Corinna Ziemer

Parameterization of the Sedimentation of Raindrops with Finite Maximum Diameter

In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model.

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 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.