| | 4 | The LCM is based on the formulation of the LPM (Sect. [wiki:/doc/tec/lpm 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 d''u'',,p,i,, / d''t'' and ''τ'',,p,,^-1^ in Sect. [wiki:/doc/tec/lpm#FormulationoftheLPM 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 |
| | 5 | particles in this ensemble is referred to as the "weighting factor". For example, ''q'',,l,, of a certain LES grid volume |
| | 6 | results from all Lagrangian particles located therein considering their individual weighting factor ''A'',,n,,: |
| | 7 | {{{ |
| | 8 | #!Latex |
| | 9 | \begin{align*} |
| | 10 | q_\mathrm{l} = \frac{4/3\,\pi |
| | 11 | \rho_{\mathrm{l},0}}{\rho_0\Delta |
| | 12 | V}\,\sum\limits_{n=1}^{N_\mathrm{p}} A_n r_n^3, |
| | 13 | \end{align*} |
| | 14 | }}} |
| | 15 | 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 [#andrejczuk2008 Andrejczuk et al. (2208)] and [#shima2009 Shima et al. (2009)] for warm clouds, as well as by [#soelch2010 Sölch and Kärcher (2010)] for ice clouds. |
| | 24 | |
| | 25 | * [=#andrejczuk2008] '''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. [http://dx.doi.org/10.1029/2007JD009445 doi]. |
| | 26 | |
| | 27 | * [=#shima2009] '''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. |
| | 28 | |
| | 29 | * [=#soelch2010] ''' 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. |
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| | 31 | |
