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On the numerical treatment of hydrometeor sedimentation in bulk and hybrid bulk–bin microphysics schemes

Abstract

Hybrid bulk--bin microphysics schemes discretize particle size distributions into bins for calculating microphysical process rates, while retaining a limited number of bulk prognostic quantities and assuming an underlying analytic functional form for the particle size distributions as in traditional bulk microphysics schemes. In this paper, the treatment of sedimentation in two-moment bulk and hybrid schemes is compared using different numerical methods. Using the first-order upwind method for calculating sedimentation in conjunction with a widely used, two-step, time-splitting approach that updates model fields after transport by air motion followed by calculation of sedimentation, it is shown analytically that despite using a spectrum of fall speeds corresponding to different particle sizes, hybrid schemes converge with increasing bin resolution toward bulk schemes that utilize only characteristic moment-weighted particle fall speeds. While not strictly convergent, it is also shown that solutions using bulk and hybrid schemes are often similar for other numerical methods and approaches. Noticeable improvement using the hybrid scheme occurs in a few circumstances: when the Courant number associated with falling precipitation is large (>>1), requiring substepping, semi-implicit, or Lagrangian-type methods for numerical stability; or when a one-step approach is employed that calculates hydrometeor transport in a single step using a velocity that combines both vertical air motion and particle fall speed. Thus, it is concluded that the use of hybrid rather than bulk schemes is justified for some, but not all, applications, and care should be taken to determine the appropriateness of hybrid schemes for specific applications.

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http://n2t.net/ark:/85065/d7p84cjb

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eng

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geoscientificInformation

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publication

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2016-01-01T00:00:00Z

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2012-05-01T00:00:00Z

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Copyright 2012 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be "fair use" under Section 107 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC, as revised by P.L. 94-553) does not require the Society's permission. Republication, systematic reproduction, posting in electronic form on servers, or other uses of this material, except as exempted by the above statements, requires written permission or license from the AMS. Additional details are provided in the AMS Copyright Policies, available from the AMS at 617-227-2425 or amspubs@ametsoc.org. Permission to place a copy of this work on this server has been provided by the AMS. The AMS does not guarantee that the copy provided here is an accurate copy of the published work.

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OpenSky Support

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UCAR/NCAR - Library

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PO Box 3000

Boulder

80307-3000

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opensky@ucar.edu

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