Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation
In numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integrat...
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Online Access: | http://dx.doi.org/10.1127/0941-2948/2014/0564 |
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doaj-8d22d85d6e6d4c30ab2d1a4542413be02020-11-24T22:34:36ZengBorntraegerMeteorologische Zeitschrift0941-29482014-09-0123441142310.1127/0941-2948/2014/056484223Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentationCorinna ZiemerGary JasorUlrike WackerKlaus D. BehengWolfgang PolifkeIn numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integration limit and a quadrature method, are applied to a one-dimensional test case (‘rainshaft’) for drop sedimentation. The results are compared with those of a reference spectral model. An error norm is introduced, which is based on several characteristic properties of the drop ensemble relevant to the cloud microphysics context. This error norm makes it possible to carry out a quantitative comparison between the two methods. It turns out that the two moment methods presented constitute an improvement regarding two-moment presumed-number-density-function methods from literature for a variety of initial conditions. However, they are excelled by a traditional three-moment presumed-number-density-function method which requires less computational effort. Comparisons of error scores and moment profiles reveal that error scores alone should not be taken for a comparison of parameterisations, since moment profile characteristics can be lost in the integral value of the error norm.http://dx.doi.org/10.1127/0941-2948/2014/0564cloud microphysicssedimentationmoment methodsquadraturegamma distributionerror norm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Corinna Ziemer Gary Jasor Ulrike Wacker Klaus D. Beheng Wolfgang Polifke |
spellingShingle |
Corinna Ziemer Gary Jasor Ulrike Wacker Klaus D. Beheng Wolfgang Polifke Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation Meteorologische Zeitschrift cloud microphysics sedimentation moment methods quadrature gamma distribution error norm |
author_facet |
Corinna Ziemer Gary Jasor Ulrike Wacker Klaus D. Beheng Wolfgang Polifke |
author_sort |
Corinna Ziemer |
title |
Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
title_short |
Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
title_full |
Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
title_fullStr |
Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
title_full_unstemmed |
Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
title_sort |
quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation |
publisher |
Borntraeger |
series |
Meteorologische Zeitschrift |
issn |
0941-2948 |
publishDate |
2014-09-01 |
description |
In numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integration limit and a quadrature method, are applied to a one-dimensional test case (‘rainshaft’) for drop sedimentation. The results are compared with those of a reference spectral model. An error norm is introduced, which is based on several characteristic properties of the drop ensemble relevant to the cloud microphysics context. This error norm makes it possible to carry out a quantitative comparison between the two methods. It turns out that the two moment methods presented constitute an improvement regarding two-moment presumed-number-density-function methods from literature for a variety of initial conditions. However, they are excelled by a traditional three-moment presumed-number-density-function method which requires less computational effort. Comparisons of error scores and moment profiles reveal that error scores alone should not be taken for a comparison of parameterisations, since moment profile characteristics can be lost in the integral value of the error norm. |
topic |
cloud microphysics sedimentation moment methods quadrature gamma distribution error norm |
url |
http://dx.doi.org/10.1127/0941-2948/2014/0564 |
work_keys_str_mv |
AT corinnaziemer quantitativecomparisonofpresumednumberdensityandquadraturemomentmethodsfortheparameterisationofdropsedimentation AT garyjasor quantitativecomparisonofpresumednumberdensityandquadraturemomentmethodsfortheparameterisationofdropsedimentation AT ulrikewacker quantitativecomparisonofpresumednumberdensityandquadraturemomentmethodsfortheparameterisationofdropsedimentation AT klausdbeheng quantitativecomparisonofpresumednumberdensityandquadraturemomentmethodsfortheparameterisationofdropsedimentation AT wolfgangpolifke quantitativecomparisonofpresumednumberdensityandquadraturemomentmethodsfortheparameterisationofdropsedimentation |
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