A new snow growth model with application to radar precipitation estimates

This study describes the development of a snow growth model (SGM) that predicts the vertical evolution of ice particle size spectra based on the relative humidity or supersaturation. It is analytically formulated in terms of the processes concerning vapor diffusion and aggregation, ice crystal nucleation and cloud updrafts. By solving the moment conservation equations for number concentration and radar reflectivity, these processes are interrelated analytically, resulting in an accurate description of complex processes yet with reduced computation time relative to numerical treatments of these processes.An equation relating the properties of ice particles and the size distribution to the ice water content and the radar reflectivity was developed that allows the SGM to be initialized with operational radar reflectivities (Zw). It thus has potential use in quantitative precipitation estimates (QPE), since the lowest Zw over mountainous regions is often well above cloud base. By initializing the SGM with the lowest radar echo, the SGM may provide improved estimates of snowfall rate and amount at ground level, as demonstrated in a case study.The predicted evolution of ice particle size spectra appear to be typical of the observed evolution of size spectra in frontal clouds. Size distributions (SD) are predicted to be superexponential, with crystals less than about 200 μm in length having greater concentrations than predicted by exponential fits to the SD. A one-dimensional steady-state formulation of the SGM was tested by initializing it at cloud top for a frontal cloud case study. The predicted vertical evolution of ice particle size, concentration and ice water content agreed favorably with those observed.The SGM provides a potential explanation to a long standing mystery, which is why the SD slope λ is approximately constant in the lower regions of most frontal clouds. The reason is that aggregation broadens the SD until the dispersion in fall velocities becomes so small that aggregation growth is effectively terminated. Thereafter the SD broadens by diffusional growth only, with λ decreasing at a much slower rate.The SGM also predicts that the evolution of size spectra and the snowfall rate are sensitive to changes in ice particle shape for a given vertical profile of supersaturation. It is not likely that current cloud resolving models account for this predicted sensitivity.