Annual Exceedance Probability (AEP) is the method used by U.S. Army Corps of Engineers (USACE) to determine the probability of flooding caused by the failure of a levee or other flood control structure. This method shows the probability of flooding only at one particular location at a time. In order to overcome the limitation of AEP, a new method of studying flood probability, called an AEP map, was presented. By using hydrologic and hydraulic modeling software, an AEP map can be created to determine and visualize the spatial distribution of the probability of flooding. An AEP map represents a continuous solution of the probability of flooding and can be used to derive not only the limits of the typical 100-year inundation, but any other return period including the 20-year, 50-year, 500-year storm flood. The AEP map can be more useful than traditional flood hazard maps, since it makes it possible to evaluate the probability of flooding at any location within the floodplain. In the process of creating the AEP map, it is necessary to run number of simulations in order to accurately represent the probability distribution of flooding. The objective of this research, given a desktop computer of today's capacity, is to demonstrate the convergence of AEP maps after a reasonable number of simulations, so that users can have some guidelines to decide how many simulations are necessary. The Virgin River, UT is the primary study area for this research, with Gila River, AZ also used to support the results. The result of this research demonstrates the convergence of AEP maps by illustrating the convergence of water surface elevations computed as part of the hydraulic simulation leading up to the floodplain delineation model. If the average water surface elevations converge, then the resulting floodplain delineation (AEP maps) should also converge. The result proves that AEP maps do converge with a reasonable number of simulations. This research also shows the convergence of floodplain areas to demonstrate the convergence of AEP maps.

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method to re-evaluate surge hazard probabilities for Flood Insurance Rate Maps in the New York – New Jersey coastal areas, also termed the New York Bight. As originally developed, this method required many combinations of storm parameters to statistically characterize the local climatology for numerical model simulation. Even though high-performance computing efficiency has vastly improved in recent years, researchers have utilized different “Optimal Sampling” techniques to reduce the number of storm simulations needed in the traditional Joint Probability Method. This manuscript presents results from the simulation of over 350 synthetic tropical cyclones designed to produce significant surge in the New York Bight using the hydrodynamic Advanced Circulation numerical model, bypassing the need for Optimal Sampling schemes. This data set allowed for a careful assessment of joint probability distributions utilized for this area and the impacts of current assumptions used in deriving new flood-risk maps for the New York City area.