We apply a new efficient methodology for Bayesian global sensitivity analysis for large-scale multivariate data. A multivariate Gaussian process is used as a surrogate model to replace the expensive computer model. To improve the computational efficiency and performance of the model, compactly supported correlation functions are used. The goal is to generate sparse matrices, which give crucial advantages when dealing with large data sets. The method was applied to multivariate data from the IMPRESSIONS Integrated Assessment Platform version 2. Our empirical results on Integrated Assessment Platform version 2 data show that the proposed methods are efficient and accurate for global sensitivity analysis of complex models.