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Axel Seifert

Abstract

The relation between the slope and shape parameters of the raindrop size distribution parameterized by a gamma distribution is examined. The comparison of results of a simple rain shaft model with an empirical relation based on disdrometer measurements at the surface shows very good agreement, but a more detailed discussion reveals some difficulties—for example, deviations from the gamma shape and the overestimation of collisional breakup.

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Axel Seifert

Abstract

The process of evaporation of raindrops below cloud base is investigated by numerical simulations using a one-dimensional rainshaft model with bin microphysics. The simulations reveal a high variability of the shape of the raindrop size distributions, which has important implications for the efficiency of evaporation below cloud base.

A new parameterization of the shape of the raindrop size distribution as a function of the mean volume diameter is suggested and applied in a two-moment microphysical scheme. In addition, the effect of evaporation on the number concentration of raindrops is parameterized. A comparison of results of the revised two-moment scheme and the bin microphysics rainshaft model shows that the two-moment scheme is able to reproduce the results of the reference model in a wide parameter range.

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Axel Seifert and Bjorn Stevens

Abstract

The rain formation in shallow cumulus clouds by condensational growth and collision–coalescence of liquid drops is revisited with the aim of understanding the controls on precipitation efficiency for idealized cloud drafts. For the purposes of this analysis, a one-dimensional kinematic cloud model is introduced, which permits the efficient exploration of many microphysical aspects of liquid shallow clouds with both spectral and two-moment bulk microphysical formulations. Based on the one-dimensional model and the insights gained from both microphysical approaches, scaling relations are derived that provide a link between microphysical and macroscopic cloud properties. By introducing the concept of a macroscopic autoconversion time scale, the rain formation can be traced back to quantities such as cloud depth, average vertical velocity, lapse rate, and cloud lifetime. The one-dimensional model also suggests that the precipitation efficiency can be expressed as a function of the ratio of the macroscopic autoconversion time scale and cloud lifetime and that it exhibits threshold-like behavior.

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Ann Kristin Naumann and Axel Seifert

Abstract

In this paper, the evolution of the raindrop size distribution (RSD) is investigated for two isolated shallow cumulus clouds that are modeled with large-eddy simulations. For a two-moment bulk rain microphysics scheme that assumes the RSD to follow a gamma distribution, it is shown that the evolution of the rainwater content of an individual shallow cumulus cloud—in particular, its subcloud-layer rainwater amount and its surface precipitation rate—is highly sensitive to the choice of the shape parameter of the gamma distribution.

To further investigate the shape of the RSD, a Lagrangian drop model is used to represent warm rain microphysics without a priori assumptions on the RSD. It is found that the shape parameter is highly variable in space and time and that existing closure equations, which are established from idealized studies of more heavily precipitating cases, are not appropriate for shallow cumulus. Although a relation of the shape parameter to the mean raindrop diameter is also found for individual shallow cumulus clouds, this relation differs already for the two clouds considered. It is therefore doubtful whether a two-moment scheme with a diagnostic parameterization of the shape parameter (i.e., a local closure in space and time) can be sufficient, especially when being applied across different cloud regimes. A three-moment bulk rain microphysics scheme is able to capture the general development of the relation of the shape parameter to the mean raindrop diameter for the two simulated clouds but misses some relevant features.

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Vivek Sant, Ulrike Lohmann, and Axel Seifert

Abstract

Focusing on the formation of precipitation in marine stratiform clouds, a two-moment bulk parameterization for three liquid water classes (cloud, drizzle, and rain) is proposed to describe the process of collision–coalescence. Based on the stochastic collection equation and making use of partial moments to improve the physical representation of the shape of the drop size distribution, new rate equations for both number and mass densities are derived using the modified gamma distribution and an adapted collection kernel. Based on observations and spectral model results, the free shape parameters of the modified gamma distribution of each class are determined closing the set of equations. Idealized simulations of the new parameterization compare well to other studies and prove that the closure assumptions are appropriate, especially as the rate equations are invariant under time-stretching transformations—a key property of the stochastic collection equation. The framework of the one-dimensional kinematic cloud model is used to compare the new bulk parameterization to existing formulations and a spectral model. These results show a good agreement, especially in the sensitivity to the aerosol background concentration and the general development for updraft velocities relevant for shallow clouds. Furthermore, as drizzle dominates the formed precipitation for stratocumulus it becomes a pure transition class for more convective type clouds. The analysis reveals a different quantitative behavior of the various parameterizations in the drizzle regime, which is of special importance for precipitating stratocumulus clouds.

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Axel Seifert, Alexander Khain, Ulrich Blahak, and Klaus D. Beheng

Abstract

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.

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Yuefei Zeng, Tijana Janjić, Alberto de Lozar, Stephan Rasp, Ulrich Blahak, Axel Seifert, and George C. Craig

Abstract

Different approaches for representing model error due to unresolved scales and processes are compared in convective-scale data assimilation, including the physically based stochastic perturbation (PSP) scheme for turbulence, an advanced warm bubble approach that automatically detects and triggers absent convective cells, and additive noise based on model truncation error. The analysis of kinetic energy spectrum guides the understanding of differences in precipitation forecasts. It is found that the PSP scheme results in more ensemble spread in assimilation cycles, but its effects on the root-mean-square error (RMSE) are neutral. This leads to positive impacts on precipitation forecasts that last up to three hours. The warm bubble technique does not create more spread, but is effective in reducing the RMSE, and improving precipitation forecasts for up to 3 h. The additive noise approach contributes greatly to ensemble spread, but it results in a larger RMSE during assimilation cycles. Nevertheless, it considerably improves the skill of precipitation forecasts up to 6 h. Combining the additive noise with either the PSP scheme or the warm bubble technique reduces the RMSE within cycles and improves the skill of the precipitation forecasts, with the latter being more beneficial.

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Michael Baldauf, Axel Seifert, Jochen Förstner, Detlev Majewski, Matthias Raschendorfer, and Thorsten Reinhardt

Abstract

Since April 2007, the numerical weather prediction model, COSMO (Consortium for Small Scale Modelling), has been used operationally in a convection-permitting configuration, named COSMO-DE, at the Deutscher Wetterdienst (DWD; German weather service). Here the authors discuss the model changes that were necessary for the convective scale, and report on the experience from the first years of operational application of the model. For COSMO-DE the ability of the numerical solver to treat small-scale structures has been improved by using a Runge–Kutta method, which allows for the use of higher-order upwind advection schemes. The one-moment cloud microphysics parameterization has been extended by a graupel class, and adaptations for describing evaporation of rain and stratiform precipitation processes were made. Comparisons with a much more sophisticated two-moment scheme showed only minor differences in most cases with the exception of strong squall-line situations. Whereas the deep convection parameterization was switched off completely, small-scale shallow convection was still parameterized by the appropriate part of the Tiedtke scheme. During the first year of operational use, convective events in synoptically driven situations were satisfactorily simulated. Also the daily cycles of summertime 10-m wind and 1-h precipitation sums were well captured. However, it became evident that the boundary layer description had to be adapted to enhance convection initiation in airmass convection situations. Here the asymptotic Blackadar length scale l had proven to be a sensitive parameter.

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Barry H. Lynn, Alexander P. Khain, Jimy Dudhia, Daniel Rosenfeld, Andrei Pokrovsky, and Axel Seifert

Abstract

Considerable research investments have been made to improve the accuracy of forecasting precipitation systems in cloud-resolving, mesoscale atmospheric models. Yet, despite a significant improvement in model grid resolution and a decrease in initial condition uncertainty, the accurate prediction of precipitation amount and distribution still remains a difficult problem. Now, the development of a fast version of spectral (bin) microphysics (SBM Fast) offers significant potential for improving the description of precipitation-forming processes in mesoscale atmospheric models.

The SBM Fast is based on solving a system of equations for size distribution functions for water drops and three types of ice crystals (plates, columns, and dendrites), as well as snowflakes, graupel, and hail/frozen drops. Ice processes are represented by three size distributions, instead of six in the original SBM code. The SBM uses first principles to simulate microphysical processes such as diffusional growth and collision. A budget for aerosols is used to obtain the spectrum of condensation nuclei, which is used to obtain the initial drop spectrum. Hence, SBM allows one to take into account aerosol effects on precipitation, and corresponding cloud effects on the atmospheric aerosol concentration and distribution. SBM Fast has been coupled with the three-dimensional fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5), which allows SBM Fast to simulate microphysics within a realistic, time-varying mesoscale environment.

This paper describes the first three-dimensional SBM mesoscale model and presents results using 1-km resolution to simulate initial development of a cloud system over Florida on 27 July 1991. The focus is on initial cloud development along the west coast, just prior to sea-breeze formation. The results indicate that the aerosol concentration had a very important impact on cloud dynamics, microphysics, and rainfall.

Vertical cross sections of clouds obtained using SBM Fast are compared to those from a version of the “Reisner2” bulk-parameterization scheme that uses the Kessler autoconversion formula. The results show that this version of “Reisner2” produced vertically upright clouds that progressed very quickly from initial cloud formation to raindrop formation. In contrast, clouds obtained using SBM were relatively long lasting with greater production of stratiform clouds.

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Winfried Straub, Klaus Dieter Beheng, Axel Seifert, Jan Schlottke, and Bernhard Weigand

Abstract

Results of numerically investigated binary collisions of 32 drop pairs presented in 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 stationary size distribution (SSD) from solving the kinetic coagulation–breakup equation until a time-independent state is reached. Although with the parameterizations of Low and List, the SSD shows an often-reported three-peak structure, with the new parameterizations the second peak vanishes completely.

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