Original paper

Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation

Ziemer, Corinna; Jasor, Gary; Wacker, Ulrike; Beheng, Klaus D.; Polifke, Wolfgang

Meteorologische Zeitschrift Vol. 23 No. 4 (2014), p. 411 - 423

31 references

published: Sep 26, 2014
published online: Aug 27, 2014
manuscript accepted: May 28, 2014
manuscript revision received: May 28, 2014
manuscript revision requested: Mar 2, 2014
manuscript received: Dec 13, 2013

DOI: 10.1127/0941-2948/2014/0564

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Abstract

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.

Keywords

cloud microphysicssedimentationmoment methodsquadraturegamma distributionerror norm