Recent internationally coordinated efforts have used deterministic climate models for a common set of experiments and have produced large datasets of future climate projections. These ensembles are subject to many sources of variability, and we propose an analysis of variance procedure to quantify the contribution from several sources to the overall variation. This procedure is based on a Bayesian linear model parameterization and is applicable for large spatial data. A key feature is that individual sources of variability are modeled through batches and assessed through the batches superpopulation variance, individual batch-level predictions, and finite population covariance. Further, for a large class of models, we show that the full posterior can be factored into conditionally independent distributions, consisting of a batch's superpopulation and batch levels. By doing so, we obviate the need for Markov chain Monte Carlo methods. Finally, this approach is applied to decadal summer temperatures for different climate models and various scenarios.