ‘‘A-Train’’ can help to characterize the vertical structure of clouds is presented. In the case of monolayered clouds, the standard POLDER cloud oxygen pressure product PO2 is shown to be sensitive to the cloud geometrical thickness H in two complementary ways: 1) PO2 is, on average, close to the pressure at the geometrical middle of the cloud layer (MCP) and methods are proposed for reducing the pressure difference PO2 – MCP and 2) the angular standard deviation of PO2 and the cloud geometrical thickness H are tightly correlated for liquid clouds. Accounting for cloud phase, there is thus the potential to obtain a statistically reasonable estimate of H. Such derivation from passive measurements, as compared with or supplementing other observations, is expected to be of interest in a broad range of applications for which it is important to define better the macrophysical cloud parameters in a practical way.