Summary. Projections of future climate are often based on deterministic models of the Earth’s atmosphere and oceans. However, these projections can vary widely between models, with differences becoming more pronounced at the relatively fine spatial and temporal scales that are relevant in many applications. We suggest that the resulting uncertainty can be handled in a logically coherent and interpretable way by using a hierarchical statistical model, implemented in a Bayesian framework. Model fitting using Markov chain Monte Carlo techniques is feasible but moderately time consuming; the computational efficiency can, however, be improved dramatically by substituting maximum likelihood estimates for the original data. The work was motivated by the need for future precipitation scenarios in the UK, in applications such as flood risk assessment and water resource management. We illustrate the methodology by considering the generation of multivariate time series of atmospheric variables, that can be used to drive stochastic simulations of high resolution precipitation for risk assessment purposes.