International Journal of
Water Resources and Environmental Engineering

  • Abbreviation: Int. J. Water Res. Environ. Eng.
  • Language: English
  • ISSN: 2141-6613
  • DOI: 10.5897/IJWREE
  • Start Year: 2009
  • Published Articles: 315

Full Length Research Paper

Continuous and stochastic methods for modeling rain drop growth in clouds

Rehan Siddiqui
  • Rehan Siddiqui
  • Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, M3J 1P3 Canada.
  • Google Scholar
Brendan M. Quine
  • Brendan M. Quine
  • Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, M3J 1P3 Canada.
  • Google Scholar

  •  Received: 26 November 2015
  •  Accepted: 22 March 2016
  •  Published: 30 April 2016


Two models for raindrop growth in clouds are developed and compared with an interpretation to elucidate the rain drop relationship among both the models. A continuous accretion model is solved numerically for drop growth from 20 to 50 microns, using a polynomial approximation to the collection kernel, and is shown to underestimate growth rates. A Monte Carlo simulation for stochastic growth have also been implemented to demonstrate the discrete drop growth. The approach models the effect of decreased average time between captures as the drop size increases. It is found that the stochastic model yields a more realistic growth rate, especially for larger drop sizes. It is concluded that the stochastic model shows faster droplet accumulation and hence shorter time for drop growth.

Key words: Raindrop growth, continuous collection, stochastic collection, Monte Carlo method, implicit and semi-implicit technique.