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Schmidt, JM, Flatau PJ, Harasti PR.  2017.  Evidence for a nimbostratus uncinus in a convectively generated mixed-phase stratiform cloud shield. Journal of the Atmospheric Sciences. 74:4093-4116.   10.1175/jas-d-17-0074.1   AbstractWebsite

The structure of a melting layer associated with a mesoconvective system is examined using a combination of in situ aircraft measurements and a unique Doppler radar operated by the U.S. Navy that has a range resolution as fine as 0.5 m. Interest in this case was motivated by ground-based all-sky camera images that captured the transient development of midlevel billow cloud structures within a precipitating trailing stratiform cloud shield associated with a passing deep convective system. A sequence of high-fidelity time-height radar measurements taken of this storm system reveal that the movement of the billow cloud structure over the radar site corresponded with abrupt transitions in the observed low-level precipitation structure. Of particular note is an observed transition from stratiform to more periodic and vertically slanted rain shaft structures that both radar and aircraft measurements indicate have the same temporal periodicity determined to arise visually between successive billow cloud bands. Doppler, balloon, and aircraft measurements reveal these transient bands are associated with a shallow circulation field that resides just above the melting level in a layer of moist neutral stability and strong negative vertical wind shear. The nature of these circulations and their impact on the evolving precipitation field are described in the context of known nimbostratus cloud types.

Verlinde, J, Flatau PJ, Cotton WR.  1990.  Analytical Solutions to the Collection Growth Equation - Comparison with Approximate Methods and Application to Cloud Microphysics Parameterization Schemes. Journal of the Atmospheric Sciences. 47:2871-2880.   10.1175/1520-0469(1990)047<2871:asttcg>;2   AbstractWebsite

A closed form solution for the collection growth equation as used in bulk microphysical parameterizations is derived. Although the general form is mathematically complex, it can serve as a benchmark for testing a variety of approximations. Two special cases that can immediately be implemented in existing cloud models are also presented. This solution is used to evaluate two commonly used approximations. The effect of the selection of different basis functions is also investigated.