This thesis proposes an alternative for mapping flood risk and applies the methodology to the Houston area, where recent storm events and subsequent flood damages have highlighted the need for improved flood risk mapping. Houston’s flat slopes, intense rain, and high urbanization cause significant flooding that is not captured in official floodplain maps. These floodplain maps form the basis of flood insurance requirements, so it is critical that they accurately represent the properties that are at risk of flooding. This thesis proposes the use of stochastic storm transposition, which is able to create artificial rainfall records on the order of hundreds of years while maintaining storm structure. This method is then used in conjunction with probabilistic modeling to account for uncertainty in rain events. While many studies have explored the use of probabilistic flood modeling to better map flood hazard, few studies have captured the range of uncertainty in the rainfall input due to spatiotemporal variation, duration, and intensity of rain events. Additionally, 2D hydraulic modeling is used to capture local flooding in addition to riverine flooding. The resulting flood hazard maps more reliably capture flood hazard than official FEMA floodplains maps, demonstrating that the methodology presented here in this thesis should be further explored and considered as an alternative to the current official floodplain maps.