Articles | Volume 24, issue 9
https://doi.org/10.5194/hess-24-4523-2020
© Author(s) 2020. 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-24-4523-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
17 Sep 2020
Research article |
| 17 Sep 2020
| 17 Sep 2020
Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics
Stephanie Thiesen
CORRESPONDING AUTHOR
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
Diego M. Vieira
Department for Microsystems Engineering, University of Freiburg,
Freiburg, Germany
Bernstein Center Freiburg, University of Freiburg, Freiburg, Germany
Mirko Mälicke
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
Ralf Loritz
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
J. Florian Wellmann
Computational Geosciences and Reservoir Engineering, RWTH Aachen
University, Aachen, Germany
Uwe Ehret
Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology, Karlsruhe, Germany
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Friedrich Carl, Peter Achtziger-Zupančič, Jian Yang, Marlise Colling Cassel, and Florian Wellmann
EGUsphere, https://doi.org/10.5194/egusphere-2025-3203, https://doi.org/10.5194/egusphere-2025-3203, 2025
This preprint is open for discussion and under review for Solid Earth (SE).
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A method for shape quantification based on geometrical parameters is proposed alongside a set of regular geometries established as geomodeling benchmarks. Dimensions, gradient and curvature data is obtained on cross-sections. Data analyses provide insight into the main geometrical characteristics of the benchmark models and visualizes geometrical dis-/similarities between bodies. The method and benchmarks are usable in geomodeling workflows and structural comparisons based on sparse data.
Sarah Quỳnh-Giang Ho and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 2785–2810, https://doi.org/10.5194/hess-29-2785-2025, https://doi.org/10.5194/hess-29-2785-2025, 2025
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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.
Denise Degen, Moritz Ziegler, Oliver Heidbach, Andreas Henk, Karsten Reiter, and Florian Wellmann
Solid Earth, 16, 477–502, https://doi.org/10.5194/se-16-477-2025, https://doi.org/10.5194/se-16-477-2025, 2025
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Obtaining reliable estimates of the subsurface state distributions is essential to determine the location of, e.g., potential nuclear waste disposal sites. However, providing these is challenging since it requires solving the problem numerous times, yielding high computational cost. To overcome this, we use a physics-based machine learning method to construct surrogate models. We demonstrate how it produces physics-preserving predictions, which differentiates it from purely data-driven approaches.
Judith Nijzink, Ralf Loritz, Laurent Gourdol, Davide Zoccatelli, Jean François Iffly, and Laurent Pfister
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-482, https://doi.org/10.5194/essd-2024-482, 2025
Preprint under review for ESSD
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The CAMELS-LUX dataset (Catchment Attributes and MEteorology for Large-sample Studies – LUXembourg) contains hydrologic, meteorologic and thunderstorm formation relevant atmospheric time series of 56 Luxembourgish catchments (2004–2021). These catchments are characterized by a large physiographic variety on a relatively small scale in a homogeneous climate. The dataset can be applied for (regional) hydrological analyses.
Manuel Álvarez Chaves, Eduardo Acuña Espinoza, Uwe Ehret, and Anneli Guthke
EGUsphere, https://doi.org/10.5194/egusphere-2025-1699, https://doi.org/10.5194/egusphere-2025-1699, 2025
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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.
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
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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.
Maria Staudinger, Anna Herzog, Ralf Loritz, Tobias Houska, Sandra Pool, Diana Spieler, Paul D. Wagner, Juliane Mai, Jens Kiesel, Stephan Thober, Björn Guse, and Uwe Ehret
EGUsphere, https://doi.org/10.5194/egusphere-2025-1076, https://doi.org/10.5194/egusphere-2025-1076, 2025
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Four process-based and four data-driven hydrological models are compared using different training data. We found process-based models to perform better with small data sets 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.
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
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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.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2025-425, https://doi.org/10.5194/egusphere-2025-425, 2025
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This study evaluates the extrapolation performance of Long Short-Term Memory (LSTM) networks in rainfall-runoff modeling, specifically under extreme conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit, which is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of cell states alone.
Ashish Manoj J, Ralf Loritz, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-375, https://doi.org/10.5194/hess-2024-375, 2024
Revised manuscript under review for HESS
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Traditional hydrological models typically operate in a forward mode, simulating streamflow and other catchment fluxes based on precipitation input. In this study, we explored the possibility of reversing this process—inferring precipitation from streamflow data—to improve flood event modelling. We then used the generated precipitation series to run hydrological models, resulting in more accurate estimates of streamflow and soil moisture.
Ralf Loritz, Alexander Dolich, Eduardo Acuña Espinoza, Pia Ebeling, Björn Guse, Jonas Götte, Sibylle K. Hassler, Corina Hauffe, Ingo Heidbüchel, Jens Kiesel, Mirko Mälicke, Hannes Müller-Thomy, Michael Stölzle, and Larisa Tarasova
Earth Syst. Sci. Data, 16, 5625–5642, https://doi.org/10.5194/essd-16-5625-2024, https://doi.org/10.5194/essd-16-5625-2024, 2024
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The CAMELS-DE dataset features data from 1582 streamflow gauges across Germany, with records spanning from 1951 to 2020. This comprehensive dataset, which includes time series of up to 70 years (median 46 years), enables advanced research on water flow and environmental trends and supports the development of hydrological models.
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
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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
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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.
Denise Degen, Daniel Caviedes Voullième, Susanne Buiter, Harrie-Jan Hendricks Franssen, Harry Vereecken, Ana González-Nicolás, and Florian Wellmann
Geosci. Model Dev., 16, 7375–7409, https://doi.org/10.5194/gmd-16-7375-2023, https://doi.org/10.5194/gmd-16-7375-2023, 2023
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In geosciences, we often use simulations based on physical laws. These simulations can be computationally expensive, which is a problem if simulations must be performed many times (e.g., to add error bounds). We show how a novel machine learning method helps to reduce simulation time. In comparison to other approaches, which typically only look at the output of a simulation, the method considers physical laws in the simulation itself. The method provides reliable results faster than standard.
Michael Hillier, Florian Wellmann, Eric A. de Kemp, Boyan Brodaric, Ernst Schetselaar, and Karine Bédard
Geosci. Model Dev., 16, 6987–7012, https://doi.org/10.5194/gmd-16-6987-2023, https://doi.org/10.5194/gmd-16-6987-2023, 2023
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Neural networks can be used effectively to model three-dimensional geological structures from point data, sampling geological interfaces, units, and structural orientations. Existing neural network approaches for this type of modelling are advanced by the efficient incorporation of unconformities, new knowledge inputs, and improved data fitting techniques. These advances permit the modelling of more complex geology in diverse geological settings, different-sized areas, and various data regimes.
Uwe Ehret and Pankaj Dey
Hydrol. Earth Syst. Sci., 27, 2591–2605, https://doi.org/10.5194/hess-27-2591-2023, https://doi.org/10.5194/hess-27-2591-2023, 2023
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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.
Mohammad Moulaeifard, Simon Bernard, and Florian Wellmann
Geosci. Model Dev., 16, 3565–3579, https://doi.org/10.5194/gmd-16-3565-2023, https://doi.org/10.5194/gmd-16-3565-2023, 2023
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In this work, we propose a flexible framework to generate and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the flexible control mesh, topologically similar to the main geological structure, watertight and controllable with few control points, to manage the geological structures. We exploited the subdivision surface method in our work, which is commonly used in the animation and gaming industry.
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
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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
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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.
Michał P. Michalak, Lesław Teper, Florian Wellmann, Jerzy Żaba, Krzysztof Gaidzik, Marcin Kostur, Yuriy P. Maystrenko, and Paulina Leonowicz
Solid Earth, 13, 1697–1720, https://doi.org/10.5194/se-13-1697-2022, https://doi.org/10.5194/se-13-1697-2022, 2022
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When characterizing geological/geophysical surfaces, various geometric attributes are calculated, such as dip angle (1D) or dip direction (2D). However, the boundaries between specific values may be subjective and without optimization significance, resulting from using default color palletes. This study proposes minimizing cosine distance among within-cluster observations to detect 3D anomalies. Our results suggest that the method holds promise for identification of megacylinders or megacones.
Ralf Loritz, Maoya Bassiouni, Anke Hildebrandt, Sibylle K. Hassler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 4757–4771, https://doi.org/10.5194/hess-26-4757-2022, https://doi.org/10.5194/hess-26-4757-2022, 2022
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In this study, we combine a deep-learning approach that predicts sap flow with a hydrological model to improve soil moisture and transpiration estimates at the catchment scale. Our results highlight that hybrid-model approaches, combining machine learning with physically based models, are a promising way to improve our ability to make hydrological predictions.
Mirko Mälicke
Geosci. Model Dev., 15, 2505–2532, https://doi.org/10.5194/gmd-15-2505-2022, https://doi.org/10.5194/gmd-15-2505-2022, 2022
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I preset SciKit-GStat, a well-documented and tested Python package for variogram estimation. The variogram is the core means of geostatistics, which almost all other methods rely on. Geostatistical interpolation and field generation are widely spread in geoscience, i.e., for data assimilation or modeling.
While SciKit-GStat focuses on effective and intuitive variogram estimation, it can interface with other prominent packages and make its variograms available for a multitude of methods.
Alexander Sternagel, Ralf Loritz, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 1615–1629, https://doi.org/10.5194/hess-26-1615-2022, https://doi.org/10.5194/hess-26-1615-2022, 2022
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We present a (physically based) Lagrangian approach to simulate diffusive mixing processes on the pore scale beyond perfectly mixed conditions. Results show the feasibility of the approach for reproducing measured mixing times and concentrations of isotopes over pore sizes and that typical shapes of breakthrough curves (normally associated with non-uniform transport in heterogeneous soils) may also occur as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.
Erwin Zehe, Ralf Loritz, Yaniv Edery, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 25, 5337–5353, https://doi.org/10.5194/hess-25-5337-2021, https://doi.org/10.5194/hess-25-5337-2021, 2021
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This study uses the concepts of entropy and work to quantify and explain the emergence of preferential flow and transport in heterogeneous saturated porous media. We found that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity – a stronger self-organization despite a higher randomness.
Alexander Schaaf, Miguel de la Varga, Florian Wellmann, and Clare E. Bond
Geosci. Model Dev., 14, 3899–3913, https://doi.org/10.5194/gmd-14-3899-2021, https://doi.org/10.5194/gmd-14-3899-2021, 2021
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Uncertainty is an inherent property of any model of the subsurface. We show how geological topology information – how different regions of rocks in the subsurface are connected – can be used to train uncertain geological models to reduce uncertainty. More widely, the method demonstrates the use of probabilistic machine learning (Bayesian inference) to train structural geological models on auxiliary geological knowledge that can be encoded in graph structures.
Alexander Sternagel, Ralf Loritz, Julian Klaus, Brian Berkowitz, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 1483–1508, https://doi.org/10.5194/hess-25-1483-2021, https://doi.org/10.5194/hess-25-1483-2021, 2021
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The key innovation of the study is a method to simulate reactive solute transport in the vadose zone within a Lagrangian framework. We extend the LAST-Model with a method to account for non-linear sorption and first-order degradation processes during unsaturated transport of reactive substances in the matrix and macropores. Model evaluations using bromide and pesticide data from irrigation experiments under different flow conditions on various timescales show the feasibility of the method.
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
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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.
Ralf Loritz, Markus Hrachowitz, Malte Neuper, and Erwin Zehe
Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, https://doi.org/10.5194/hess-25-147-2021, 2021
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This study investigates the role and value of distributed rainfall in the runoff generation of a mesoscale catchment. We compare the performance of different hydrological models at different periods and show that a distributed model driven by distributed rainfall yields improved performances only during certain periods. We then step beyond this finding and develop a spatially adaptive model that is capable of dynamically adjusting its spatial model structure in time.
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Short summary
A spatial interpolator has been proposed for exploring the information content of the data in the light of geostatistics and information theory. It showed comparable results to traditional interpolators, with the advantage of presenting generalization properties. We discussed three different ways of combining distributions and their implications for the probabilistic results. By its construction, the method provides a suitable and flexible framework for uncertainty analysis and decision-making.
A spatial interpolator has been proposed for exploring the information content of the data in...
