A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision

In this paper, a new Lagrangian cloud model (LCM) is introduced in which the flow field is simulated by large-eddy simulation, and the droplets are treated as Lagrangian particles responding to the simulated flow field. In order to handle the extremely large number of droplets within a cloud, the concept of a super-droplet, which represents a large number of real droplets of the same size, is introduced, and the number of contributing real droplets is called the weighting factor. A novel method is developed to realize the collision/coalescence of droplets, in which the consequent variation of the droplet spectrum is represented in terms of the modification of the radius and weighting factor of super-droplets, while keeping the number of super-droplets unchanged. Using an idealized single cloud and trade wind cumuli, the LCM is shown to reproduce the general features of shallow cumulus clouds in agreement with traditional bulk models. The droplet spectrum simulated by the LCM, using collision kernels with and without the effects of turbulence, also shows a pattern consistent with the spectral bin model. Furthermore, the sensitivity of the LCM to two model parameters, the time step and the number of super-droplets, is examined.