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

Abstract

Abstract. This study presents a comprehensive ice cloud formation parameterization that computes the ice crystal number, size distribution, and maximum supersaturation from precursor aerosol and ice nuclei with any size distribution and chemical composition. The parameterization provides an analytical solution of the cloud parcel model equations and accounts for the competition effects between homogeneous and heterogeneous freezing, and, between heterogeneous freezing in different modes. The diversity of heterogeneous nuclei is described through a nucleation spectrum function which is allowed to follow any form (i.e., derived from classical nucleation theory or from empirical observations). The parameterization reproduced the predictions of a detailed numerical parcel model over a wide range of conditions, and several expressions for the nucleation spectrum. The average error in ice crystal number concentration was −2.0±8.5% for conditions of pure heterogeneous freezing, and, 4.7±21% when both homogeneous and heterogeneous freezing were active. Apart from its rigor, excellent performance and versatility, the formulation is extremely fast and free from requirements of numerical integration.