Flood-frequency estimation for very low annual exceedance probabilities using historical, paleoflood, and regional information with consideration of nonstationarity

Streamflow estimates for floods with an annual exceedance probability of 0.001 or lower are needed to accurately portray risks to critical infrastructure, such as nuclear powerplants and large dams. However, extrapolating flood-frequency curves developed from at-site systematic streamflow records to very low annual exceedance probabilities (less than 0.001) results in large uncertainties in the streamflow estimates. Traditionally, methods for statistically estimating flood frequency have relied on the systematic streamflow record, which provides a time series of annual maximum flood peaks, often including some historical peaks. However, most peak-flow records are less than 100 years, and uncertainties are large when trying to extrapolate magnitudes of very low annual exceedance probability events.

Other data may be available that extend the record beyond the systematic dataset. Historical data are defined as data from outside the period of systematic records but within the period of human records. Examples of historical information include flood estimates from other agencies and newspaper accounts that can be translated to flood magnitude point estimates, interval estimates, or perception thresholds (such as a statement that an 1880 flood was the largest since 1869). Paleoflood data, which may also extend the dataset, include a broad range of information about flood occurrence or magnitude from sources like sediment deposits or tree rings.

Several assumptions are made in flood-frequency analysis, and an understanding of whether the data conform to these assumptions is desired. A particularly difficult assumption to evaluate for flood-frequency analysis is the underlying assumption that the flood series is stationary—the assumption that a time series of peak flow varies around a constant mean within a particular range of values (constant variance). As the hydrologic community’s understanding of natural systems and anthropogenic effects on streamflows has evolved, the community has come to understand that many surface-water systems exhibit one or more forms of nonstationarity, and thus the stationarity assumption is often violated to some degree. However, there is currently (2020) no consensus among hydrologists regarding the most appropriate flood-frequency-analysis methods for nonstationary systems, and this topic remains an active area of research.

A literature review was completed to summarize the state of the science of flood frequency. The literature review highlights tools available to detect nonstationarities and identifies approaches that include external information to inform flood-frequency analysis. To demonstrate methods for initial data analysis and for incorporating historical and paleoflood information in flood-frequency analysis, five sites were selected: the Red River of the North at James Avenue Pumping Station, Winnipeg, Manitoba, Canada; lower reach, Rapid Creek, South Dakota; Spring Creek, South Dakota; Cherry Creek near Melvin, Colorado; and Escalante River near Escalante, Utah. The sites were chosen for the availability of published historical and paleoflood data and for their geographic diversity and unique characteristics, which highlighted issues such as autocorrelation, change points, trends, outlier peaks, or short periods of record.

An initial data analysis that involved examining records for autocorrelation, change points, and trends was completed for all sites. The flood-frequency analysis completed for this study used version 7.2 of the U.S. Geological Survey PeakFQ program. Multiple analyses were done on each site documenting the change in the flood-frequency curve when additional historical or paleoflood data were added. When other flood-frequency studies were available, their results were compared to the results here. The comparisons in some cases simply show the effect of additional years of data, whereas other comparisons show results from probability distributions or fitting methods other than those used in PeakFQ.

For the Red River of the North, flood-frequency analysis shows that paleoflood data appear necessary to reasonably estimate very low annual exceedance probabilities. For the analysis of the lower reach of Rapid Creek and Spring Creek, paleoflood information helped put a high outlier from the systematic period in context; however, very low annual exceedance probabilities at these sites still had extraordinarily large confidence bounds. These sites also showed that paleoflood information might be transferred from one site to another, with the caveat that this is a case where we had existing paleoflood data to test the transfer of paleoflood information—this is not the case at many sites, and transferring paleoflood information requires assumptions about the comparability of floods at the sites. The Cherry Creek analysis affirmed the result of an earlier study that showed that the generalized Pareto distribution was not a good distribution for estimating very low annual exceedance probabilities. The Escalante River analysis showed that adding paleoflood information might increase uncertainty for very low annual exceedance probabilities, compared to analysis with the systematic period of record information only, when the paleoflood peaks are of much larger magnitudes than the systematic record.