Flood Protection Reliability: The Impact of Uncertainty and Nonstationarity. Issue 2 (31st January 2023) - Stephens, T. A.; Bledsoe, B. P.
Abstract: Recent catastrophic flood events, increasing flood losses, and climate change challenge current reliability estimates defined by the probability that flood levels will not exceed protection measures over a planning horizon. These estimates depict an expected reliability that mask uncertainty in streamflow and the capacity of river channels and floodplains. We described reliability as a random variable whose distribution depends on uncertainty and nonstationarity in annual maximum flood (AMF) distributions and flow capacity uncertainty. Numerical experiments quantified the impacts of nonstationarity and variance in AMFs and flow capacity uncertainty on estimates of flood protection reliability, thereby providing the first examination of their interacting effects. The distribution of reliability along a regulatory floodplain boundary was quantified through a bootstrap scheme that accounts for nonstationarity and uncertainty in AMFs and flow capacity uncertainty. Results indicated that accounting for uncertainty in flow capacity substantially reduces reliability compared to estimates based solely on flood likelihood; the divergence is greater in the presence of nonstationary AMFs. The distribution of reliability along the regulatory floodplain boundary was spatially heterogeneous due to within‐reach variation in flow capacity uncertainty. Quantifying the distribution of reliability for flood protection measures enables transparent communication and selection of a desired confidence level that is commensurate with a contextually appropriate risk tolerance. Similarly, we show that a desired level of confidence in reliability can be specified to estimate a design flood protection level. These results reveal how the combined impacts of uncertainty and nonstationarity can impact reliability estimates and confidence in those estimates. Plain Language Summary: Flood protection reliability is subject to uncertainty, and estimates can be described with a level of confidence (e.g., 90% confidence in 90% reliability over a planning horizon). In addition, changes in the magnitude and frequency of flood events can cause reliability to change through time. In other words, flood events are nonstationary; their statistical properties can change through time. However, flood protection reliability is often communicated as a precisely known value without conveying the confidence, uncertainty, or changing flood events in that estimate. We developed a method that accounts for nonstationarity and uncertainty to quantify the distribution of flood protection reliability for a given location on the floodplain. Results show that nonstationarity and uncertainty can substantially reduce flood protection reliability and require a significant increase in design flood flows depending on the desired level of confidence in a reliability estimate. These results suggest flood hazard maps that do not account for and describe uncertainty and reliability may substantially underestimate exposure to future flooding and provide a false sense of protection. Key Points: Uncertainty and nonstationarity reduce reliability of flood protection compared to estimates based only on stationary flood likelihood Flood protection reliability distributions differ at proximate locations due to uncertainty in channel and floodplain characteristics Quantifying the distribution of reliability enables more transparent description of confidence and specifying contextually appropriate design floods