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

Abstract

The bispectral method retrieves cloud optical thickness (τ) and cloud droplet effective radius (re) 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 re. In the literature, the retrievals of τ and re 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 re 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 re 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 re 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 re retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in re retrievals, leading to a potential contribution of positive bias to the re 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 re retrievals between two instruments.

Comparisons of bispectral and polarimetric retrievals of marine boundary layer cloud microphysics: case studies using a LES–satellite retrieval simulator

“…In contrast, total reflectance uncertainty did produce a slight systematic bias of −2.43 % in the polarimetric τ (pol) retrieval that can be linked to the convexity of the single-band LUT used to perform the retrieval. This sort of bias could perhaps be accounted for by introducing a Taylor expansion correction similar to the one discussed in Zhang et al (2016) in the context of unresolved inhomogeneity. Beyond these systematic biases, we found that the induced uncertainties in the bispectral retrievals were δr e = 5 or δτ = 7 %.…”

“…Recently, great effort has been made to account for the influence of the PPH bias on bispectral MODIS retrievals. The 2-D Taylor expansion technique implemented by Zhang et al (2016) offers the possibility of quantifying (and potentially correcting for) the impact of PPH bias on bispectral retrievals. This approach requires high-spatial-resolution measurements in at least one spectral band to obtain the sub-pixel reflectance variability, which is used to determine corrections for the bias of r e and τ .…”

“…PPH bias induced by the curvature of the bispectral LUT with respect to the optical thickness (Zhang and Platnick, 2011;Zhang et al, 2012Zhang et al, , 2016. The PPH bias has a stronger influence on the 2.13 µm retrieval compared to the 3.75 µm retrieval (shown in Fig.…”

“…Sub-pixel inhomogeneity. The impact of spatial resolution and unresolved sub-pixel cloud inhomogeneity on bispectral retrievals has been well studied (Zhang and Platnick, 2011;Zhang et al, 2012Zhang et al, , 2016). An important conclusion from these studies is that the so-called planeparallel homogenous bias (PPHB) can cause the bispectral technique to significantly overestimate r e .…”

“…For example, the polarimetric and bispectral methods have different sensitivity to the cloud vertical profile, and at the same time they are also both affected by cloud horizontal inhomogeneity (Zinner et al, 2010;Zhang et al, 2012Zhang et al, , 2016Miller et al, 2016). It is difficult, if not impossible, to disentangle these factors based on observations alone.…”