Flood frequency analysis: assumptions and alternatives

Flood frequency analysis (FFA) is a form of risk analysis, yet a risk analysis of the activity of FFA itself is rarely undertaken. The recent literature of FFA has been characterized by: (1) a proliferation of mathematical models, lacking theoretical hydrologic justification, but used to extrapolate the return periods of floods beyond the gauged record; (2) official mandating of particular models, which has resulted in (3) research focused on increasingly reductionist and statistically sophisticated procedures for parameter fitting to these models from the limited gauged data. These trends have evolved to such a refined state that FFA may be approaching the ‘limits of splitting’; at the very least, the emphasis was shifted early in the history of FFA from predicting and explaining extreme flood events to the more soluble issue of fitting distributions to the bulk of the data. However, recent evidence indicates that the very modelling basis itself may be ripe for revision. Self-similar (power law) models are not only analytically simpler than conventional models, but they also offer a plausible theoretical basis in complexity theory. Of most significance, however, is the empirical evidence for self-similarity in flood behaviour. Self-similarity is difficult to detect in gauged records of limited length; however, one positive aspect of the application of statistics to FFA has been the refinement of techniques for the incorporation of historical and palaeoflood data. It is these data types, even over modest timescales such as 100 years, which offer the best promise for testing alternative models of extreme flood behaviour across a wider range of basins. At stake is the accurate estimation of flood magnitude, used widely for design purposes: the power law model produces far more conservative estimates of return period of large floods compared to conventional models, and deserves closer study.