A Decision-Oriented Approach for Detecting and Modeling Non-Stationary Flood Frequency

Abstract:

Changes in the frequency of extreme floods have been observed and anticipated in many hydrologic settings in response to numerous drivers of environmental change, including climate, land cover, and infrastructure. To help decision-makers design flood control infrastructure in settings with non-stationary hydrologic regimes, a parsimonious approach for detecting and modeling trends in extreme floods is needed. An approach using ordinary least squares (OLS) regression can accommodate nonstationarity in both the mean and variance of flood series while simultaneously offering a means of (i) analytically evaluating type I and type II trend detection errors, (ii) analytically generating expressions of uncertainty, such as confidence and prediction intervals, (iii) providing updated estimates of the frequency of floods exceeding the flood of record, (iv) accommodating a wide range of non-linear functions through ladder of powers transformations, and (v) communicating hydrologic changes in a single graphical image. Previous research has shown that the two-parameter lognormal distribution can adequately model the annual maximum flood distribution of both stationary and non-stationary hydrologic regimes in many regions of the United States. A simple logarithmic transformation of annual maximum flood series makes an OLS regression modeling approach especially suitable for creating a non-stationary flood frequency distribution with parameters that are conditional upon time or a physically meaningful covariate. While the heteroscedasticity of some OLS models may be viewed as an impediment, it also presents an opportunity for characterizing both the conditional mean and variance of annual maximum floods. Through a case study of an urbanizing watershed, we demonstrate that accounting for trends in both the mean and variance can yield substantially different estimates of time-dependent extreme flood quantiles than only considering trends in the mean. When applied to risk-based optimization, including trends in the variance strongly influences the flood magnitude for which flood control infrastructure should be designed over a given planning horizon. This approach can easily be extended to multivariate regression equations that take physically meaningful covariates into account.