ensAR - Autoregressive postprocessing methods for ensemble forecasts

Groß J, Möller AC. ensAR - Autoregressive postprocessing methods for ensemble forecasts. GitHub; 2019

Bivariate ensemble model output statistics approach for joint forecasting of wind speed and temperature

Baran S, Möller AC. Bivariate ensemble model output statistics approach for joint forecasting of wind speed and temperature. Meteorology and Atmospheric Physics. 2017;129(1):99-112.Forecast ensembles are typically employed to account for prediction uncertainties in numerical weather prediction models. However, ensembles often exhibit biases and dispersion errors, thus they require statistical post-processing to improve their predictive performance. Two popular univariate post-processing models are the Bayesian model averaging (BMA) and the ensemble model output statistics (EMOS). In the last few years, increased interest has emerged in developing multivariate post-processing models, incorporating dependencies between weather quantities, such as for example a bivariate distribution for wind vectors or even a more general setting allowing to combine any types of weather variables. In line with a recently proposed approach to model temperature and wind speed jointly by a bivariate BMA model, this paper introduces an EMOS model for these weather quantities based on a bivariate truncated normal distribution. The bivariate EMOS model is applied to temperature and wind speed forecasts of the 8-member University of Washington mesoscale ensemble and the 11-member ALADIN-HUNEPS ensemble of the Hungarian Meteorological Service and its predictive performance is compared to the performance of the bivariate BMA model and a multivariate Gaussian copula approach, post-processing the margins with univariate EMOS. While the predictive skills of the compared methods are similar, the bivariate EMOS model requires considerably lower computation times than the bivariate BMA method

Probabilistic temperature forecasting with a heteroscedastic autoregressive ensemble postprocessing model

Möller AC, Groß J. Probabilistic temperature forecasting with a heteroscedastic autoregressive ensemble postprocessing model. Quarterly Journal of the Royal Meteorological Society. 2020;146(726):211-224.To account for uncertainty in numerical weather prediction (NWP) models it has become common practice to employ ensembles of NWP forecasts. However, forecast ensembles often exhibit forecast biases and dispersion errors, thus require statistical postprocessing to improve reliability of the ensemble forecasts.<br>This work proposes an extension of a recently developed postprocessing model for temperature utilizing autoregressive information present in the forecast error of the raw ensemble members. The original approach is modified to let the variance parameter additionally depend on the ensemble spread, yielding a two-fold heteroscedastic model. Furthermore, a high-resolution forecast is included into the postprocessing model, yielding improved predictive performance. Finally, it is outlined how the autoregressive model can be utilized to postprocess ensemble forecasts with higher forecast horizons, without the necessity of making fundamental changes to the original model. To illustrate the performance of the heteroscedastic extension of the autoregressive model, and its use for higher forecast horizons we present a case study for a data set containing 12 years of temperature forecasts and observations over Germany. The case study indicates that the autoregressive model yields particularly strong improvements for forecast horizons beyond 24 hours ahead

Various Approaches to Statistical Calibration of Ensemble Weather Forecasts

Baran S, Möller AC. Various Approaches to Statistical Calibration of Ensemble Weather Forecasts. ERCIM News. 01.04.2020;(121):30-31

Ensemble AR Modification

Möller AC, Groß J. Probabilistic temperature forecasting based on an ensemble autoregressive modification. Quarterly Journal of the Royal Meteorological Society. 2016;142(696):1385-1394.To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts, the NWP model is run multiple times, each time with variations in the mathematical representations of the model and/or initial or boundary conditions. To correct for possible biases and dispersion errors in the ensemble, statistical postprocessing models are frequently employed. These statistical models yield full predictive probability distributions for a weather quantity of interest and thus allow for a more accurate representation of forecast uncertainty. This article proposes to combine the state-of-the-art Ensemble Model Output Statistics (EMOS) with an ensemble that is adjusted by an autoregressive process fitted to the respective error series by a spread-adjusted linear pool in the case of temperature forecasts. The basic ensemble modification technique we introduce may be used to simply adjust the ensemble itself as well as to obtain a full predictive distribution for the weather quantity. As demonstrated for temperature forecasts from the European Centre for Medium-Range Weather Forecasts ensemble, the proposed procedure gives rise to improved results over the basic (local) EMOS method

A Note on Cohen's d From a Partitioned Linear Regression Model

Groß J, Möller AC. A Note on Cohen's d From a Partitioned Linear Regression Model. Journal of Statistical Theory and Practice. 2023;17(2): 22.In this note, we introduce a generalized formula for Cohen's d under the presence of additional independent variables, providing a measure for the size of a possible effect concerning the size of a difference location effect of a variable in two groups. This is done by employing the so-called Frisch-Waugh-Lovell theorem in a partitioned linear regression model. The generalization is motivated by demonstrating the relationship to appropriate t and F statistics. Our discussion is further illustrated by inference about a publicly available data set

D-vine-copula-based postprocessing of wind speed ensemble forecasts

Jobst D, Möller AC, Gross J. D-vine-copula-based postprocessing of wind speed ensemble forecasts. Quarterly Journal of the Royal Meteorological Society. 2023.Current practice in predicting future weather is the use of numerical weather prediction (NWP) models to produce ensemble forecasts. Despite of enormous improvements over the last few decades, they still tend to exhibit bias and dispersion errors and, consequently, lack calibration. Therefore, these forecasts may be improved by statistical postprocessing. In this work, we propose a D-vine-copula-based postprocessing for 10 m surface wind speed ensemble forecasts. This approach makes use of quantile regression related to D-vine copulas, which is highly data driven and allows one to adopt more general dependence structures as the state-of-the-art zero-truncated ensemble model output statistic (tEMOS) model. We compare local and global D-vine copula quantile regression (DVQR) models to the corresponding tEMOS models and their gradient-boosting extensions (tEMOS-GB) for different sets of predictor variables using one lead time and 60 surface weather stations in Germany. Furthermore, we investigate which types of training periods can improve the performance of tEMOS and the D-vine-copula-based method for wind speed postprocessing. We observe that the D-vine-based postprocessing yields a comparable performance with respect to tEMOS if only wind speed ensemble variables are included and to substantial refinements if additional meteorological and station-specific weather variables are integrated. As our main result, we note that, in the global setting, DVQR is able to provide better scores than tEMOS-GB in general, whereas the local DVQR is able to substantially outperform the local tEMOS-GB at particular stations admitting nonlinear relationships among the variables. In addition, we remark that training periods capturing seasonal patterns perform the best. Last but not least, we adapt a criterion for calculating the variable importance in D-vine copulas and we outline which predictor variables are due to this approach the most important for the correction of wind speed ensemble forecasts

Random forests for functional covariates

Möller AC, Tutz G, Gertheiss J. Random forests for functional covariates. Journal of Chemometrics. 2016;30(12):715-725.We propose a form of random forests that is especially suited for functional covariates. The method is based on partitioning the functions' domain in intervals and using the functions' mean values across those intervals as predictors in regression or classification trees. This approach appears to be more intuitive to applied researchers than usual methods for functional data, while also performing very well in terms of prediction accuracy. The intervals are obtained from randomly drawn, exponentially distributed waiting times. We apply our method to data from Raman spectra on boar meat as well as near-infrared absorption spectra. The predictive performance of the proposed functional random forests is compared with commonly used parametric and nonparametric functional methods and with a nonfunctional random forest using the single measurements of the curve as covariates. Further, we present a functional variable importance measure, yielding information about the relevance of the different parts of the predictor curves. Our variable importance curve is much smoother and hence easier to interpret than the one obtained from nonfunctional random forests

Predicting school transition rates in Austria with classification trees

Möller AC, George AC, Gross J. Predicting school transition rates in Austria with classification trees. International Journal of Research & Method in Education . 2022.Methods based on machine learning have become increasingly popular in many areas as they allow models to be fitted in a highly-data driven fashion and often show comparable or even increased performance in comparison to classical methods. However, in the area of educational sciences, the application of machine learning is still quite uncommon. This work investigates the benefit of using classification trees for analysing data from educational sciences. An application to data on school transition rates in Austria indicates different aspects of interest in the context of educational sciences: (i) the trees select variables for predicting school transition rates in a data-driven fashion which are well in accordance with existing confirmatory theories from educational sciences, (ii) trees can be employed for performing variable selection for regression models, and (iii) the classification performance of trees is comparable to that of binary regression models. These results indicate that trees and possibly other machine-learning methods may also be helpful to explore high-dimensional educational data sets, especially where no confirmatory theories have been developed yet

Spatially adaptive, Bayesian estimation for probabilistic temperature forecasts

Möller AC, Thorarinsdottir TL, Lenkoski A, Gneiting T. Spatially adaptive, Bayesian estimation for probabilistic temperature forecasts. arXiv:1507.05066. 2015.Uncertainty in the prediction of future weather is commonly assessed through the use of forecast ensembles that employ a numerical weather prediction model in distinct variants. Statistical postprocessing can correct for biases in the numerical model and improves calibration. We propose a Bayesian version of the standard ensemble model output statistics (EMOS) postprocessing method, in which spatially varying bias coefficients are interpreted as realizations of Gaussian Markov random fields. Our Markovian EMOS (MEMOS) technique utilizes the recently developed stochastic partial differential equation (SPDE) and integrated nested Laplace approximation (INLA) methods for computationally efficient inference. The MEMOS approach shows good predictive performance in a comparative study of 24-hour ahead temperature forecasts over Germany based on the 50-member ensemble of the European Centre for Medium-Range Weather Forecasting (ECMWF)