This　paper　introduces　a　novel　back　propagation　(BP)　neural　network　method　to　accurately　characterize　optical　properties　of　liquid　cloud　droplets,　including　black　carbon.　The　model　establishes　relationships　between　black　carbon　volume　fraction,　wavelength,　cloud　effective　radius,　and　optical　properties.　Evaluated　on　a　test　set,　the　value　of　the　root　mean　square　error　(RMSE)　of　the　asymmetry　factor,　extinction　coefficient,　single-scattering　albedo,　and　the　first　4　moments　of　the　Legendre　expansion　of　the　phase　function　are　less　than　0.003,　with　the　maximum　mean　relative　error　(MRE)　reaching　0.2%,　which　are　all　better　than　the　traditional　method　that　only　uses　polynomials　to　fit　the　relationship　between　the　effective　radius　and　optical　properties.　Notably,　the　BP　neural　network　significantly　compresses　the　optical　property　database　size　by　37,800　times.　Radiative　transfer　simulations　indicate　that　mixing　black　carbon　particles　in　water　clouds　reduces　the　top-of-atmosphere　(TOA)　reflectance　and　heats　the　atmosphere.　However,　if　the　volume　fraction　of　black　carbon　is　less　than　10−6,　the　black　carbon　mixed　in　the　water　cloud　has　a　tiny　effect　on　the　simulated　TOA　reflectance.　©　2023　OSA　-　The　Optical　Society.　All　rights　reserved.