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Abstract: For a long time, classical ensemble forecasts have concentrated on simulating the uncertainties of the observations by variations of the initial and boundary conditions. To supplement this with inherent contributions from the forecast model itself, stochastic physics has been proposed as an appropriate approach to improve the forecast quality and to increase the ensemble spread of underdispersive ensembles. Concentrating on cloud processes and their temporal development we here introduce a set of stochastic parameters into existing deterministic physical parameterization schemes as for the trigger function, closure assumption and turbulent mixing in the convection scheme, for the initial ice concentration and turbulent collection kernel in the grid scale precipitation/microphysics scheme and for the subgrid scale cloud cover in the radiation scheme. Considering the stochastic parameters to be subject to unresolved turbulent fluctuations, we derive the corresponding stochastic processes from a Langevin equation based on an approach of direct numeric simulation. This allows for the inclusion of a turbulent autocorrelation time calculated from the eddy dissipation rate and the turbulent kinetic energy of the hosting model. Ensemble simulations of two meteorologicaly different real cases are compared to deterministic control simulations and observations of 1h precipitation sums. The turbulent autocorrelation time shows pronounced spatial variability correlated with frontal dynamics and convective activity. Maps of spatial precipitation patterns and continuous ranked probability score (CRPS) improvements show a better forecast quality of the ensemble mean including stochastic physics. Depending on the meteorological situation, the ensemble spread and the CRPS improvement both exhibit a spin up time and reach a saturation. For air-mass convection/postfrontal showers the spread and the CRPS improvement are higher than for frontal precipitation. The stochastic parameterization of subgrid scale cloud cover is found to degrade the forecast quality of the ensemble. This is explained by a too homogeneous spatial distribution of the added variability. Consequently, this part of the stochastic parameterization has been excluded from the ensemble simulations and is left in its operational deterministic version. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a rigorous derivation of a model equation system for the mass and energy open precipitating atmosphere. The derivation is based on the treatment of the atmosphere in terms of three open thermodynamic subsystems consisting of cloudy air, rain water and snow, respectively. Each of the three subsystems moves with a different velocity as caused by the different fall velocities of rain and snow in comparison to the cloudy air. A basic assumption of the model consists in the neglect of the inertia terms in the momentum equation of the falling hydrometeors. It will be shown that this simplification yields additional source terms in the budget equations of the total momentum and the total kinetic energy of the system. However, the prognostic equations for the atmospheric wind field and the corresponding kinetic energy equation remain free of these source terms. The model equations strictly conserve the total mass and energy of the system. It is concluded that the combination of the barycentric velocity of the cloudy air and the total density of the system is the best choice to describe the time evolution of the atmospheric wind field. [Copyright &y& Elsevier]