An investigation of weighting schemes suitable for incorporating large ensembles into multi-model ensembles

Multi-model ensembles can be used to estimate uncertainty in projections of regional climate, but this uncertainty often depends on the constituents of the ensemble. The dependence of uncertainty on ensemble composition is clear when single-model initial condition large ensembles (SMILEs) are included within a multi-model ensemble. SMILEs allow for the quantification of internal variability, a non-negligible component of uncertainty on regional scales, but may also serve to inappropriately narrow uncertainty by giving a single model many additional votes. In advance of the mixed multi-model, the SMILE Coupled Model Intercomparison version 6 (CMIP6) ensemble, we investigate weighting approaches to incorporate 50 members of the Community Earth System Model (CESM1.2.2-LE), 50 members of the Canadian Earth System Model (CanESM2-LE), and 100 members of the MPI Grand Ensemble (MPI-GE) into an 88-member Coupled Model Intercomparison Project Phase 5 (CMIP5) ensemble. The weights assigned are based on ability to reproduce observed climate (performance) and scaled by a measure of redundancy (dependence). Surface air temperature (SAT) and sea level pressure (SLP) predictors are used to determine the weights, and relationships between present and future predictor behavior are discussed. The estimated residual thermodynamic trend is proposed as an alternative predictor to replace 50-year regional SAT trends, which are more susceptible to internal variability. Uncertainty in estimates of northern European winter and Mediterranean summer end-of-century warming is assessed in a CMIP5 and a combined SMILE-CMIP5 multi-model ensemble. Five different weighting strategies to account for the mix of initial condition (IC) ensemble members and individually represented models within the multi-model ensemble are considered. Allowing all multi-model ensemble members to receive either equal weight or solely a performance weight (based on the root mean square error (RMSE) between members and observations over nine predictors) is shown to lead to uncertainty estimates that are dominated by the presence of SMILEs. A more suitable approach includes a dependence assumption, scaling either by 1/N, the number of constituents representing a "model", or by the same RMSE distance metric used to define model performance. SMILE contributions to the weighted ensemble are smallest (< 10 %) when a model is defined as an IC ensemble and increase slightly (< 20 %) when the definition of a model expands to include members from the same institution and/or development stream. SMILE contributions increase further when dependence is defined by RMSE (over nine predictors) amongst members because RMSEs between SMILE members can be as large as RMSEs between SMILE members and other models. We find that an alternative RMSE distance metric, derived from global SAT and hemispheric SLP climatology, is able to better identify IC members in general and SMILE members in particular as members of the same model. Further, more subtle dependencies associated with resolution differences and component similarities are also identified by the global predictor set.