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Understanding the dynamic behavior of parallel programs is key to developing efficient system software and runtime environments; this is even more true on emerging computational Grids where resource availability and performance can change in unpredictable ways. Event tracing provides details on behavioral dynamics, albeit often at great cost. We describe an intermediate approach, based on curve fitting, that retains many of the advantages of event tracing but with lower overhead. These compact "application signatures" summarize the time-varying resource needs of scientific codes from historical trace data. We also developed a comparison scheme that measures similarity between two signatures, both across executions and across execution environments.