Abstract
Abstract. The time-dependent freezing rate (TDFR) model here described represents the formation of ice particles by immersion freezing within an air parcel. The air parcel trajectory follows an adiabatic ascent and includes a period in time when the parcel remains stationary at the top of its ascent. The description of the ice nucleating particles (INPs) in the air parcel is taken from laboratory experiments with cloud and precipitation samples and is assumed to represent the INP content of the cloud droplets in the parcel. Time dependence is included to account for variations in updraft velocity and for the continued formation of ice particles under isothermal conditions. The magnitudes of these factors are assessed on the basis of laboratory measurements. Results show that both factors give rise to three-fold variations in ice concentration for a realistic range of the input parameters. Refinements of the parameters specifying time dependence and INP concentrations are needed to make the results more specific to different atmospheric aerosol types. The simple model framework described in this paper can be adapted to more elaborate cloud models. The results here presented can help guide decisions on whether to include a time-dependent ice nucleation scheme or a simpler singular description in models.
Highlights
While it is widely recognized that the formation of ice is a major factor in the evolution of many tropospheric clouds and in the formation of precipitation, formulations of ice nucleation in cloud models are still tentative
This paper presents an implementation of the laboratory results of Vali (1994) in an adiabatic parcel model called the time-dependent freezing rate (TDFR) model
The TDFR model demonstrates that the time dependence of ice nucleation can be taken into account within cloud models in a relatively simple manner
Summary
While it is widely recognized that the formation of ice is a major factor in the evolution of many tropospheric clouds and in the formation of precipitation, formulations of ice nucleation in cloud models are still tentative. The large spatial, temporal, and compositional variability of atmospheric aerosols, and of the subset of ice nucleating particles (INPs), makes generalizations difficult This difficulty has been well documented in the literature because it is a problem for other aspects of cloud and climate models as well. All forms of the parameterization treat ice nucleation as a function of temperature This is done with either the number of ice nucleation events or their rate per unit time as the starting point. Laboratory measurements with water samples, as those of Vali (1994), have the advantage of direct observations of the time dependence of ice nucleation This aspect of the model has a solid foundation within the limits of available data. For isothermal conditions, the stochastic description leads to overestimates compared to either the singular description or the TDFR model
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