Flood Risk Analysis Using Non-Stationary Models: Application to 1500 Records and Assessment of Predictive Ability

Abstract:

Urbanization and shifts in precipitation patterns have altered the risk of inland flooding. Methods to assess the flood risk, such as flood frequency analysis, are based on the key assumption of stationarity (ST). Under the ST assumption, the behavior of the hydroclimatic system (precipitation, temperature) and watershed is assumed to be time invariant. This ST assumption is quite restrictive and perhaps not accurate for flood risk assessment in watersheds that have undergone significant urbanization. Consequently, there is an urgent need for statistical methods that can account explicitly for system non-stationarity (NS) in the analysis and quantification of flood risks. One approach is to use time variant parameters in an extreme value distribution. This approach, called NEVA, has shown to improve the statistical representation of observed data (within-sample), yet NEVA has not been comprehensively evaluated for predictive analysis (out-of-sample). We apply NEVA to 1,548 records of observed annual maximum discharges with the goal to (1) assess which of the two approaches (ST/NS) and their parametric models, in Log-Pearson Type III (LPIII) distribution, best describe the statistical representation of future flood risks, and (2) which diagnostic is most suitable for model selection (NS/ST). To explore these questions, we use the first half of each flood record for inference of the LPIII model parameters using MCMC simulation with the DREAM_(ZS) algorithm – and the second part of the record is used for evaluation purposes (predictive analysis). Our results show that in about 70% of the records with a trend, the LPIII ST model performed better during evaluation than the LPIII NS model – unless the “trend” record is more than 55-years long; then the NS model is always preferred. If trend classification of the 1,548 records was done using summary metrics of watershed processes (runoff coefficient) rather than the peak discharges, the performance of the NS model improved markedly. Altogether, our results demonstrate that summary metrics rooted in hydrologic theory are more useful for assessing NS than trends in peak discharges, and NEVA is reliable for predictive analysis if records are sufficiently long or NS can be attributed to physical changes in watershed processes.