  Predictive uncertainty in hydrological modelling is quantified by using
post-processing or Bayesian-based methods. The former methods are not
straightforward and the latter ones are not distribution-free (i.e. assumptions
on the probability distribution of the hydrological model's output are
necessary). To alleviate possible limitations related to these specific
attributes, in this work we propose the calibration of the hydrological model
by using the quantile loss function. By following this methodological approach,
one can directly simulate pre-specified quantiles of the predictive
distribution of streamflow. As a proof of concept, we apply our method in the
frameworks of three hydrological models to 511 river basins in contiguous US.
We illustrate the predictive quantiles and show how an honest assessment of the
predictive performance of the hydrological models can be made by using proper
scoring rules. We believe that our method can help towards advancing the field
of hydrological uncertainty.
