The super‐droplet method for the numerical simulation of clouds and precipitation: a particle‐based and probabilistic microphysics model coupled with a non‐hydrostatic model

Abstract A novel, particle‐based, probabilistic approach for the simulation of cloud microphysics is proposed, which is named the super‐droplet method (SDM). This method enables the accurate simulation of cloud microphysics with a less demanding cost in computation. SDM is applied to a warm‐cloud system, which incorporates sedimentation, condensation/evaporation and stochastic coalescence. The methodology to couple super‐droplets and a non‐hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the stochastic coalescence of super‐droplets agrees fairly well with the solutions of the stochastic coalescence equation. The behaviour of the model is evaluated using a simple test problem, that of a shallow maritime cumulus formation initiated by a warm bubble. Possible extensions of SDM are briefly discussed. A theoretical analysis suggests that the computational cost of SDM becomes lower than the spectral (bin) method when the number of attributes—the variables that identify the state of each super‐droplet—becomes larger than some critical value, which we estimate to be in the range $2\sim4$ . Copyright © 2009 Royal Meteorological Society