Application of the Bayesian Processor of Ensemble to the Combination and Calibration of Ensemble Forecasts

  • Yi Wang
  • Xiaomei ZhangEmail author
  • Zoltan Toth
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 550)


Ensemble forecasts are developed to assess and convey uncertainty in weather forecasts. Unfortunately, ensemble prediction systems (EPS) usually underestimate uncertainty and thus are statistically not reliable. In this study, we apply the Bayesian Processor of Ensemble (BPE), which is an extension of the statistical post-processing method of Bayesian Processor of Forecasts (BPF) to calibrate ensemble forecasts. BPE is performed to obtain a posterior function through the combination of a regression-based likelihood function and a climatological prior. The method is applied to 1–10 day lead time EPS forecasts from the NCEP Global Ensemble Forecast System (GEFS) and the Canadian Meteorological Centre (CMC) of 2-m temperature at 24 stations over the continental United States (CONUS). Continuous rank probability score is used to evaluate the performance of posterior probability forecasts. Results show that post-processed ensembles are much better calibrated than the raw ensemble. In addition, merging two ensemble forecasts by incorporating the CMC ensemble mean as another predictor in addition to GEFS ensemble forecasts is shown to provide more skillful and reliable probabilistic forecasts. BPE has a broad potential use in the future given its flexible framework for calibrating and combining ensemble forecast.


Ensemble forecasting Statistical post-processing 



We thank Kevin Kelleher, former Director of GSD/ESRL/NOAA for his support. The work was sponsored by the National Key Research and Development Program of China (2017YFC1502004) and “Key technology research on medium range forecast” (2015BAC03B01) project. The detailed algorithm of the BPE was developed by Professor Krzysztofowicz of the University of Virginia and coded by Geary Layne of GSD. We acknowledge discussions with Mark Antolik and Jeffrey Craven of MDL. Data were kindly provided by John Wagner and Carly Buxton of MDL.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.National Meteorological CentreChina Meteorological AdministrationBeijingChina
  2. 2.Public Meteorological Service CentreChina Meteorological AdministrationBeijingChina
  3. 3.Global Systems Division, Earth System Research LaboratoryNational Oceanic and Atmospheric AdministrationBoulderUSA

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