Hydrological post-processing for predicting extreme quantiles

Hydrological post-processing using quantile regression algorithms constitutes a prime means of estimating the uncertainty of hydrological predictions. Nonetheless, conventional large-sample theory for quantile regression does not apply sufficiently far in the tails of the probability distribution of the dependent variable. To overcome this limitation that could be crucial when the interest lies on flood events, hydrological post-processing through extremal quantile regression is introduced here for estimating the extreme quantiles of hydrological model's responses. In summary, the new hydrological post-processing method exploits properties of the Hill's estimator from the extreme value theory to extrapolate quantile regression's predictions to high quantiles. As a proof of concept, the new method is here tested in post-processing daily streamflow simulations provided by three process-based hydrological models for 180 basins in the contiguous United States (CONUS) and is further compared to conventional quantile regression. With this large-scale comparison, it is demonstrated that hydrological post-processing using conventional quantile regression severely underestimates high quantiles (at the quantile level 0.9999) compared to hydrological post-processing using extremal quantile regression, although both methods are equivalent at lower quantiles (at the quantile level 0.9700). Moreover, it is shown that, in the same context, extremal quantile regression estimates the high predictive quantiles with efficiency that is, on average, equivalent in the large-sample study for the three process-based hydrological models.