EGU21-13308, updated on 14 Jan 2022
EGU General Assembly 2021
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Uncertainty estimation with LSTM based rainfall-runoff models

Daniel Klotz1, Frederik Kratzert1, Martin Gauch1, Alden K. Sampson2, Günter Klambauer1, Johannes Brandstetter1, Sepp Hochreiter1, and Grey Nearing3
Daniel Klotz et al.
  • 1ELLIS Unit Linz and LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria
  • 2Upstream Tech, Natel Energy Inc.; Alameda, CA, USA
  • 3Google Research, Mountain View, CA, USA

Uncertainty is a central part of hydrological inquiry. Deep Learning provides us with new tools for estimating these inherent uncertainties. The currently best performing rainfall-runoff models are based on Long Short-Term Memory (LSTM) networks. However, most LSTM-based modelling studies focus on point estimates.

Building on the success of LSTMs for estimating point predictions, this contribution explores different extensions to directly provide uncertainty estimations. We find that the resulting models provide excellent estimates in our benchmark for daily rainfall-runoff across hundreds basins. We provide an intuitive overview of these strong results, the benchmarking procedure, and the approaches used for obtaining them.

In short, we extend the LSTMs in two ways to obtain uncertainty estimations. First, we parametrize LSTMs so that they directly provide uncertainty estimates in the form of mixture densities. This is possible because it is a general function approximation approach. It requires minimal a-priori knowledge of the sampling distribution and provides us with an estimation technique for the aleatoric uncertainty of the given setup.  Second, we use Monte Carlo Dropout to randomly mask out random connections of the network. This enforces an implicit approximation to a Gaussian Process and therefore provides us with a tool to estimate a form of epistemic uncertainty. In the benchmark the mixture density based approaches provide better estimates, especially the ones that use Asymmetric Laplacians as components.

How to cite: Klotz, D., Kratzert, F., Gauch, M., K. Sampson, A., Klambauer, G., Brandstetter, J., Hochreiter, S., and Nearing, G.: Uncertainty estimation with LSTM based rainfall-runoff models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13308,, 2021.

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