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Christoph Schär, Daniel Leuenberger, Oliver Fuhrer, Daniel Lüthi, and Claude Girard

Abstract

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 terrain-following 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.

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Christoph Heim, Davide Panosetti, Linda Schlemmer, Daniel Leuenberger, and Christoph Schär

Abstract

Currently, major efforts are under way to refine the horizontal resolution of weather and climate models to kilometer-scale grid spacing (Δx). Besides refining the representation of the atmospheric dynamics and enabling the use of explicit convection, this will also provide higher resolution in the representation of orography. This study investigates the influence of these resolution increments on the simulation of orographic moist convection. Nine days of fair-weather thermally driven flow over the Alps are analyzed. Two sets of simulations with the COSMO model are compared, each consisting of three runs at Δx of 4.4, 2.2, and 1.1 km: one set using a fixed representation of orography at a resolution of 8.8 km, and one with varying representation at the resolution of the computational mesh. The spatial distribution of precipitation during daytime is only marginally affected by the orographic details, but nighttime convection to the south of the Alps—triggered by cold-air outflow from the valleys—is very sensitive to orography and precipitation is enhanced if more detailed orography is provided. During daytime, the onset of precipitation is delayed. The amplitude of the diurnal cycle of precipitation is reduced, even though more moisture converges toward the Alpine region during the afternoon. The hereby accumulated moisture sustains precipitation during the evening and nighttime over the surrounding plains. For these differences, the effects of changes in orographic detail are more important than changes in grid spacing. In addition, the individual convective cells are weaker, but their number increases with higher resolved orography.

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Daniel Leuenberger, Marcel Koller, Oliver Fuhrer, and Christoph Schär

Abstract

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.

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Daniele Nerini, Loris Foresti, Daniel Leuenberger, Sylvain Robert, and Urs Germann

Abstract

A Bayesian precipitation nowcasting system based on the ensemble Kalman filter is formulated. Starting from the last available radar observations, the prediction step of the filter consists of a stochastic radar extrapolation technique, while the correction step updates the radar extrapolation nowcast using information from the most recent forecast by the numerical weather prediction model (NWP). The result is a flow-dependent and seamless blending scheme that is based on the spread of the nowcast and NWP ensembles, used as the definition of the forecast error. To simplify the matrix operations, the Bayesian update is performed in the subspace spanned by the principal components, hence the term reduced space. Synthetic data experiments demonstrated that the Bayesian nowcast correctly captures the flow dependency in both the NWP forecast and the radar extrapolation skills. Four experiments with real precipitation data and a relatively small ensemble size (21 members) represented a first test under realistic conditions, such as stratiform wintertime precipitation and localized summertime convection. The skill was quantified in terms of fractions skill score at 32-km scale and 2.0 mm h−1 intensity. The results indicate that the system is able to produce blended forecasts that are at least as skillful as the nowcast-only or the NWP-only forecasts at any lead time.

Open access
Daniel Leuenberger, Alexander Haefele, Nadja Omanovic, Martin Fengler, Giovanni Martucci, Bertrand Calpini, Oliver Fuhrer, and Andrea Rossa

Abstract

The current atmospheric observing systems fail to provide a satisfactory amount of spatially and temporally resolved observations of temperature and humidity in the planetary boundary layer (PBL) despite their potential positive impact on numerical weather prediction (NWP). This is particularly critical for humidity, which exhibits a very high variability in space and time or for the vertical distribution of temperature, determining the atmosphere’s stability. Novel ground-based lidar remote sensing technologies and in situ measurements from unmanned aerial vehicles can fill this observational gap, but operational maturity was so far lacking. Only recently, commercial lidar systems for temperature and humidity profiling in the lower troposphere and automated observations on board of drones have become available. Raman lidar can provide profiles of temperature and humidity with high temporal and vertical resolution in the troposphere. Drones can provide high-quality in situ observations of various meteorological variables with high temporal and vertical resolution, but flights are complicated in high-wind situations, icing conditions, and can be restricted by aviation activity. Both observation systems have shown to considerably improve analyses and forecasts of high-impact weather, such as thunderstorms and fog in an operational, convective-scale NWP framework. The results of this study demonstrate the necessity for and the value of additional, high-frequency PBL observations for NWP and how lidar and drone observations can fill the gap in the current operational observing system.

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Monika Feldmann, Curtis N. James, Marco Boscacci, Daniel Leuenberger, Marco Gabella, Urs Germann, Daniel Wolfensberger, and Alexis Berne

Abstract

Region-based Recursive Doppler Dealiasing (R2D2) is a novel dealiasing algorithm to unfold Doppler velocity fields obtained by operational radar measurements. It specializes in resolving issues when the magnitude of the gate-to-gate velocity shear approaches or exceeds the Nyquist velocity. This occurs either in highly sheared situations, or when the Nyquist velocity is low. Highly sheared situations, such as convergence lines or mesocyclones, are of particular interest for nowcasting and warnings. R2D2 masks high-shear areas and adds a spatial buffer around them. The areas between the buffers are then identified as continuous regions that lie within the same Nyquist interval. Each region subsequently is assigned its most likely Nyquist interval by applying vertical and temporal continuity constraints, as well as supplemental wind information from an operational mesoscale model. The shear zones are then resolved using 2D continuity in azimuth and range. This 4D procedure is repeated until no further improvement can be achieved. Each iteration with fewer folds identifies fewer but larger continuous regions and less shear zones until an optimum is reached. Residual errors, often related to shear greater than the Nyquist velocity, are contained to small areas within the buffer zones. This approach maximizes operational performance in high-shear situations and restricts errors to minimal areas to mitigate error propagation.

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