Revisiting flood peak distributions: A pan-Canadian investigation

Abstract

Safe and cost-effective design of infrastructures, such as dams, bridges, highways, often requires knowing the magnitude and frequency of peak floods. The Generalized Extreme Value distribution (GEV) prevailed in flood frequency analysis along with distributions comprising location, scale, and shape parameters. Here we explore alternative models and propose power-type models, having one scale and two shape parameters. The Burr type III (ƁrIII) and XII (ƁrXII) distributions are compared against the GEV in 1088 streamflow records of annual peaks across Canada. A generic L-moment algorithm is devised to fit the distributions, also applicable to distributions without analytical L-moment expressions. The analysis shows: (1) the models perform equally well when describing the observed annual peaks; (2) the right tail appears heavier in the ƁrIII and ƁrXII models leading to larger streamflow predictions when compared to those of GEV; (3) the GEV predicts upper streamflow limits in 39.1% of the records—these limits have realistic exceedance probabilities based on the other two models; (4) the tail heaviness estimation seems not robust in the GEV case when compared to the ƁrIII and ƁrXII models and this could challenge GEV’s reliability in predicting streamflow at large return periods; and, (5) regional variation is observed in the behaviour of flood peaks across different climatic regions of Canada. The findings of this study reveal potential limitations in using the GEV for flood frequency analysis and suggest the ƁrIII and ƁrXII as consistent alternatives worth exploring.