Articles | Volume 27, issue 13
https://doi.org/10.5194/hess-27-2535-2023
© 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-27-2535-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Jul 2023
Research article |
| 11 Jul 2023
| 11 Jul 2023
Energy efficiency in transient surface runoff and sediment fluxes on hillslopes – a concept to quantify the effectiveness of extreme events
Samuel Schroers
CORRESPONDING AUTHOR
Institute of Water Resources and River Basin Management, Karlsruhe
Institute of Technology – KIT, Karlsruhe, Germany
Ulrike Scherer
Engler-Bunte-Institut, Water Chemistry and Water Technology – KIT,
Karlsruhe, Germany
Erwin Zehe
Institute of Water Resources and River Basin Management, Karlsruhe
Institute of Technology – KIT, Karlsruhe, Germany
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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.
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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.
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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.
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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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EGUsphere, https://doi.org/10.22541/essoar.173687429.91307309/v1, https://doi.org/10.22541/essoar.173687429.91307309/v1, 2025
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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.
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).
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.
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.
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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Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2021-174, https://doi.org/10.5194/hess-2021-174, 2021
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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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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.
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.
Mirko Mälicke, Sibylle K. Hassler, Theresa Blume, Markus Weiler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, https://doi.org/10.5194/hess-24-2633-2020, 2020
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We could show that distributed soil moisture time series bear a considerable amount of information about dynamic changes in soil moisture. We developed a new method to describe spatial patterns and analyze their persistency. By combining uncertainty propagation with information theory, we were able to calculate the information content of spatial similarity with respect to measurement uncertainty. This does help to understand when and why the soil is drying in an organized manner.
Brian Berkowitz and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 1831–1858, https://doi.org/10.5194/hess-24-1831-2020, https://doi.org/10.5194/hess-24-1831-2020, 2020
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We present a
blueprintfor a unified modelling framework to quantify chemical transport in both surface water and groundwater systems. There has been extensive debate over recent decades, particularly in the surface water literature, about how to explain and account for long travel times of chemical species that are distinct from water flow (rainfall-runoff) travel times. We suggest a powerful modelling framework known to be robust and effective from the field of groundwater hydrology.
Alexander Sternagel, Ralf Loritz, Wolfgang Wilcke, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 4249–4267, https://doi.org/10.5194/hess-23-4249-2019, https://doi.org/10.5194/hess-23-4249-2019, 2019
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We present our hydrological LAST-Model to simulate preferential soil water flow and tracer transport in macroporous soils. It relies on a Lagrangian perspective of the movement of discrete water particles carrying tracer masses through the subsoil and is hence an alternative approach to common models. Sensitivity analyses reveal the physical validity of the model concept and evaluation tests show that LAST can depict well observed tracer mass profiles with fingerprints of preferential flow.
Axel Kleidon, Erwin Zehe, and Ralf Loritz
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-52, https://doi.org/10.5194/esd-2019-52, 2019
Manuscript not accepted for further review
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Many fluxes in Earth systems are not homogeneously distributed across space, but occur highly concentrated in structures, such as turbulent eddies, river networks, vascular networks of plants, or human-made infrastructures. Yet, the highly-organized nature of these fluxes is typically only described at a rudimentary level, if at all. We propose that it requires a novel approach to describe these structures that focuses on the work done to build and maintain these structures, and the feedbacks.
Ralf Loritz, Axel Kleidon, Conrad Jackisch, Martijn Westhoff, Uwe Ehret, Hoshin Gupta, and Erwin Zehe
Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, https://doi.org/10.5194/hess-23-3807-2019, 2019
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In this study, we develop a topographic index explaining hydrological similarity within a energy-centered framework, with the observation that the majority of potential energy is dissipated when rainfall becomes runoff.
Erwin Zehe, Ralf Loritz, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Theresa Blume, Sibylle K. Hassler, and Hubert H. Savenije
Hydrol. Earth Syst. Sci., 23, 971–987, https://doi.org/10.5194/hess-23-971-2019, https://doi.org/10.5194/hess-23-971-2019, 2019
Martijn Westhoff, Axel Kleidon, Stan Schymanski, Benjamin Dewals, Femke Nijsse, Maik Renner, Henk Dijkstra, Hisashi Ozawa, Hubert Savenije, Han Dolman, Antoon Meesters, and Erwin Zehe
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2019-6, https://doi.org/10.5194/esd-2019-6, 2019
Publication in ESD not foreseen
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Even models relying on physical laws have parameters that need to be measured or estimated. Thermodynamic optimality principles potentially offer a way to reduce the number of estimated parameters by stating that a system evolves to an optimum state. These principles have been applied successfully within the Earth system, but it is often unclear what to optimize and how. In this review paper we identify commonalities between different successful applications as well as some doubtful applications.
Nevil Quinn, Günter Blöschl, András Bárdossy, Attilio Castellarin, Martyn Clark, Christophe Cudennec, Demetris Koutsoyiannis, Upmanu Lall, Lubomir Lichner, Juraj Parajka, Christa D. Peters-Lidard, Graham Sander, Hubert Savenije, Keith Smettem, Harry Vereecken, Alberto Viglione, Patrick Willems, Andy Wood, Ross Woods, Chong-Yu Xu, and Erwin Zehe
Proc. IAHS, 380, 3–8, https://doi.org/10.5194/piahs-380-3-2018, https://doi.org/10.5194/piahs-380-3-2018, 2018
Nevil Quinn, Günter Blöschl, András Bárdossy, Attilio Castellarin, Martyn Clark, Christophe Cudennec, Demetris Koutsoyiannis, Upmanu Lall, Lubomir Lichner, Juraj Parajka, Christa D. Peters-Lidard, Graham Sander, Hubert Savenije, Keith Smettem, Harry Vereecken, Alberto Viglione, Patrick Willems, Andy Wood, Ross Woods, Chong-Yu Xu, and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 5735–5739, https://doi.org/10.5194/hess-22-5735-2018, https://doi.org/10.5194/hess-22-5735-2018, 2018
Mirko Mälicke, Sibylle K. Hassler, Markus Weiler, Theresa Blume, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2018-396, https://doi.org/10.5194/hess-2018-396, 2018
Manuscript not accepted for further review
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In this study we use time dependent variograms to identify periods of organized soil moisture during drying. We could identify emerging spatial patterns which imply periods of terrestrial control on soil moisture organization. The coupling of time dependent variograms with density based clustering is a new approach to detect similarity in spatial patterns. The presented method is useful to describe states of organization and improve kriging workflows by extending their prerequisites.
Ralf Loritz, Hoshin Gupta, Conrad Jackisch, Martijn Westhoff, Axel Kleidon, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, https://doi.org/10.5194/hess-22-3663-2018, 2018
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In this study we explore the role of spatially distributed information on hydrological modeling. For that, we develop and test an approach which draws upon information theory and thermodynamic reasoning. We show that the proposed set of methods provide a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time and, hence, when which landscape characteristic is important in a model application.
Conrad Jackisch and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 3639–3662, https://doi.org/10.5194/hess-22-3639-2018, https://doi.org/10.5194/hess-22-3639-2018, 2018
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We present a Lagrangian model for non-uniform soil water dynamics. It handles 2-D diffusion (based on a spatial random walk and implicit pore space redistribution) and 1-D advection in representative macropores (as film flow with dynamic interaction with the soil matrix). The interplay between the domains is calculated based on an energy-balance approach which does not require any additional parameterisation. Model tests give insight into the evolution of the non-uniform infiltration patterns.
Simon Höllering, Jan Wienhöfer, Jürgen Ihringer, Luis Samaniego, and Erwin Zehe
Hydrol. Earth Syst. Sci., 22, 203–220, https://doi.org/10.5194/hess-22-203-2018, https://doi.org/10.5194/hess-22-203-2018, 2018
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Hydrological fingerprints are introduced as response targets for sensitivity analysis and combined with a conventional approach using streamflow data for a temporally resolved sensitivity analysis. The joint benefit of both approaches is presented for several headwater catchments. The approach allows discerning a clarified pattern for parameter influences pinpointed to diverse response characteristics and detecting even slight regional differences.
Lisa Angermann, Conrad Jackisch, Niklas Allroggen, Matthias Sprenger, Erwin Zehe, Jens Tronicke, Markus Weiler, and Theresa Blume
Hydrol. Earth Syst. Sci., 21, 3727–3748, https://doi.org/10.5194/hess-21-3727-2017, https://doi.org/10.5194/hess-21-3727-2017, 2017
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This study investigates the temporal dynamics and response velocities of lateral preferential flow at the hillslope. The results are compared to catchment response behavior to infer the large-scale implications of the observed processes. A large portion of mobile water flows through preferential flow paths in the structured soils, causing an immediate discharge response. The study presents a methodological approach to cover the spatial and temporal domain of these highly heterogeneous processes.
Conrad Jackisch, Lisa Angermann, Niklas Allroggen, Matthias Sprenger, Theresa Blume, Jens Tronicke, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 3749–3775, https://doi.org/10.5194/hess-21-3749-2017, https://doi.org/10.5194/hess-21-3749-2017, 2017
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Rapid subsurface flow in structured soils facilitates fast vertical and lateral redistribution of event water. We present its in situ exploration through local measurements and irrigation experiments. Special emphasis is given to a coherent combination of hydrological and geophysical methods. The study highlights that form and function operate as conjugated pairs. Dynamic imaging through time-lapse GPR was key to observing both and to identifying hydrologically relevant structures.
Simon Paul Seibert, Conrad Jackisch, Uwe Ehret, Laurent Pfister, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 2817–2841, https://doi.org/10.5194/hess-21-2817-2017, https://doi.org/10.5194/hess-21-2817-2017, 2017
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Runoff production mechanisms and their corresponding physiographic controls continue to pose major research challenges in catchment hydrology. We propose innovative data-driven diagnostic signatures for overcoming the prevailing status quo in inter-comparison studies. Specifically, we present dimensionless double mass curves which allow us to infer information on runoff generation at the seasonal and annual timescales. The method is based on commonly available data.
Ralf Loritz, Sibylle K. Hassler, Conrad Jackisch, Niklas Allroggen, Loes van Schaik, Jan Wienhöfer, and Erwin Zehe
Hydrol. Earth Syst. Sci., 21, 1225–1249, https://doi.org/10.5194/hess-21-1225-2017, https://doi.org/10.5194/hess-21-1225-2017, 2017
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In this study we examine whether we can step beyond the qualitative character of perceptual models by using them as a blueprint for setting up representative hillslope models. Thereby we test the hypothesis of whether a single hillslope can represent the functioning of an entire lower mesoscale catchment in a spatially aggregated way.
Simon Paul Seibert, Uwe Ehret, and Erwin Zehe
Hydrol. Earth Syst. Sci., 20, 3745–3763, https://doi.org/10.5194/hess-20-3745-2016, https://doi.org/10.5194/hess-20-3745-2016, 2016
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While the assessment of "vertical" (magnitude) errors of streamflow simulations is standard practice, "horizontal" (timing) errors are rarely considered. To assess their role, we propose a method to quantify both errors simultaneously which closely resembles visual hydrograph comparison. Our results reveal differences in time–magnitude error statistics for different flow conditions. The proposed method thus offers novel perspectives for model diagnostics and evaluation.
Erwin Zehe and Conrad Jackisch
Hydrol. Earth Syst. Sci., 20, 3511–3526, https://doi.org/10.5194/hess-20-3511-2016, https://doi.org/10.5194/hess-20-3511-2016, 2016
Simon Höllering, Jürgen Ihringer, Luis Samaniego, and Erwin Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-249, https://doi.org/10.5194/hess-2016-249, 2016
Preprint withdrawn
M. Westhoff, E. Zehe, P. Archambeau, and B. Dewals
Hydrol. Earth Syst. Sci., 20, 479–486, https://doi.org/10.5194/hess-20-479-2016, https://doi.org/10.5194/hess-20-479-2016, 2016
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We derived mathematical formulations of relations between relative wetness and gradients driving run-off and evaporation for a one-box model such that, when conductances are optimized with the maximum power principle, the model leads exactly to a point on the Budyko curve.
With dry spells and dynamics in actual evaporation added, the model compared well with catchment observations without calibrating any parameter.
The maximum-power principle may thus be used to derive the Budyko curve.
U. Scherer and E. Zehe
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-12-3527-2015, https://doi.org/10.5194/hessd-12-3527-2015, 2015
Revised manuscript not accepted
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This paper presents the development, parameterization and verification of a process-based soil erosion model for the catchment scale, which balances necessary complexity with greatest possible simplicity. We used the hydrologic model CATFLOW as a platform and further developed it to CATFLOW-SED by integrating approaches to simulate soil erosion. The model was validated on a hierarchy of scales which is characteristic for the governing processes.
E. Zehe, U. Ehret, L. Pfister, T. Blume, B. Schröder, M. Westhoff, C. Jackisch, S. J. Schymanski, M. Weiler, K. Schulz, N. Allroggen, J. Tronicke, L. van Schaik, P. Dietrich, U. Scherer, J. Eccard, V. Wulfmeyer, and A. Kleidon
Hydrol. Earth Syst. Sci., 18, 4635–4655, https://doi.org/10.5194/hess-18-4635-2014, https://doi.org/10.5194/hess-18-4635-2014, 2014
U. Ehret, H. V. Gupta, M. Sivapalan, S. V. Weijs, S. J. Schymanski, G. Blöschl, A. N. Gelfan, C. Harman, A. Kleidon, T. A. Bogaard, D. Wang, T. Wagener, U. Scherer, E. Zehe, M. F. P. Bierkens, G. Di Baldassarre, J. Parajka, L. P. H. van Beek, A. van Griensven, M. C. Westhoff, and H. C. Winsemius
Hydrol. Earth Syst. Sci., 18, 649–671, https://doi.org/10.5194/hess-18-649-2014, https://doi.org/10.5194/hess-18-649-2014, 2014
J. Wienhöfer and E. Zehe
Hydrol. Earth Syst. Sci., 18, 121–138, https://doi.org/10.5194/hess-18-121-2014, https://doi.org/10.5194/hess-18-121-2014, 2014
M. Liu, A. Bárdossy, and E. Zehe
Hydrol. Earth Syst. Sci., 17, 4685–4699, https://doi.org/10.5194/hess-17-4685-2013, https://doi.org/10.5194/hess-17-4685-2013, 2013
E. Zehe, U. Ehret, T. Blume, A. Kleidon, U. Scherer, and M. Westhoff
Hydrol. Earth Syst. Sci., 17, 4297–4322, https://doi.org/10.5194/hess-17-4297-2013, https://doi.org/10.5194/hess-17-4297-2013, 2013
M. C. Westhoff and E. Zehe
Hydrol. Earth Syst. Sci., 17, 3141–3157, https://doi.org/10.5194/hess-17-3141-2013, https://doi.org/10.5194/hess-17-3141-2013, 2013
A. Kleidon, E. Zehe, U. Ehret, and U. Scherer
Hydrol. Earth Syst. Sci., 17, 225–251, https://doi.org/10.5194/hess-17-225-2013, https://doi.org/10.5194/hess-17-225-2013, 2013
J. Wienhöfer, K. Germer, F. Lindenmaier, A. Färber, and E. Zehe
Hydrol. Earth Syst. Sci., 13, 1145–1161, https://doi.org/10.5194/hess-13-1145-2009, https://doi.org/10.5194/hess-13-1145-2009, 2009
Related subject area
Subject: Hillslope hydrology | Techniques and Approaches: Theory development
Hillslope subsurface flow is driven by vegetation more than soil properties in colonized valley moraines along a humid mountain elevation
Young and new water fractions in soil and hillslope waters
Morphological controls on surface runoff: an interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework
Soil moisture: variable in space but redundant in time
A history of the concept of time of concentration
Are dissolved organic carbon concentrations in riparian groundwater linked to hydrological pathways in the boreal forest?
The influence of diurnal snowmelt and transpiration on hillslope throughflow and stream response
Slope–velocity equilibrium and evolution of surface roughness on a stony hillslope
Assessment of land use impact on hydraulic threshold conditions for gully head cut initiation
Technical note: Inference in hydrology from entropy balance considerations
Ecohydrological effects of stream–aquifer water interaction: a case study of the Heihe River basin, northwestern China
Hillslope-scale experiment demonstrates the role of convergence during two-step saturation
Impacts of climate variability on wetland salinization in the North American prairies
Resolving structural errors in a spatially distributed hydrologic model using ensemble Kalman filter state updates
Runoff formation from experimental plot, field, to small catchment scales in agricultural North Huaihe River Plain, China
Addressing secondary school students' everyday ideas about freshwater springs in order to develop an instructional tool to promote conceptual reconstruction
Hydrological heterogeneity in Mediterranean reclaimed slopes: runoff and sediment yield at the patch and slope scales along a gradient of overland flow
Effect of hydraulic parameters on sediment transport capacity in overland flow over erodible beds
Large-scale runoff generation – parsimonious parameterisation using high-resolution topography
Estimating surface fluxes over middle and upper streams of the Heihe River Basin with ASTER imagery
Seasonal evaluation of the land surface scheme HTESSEL against remote sensing derived energy fluxes of the Transdanubian region in Hungary
Analysis of surface soil moisture patterns in agricultural landscapes using Empirical Orthogonal Functions
Modelling field scale water partitioning using on-site observations in sub-Saharan rainfed agriculture
Evaluation of alternative formulae for calculation of surface temperature in snowmelt models using frequency analysis of temperature observations
Growth of a high-elevation large inland lake, associated with climate change and permafrost degradation in Tibet
Selection of an appropriately simple storm runoff model
Spatial mapping of leaf area index using hyperspectral remote sensing for hydrological applications with a particular focus on canopy interception
Use of satellite-derived data for characterization of snow cover and simulation of snowmelt runoff through a distributed physically based model of runoff generation
A contribution to understanding the turbidity behaviour in an Amazon floodplain
Global spatial optimization with hydrological systems simulation: application to land-use allocation and peak runoff minimization
Implementing small scale processes at the soil-plant interface – the role of root architectures for calculating root water uptake profiles
Uncertainty in the determination of soil hydraulic parameters and its influence on the performance of two hydrological models of different complexity
Modelling the inorganic nitrogen behaviour in a small Mediterranean forested catchment, Fuirosos (Catalonia)
Soil bioengineering for risk mitigation and environmental restoration in a humid tropical area
Climate and terrain factors explaining streamflow response and recession in Australian catchments
Soil moisture active and passive microwave products: intercomparison and evaluation over a Sahelian site
Characteristics of 2-D convective structures in Catalonia (NE Spain): an analysis using radar data and GIS
The contribution of groundwater discharge to the overall water budget of two typical Boreal lakes in Alberta/Canada estimated from a radon mass balance
Actual daily evapotranspiration estimated from MERIS and AATSR data over the Chinese Loess Plateau
Calibration analysis for water storage variability of the global hydrological model WGHM
Earth's Critical Zone and hydropedology: concepts, characteristics, and advances
Reducing scale dependence in TOPMODEL using a dimensionless topographic index
Spatial variation in soil active-layer geochemistry across hydrologic margins in polar desert ecosystems
Nitrogen retention in natural Mediterranean wetland-streams affected by agricultural runoff
Recent trends in groundwater levels in a highly seasonal hydrological system: the Ganges-Brahmaputra-Meghna Delta
Water availability, demand and reliability of in situ water harvesting in smallholder rain-fed agriculture in the Thukela River Basin, South Africa
Variability of the groundwater sulfate concentration in fractured rock slopes: a tool to identify active unstable areas
Copula based multisite model for daily precipitation simulation
Solid phase evolution in the Biosphere 2 hillslope experiment as predicted by modeling of hydrologic and geochemical fluxes
Deriving a global river network map and its sub-grid topographic characteristics from a fine-resolution flow direction map
Fei Wang, Genxu Wang, Junfang Cui, Xiangyu Tang, Ruxin Yang, Kewei Huang, Jianqing Du, and Li Guo
EGUsphere, https://doi.org/10.5194/egusphere-2025-1254, https://doi.org/10.5194/egusphere-2025-1254, 2025
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We aim to understand how the ground layer and the preferential flow paths in vegetated valley moraines influence subsurface flow. Our results showed that the presence of ground layer facilitates lateral flow while reduces rainwater mixing within the soil, thus increasing the peak flow amount. The percentage of preferential flow paths involved in subsurface flow is similar between forests and is related to fine roots, driven by coarse-textured soil in moraines.
Marius G. Floriancic, Scott T. Allen, and James W. Kirchner
Hydrol. Earth Syst. Sci., 28, 4295–4308, https://doi.org/10.5194/hess-28-4295-2024, https://doi.org/10.5194/hess-28-4295-2024, 2024
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We use a 3-year time series of tracer data of streamflow and soils to show how water moves through the subsurface to become streamflow. Less than 50% of soil water consists of rainfall from the last 3 weeks. Most annual streamflow is older than 3 months, and waters in deep subsurface layers are even older; thus deep layers are not the only source of streamflow. After wet periods more rainfall was found in the subsurface and the stream, suggesting that water moves quicker through wet landscapes.
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.
Mirko Mälicke, Sibylle K. Hassler, Theresa Blume, Markus Weiler, and Erwin Zehe
Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, https://doi.org/10.5194/hess-24-2633-2020, 2020
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We could show that distributed soil moisture time series bear a considerable amount of information about dynamic changes in soil moisture. We developed a new method to describe spatial patterns and analyze their persistency. By combining uncertainty propagation with information theory, we were able to calculate the information content of spatial similarity with respect to measurement uncertainty. This does help to understand when and why the soil is drying in an organized manner.
Keith J. Beven
Hydrol. Earth Syst. Sci., 24, 2655–2670, https://doi.org/10.5194/hess-24-2655-2020, https://doi.org/10.5194/hess-24-2655-2020, 2020
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The concept of time of concentration in the analysis of catchment responses dates back over 150 years. It is normally discussed in terms of the velocity of flow of a water particle from the furthest part of a catchment to the outlet. This is also the basis for the definition in the International Glossary of Hydrology, but this is in conflict with the way in which it is commonly used. This paper provides a clarification of the concept and its correct useage.
Stefan W. Ploum, Hjalmar Laudon, Andrés Peralta-Tapia, and Lenka Kuglerová
Hydrol. Earth Syst. Sci., 24, 1709–1720, https://doi.org/10.5194/hess-24-1709-2020, https://doi.org/10.5194/hess-24-1709-2020, 2020
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Near-stream areas, or riparian zones, are important for the health of streams and rivers. If these areas are disturbed by forestry or other anthropogenic activity, the water quality and all life in streams may be at risk. We examined which riparian areas are particularly sensitive. We found that only a few wet areas bring most of the rainwater from the landscape to the stream, and they have a unique water quality. In order to maintain healthy streams and rivers, these areas should be protected.
Brett Woelber, Marco P. Maneta, Joel Harper, Kelsey G. Jencso, W. Payton Gardner, Andrew C. Wilcox, and Ignacio López-Moreno
Hydrol. Earth Syst. Sci., 22, 4295–4310, https://doi.org/10.5194/hess-22-4295-2018, https://doi.org/10.5194/hess-22-4295-2018, 2018
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The hydrology of high-elevation headwaters in midlatitudes is typically dominated by snow processes, which are very sensitive to changes in energy inputs at the top of the snowpack. We present a data analyses that reveal how snowmelt and transpiration waves induced by the diurnal solar cycle generate water pressure fluctuations that propagate through the snowpack–hillslope–stream system. Changes in diurnal energy inputs alter these pressure cycles with potential ecohydrological consequences.
Mark A. Nearing, Viktor O. Polyakov, Mary H. Nichols, Mariano Hernandez, Li Li, Ying Zhao, and Gerardo Armendariz
Hydrol. Earth Syst. Sci., 21, 3221–3229, https://doi.org/10.5194/hess-21-3221-2017, https://doi.org/10.5194/hess-21-3221-2017, 2017
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This study presents novel scientific understanding about the way that hillslope surfaces form when exposed to rainfall erosion, and the way those surfaces interact with and influence runoff velocities during rain events. The data show that hillslope surfaces form such that flow velocities are independent of slope gradient and dependent on flow rates alone. This result represents a shift in thinking about surface water runoff.
Aliakbar Nazari Samani, Qiuwen Chen, Shahram Khalighi, Robert James Wasson, and Mohammad Reza Rahdari
Hydrol. Earth Syst. Sci., 20, 3005–3012, https://doi.org/10.5194/hess-20-3005-2016, https://doi.org/10.5194/hess-20-3005-2016, 2016
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We hypothesized that land use had important effects on hydraulic threshold conditions for gully head cut initiation. We investigated the effects using an experimental plot. The results indicated that the use of a threshold value of τcr = 35 dyne cm−2 and ωu = 0.4 Cm S−1 in physically based soil erosion models is susceptible to high uncertainty when assessing gully erosion.
Stefan J. Kollet
Hydrol. Earth Syst. Sci., 20, 2801–2809, https://doi.org/10.5194/hess-20-2801-2016, https://doi.org/10.5194/hess-20-2801-2016, 2016
Yujin Zeng, Zhenghui Xie, Yan Yu, Shuang Liu, Linying Wang, Binghao Jia, Peihua Qin, and Yaning Chen
Hydrol. Earth Syst. Sci., 20, 2333–2352, https://doi.org/10.5194/hess-20-2333-2016, https://doi.org/10.5194/hess-20-2333-2016, 2016
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In arid areas, stream–aquifer water exchange essentially sustains the growth and subsistence of riparian ecosystem. To quantify this effect for intensity and range, a stream–riverbank scheme was incorporated into a state-of-the-art land model, and some runs were set up over Heihe River basin, northwestern China. The results show that the hydrology circle is significantly changed, and the ecological system is benefitted greatly by the river water lateral transfer within a 1 km range to the stream.
A. I. Gevaert, A. J. Teuling, R. Uijlenhoet, S. B. DeLong, T. E. Huxman, L. A. Pangle, D. D. Breshears, J. Chorover, J. D. Pelletier, S. R. Saleska, X. Zeng, and P. A. Troch
Hydrol. Earth Syst. Sci., 18, 3681–3692, https://doi.org/10.5194/hess-18-3681-2014, https://doi.org/10.5194/hess-18-3681-2014, 2014
U. Nachshon, A. Ireson, G. van der Kamp, S. R. Davies, and H. S. Wheater
Hydrol. Earth Syst. Sci., 18, 1251–1263, https://doi.org/10.5194/hess-18-1251-2014, https://doi.org/10.5194/hess-18-1251-2014, 2014
J. H. Spaaks and W. Bouten
Hydrol. Earth Syst. Sci., 17, 3455–3472, https://doi.org/10.5194/hess-17-3455-2013, https://doi.org/10.5194/hess-17-3455-2013, 2013
S. Han, D. Xu, and S. Wang
Hydrol. Earth Syst. Sci., 16, 3115–3125, https://doi.org/10.5194/hess-16-3115-2012, https://doi.org/10.5194/hess-16-3115-2012, 2012
S. Reinfried, S. Tempelmann, and U. Aeschbacher
Hydrol. Earth Syst. Sci., 16, 1365–1377, https://doi.org/10.5194/hess-16-1365-2012, https://doi.org/10.5194/hess-16-1365-2012, 2012
L. Merino-Martín, M. Moreno-de las Heras, S. Pérez-Domingo, T. Espigares, and J. M. Nicolau
Hydrol. Earth Syst. Sci., 16, 1305–1320, https://doi.org/10.5194/hess-16-1305-2012, https://doi.org/10.5194/hess-16-1305-2012, 2012
M. Ali, G. Sterk, M. Seeger, M. Boersema, and P. Peters
Hydrol. Earth Syst. Sci., 16, 591–601, https://doi.org/10.5194/hess-16-591-2012, https://doi.org/10.5194/hess-16-591-2012, 2012
L. Gong, S. Halldin, and C.-Y. Xu
Hydrol. Earth Syst. Sci., 15, 2481–2494, https://doi.org/10.5194/hess-15-2481-2011, https://doi.org/10.5194/hess-15-2481-2011, 2011
W. Ma, Y. Ma, Z. Hu, Z. Su, J. Wang, and H. Ishikawa
Hydrol. Earth Syst. Sci., 15, 1403–1413, https://doi.org/10.5194/hess-15-1403-2011, https://doi.org/10.5194/hess-15-1403-2011, 2011
E. L. Wipfler, K. Metselaar, J. C. van Dam, R. A. Feddes, E. van Meijgaard, L. H. van Ulft, B. van den Hurk, S. J. Zwart, and W. G. M. Bastiaanssen
Hydrol. Earth Syst. Sci., 15, 1257–1271, https://doi.org/10.5194/hess-15-1257-2011, https://doi.org/10.5194/hess-15-1257-2011, 2011
W. Korres, C. N. Koyama, P. Fiener, and K. Schneider
Hydrol. Earth Syst. Sci., 14, 751–764, https://doi.org/10.5194/hess-14-751-2010, https://doi.org/10.5194/hess-14-751-2010, 2010
H. Makurira, H. H. G. Savenije, and S. Uhlenbrook
Hydrol. Earth Syst. Sci., 14, 627–638, https://doi.org/10.5194/hess-14-627-2010, https://doi.org/10.5194/hess-14-627-2010, 2010
C. H. Luce and D. G. Tarboton
Hydrol. Earth Syst. Sci., 14, 535–543, https://doi.org/10.5194/hess-14-535-2010, https://doi.org/10.5194/hess-14-535-2010, 2010
J. Liu, S. Kang, T. Gong, and A. Lu
Hydrol. Earth Syst. Sci., 14, 481–489, https://doi.org/10.5194/hess-14-481-2010, https://doi.org/10.5194/hess-14-481-2010, 2010
A. I. J. M. van Dijk
Hydrol. Earth Syst. Sci., 14, 447–458, https://doi.org/10.5194/hess-14-447-2010, https://doi.org/10.5194/hess-14-447-2010, 2010
H. H. Bulcock and G. P. W. Jewitt
Hydrol. Earth Syst. Sci., 14, 383–392, https://doi.org/10.5194/hess-14-383-2010, https://doi.org/10.5194/hess-14-383-2010, 2010
L. S. Kuchment, P. Romanov, A. N. Gelfan, and V. N. Demidov
Hydrol. Earth Syst. Sci., 14, 339–350, https://doi.org/10.5194/hess-14-339-2010, https://doi.org/10.5194/hess-14-339-2010, 2010
E. Alcântara, E. Novo, J. Stech, J. Lorenzzetti, C. Barbosa, A. Assireu, and A. Souza
Hydrol. Earth Syst. Sci., 14, 351–364, https://doi.org/10.5194/hess-14-351-2010, https://doi.org/10.5194/hess-14-351-2010, 2010
I.-Y. Yeo and J.-M. Guldmann
Hydrol. Earth Syst. Sci., 14, 325–338, https://doi.org/10.5194/hess-14-325-2010, https://doi.org/10.5194/hess-14-325-2010, 2010
C. L. Schneider, S. Attinger, J.-O. Delfs, and A. Hildebrandt
Hydrol. Earth Syst. Sci., 14, 279–289, https://doi.org/10.5194/hess-14-279-2010, https://doi.org/10.5194/hess-14-279-2010, 2010
G. Baroni, A. Facchi, C. Gandolfi, B. Ortuani, D. Horeschi, and J. C. van Dam
Hydrol. Earth Syst. Sci., 14, 251–270, https://doi.org/10.5194/hess-14-251-2010, https://doi.org/10.5194/hess-14-251-2010, 2010
C. Medici, S. Bernal, A. Butturini, F. Sabater, M. Martin, A. J. Wade, and F. Frances
Hydrol. Earth Syst. Sci., 14, 223–237, https://doi.org/10.5194/hess-14-223-2010, https://doi.org/10.5194/hess-14-223-2010, 2010
A. Petrone and F. Preti
Hydrol. Earth Syst. Sci., 14, 239–250, https://doi.org/10.5194/hess-14-239-2010, https://doi.org/10.5194/hess-14-239-2010, 2010
A. I. J. M. van Dijk
Hydrol. Earth Syst. Sci., 14, 159–169, https://doi.org/10.5194/hess-14-159-2010, https://doi.org/10.5194/hess-14-159-2010, 2010
C. Gruhier, P. de Rosnay, S. Hasenauer, T. Holmes, R. de Jeu, Y. Kerr, E. Mougin, E. Njoku, F. Timouk, W. Wagner, and M. Zribi
Hydrol. Earth Syst. Sci., 14, 141–156, https://doi.org/10.5194/hess-14-141-2010, https://doi.org/10.5194/hess-14-141-2010, 2010
M. Barnolas, T. Rigo, and M. C. Llasat
Hydrol. Earth Syst. Sci., 14, 129–139, https://doi.org/10.5194/hess-14-129-2010, https://doi.org/10.5194/hess-14-129-2010, 2010
A. Schmidt, J. J. Gibson, I. R. Santos, M. Schubert, K. Tattrie, and H. Weiss
Hydrol. Earth Syst. Sci., 14, 79–89, https://doi.org/10.5194/hess-14-79-2010, https://doi.org/10.5194/hess-14-79-2010, 2010
R. Liu, J. Wen, X. Wang, L. Wang, H. Tian, T. T. Zhang, X. K. Shi, J. H. Zhang, and SH. N. Lv
Hydrol. Earth Syst. Sci., 14, 47–58, https://doi.org/10.5194/hess-14-47-2010, https://doi.org/10.5194/hess-14-47-2010, 2010
S. Werth and A. Güntner
Hydrol. Earth Syst. Sci., 14, 59–78, https://doi.org/10.5194/hess-14-59-2010, https://doi.org/10.5194/hess-14-59-2010, 2010
H. Lin
Hydrol. Earth Syst. Sci., 14, 25–45, https://doi.org/10.5194/hess-14-25-2010, https://doi.org/10.5194/hess-14-25-2010, 2010
A. Ducharne
Hydrol. Earth Syst. Sci., 13, 2399–2412, https://doi.org/10.5194/hess-13-2399-2009, https://doi.org/10.5194/hess-13-2399-2009, 2009
J. E. Barrett, M. N. Gooseff, and C. Takacs-Vesbach
Hydrol. Earth Syst. Sci., 13, 2349–2358, https://doi.org/10.5194/hess-13-2349-2009, https://doi.org/10.5194/hess-13-2349-2009, 2009
V. García-García, R. Gómez, M. R. Vidal-Abarca, and M. L. Suárez
Hydrol. Earth Syst. Sci., 13, 2359–2371, https://doi.org/10.5194/hess-13-2359-2009, https://doi.org/10.5194/hess-13-2359-2009, 2009
M. Shamsudduha, R. E. Chandler, R. G. Taylor, and K. M. Ahmed
Hydrol. Earth Syst. Sci., 13, 2373–2385, https://doi.org/10.5194/hess-13-2373-2009, https://doi.org/10.5194/hess-13-2373-2009, 2009
J. C. M. Andersson, A. J. B. Zehnder, G. P. W. Jewitt, and H. Yang
Hydrol. Earth Syst. Sci., 13, 2329–2347, https://doi.org/10.5194/hess-13-2329-2009, https://doi.org/10.5194/hess-13-2329-2009, 2009
S. Binet, L. Spadini, C. Bertrand, Y. Guglielmi, J. Mudry, and C. Scavia
Hydrol. Earth Syst. Sci., 13, 2315–2327, https://doi.org/10.5194/hess-13-2315-2009, https://doi.org/10.5194/hess-13-2315-2009, 2009
A. Bárdossy and G. G. S. Pegram
Hydrol. Earth Syst. Sci., 13, 2299–2314, https://doi.org/10.5194/hess-13-2299-2009, https://doi.org/10.5194/hess-13-2299-2009, 2009
K. Dontsova, C. I. Steefel, S. Desilets, A. Thompson, and J. Chorover
Hydrol. Earth Syst. Sci., 13, 2273–2286, https://doi.org/10.5194/hess-13-2273-2009, https://doi.org/10.5194/hess-13-2273-2009, 2009
D. Yamazaki, T. Oki, and S. Kanae
Hydrol. Earth Syst. Sci., 13, 2241–2251, https://doi.org/10.5194/hess-13-2241-2009, https://doi.org/10.5194/hess-13-2241-2009, 2009
Cited articles
Bagnold, R. A.: An approach to the sediment transport problem from general
physics, US. geol. Surv. Prof. Paper 422-I, US Geological Survey, https://pubs.usgs.gov/pp/0422i/report.pdf (last access 15 June 2022), 1966.
Berkowitz, B. and Zehe, E.: Surface water and groundwater: unifying conceptualization and quantification of the two “water worlds”, Hydrol. Earth Syst. Sci., 24, 1831–1858, https://doi.org/10.5194/hess-24-1831-2020, 2020.
Beven, K. J.: The effect of ordering on the geomorphic effectiveness of
hydrologic events, Intl. Assoc. Hydrol. Sci. Pub., 132, 510–526, 1981.
Beven, K. J.: Equifinality and uncertainty in geomorphological modelling,
in: The Scientific Nature of Geomorphology, edited by: Rhoads, B. L. and Thorn, C. E., Wiley, Chichester, ISBN 0-471-96811-0, 1996.
Blatter, A. S., Liebert, J., Preuss, P. A., Szabadics, J., and Ihringer, J.: Information system “BW_Abfluss”: regionalisation of flood, mean and low flow parameters, Adv. Geosci., 11, 57–61, https://doi.org/10.5194/adgeo-11-57-2007, 2007.
Bonetti, S., Hooshyar, M., Camporeale, C., and Porporato, A.: Channelization
cascade in landscape evolution, P. Natl. Acad. Sci. USA, 117, 1375–1382, https://doi.org/10.1073/pnas.1911817117, 2020.
Causon, D. M. and Mingham, C. G.: Introductory finite difference methods for
PDEs, Ventus Publishing ApS, ISBN 978-87-7681-642-1, 2010.
Celia, M. A., Bouloutas, E. T., and Zarba, R. L.: A general mass-conservative
numerical solution for the unsaturated flow equation, Water Resour. Res., 26, 1483–1496, https://doi.org/10.1029/WR026i007p01483, 1990.
Chow, V. T.: Open channel hydraulics, McGraw-Hill, ISBN 9780070859067, 1959.
Conte, L., Renner, M., Brando, P., Oliveira dos Santos, C., Silvério,
D., Kolle, O., Trumbore, S., and Kleidon, A.: Effects of tropical deforestation on surface energy balance partitioning in southeastern Amazonia estimated from maximum convective power, Geophys. Res. Lett., 46, 4396–4403, https://doi.org/10.1029/2018GL081625, 2019.
Das, S. K. and Bagheri, J.: Modelling of shallow-water equations by using
compact MacCormack-Type schemes with application to dam-break problem, Int. J. Adv. Appl. Math. Mech., 2, 60–71, 2015.
Dietrich, W. E., Dunne, T., Humphrey, N. F., and Reid, L. M.: Construction of
sediment budgets for drainage basins, in: Sediment Budgets and Routing in
Forested Drainage Basins, Proceedings of the Symposium (PNW-141), 31 May–1 June 1982, Corvallis, Oregon, USA, https://www.fs.usda.gov/treesearch/pubs/7749 (last access: 28 September 2022), 1982.
Dunne, T. and Dietrich, W. E.: Experimental investigation of Horton overland
flow on tropical hillslopes. Part II: Hydraulic characteristics and
hillslope hydrographs, Z. Geomorphol., 35, 60–80,1980.
Dunne, T., Mertes, L. A. K., Meade, R. H., Richey, J. E., and Forsberg, B. R.: Exchanges of sediment between the flood plain and channel of teh Amazon
River in Brazil, Geol. Soc. Am. Bull., 110, 450–467, https://doi.org/10.1130/0016-7606(1998)110<0450:EOSBTF>2.3.CO;2, 1998.
Emmett, W. W.: The Hydraulics of Overland Flow on Hillslopes, US geol.
Surv. Prof. Paper 662, US Geological Survey, https://pubs.usgs.gov/pp/0662a/report.pdf (last access: 28 September 2022), 1970.
Engelund, F. and Hansen, E.: A monograph on sediment transport in alluvial
streams, Hydraulic Engineering Reports, TU Delft, http://resolver.tudelft.nl/uuid:81101b08-04b5-4082-9121-861949c336c9
(last access: 28 September 2022), 1967.
Gerlinger, K.: Erosionsprozesse auf Lössböden: Experimente und
Modellierung, Dissertation, Mitteilungen des Institutes für Wasserbau
und Kulturtechnik der Universität Karlsruhe (TH), Karlsruhe, 194 pp., https://publikationen.bibliothek.kit.edu/11097 (last access: 1 July 2023), 1996.
Gillett, S. L.: Entropy and its misuse, I. Energy, free and otherwise, Ecol. Econ., 56, 58–70, https://doi.org/10.1016/j.ecolecon.2004.12.019, 2006.
Giménez, R. and Govers, G.: Flow detachment by concentrated flow on smooth and irregular beds, Soil Sci. Soc. Am. J., 66, 1475–1483, https://doi.org/10.2136/sssaj2002.1475, 2002.
Gob, F., Bravard, J. P., and Petit, F.: The influence of sediment size, relative grain size and channel slope on initiation of sediment motion in boulder bed rivers. A lichenometric study, Earth Surf. Proc. Land., 35,
1535–1547, https://doi.org/10.1002/esp.1994, 2010.
Hack, J. T.: Studies of longitudinal stream profiles in Virginia and Maryland, US geol. Surv. Prof. Paper 294-B, US Geological Survey,
https://pubs.usgs.gov/pp/0294b/report.pdf (last access: 28 September 2022), 1957.
Howard, A. D.: Theoretical model of optimal drainage networks, Water Resour. Res., 26, 2107–2117, https://doi.org/10.1029/WR026i009p02107, 1990.
Junghänel, T., Ertel, H., and Deutschländer, T.: KOSTRA-DWD-2010R –
Bericht zur Revision der koordinierten Starkregenregionalisierung und
-auswertung des Deutschen Wetterdienstes, Version 2010, https://www.dwd.de/DE/leistungen/kostra_dwd_rasterwerte/download/bericht_kostra_dwd_2010_pdf.pdf (last access: 29 September 2022), 2010.
Kinnell, P. I. A.: The influence of time and other factors on soil loss
produced by rain-impacted flow under artificial rainfall, J. Hydrol., 587, 125004, https://doi.org/10.1016/j.jhydrol.2020.125004, 2020.
Kirkby, M. J.: Hillslope process-response models based in the continuity
equation, Spec. Publ. Inst. Brit. Geogr., 3, 15–30, 1971.
Kleidon, A.: Thermodynamic foundations of the Earth system, Cambridge University Press, New York, NY, ISBN 9781107029941, 2016.
Kleidon, A. and Renner, M.: Diurnal land surface energy balance partitioning
estimated from the thermodynamic limit of a cold heat engine, Earth Syst.
Dynam., 9, 1127–1140, https://doi.org/10.5194/esd-9-1127-2018, 2018.
Kleidon, A., Zehe, E., Ehret, U., and Scherer, U.: Thermodynamics, maximum
power, and the dynamics of preferential river flow structures at the
continental scale, Hydrol. Earth Syst. Sci., 17, 225–251, https://doi.org/10.5194/hess-17-225-2013, 2013.
Kondepui, D. and Prigogine, I.: Modern thermodynamics. From heat engines to
dissipative structures, John Wiley & Sons, Ltd, ISBN 0471973939, 1952.
Langbein, W. B.: Profiles of rivers of uniform discharge, US. geol. Surv.
Prof. Paper 501 B, US Geological Surevey, 119–122, https://pubs.usgs.gov/pp/0501b/report.pdf (last access: 28 September 2022),1964.
Leopold, L. B. and Langbein, W. B.: The concept of entropy in landscape
evolution, US geol. Surv. Prof. Paper 500-A, US Geological Survey,
https://pubs.usgs.gov/pp/0500a/report.pdf (last access: 28 September 2022), 1962.
Leopold, L. B. and Maddock, T.: The hydraulic geometry of stream channels and
some physiographic implications, US geol. Surv. Prof. Paper 252, US Geological Survey, https://doi.org/10.3133/pp252, 1953.
Liang, D., Falconer, R. A., and Lin, B.: Comparison between TVD – MacCormack and ADI-type solvers of the shallow water equations, Adv. Water Resour., 29, 1833–1845, https://doi.org/10.1016/j.advwatres.2006.01.005, 2006.
Liang, D., Lin, B., and Falconer, R. A.: Simulation of rapidly varying flow using an efficient TVD – MacCormack scheme, Int. J. Numer. Meth. Fluids, 53, 811–826, https://doi.org/10.1002/fld.1305, 2007.
Loritz, R., Kleidon, A., Jackisch, C., Westhoff, M., Ehret, U., Gupta, H., and Zehe, E.: A topographic index explaining hydrological similarity by
accounting for the joint controls of runoff formation, Hydrol. Earth Syst. Sci., 23, 3807–3821, https://doi.org/10.5194/hess-23-3807-2019, 2019.
Lotka, A. J.: Contribution to the energetics of evolution, Biology, 8, 147–151, https://doi.org/10.1073/pnas.8.6.147, 1922.
MacCormack, R. W.: The effect of viscosity in hypervelocity impact cratering, J. Spacecraft Rocket., 69, 5, https://doi.org/10.2514/2.6901, 1969.
Maurer, T.: Physikalisch begründete, zeitkontinuierliche Modellierung
des Wassertransports in kleinen ländlichen Einzugsgebieten, Hochschulschrift 61, Universität Karlsruhe (TH), Karlsruhe, https://doi.org/10.5445/IR/65797, 1997.
Meyer, L. D. and Wischmeier, W. H.: Mathematical simulation of the process of
soil erosion by water, T. ASAE, 12, 754–758, https://doi.org/10.13031/2013.38945, 1969.
Nearing, M. A., Norton, L. D., Bulgakov, D. A., Larionov, G. A., West, L. T., and Dontsova, K. M.: Hydraulics and erosion in eroding rills, Water Resour. Res., 33, 865–876, https://doi.org/10.1029/97WR00013, 1997.
Perron, J. T., Kirchner, J. W., and Dietrich, W. E.: Formation of evenly spaced ridges and valleys, Nature, 460, 502–505, https://doi.org/10.1038/nature08174, 2009.
Plate, E. and Zehe, E.: Hydrologie und Stoffdynamik kleiner Einzugsgebiete, in: Prozesse und Modelle, Schweizerbart Science Publishers, Stuttgart,
ISBN 978-3-510-65238-9, 2008.
Popovic, M.: Researchers in an entropy wonderland: A review of the entropy concept, arxiv [preprint], https://arxiv.org/pdf/1711.07326 (last access: 28 September 2022), 2017.
Prigogine, I. and Wiame, J. M.: Biologie et thermodynamique des phenomenes
irreversibles, Experientia, 2, 451–453, https://doi.org/10.1007/BF02153597, 1946.
Rieke-Zapp, D. H. and Nearing, M. A.: Slope shape effects on erosion: a
laboratory study, Soil Sci. Soc. Am. J., 69, 1463–1471, https://doi.org/10.2136/sssaj2005.0015, 2005.
Riggs, H. C.: A simplified slope-area method for estimating flood discharges
in natural channels, US Geological Survey, https://pubs.usgs.gov/journal/1976/vol4issue3/report.pdf (last access:
28 September 2022), 1976.
Rodriguez-Iturbe, I., Rinaldo, A., Rigon, R., Bras, R. L., Marani, A., and
Ijjasz-Vasquez, E.: Energy dissipation, runoff production, and the three dimensional structure of river basins, Water Resour. Res., 4, 1095–1103, https://doi.org/10.1029/91WR03034, 1992.
Scherer, U.: Prozessbasierte Modellierung der Bodenerosion in einer
Lösslandschaft, Schriftenreihe SWW 129, Diss., Univ. Karlsruhe, Karlsruhe, https://doi.org/10.5445/IR/1000009238, 2008.
Scherer, U., Zehe, E., Träbing, K., and Gerlinger, K.: Prediction of soil
detachment in agricultural loess catchments: Model development and
parameterisation, Catena, 90, 63–75, https://doi.org/10.1016/j.catena.2011.11.003, 2012.
Schmidt, J.: Entwicklung und Anwendung eines physikalisch begründeten
Simulationsmodells für die Erosion geneigter landwirtschaftlicher
Nutzflächen, With assistance of FID GEO: Selbstverl. des Inst. für
Geograph. Wiss., Berlin, ISBN 3-88009-062-9, https://e-docs.geo-leo.de/handle/11858/7519?locale-attribute=en (last access: 28 September 2022), 1996.
Schroers, S.: shmulik1990/swe_cormack: VersionZero (Version V0), Zenodo [code], https://doi.org/10.5281/zenodo.8092037, 2023.
Schroers, S., Eiff, O., Kleidon, A., Scherer, U., Wienhöfer, J., and Zehe, E.: Morphological controls on surface runoff: an interpretation of
steady-state energy patterns, maximum power states and dissipation regimes
within a thermodynamic framework, Hydrol. Earth Syst. Sci., 26, 3125–3150, https://doi.org/10.5194/hess-26-3125-2022, 2022.
Shreve, R. L.: Statistical law of stream numbers, J. Geol., 74, 17–37, https://doi.org/10.1086/627137, 1966.
Singh, V. P.: On the theories of hydraulic geometry, Int. J. Sediment Res., 18, 196–218, 2003.
Tanner, W. F.: The river profile, J. Geol., 79, 482–492, 1971.
Tarboton, D. G., Bras, R. L., and Rodriguez-Iturbe, I.: A physical basis for
drainage density, Geomorphology, 5, 59–76, https://doi.org/10.1016/0169-555X(92)90058-V, 1992.
Tribus, M. and McIrvine, E. C.: Energy and information, Scient. Am., 224, 179–188, https://doi.org/10.1038/scientificamerican0971-179, 1971.
Vincent, S., Caltagirone, J.-P., and Bonneton, P.: Numerical modelling of bore propagation and run-up on sloping beaches using a MacCormack TVD scheme,
J. Hydraul. Res., 39, 41–49, https://doi.org/10.1080/00221680109499801 ,2001.
Willgoose, G., Bras, R. L., and Rodriguez-Iturbe, I.: Results from a new model of river basin evolution, Earth Surf. Process., 16, 237–254https://doi.org/10.1002/esp.3290160305, 1991.
Wolman, M. G. and Gerson, R.: Relative scales of time and effectiveness of
climate in watershed geomorphology, Earth Surf. Process., 3, 189–208, https://doi.org/10.1002/esp.3290030207, 1978.
Wolman, M. G. and Miller, J. P.: Magnitude and frequency of forces in geomorphic processes, J. Geol., 68, 54–75, 1960.
Yang, C. T.: Potential Energy and Stream Morphology, Water Resour. Res., 7, 311–322, https://doi.org/10.1029/WR007i002p00311, 1971.
Zehe, E.: Stofftransport in der ungesättigten Bodenzone auf verschiedenen Skalen: Universität Karlsruhe (TH) (Hochschulschrift, 64), PhD dissertation, https://doi.org/10.5445/IR/60999, 1999.
Zehe, E. and Sivapalan, M.: Threshold behaviour in hydrological systems as
(human) geo-ecosystems: manifestations, controls, implications, Hydrol. Earth Syst. Sci., 13, 1273–1297, https://doi.org/10.5194/hess-13-1273-2009, 2009.
Zehe, E., Maurer, T., Ihringer, J., and Plate, E.: Modeling water flow and mass transport in a loess catchment, Phys. Chem. Earth Pt. B, 26, 487–507, https://doi.org/10.1016/S1464-1909(01)00041-7, 2001.
Zehe, E., Becker, R., Bárdossy, A., and Plate, E.: Uncertainty of simulated catchment runoff response in the presence of threshold processes: Role of initial soil moisture and precipitation, J. Hydrol., 315, 183–202, https://doi.org/10.1016/j.jhydrol.2005.03.038, 2005.
Zehe, E., Blume, T., and Blöschl, G.: The principle of “maximum energy
dissipation”: a novel thermodynamic perspective on rapid water flow in
connected soil structures, Philos. T. Roy. Soc. Lond. B, 365, 1377–1386,
https://doi.org/10.1098/rstb.2009.0308, 2010.
Zehe, E., Ehret, U., Blume, T., Kleidon, A., Scherer, U., and Westhoff, M.: A
thermodynamic approach to link self-organization, preferential flow and
rainfall–runoff behaviour, Hydrol. Earth Syst. Sci., 17, 4297–4322, https://doi.org/10.5194/hess-17-4297-2013, 2013.
Zehe, E., Loritz, R., Edery, Y., and Berkowitz, B.: Preferential pathways for
fluid and solutes in heterogeneous groundwater systems: self-organization,
entropy, work, Hydrol. Earth Syst. Sci., 25, 5337–5353, https://doi.org/10.5194/hess-25-5337-2021, 2021.
Short summary
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.
The hydrological cycle shapes our landscape. With an accelerating change of the world's climate...
