Improving a Snow Growth Model with Application to Radar Quantitative Precipitation Estimates

This study improves a steady-state snow growth model (SGM) developed by Mitchell et al. (2006) that utilizes supersaturation, temperature and ice particle shape dependent mass-dimension power laws to predict the ice particle size distribution (PSD) by solving the zeroth- and second- moment conservation equations with respect to mass.  This SGM predicts the height evolution of the ice PSD through the growth processes of vapor diffusion and aggregation, and also through the PSD dependence on ice nucleation rates and the cloud updraft.

Ice particle growth rates are uniquely formulated in the SGM in terms of ice particle mass-dimension (m-D) power laws of the form m = αD^β, and in this way the impact of ice particle shape on particle growth rates and fall speeds is accounted for.  These growth rates appear qualitatively consistent with empirical growth rates based on wind-tunnel experiments by Takahashi and colleagues, with slower growth rates predicted for more isometric shapes (β near 3) and the highest growth rates predicted for the lowest β values. 

It is well known that for a given ice particle habit, the m-D power law for the smallest ice particles differs considerably from the power law for the largest particles, with β being much larger for the smallest crystals.  Our recent work quantitatively predicts β and α for cirrus clouds as a function of maximum dimension D where the m-D expression is a second-order polynomial (based on aircraft measurements of ice particle projected area and ground-based measurements of ice particle mass).  Moreover, a given m-D power law (predicted from the 2^nd order polynomial) is only valid over a given size range corresponding to a specific PSD moment.  This new m-D formulation was applied to the SGM by calculating α and β for the PSD moment of interest regarding the SGM equations.  By tailoring the m-D power law to the relevant PSD moments, the SGM ice particle growth rates and fall speeds should become more accurate and realistic.  This expectation will be tested by comparing predicted PSD with observed PSD obtained from spiral descents through widespread cirrus clouds, sampled during the Department of Energy/Atmospheric System Research (DOE/ASR) Small Particles In Cirrus (SPARTICUS) field campaign in 2010.

If these model improvements are realized, they will not be restricted to this SGM.  By implementing this m-D treatment in any cloud resolving model or climate model, the ice particle growth rates should become more accurate.  The height evolution of the ice PSD and ice water content based on a constant m-D power law will be contrasted with the same cloud properties based on the new m-D approach.

In addition to improving the modeling of cirrus clouds, this SGM can improve radar snowfall rate estimates. Since the lowest radar reflectivity (Z_w) over complex topography is often considerably above cloud base, radar quantitative precipitation estimates (QPE) often underestimate the precipitation at ground level.  Our SGM is capable of being initialized with Z_w (e.g. like at the lowest reliable radar echo) and consequently may improve QPE at ground level.