Surrogate modeling of computational simulations via local models, which induce sparsity by only considering short range interactions, can tackle huge analyses of complicated input-output relationships. However, narrowing focus to local scale means that global trends must be relearned over and over again. We first demonstrate how to use Gaussian processes to efficiently perform a global sensitivity analysis on an expensive black box simulator. We next propose a framework for incorporating information from this global sensitivity analysis into the surrogate model as an input rotation and rescaling preprocessing step. We discuss the relationship between several sensitivity analysis methods based on kernel regression before describing how they give rise to a transformation of the input variables. Specifically, we perform an input warping such that the "warped simulator" is equally sensitive to all input directions, freeing local models to focus on local dynamics. Numerical experiments on observational data and benchmark test functions, including a high-dimensional computer simulator from the automotive industry, provide empirical validation.