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Cloud droplets containing ice-nucleating particles (INPs) may freeze attemperatures above than the homogeneous freezing threshold. This process,referred to as immersion freezing, is one of the major modulator ofaerosol-cloud interactions in the Earth's atmosphere that impacts cloudradiative properties, and thus, climate. In modeling studies, immersionfreezing is often implemented using either so-called "singular" or"time-dependent" parameterizations. In this paper, we juxtapose both approachesand discuss them in the context of probabilistic particle-based cloudmicrophysics modeling, referred to as the super-particle or super-droplettechniques. These techniques work by populating the particle-attribute phasespace with large numbers of computational particles and tracking the evolutionof particle attributes. We outline the congruence of the singular andtime-dependent approaches with Poissonian process description and point tolimitations pertinent to the singular approach. Simulations with both box andtwo-dimensional kinematic models focus on the following aspects of immersionfreezing modeling. First, we contrast how both parameterizations respond todifferent idealized ambient cooling rate profiles. Second, we quantify how thepolydispersity of the immersed surface spectrum impacts macroscopic features ofthe system. Third, we illustrate the implications of applying the singularmodel in simulations with flow regimes relevant to ambient cloud conditionsrather than to the cloud-chamber experiments on which these parameterizationsare built upon. We discuss the critical role of the attribute-space samplingstrategy for particle-based model simulations in modeling heterogeneous icenucleation which is contingent on the presence of relatively sparse immersedINPs.

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