Parameterization of Autoconversion for Turbulent Kernels

New sets of collision efficiencies were obtained by Khain-Pinsky for turbulent environments characterized by different energy dissipation rates. The objective of this study was exploring an inexpensive way to take into account the effects of turbulence on autoconversion, as the explicit solution of the SCE is too computationally expensive to be considered within most atmospheric models. Certain properties of the stochastic collection equation (SCE) solutions have been studied using the above-mentioned collision efficiencies for 5 different energy dissipation rates. The numerical scheme to solve the SCE is based on direct integration and its general structure is similar to that proposed by Berry and Reinhardt(BR). However, a finer partition partition was used to maximize the accuracy of the solutions. The mass spectrum was discretized into 110 categories between 2 and approximately 1000 microns (mass doubling every 4 categories). Initial droplet spectra were characterized mean mass radii ranging from 10 to 18 microns and mass relative variances between 0.2 and 1. Evolutions have shown the same features that lead to the widely used BR's parameterization for a non-turbulent collection kernel. As expected, the time necessary for the predominant radius to reach 40 microns (T40) decreased significantly when considering a more turbulent environment (and the same initial spectrum). However, an remarkable asymptotic behavior was observed for all turbulent kernels: size spectra resulted almost identical when they were compared at given times of evolution after their corresponding T40, independently of parameters of the initial distribution. The water mass that corresponds to drops with radii above 40 microns at T40 (Q40) have been obtained for more than thousand simulations corresponding to different initial parameters and turbulent dissipation rates. As an autoconversion rate can be expressed in terms of the ratio Q40/Q40, functional fits were obtained for these two quantities. Therefore, an expression analogous to that of BR was obtained for each turbulent dissipation rate. Additionally, a second set of formulae was adjusted to be used as factors multiplying an existing (non- turbulent) autoconversion parameterization, or to build a look-up table if the model is able to estimate the intensity of the turbulence.