Evaluation of crop model prediction and uncertainty using Bayesian parameter estimation and Bayesian model averaging

Yujing Gao, Daniel Wallach, Toshihiro Hasegawa, Liang Tang, Ruoyang Zhang, Senthold Asseng, Tamer Kahveci, Leilei Liu, Jianqiang He, Gerrit Hoogenboom

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


A recent trend in crop modeling has been the use of multi-model ensembles (MMEs) for impact assessment, especially as it relates to climate change. Studies have shown that, compared to individual models, the mean or median of a MME is a better predictor that is more accurate in making predictions and capable of providing model uncertainty information. In previous studies that used MMEs, each individual model was assigned an equal weight by simply averaging the predictions over all the models. Here we adopted a different method of creating MMEs, namely using Bayesian model averaging (BMA), which assigns different weights to individual models according to their performance of reproducing historical data. The main purpose of this study is to illustrate how BMA can be applied to crop models, and to compare its performance with simple model averaging. In addition, we also illustrate a full chain of analysis for crop model ensembles, which includes parameter estimation, ensemble creation and evaluation, uncertainty quantification and evaluation. The approaches were implemented with simulations of rice phenology using a small, three-member model ensemble. The results showed that the ensemble model e-BMA had nearly the same prediction accuracy as the best single model and that it predicts quite a bit better than the simply averaging ensemble named e-equal here. Squared bias was found to be the largest contributor to overall prediction uncertainty, both for the individual models and the ensemble models, and thus should be the first priority for model improvement. The estimated prediction uncertainties were larger than the variance of the observations. In the future, BMA should be tested more widely.

Original languageEnglish
Article number108686
JournalAgricultural and Forest Meteorology
StatePublished - 15 Dec 2021
Externally publishedYes


  • Crop models
  • MCMC
  • Model weighting
  • Multi-model ensemble
  • Reliability diagram


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