Evolution of Snow-Size Spectra in Cyclonic Storms. Part I: Snow Growth by Vapor Deposition and Aggregation

Abstract

Based on the stochastic collection equation, height- and time-dependent snow growth models were developed for unrimed stratiform snowfall. Moment conservation equations were parameterized and solved by constraining the size distribution to be of the form N(D)dD = N0 exp(?&lambdaD)dD, yielding expressions for the slope parameter, ?, and the y-intercept parameters, NO, as functions of height or time. The processes of vapor deposition and aggregation were treated analytically without neglecting changes in ice crystal habits, while the ice particle breakup process was dealt with empirically. The models were compared against vertical profiles of snow-size spectra, obtained from aircraft measurements, for three case studies. The predicted spectra are in good agreement with the observed evolution of snow-size spectra in all three cases, indicating the proposed scheme for ice particle aggregation was successful. The temperature dependence of aggregation was assumed to result from differences in ice crystal habit. Using data from an earlier study, the aggregation efficiency between two levels in a cloud was calculated. Finally, other height-dependent, steady-state snowfall models in the literature were compared against spectra from one of the above case studies. The agreement between the predicted and observed spectra regarding these models was less favorable than was obtained from the models presented here.