Most numerical weather prediction models rely on a terrain-following coordinate framework. The computational mesh is thus characterized by inhomogeneities with scales determined by the underlying topography. Such inhomogeneities may affect the truncation error of numerical schemes. In this study, a new class of terrainfollowing coordinate systems for use in atmospheric prediction models is proposed. Unlike conventional systems, the new smooth level vertical (SLEVE) coordinate yields smooth coordinates at mid-and upper levels. The basic concept of the new coordinate is to employ a scale-dependent vertical decay of underlying terrain features. The decay rate is selected such that small-scale topographic variations decay much faster with height than their large-scale counterparts. This generalization implies a nonlocal coordinate transformation. The new coordinate is tested and compared against standard sigma and hybrid coordinate systems using an idealized advection test. It is demonstrated that the presence of coordinate transformations induces substantial truncation errors. These are critical for grid inhomogeneities with wavelengths smaller than approximately eight grid increments, and may overpower the regular-grid truncation error of the underlying finite-difference approximation. These results are confirmed by a theoretical analysis of the truncation error. In addition, the new coordinate is tested in idealized and real-case numerical experiments using a nonhydrostatic model. The simulations using the new coordinate yield a substantial reduction of small-scale noise in dynamical and thermodynamical model fields.

Data assimilation (DA) methods for convective‐scale numerical weather prediction at operational centres are surveyed. The operational methods include variational methods (3D‐Var and 4D‐Var), ensemble methods (LETKF) and hybrids between variational and ensemble methods (3DEnVar and 4DEnVar). At several operational centres, other assimilation algorithms, like latent heat nudging, are additionally applied to improve the model initial state, with emphasis on convective scales. It is demonstrated that the quality of forecasts based on initial data from convective‐scale DA is significantly better than the quality of forecasts from simple downscaling of larger‐scale initial data. However, the duration of positive impact depends on the weather situation, the size of the computational domain and the data that are assimilated. Furthermore it is shown that more advanced methods applied at convective scales provide improvements over simpler methods. This motivates continued research and development in convective‐scale DA. Challenges in research and development for improvements of convective‐scale DA are also reviewed and discussed. The difficulty of handling the wide range of spatial and temporal scales makes development of multi‐scale assimilation methods and space–time covariance localization techniques important. Improved utilization of observations is also important. In order to extract more information from existing observing systems of convective‐scale phenomena (e.g. weather radar data and satellite image data), it is necessary to provide improved statistical descriptions of the observation errors associated with these observations.

The identification of low-level thermal fronts is particularly challenging in high-resolution model fields over complex terrain. Firstly, direct model output often contains numerical noise which spuriously influences the highfrequency variability of thermal parameters. Secondly, the boundary layer interferes via convection and consequently leaves its thermal marks on low levels. Here, an automated objective method for the detection of frontal lines is introduced which is designed to be insusceptible to consequences of small grid spacings. To this end, existing algorithms are readopted and combined in a novel way. The overall technique subdivides into a basic detection of fronts and a supplemental division into local fronts and synoptic fronts. The fundamental parts of the detection are: (1) a smoothing of the initial fields, (2) a definition of the frontal strength, and, (3) a localisation with the thermal front parameter. The local fronts are identified by means of a classification of open and closed thermal contours. The resulting data comprise the spatial outline of the frontal structures in a binary field as well as their type and movement. The novel methodology is applied to a 3 year high-resolution reanalysis over central Europe computed with the COSMO model using a grid spacing of 7 km. Grid-point based climatologies are derived for the Alpine region. Frequencies of occurrence and characteristics of motion are analysed for different frontal types. The novel climatology also provides quantitative evidence of dynamical properties such as the retardation of cold fronts ahead of mountains and the dissolution of warm fronts over mountains.

Most atmospheric models use terrain-following coordinates, and it is well known that the associated deformation of the computational mesh leads to numerical inaccuracies. In a previous study, the authors proposed a new terrain-following coordinate formulation [the smooth level vertical (SLEVE) coordinate], which yields smooth vertical coordinate levels at mid and upper levels and thereby considerably reduces numerical errors in the simulation of flow past complex topography. In the current paper, a generalization of the SLEVE coordinate is presented by using a modified vertical decay of the topographic signature with height. The new formulation enables an almost uniform thickness of the lowermost computational layers, while preserving the fast transition to smooth levels in the mid and upper atmosphere. This allows for a more consistent and more stable coupling with planetary boundary layer schemes, while retaining the advantages over classic sigma coordinates at upper levels. The generalized SLEVE coordinate is implemented and successfully tested in real-case simulations using an operational nonhydrostatic atmospheric model.

Hail is the costliest atmospheric hazard in Switzerland, causing substantial damage to agriculture, cars and buildings every year. In this study, a 12-year statistic of objectively identified cold fronts and a radar-based hail statistic are combined to investigate the co-occurrence of cold fronts and hail in Switzerland. In a first step, an automated front identification scheme, which has previously been designed for and applied to global reanalysis data, is modified for a high-resolution regional analysis data set. This front detection method is then adapted, tested and applied to the Consortium for Small Scale Modelling (COSMO) analysis data for the extended hail season (May to September) in the years 2002-2013. The resulting cold front statistic is presented and discussed. In a second step, the frequency of cold fronts is linked to a high-resolution radar-based hail statistic to determine the relative fraction of hail initiation events in pre-frontal environments. Up to 45% of all detected hail events in north-eastern and southern Switzerland form in pre-frontal zones. Similar fractions are identified upstream of the Jura and the Black Forest mountains. The percentage of front-related hail formation is highest in regions where hail is statistically less frequent, with the exception of southern Switzerland. Furthermore, it is shown that fronts create wind-sheared environments, which are favourable for hail cells.