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This study presents a comprehensive ice cloud formation parameterizationthat computes the ice crystal number, size distribution, and maximumsupersaturation from precursor aerosol and ice nuclei. The parameterizationprovides an analytical solution of the cloud parcel model equations andaccounts for the competition effects between homogeneous and heterogeneousfreezing, and, between heterogeneous freezing in different modes. Thediversity of heterogeneous nuclei is described through a nucleation spectrumfunction which is allowed to follow any form (i.e., derived from classicalnucleation theory or from observations). The parameterization reproduces thepredictions of a detailed numerical parcel model over a wide range ofconditions, and several expressions for the nucleation spectrum. The averageerror in ice crystal number concentration was −2.0±8.5% forconditions of pure heterogeneous freezing, and, 4.7±21% when bothhomogeneous and heterogeneous freezing were active. The formulationpresented is fast and free from requirements of numerical integration

Parameterizing the competition between homogeneous and heterogeneous freezing in ice cloud formation – polydisperse ice nuclei