Accounting for Mixed Populations in Flood Frequency Analysis: Bulletin 17C Perspective

Abstract

Bulletin 17B and its proposed update, Bulletin 17C, continue to recognize difficulties in determining flood frequency estimates among streamflow records that contain flood peaks coming from different flood-generating mechanisms, as is the case in the western United States [Interagency Advisory Committee on Water Data (1982). “Guidelines for determining flood flow frequency: Hydrology Subcommittee Bulletin 17B.” Reston, VA: USGS]. In the “Future Studies” section of Bulletin 17C, the Work Group identified the need for “the identification and treatment of mixed distributions, including those based on hydrometeorological…conditions” [England, J. F., Jr., T. A. Cohn, B. A. Faber, J. R. Stedinger, W. O. Thomas, Jr., A. G. Veilleux, J. E. Kiang, and R. R. Mason, Jr. (2018). “Guidelines for determining flood flow frequency—Bulletin 17C.” Chap. B5 in USGS Techniques and Methods, Book 4. Reston, VA: USGS]. This study provides a general statistical framework to perform a process-driven flood frequency analysis using a weighted mixed population approach. Furthermore, it allows for accounting for both sampling and mixing uncertainties. Analyses are based on 43 long-term USGS stream gauges in the western US with at least 50 years of annual peak flow data, at least 25 of which are generated by atmospheric rivers (ARs). Visual and quantitative goodness-of-fit assessments are made to evaluate the performance of the weighted mixed population approach with respect to the observations. Thirty-four (80%) of the 43 sites have similar flood frequency curves from both the homogeneous (single) and heterogeneous (weighted mixed) population methodological approaches. Yet nine (20%) of the sites have notably different quantile estimates in the upper tail of the distribution. Two important factors contribute to the overall differences in the flood frequency estimates among these sites, regardless of their physiographic locations. The best goodness of fit in the upper tail of the distribution, the portion of most concern in designing flood flow structures, is found when (1) potentially influential low floods (PILFS) are identified, and/or (2) the composite distribution contains markedly different at-site log-unit skews (shape parameter) among the AR/non-AR subpopulations compared with the single homogeneous population. Furthermore, the weighted mixed population confidence intervals tend to be wider than the single population in both tails of the distribution, due primarily to the reduced sample size from separating the observed flow series into AR/non-AR subpopulations and the contributions from the mixing fraction of ARs. However, we found similar interval widths throughout the remaining distribution, implying that our simulation framework can capture the improved procedures for quantifying quantile estimate uncertainties described in Bulletin 17C in addition to the mixing ratio uncertainties.