LAUSR

The major formation pathway of ice crystals in the low-temperature regime below $${235}\hbox { K}$$235K is homogeneous freezing of solution droplets. This mechanism is known to be very sensitive to environmental conditions, i.e., temperature and humidity. Nucleation events are characterized by an explosive increase in ice crystal number concentrations. For a better understanding of ice nucleation in this temperature regime, we have to analyze these nucleation events carefully. In this study, we consider the description of a single nucleation event using a slightly simpler system which features the same sharp increase in ice crystal number concentration. We analyze the simpler system with the help of asymptotic methods and construct a leading order approximation to the exact solution. This gives insight into a single homogeneous nucleation event from a mathematical perspective, without introducing further assumptions apart from the transition to the simplified system. In addition, we use the asymptotic approximation to construct a new parameterization, relating the updraft velocity to the homogeneously nucleated number of ice crystals, and compare the results with a widely used parameterization.