As wind energy penetration continues to grow, there is a critical need for probabilistic forecasts of wind resources. In addition, there are many other societally relevant uses for forecasts of wind speed, ranging from aviation to ship routing and recreational boating. Over the past two decades, ensembles of dynamical weather prediction models have been developed, in which multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic forecasts. However, even state of the art ensemble systems are uncalibrated and biased. Here we propose a novel way of statistically post-processing dynamical ensembles for wind speed by using heteroscedastic censored (tobit) regression, where location and spread derive from the ensemble. The resulting ensemble model output statistics method is applied to 48-h-ahead forecasts of maximum wind speed over the North American Pacific Northwest by using the University of Washington mesoscale ensemble. The statistically post-processed density forecasts turn out to be calibrated and sharp, and result in a substantial improvement over the unprocessed ensemble or climatological reference forecasts. Copyright (c) 2009 Royal Statistical Society.

Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate crossvariable, spatial and temporal dependence structures, with weather and climate predictions being key examples. There is a strongly increasing recognition of the need for uncertainty quantification in such settings, for which we propose and review a general multi-stage procedure called ensemble copula coupling (ECC), proceeding as follows:1. Generate a raw ensemble, consisting of multiple runs of the computer model that differ in the inputs or model parameters in suitable ways.2. Apply statistical postprocessing techniques, such as Bayesian model averaging or nonhomogeneous regression, to correct for systematic errors in the raw ensemble, to obtain calibrated and sharp predictive distributions for each univariate output variable individually.3. Draw a sample from each postprocessed predictive distribution. 4. Rearrange the sampled values in the rank order structure of the raw ensemble to obtain the ECC postprocessed ensemble.The use of ensembles and statistical postprocessing have become routine in weather forecasting over the past decade. We show that seemingly unrelated, recent advances can be interpreted, fused and consolidated within the framework of ECC, the common thread being the adoption of the empirical copula of the raw ensemble. Depending on the use of Quantiles, Random draws or Transformations at the sampling stage, we distinguish the ECC-Q, ECC-R and ECC-T variants, respectively. We also describe relations to the Schaake shuffle and extant copula-based techniques. In a case study, the ECC approach is applied to predictions of temperature, pressure, precipitation and wind over Germany, based on the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble.

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We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint distribution. To correct this, we propose the use of a Gaussian copula, which offers a simple procedure for recovering the dependence that is lost in the estimation of the ensemble BMA marginals. Our method is applied to 48 h forecasts of a set of five weather quantities using the eight-member University of Washington mesoscale ensemble. We show that our method recovers many well-understood dependencies between weather quantities and subsequently improves calibration and sharpness over both the raw ensemble and a method which does not incorporate joint distributional information. Copyright c 2012 Royal Meteorological Society Key Words: ensemble post-processing; joint predictive distributions; copula methods

In weather forecasting, non-homogeneous regression (NR) is used to statistically post-process forecast ensembles in order to obtain calibrated predictive distributions. For wind speed forecasts, the regression model is given by a truncated normal (TN) distribution, where location and spread derive from the ensemble. This article proposes two alternative approaches which utilise the generalised extreme value (GEV) distribution. A direct alternative to the TN regression is to apply a predictive distribution from the GEV family, while a regime-switching approach based on the median of the forecast ensemble incorporates both distributions. In a case study on daily maximum wind speed over Germany with the forecast ensemble from the European Centre for Medium-Range Weather Forecasts (ECMWF), all three approaches significantly improve the calibration as well as the overall skill of the raw ensemble with the regime-switching approach showing the highest skill in the upper tail

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations has unexpected and undesired effects, and is bound to discredit skillful forecasts when the signal-to-noise ratio in the data generating process is low. Conditioning on outcomes is incompatible with the theoretical assumptions of established forecast evaluation methods, thereby confronting forecasters with what we refer to as the forecaster's dilemma. For probabilistic forecasts, proper weighted scoring rules have been proposed as decision theoretically justifiable alternatives for forecast evaluation with an emphasis on extreme events. Using theoretical arguments, simulation experiments, and a real data study on probabilistic forecasts of U.S. inflation and gross domestic product (GDP) growth, we illustrate and discuss the forecaster's dilemma along with potential remedies.Key words and phrases: Diebold-Mariano test, likelihood ratio test, Neyman-Pearson lemma, predictive performance, probabilistic forecast, proper weighted scoring rule, rare and extreme events.Quod male consultum cecidit feliciter, Ancus, Arguitur sapiens, quo modo stultus erat. Quod prudenter erat provisum, si male vortat, Ipse Cato (populo iudice) stultus erat. 1

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A bivariate ensemble model output statistics (EMOS) technique for the postprocessing of ensemble forecasts of two-dimensional wind vectors is proposed, where the postprocessed probabilistic forecast takes the form of a bivariate normal probability density function. The postprocessed means and variances of the wind vector components are linearly bias-corrected versions of the ensemble means and ensemble variances, respectively, and the conditional correlation between the wind components is represented by a trigonometric function of the ensemble mean wind direction. In a case study on 48-hour forecasts of wind vectors over the North American Pacific Northwest with the University of Washington Mesoscale Ensemble, the bivariate EMOS density forecasts were calibrated and sharp, and showed considerable improvement over the raw ensemble and reference forecasts, including ensemble copula coupling.