author = {Moritz N. Lang and Lisa Schlosser and Torsten Hothorn and Georg J. Mayr and Reto Stauffer and Achim Zeileis},
  title = {Circular regression trees and forests with an application to probabilistic wind direction forecasting},
  journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
  year = {2020},
  volume = {69},
  number = {5},
  pages = {1357--1374},
  keywords = {Circular data, Distributional regression, Probabilistic forecasting, Random forests, Regression trees, von Mises distribution},
  doi = {10.1111/rssc.12437},
  abstract = {Summary Although circular data occur in a wide range of scientific fields, the methodology for distributional modelling and probabilistic forecasting of circular response variables is quite limited. Most of the existing methods are built on generalized linear and additive models, which are often challenging to optimize and interpret. Specifically, capturing abrupt changes or interactions is not straightforward but often relevant, e.g. for modelling wind directions subject to different wind regimes. Additionally, automatic covariate selection is desirable when many predictor variables are available, as is often the case in weather forecasting. To address these challenges we suggest a general distributional approach using regression trees and random forests to obtain probabilistic forecasts for circular responses. Using trees simplifies model estimation as covariates are used only for partitioning the data and subsequently just a simple von Mises distribution is fitted in the resulting subgroups. Circular regression trees are straightforward to interpret, can capture non-linear effects and interactions, and automatically select covariates affecting location and/or scale in the von Mises distribution. Circular random forests regularize and smooth the effects from an ensemble of trees. The new methods are applied to probabilistic wind direction forecasting at two Austrian airports, considering other common approaches as a benchmark.}
  author = {Lang, M. N. and Lerch, S. and Mayr, G. J. and Simon, T. and Stauffer, R. and Zeileis, A.},
  title = {Remember the past: a comparison of time-adaptive training schemes for non-homogeneous regression},
  journal = {Nonlinear Processes in Geophysics},
  volume = {27},
  year = {2020},
  number = {1},
  pages = {23--34},
  doi = {10.5194/npg-27-23-2020},
  abstract = {Non-homogeneous regression is a frequently used post-processing method for increasing the predictive skill of probabilistic ensemble weather forecasts. To adjust for seasonally varying error characteristics between ensemble forecasts and corresponding observations, different time-adaptive training schemes, including the classical sliding training window, have been developed for non-homogeneous regression. This study compares three such training approaches with the sliding-window approach for the application of post-processing near-surface air temperature forecasts across central Europe. The predictive performance is evaluated conditional on three different groups of stations located in plains, in mountain foreland, and within mountainous terrain, as well as on a specific change in the ensemble forecast system of the European Centre for Medium-Range Weather Forecasts (ECMWF) used as input for the post-processing. The results show that time-adaptive training schemes using data over multiple years stabilize the temporal evolution of the coefficient estimates, yielding an increased predictive performance for all station types tested compared to the classical sliding-window approach based on the most recent days only. While this may not be surprising under fully stable model conditions, it is shown that “remembering the past” from multiple years of training data is typically also superior to the classical sliding-window approach when the ensemble prediction system is affected by certain model changes. Thus, reducing the variance of the non-homogeneous regression estimates due to increased training data appears to be more important than reducing its bias by adapting rapidly to the most current training data only.}
  author = {Achim Zeileis and Jason C. Fisher and Kurt Hornik and Ross Ihaka and Claire D. McWhite and Paul Murrell and Reto Stauffer and Claus O. Wilke},
  title = {colorspace: A Toolbox for Manipulating and Assessing Colors and Palettes},
  journal = {Journal of Statistical Software, Articles},
  volume = {96},
  number = {1},
  year = {2020},
  keywords = {color; palette; HCL; RGB; hue; color vision deficiency; R},
  abstract = {The R package colorspace provides a flexible toolbox for selecting individual colors or color palettes, manipulating these colors, and employing them in statistical graphics and data visualizations. In particular, the package provides a broad range of color palettes based on the HCL (hue-chroma-luminance) color space. The three HCL dimensions have been shown to match those of the human visual system very well, thus facilitating intuitive selection of color palettes through trajectories in this space. Using the HCL color model, general strategies for three types of palettes are implemented: (1) Qualitative for coding categorical information, i.e., where no particular ordering of categories is available. (2) Sequential for coding ordered/numeric information, i.e., going from high to low (or vice versa). (3) Diverging for coding ordered/numeric information around a central neutral value, i.e., where colors diverge from neutral to two extremes. To aid selection and application of these palettes, the package also contains scales for use with ggplot2, shiny and tcltk apps for interactive exploration, visualizations of palette properties, accompanying manipulation utilities (like desaturation and lighten/darken), and emulation of color vision deficiencies. The shiny apps are also hosted online at},
  issn = {1548-7660},
  pages = {1--49},
  doi = {10.18637/jss.v096.i01}
  title = {Bivariate {G}aussian Models for Wind Vectors in a Distributional Regression Framework},
  author = {Moritz N. Lang and Georg J. Mayr and Reto Stauffer and Achim Zeileis},
  journal = {Advances in Statistical Climatology, Meteorology and Oceanography},
  volume = {5},
  year = {2019},
  number = {2},
  pages = {115--132},
  doi = {10.5194/ascmo-5-115-2019},
  abstract = {A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies, all parameters of the distribution are simultaneously modeled, namely the location and scale parameters for both wind components and also the correlation coefficient between them employing flexible regression splines. To capture a possible mismatch between the predicted and observed wind direction, ensemble forecasts of both wind components are included using flexible two-dimensional smooth functions. This encompasses a smooth rotation of the wind direction conditional on the season and the forecasted ensemble wind direction. The performance of the new method is tested for stations located in plains, in mountain foreland, and within an alpine valley, employing ECMWF ensemble forecasts as explanatory variables for all distribution parameters. The rotation-allowing model shows distinct improvements in terms of predictive skill for all sites compared to a baseline model that post-processes each wind component separately. Moreover, different correlation specifications are tested, and small improvements compared to the model setup with no estimated correlation could be found for stations located in alpine valleys.}
  title = {Skewed Logistic Distribution for Statistical Temperature Post-processing in Mountainous Areas},
  author = {Gebetsberger, Manuel and Stauffer, Reto and Mayr, Georg J. and Zeileis, Achim},
  year = {2019},
  keywords = {Statistical post-processing; Probabilistic temperature forecast; Skewed distribution; Distributional regression},
  journal = {Advances in Statistical Climatology, Meteorology and Oceanography},
  volume = {5},
  number = {1},
  pages = {87--100},
  doi = {10.5194/ascmo-5-87-2019},
  abstract = {Non-homogeneous post-processing is often used to improve the predictive performance of probabilistic ensemble forecasts. A common quantity to develop, test, and demonstrate new methods is the near-surface air temperature frequently assumed to follow a Gaussian response distribution. However, Gaussian regression models with only few covariates are often not able to account for site-specific local features leading to strongly skewed residuals. This residual skewness remains even if many covariates are incorporated. Therefore, a simple refinement of the classical non-homogeneous Gaussian regression model is proposed to overcome this problem by assuming a skewed response distribution to account for possible skewness. This study shows a comprehensive analysis of the performance of non-homogeneous post-processing for 2m temperature for three different site types comparing Gaussian, logistic, and skewed logistic response distributions. Satisfying results for the skewed logistic distribution are found, especially for sites located in mountainous areas. Moreover, both alternative model assumptions but in particular the skewed response distribution, can improve on the classical Gaussian assumption with respect to overall performance, sharpness, and calibration of the probabilistic predictions.}
  author = {Schlosser, Lisa and Hothorn, Torsten and Stauffer, Reto and Zeileis, Achim},
  year = {2019},
  month = {9},
  volume = {13},
  number = {3},
  pages = {1564--1589},
  fjournal = {The Annals of Applied Statistics},
  journal = {Annals of Applied Statistics},
  publisher = {The Institute of Mathematical Statistics},
  title = {Distributional regression forests for probabilistic precipitation forecasting in complex terrain},
  doi = {10.1214/19-AOAS1247},
  abstract = {To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this only captures the location of the distribution but over the last decade there has been increasing interest in distributional regression approaches modeling all parameters including location, scale and shape. Notably, so-called nonhomogeneous {G}aussian regression (NGR) models both mean and variance of a {G}aussian response and is particularly popular in weather forecasting. Moreover, generalized additive models for location, scale and shape ({GAMLSS}) provide a framework where each distribution parameter is modeled separately capturing smooth linear or nonlinear effects. However, when variable selection is required and/or there are nonsmooth dependencies or interactions (especially unknown or of high-order), it is challenging to establish a good {GAMLSS}. A natural alternative in these situations would be the application of regression trees or random forests but, so far, no general distributional framework is available for these. Therefore, a framework for distributional regression trees and forests is proposed that blends regression trees and random forests with classical distributions from the {GAMLSS} framework as well as their censored or truncated counterparts. To illustrate these novel approaches in practice, they are employed to obtain probabilistic precipitation forecasts at numerous sites in a mountainous region ({T}yrol, {A}ustria) based on a large number of numerical weather prediction quantities. It is shown that the novel distributional regression forests automatically select variables and interactions, performing on par or often even better than {GAMLSS} specified either through prior meteorological knowledge or a computationally more demanding boosting approach.}
  title = {Hourly Probabilistic Snow Forecasts over Complex Terrain: A Hybrid Ensemble Postprocessing Approach},
  author = {Reto Stauffer and Georg J. Mayr and Jakob W. Messner and Achim Zeileis},
  journal = {Advances in Statistical Climatoloy, Meteorology and Oceanography},
  year = {2018},
  volume = {4},
  number = {1/2},
  pages = {65--86},
  doi = {10.5194/ascmo-4-65-2018},
  abstract = {Accurate and high-resolution snowfall and fresh snow forecasts are important for a range of economic sectors as well as for the safety of people and infrastructure, especially in mountainous regions. In this article a new hybrid statistical postprocessing method is proposed, which combines standardized anomaly model output statistics (SAMOS) with ensemble copula coupling (ECC) and a novel re-weighting scheme to produce spatially and temporally high-resolution probabilistic snow forecasts. Ensemble forecasts and hindcasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) serve as input for the statistical postprocessing method, while measurements from two different networks provide the required observations.  This new approach is applied to a region with very complex topography in the eastern European Alps. The results demonstrate that the new hybrid method allows one not only to provide reliable high-resolution forecasts, but also to combine different data sources with different temporal resolutions to create hourly probabilistic and physically consistent predictions.}
  author = {Reto Stauffer and Nikolaus Umlauf and Jakob W. Messner and Georg J. Mayr and Achim Zeileis},
  title = {Ensemble Postprocessing of Daily Precipitation Sums over Complex Terrain Using Censored High-Resolution Standardized Anomalies},
  journal = {Monthly Weather Review},
  volume = {145},
  number = {3},
  pages = {955-969},
  year = {2017},
  doi = {10.1175/MWR-D-16-0260.1},
  abstract = {Probabilistic forecasts provided by numerical ensemble prediction systems have systematic errors and are typically underdispersive. This is especially true over complex topography with extensive terrain-induced small-scale effects, which cannot be resolved by the ensemble system. To alleviate these errors, statistical postprocessing methods are often applied to calibrate the forecasts. This article presents a new full-distributional spatial postprocessing method for daily precipitation sums based on the standardized anomaly model output statistics (SAMOS) approach. Observations and forecasts are transformed into standardized anomalies by subtracting the long-term climatological mean and dividing by the climatological standard deviation. This removes all site-specific characteristics from the data and makes it possible to fit one single regression model for all stations at once. As the model does not depend on the station locations, it directly allows the creation of probabilistic forecasts for any arbitrary location. SAMOS uses a left-censored power-transformed logistic response distribution to account for the large fraction of zero observations (dry days), the limitation to nonnegative values, and the positive skewness of the data. ECMWF reforecasts are used for model training and to correct the ECMWF ensemble forecasts with the big advantage that SAMOS does not require an extensive archive of past ensemble forecasts as only the most recent four reforecasts are needed, and it automatically adapts to changes in the ECMWF ensemble model. The application of the new method to the central Alps shows that the new method is able to depict the small-scale properties and returns accurate fully probabilistic spatial forecasts.}
  author = {Reto Stauffer and Georg J. Mayr and Jakob W. Messner and Nikolaus Umlauf and Achim Zeileis},
  title = {Spatio-Temporal Precipitation Climatology Over Complex Terrain Using a Censored Additive Regression Model},
  journal = {International Journal of Climatology},
  volume = {37},
  number = {7},
  publisher = {John Wiley \& Sons, Ltd},
  issn = {1097-0088},
  doi = {10.1002/joc.4913},
  pages = {3264--3275},
  keywords = {climatology, precipitation, complex terrain, GAMLSS, censoring, daily resolution},
  year = {2017},
  abstract = {Flexible spatio-temporal models are widely used to create reliable and accurate estimates for precipitation climatologies. Most models are based on square root transformed monthly or annual means, where a normal distribution seems to be appropriate. This assumption becomes invalid on a daily time scale as the observations involve large fractions of zero observations and are limited to non-negative values.We develop a novel spatio-temporal model to estimate the full climatological distribution of precipitation on a daily time scale over complex terrain using a left-censored normal distribution. The results demonstrate that the new method is able to account for the non-normal distribution and the large fraction of zero observations. The new climatology provides the full climatological distribution on a very high spatial and temporal resolution, and is competitive with, or even outperforms existing methods, even for arbitrary locations.}
  author = {Reto Stauffer and Georg J. Mayr and Markus Dabernig and Achim Zeileis},
  title = {Somewhere Over the Rainbow: How to Make Effective Use of Colors in Meteorological Visualizations},
  journal = {Bulletin of the American Meteorological Society},
  volume = {96},
  number = {2},
  pages = {203-216},
  year = {2015},
  doi = {10.1175/BAMS-D-13-00155.1},
  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. }
  author = {Susanne Drechsel and Georg J. Mayr and Jakob W. Messner and Reto Stauffer},
  title = {Wind Speeds at Heights Crucial for Wind Energy: Measurements and Verification of Forecasts},
  journal = {Journal of Applied Meteorology and Climatology},
  volume = {51},
  number = {9},
  pages = {1602-1617},
  year = {2012},
  doi = {10.1175/JAMC-D-11-0247.1},
  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. }