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We advocate an application-driven approach to compressing and rendering large-scale time-varying scientific-simulation data. Scientists often have specific visualization tasks in mind based on certain domain knowledge. For example, in the context of time-varying, multivariate volume-data visualization, a scientist's domain knowledge might include the salient isosurface of interest for some variable. Given this knowledge, the scientist might want to observe spatiotemporal relationships among other variables in the neighborhood of that isosurface. We've tried to directly incorporate such knowledge and tasks into data reduction, compression, and rendering. Here, we present our solution andexperimental results for two largescale time-varying, multivariate scientific data sets.