K. D. Beheng

A parameterization of warm cloud microphysical conversion processes

Abstract A parameterization scheme is presented by which coagulation growth of drops is simulated. It is oriented at the common parameterization idea of partitioning the total water substance in a cloud water and a rainwater portion. This concept is accordingly applied to the stochastic collection equation by which the time evolution of a drop spectrum is described. Thus, the distinct conversion rates selfcollection, autoconversion and accretion can mathematically be formulated for number and mass densities of cloud water and rainwater which can then be numerically evaluated. With these results as standards a new parameter scheme is developed whose constituting equations consist in rates combining number and mass densities as well as a width parameter. The range of variables for which this parameterization is valid covers a wide range of relevant cloudphysical variables. Comparisons with other parameterizations are presented.

Modeling artifacts in the simulation of the sedimentation of raindrops with a Quadrature Method of Moments

The Quadrature Method of Moments (QMoM) is applied to a one-dimensional test case for sedimentation of raindrops. Comparison of the results with a reference spectral method exhibits discrepancies (“step patterns”) that must be considered as modeling artifacts. As the QMoM has been demonstrated to be effective and accurate in various contexts, the origin of these artifacts is investigated and found to be related to the transport of the quadrature abscissas. Further test cases are considered to examine the influence of different initial conditions on the development of the modeling artifacts. The study shows that these artifacts are inherent to the application of QMoM in pure sedimentation context.

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.

Influence of turbulence on the drop growth in warm clouds, Part I: comparison of numerically and experimentally determined collision kernels

This study deals with the comparison of numerically and experimentally determined collision kernels of water drops in air turbulence. The numerical and experimental setups are matched as closely as possible. However, due to the individual numerical and experimental restrictions, it could not be avoided that the turbulent kinetic energy dissipation rate of the measurement and the simulations differ. Direct numerical simulations (DNS) are performed resulting in a very large database concerning geometric collision kernels with 1470 individual entries. Based on this database a fit function for the turbulent enhancement of the collision kernel is developed. In the experiments, the collision rates of large drops (radius > 7.5μm

Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds

> 7.5,text{textmu{}m}

Influence of turbulence on the drop growth in warm clouds, Part II: Sensitivity studies with a spectral bin microphysics and a Lagrangian cloud model

) are measured. These collision rates are compared with the developed fit, evaluated at the measurement conditions. Since the total collision rates match well for all occurring dissipation rates the distribution information of the fit could be used to enhance the statistical reliability and for the first time an experimental collision kernel could be constructed. In addition to the collision rates, the drop size distributions at three consecutive streamwise positions are measured. The drop size distributions contain mainly small drops (radius < 7.5μm

Application of Quadrature Method of Moments for Sedimentation and Coagulation of Raindrops

< 7.5,text{textmu{}m}

Skalenuebergreifende Modellierung der Populationsdynamik von Hydrometeoren mit Momentenverfahren

). The measured evolution of the drop size distribution is confronted with model calculations based on the newly derived fit of the collision kernel. It turns out that the observed fast evolution of the drop size distribution can only be modeled if the collision kernel for small drops is drastically increased. A physical argument for this amplification is missing since for such small drops, neither DNSs nor experiments have been performed. For large drops, for which a good agreement of the collision rates was found in the DNS and the experiment, the time for the evolution of the spectrum in the wind tunnel is too short to draw any conclusion. Hence, the long-time evolution of the drop size distribution is presented in a submitted paper by Riechelmann etu2009al.