An errors-in-variables extreme-value model for estimating interpolated extreme streamflows at ungauged river sections

Abstract. Estimating extreme streamflows is critical for delimiting flood zones and designing fluvial infrastructure, but for the vast majority of river sections, no measurements are available. Estimated streamflows at ungauged river sections using spatial interpolation and hydrological modeling are uncertain, and in the context of extreme value analysis, this uncertainty can be crucial when estimating return levels. In the present paper, an errors-in-variables extreme value model is proposed to account for the estimated streamflow uncertainty at ungauged river sections. The true unobserved streamflows correspond to the missing variables in a Bayesian hierarchical model. In this model, the uncertainty of the unobserved streamflows propagates to the uncertainty in the estimated return levels. The model was implemented to estimate the streamflow return levels of 211 ungauged sections of the Chaudière River watershed in Southern Quebec, Canada.