Sinkhole Mapping Act of 2019 This bill directs the United States Geological Survey (USGS) to establish a program to study the short-term and long-term mechanisms that cause sinkholes, including extreme storm events, prolonged droughts causing shifts in water management practices, aquifer depletion, and other major changes in water use; and develop maps depicting the zones that are at greater risk of forming sinkholes. The USGS must establish a public website that displays such maps and other relevant information critical for use by community planners and emergency managers.