Partitioning Uncertainty Components of an Incomplete Ensemble of Climate Projections Using Data Augmentation

The quantification of uncertainty sources in ensembles of climate projections obtained from combinations of different scenarios and climate and impact models is a key issue in climate impact studies. The small size of the ensembles of simulation chains and their incomplete sampling of scenario and climate model combinations makes the analysis difficult. In the popular single-time ANOVA approach for instance, a precise estimate of internal variability requires multiple members for each simulation chain (e.g., each emission scenario-climate model combination), but multiple members are typically available for a few chains only. In most ensembles also, a precise partition of model uncertainty components is not possible because the matrix of available scenario/models combinations is incomplete (i.e., projections are missing for many scenario-model combinations). The method we present here, based on data augmentation and Bayesian techniques, overcomes such limitations and makes the statistical analysis possible for single-member and incomplete ensembles. It provides unbiased estimates of climate change responses of all simulation chains and of all uncertainty variables. It additionally propagates uncertainty due to missing information in the estimates. This approach is illustrated for projections of regional precipitation and temperature for four mountain massifs in France. It is applicable for any kind of ensemble of climate projections, including those produced from ad hoc impact models.