On the droplet spectral broadening numerics

Owing to its key role in determining both the droplet collision probabilities and the radiative-transfer-relevant spectrum characteristics, the evolution of droplet spectral width has long been the focus of cloud modelling studies. Cloud simulations with detailed treatment of droplet microphysics face a twofold challenge in prognosing the droplet spectrum width. First, it is challenging to model and numerically represent the subtleties of condensational growth, even more so when considering the interplay between particle population dynamics and supersaturation fluctuations. Second, the discretisation strategies employed in representing the particle size spectrum and its evolution are characterised by inherent limitations. 

In the poster, we will present results of both Eulerian and Lagrangian numerical representations of spectrum width evolution. In the case of Lagrangian approach, we will discuss the differences in numerical integration procedures between (a) the sophisticated solvers typically used in parcel-model frameworks with moving-sectional spectrum representation and (b) the simpler solvers typically used in mathematically-analogous particle-based (super-droplet) microphysics representations used in multi-dimensional models.

In the case of Eulerian (bin microphysics) approach, we will present condensational growth simulations performed with the MPDATA numerical scheme using the newly developed MPyDATA package (http://github.com/atmos-cloud-sim-uj/MPyDATA/). The MPDATA family of numerical schemes for solving advective transport problems has been in continuous development for almost four decades. MPDATA features a variety of options allowing to pick an algorithm variant appropriate to the problem at hand. We will focus on the importance the MPDATA algorithm variant choice and the grid setup for the resultant numerical diffusion.

In the case of Lagrangian approach, we will present simulations performed using the newly developed PySDM package (https://github.com/atmos-cloud-sim-uj/PySDM) that features a set of cloud microphysics algorithms including condensational growth solvers. In the discussion, we will focus on: (a) the numerical realisability of the Ostwald ripening process (i.e. the growth of larger particles at the expense of water content of the smaller ones) and (b) the numerical approaches available for integrating stochastic fluctuations of ambient thermodynamic properties that drive the water vapour saturation.