Co-kriging is an established framework for the statistical analysis of expensive computer models running at different fidelity levels. Motivated by a Weather Research and Forecasting (WRF) climate model with different resolutions, we develop a new Bayesian treed co-krigin model. The proposed method, unlike existing ones, can take into account local features and discrepancies, while it can be used with non-nested experimental designs. Our procedure utilizes binary treed partition ideas that allow input dependent discrepancies, representation of local features, and discovery of sudden changes in the multifidelity setting. To facilitate the parameter and predictive inference, when the original design is non hierarchically nested, we design a reversible jump MCMC sampler, tailored to the proposed model, which involves collapsed blocks and direct simulation from conditional distributions This is achieved by introducing an imputation scheme which artificially creates a hierarchically nested design, allows integrating out parameters from the posterior and allows specifying conditionally conjugate priors for a number of paramerters.