The goal of this dissertation is to improve flood risk management by enhancing the computational capability of two-dimensional models and incorporating data and parameter uncertainty to more accurately represent flood risk. Improvement of computational performance is accomplished by using the Graphics Processing Unit (GPU) approach, programmed in NVIDIA's Compute Unified Development Architecture (CUDA), to create a new two-dimensional hydrodynamic model, Flood2D-GPU. The model, based on the shallow water equations, is designed to execute simulations faster than the same code programmed using a serial approach (i.e., using a Central Processing Unit (CPU)). Testing the code against an identical CPU-based version demonstrated the improved computational efficiency of the GPU-based version (approximate speedup of more than 80 times).

Given the substantial computational efficiency of Flood2D-GPU, a new Monte Carlo based flood risk modeling framework was created. The framework developed operates by performing many Flood2D-GPU simulations using randomly sampled model parameters and input variables. The Monte Carlo flood risk modeling framework is demonstrated in this dissertation by simulating the flood risk associated with a 1% annual probability flood event occurring in the Swannanoa River in Buncombe County near Asheville, North Carolina. The Monte Carlo approach is able to represent a wide range of possible scenarios, thus leading to the identification of areas outside a single simulation inundation extent that are susceptible to flood hazards. Further, the single simulation results underestimated the degree of flood hazard for the case study region when compared to the flood hazard map produced by the Monte Carlo approach.

The Monte Carlo flood risk modeling framework is also used to determine the relative benefits of flood management alternatives for flood risk reduction. The objective of the analysis is to investigate the possibility of identifying specific annual exceedance probability flood events that will have greater benefits in terms of annualized flood risk reduction compared to an arbitrarily-selected discrete annual probability event. To test the hypothesis, a study was conducted on the Swannanoa River to determine the distribution of annualized risk as a function of average annual probability. Simulations of samples of flow rate from a continuous flow distribution provided the range of annual probability events necessary. The results showed a variation in annualized risk as a function of annual probability. And as hypothesized, a maximum annualized risk reduction could be identified for a specified annual probability. For the Swannanoa case study, the continuous flow distribution suggested targeting flood proofing to control the 12% exceedance probability event to maximize the reduction of annualized risk. This suggests that the arbitrary use of a specified risk of 1% exceedance may not in some cases be the most efficient allocation of resources to reduce annualized risk.