A new parameterisation for homogeneous ice nucleation driven by highly variable dynamical forcings

Abstract. The present work aims to extend the parameterisation of homogeneous ice nucleation introduced in Dolaptchiev et al. (2023) by incorporating variable ice mean mass and generalizing the approach under different conditions. The proposed method involves introducing an empirically derived correction based on a large data set of parcel model simulations. The method is validated against ensemble simulations using double-moment ice microphysics, showing a mean deviation of less than 16 % from the reference solution, with robust performance across a range of conditions. The uncertainty of the extended parameterisation is evaluated for the increasing integration time steps. The method remains computationally efficient and produces sufficiently accurate results, even with larger time steps, making it suitable for integration into numerical weather prediction models. It is shown that the generalized approach not only provides a good representation of individual nucleation events but also effectively captures the statistics across the ensemble data. The prediction of ice mixing ratio is also assessed against the reference full double-moment system results. Despite a significant error in the initial prediction, it is demonstrated that the integration of the system over several time steps equilibrates the inconsistencies. This refined parameterisation offers a more accurate prediction of ice number concentration and ice mixing ratio and is not limited to gravity wave induced perturbations and can be supplemented by other relevant dynamical effects, such as turbulence.