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Reto Stauffer, Georg J. Mayr, Markus Dabernig, and Achim Zeileis

Abstract

Results of many atmospheric science applications are processed graphically. Visualizations are a powerful tool to display and communicate data. However, to create effective figures, a wide scope of challenges has to be considered. Therefore, this paper offers several guidelines with a focus on colors. Colors are often used to add additional information or to code information. Colors should (i) allow humans to process the information rapidly, (ii) guide the reader to the most important information, and (iii) represent the data appropriately without misleading distortion. The second and third requirements necessitate tailoring the visualization and the use of colors to the specific purpose of the graphic. A standard way of deriving color palettes is via transitions through a particular color space. Most of the common software packages still provide default palettes derived in the red–green–blue (RGB) color model or “simple” transformations thereof. Confounding perceptual properties such as hue and brightness make RGB-based palettes more prone to misinterpretation. Switching to a color model corresponding to the perceptual dimensions of human color vision avoids these problems. The authors show several practically relevant examples using one such model, the hue–chroma–luminance (HCL) color model, to explain how it works and what its advantages are. Moreover, the paper contains several tips on how to easily integrate this knowledge into software commonly used by the community. The guidelines and examples should help readers to switch over to the alternative HCL color model, which will result in a greatly improved quality and readability of visualized atmospheric science data for research, teaching, and communication of results to society.

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Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Raw ensemble forecasts of precipitation amounts and their forecast uncertainty have large errors, especially in mountainous regions where the modeled topography in the numerical weather prediction model and real topography differ most. Therefore, statistical postprocessing is typically applied to obtain automatically corrected weather forecasts. This study applies the nonhomogenous regression framework as a state-of-the-art ensemble postprocessing technique to predict a full forecast distribution and improves its forecast performance with three statistical refinements. First of all, a novel split-type approach effectively accounts for unanimous zero precipitation predictions of the global ensemble model of the ECMWF. Additionally, the statistical model uses a censored logistic distribution to deal with the heavy tails of precipitation amounts. Finally, it is investigated which are the most suitable link functions for the optimization of regression coefficients for the scale parameter. These three refinements are tested for 10 stations in a small area of the European Alps for lead times from +24 to +144 h and accumulation periods of 24 and 6 h. Together, they improve probabilistic forecasts for precipitation amounts as well as the probability of precipitation events over the default postprocessing method. The improvements are largest for the shorter accumulation periods and shorter lead times, where the information of unanimous ensemble predictions is more important.

Open access
Markus Dabernig, Georg J. Mayr, and Jakob W. Messner

Abstract

Energy traders and decision-makers need accurate wind power forecasts. For this purpose, numerical weather predictions (NWPs) are often statistically postprocessed to correct systematic errors. This requires a dataset of past forecasts and observations that is often limited by frequent NWP model enhancements that change the statistical model properties. Reforecasts that recompute past forecasts with a recent model provide considerably longer datasets but usually have weaker setups than operational models. This study tests the reforecasts from the National Oceanic and Atmospheric Administration (NOAA) and the European Centre for Medium-Range Weather Forecasts (ECMWF) for wind power predictions. The NOAA reforecast clearly performs worse than the ECMWF reforecast, the operational ECMWF deterministic and ensemble forecasts, and a limited-area model of the Austrian weather service [Zentralanstalt für Meteorologie und Geodynamik (ZAMG)]. On the contrary, the ECMWF reforecast has, of all tested models, the smallest squared errors and one of the highest financial values in an energy market.

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Markus Dabernig, Georg J. Mayr, Jakob W. Messner, and Achim Zeileis

Abstract

Separate statistical models are typically fit for each forecasting lead time to postprocess numerical weather prediction (NWP) ensemble forecasts. Using standardized anomalies of both NWP values and observations eliminates most of the lead-time-specific characteristics so that several lead times can be forecast simultaneously. Standardized anomalies are formed by subtracting a climatological mean and dividing by the climatological standard deviation. Simultaneously postprocessing forecasts between +12 and +120 h increases forecast coherence between lead times, yields a temporal resolution as high as the observation interval (e.g., up to 10 min), and speeds up computation times while achieving a forecast skill comparable to the conventional method.

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Susanne Drechsel, Georg J. Mayr, Michel Chong, and Fotini K. Chow

Abstract

Dual-Doppler lidar volume scans for 3D wind retrieval must accommodate the conflicting goals of dense spatial coverage and short scan duration. In this work, various scanning strategies are evaluated with semisynthetic wind fields from analytical solutions and numerical simulations over flat and complex terrain using the Multiple-Doppler Synthesis and Continuity Adjustment Technique (MUSCAT) retrieval algorithm. The focus of this study is to determine how volume scan strategies affect performance of the wind retrieval algorithm. Interlaced scanning methods that take into account actual maximum measurement ranges are found to be optimal because they provide the best trade-off between retrieval accuracy, volume coverage, and scan time. A recommendation for scanning strategies is given, depending on actual measurement ranges, the variability of the wind situation, and the trade-off between spatial coverage and temporal smoothing.

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Susanne Drechsel, Georg J. Mayr, Jakob W. Messner, and Reto Stauffer

Abstract

Wind speed measurements from one year from meteorological towers and wind turbines at heights between 20 and 250 m for various European sites are analyzed and are compared with operational short-term forecasts of the global ECMWF model. The measurement sites encompass a variety of terrain: offshore, coastal, flat, hilly, and mountainous regions, with low and high vegetation and also urban influences. The strongly differing site characteristics modulate the relative contribution of synoptic-scale and smaller-scale forcing to local wind conditions and thus the performance of the NWP model. The goal of this study was to determine the best-verifying model wind among various standard wind outputs and interpolation methods as well as to reveal its skill relative to the different site characteristics. Highest skill is reached by wind from a neighboring model level, as well as by linearly interpolated wind from neighboring model levels, whereas the frequently applied 10-m wind logarithmically extrapolated to higher elevations yields the largest errors. The logarithmically extrapolated 100-m model wind reaches the best compromise between availability and low cost for data even when the vertical resolution of the model changes. It is a good choice as input for further statistical postprocessing. The amplitude of measured, height-dependent diurnal variations is underestimated by the model. At low levels, the model wind speed is smaller than observed during the day and is higher during the night. At higher elevations, the opposite is the case.

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Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Nonhomogeneous regression is often used to statistically postprocess ensemble forecasts. Usually only ensemble forecasts of the predictand variable are used as input, but other potentially useful information sources are ignored. Although it is straightforward to add further input variables, overfitting can easily deteriorate the forecast performance for increasing numbers of input variables. This paper proposes a boosting algorithm to estimate the regression coefficients, while automatically selecting the most relevant input variables by restricting the coefficients of less important variables to zero. A case study with ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) shows that this approach effectively selects important input variables to clearly improve minimum and maximum temperature predictions at five central European stations.

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Manfred H. Bauer, Georg J. Mayr, Ignaz Vergeiner, and Helmut Pichler

Abstract

The influence of the obstacle shape, expressed through the ratio of spanwise to streamwise extension β, on flow over and around a mesoscale mountain is examined numerically. The initial wind U as well as the buoyancy frequency N are constant; the earth’s rotation and surface friction are neglected. In these conditions the flow response depends primarily on the nondimensional mountain height H m = h m N/U (where h m is the maximum mountain height) and the horizontal aspect ratio β. A regime diagram for the onset of wave breaking, lee vortex formation, and windward stagnation is compiled. When β is increased, smaller H m are required for the occurrence of all three features. It is demonstrated that lee vortices can form with neither wave breaking above the lee slope nor upstream stagnation. For β ⩽ 0.5 a vortex pair can appear although the isentropes above the lee slope do not overturn for any H m. For β > 1, on the other hand, lee vortex formation is triggered by wave breaking. On the windward side two distinct processes can lead to a complete blocking of the flow: the piling up of heavier air ahead of the barrier and the upstream propagation of columnar modes, which are generated by the wave breaking process for β > 1. “High-drag” states and “downslope windstorms” exist above the threshold of wave breaking as long as no lee vortices appear (or, at least, as long as they are very small). Hence, the interval of H m where a high-drag state occurs becomes progressively larger for larger β. With the growth of lee vortices the maximum wind speed along the leeward slope is dampened. The normalized drag drops rapidly below its linear counterpart and asymptotically approaches zero.

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Jakob W. Messner, Georg J. Mayr, Daniel S. Wilks, and Achim Zeileis

Abstract

Extended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete categories whereas full predictive distributions were better predicted by censored regression.

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Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Nonhomogeneous regression models are widely used to statistically postprocess numerical ensemble weather prediction models. Such regression models are capable of forecasting full probability distributions and correcting for ensemble errors in the mean and variance. To estimate the corresponding regression coefficients, minimization of the continuous ranked probability score (CRPS) has widely been used in meteorological postprocessing studies and has often been found to yield more calibrated forecasts compared to maximum likelihood estimation. From a theoretical perspective, both estimators are consistent and should lead to similar results, provided the correct distribution assumption about empirical data. Differences between the estimated values indicate a wrong specification of the regression model. This study compares the two estimators for probabilistic temperature forecasting with nonhomogeneous regression, where results show discrepancies for the classical Gaussian assumption. The heavy-tailed logistic and Student’s t distributions can improve forecast performance in terms of sharpness and calibration, and lead to only minor differences between the estimators employed. Finally, a simulation study confirms the importance of appropriate distribution assumptions and shows that for a correctly specified model the maximum likelihood estimator is slightly more efficient than the CRPS estimator.

Open access