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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 13 Aug 2018

Research article | 13 Aug 2018

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This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

A framework for likelihood functions of deterministic hydrological models

Lorenz Ammann1,2, Peter Reichert1,2, and Fabrizio Fenicia1 Lorenz Ammann et al.
  • 1Swiss Federal Institute of Aquatic Science and Technology (Eawag), Dubendorf, Switzerland
  • 2Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland

Abstract. The widespread application of deterministic hydrological models in research and practise calls for suitable methods to describe their uncertainty. The errors of those models are often heteroscedastic, non-Gaussian and correlated due to the memory effect of errors in state variables. Still, the residual error models used to describe them are usually highly simplified, often neglecting some of the mentioned characteristics. This is partly because general approaches to account for all of those characteristics are lacking, and partly because the benefits of more complex error models in terms of achieving better predictions are unclear. For example, the joint inference of autocorrelation and hydrological model parameters has been shown to lead to poor predictions. This study presents a framework for likelihood functions for deterministic hydrological models that considers correlated errors and allows for an arbitrary probability distribution of observed streamflow. The choice of this distribution reflects prior knowledge about non-normality of the errors. The framework was used to evaluate increasingly complex error models with data of varying temporal resolution (daily to hourly) in two catchments. We found that (1) the joint inference of hydrological and error model parameters leads to poor predictions when conventional error models with stationary correlation are used, which confirms previous studies, (2) the quality of these predictions worsens with higher temporal resolution of the data, (3) accounting for a non-stationary autocorrelation of the errors, i.e. allowing it to vary between wet and dry periods, largely alleviates the observed problems, and (4) accounting for autocorrelation leads to more realistic model output as shown by signatures such as the Flashiness Index. Overall, this study contributes to a better description of residual errors of deterministic hydrological models.

Lorenz Ammann et al.
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Lorenz Ammann et al.
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Publications Copernicus
Short summary
The uncertainty of hydrological models can be substantial, and its quantification and realistic description are often difficult. Proposing a new flexible framework to describe and quantify those errors, we found that non-stationarity can be an important characteristic of the errors that needs to be considered to reach better results. Especially accounting for non-stationarity of correlation is a promising avenue for improving uncertainty estimation in hydrology.
The uncertainty of hydrological models can be substantial, and its quantification and realistic...