In this study, an attempt is made to better understand the effect coarsening of the parameter space has on the uncertainty representation of the response. Firstly, an HF ensemble of channelized reservoir models is constructed using a Multi-Point Statistic (MPS) approach. Several levels of coarsening are generated using a flow-based upscaling algorithm. A water injection strategy is simulated for each scale of the hierarchical ensemble. Dynamic analysis is performed on a reduced representation of the response uncertainty obtained via Multidimensional Scaling (MDS). We introduce an Uncertainty Trajectory (UT), which quantifies the coarsening effect in terms of deviation from the HF ensemble response uncertainty. The UT also includes the temporal behavior of the response uncertainty of each ensemble scale. The mean integrated distance from the HF ensemble UT can be used as a measure of dissimilarity in the flow behavior of consecutive coarser ensembles scales. Reducing the number of HF flow simulations required for uncertainty quantification can be achieved via the proposed methodology and thereby greatly reducing the overall computational cost.