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For inhomogeneous cirrus clouds, cloud optical thickness (COT) and effective diameter (De) provided by the Moderate Resolution Imaging Spectrometer (MODIS) Collection 6 cloud products are associated with errors due to the single habit assumption (SHA), independent pixel assumption (IPA), photon absorption effect (PAE), and plane-parallel assumption (PPA). SHA means that every cirrus cloud is assumed to have the same shape habit of ice crystals. IPA errors are caused by three-dimensional (3D) radiative effects. PPA and PAE errors are caused by cloud inhomogeneity. We proposed a method to single out these different errors. These errors were examined using the Spherical Harmonics Discrete Ordinate Method simulations done for the MODIS 0.86m and 2.13m bands. Four midlatitude and tropical cirrus cases were studied. For the COT retrieval, the impacts of SHA and IPA were especially large for optically thick cirrus cases. SHA errors in COT varied distinctly with scattering angles. For the De retrieval, SHA decreased De under most circumstances. PAE decreased De for optically thick cirrus cases. For the COT and De retrievals, the dominant error source was SHA for overhead sun whereas for oblique sun, it could be any of SHA, IPA, and PAE, varying with cirrus cases and sun-satellite viewing geometries. On the domain average, the SHA errors in COT (De) were within -16.1%-42.6% (-38.7%-2.0%), whereas the 3-D radiative effects- and cloud inhomogeneity-induced errors in COT (De) were within -5.6%-19.6% (-2.9%-8.0%) and -2.6%-0% (-3.7%-9.8%), respectively.