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A novel type of limited double-moment scheme for bulk microphysics is presented here for cloud-systemresolving models (CSRMs). It predicts the average size of cloud droplets and crystals, which is important for representing the radiative impact of clouds on the climate system. In this new scheme, there are interactive components for ice nuclei (IN) and cloud condensation nuclei (CCN). For cloud ice, the processes of primary ice nucleation, Hallett-Mossop (HM) multiplication of ice particles (secondary ice production), and homogeneous freezing of aerosols and droplets provide the source of ice number. The preferential evaporation of smaller droplets during homogeneous freezing of cloud liquid is represented for the first time. Primary and secondary (i.e., in cloud) droplet nucleation are also represented, by predicting the supersaturation as a function of the vertical velocity and local properties of cloud liquid. A linearized scheme predicts the supersaturation, explicitly predicting rates of condensation and vapor deposition onto liquid (cloud liquid, rain) and ice (cloud ice, snow, graupel) species. The predicted supersaturation becomes the input for most nucleation processes, including homogeneous aerosol freezing and secondary droplet activation.

Comparison of the scheme with available aircraft and satellite data is performed for two cases of deep convection over the tropical western Pacific Ocean. Sensitivity tests are performed with respect to a range of nucleation processes. The HM process of ice particle multiplication has an important impact on the domain-wide ice concentration in the lower half of the mixed-phase region, especially when a lack of upper-level cirrus suppresses homogeneous freezing. Homogeneous freezing of droplets and, especially, aerosols is found to be the key control on number and sizes of cloud particles in the simulated cloud ensemble. Preferential evaporation of smaller droplets during homogeneous freezing produces a major impact on ice concentrations aloft. Aerosols originating from the remote free troposphere become activated in deep convective updrafts and produce most of the supercooled cloud droplets that freeze homogeneously aloft. Homogeneous aerosol freezing is found to occur only in widespread regions of weak ascent while homogeneous droplet freezing is restricted to deep convective updrafts. This means that homogeneous aerosol freezing can produce many more crystals than homogeneous droplet freezing, if conditions in the upper troposphere are favorable.

These competing mechanisms of homogeneous freezing determine the overall response of the ice concentration to environmental CCN concentrations in the simulated cloud ensemble. The corresponding sensitivity with respect to environmental IN concentrations is much lower. Nevertheless, when extremely high concentrations of IN are applied, that are typical for plumes of desert dust, the supercooled cloud liquid is completely eliminated in the upper half of the mixed phase region. This shuts down the process of homogeneous droplet freezing.