Independent Pixel and Two-Dimensional Estimates of Landsat-Derived Cloud Field Albedo

Abstract

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane-parallel (PP?IPA) and independent pixel (IPA?2D) approximations for a wide range of 2D cloud fields obtained from Landsat. They include single-layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter ? (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP?IPA bias, ?0.12 for IPA?2D bias) for large ?. On a scene-average basis, PP?IPA bias can reach 0.30, while IPA?2D bias reaches its largest magnitude at ?0.07. Biases due to horizontal transport (IPA?2D) are much smaller than PP?IPA biases but account for 20% rms of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The Landsat data used may also be affected by radiative smoothing.