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The Digital Library Research Laboratory (DLRL) has collected over 3.5 billion tweets on different events for the Coordinated, Behaviorally-Aware Recovery for Transportation and Power Disruptions (CBAR-tpd), the Integrated Digital Event Archiving and Library (IDEAL), and the Global Event Trend Archive Research (GETAR) projects. The tweet collection topics include heart attack, solar eclipse, terrorism, etc. There are several collections on naturally occurring events such as hurricanes, floods, and solar eclipses. Such naturally occurring events are distributed across space and time. It would be beneficial to researchers if we can perform a spatial-temporal analysis to test some hypotheses, and to find any trends that tweets would reveal for such events. I apply an existing algorithm to detect locations from tweets by modifying it to work better with the type of datasets I work with. I use the time captured in tweets and also identify the tense of the sentences in tweets to perform the temporal analysis. I build a rule-based model for obtaining the tense of a tweet. The results from these two algorithms are merged to analyze naturally occurring moving events such as solar eclipses and hurricanes. Using the spatial-temporal information from tweets, I study if tweets can be a relevant source of information in understanding the movement of the event. I create visualizations to compare the actual path of the event with the information extracted by my algorithms. After examining the results from the analysis, I noted that Twitter can be a reliable source to identify places affected by moving events almost immediately. The locations obtained are at a more detailed level than in news-wires. We can also identify the time that an event affected a particular region by date.