Representing turbulentmixing of non-conservative values in Eulerian and Lagrangian cloud models

In many explicit microphysics cloud models the description of turbulent mixing of droplet size distributions (DSDs) treats them as conservative quantities, which leads to changes in DSDs for adiabatic profiles of liquid water. A new approach representing turbulent diffusion of DSD in Eulerian and Lagrangian cloud models is proposed. The approach is an extension of the classical K-theory (used for calculation of turbulent fluxes) to the mixing of non-conservative quantities. The proposed approach takes into account the growth/evaporation of drops as well as nucleation/denucleation in the course of the turbulent mixing. Implementation of the method is illustrated by the analysis of mixing between several different pairs of adjacent Lagrangian parcels: two cloudy parcels, a cloudy parcel with a drop-free one, and two drop-free parcels. The initial values of DSD and other parameters of the parcels are taken from simulations of stratocumulus clouds using the Lagrangian trajectory ensemble model. It is shown that taking into account the non-conservativity of DSD makes the rate and the results of mixing strongly dependent on the mutual locations of the parcels. The effects of mixing increase with the deviation of the vertical profile of liquid water content (LWC) from the adiabatic one. If the upper parcel contains a larger LWC, the effect of mixing on the DSD is significantly weaker than for lower LWC in the upper parcel. Themixing near cloud base and cloud top is more intense. The standard method underestimates the rate of mixing near cloud top and overestimates it near cloud base. The proposed approach can serve as an efficient tool for investigating the role of mixing in Eulerian and Lagrangian models of stratocumulus and cumulus clouds.