Evaporation of cloud particles: solutions to the population balance equation and formulation of memory based bulk schemes (MBBS, v1.0)

Abstract. One of the main cloud processes is the annihilation of particles by evaporation. If the saturation ratio drops below the equilibrium level, water evaporates and diffusion transports the water vapor through the environment of the particles. While other cloud processes are investigated carefully, evaporation is somewhat neglected, and the process' formulation in models is quite simplified. In this contribution, we investigate evaporation using the population balance equation (PBE) for mass distributions. A simplified regime is chosen which allows analytical treatment of the evaporation process. The theoretical results justify the inclusion of memory variables in evaporation modeling. We develop a family of Memory-Based Bulk Schemes (MBBS) that improve the representation of number concentration loss during evaporation by tracking memory variables of the particle mass distribution. We focus on number concentration because, unlike the mass concentration, its evaporation rate depends on a point-wise value of the distribution and therefore cannot be captured reliably by standard moment-based closures. Comparisons against the full PBE solutions for idealized downdraft and oscillatory scenarios show that the higher-complexity MBBS variants, in particular the two-memory-variable scheme, substantially improve the representation of number concentration during evaporation.