Our current research has been focused on numerical experiments using a nonhydrostatic cloud model. The objective has been to examine the relationship between vertical mass flux in deep convection and microphysical processes in a variety of convectively active environments. We have taken this approach to develop better understanding of the governing physical processes rather than to develop an algorithm based on model output.

The compressible nonhydrostatic option of the Regional Atmospheric Modeling System is used in this study. The model is run in two dimensions, with a domain 1000 km wide and 23 km in height, periodic in the east-west direction. The Coriolis force is included. The horizontal grid interval is 1 km, with a vertical grid interval of 300 m at the lower boundary, increasing gradually to 900 m above 13 km

All experiments were run for 12 hours, and time series of horizontally and vertically integrated precipitating ice content and time series of one-minute averages of horizontally and vertically integrated cloud mass flux above the melting level were computed for each experiment. The cloud mass flux, separately for updrafts and for all cloudy grid points, was integrated vertically from the 0 C level up to cloud top.

The time series for the first experiment are shown in Fig. 1. Convection grows rapidly from the initial perturbation and is sustained until it dissipates over a few hours, beginning at around sunset. As expected, ice forms in a cloud updraft and remains aloft not only while the strength of the updraft fluctuates, but also for some time after the updraft dissipates. The resulting time series of ice lags and is smoother than the time series of vertically integrated mass flux. Therefore, in order to derive a diagnostic relationship between ice and vertically integrated cloud mass flux, each point in the time series of mass fluxes was replaced by the average over the previous 60 minutes. As seen in Fig. 2, the ice content multiplied by 310 matches the smoothed net mass flux.

By computing root-mean-square differences between the smoothed time series of cloud mass flux and various multiples of the time series of ice, the best fit between ice and smoothed cloud mass flux was determined for each simulation. These ratios between time series of ice and time series of mass flux averaged over the previous hour vary among the simulations. By analyzing the physical mechanisms that produce these differences in the simulations, we have identified the independent variables that can be used in an observational study to derive a relationship between ice and cloud mass flux. Our findings are summarized as follows:

1. The ratios of precipitating ice to vertically integrated updraft and net mass fluxes are sensitive to the in- cloud water vapor mixing ratio at the freezing level. Colder atmospheres thus show less ice production for a given amount of integrated updraft only and net mass flux. This effect has by far the most impact on relationships between ice and vertical mass fluxes. One might expect the in-cloud water vapor mixing ratio estimated by simple parcel theory to be quite accurate in most situations.
2. In this 2-D model, cloudy downdrafts at upper levels are a pervasive and largely stable fraction of the updraft mass flux.
3. Large changes in the ratio of graupel to total ice do not produce large changes in the ice mass to vertical mass flux relationship.
4. Sensitivity to vertical wind shear is present but small in these 2-D simulations with net cloud mass flux to ice ratios varying by approximately 10% in the three different shears examined for maritime and continental clouds.

The consistent, repeatable patterns in the ratios of ice to integrated vertical mass fluxes, and the fact that differences between experiments are related to gross thermodynamics of the environmental sounding are encouraging for future studies that might try to relate precipitating ice signatures as seen by microwave imagers in space (e.g. SSM/I and SSM/T2) to bulk vertical motion in cloud systems. Fig. 1. Time series of horizontally and vertically integrated 2D precipitating ice (10**4 kg/m; dotted), and upward (dashed) and net (solid) cloud mass flux above the 0 deg C level ( (10**7 kg m/s) /m). Fig. 2. Time series of horizontally and vertically integrated 2D precipitating ice (10**4 kg/m; dotted), multiplied by 310, and net cloud mass flux above the 0 deg C level ( (10**7 kg m/s) /m,dashed) smoothed by replacing each point with the mean of the previous 60 minutes.