On the use of observations in assessment of multi-model climate ensemble

  • Donghui Xu
  • Valeriy Y. IvanovEmail author
  • Jongho Kim
  • Simone Fatichi
Original Paper


The Bayesian weighted averaging (BWA) method is commonly used to integrate over multi-model ensembles of climate series. This method relies on two criteria to assign weights to individual outputs: model skill in reproducing historical observations, and inter-model agreement in simulating future period. Observations are generally thought to be relevant for correcting biases in model outputs in the BWA framework. However, they concurrently may introduce unpredictable impacts in the context of the downscaling process, in particular, when model output on precipitation is of interest. Specifically, the posterior distribution may excessively depend on few ‘outlier models’ being close to the observation, when all other models fail to capture observation of the historical period—a common situation for precipitation metrics. Another issue emerges for climates with very dry months: the inclusion of observation in BWA may result in a significant spread of the posterior distribution into the negative region. To address these problems, a modified version of the BWA method that removes observations in the initial phase of downscaling (computation of Factors of Change) and adds them in the estimation of posterior distributions is explored in this work. Comparisons of simulation results for the locations of Miami (FL), Fresno (CA), and Flint (MI) between the modified BWA and the traditional BWA demonstrate consistent outcomes with regards to the effect of observation in the Bayesian framework. Further, the modified BWA approach generally reduces uncertainty, as compared to ‘simple averaging’ in the Bayesian context, which assigns equal weights to all model outputs.


Bayesian weighted averaging Multi-model ensemble Weighting skill Model bias Observations Factor of change 



This study was supported by the NSF Grant EAR 1151443. Jongho Kim was supported by a Grant (18AWMP-B127554-02) from the Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government. We acknowledge the modeling groups listed in Table 1, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modelling (WGCM) for making the CMIP5 multi-model dataset available. We also thank the Office of Support, U.S. Department of Energy for providing the support of this dataset.

Supplementary material

477_2018_1621_MOESM1_ESM.docx (10.6 mb)
Supplementary material 1 (DOCX 10823 kb)


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.School of Civil and Environmental EngineeringUniversity of UlsanUlsanSouth Korea
  3. 3.Department of Civil and Environmental EngineeringSejong UniversitySeoulSouth Korea
  4. 4.Institute of Environmental Engineering, ETH ZurichZurichSwitzerland

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