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- ItemNonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit(College Park, MD : Institute of Physics Publishing, 2009) Senf, F.; Altrock, P.M.; Behn, U.A finite array of N globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling, there is a clear separation of timescales of centre of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the centre of mass coordinate. We compute analytically the stationary probability distribution and the moments of the centre of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter ac(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from ac. The crossover point approaches ac in the limit N →∞ which reproduces previous results for infinite arrays. Our results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on N and is determined by the scaling behaviour near a fixed point of the stochastic flow. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemThe impact of mineral dust on cloud formation during the Saharan dust event in April 2014 over Europe(Göttingen : Copernicus GmbH, 2018) Weger, M.; Heinold, B.; Engler, C.; Schumann, U.; Seifert, A.; Fößig, R.; Voigt, C.; Baars, H.; Blahak, U.; Borrmann, S.; Hoose, C.; Kaufmann, S.; Krämer, M.; Seifert, P.; Senf, F.; Schneider, J.; Tegen, I.A regional modeling study on the impact of desert dust on cloud formation is presented for a major Saharan dust outbreak over Europe from 2 to 5 April 2014. The dust event coincided with an extensive and dense cirrus cloud layer, suggesting an influence of dust on atmospheric ice nucleation. Using interactive simulation with the regional dust model COSMO-MUSCAT, we investigate cloud and precipitation representation in the model and test the sensitivity of cloud parameters to dust-cloud and dust-radiation interactions of the simulated dust plume. We evaluate model results with ground-based and spaceborne remote sensing measurements of aerosol and cloud properties, as well as the in situ measurements obtained during the ML-CIRRUS aircraft campaign. A run of the model with single-moment bulk microphysics without online dust feedback considerably underestimated cirrus cloud cover over Germany in the comparison with infrared satellite imagery. This was also reflected in simulated upper-Tropospheric ice water content (IWC), which accounted for only 20 % of the observed values. The interactive dust simulation with COSMO-MUSCAT, including a two-moment bulk microphysics scheme and dust-cloud as well as dust-radiation feedback, in contrast, led to significant improvements. The modeled cirrus cloud cover and IWC were by at least a factor of 2 higher in the relevant altitudes compared to the noninteractive model run. We attributed these improvements mainly to enhanced deposition freezing in response to the high mineral dust concentrations. This was corroborated further in a significant decrease in ice particle radii towards more realistic values, compared to in situ measurements from the ML-CIRRUS aircraft campaign. By testing different empirical ice nucleation parameterizations, we further demonstrate that remaining uncertainties in the ice-nucleating properties of mineral dust affect the model performance at least as significantly as including the online representation of the mineral dust distribution. Dust-radiation interactions played a secondary role for cirrus cloud formation, but contributed to a more realistic representation of precipitation by suppressing moist convection in southern Germany. In addition, a too-low specific humidity in the 7 to 10 km altitude range in the boundary conditions was identified as one of the main reasons for misrepresentation of cirrus clouds in this model study.