Articles | Volume 27, issue 24
https://doi.org/10.5194/hess-27-4579-2023
© 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-27-4579-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
20 Dec 2023
Research article |
| 20 Dec 2023
| 20 Dec 2023
Prediction of absolute unsaturated hydraulic conductivity – comparison of four different capillary bundle models
Andre Peters
CORRESPONDING AUTHOR
Division of Soil Science and Soil Physics, Institute of Geoecology, Technische Universität Braunschweig, Braunschweig, Germany
now at: Thünen Institute of Agricultural Technology, Braunschweig, Germany
Sascha C. Iden
Division of Soil Science and Soil Physics, Institute of Geoecology, Technische Universität Braunschweig, Braunschweig, Germany
Wolfgang Durner
Division of Soil Science and Soil Physics, Institute of Geoecology, Technische Universität Braunschweig, Braunschweig, Germany
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Tobias L. Hohenbrink, Conrad Jackisch, Wolfgang Durner, Kai Germer, Sascha C. Iden, Janis Kreiselmeier, Frederic Leuther, Johanna C. Metzger, Mahyar Naseri, and Andre Peters
Earth Syst. Sci. Data, 15, 4417–4432, https://doi.org/10.5194/essd-15-4417-2023, https://doi.org/10.5194/essd-15-4417-2023, 2023
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The article describes a collection of 572 data sets of soil water retention and unsaturated hydraulic conductivity data measured with state-of-the-art laboratory methods. Furthermore, the data collection contains basic soil properties such as soil texture and organic carbon content. We expect that the data will be useful for various important purposes, for example, the development of soil hydraulic property models and related pedotransfer functions.
Moreen Willaredt, Thomas Nehls, and Andre Peters
Hydrol. Earth Syst. Sci., 27, 3125–3142, https://doi.org/10.5194/hess-27-3125-2023, https://doi.org/10.5194/hess-27-3125-2023, 2023
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This study proposes a model to predict soil hydraulic properties (SHPs) of constructed Technosols for urban greening. The SHPs are determined by the Technosol composition and describe their capacity to store and supply water to plants. The model predicts SHPs of any binary mixture based on the SHPs of its two pure components, facilitating simulations of flow and transport processes before production. This can help create Technosols designed for efficient urban greening and water management.
Andre Peters, Tobias L. Hohenbrink, Sascha C. Iden, Martinus Th. van Genuchten, and Wolfgang Durner
Hydrol. Earth Syst. Sci., 27, 1565–1582, https://doi.org/10.5194/hess-27-1565-2023, https://doi.org/10.5194/hess-27-1565-2023, 2023
Short summary
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The soil hydraulic conductivity function is usually predicted from the water retention curve (WRC) with the requirement of at least one measured conductivity data point for scaling the function. We propose a new scheme of absolute hydraulic conductivity prediction from the WRC without the need of measured conductivity data. Testing the new prediction with independent data shows good results. This scheme can be used when insufficient or no conductivity data are available.
Andre Peters, Thomas Nehls, and Gerd Wessolek
Hydrol. Earth Syst. Sci., 20, 2309–2315, https://doi.org/10.5194/hess-20-2309-2016, https://doi.org/10.5194/hess-20-2309-2016, 2016
Short summary
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The AWAT (Adaptive Window and Adaptive Threshold) filter routine for high-resolution lysimeter data is improved. The threshold scheme with original step interpolation yields unrealistic fluxes for high temporal resolution. Improvement applies linear and spline interpolation schemes so that fluxes in high temporal resolution are automatically calculated. The spline scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound.
A. Peters, T. Nehls, H. Schonsky, and G. Wessolek
Hydrol. Earth Syst. Sci., 18, 1189–1198, https://doi.org/10.5194/hess-18-1189-2014, https://doi.org/10.5194/hess-18-1189-2014, 2014
Tobias L. Hohenbrink, Conrad Jackisch, Wolfgang Durner, Kai Germer, Sascha C. Iden, Janis Kreiselmeier, Frederic Leuther, Johanna C. Metzger, Mahyar Naseri, and Andre Peters
Earth Syst. Sci. Data, 15, 4417–4432, https://doi.org/10.5194/essd-15-4417-2023, https://doi.org/10.5194/essd-15-4417-2023, 2023
Short summary
Short summary
The article describes a collection of 572 data sets of soil water retention and unsaturated hydraulic conductivity data measured with state-of-the-art laboratory methods. Furthermore, the data collection contains basic soil properties such as soil texture and organic carbon content. We expect that the data will be useful for various important purposes, for example, the development of soil hydraulic property models and related pedotransfer functions.
Moreen Willaredt, Thomas Nehls, and Andre Peters
Hydrol. Earth Syst. Sci., 27, 3125–3142, https://doi.org/10.5194/hess-27-3125-2023, https://doi.org/10.5194/hess-27-3125-2023, 2023
Short summary
Short summary
This study proposes a model to predict soil hydraulic properties (SHPs) of constructed Technosols for urban greening. The SHPs are determined by the Technosol composition and describe their capacity to store and supply water to plants. The model predicts SHPs of any binary mixture based on the SHPs of its two pure components, facilitating simulations of flow and transport processes before production. This can help create Technosols designed for efficient urban greening and water management.
Benjamin Guillaume, Hanane Aroui Boukbida, Gerben Bakker, Andrzej Bieganowski, Yves Brostaux, Wim Cornelis, Wolfgang Durner, Christian Hartmann, Bo V. Iversen, Mathieu Javaux, Joachim Ingwersen, Krzysztof Lamorski, Axel Lamparter, András Makó, Ana María Mingot Soriano, Ingmar Messing, Attila Nemes, Alexandre Pomes-Bordedebat, Martine van der Ploeg, Tobias Karl David Weber, Lutz Weihermüller, Joost Wellens, and Aurore Degré
SOIL, 9, 365–379, https://doi.org/10.5194/soil-9-365-2023, https://doi.org/10.5194/soil-9-365-2023, 2023
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Measurements of soil water retention properties play an important role in a variety of societal issues that depend on soil water conditions. However, there is little concern about the consistency of these measurements between laboratories. We conducted an interlaboratory comparison to assess the reproducibility of the measurement of the soil water retention curve. Results highlight the need to harmonize and standardize procedures to improve the description of unsaturated processes in soils.
Andre Peters, Tobias L. Hohenbrink, Sascha C. Iden, Martinus Th. van Genuchten, and Wolfgang Durner
Hydrol. Earth Syst. Sci., 27, 1565–1582, https://doi.org/10.5194/hess-27-1565-2023, https://doi.org/10.5194/hess-27-1565-2023, 2023
Short summary
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The soil hydraulic conductivity function is usually predicted from the water retention curve (WRC) with the requirement of at least one measured conductivity data point for scaling the function. We propose a new scheme of absolute hydraulic conductivity prediction from the WRC without the need of measured conductivity data. Testing the new prediction with independent data shows good results. This scheme can be used when insufficient or no conductivity data are available.
Mahyar Naseri, Sascha C. Iden, and Wolfgang Durner
SOIL, 8, 99–112, https://doi.org/10.5194/soil-8-99-2022, https://doi.org/10.5194/soil-8-99-2022, 2022
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We simulated stony soils with low to high volumes of rock fragments in 3D using evaporation and multistep unit-gradient experiments. Hydraulic properties of virtual stony soils were identified under a wide range of soil matric potentials. The developed models for scaling the hydraulic conductivity of stony soils were evaluated under unsaturated flow conditions.
Conrad Jackisch, Kai Germer, Thomas Graeff, Ines Andrä, Katrin Schulz, Marcus Schiedung, Jaqueline Haller-Jans, Jonas Schneider, Julia Jaquemotte, Philipp Helmer, Leander Lotz, Andreas Bauer, Irene Hahn, Martin Šanda, Monika Kumpan, Johann Dorner, Gerrit de Rooij, Stefan Wessel-Bothe, Lorenz Kottmann, Siegfried Schittenhelm, and Wolfgang Durner
Earth Syst. Sci. Data, 12, 683–697, https://doi.org/10.5194/essd-12-683-2020, https://doi.org/10.5194/essd-12-683-2020, 2020
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Soil water content and matric potential are central hydrological state variables. A large variety of automated probes and sensor systems for field monitoring exist. In a field experiment under idealised conditions we compared 15 systems for soil moisture and 14 systems for matric potential. The individual records of one system agree well with the others. Most records are also plausible. However, the absolute values of the different measuring systems span a very large range of possible truths.
Tobias Karl David Weber, Sascha Christian Iden, and Wolfgang Durner
Hydrol. Earth Syst. Sci., 21, 6185–6200, https://doi.org/10.5194/hess-21-6185-2017, https://doi.org/10.5194/hess-21-6185-2017, 2017
Andre Peters, Thomas Nehls, and Gerd Wessolek
Hydrol. Earth Syst. Sci., 20, 2309–2315, https://doi.org/10.5194/hess-20-2309-2016, https://doi.org/10.5194/hess-20-2309-2016, 2016
Short summary
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The AWAT (Adaptive Window and Adaptive Threshold) filter routine for high-resolution lysimeter data is improved. The threshold scheme with original step interpolation yields unrealistic fluxes for high temporal resolution. Improvement applies linear and spline interpolation schemes so that fluxes in high temporal resolution are automatically calculated. The spline scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound.
M. Hannes, U. Wollschläger, F. Schrader, W. Durner, S. Gebler, T. Pütz, J. Fank, G. von Unold, and H.-J. Vogel
Hydrol. Earth Syst. Sci., 19, 3405–3418, https://doi.org/10.5194/hess-19-3405-2015, https://doi.org/10.5194/hess-19-3405-2015, 2015
B. Scharnagl, S. C. Iden, W. Durner, H. Vereecken, and M. Herbst
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-12-2155-2015, https://doi.org/10.5194/hessd-12-2155-2015, 2015
Preprint withdrawn
A. Peters, T. Nehls, H. Schonsky, and G. Wessolek
Hydrol. Earth Syst. Sci., 18, 1189–1198, https://doi.org/10.5194/hess-18-1189-2014, https://doi.org/10.5194/hess-18-1189-2014, 2014
Related subject area
Subject: Vadose Zone Hydrology | Techniques and Approaches: Theory development
Prediction of the absolute hydraulic conductivity function from soil water retention data
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Recharge estimation and soil moisture dynamics in a Mediterranean, semi-arid karst region
Relations between macropore network characteristics and the degree of preferential solute transport
Impacts of conservation tillage on the hydrological and agronomic performance of Fanya juus in the upper Blue Nile (Abbay) river basin
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Andre Peters, Tobias L. Hohenbrink, Sascha C. Iden, Martinus Th. van Genuchten, and Wolfgang Durner
Hydrol. Earth Syst. Sci., 27, 1565–1582, https://doi.org/10.5194/hess-27-1565-2023, https://doi.org/10.5194/hess-27-1565-2023, 2023
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The soil hydraulic conductivity function is usually predicted from the water retention curve (WRC) with the requirement of at least one measured conductivity data point for scaling the function. We propose a new scheme of absolute hydraulic conductivity prediction from the WRC without the need of measured conductivity data. Testing the new prediction with independent data shows good results. This scheme can be used when insufficient or no conductivity data are available.
Laurent Lassabatere, Pierre-Emmanuel Peyneau, Deniz Yilmaz, Joseph Pollacco, Jesús Fernández-Gálvez, Borja Latorre, David Moret-Fernández, Simone Di Prima, Mehdi Rahmati, Ryan D. Stewart, Majdi Abou Najm, Claude Hammecker, and Rafael Angulo-Jaramillo
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Sorptivity is one of the most important parameters for quantifying water infiltration into soils. In this study, we propose a mixed formulation that avoids numerical issues and allows for the computation of sorptivity for all types of models chosen for describing the soil hydraulic functions and all initial and final conditions. We show the benefits of using the mixed formulation with regard to modeling water infiltration into soils.
Martin Schrön, Markus Köhli, and Steffen Zacharias
Hydrol. Earth Syst. Sci., 27, 723–738, https://doi.org/10.5194/hess-27-723-2023, https://doi.org/10.5194/hess-27-723-2023, 2023
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Gerrit Huibert de Rooij
Hydrol. Earth Syst. Sci., 26, 5849–5858, https://doi.org/10.5194/hess-26-5849-2022, https://doi.org/10.5194/hess-26-5849-2022, 2022
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Nurit Goldberg-Yehuda, Shmuel Assouline, Yair Mau, and Uri Nachshon
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In this work the interactions between soil compaction, evaporation, and salt accumulation at the vadose zone are discussed. Changes at the micro and macro scales of the soil physical and hydraulic properties were studied using high-resolution imagining techniques, alongside column experiments, aiming to characterize water flow and evaporation processes at natural, compacted, and tilled soil conditions. In addition, salt accumulation at the soil profile was examined for these setups.
Jiří Mls
Hydrol. Earth Syst. Sci., 26, 397–406, https://doi.org/10.5194/hess-26-397-2022, https://doi.org/10.5194/hess-26-397-2022, 2022
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In the paper the evaporation front is considered the interface that separates the wet part of a porous medium from its dry surroundings, and its exact definition in time and space is given. Subsequently, the law of the front's motion is derived. The general problem governing completely the front's motion is formulated and, for a special case, solved numerically. It is shown that the solution makes it possible to locate the rate of vaporization in time and space.
Isaac Kramer, Yuval Bayer, Taiwo Adeyemo, and Yair Mau
Hydrol. Earth Syst. Sci., 25, 1993–2008, https://doi.org/10.5194/hess-25-1993-2021, https://doi.org/10.5194/hess-25-1993-2021, 2021
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Salinity and sodicity can cause irreversible degradation to soil, threatening agricultural production and food security. To date, very little is known about the degree to which soil degradation can be reversible. We introduce a model for describing this partial reversibility (hysteresis) and lay out the experimental procedures necessary for characterizing the soil in this regard. We must shift our focus from degradation measurements to reversal measurements so that we can maintain healthy soils.
Peter F. Germann
Hydrol. Earth Syst. Sci., 25, 1097–1101, https://doi.org/10.5194/hess-25-1097-2021, https://doi.org/10.5194/hess-25-1097-2021, 2021
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This is the last paper submitted by Peter Germann before he died in December 2020. Peter reviews the development of capillary flow theory since the work of Briggs (1897) and Richards (1931), who raised capillary flow to a soil hydrological dogma. Attempts to correct the dogma led to concepts of non-equilibrium flow, macropore flow, and preferential flow during infiltration. Viscous film flow is proposed as an alternative approach to capillarity-driven flow during unsaturated infiltration.
Gerrit Huibert de Rooij, Juliane Mai, and Raneem Madi
Hydrol. Earth Syst. Sci., 25, 983–1007, https://doi.org/10.5194/hess-25-983-2021, https://doi.org/10.5194/hess-25-983-2021, 2021
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The way soils capture infiltrating water affects crops and natural vegetation and groundwater recharge. This retention of soil water is described by a mathematical function that covers all water contents from very dry to water saturated. We combined two existing lines of research to improve the behaviour of a popular function for very dry and very wet conditions. Our new function could handle a wider range of conditions than earlier curves. We provide fits to a wide range of soils.
William J. Massman
Hydrol. Earth Syst. Sci., 25, 685–709, https://doi.org/10.5194/hess-25-685-2021, https://doi.org/10.5194/hess-25-685-2021, 2021
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Increasing fire frequency and severity now poses a threat to most of the world's wildlands and forested ecosystems and their benefits. The HMV (Heat–Moisture–Vapor) model is a tool to manage fuels to help mitigate the consequences of fire and promote soil and vegetation recovery after fire. The model's performance is surprisingly good, but it also provides insights into the existence of previously unobserved feedbacks and other physical processes that occur during fire.
Joost Buitink, Anne M. Swank, Martine van der Ploeg, Naomi E. Smith, Harm-Jan F. Benninga, Frank van der Bolt, Coleen D. U. Carranza, Gerbrand Koren, Rogier van der Velde, and Adriaan J. Teuling
Hydrol. Earth Syst. Sci., 24, 6021–6031, https://doi.org/10.5194/hess-24-6021-2020, https://doi.org/10.5194/hess-24-6021-2020, 2020
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The amount of water stored in the soil is critical for the productivity of plants. Plant productivity is either limited by the available water or by the available energy. In this study, we infer this transition point by comparing local observations of water stored in the soil with satellite observations of vegetation productivity. We show that the transition point is not constant with soil depth, indicating that plants use water from deeper layers when the soil gets drier.
Stefano Barontini and Matteo Settura
Hydrol. Earth Syst. Sci., 24, 1907–1926, https://doi.org/10.5194/hess-24-1907-2020, https://doi.org/10.5194/hess-24-1907-2020, 2020
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More than 300 years after its first appearance, Perrault's De l'origine des fontaines provokes intriguing stimuli and suggestions. We discuss its epistemological relevance through the lens of the repeatability of the experiments, of the didactic aspects which arise for modern teaching of hydrology, and of the author's attitude in facing the complexity of the hydrological processes. The analysis shows that the birth of modern hydrology and the scientific revolution were closely entwined.
Matthias Sprenger, Pilar Llorens, Carles Cayuela, Francesc Gallart, and Jérôme Latron
Hydrol. Earth Syst. Sci., 23, 2751–2762, https://doi.org/10.5194/hess-23-2751-2019, https://doi.org/10.5194/hess-23-2751-2019, 2019
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We find that the stable isotopic compositions of mobile and matrix bound soil water are continuously different over 8 months. Long-term data further show that these isotopic differences result from the refilling of small soil pores by isotopically depleted rains during low soil moisture conditions. Thus, subsurface water is not well mixed, but flow velocities and storage in soils are highly variable; this has important implications for ecohydrological studies and soil hydrological modeling.
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
Kashif Mahmud, Gregoire Mariethoz, Andy Baker, and Pauline C. Treble
Hydrol. Earth Syst. Sci., 22, 977–988, https://doi.org/10.5194/hess-22-977-2018, https://doi.org/10.5194/hess-22-977-2018, 2018
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This study explores the relationship between drip water and rainfall in a SW Australian karst, where both intra- and interannual hydrological variations are strongly controlled by seasonal variations in recharge. The hydrological behavior of cave drips is examined at daily resolution with respect to mean discharge and the flow variation. We demonstrate that the analysis of the time series produced by cave drip loggers generates useful hydrogeological information that can be applied generally.
Matthias Sprenger, Doerthe Tetzlaff, and Chris Soulsby
Hydrol. Earth Syst. Sci., 21, 3839–3858, https://doi.org/10.5194/hess-21-3839-2017, https://doi.org/10.5194/hess-21-3839-2017, 2017
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We sampled the isotopic composition in the top 20 cm at four different sites in the Scottish Highlands at 5 cm intervals over 1 year. The relationship between the soil water isotopic fractionation and evapotranspiration showed a hysteresis pattern due to a lag response to onset and offset of the evaporative losses. The isotope data revealed that vegetation had a significant influence on the soil evaporation with evaporation being double from soils beneath Scots pine compared to heather.
Yonggang Yang and Bojie Fu
Hydrol. Earth Syst. Sci., 21, 1757–1767, https://doi.org/10.5194/hess-21-1757-2017, https://doi.org/10.5194/hess-21-1757-2017, 2017
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This paper investigates soil water migration processes in the Loess Plateau using isotopes. The soil water migration is dominated by piston-type flow, but rarely preferential flow. Soil water from the soil lay (20–40 cm) contributed to 6–12% of plant xylem water, while soil water at the depth of 40–60 cm is the largest component (range from 60 to 66 %), soil water below 60 cm depth contributed 8–14 % to plant xylem water, and only 5–8 % is derived from precipitation.
M. Levent Kavvas, Ali Ercan, and James Polsinelli
Hydrol. Earth Syst. Sci., 21, 1547–1557, https://doi.org/10.5194/hess-21-1547-2017, https://doi.org/10.5194/hess-21-1547-2017, 2017
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In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. By the introduction of the Brooks–Corey constitutive relationships, an explicit form of the equations is obtained. The developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations.
Anke Hildebrandt, Axel Kleidon, and Marcel Bechmann
Hydrol. Earth Syst. Sci., 20, 3441–3454, https://doi.org/10.5194/hess-20-3441-2016, https://doi.org/10.5194/hess-20-3441-2016, 2016
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This theoretical paper describes the energy fluxes and dissipation along the flow paths involved in root water uptake, an approach that is rarely taken. We show that this provides useful additional insights for understanding the biotic and abiotic impediments to root water uptake. This approach shall be applied to explore efficient water uptake strategies and help locate the limiting processes in the complex soil–plant–atmosphere system.
D. Kurtzman, S. Baram, and O. Dahan
Hydrol. Earth Syst. Sci., 20, 1–12, https://doi.org/10.5194/hess-20-1-2016, https://doi.org/10.5194/hess-20-1-2016, 2016
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Vertisols are cracking clayey, arable soils that often overlay groundwater reservoirs. The soil cracks enable flow that bypasses soil blocks, which results in both relatively fresh recharge of the underlying groundwater and contamination with reactive contaminants. These special phenomena, as well as unique mechanism of salinization after cultivation and relative resilience to contamination by nitrate typical to groundwater under vertisols, are reviewed in this study.
A.-M. Kurth, C. Weber, and M. Schirmer
Hydrol. Earth Syst. Sci., 19, 2663–2672, https://doi.org/10.5194/hess-19-2663-2015, https://doi.org/10.5194/hess-19-2663-2015, 2015
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This study investigates the effects of river restoration on groundwater–surface water interactions in a losing urban stream. Investigations were performed using Distributed Temperature Sensing (DTS). The results indicate that the highest surface water downwelling occurred at the tip of a gravel island newly installed during river restoration, leading to the conclusion that in this specific setting, river restoration was effective in locally enhancing groundwater–surface water interactions.
F. Ries, J. Lange, S. Schmidt, H. Puhlmann, and M. Sauter
Hydrol. Earth Syst. Sci., 19, 1439–1456, https://doi.org/10.5194/hess-19-1439-2015, https://doi.org/10.5194/hess-19-1439-2015, 2015
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Soil moisture was observed along a strong semi-arid climatic gradient in a Mediterranean karst area. Soil moisture data and soil hydraulic modelling with Hydrus-1D revealed a strong dependency of percolation fluxes with rainfall amounts and intensity during heavy rainfall events. Spatial and temporal extrapolation of the model illustrated the high variability of seasonal percolation amounts among single years and showed strong correlations between soil depth and potential groundwater recharge.
M. Larsbo, J. Koestel, and N. Jarvis
Hydrol. Earth Syst. Sci., 18, 5255–5269, https://doi.org/10.5194/hess-18-5255-2014, https://doi.org/10.5194/hess-18-5255-2014, 2014
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The characteristics of the macropore network determine the potential for fast transport of solutes through soil. Such characteristics computed from 3-dimensional X-ray tomography images were combined with measured solute breakthrough curves and near-saturated hydraulic conductivities. At a given flow rate, smaller macroporosities, poorer local connectivity of the macropore network and smaller near-saturated hydraulic conductivities resulted in a greater degree of preferential transport.
M. Temesgen, S. Uhlenbrook, B. Simane, P. van der Zaag, Y. Mohamed, J. Wenninger, and H. H. G. Savenije
Hydrol. Earth Syst. Sci., 16, 4725–4735, https://doi.org/10.5194/hess-16-4725-2012, https://doi.org/10.5194/hess-16-4725-2012, 2012
G. H. de Rooij
Hydrol. Earth Syst. Sci., 15, 1601–1614, https://doi.org/10.5194/hess-15-1601-2011, https://doi.org/10.5194/hess-15-1601-2011, 2011
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Short summary
While various expressions for the water retention curve are commonly compared, the capillary conductivity model proposed by Mualem is widely used but seldom compared to alternatives. We compare four different capillary bundle models in terms of their ability to fully predict the hydraulic conductivity. The Mualem model outperformed the three other models in terms of predictive accuracy. Our findings suggest that the widespread use of the Mualem model is justified.
While various expressions for the water retention curve are commonly compared, the capillary...
