Immersion freezing in particle-based aerosol-cloud microphysics: a probabilistic perspective on singular and time-dependent models

Abstract

Cloud droplets containing ice-nucleating particles (INPs) may freeze at temperatures above the homogeneous freezing threshold temperature. This process, referred to as immersion freezing, is one of the modulators of aerosol-cloud interactions in the Earth's atmosphere. In modeling studies, immersion freezing is often described using either so-called "singular" or "time-dependent" parameterizations. Here, we juxtapose both approaches and discuss them in the context of probabilistic particle-based cloud microphysics modeling. First, using a box model, we contrast how both parameterizations respond to different idealized ambient cooling rate profiles and quantify the impact of the polydispersity of the immersed surface spectrum on the frozen fraction evolution. Second, using a prescribed-flow two-dimensional cloud model, we illustrate the implications of applying the singular model in simulations with flow regimes relevant to ambient cloud conditions rather than to the cloud-chamber experiments on which these parameterizations are built upon. We discuss the critical role of the attribute-space sampling strategy for particle-based model simulations in modeling heterogeneous ice nucleation which is contingent on the presence of relatively sparse immersed INPs. The key takeaways include: (i) The singular approach, constituting a time-integrated form of a more general time-dependent approach, is only applicable under a limited range of ambient cooling rates. (ii) The time-dependent approach, especially when based on water-activity, is suitable for integration with particle-based model components of detailed aerosol composition and collisional growth/breakup. (iii) A flow-coupled aerosol-budget-resolving simulation shows the benefits and challenges of modeling cloud condensation nuclei activation and immersion freezing on insoluble ice nuclei with super-particle methods.