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| Titel |
Analyzing numerics of bulk microphysics schemes in community models: warm rain processes |
| VerfasserIn |
I. Sednev, S. Menon |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 5, no. 4 ; Nr. 5, no. 4 (2012-08-03), S.975-987 |
| Datensatznummer |
250002767
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| Publikation (Nr.) |
 copernicus.org/gmd-5-975-2012.pdf |
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| Zusammenfassung |
Implementation of bulk cloud microphysics (BLK) parameterizations
in atmospheric models of
different scales has gained momentum in the last two decades.
Utilization of these parameterizations in cloud-resolving models when timesteps used for the host
model integration are a few seconds or less is justified from the point of view of cloud physics.
However, mechanistic extrapolation
of the applicability of BLK schemes
to the regional or global scales and the utilization
of timesteps of hundreds up to thousands of seconds affect both physics and
numerics.
We focus on the mathematical aspects of BLK schemes, such as
stability and positive-definiteness. We provide a strict mathematical definition for the
problem of warm rain formation. We also derive a general analytical condition
(SM-criterion) that remains valid regardless of parameterizations for warm rain
processes in an explicit Eulerian
time integration framework used to advanced finite-difference equations, which
govern warm rain formation processes in microphysics packages in
the Community Atmosphere Model and the Weather Research and Forecasting model.
The SM-criterion
allows for the
existence of a unique positive-definite stable mass-conserving numerical solution, imposes
an additional constraint on the timestep permitted due to the microphysics
(like the Courant-Friedrichs-Lewy condition for the advection equation), and prohibits use of any
additional assumptions not included in the strict mathematical definition of the
problem under consideration.
By analyzing the numerics of warm rain processes in source codes
of BLK schemes implemented
in community models we provide general guidelines regarding
the appropriate choice
of time steps in these models. |
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