Abstract
A physically based parameterization for the autoconversion is derived by solving the stochastic collection equation (SCE) with an approximated collection kernel. The collection kernel is constructed using the terminal velocity of cloud droplets and the collision efficiency between cloud droplets that is obtained using a particle trajectory model. The new parameterization proposed in this study is validated through comparison with results obtained by a bin-based direct SCE solver and other autoconversion parameterizations using a box model. The autoconversion-related time scale and drop number concentration are employed for the validation. The results of the new parameterization are shown to most closely match those of the direct SCE solver. It is also shown that the dependency of the autoconversion rate on drop number concentration in the new parameterization is similar to that in the direct SCE solver, which is partially caused by the shape of drop size distribution. The new parameterization and other parameterizations are implemented into a cloud-resolving model, and idealized shallow warm clouds are simulated. The autoconversion parameterizations that yield the small (large) autoconversion rate tend to predict large (small) cloud optical thickness, small (large) cloud fraction, and small (large) surface precipitation amount. Cloud optical thickness and cloud fraction are changed by up to ~45% and ~20% by autoconversion parameterizations, respectively. The new parameterization tends to yield the moderate autoconversion rate among the autoconversion parameterizations. Moreover, it predicts cloud optical thickness, cloud fraction, and surface precipitation amount that are generally the closest to those of the bin microphysics scheme.
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