A HISTORY OF GLOBAL NUMERICAL WEATHERPREDICTION. The spectacular development of computational resources in the past decades has had a profound impact on the field of numerical weather and climate modeling. It has facilitated significant improvements in the description of key physical processes such as radiative transfer and has led to more accurate flow solvers. In addition, it has enabled sophisticated data-assimilation and ensemble-prediction schemes, both of which have turned out to be vital for improved prediction skill. Parallel to these developments, the increased computational power has led to a gradual but steady refinement of the computational grid. This has allowed models to resolve an increasingly large portion of the atmospheric scales of motion visualized in Fig. 1. The unresolved scales need to be approximated in a statistical way through statistical parameterizations, inevitably involving uncertain The historic evolution of computational grids is illustrated in the top panel of Fig. 2, which shows how the spatial scales treated by operational global numerical weather prediction (NWP) models have evolved in time. The range of resolved scales is visualized by a horizontal bar, with the largest scale (domain size) at the right and the smallest scale (resolution) at the left. The width of the bar is therefore a key measure of computational cost. Due to ever-increasing computational resources, operational NWP models have undergone an exponential increase in horizontal resolution. This growth started in 1974 with the model of the National Meteorological Center (NMC) at 300-km resolution (denoted N74; see Shuman 1989) and continued up to the resolution of 16 km that is now used by the latest version of the European Centre for Medium-Range Weather Forecasts model (E79-E10; see e.g., Simmons et al. 1989; European Centre for Medium-Range Weather Forecasts 2014). The red bars illustrate the computational breakthroughs by Miura et al. (M06;, who simulated the global weather for one week at 3.5-km resolution, and by Miyamoto et al. (M13;, who simulated 12 h at 0.87-km resolution some years later. While such exceptional cases cannot be performed on a Operational global NWP models are presently on the verge of using resolutions finer than the depth of the troposphere, L Trop (10 km) (see Fig. 1). This implies that they are beginning to resolve the vertical convective overturning by cumulus clouds, but still need its partial parameterized representation. This obstacle, known as the "gray zone" or "Terra Incognita" (Wyngaard 2004) is like the proverbial "chasm" that cannot be crossed in small steps. Ideally the representation of convective overturning at these resolutions should be distributed smoothly (i.e., as a function of resolution), between the subgrid parameterizations on the one hand and explicit simulation on the other (Molinari and Dudek 1992;Wyngaard 2004;Arakawa et al. 2011). This can be achieved by making parameterizations "scale aware," but a general framework for such an approach is presently lackin...