In this paper we present a workflow management system which permits the kinds of data-driven workflows required by urgent computing, namely where new data is integrated into the workflow as a disaster progresses in order refine the predictions as time goes on. This allows the workflow to adapt to new data at runtime, a capability that most workflow management systems do not possess. The workflow management system was developed for the EU-funded VESTEC project, which aims to fuse HPC with real-time data for supporting urgent decision making. We first describe an example workflow from the VESTEC project, and show why existing workflow technologies do not meet the needs of the project. We then go on to present the design of our Workflow Management System, describe how it is implemented into the VESTEC system, and provide an example of the workflow system in use for a test case.