Abstract
This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes.
Highlights
Clouds and precipitation are an important part of the atmosphere
Γ- and Log-Normal Distributions used in a parameterization scheme of condensation and collection
The reference solution is found from the budget equation for the drop size distribution function f :
Summary
Clouds and precipitation are an important part of the atmosphere They are included in numerical weather forecast models as ensembles of solid or liquid water particles (hydrometeors). Cloud properties are forecasted using the bulk modeling approach as the parameterization. As a benchmark for the results of the parameterizations, the output of a spectral (bin) model can be used This model describes the evolution of the hydrometeor size distribution function (spectrum). The particle size coordinate (internal coordinate) is divided into several tens of bins. The results of this spectral model are more accurate than those of bulk models, but the computational costs are high. We will examine how the choice of the functional form for the distribution function influences the results and the implementation of the bulk model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
