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The memory wall and global data movement have become the dominant performance bottleneck for many scientific applications. New characterizations of data access streams and related benchmarks to measure their performances are therefore needed to compare HPC systems, software, and programming paradigms effectively. In this paper, we introduce a novel global data access benchmark, Apex-Map. It is a parameterized synthetic performance probe and integrates concepts for temporal and spatial locality into its design. We measured Apex-Map performance for a whole range of temporal and spatial localities on several advanced processors and parallel computing platforms and use the generated performance surfaces forperformance comparisons and to study the characteristics of these different architectures. We demonstrate that the results of Apex-Map clearly reflect many specific characteristics of the used systems. We also show the utility of Apex-Map for analyzing the performance effects of three leading parallel programming models and demonstrate their relative merits.