Many hydrological applications require high-resolution rainfall data under scenarios of climate change. This thesis uses numerical climate model output at a coarse spatial resolution to condition simulations of sub-daily rainfall sequences at individual sites. Downscaling techniques based on generalised linear models are employed, along with stochastic models based on Poisson cluster processes. The two model classes are coupled using stable relationships between the properties of observed rainfall sequences at different time scales. It is recognised that projections of future climate can differ widely between climate models and it is therefore necessary to account for climate model uncertainty. A hierarchical statistical model is proposed, and implemented in a Bayesian framework, which provides a logically coherent and interpretable way to describe uncertainty in multivariate sequences of climate model output. A way of dramatically reducing the computing time needed to fit such a model, based on condensing the data via the use of maximum likelihood estimates, is also discussed. The ideas are illustrated by considering the generation of future daily rainfall sequences at sites in the UK, using climate model outputs under the SRES A2 emissions scenario.