A framework based on 2‐D Taylor expansion for quantifying the impacts of subpixel reflectance variance and covariance on cloud optical thickness and effective radius retrievals based on the bispectral method. Issue 12 (18th June 2016) - Zhang, Z.; Werner, F.; Cho, H.‐M.; Wind, G.; Platnick, S.; Ackerman, A. S.; Di Girolamo, L.; Marshak, A.; Meyer, K.
Abstract: The bispectral method retrieves cloud optical thickness ( τ ) and cloud droplet effective radius ( r e ) simultaneously from a pair of cloud reflectance observations, one in a visible or near‐infrared (VIS/NIR) band and the other in a shortwave infrared (SWIR) band. A cloudy pixel is usually assumed to be horizontally homogeneous in the retrieval. Ignoring subpixel variations of cloud reflectances can lead to a significant bias in the retrieved τ and r e . In the literature, the retrievals of τ and r e are often assumed to be independent and considered separately when investigating the impact of subpixel cloud reflectance variations on the bispectral method. As a result, the impact on τ is contributed only by the subpixel variation of VIS/NIR band reflectance and the impact on r e only by the subpixel variation of SWIR band reflectance. In our new framework, we use the Taylor expansion of a two‐variable function to understand and quantify the impacts of subpixel variances of VIS/NIR and SWIR cloud reflectances and their covariance on the τ and r e retrievals. This framework takes into account the fact that the retrievals are determined by both VIS/NIR and SWIR band observations in a mutually dependent way. In comparison with previous studies, it provides a more comprehensive understanding of how subpixel cloud reflectance variations impact the τ and r e retrievals based on the bispectral method. In particular, our framework provides a mathematical explanation of how the subpixel variation in VIS/NIR band influences the r e retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in r e retrievals, leading to a potential contribution of positive bias to the r e retrieval. We test our framework using synthetic cloud fields from a large‐eddy simulation and real observations from Moderate Resolution Imaging Spectroradiometer. The predicted results based on our framework agree very well with the numerical simulations. Our framework can be used to estimate the retrieval uncertainty from subpixel reflectance variations in operational satellite cloud products and to help understand the differences in τ and r e retrievals between two instruments. Key Points: Subpixel reflectance variance can cause cloud retrieval uncertainty Previous studies assume COT and CER retrievals to be independent A new framework developed to better understand the influence