A parameterization of sticking efficiency for collisions of snow and graupel with ice crystals: Theory and comparison with observations

A new parameterization of sticking efficiency for aggregation of ice crystals onto snow and graupel is presented. This parameter plays a crucial role for the formation of ice precipitation and for electrification processes. The parameterization is intended to be used in atmospheric models simulating the aggregation of ice particles in glaciated clouds. It should improve the ability to forecast snow. Based on experimental results and general considerations of collision processes, dependencies of the sticking efficiency on temperature, surface area, and collision kinetic energy of impacting particles are derived. The parameters have been estimated from some laboratory observations by simulating the experiments and minimizing the squares of the errors of the prediction of observed quantities. The predictions from the new scheme are compared with other available laboratory and field observations. The comparisons show that the parameterization is able to reproduce the thermal behavior of sticking efficiency, observed in published laboratory studies, with a peak around -15°C corresponding to dendritic vapor growth of ice. Finally, a new theory of sticking efficiency is proposed. It explains the empirically derived parameterization in terms of a probability distribution of the work that would be required to separate two contacting particles colliding in all possible ways among many otherwise identical collisions of the same pair with a given initial collision kinetic energy. For each collision, if this work done would exceed the initial collision kinetic energy, then there is no separation after impact. The probability of that occurring equals the sticking efficiency.