This paper presents a simple approach to estimate the uncertainties that arise in satellite retrievals of cloud optical depth when the retrievals use one-dimensional radiative transfer theory for heterogeneous clouds that have variations in all three dimensions. For the first time, preliminary error bounds are set to estimate the uncertainty of cloud optical depth retrievals. These estimates can help us better understand the nature of uncertainties that three-dimensional effects can introduce into retrievals of this important product of the MODIS instrument. The probability distribution of resulting retrieval errors is examined through theoretical simulations of shortwave cloud reflection for a wide variety of cloud fields. The results are used to illustrate how retrieval uncertainties change with observable and known parameters, such as solar elevation or cloud brightness. Furthermore, the results indicate that a tendency observed in an earlier study, clouds appearing thicker for oblique sun, is indeed caused by three-dimensional radiative effects.

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