Articles | Volume 27, issue 14
https://doi.org/10.5194/hess-27-2591-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-27-2591-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note: Complexity–uncertainty curve (c-u-curve) – a method to analyse, classify and compare dynamical systems
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Pankaj Dey
Department of Hydrology, Indian Institute of Technology, Roorkee, India
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This study evaluates hybrid hydrological models that combine physics-based and data-driven components, using Information Theory to measure their relative contributions. When testing conceptual models with LSTMs that adjust parameters over time, we found performance primarily comes from the data-driven component, with physics constraints adding minimal value. We propose a quantitative tool to analyse this behaviour and suggest a workflow for diagnosing hybrid models.
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Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
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Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
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Three process-based and four data-driven hydrological models are compared using different training data. We found that process-based models perform better with small datasets but stop learning soon, while data-driven models learn longer. The study highlights the importance of memory in data and the impact of different data sampling methods on model performance. The direct comparison of these models is novel and provides a clear understanding of their performance under various data conditions.
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Droughts are becoming more common in Europe. Our study used vast climate data to uncover extreme unseen low-water events. These simulations show the potential droughts becoming more severe and lasting longer than the damaging 2018 event, which impacted shipping and industry. This research highlights the urgent need for adaptation measures to prevent costly economic and ecological consequences for the Rhine's waterway.
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In this paper, we use models to demonstrate that even small flood reservoirs – which capture water to avoid floods downstream – can be repurposed to release water in drier conditions without affecting their ability to protect against floods. By capturing water and releasing it once levels are low, we show that reservoirs can greatly increase the water available in drought. Having more water available to the reservoir, however, is not necessarily better for drought protection.
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Short summary
Short summary
This study evaluates hybrid hydrological models that combine physics-based and data-driven components, using Information Theory to measure their relative contributions. When testing conceptual models with LSTMs that adjust parameters over time, we found performance primarily comes from the data-driven component, with physics constraints adding minimal value. We propose a quantitative tool to analyse this behaviour and suggest a workflow for diagnosing hybrid models.
Eduardo Acuña Espinoza, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Ralf Loritz, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, https://doi.org/10.5194/hess-29-1749-2025, 2025
Short summary
Short summary
Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
Eduardo Acuña Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, https://doi.org/10.5194/hess-29-1277-2025, 2025
Short summary
Short summary
Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
Andrea L. Campoverde, Uwe Ehret, Patrick Ludwig, and Joaquim G. Pinto
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-134, https://doi.org/10.5194/gmd-2024-134, 2024
Revised manuscript not accepted
Short summary
Short summary
We looked at how well the model WRF-Hydro performed during the 2018 drought event in the River Rhine basin, even though it is typically used for floods. We used the meteorological ERA5 reanalysis dataset to simulate River Rhine’s streamflow and adjusted the model using parameters and actual discharge measurements. We focused on Lake Constance, a key part of the basin, but found issues with the model’s lake outflow simulation. By removing the lake module, we obtained more accurate results.
Eduardo Acuña Espinoza, Ralf Loritz, Manuel Álvarez Chaves, Nicole Bäuerle, and Uwe Ehret
Hydrol. Earth Syst. Sci., 28, 2705–2719, https://doi.org/10.5194/hess-28-2705-2024, https://doi.org/10.5194/hess-28-2705-2024, 2024
Short summary
Short summary
Hydrological hybrid models promise to merge the performance of deep learning methods with the interpretability of process-based models. One hybrid approach is the dynamic parameterization of conceptual models using long short-term memory (LSTM) networks. We explored this method to evaluate the effect of the flexibility given by LSTMs on the process-based part.
Patrick Ludwig, Florian Ehmele, Mário J. Franca, Susanna Mohr, Alberto Caldas-Alvarez, James E. Daniell, Uwe Ehret, Hendrik Feldmann, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Michael Kunz, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 1287–1311, https://doi.org/10.5194/nhess-23-1287-2023, https://doi.org/10.5194/nhess-23-1287-2023, 2023
Short summary
Short summary
Heavy precipitation in July 2021 led to widespread floods in western Germany and neighboring countries. The event was among the five heaviest precipitation events of the past 70 years in Germany, and the river discharges exceeded by far the statistical 100-year return values. Simulations of the event under future climate conditions revealed a strong and non-linear effect on flood peaks: for +2 K global warming, an 18 % increase in rainfall led to a 39 % increase of the flood peak in the Ahr river.
Susanna Mohr, Uwe Ehret, Michael Kunz, Patrick Ludwig, Alberto Caldas-Alvarez, James E. Daniell, Florian Ehmele, Hendrik Feldmann, Mário J. Franca, Christian Gattke, Marie Hundhausen, Peter Knippertz, Katharina Küpfer, Bernhard Mühr, Joaquim G. Pinto, Julian Quinting, Andreas M. Schäfer, Marc Scheibel, Frank Seidel, and Christina Wisotzky
Nat. Hazards Earth Syst. Sci., 23, 525–551, https://doi.org/10.5194/nhess-23-525-2023, https://doi.org/10.5194/nhess-23-525-2023, 2023
Short summary
Short summary
The flood event in July 2021 was one of the most severe disasters in Europe in the last half century. The objective of this two-part study is a multi-disciplinary assessment that examines the complex process interactions in different compartments, from meteorology to hydrological conditions to hydro-morphological processes to impacts on assets and environment. In addition, we address the question of what measures are possible to generate added value to early response management.
Elnaz Azmi, Uwe Ehret, Steven V. Weijs, Benjamin L. Ruddell, and Rui A. P. Perdigão
Hydrol. Earth Syst. Sci., 25, 1103–1115, https://doi.org/10.5194/hess-25-1103-2021, https://doi.org/10.5194/hess-25-1103-2021, 2021
Short summary
Short summary
Computer models should be as simple as possible but not simpler. Simplicity refers to the length of the model and the effort it takes the model to generate its output. Here we present a practical technique for measuring the latter by the number of memory visits during model execution by
Strace, a troubleshooting and monitoring program. The advantage of this approach is that it can be applied to any computer-based model, which facilitates model intercomparison.
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Short summary
We propose the
c-u-curvemethod to characterize dynamical (time-variable) systems of all kinds.
Uis for uncertainty and expresses how well a system can be predicted in a given period of time.
Cis for complexity and expresses how predictability differs between different periods, i.e. how well predictability itself can be predicted. The method helps to better classify and compare dynamical systems across a wide range of disciplines, thus facilitating scientific collaboration.
We propose the
c-u-curvemethod to characterize dynamical (time-variable) systems of all kinds....