Statistical properties of a stochastic model of eddy hopping

Abstract. Statistical properties are investigated for the stochastic model of eddy hopping, which is a novel cloud microphysical model that accounts for the effect of the supersaturation fluctuation at unresolved scales on the growth of cloud droplets and on spectral broadening. It is shown that the model fails to reproduce a proper scaling for a certain range of parameters, resulting in a deviation of the model prediction from the reference data taken from direct numerical simulations and large-eddy simulations (LESs). Corrections to the model are introduced so that the corrected model can accurately reproduce the reference data with the proper scaling. In addition, a possible simplification of the model is discussed, which may contribute to a reduction in computational cost while keeping the statistical properties almost unchanged in the typical parameter range for the model implementation in the LES Lagrangian cloud model.