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Lagrangian cloud model (LCM)

The LCM is based on the formulation of the LPM (Sect. lagrangian particle model). For the LCM, however, the Lagrangian particles are representing droplets and aerosols. The droplet advection and sedimentation is given by the Eqs. for du_p,i / dt and τ_p^-1 in Sect. formulation of the LPM with ρ_p,0 = ρ_l,0. At present it is computationally not feasible to simulate a realistic amount of particles. A single Lagrangian particle thus represents an ensemble of identical particles (i.e., same radius, velocity, mass of solute aerosol) and is referred to as "super-droplet". The number of particles in this ensemble is referred to as the "weighting factor". For example, q_l of a certain LES grid volume results from all Lagrangian particles located therein considering their individual weighting factor A_n:

with N_p being the number of particles inside the grid volume of size ΔV, and r_n being the radius of the particle. The concept of weighting factors and super-droplets in combination with LES has been also used similarly by Andrejczuk et al. (2208) and Shima et al. (2009) for warm clouds, as well as by Sölch and Kärcher (2010) for ice clouds.

Diffusional growth

Collision and coalescence

Recent applications

References

• Andrejczuk M, Reisner JM, Henson B, Dubey MK, Jeffery CA. 2008. The potential impacts of pollution on a nondrizzling stratus deck: Does aerosol number matter more than type?. J. Geophys. Res. 113: D19204. ​doi.

• Shima S-I, Kusano K, Kawano A, Sugiyama T, Kawahara S. 2009. 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. Q. J. Roy. Meteor. Soc. 135: 1307–1320.

• Sölch I, Kärcher B. 2010. A large-eddy model for cirrus clouds with explicit aerosol and ice microphysics and Lagrangian ice particle tracking. Q. J. Roy. Meteor. Soc. 136: 2074–2093.