Accounting for rating curve imprecision in flood frequency analysis using likelihood-based methods

This paper examines the joint impact of sample variability and rating curve imprecision in at-site flood frequency analysis. A novel likelihood-based framework is developed for this purpose, assuming a power-law model for the stage-discharge measurements and a generalised extreme value (GEV) model for the annual maximum discharges. It is shown that the two models can be pooled into one likelihood function. This allows for simultaneous estimation of the rating curve and GEV parameters, and the assessment of the uncertainty of a T-year flood estimate due to both sample variability and rating curve imprecision. Sampling experiments show that (1) the novel method is computationally feasible and little affected by estimation bias, and (2) the chief effect of rating curve imprecision is to inflate the estimation variability of the GEV quantile estimates. The application of the method to data from 12 Norwegian gauging stations illustrates that (3) the novel and traditional methods give very similar rating curve and GEV parameter estimates and (4) the net effect of sample variability and rating curve imprecision can give rise to significant wide confidence intervals for the estimated T-year flood.