Plane parallel biases of water clouds based on MODIS optical properties

The classic study of Cahalan et al. (JAS, 1994) while providing the theoretical framework of plane parallel albedo bias, focused its quantitative analysis of cloud inhomogeneity and albedo bias on marine stratocumulus clouds with properties described by surface microwave radiometer observations. Cloud microphysics (e.g., droplet effective radius) was assumed constant and radiative transfer remained monochromatic. Our current presentation extends the bias calculations in several important aspects: all water cloud types are considered, cloud effective radius is allowed to be spatially variable, and radiative transfer is broadband, making estimates of bias for transmittance and absorptance (in addition to albedo) also meaningful. The cloud optical properties come from the two months (July 2003 and January 2004) of MODIS (both Terra and Aqua) Level-3 data used in Oreopoulos and Cahalan (JCLI, 2005). Specifically, we use gridded (1°x1°) daily means, marginal histograms, and joint histograms of cloud optical thickness and effective radius. This data forms the input for our broadband radiative transfer calculations which are performed with a modified version of Goddard's GEOS GCM Column Radiation Model. The plane parallel calculations are based on the mean properties, while Independent Pixel Approximation calculations are based on the 1-D and 2-D histograms. Several different types of biases are examined: (1) the bias due to the horizontal inhomogeneity of optical thickness alone (the effective radius is assumed equal to the grid mean); (2) the bias due to the horizontal inhomogeneity of effective radius alone (the optical thickness is assumed equal to the grid mean); and (3) the bias due to simultaneous variations of optical thickness and effective radius as derived from their joint histograms. The geographical and seasonal patterns of these biases are examined for the entire solar spectrum as well as separately for the UV-VIS and NIR portions. We discuss the importance of these biases in radiative energy budgets terms after atmospheric effects, surface reflectivity, and solar geometry are taken into account, and what they signify for the modeling of cloud-radiation interactions in Global Climate Models.