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 generalising the approach under different conditions. The proposed method involves introducing an empirically derived correction to the parameterisation based on a large data set of parcel model simulations to account for the mean ice particle mass variations. The method is validated against ensemble simulations using time-resolved double-moment ice microphysics, showing a mean relative error of less than 16 %, with robust performance across a range of conditions. The uncertainty of the proposed parameterisation is evaluated for 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 and climate models. It is shown that the generalised approach not only provides a good representation of individual nucleation events but also effectively captures the statistics across the ensemble data. The prediction of the ice mixing ratio is also assessed against the reference double-moment system results. It is demonstrated that, following the nucleation event and re-initialisation of the ice mixing ratio, the system equilibrates toward the reference solution within a few time steps. This refined parameterisation offers a more accurate prediction of ice number concentration and ice mixing ratio, is not limited to perturbations induced by gravity waves (GWs), and can be supplemented by other relevant dynamical effects, such as large-scale motions or even turbulence.