Interpretation of Multiwavelength-Retrieved Droplet Effective Radii for Warm Water Clouds in Terms of In-Cloud Vertical Inhomogeneity by Using a Spectral Bin Microphysics Cloud Model

This study examines the impact of in-cloud vertical inhomogeneity on cloud droplet effective radii (CDERs) of water-phase cloud retrieved from 1.6-, 2.1-, and 3.7-mm-band measurements (denoted by r1.6, r2.1, and r3.7, respectively). Discrepancies between r1.6, r2.1, and r3.7 due to in-cloud vertical inhomogeneity are simulated by using a spectral bin microphysics cloud model and one-dimensional (1D) remote sensing simulator under assumptions that cloud properties at the subpixel scale have horizontal homogeneity and 3D radiative transfer effects can be ignored. Two-dimensional weighting functions for the retrieved CDERs with respect to cloud optical depth and droplet size are introduced and estimated by least squares fitting to the relation between the model-simulated droplet size distribution functions and the retrieved CDERs. The results show that the 2D weighting functions can explain CDER discrepancies due to in-cloud vertical inhomogeneity and size spectrum characteristics. The difference between r1.6 and r2.1 is found to primarily depend on the vertical difference in droplet size distribution because the peak widths of their weighting functions differ in terms of cloud optical depth. The difference between r3.7 and r2.1, in contrast, is highly dependent on r2.1 because the magnitude of its weighting function is always greater than that of r3.7 over the entire range of optical depths and droplet sizes, except for the cloud top. The overestimation of retrieved CDER compared with in situ CDER in a typical adiabatic cloud case is also interpreted in terms of in-cloud vertical inhomogeneity based on the 2D weighting functions and simulation results.