Articles | Volume 25, issue 3
https://doi.org/10.5194/hess-25-1483-2021
© Author(s) 2021. 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-25-1483-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Simulation of reactive solute transport in the critical zone: a Lagrangian model for transient flow and preferential transport
Alexander Sternagel
CORRESPONDING AUTHOR
Karlsruhe Institute of Technology (KIT), Institute of Water
Resources and River Basin Management, Hydrology, Karlsruhe, Germany
Ralf Loritz
Karlsruhe Institute of Technology (KIT), Institute of Water
Resources and River Basin Management, Hydrology, Karlsruhe, Germany
Julian Klaus
Luxembourg Institute of Science and Technology (LIST),
Environmental Research and Innovation Department, Catchment and
Eco-Hydrology Research Group, Esch-sur-Alzette, Luxembourg
Brian Berkowitz
Department of Earth and Planetary Sciences, Weizmann Institute of
Science, Rehovot, Israel
Erwin Zehe
Karlsruhe Institute of Technology (KIT), Institute of Water
Resources and River Basin Management, Hydrology, Karlsruhe, Germany
Related authors
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.
Dan Elhanati, Erwin Zehe, Ishai Dror, and Brian Berkowitz
EGUsphere, https://doi.org/10.5194/egusphere-2025-3365, https://doi.org/10.5194/egusphere-2025-3365, 2025
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
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Measurements of water isotopes are often used to estimate water transit time distributions and aquifer storage thickness in catchments. However, laboratory-scale measurements show that water isotopes exhibit transport behavior identical to that of inert chemical tracers rather than of pure water. The measured mean tracer and apparent mean water velocities are not necessarily equal; recognition of this inequality is critical when estimating catchment properties such as aquifer storage thickness.
Mortimer L. Bacher, Julian Klaus, Adam S. Ward, Jasmine Krause, Catalina Segura, and Clarissa Glaser
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Slug tracer experiments are biased toward faster flow paths, underscoring the need for tracers that reveal temporally longer timescales. We explore integrating solute tracers with naturally occurring radon to quantify flow paths of different timescales at the reach scale. Joint calibration of a transient storage model with both tracers better constrains model parameters, highlighting that this approach is critical for improving solute transport estimates in future studies.
Karl Nicolaus van Zweel, Laurent Gourdol, Jean François Iffly, Loïc Léonard, François Barnich, Laurent Pfister, Erwin Zehe, and Christophe Hissler
Earth Syst. Sci. Data, 17, 2217–2229, https://doi.org/10.5194/essd-17-2217-2025, https://doi.org/10.5194/essd-17-2217-2025, 2025
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Our study monitored groundwater in a Luxembourg forest over a year to understand water and chemical changes. We found seasonal variations in water chemistry, influenced by rainfall and soil interactions. These data help predict environmental responses and manage water resources better. By measuring key parameters like pH and dissolved oxygen, our research provides valuable insights into groundwater behaviour and serves as a resource for future environmental studies.
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.
Svenja Hoffmeister, Sibylle Kathrin Hassler, Friederike Lang, Rebekka Maier, Betserai Isaac Nyoka, and Erwin Zehe
EGUsphere, https://doi.org/10.5194/egusphere-2025-1719, https://doi.org/10.5194/egusphere-2025-1719, 2025
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Combining trees and crops in agroforestry systems can potentially be a sustainable option for agriculture facing climate change impacts. We used methods from soil science and hydrology to assess the effect of adding gliricidia trees to maize fields, on carbon content, soil properties and water availability. Our results show a clear increase in carbon contents and effects on physical soil characteristics and water uptake and retention as a consequence of the agroforestry treatment.
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.
Evgeny Shavelzon, Erwin Zehe, and Yaniv Edery
EGUsphere, https://doi.org/10.22541/essoar.173687429.91307309/v1, https://doi.org/10.22541/essoar.173687429.91307309/v1, 2025
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We analyze how chemical reactions and fluid movement interact in porous materials, focusing on how water paths form in underground environments. Using a thermodynamic approach, we track energy dissipation and entropy changes to understand this process. Over time, water channels become more defined, reducing chemical mixing and energy loss. Eventually, the system stabilizes, with flow concentrated in efficient pathways, minimizing further reactions and energy use.
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.
Samuele Ceolin, Stanislaus J. Schymanski, Dagmar van Dusschoten, Robert Koller, and Julian Klaus
Biogeosciences, 22, 691–703, https://doi.org/10.5194/bg-22-691-2025, https://doi.org/10.5194/bg-22-691-2025, 2025
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We investigated if and how roots of maize plants respond to multiple abrupt changes in soil moisture. We measured root lengths using a magnetic resonance imaging technique and calculated changes in growth rates after applying water pulses. The root growth rates increased in wetted soil layers within 48 hours and decreased in non-wetted layers, indicating fast adaptation of the root systems to moisture changes. Our findings could improve irrigation management and vegetation models.
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.
Dan Elhanati, Nadine Goeppert, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 28, 4239–4249, https://doi.org/10.5194/hess-28-4239-2024, https://doi.org/10.5194/hess-28-4239-2024, 2024
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A continuous time random walk framework was developed to allow modeling of a karst aquifer discharge response to measured rainfall. The application of the numerical model yielded robust fits between modeled and measured discharge values, especially for the distinctive long tails found during recession times. The findings shed light on the interplay of slow and fast flow in the karst system and establish the application of the model for simulating flow and transport in such systems.
Svenja Hoffmeister, Rafael Bohn Reckziegel, Ben du Toit, Sibylle K. Hassler, Florian Kestel, Rebekka Maier, Jonathan P. Sheppard, and Erwin Zehe
Hydrol. Earth Syst. Sci., 28, 3963–3982, https://doi.org/10.5194/hess-28-3963-2024, https://doi.org/10.5194/hess-28-3963-2024, 2024
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We studied a tree–crop ecosystem consisting of a blackberry field and an alder windbreak. In the water-scarce region, irrigation provides sufficient water for plant growth. The windbreak lowers the irrigation amount by reducing wind speed and therefore water transport into the atmosphere. These ecosystems could provide sustainable use of water-scarce landscapes, and we studied the complex interactions by observing several aspects (e.g. soil, nutrients, carbon assimilation, water).
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.
Ginevra Fabiani, Julian Klaus, and Daniele Penna
Hydrol. Earth Syst. Sci., 28, 2683–2703, https://doi.org/10.5194/hess-28-2683-2024, https://doi.org/10.5194/hess-28-2683-2024, 2024
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There is a limited understanding of the role that topography and climate play in tree water use. Through a cross-site comparison in Luxembourg and Italy, we investigated beech water use along slopes in different climates. Our findings indicate that in landscapes characterized by stronger hydraulic and climatic gradients there is greater spatial variation in tree physiological responses. This highlights how differing growing conditions across landscapes can lead to contrasting tree performances.
Samuel Schroers, Ulrike Scherer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 27, 2535–2557, https://doi.org/10.5194/hess-27-2535-2023, https://doi.org/10.5194/hess-27-2535-2023, 2023
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The hydrological cycle shapes our landscape. With an accelerating change of the world's climate and hydrological dynamics, concepts of evolution of natural systems become more important. In this study, we elaborated a thermodynamic framework for runoff and sediment transport and show from model results as well as from measurements during extreme events that the developed concept is useful for understanding the evolution of the system's mass, energy, and entropy fluxes.
Judith Meyer, Malte Neuper, Luca Mathias, Erwin Zehe, and Laurent Pfister
Hydrol. Earth Syst. Sci., 26, 6163–6183, https://doi.org/10.5194/hess-26-6163-2022, https://doi.org/10.5194/hess-26-6163-2022, 2022
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We identified and analysed the major atmospheric components of rain-intense thunderstorms that can eventually lead to flash floods: high atmospheric moisture, sufficient latent instability, and weak thunderstorm cell motion. Between 1981 and 2020, atmospheric conditions became likelier to support strong thunderstorms. However, the occurrence of extreme rainfall events as well as their rainfall intensity remained mostly unchanged.
Enrico Bonanno, Günter Blöschl, and Julian Klaus
Hydrol. Earth Syst. Sci., 26, 6003–6028, https://doi.org/10.5194/hess-26-6003-2022, https://doi.org/10.5194/hess-26-6003-2022, 2022
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There is an unclear understanding of which processes regulate the transport of water, solutes, and pollutants in streams. This is crucial since these processes control water quality in river networks. Compared to other approaches, we obtained clearer insights into the processes controlling solute transport in the investigated reach. This work highlights the risks of using uncertain results for interpreting the processes controlling water movement in streams.
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.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Ulrike Scherer, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 26, 3125–3150, https://doi.org/10.5194/hess-26-3125-2022, https://doi.org/10.5194/hess-26-3125-2022, 2022
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In hydrology the formation of landform patterns is of special interest as changing forcings of the natural systems, such as climate or land use, will change these structures. In our study we developed a thermodynamic framework for surface runoff on hillslopes and highlight the differences of energy conversion patterns on two related spatial and temporal scales. The results indicate that surface runoff on hillslopes approaches a maximum power state.
Brian Berkowitz
Hydrol. Earth Syst. Sci., 26, 2161–2180, https://doi.org/10.5194/hess-26-2161-2022, https://doi.org/10.5194/hess-26-2161-2022, 2022
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Extensive efforts have focused on quantifying conservative chemical transport in geological formations. We assert that an explicit accounting of temporal information, under uncertainty, in addition to spatial information, is fundamental to an effective modeling formulation. We further assert that efforts to apply chemical transport equations at large length scales, based on measurements and model parameter values relevant to significantly smaller length scales, are an unattainable
holy grail.
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.
Jan Bondy, Jan Wienhöfer, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-174, https://doi.org/10.5194/hess-2021-174, 2021
Manuscript not accepted for further review
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The Budyko curve is a widely-used and simple framework to predict the mean water balance of river catchments. While many catchments are in close accordance with the Budyko curve, others show more or less significant deviations. Our study aims at better understanding the role of soil storage characteristics in the mean water balance and offsets from the Budyko curve. Soil storage proved to be a very sensitive property and potentially explains significant deviations from the curve.
Samuel Schroers, Olivier Eiff, Axel Kleidon, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-79, https://doi.org/10.5194/hess-2021-79, 2021
Manuscript not accepted for further review
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In this study we ask the basic question why surface runoff forms drainage networks and confluences at all and how structural macro form and micro topography is a result of thermodynamic laws. We find that on a macro level hillslopes should tend from negative exponential towards exponential forms and that on a micro level the formation of rills goes hand in hand with drainage network formation of river basins. We hypothesize that we can learn more about erosion processes if we extend this theory.
Nicolas Björn Rodriguez, Laurent Pfister, Erwin Zehe, and Julian Klaus
Hydrol. Earth Syst. Sci., 25, 401–428, https://doi.org/10.5194/hess-25-401-2021, https://doi.org/10.5194/hess-25-401-2021, 2021
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Different parts of water have often been used as tracers to determine the age of water in streams. The stable tracers, such as deuterium, are thought to be unable to reveal old water compared to the radioactive tracer called tritium. We used both tracers, measured in precipitation and in a stream in Luxembourg, to show that this is not necessarily true. It is, in fact, advantageous to use the two tracers together, and we recommend systematically using tritium in future studies.
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.
Conrad Jackisch, Samuel Knoblauch, Theresa Blume, Erwin Zehe, and Sibylle K. Hassler
Biogeosciences, 17, 5787–5808, https://doi.org/10.5194/bg-17-5787-2020, https://doi.org/10.5194/bg-17-5787-2020, 2020
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We developed software to calculate the root water uptake (RWU) of beech tree roots from soil moisture dynamics. We present our approach and compare RWU to measured sap flow in the tree stem. The study relates to two sites that are similar in topography and weather but with contrasting soils. While sap flow is very similar between the two sites, the RWU is different. This suggests that soil characteristics have substantial influence. Our easy-to-implement RWU estimate may help further studies.
Stephanie Thiesen, Diego M. Vieira, Mirko Mälicke, Ralf Loritz, J. Florian Wellmann, and Uwe Ehret
Hydrol. Earth Syst. Sci., 24, 4523–4540, https://doi.org/10.5194/hess-24-4523-2020, https://doi.org/10.5194/hess-24-4523-2020, 2020
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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.
Uwe Ehret, Rik van Pruijssen, Marina Bortoli, Ralf Loritz, Elnaz Azmi, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 4389–4411, https://doi.org/10.5194/hess-24-4389-2020, https://doi.org/10.5194/hess-24-4389-2020, 2020
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In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during the runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. With the example of a hydrological model, we show that this saves considerable computation time, while largely maintaining the output quality.
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Short summary
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.
The key innovation of the study is a method to simulate reactive solute transport in the vadose...