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=αNc -1/3 qc 7/3 H(R2RT) and C=βqcqr, where qc and Nc are the mixing ratio and the number concentration of cloud droplets, qr is the mixing ratio of raindrops, RT is the threshold volume radius, and His the Heaviside function. Furthermore, it is found that a increases linearly with the dissipation rate « and the standard deviation of radius s and that RT decreases rapidly with σ while disappearing at σ > 3.5 μm. The LCMalso reveals that σ and ε increase with time during the period of autoconversion, which helps to suppress the early precipitation by reducing A with smaller a and larger RT in the initial stage. Finally, β is found to be affected by the accumulated collisional growth, which determines the drop size distribution.
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