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Large-eddy simulations (LES) with the new ICOsahedral Non-hydrostatic atmosphere model (ICON) covering Germany are evaluated for four days in spring 2013 using observational data from various sources. Reference simulations with the established Consortium for Small-scale Modelling (COSMO) numerical weather prediction model and further standard LES codes are performed and used as a reference. This comprehensive evaluation approach covers multiple parameters and scales, focusing on boundary-layer variables, clouds and precipitation. The evaluation points to the need to work on parametrizations influencing the surface energy balance, and possibly on ice cloud microphysics. The central purpose for the development and application of ICON in the LES configuration is the use of simulation results to improve the understanding of moist processes, as well as their parametrization in climate models. The evaluation thus aims at building confidence in the model's ability to simulate small- to mesoscale variability in turbulence, clouds and precipitation. The results are encouraging: the high-resolution model matches the observed variability much better at small- to mesoscales than the coarser resolved reference model. In its highest grid resolution, the simulated turbulence profiles are realistic and column water vapour matches the observed temporal variability at short time-scales. Despite being somewhat too large and too frequent, small cumulus clouds are well represented in comparison with satellite data, as is the shape of the cloud size spectrum. Variability of cloud water matches the satellite observations much better in ICON than in the reference model. In this sense, it is concluded that the model is fit for the purpose of using its output for parametrization development, despite the potential to improve further some important aspects of processes that are also parametrized in the high-resolution model.
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.
Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper, we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for weighted treewidth. They generalise many of the existing reduction rules for treewidth. Experimental results show that these reduction rules can significantly reduce the problem size for several instances of real-life probabilistic networks.