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Hyunho Lee and Jong-Jin Baik
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Hyunho Lee and Jong-Jin Baik

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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Han-Gyul Jin, Hyunho Lee, and Jong-Jin Baik

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A new parameterization of the accretion of cloud water by graupel for use in bulk microphysics schemes is derived by analytically integrating the stochastic collection equation (SCE). In this parameterization, the collection efficiency between graupel particles and cloud droplets is expressed in a functional form using the data obtained from a particle trajectory model by a previous study. The new accretion parameterization is evaluated through box model simulations in comparison with a bin-based direct SCE solver and two previously developed accretion parameterizations that employ the continuous collection equation and a simplified SCE, respectively. Changes in cloud water and graupel mass contents via the accretion process predicted by the new parameterization are closest to those predicted by the direct SCE solver. Furthermore, the new parameterization predicts a decrease in the cloud droplet number concentration that is smaller than the decreases predicted by the other accretion parameterizations, consistent with the direct SCE solver. The new and the other accretion parameterizations are implemented into a cloud-resolving model. Idealized deep convective cloud simulations show that among the accretion parameterizations, the new parameterization predicts the largest rate of accretion by graupel and the smallest rate of accretion by snow, which overall enhances rainfall through the largest rate of melting of graupel. Real-case simulations for a precipitation event over the southern Korean Peninsula show that among the examined accretion parameterizations, the new parameterization simulates precipitation closest to observations. Compared to the other accretion parameterizations, the new parameterization decreases the fractions of light and moderate precipitation amounts and increases the fraction of heavy precipitation amount.

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Hyunho Lee, Ann M. Fridlind, and Andrew S. Ackerman

Abstract

This study evaluates some available schemes designed to solve the stochastic collection equation (SCE) for collision–coalescence of hydrometeors using a size-resolved (bin) microphysics approach and documents their numerical properties within the framework of a box model. Comparing three widely used SCE schemes, we find that all converge to almost identical solutions at sufficiently fine mass grids. However, one scheme converges far slower than the other two and shows pronounced numerical diffusion at the large-drop tail of the size distribution. One of the remaining two schemes is recommended on the basis that it is well converged on a relatively coarse mass grid, stable for large time steps, strictly mass conservative, and computationally efficient. To examine the effects of SCE scheme choice on simulating clouds and precipitation, two of the three schemes are compared in large-eddy simulations of a drizzling stratocumulus field. A forward simulator that produces Doppler spectra from the large-eddy simulation results is used to compare the model output directly with radar observations. The scheme with pronounced numerical diffusion predicts excessively large mean Doppler velocities and overly broad and negatively skewed spectra compared with observations, consistent with numerical diffusion demonstrated in the box model. Statistics obtained using the recommended scheme are closer to observations, but notable differences remain, indicating that factors other than SCE scheme accuracy are limiting simulation fidelity.

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Hyunho Lee, Ann M. Fridlind, and Andrew S. Ackerman

Abstract

Accurate numerical modeling of clouds and precipitation is essential for weather forecasting and climate change research. While size-resolved (bin) cloud microphysics models predict particle size distributions without imposing shapes, results are subject to artificial size distribution broadening owing to numerical diffusion associated with various processes. Whereas Part I of this study addressed collision–coalescence, here we investigate numerical diffusion that occurs in solving condensation and evaporation. In a parcel model framework, all of the numerical schemes examined converge to one solution of condensation and evaporation as the mass grid is refined, and the advection-based schemes are recommended over the reassigning schemes. Including Eulerian vertical advection in a column limits the convergence to some extent, but that limitation occurs at a sufficiently fine mass grid, and the number of iterations in solving vertical advection should be minimized to reduce numerical diffusion. Insubstantial numerical diffusion in solving condensation can be amplified if collision–coalescence is also active, which in turn can be substantially diminished if turbulence effects on collision are incorporated. Large-eddy simulations of a drizzling stratocumulus field reveal that changes in moments of Doppler spectra obtained using different mass grids are consistent with those obtained from the simplified framework, and that spectral moments obtained using a mass grid designed to effectively reduce numerical diffusion are generally closer to observations. Notable differences between the simulations and observations still exist, and our results suggest a need to consider whether factors other than numerical diffusion in the fundamental process schemes employed can cause such differences.

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