Predicting nonstationary flood frequencies: Evidence supports an updated stationarity thesis in the United States

Abstract

Nonstationary extreme value analysis (NEVA) can improve the statistical representation of observed flood peak distributions compared to stationary (ST) analysis, but management of flood risk relies on predictions of out‐of‐sample distributions for which NEVA has not been comprehensively evaluated. In this study, we apply split‐sample testing to 1250 annual maximum discharge records in the United States and compare the predictive capabilities of NEVA relative to ST extreme value analysis using a log‐Pearson Type III (LPIII) distribution. The parameters of the LPIII distribution in the ST and nonstationary (NS) models are estimated from the first half of each record using Bayesian inference. The second half of each record is reserved to evaluate the predictions under the ST and NS models. The NS model is applied for prediction by (1) extrapolating the trend of the NS model parameters throughout the evaluation period and (2) using the NS model parameter values at the end of the fitting period to predict with an updated ST model (uST). Our analysis shows that the ST predictions are preferred, overall. NS model parameter extrapolation is rarely preferred. However, if fitting period discharges are influenced by physical changes in the watershed, for example from anthropogenic activity, the uST model is strongly preferred relative to ST and NS predictions. The uST model is therefore recommended for evaluation of current flood risk in watersheds that have undergone physical changes. Supporting information includes a MATLAB® program that estimates the (ST/NS/uST) LPIII parameters from annual peak discharge data through Bayesian inference.

The Effect of Global Warming on Future Water Availability: CMIP5 Synthesis

“…It is common practice in statistical downscaling (e.g., Ho et al, ; Watanabe et al, ) to assume that historical model biases in magnitude and seasonality will remain constant in near future projections. Such an assumption is imperfect given that it presumes stationarity but nonetheless reasonable in the context of monthly large basin‐scale terms and the uncertainties of accounting for nonstationarity (e.g., Hurst, ; Luke et al, ; Serinaldi & Kilsby, ).…”

On return period and probability of failure in hydrology

“…It is not within the scope of this study to provide a comprehensive discussion on the assumption of stationary or nonstationary models; yet it is relevant to stress that change in the observed data does not necessarily imply a nonstationary underlying process (Cohn & Lins, 2005;Koutsoyiannis & Montanari, 2015). Further, a nonstationary framework cannot be generally inferred from the observed data alone (Koutsoyiannis, 2016;Luke, Vrugt, AghaKouchak, Matthew, & Sanders, 2017;Serinaldi & Kilsby, 2015). Indeed, estimates based on historical records are typically used to extrapolate projections for planning and design purposes up to very large values of return period, by supposing that future events will statistically occur as in observed series.…”

“…The variability with time of the marginal distribution function to be used in the previous equation can be easily represented by introducing a probability model whose parameters change with time or with a covariate that is ruled by time (e.g., a climatic index). Many of the works proposing this approach make use of the generalized extreme value distribution as a model for hydrological extremes (Cheng, AghaKouchak, Gilleland, & Katz, 2014;Coles, 2001;Luke et al, 2017;Salas & Obeysekera, 2014).…”

Classification of mechanisms, climatic context, areal scaling, and synchronization of floods: the hydroclimatology of floods in the Upper Paraná River basin, Brazil

“…To make progress on understanding and mod-response, and large-scale circulation patterns associated with the forecast and diagnosis of rainfall events (Maddox, 1983;Kunkel et al, 1994;Pal and Eltahir, 2002;Schumacher and Johnson, 2005;Amengual et al, 2007;Viglione et al, 2010;Li et al, 2013). There is also extensive literature related to the statistical analysis and modeling of flood frequency from local and regional data of rainfall, streamflow, and water basin attributes, including nonstationary approaches (e.g., Thomas and Benson, 1970;Stedinger and Cohn, 1986;Stedinger et al, 1993;Kroll and Stedinger, 1998;Kwon et al, 2008;Lima and Lall, 2010;Cheng et al, 2014;Luke et al, 2017).…”