Spurious Broadening of Modeled Cloud Droplet Spectra Using Bin Microphysics in an Eulerian Spatial Domain

This study investigates numerical errors that arise when modeling condensational growth and droplet spatial transport using bin microphysics. The two-moment top hat method-of-moments, a state-of-the-art approach for solving condensational growth in bin schemes, accurately evolves the droplet size distribution (DSD) for a rising parcel compared to benchmark analytic and Lagrangian solutions, especially using fine bin resolution. However, when combined with vertical advection in an Eulerian dynamical framework, there is considerable artificial DSD broadening even though profiles of bulk cloud mass and mean radius are accurately simulated. This DSD broadening is caused by numerical diffusion in physical space that leads to excessive diffusion in mass space. Broad DSDs in turn lead to significant collision-coalescence growth being diagnosed. Error increases with the droplet growth rate, and hence increases as the droplet number is decreased. Over the same range of Courant-Friedrichs-Lewy number, artificial broadening decreases as the grid spacing is decreased but there is less sensitivity to vertical velocity and little sensitivity to time step. Increasing the bin resolution does not reduce error, nor in general does using higher- compared to lower-order spatial advection schemes. Large eddy simulations of warm stratocumulus using bin microphysics that includes only droplet activation, condensation, and evaporation show signatures of this problem, particularly the occurrence of broad DSD tails and large drops near cloud base. It is concluded that the DSD shape and initial generation of rain in bin schemes coupled with Eulerian dynamical models may often be influenced by numerical errors from the combination of condensational growth and advection, and care should be taken when interpreting results from such models.

A correction to this problem that limits spurious DSD broadening is proposed and tested within the one-dimensional framework. This method combines condensational growth and advection in physical space in a single step, and numerically calculates advection and growth based on the concept of a growth “potential”. Bulk mass and number mixing ratios are conserved by separately advecting these quantities and adjusting the DSDs for consistency.