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Terminal Velocity Adjustments for Plate-like Crystals and Graupel

Kenneth V. BeardDepartment of Atmospheric Sciences, University of Illinois, Urbana, Illinois

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Andrew J. HeymsfieldNational Center for Atmospheric Research, Boulder, Colorado 80307

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Abstract

Velocity adjustments are evaluated for altitude changes using Reynolds number-Davies number correlations of the form Re = aXb which have been obtained from empirical fall velocities of ice particles. In general, the altitude adjustment was found to vary with both pressure and temperature, except for a temperature-independent range near b ≈ 0.7. A quantitative evaluation of b, using the drag on a sphere, shows that altitude adjustments for precipitation particles are less sensitive to changes in temperature than pressure, and that the net adjustment is reduced by compensation between the two effects. A comparison between the X-Re method of Heymsfield and Kajikawa (1987) and the Reynolds number method of Beard (1980), developed from drag data using models of hydrometeor shapes, yields similar velocity adjustments for altitude changes. The agreement suggests that X-Re formulas, based on X for ice particles of one type, but different masses, can also be used for altitude adjustments because the shape is relatively invariant for the small changes in X typical of altitude adjustments. For larger changes in X the constant shape method of Beard is suited to calculating velocity adjustments for charged particles whereas the empirical X-Re formulas of Heymsfield and Kajikawa are appropriate for computing velocities changes from riming.

Abstract

Velocity adjustments are evaluated for altitude changes using Reynolds number-Davies number correlations of the form Re = aXb which have been obtained from empirical fall velocities of ice particles. In general, the altitude adjustment was found to vary with both pressure and temperature, except for a temperature-independent range near b ≈ 0.7. A quantitative evaluation of b, using the drag on a sphere, shows that altitude adjustments for precipitation particles are less sensitive to changes in temperature than pressure, and that the net adjustment is reduced by compensation between the two effects. A comparison between the X-Re method of Heymsfield and Kajikawa (1987) and the Reynolds number method of Beard (1980), developed from drag data using models of hydrometeor shapes, yields similar velocity adjustments for altitude changes. The agreement suggests that X-Re formulas, based on X for ice particles of one type, but different masses, can also be used for altitude adjustments because the shape is relatively invariant for the small changes in X typical of altitude adjustments. For larger changes in X the constant shape method of Beard is suited to calculating velocity adjustments for charged particles whereas the empirical X-Re formulas of Heymsfield and Kajikawa are appropriate for computing velocities changes from riming.

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