A stochastic closure for two-moment bulk microphysics of warm clouds: part II, parameter constraint and validation


The representation of clouds and associated processes of rain and snow formation remain one of the major uncertainties in climate and weather prediction models. In a companion paper (part I), we systematically derived a two-moment bulk cloud microphysics model for warm rain based on the kinetic coalescence equation (KCE) and the use of stochastic approximations to close the high order moment terms, independently of the collision kernel. Conservation of mass and consistency of droplet number concentration of the evolving cloud distribution combined with numerical simulations are used as design principles to reduce the parametrization problem to three key parameters. Here, we further derive physical limits or region of validity for these three parameters based on the physics of collision and coalescence processes: “the stochastic region of validity”. More importantly, in this second part, we validate the stochastically derived bulk cloud microphysics model against detailed simulations based on the KCE and in comparison with a similar model by Seifert and Beheng (J Atmos Sci 59–60:265–281, 2001; hereafter SB01) who instead prescribed the shapes of the droplet distributions of rain and clouds in order to close the high-order moments and have done so specifically for one given kernel only. A thorough parameter exploration of the stochastic validity region is conducted, and parameter values that faithfully reproduce the detailed KCE results are identified. The results show that for typical parameter values, dependent on the environmental conditions, the new parameterization outperforms that of SB01 when compared to the KCE benchmark simulations. These results can be explored in the future to design a Markov jump process to randomly select adequate parameters within the validity region conditional on the environmental conditions and the age of the cloud. Furthermore, sensitivity tests indicate that the stochastically derived model can be used with a time step as large as 30 s without significantly compromising accuracy, which makes it very attractive to use in medium to long range weather prediction models.

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This research is part of D. C.’s Ph.D. thesis. The research of B. K. is partly supported by a grant from the Natural Sciences and Engineering Research Council of Canada. D. C.’s fellowship is partly funded through this grant.

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Correspondence to Boualem Khouider.

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Collins, D., Khouider, B. A stochastic closure for two-moment bulk microphysics of warm clouds: part II, parameter constraint and validation. Res Math Sci 8, 15 (2021). https://doi.org/10.1007/s40687-021-00247-6

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  • Cloud microphysics
  • Bulk parameterizations
  • Stochastic differential equations
  • Kinetic collection equation
  • Collision and coalescence
  • Two moment closure