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

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.

Ensembles of forecasts are typically employed to account for the forecast uncertainties inherent in predictions of future weather states. However, biases and dispersion errors often present in forecast ensembles require statistical post-processing. Univariate post-processing models such as Bayesian model averaging (BMA) have been successfully applied for various weather quantities. Nonetheless, BMA and many other standard post-processing procedures are designed for a single weather variable, thus ignoring possible dependencies among weather quantities. In line with recently upcoming research to develop multivariate post-processing procedures, e.g., BMA for bivariate wind vectors, or flexible procedures applicable for multiple weather quantities of different types, a bivariate BMA model for joint calibration of wind speed and temperature forecasts is proposed based on the bivariate truncated normal distribution. It extends the univariate truncated normal BMA model designed for post-processing ensemble forecast of wind speed by adding a normally distributed temperature component with a covariance structure representing the dependency among the two weather quantities.The method is applied to wind speed and temperature forecasts of the eight-member University of Washington mesoscale ensemble and of the eleven-member ALADIN-HUNEPS ensemble of the Hungarian Meteorological Service and its predictive performance is compared to that of the general Gaussian copula method. The results indicate improved calibration of probabilistic and accuracy of point forecasts in comparison to the raw ensemble and the overall performance of this model is able to keep up with that of the Gaussian copula method.

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 a bivariate EMOS model for these weather quantities based on a truncated normal distribution.The bivariate EMOS model is applied to temperature and wind speed forecasts of the eight-member University of Washington mesoscale ensemble and of the elevenmember 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.

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.