Uncertainty Quantification and global Sensitivity Analysis problems are made more difficult in the case of applications which involve expensive computer simulations. This because a limited amount of simulations is available to build a sufficiently accurate metamodel of the quantities of interest. In this work, a numerical technique for the construction of a low-cost and accurate metamodel is proposed, having in mind applications with expensive computer codes. Two main points are intro- duced. Firstly, a technique which couples Universal Kriging with sparse Polynomial Dimensional Decomposition (PDD) to build a metamodel with improved accuracy. The polynomials selected by the adaptive PDD representation are used as a sparse basis to build an Universal Kriging surrogate model. The second is a strategy, derived from anisotropic mesh adaptation, to adaptively add a fixed number of new training points to an existing Design of Experiments. The convergence of the proposed algorithm is analyzed and assessed on different test functions with an increasing size of the input space. Finally, the algorithm is used to propagate uncertainties in two high-dimensional real problems related to the atmospheric reentry.