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 superdroplet -becomes larger than some critical value, which we estimate to be in the range 2 ∼ 4.

Lagrangian condensation microphysics with Twomey CCN activation

“…Among those, the particle-based Lagrangian method, referred to as the Lagrangian cloud model (Andrejczuk et al, 2008(Andrejczuk et al, , 2010 or the "super-droplet method" (Shima et al, 2009), is of particular relevance (see also Riechelmann et al, 2012;Arabas et al, 2015;Hoffmann et al, 2015, among others). By representing formation and growth of natural cloud particles using a subset of those particles ("super-particles"), many problems haunting traditional Eulerian approaches are either eliminated or significantly reduced.…”

“…Considering typical cloud droplet concentrations in natural clouds, from several tens to a few thousands per cubic centimeter, it is computationally impossible to follow all cloud droplets in the entire volume of even a very small cloud. Thus, the Lagrangian methodology involves following only a selected (typically relatively small) subset of cloud droplets, referred to as super-droplets following Shima et al (2009). This is again in the spirit of using a finite (and typically relatively small) number of classes (bins) in the Eulerian bin microphysics scheme.…”

“…This is again in the spirit of using a finite (and typically relatively small) number of classes (bins) in the Eulerian bin microphysics scheme. As in Andrejczuk et al (2008), Andrejczuk et al (2010), Shima et al (2009), andRiechelmann et al (2012), among others, the list of attributes for each super-droplet includes the position x i , radius r i , and multiplicity. The latter depicts the number of particles represented by a single super-droplet.…”

“…The key element of the scheme presented here that makes it distinct from the approach used in Andrejczuk et al (2008Andrejczuk et al ( , 2010, Shima et al (2009), Riechelmann et al (2012, Arabas et al (2015), and others, is the way super-droplets are created. The original implementations assume that superdroplets fill the entire computational domain, and they initially represent deliquesced (humidified) CCN in equilibrium with their local environment.…”

Droplet growth in warm turbulent clouds

“…Recently, a different Lagrangian approach was developed, with the focus not on air parcels but on particles carried by the flow such as cloud droplets. In such an approach, the Eulerian fluid flow model is coupled to the Lagrangian representation of the thermodynamics (see, for example, Andrejczuk et al, 2008Andrejczuk et al, , 2010Shima et al, 2009). This approach is in the spirit of the pseudo-LES simulations presented in Lanotte et al (2009) and discussed in section 4.1.3.…”