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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.

An Evaluation of Size-Resolved Cloud Microphysics Scheme Numerics for Use with Radar Observations. Part I: Collision–Coalescence