Power-law extreme flood frequency

Abstract

Abstract Conventional Flood Frequency Analysis (FFA) has been criticized both for its questionable theoretical basis, and for its failure in extreme event prediction. An important research issue for FFA is the exploration of models that have theoretical/explanatory value as the first step towards more accurate predictive attempts. Self-similar approaches offer one such alternative, with a plausible theoretical basis in complexity theory that has demonstrable wide applicability across the geophysical sciences. This paper explores a simple self-similar approach to the prediction of extreme floods. Fifty river gauging records from the USA exhibiting an outlier event were studied. Fitting a simple power law (PL) relation to events with return period of 10 years or greater resulted in more accurate discharge and return period estimates for outlier events relative to the Log-Pearson III model. Similar success in predicting record events is reported for 12 long-term rainfall records from the UK. This empirical success is interpreted as evidence that self-similarity may well represent the underlying physical processes generating hydrological variables. These findings have important consequences for the prediction of extreme flood events; the PL model produces return period estimates that are far more conservative than conventional distributions.