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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: A method is presented to reduce the time-splitting errors of one-dimensional flux form advection schemes. In multidimensional applications deformational correction terms are included in each one-dimensional advection step whereby all correction terms add up to zero. With the correction terms a consistent form of a given one-dimensional advection scheme is achieved when time-splitting is performed. Positive definiteness and shape preservation of the scheme are obtained by nonlinear limitation of the advective fluxes and the deformational correction terms. Large Courant numbers are treated by applying local timestep reduction. The resulting scheme is strictly one-dimensional, mass conservative and positive definite. Shape preservation of the method is nearly achieved. Two- and three-dimensional test runs are presented demonstrating that the method yields satisfactory results. The horizontal flow in a terrain with a steep mountain ridge is investigated by utilizing a terrain following vertical coordinate. It is shown that even in steep orographical terrain the method works quite well, however, small errors occur in the shape preservation of the scheme. These errors increase with increasing spatial variation of the vertical grid mesh. [ABSTRACT FROM AUTHOR]