Cloud microphysics parameterizations for shallow cumulus clouds are analyzed based on Lagrangian cloud model (LCM) data, focusing on autoconversion and accretion. The autoconversion and accretion rates, A and C, respectively, are calculated directly by capturing the moment of the conversion of individual Lagrangian droplets from cloud droplets to raindrops, and it results in the reproduction of the formulas of A and C for the first time. Comparison with various parameterizations reveals the closest agreement with Tripoli and Cotton, such as A = alpha N(c)(-1/3)q(c)(7/3) H(R - R-T) and C = beta q(c)q(r), where q(c) and N-c are the mixing ratio and the number concentration of cloud droplets, q(r) is the mixing ratio of raindrops, R-T is the threshold volume radius, andHis the Heaviside function. Furthermore, it is found that a increases linearly with the dissipation rate epsilon and the standard deviation of radius sigma and that R-T decreases rapidly with sigma while disappearing at sigma > 3.5 mu m. The LCMalso reveals that sigma and epsilon increase with time during the period of autoconversion, which helps to suppress the early precipitation by reducing A with smaller alpha and larger R-T in the initial stage. Finally, beta is found to be affected by the accumulated collisional growth, which determines the drop size distribution.

http://dx.doi.org/10.1175/jas-d-18-0080.1

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