Quantile-based hydrological modelling

TL;DR

This paper introduces a quantile loss function approach for hydrological model calibration, enabling direct simulation of predictive quantiles and improving uncertainty assessment without distributional assumptions.

Contribution

The novel method calibrates hydrological models using quantile loss, allowing direct quantile prediction and more honest uncertainty evaluation.

Findings

Applied in three hydrological models across 511 US basins.

Demonstrated effective quantile prediction and performance assessment.

Enhanced hydrological uncertainty quantification.

Abstract

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.