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A robust numerical solution of the stochastic collection-breakup equation for warm rain

Publication ,  Journal Article
Prat, OP; Barros, AP
Published in: Journal of Applied Meteorology and Climatology
September 1, 2007

The focus of this paper is on the numerical solution of the stochastic collection equation-stochastic breakup equation (SCE-SBE) describing the evolution of raindrop spectra in warm rain. The drop size distribution (DSD) is discretized using the fixed-pivot scheme proposed by Kumar and Ramkrishna, and new discrete equations for solving collision breakup are presented. The model is evaluated using established coalescence and breakup parameterizations (kernels) available in the literature, and in that regard this paper provides a substantial review of the relevant science. The challenges posed by the need to achieve stable and accurate numerical solutions of the SCE-SBE are examined in detail. In particular, this paper focuses on the impact of varying the shape of the initial DSD on the equilibrium solution of the SCE-SBE for a wide range of rain rates and breakup kernels. The results show that, although there is no dependence of the equilibrium DSD on initial conditions for the same rain rate and breakup kernel, there is large variation in the time that it takes to reach steady state. This result suggests that, in coupled simulations of in-cloud motions and microphysics and for short time scales (<30 min) for which transient conditions prevail, the equilibrium DSD may not be attainable except for very heavy rainfall. Furthermore, simulations for the same initial conditions show a strong dependence of the dynamic evolution of the DSD on the breakup parameterization. The implication of this result is that, before the debate on the uniqueness of the shape of the equilibrium DSD can be settled, there is critical need for fundamental research including laboratory experiments to improve understanding of collisional mechanisms in DSD evolution. © 2007 American Meteorological Society.

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Published In

Journal of Applied Meteorology and Climatology

DOI

ISSN

1558-8424

Publication Date

September 1, 2007

Volume

46

Issue

9

Start / End Page

1480 / 1497

Related Subject Headings

  • Meteorology & Atmospheric Sciences
  • 3702 Climate change science
  • 3701 Atmospheric sciences
  • 0701 Agriculture, Land and Farm Management
  • 0502 Environmental Science and Management
  • 0401 Atmospheric Sciences
 

Citation

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Prat, O. P., & Barros, A. P. (2007). A robust numerical solution of the stochastic collection-breakup equation for warm rain. Journal of Applied Meteorology and Climatology, 46(9), 1480–1497. https://doi.org/10.1175/JAM2544.1
Prat, O. P., and A. P. Barros. “A robust numerical solution of the stochastic collection-breakup equation for warm rain.” Journal of Applied Meteorology and Climatology 46, no. 9 (September 1, 2007): 1480–97. https://doi.org/10.1175/JAM2544.1.
Prat OP, Barros AP. A robust numerical solution of the stochastic collection-breakup equation for warm rain. Journal of Applied Meteorology and Climatology. 2007 Sep 1;46(9):1480–97.
Prat, O. P., and A. P. Barros. “A robust numerical solution of the stochastic collection-breakup equation for warm rain.” Journal of Applied Meteorology and Climatology, vol. 46, no. 9, Sept. 2007, pp. 1480–97. Scopus, doi:10.1175/JAM2544.1.
Prat OP, Barros AP. A robust numerical solution of the stochastic collection-breakup equation for warm rain. Journal of Applied Meteorology and Climatology. 2007 Sep 1;46(9):1480–1497.

Published In

Journal of Applied Meteorology and Climatology

DOI

ISSN

1558-8424

Publication Date

September 1, 2007

Volume

46

Issue

9

Start / End Page

1480 / 1497

Related Subject Headings

  • Meteorology & Atmospheric Sciences
  • 3702 Climate change science
  • 3701 Atmospheric sciences
  • 0701 Agriculture, Land and Farm Management
  • 0502 Environmental Science and Management
  • 0401 Atmospheric Sciences