In several applications, interest lies on understanding the behaviour as well as the underlying mechanisms of real systems such as physical procedures or engineering experiments. Computer experiments often use computer models to simulate the behaviour of the real system. Here, we focus on cases where the computer models are expensive, and can run at different levels of fidelity. We discuss about statistical methods for the analysis of multi-fidelity computer models in the Bayesian framework. Motivated by a Weather Research and Forecasting climate model with different resolutions, we introduce a new Bayesian procedure suitable for applications where the landscape of the computer model output presents discontinuities, while the available data-sets from different fidelity levels are not hierarchically nested.