Reservoir Re-operation, Risk, and Levee Failure Analysis: Mokelumne River Case

Reservoir operation for flood control requires accurate inflow frequency analysis which involves the multivariate characteristics of flood peaks, volumes and duration. A complete understanding of flood events involves the joint probabilistic behaviors of these correlated variables. The inflow raw data are commonly transformed for flood frequency analysis, often to a form of lognormal distribution. The multivariate distribution is important for analyzing a flood episode. Flood hydrograph design is a key component flood control rule design in reservoir operation. Numerous methods have been developed to represent flood hydrograph magnitude, duration, volume and shape. Using probability density functions (PDFs) to fit the shapes of flood hydrographs has drawn more attention recently due to improvements in statistical techniques, including algorithms for fitting. Reservoirs transform unregulated flow to regulated flow with different operation rules. Regulated versus unregulated flow curves represent aspects of a reservoir flood control system. However, an accurate curve is difficult due to the complicated physical setting and uncertainties from operations. Lastly, levee failure has drawn attention due to rapid urbanization behind levees and climate change increasing hydrologic extremes. Levee failure can have several mechanisms. In California, levee failure mechanisms mainly are overtopping and erosion.;To address these issues, this dissertation presents a vertical process from inflow analysis through reservoir re-operation to levee failure analysis. First, it presents a procedure for using the bivariate normal distribution to describe the joint distributions of correlated flood peaks and volumes, and correlated flood volumes and durations. Joint distributions, conditional distributions, and the associated return periods of these random variables can be readily derived from their marginal distributions. The theoretical distributions show a good fit to observed ones. The return periods will be used for risk analysis of flood storage space changes.;After inflow multivariate analysis, this dissertation presents three steps to design flood hydrographs for reservoir reoperation: (1) Flood hydrographs separation and modification: Typical flood hydrographs were separated, selected and converted to dimensionless ones; (2) PDF fitting and selection: Beta, Gamma. Lognormal and Weibull distributions were selected and compared to be scaled to fit modified hydrographs based on goodness of fit criteria including RMSE and coefficients of determinations. (3) Development of design flood hydrographs: Design shape variables were estimated from frequency analysis and finally, design flood hydrographs including 10-, 20-, 50-, 100- and 200-year return periods were derived from the combinations of hydrographs shape, flood volume and durations.;To estimate regulated flow frequency for a reservoir's flood storage allocation, this dissertation presents three main steps including: unregulated flow frequency analysis, unregulated/regulated flow transformation and regulated flow frequency estimation. The main contributions include separating flood pulses from daily inflow time series by base flow criteria, modification of unregulated flow calculations, and fitting unregulated and regulated flow to appropriate probability distributions. Unregulated versus regulated flow curves are found using USACE's ResSim software.;Lastly, this dissertation introduces a framework to assess levee failure probability from both overtopping and erosion incorporating uncertainties from hydrologic, hydraulic and geotechnical factors. Two main contributions include overall risk estimation and load-resistance interference risk analysis. Overtopping and erosion failure probability analysis are performed separately in water resources and geotechnical engineering. This chapter presents a more comprehensive risk combining these two failure mechanisms. Load-resistance interference risk analysis is introduced to consider overtopping between flood magnitude and levee capacity and erosion failure between velocity and soil strength. Both analyses are performed by Monte Carlo simulation to estimate overall levee failure probability. Failure probability can be very sensitive to geotechnical variables and less sensitive to reservoir operation.;Camanche and Pardee reservoirs and Lower Mokelumne River levee system in Northern California are used as example applications.