Klaus D. Beheng

A double-moment parameterization for simulating autoconversion, accretion and selfcollection

Abstract A double-moment parameterization of microphysical processes in warm clouds is derived directly from the stochastic collection equation. Explicit rate equations for autoconversion, accretion and selfcollection are formulated using Longs piecewise polynomial collection kernel and universal functions following from a fundamental similarity relationship. These universal functions are estimated by numerically solving the stochastic collection equation. A comparison of results of the new parameterization and other double-moment parameterizations is given and the detailed spectral approach is used as a reference method. As an idealized test problem a one-dimensional rainshaft model is applied. The new parameterization is able to reproduce the results of the spectral reference model within a wide range of initial conditions, while other parameterizations show large errors when assuming continental clouds with small mean radii.

Possible Effects of Collisional Breakup on Mixed-Phase Deep Convection Simulated by a Spectral (Bin) Cloud Model

The effects of the collisional breakup of raindrops are investigated using the Hebrew University Cloud Model (HUCM). The parameterizations, which are combined in the new breakup scheme, are those of Low and List, Beard and Ochs, as well as Brown. A sensitivity study reveals strong effects of collisional breakup on the precipitation formation in mixed-phase deep convective clouds for strong as well as for weak precipitation events. Collisional breakup reduces the number of large raindrops, increases the number of small raindrops, and, as a consequence, decreases surface rain rates and considerably reduces the speed of rain formation. In addition, it was found that including breakup can lead to a more intense triggering of secondary convective cells. But a statistical comparison with observed raindrop size distributions shows that the parameterizations might systematically overestimate collisional breakup.

Numerical Investigation of Collision-Induced Breakup of Raindrops. Part II: Parameterizations of Coalescence Efficiencies and Fragment Size Distributions

Abstract Results of numerically investigated binary collisions of 32 drop pairs presented in Part I of this study are used to parameterize coalescence efficiencies and size distributions of breakup fragments of large raindrops. In contrast to the well-known results of Low and List, it is shown that coalescence efficiencies Ec can be described best by means of the Weber number We yielding Ec = exp(−1.15We). The fragment size distributions gained from our numerical investigations were parameterized by fitting normal, lognormal, and delta distributions and relating the parameters of the distribution functions to physical quantities relevant for the breakup event. Thus, this parameterization has formally a substantial similarity to the one of Low and List, although no reference is made to breakup modes such as filament, disk, and sheet. Additionally, mass conservation is guaranteed in the present approach. The parameterizations from Low and List, as well as the new parameterizations, are applied to compute a ...

Numerical Investigation of Collision-Induced Breakup of Raindrops. Part I: Methodology and Dependencies on Collision Energy and Eccentricity

Abstract Binary collisions of large raindrops moving with terminal fall velocity are numerically investigated using FS3D, a direct numerical simulation (DNS) code based on the “volume of fluid” method. The result of this process can be a permanent coalescence or a temporal coalescence followed by a breakup of the coalesced system into smaller-sized remnants of the original raindrops and a number of fragment droplets of different sizes. In total, 32 drop pairs are studied with sizes chosen to cover nearly completely the entire size parameter range relevant to breakup. This is an important extension of investigations performed in 1982 by Low and List, who studied 10 drop pairs only. Moreover, eccentricity has been introduced as an additional parameter controlling the collision outcome. Eccentricity is defined as the horizontal distance of the initial drops’ centers with values equal to approximately 0 for centric and 1 for grazing collisions. The main results include numerically calculated data of coalescen...

The influence of deep convective motions on the variability of Z-R relations

Abstract Effects of deep convection on the precipitation rate R leading to variations in radar meteorological Z – R relations are studied. The basic contributions to this subject come from vertical and horizontal air motions as well as decreasing air density with height. Their influence on Z – R relations is investigated both with an analytical approach from cloud microphysics distinguishing between two characteristic spectral forms, and a mesoscale bulk model case study of a single cumulonimbus cloud. The precipitation rate is strongly affected by deep convective motions leading to increased mean value and standard deviation of the prefactor a in Z – R relations Z = aR b . To a lesser extent, density stratification tends to diminish the prefactor. The exponent b , which can, without deep convection, vary from b =1 to b =7/4 depending on characteristic spectral form, remains unaffected by any of the dynamical effects studied here. Values of b can only be altered by such changes of the particle spectra, which affect the distribution of terminal velocity with hydrometeor size: in practice, this implies phase changes or variations in composition of the mixed-type hydrometeor ensemble. In spite of the variations in Z – R relations found in the present study, when performing an average over the whole cloud and precipitation volume , standard Z – R relations proposed for stagnant air still hold in a statistical sense. Furthermore, the effects of vertical air density gradients can be compensated, which should also help to improve quantitative rainfall estimates at large ranges from the radar site.

Numerical Simulation of Graupel Development

Abstract The variation in time of an ice particle size spectrum resulting from collisions of ice particles with super-cooled drops, and the simultaneous variation in time of a size spectrum of supercooled cloud droplets resulting from collisions and coalescence and from drop depletion caused by riming are described in terms of numerical solutions to the stochastic collection equations. The ice crystals were assumed to have the shape of thin hexagonal plates, and to follow Gaussian mass distributions corresponding to a mean ice crystal radius ranging from 205 to 479 mu;m and corresponding to an initial ice crystal concentration ranging from 2.5 × 103 to 5.0 × 104 m−3. The initial mass distribution of the cloud drops was that given by Berry and Reinhardt (1974) corresponding to a mean drop radius of 14 µm and a liquid water content of 1.0 × 10−3 kg m−3. The efficiency with which ice crystal plates collide with water drops was assumed to be that computed by Pitter and Pruppacher (1974). The collection effici...

The evolution of liquid water/ice contents of a mid-latitude convective storm derived from radar data and results from a cloud-resolving model

In a case study the evolution of the liquid water/ice content of an isolated thunderstorm observed by a C-band Doppler radar is investigated. To this end, a 3D cloud resolving mesoscale model is applied yielding the microphysical development of the observed storm including its radar reflectivities. The numerical results are used to derive relations between radar reflectivity Z and cloud mass L which are, on average, valid, on one hand, for mixed-phase cloud regions and, on the other hand, for those containing mostly liquid precipitation particles. These two model-based Z/L-relations are applied for calculating liquid water/ice contents of the observed storm. The liquid water/ice contents such obtained differ significantly from those employing commonly used Z/L-relations. The cloud water inside the cell volume is compared to the maximum available -pseudo-adiabatically determined - showing a good agreement only for the undiluted core of that cell. Finally, the precipitation efficiency is estimated resulting in an upper bound of about 60%.

Direct Numerical Simulation of Breakup Phenomena in Liquid Jets and of Colliding Raindrops

Since powerful computational ressources are available, numerical simulation is one of the most attractive tools to bridge the gap between the experimental and analytical description of fluid flow phenomena. One of these tools is the direct numerical simulation (DNS) technique relying on a very high spatial and temporal resolution of fluid systems. Thus, all length scales of a fluid flow, only limited by the grid size, are captured by DNS. Since investigations of many fluid systems require a very fine resolution, considerable progress can only be made by both applying sophisticated numerical methods and using high performance computers. With the inhouse 3D DNS program FS3D (Free Surface 3D) based on the Volume-of-Fluid method it is possible to simulate two phase flows of fundamental interest in the automotive and aerospace industry, in meteorology and agriculture but also in the oil industry or medicine.

Effects of Intentional and Inadvertent Hygroscopic Cloud Seeding

In order to study possible effects of intentional cloud seeding and air pollution on clouds and precipitation, investigations were performed with the numerical weather prediction model COSMO (formerly called LM) using a sophisticated cloud microphysics scheme developed at the Institut fur Meteorologie und Klimaforschung. Simulations with this model system on the high performance computer (HP XC400) operated by the computing center at the University of Karlsruhe show that in a land-sea breeze situation, typical for wintertime in the Eastern Mediterranean, aerosols have a considerable impact on the amount and spatial distribution of precipitation at the ground. The results suggest that it might be possible to gain a significant amount of freshwater shifting precipitation from sea to land by seeding the clouds with hygroscopic particles. It could also be shown that the model system is able to reproduce the spatial and temporal evolution of a hailstorm that was observed in South-West Germany, producing realistic radar reflectivities and amounts of precipitation and hail. Sensitivity studies reveal that CCN concentration has a significant impact on the severity of the hailstorm.