Wireless sensor networks are being used in many disaster-related applications. Certain types of disasters are studied and modeled with different and dynamic risk estimations in different areas, hence requiring different levels of monitoring. Such nonuniform and dynamic coverage requirements pose a challenge to a sensor coverage problem. This work proposes the Mobile sensor Relocation using Delaunay triangulation And Shifting on Hill climbing (MR-DASH) approach, which calculates an appropriate location for each mobile sensor as an attempt to maximize coverage ratio. Based on a probabilistic sensing model, it constructs a Delaunay triangulation from static sensors' locations and vertices of interesting regions. The resulting triangles are then prioritized based on their sizes and corresponding levels of requirement so that mobile sensors can be relocated accordingly. The proposed method was both compared with an existing previous work and demonstrated with real-world disaster scenarios by simulation. The result showed that MR-DASH gives appropriate target locations that significantly improve the coverage ratio with relatively low total sensors' moving distance, while properly adapting to variations in coverage requirements.