Parameterization of optical properties for liquid cloud droplets containing black carbon based on neural network

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.