Influence of cloud retrieval errors due to three-dimensional radiative effects on calculations of broadband shortwave cloud radiative effect

We investigate how cloud retrieval errors due to the three-dimensional (3D) radiative effects affect broadband shortwave (SW) cloud radiative effects (CREs) in shallow cumulus clouds. A framework based on the combination of large eddy simulations (LESs) and radiative transfer (RT) models was developed to simulate both one-dimensional (1D) and 3D radiance, as well as SW broadband fluxes. Results show that the broadband SW fluxes reflected at top of the domain, transmitted at the surface, and absorbed in the atmosphere, computed from the cloud retrievals using 1D RT (inline-formula $M1inlinescrollmathml{F}_{\mathrm{normal\; 1}\mathrm{normal\; D}}^{\ast }$ 18pt14ptsvg-formulamathimgefa2a09c44b33ce8a3122b921590a509 acp-24-3093-2024-ie00001.svg18pt14ptacp-24-3093-2024-ie00001.png ), can provide reasonable broadband radiative energy estimates in comparison with those derived from the true cloud fields using 1D RT (inline-formulaF_1D). The difference between these 1D-RT-simulated fluxes (inline-formula $M3inlinescrollmathml{F}_{\mathrm{normal\; 1}\mathrm{normal\; D}}^{\ast }$ 18pt14ptsvg-formulamathimg8bbf0706b00205df7d0eefc92403c537 acp-24-3093-2024-ie00002.svg18pt14ptacp-24-3093-2024-ie00002.png , inline-formulaF_1D) and the benchmark 3D RT simulations computed from the true cloud field (inline-formulaF_3D) depends primarily on the horizontal transport of photons in 3D RT, whose characteristics vary with the sun's geometry. When the solar zenith angle (SZA) is 5°, the domain-averaged inline-formula $M6inlinescrollmathml{F}_{\mathrm{normal\; 1}\mathrm{normal\; D}}^{\ast }$ 18pt14ptsvg-formulamathimg39ccd6790dabb26c52adacb4261395cd acp-24-3093-2024-ie00003.svg18pt14ptacp-24-3093-2024-ie00003.png values are in excellent agreement with the inline-formulaF_3D, all within 7 % relative CRE bias. When the SZA is 60°, the CRE differences between calculations from inline-formula $M8inlinescrollmathml{F}_{\mathrm{normal\; 1}\mathrm{normal\; D}}^{\ast }$ 18pt14ptsvg-formulamathimga43d8b106be3a835697e030af69cb221 acp-24-3093-2024-ie00004.svg18pt14ptacp-24-3093-2024-ie00004.png and inline-formulaF_3D are determined by how the cloud side-brightening and darkening effects offset each other in the radiance, retrieval, and broadband fluxes. This study suggests that although the cloud property retrievals based on the 1D RT theory may be biased due to the 3D radiative effects, they still provide CRE estimates that are comparable to or better than CREs calculated from the true cloud properties using 1D RT.