The Annals of Applied Statistics

Probabilistic wind speed forecasting on a grid based on ensemble model output statistics

Michael Scheuerer and David Möller

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Probabilistic forecasts of wind speed are important for a wide range of applications, ranging from operational decision making in connection with wind power generation to storm warnings, ship routing and aviation. We present a statistical method that provides locally calibrated, probabilistic wind speed forecasts at any desired place within the forecast domain based on the output of a numerical weather prediction (NWP) model. Three approaches for wind speed post-processing are proposed, which use either truncated normal, gamma or truncated logistic distributions to make probabilistic predictions about future observations conditional on the forecasts of an ensemble prediction system (EPS). In order to provide probabilistic forecasts on a grid, predictive distributions that were calibrated with local wind speed observations need to be interpolated. We study several interpolation schemes that combine geostatistical methods with local information on annual mean wind speeds, and evaluate the proposed methodology with surface wind speed forecasts over Germany from the COSMO-DE (Consortium for Small-scale Modelling) ensemble prediction system.

Article information

Ann. Appl. Stat., Volume 9, Number 3 (2015), 1328-1349.

Received: February 2014
Revised: May 2015
First available in Project Euclid: 2 November 2015

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Continuous ranked probability score density forecast ensemble prediction system numerical weather prediction Gaussian process


Scheuerer, Michael; Möller, David. Probabilistic wind speed forecasting on a grid based on ensemble model output statistics. Ann. Appl. Stat. 9 (2015), no. 3, 1328--1349. doi:10.1214/15-AOAS843.

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  • Baldauf, M., Seifert, A., Förstner, J., Majewski, D., Raschendorfer, M. and Reinhardt, T. (2011). Operational convective-scale numerical weather prediction with the COSMO model: Description and sensitivities. Monthly Weather Review 139 3887–3905.
  • Baran, S., Nemoda, D. and Horányi, A. (2013). Probabilistic wind speed forecasting in Hungary. Meteorologische Zeitschrift 22 273–282.
  • Buizza, R., Houtekamer, P. L., Toth, Z., Pellerin, G., Wei, M. and Zhu, Y. (2005). A comparison of the ECMWF, MSC and NCEP global ensemble prediction systems. Monthly Weather Review 133 1076–1097.
  • Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. Y. (1995). A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16 1190–1208.
  • Chilès, J.-P. and Delfiner, P. (2012). Geostatistics: Modeling Spatial Uncertainty, 2nd ed. Wiley, Hoboken, NJ.
  • China Internet Information Center (2011). Renewable energy law of the People’s Republic of China. Press release.
  • Courtney, J. F., Lynch, P. and Sweeney, C. (2013). High resolution forecasting for wind energy applications using Bayesian model averaging. Tellus A 65 19669.
  • Doms, G. and Schättler, U. (2002). A description of the nonhydrostatic regional model LM: Dynamics and numerics. Technical report, Deutscher Wetterdienst.
  • Durst, C. S. (1960). Wind speeds over short period of time. The Meteorological Magazine 89 181–187.
  • European Commission (2008). Climate change: Commission welcomes final adoption of Europe’s climate and energy package. Press release. Available at
  • European Wind Energy Association (2008). Pure power–wind energy scenarios up to 2030, final report. Press release. Available at
  • Friederichs, P. and Thorarinsdottir, T. L. (2012). Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction. Environmetrics 23 579–594.
  • Gebhardt, C., Theis, S. E., Paulat, M. and Ben Bouallègue, Z. (2011). Uncertainties in COSMO-DE precipitation forecasts introduced by model perturbations and variations of lateral boundaries. Atmospheric Research 100 168–177.
  • Gerth, W.-P. and Christoffer, J. (1994). Windkarten von Deutschland. Meteorologische Zeitschrift. Meteorologische Zeitschrift 3 67–77.
  • Gneiting, T. (2008). Editorial: Probabilistic forecasting. J. Roy. Statist. Soc. Ser. A 171 319–321.
  • Gneiting, T. (2011). Making and evaluating point forecasts. J. Amer. Statist. Assoc. 106 746–762.
  • Gneiting, T., Balabdaoui, F. and Raftery, A. E. (2007). Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B. Stat. Methodol. 69 243–268.
  • Gneiting, T., Larson, K., Westrick, K., Genton, M. G. and Aldrich, E. (2006). Calibrated probabilistic forecasting at the stateline wind energy center: The regime-switching space–time method. J. Amer. Statist. Assoc. 101 968–979.
  • Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359–378.
  • Gneiting, T., Raftery, A. E., Westveld, A. H. and Goldman, T. (2005). Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133 1098–1118.
  • Hamill, T. M. and Colucci, S. J. (1997). Verification of Eta-RSM short-range ensemble forecasts. Monthly Weather Review 125 1312–1327.
  • Hersbach, H. (2000). Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather and Forecasting 15 559–570.
  • Jeon, J. and Taylor, J. W. (2012). Using conditional kernel density estimation for wind power density forecasting. J. Amer. Statist. Assoc. 107 66–79.
  • Keller, J. and Hense, A. (2011). A new non-Gaussian evaluation method for ensemble forecasts based on analysis rank histograms. Meteorologische Zeitschrift 20 107–117.
  • Kleiber, W., Raftery, A. E., Baars, J., Gneiting, T., Mass, C. and Grimit, E. P. (2011). Locally calibrated probabilistic temperature foreasting using geostatistical model averaging and local Bayesian model averaging. Monthly Weather Review 139 2630–2649.
  • Lerch, S. and Thorarinsdottir, T. L. (2013). Comparison of nonhomogeneous regression models for probabilistic wind speed forecasting. Tellus A 65 21206.
  • McDonald, J. B. and Jensen, B. C. (1979). An analysis of some properties of alternative measures of income inequality based on the gamma distribution function. J. Amer. Statist. Assoc. 74 856–860.
  • Messner, J. W., Mayr, G. J., Wilks, D. S. and Zeileis, A. (2014a). Extending extended logistic regression: Extended versus separate versus ordered versus censored. Monthly Weather Review 142 3003–3014.
  • Messner, J. W., Mayr, G. J., Zeileis, A. and Wilks, D. S. (2014b). Heteroscedastic extended logistic regression for postprocessing of ensemble guidance. Monthly Weather Review 142 448–456.
  • National Research Council (2006). Completing the forecast: Characterizing and communicating uncertainty for better decisions using weather and climate forecasts. National Academies Press, Washington, DC.
  • Palmer, T. N. (2002). The economic value of ensemble forecasts as a tool for risk assessment: From days to decades. Quarterly Journal of the Royal Meteorological Society 128 747–774.
  • Pinson, P. (2013). Wind energy: Forecasting challenges for its operational management. Statist. Sci. 28 564–585.
  • Raftery, A. E., Gneiting, T., Balabdaoui, F. and Polakowski, M. (2005). Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133 1155–1174.
  • Scheuerer, M. and Büermann, L. (2014). Spatially adaptive post-processing of ensemble forecasts for temperature. J. R. Stat. Soc. Ser. C. Appl. Stat. 63 405–422.
  • Scheuerer, M., Schaback, R. and Schlather, M. (2013). Interpolation of spatial data—A stochastic or a deterministic problem? European J. Appl. Math. 24 601–629.
  • Sloughter, M., Gneiting, T. and Raftery, A. E. (2010). Probabilistic wind spread forecasting using ensembles and Bayesian model averaging. J. Amer. Statist. Assoc. 105 25–35.
  • Thorarinsdottir, T. L. and Gneiting, T. (2010). Probabilistic forecasts of wind speed: Ensemble model ouput statistics by using heteroscedastic censored regression. J. Roy. Statist. Soc. Ser. A 173 371–388.
  • Thorarinsdottir, T. L. and Johnson, M. S. (2012). Probabilistic wind gust forecasting using non-homogeneous Gaussian regression. Monthly Weather Review 140 889–897.
  • Troen, I. and Petersen, E. L. (1989). European wind atlas. Technical report, Risø National Laboratory, Roskilde.
  • U.S. Department of Energy (2008). 20% wind energy by 2030: Increasing wind energy’s contribution to U.S. electricity supply. DOE Office of Energy Efficiency and Renewable Energy Report. Available at