Examination of an improved quasi‐stochastic model for the collisional growth of drops

Abstract

The evolution of cloud drop size distribution due to the collision‐coalescence process is generally described by a quasi‐stochastic model that solves the stochastic collection equation in a deterministic way. In this study, an improved quasi‐stochastic (IQS) model, which is derived by rigorously considering a finite model time step, is examined in the context of comparison with the normal quasi‐stochastic (NQS) model. The IQS model allows a large collector drop to collide with a small collected drop more than one time in a model time step even if the collision probability is small. The number distribution of collector drops then follows the Poisson distribution with respect to the number of collisions. Using a box model that takes turbulence‐induced collision enhancement into account, it is found that large drops in the IQS model tend to have larger sizes than those in the NQS model and that the IQS model accelerates large‐drop formation by a few minutes compared to the NQS model. The effects of the IQS model depend on the model time step and the shape of initial drop size distribution. The IQS model is incorporated into a detailed bin microphysics scheme that is coupled with the Weather Research and Forecasting model, and a single warm cloud is simulated under idealized environmental conditions. It is found that the onset of surface precipitation is accelerated in the IQS model.

Evaluation of an Improved Quasi‐stochastic Collection Model Through Precipitation Prediction Over North Central Mongolia

“…The increased drop mass content in the small drop range in the IQS model results from the difference between the IQS and NQS models. However, unlike in the box model and idealized two‐dimensional simulations (Lkhamjav et al, ), in the real‐case simulation (the present study), it seems to be very difficult to find detailed reasons for the increased drop mass content in the small drop range because of the increased complexity. More activation of CCN due to the increase in upward motion can be a reason.…”

“…Many precipitation events are required to examine the impacts of the IQS model on cloud and precipitation processes, which could vary with environmental conditions, deserving an investigation. Lkhamjav et al () indicated that the effects of aerosols on the evolution of drop size distribution can be modulated by the IQS model. Aerosol effects on clouds and precipitation in the IQS model through real‐case simulations need to be also investigated to better understand cloud‐aerosol‐precipitation interactions.…”

“…Compared to Lee and Baik (), the bin microphysics scheme is further improved by considering the IQS model in which the multiple collisions of cloud particles within a time step are allowed (Lkhamjav et al, ; Young, ). If collisions of cloud particles in the i th and j th bins are considered, the rate of the change of number concentration is given as (e.g., Lkhamjav et al, ) where n i and n j are the number concentrations of cloud particles in the i th and j th bins, respectively; K ij is the collection kernel between the i th and j th bins; and Δ t is the time step. The NQS model assumes an infinitesimally small time step within which a cloud particle either collides with other cloud particle once or does not collide.…”

“…However, since the time step used is finite, a cloud particle can collide with other cloud particle more than one time within the time step. By taking account of this, the probability distribution of the number of collisions within a time step can be expressed as a Poisson distribution (Lkhamjav et al, ; Young, ). Lkhamjav et al () simulated an idealized two‐dimensional warm cloud using the improved quasi‐stochastic (IQS) model and demonstrated that the onset of surface precipitation is accelerated as much as several minutes due to multiple collisions of cloud particles within a time step compared to the normal quasi‐stochastic (NQS) model.…”

“…By taking account of this, the probability distribution of the number of collisions within a time step can be expressed as a Poisson distribution (Lkhamjav et al, ; Young, ). Lkhamjav et al () simulated an idealized two‐dimensional warm cloud using the improved quasi‐stochastic (IQS) model and demonstrated that the onset of surface precipitation is accelerated as much as several minutes due to multiple collisions of cloud particles within a time step compared to the normal quasi‐stochastic (NQS) model. As a next research step, it would be meaningful to examine differences in surface precipitation when the IQS and NQS models are compared through real‐case prediction and find reasons for the differences.…”