Articles | Volume 21, issue 3
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
13 Mar 2017
Research article |
| 13 Mar 2017
Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time
M. Levent Kavvas
CORRESPONDING AUTHOR
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
Ali Ercan
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
James Polsinelli
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
Related authors
Joaquin Meza and M. Levent Kavvas
EGUsphere, https://doi.org/10.31223/X5ND5B, https://doi.org/10.31223/X5ND5B, 2024
Short summary
Short summary
Our study develops a new model to study groundwater flow under uncertainty, using mathematical techniques to improve accuracy and efficiency. This approach allows for better management of water resources, particularly in drought-prone areas, by providing more reliable groundwater availability and movement estimations. This research combines traditional techniques with innovative methods to address water scarcity and support sustainable water use.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 11, 1–12, https://doi.org/10.5194/esd-11-1-2020, https://doi.org/10.5194/esd-11-1-2020, 2020
Short summary
Short summary
After deriving a fractional continuity equation, a previously-developed equation for water flux in porous media was combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. As demonstrated in the numerical application, the orders of the fractional space and time derivatives modulate the speed of groundwater table evolution, slowing the process with the decrease in the powers of the fractional derivatives from 1.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 1993–2005, https://doi.org/10.5194/hess-22-1993-2018, https://doi.org/10.5194/hess-22-1993-2018, 2018
Short summary
Short summary
A new method is proposed to solve the stochastic unsteady open-channel flow system in only one single simulation, as opposed to the many simulations usually done in the popular Monte Carlo approach. The derivation of this new method gave a deterministic and linear Fokker–Planck equation whose solution provided a powerful and effective approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 2007–2021, https://doi.org/10.5194/hess-22-2007-2018, https://doi.org/10.5194/hess-22-2007-2018, 2018
Short summary
Short summary
A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.
Mathieu Mure-Ravaud, Alain Dib, M. Levent Kavvas, and Elena Yegorova
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-665, https://doi.org/10.5194/hess-2017-665, 2018
Preprint withdrawn
Short summary
Short summary
This article introduces a new storm transposition method designed for the transposition (i.e. spatial shifting) of Tropical Cyclones (TCs). This method is based on the shifting of the initial vortex of the TC at the simulation start date. The objective of this method is to find the amount of shift which maximizes the precipitation depth over a given target area. The transposition method was applied to four hurricanes that had spawned torrential precipitation in the United States.
Tongbi Tu, Ali Ercan, and M. Levent Kavvas
Earth Syst. Dynam., 8, 931–949, https://doi.org/10.5194/esd-8-931-2017, https://doi.org/10.5194/esd-8-931-2017, 2017
Short summary
Short summary
Groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior, and the underlying distribution exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics. The estimated Hurst exponent is highly dependent on the length and the specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 8, 921–929, https://doi.org/10.5194/esd-8-921-2017, https://doi.org/10.5194/esd-8-921-2017, 2017
Short summary
Short summary
A dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First a continuity equation for groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained.
Ali Ercan and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-364, https://doi.org/10.5194/hess-2016-364, 2016
Manuscript not accepted for further review
Short summary
Short summary
A finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 20, 2669–2678, https://doi.org/10.5194/hess-20-2669-2016, https://doi.org/10.5194/hess-20-2669-2016, 2016
Short summary
Short summary
This article summarizes the theory and demonstrates the technique of a new scaling method known as the Lie scaling. In the course of applying the method to two example problems, classical notions of dynamical and kinematic scaling are incorporated. The two example problems are a 2-D unconfined groundwater problem in a heterogeneous soil and a 1-D contaminant transport problem. The article concludes with comments on the relative strengths and weaknesses of Lie scaling and classical scaling.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-75, https://doi.org/10.5194/hess-2016-75, 2016
Revised manuscript has not been submitted
Short summary
Short summary
A simple method is presented to model movement of water through soil in general conditions. Specifically, this method was designed to provide a rectangular profile approximation (e.g. the water moves through the soil like a piston) where the water content in the soil volumes is less than saturation. This method reverts to the classical saturated rectangular profile technique under heavy rainfall.
Joaquin Meza and M. Levent Kavvas
EGUsphere, https://doi.org/10.31223/X5ND5B, https://doi.org/10.31223/X5ND5B, 2024
Short summary
Short summary
Our study develops a new model to study groundwater flow under uncertainty, using mathematical techniques to improve accuracy and efficiency. This approach allows for better management of water resources, particularly in drought-prone areas, by providing more reliable groundwater availability and movement estimations. This research combines traditional techniques with innovative methods to address water scarcity and support sustainable water use.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 11, 1–12, https://doi.org/10.5194/esd-11-1-2020, https://doi.org/10.5194/esd-11-1-2020, 2020
Short summary
Short summary
After deriving a fractional continuity equation, a previously-developed equation for water flux in porous media was combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. As demonstrated in the numerical application, the orders of the fractional space and time derivatives modulate the speed of groundwater table evolution, slowing the process with the decrease in the powers of the fractional derivatives from 1.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 1993–2005, https://doi.org/10.5194/hess-22-1993-2018, https://doi.org/10.5194/hess-22-1993-2018, 2018
Short summary
Short summary
A new method is proposed to solve the stochastic unsteady open-channel flow system in only one single simulation, as opposed to the many simulations usually done in the popular Monte Carlo approach. The derivation of this new method gave a deterministic and linear Fokker–Planck equation whose solution provided a powerful and effective approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 2007–2021, https://doi.org/10.5194/hess-22-2007-2018, https://doi.org/10.5194/hess-22-2007-2018, 2018
Short summary
Short summary
A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.
Mathieu Mure-Ravaud, Alain Dib, M. Levent Kavvas, and Elena Yegorova
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-665, https://doi.org/10.5194/hess-2017-665, 2018
Preprint withdrawn
Short summary
Short summary
This article introduces a new storm transposition method designed for the transposition (i.e. spatial shifting) of Tropical Cyclones (TCs). This method is based on the shifting of the initial vortex of the TC at the simulation start date. The objective of this method is to find the amount of shift which maximizes the precipitation depth over a given target area. The transposition method was applied to four hurricanes that had spawned torrential precipitation in the United States.
Tongbi Tu, Ali Ercan, and M. Levent Kavvas
Earth Syst. Dynam., 8, 931–949, https://doi.org/10.5194/esd-8-931-2017, https://doi.org/10.5194/esd-8-931-2017, 2017
Short summary
Short summary
Groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior, and the underlying distribution exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics. The estimated Hurst exponent is highly dependent on the length and the specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 8, 921–929, https://doi.org/10.5194/esd-8-921-2017, https://doi.org/10.5194/esd-8-921-2017, 2017
Short summary
Short summary
A dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First a continuity equation for groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained.
Ali Ercan and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-364, https://doi.org/10.5194/hess-2016-364, 2016
Manuscript not accepted for further review
Short summary
Short summary
A finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 20, 2669–2678, https://doi.org/10.5194/hess-20-2669-2016, https://doi.org/10.5194/hess-20-2669-2016, 2016
Short summary
Short summary
This article summarizes the theory and demonstrates the technique of a new scaling method known as the Lie scaling. In the course of applying the method to two example problems, classical notions of dynamical and kinematic scaling are incorporated. The two example problems are a 2-D unconfined groundwater problem in a heterogeneous soil and a 1-D contaminant transport problem. The article concludes with comments on the relative strengths and weaknesses of Lie scaling and classical scaling.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-75, https://doi.org/10.5194/hess-2016-75, 2016
Revised manuscript has not been submitted
Short summary
Short summary
A simple method is presented to model movement of water through soil in general conditions. Specifically, this method was designed to provide a rectangular profile approximation (e.g. the water moves through the soil like a piston) where the water content in the soil volumes is less than saturation. This method reverts to the classical saturated rectangular profile technique under heavy rainfall.
Related subject area
Subject: Vadose Zone Hydrology | Techniques and Approaches: Theory development
The dimensions of deep-layer soil desiccation and its impact on xylem hydraulic conductivity in dryland tree plantations
Prediction of absolute unsaturated hydraulic conductivity – comparison of four different capillary bundle models
Hydro-pedotransfer functions: A roadmap for future development
Prediction of the absolute hydraulic conductivity function from soil water retention data
Mixed formulation for an easy and robust numerical computation of sorptivity
Signal contribution of distant areas to cosmic-ray neutron sensors – implications for footprint and sensitivity
Technical note: A sigmoidal soil water retention curve without asymptote that is robust when dry-range data are unreliable
Compaction effects on evaporation and salt precipitation in drying porous media
Evaporation front and its motion
Hysteresis in soil hydraulic conductivity as driven by salinity and sodicity – a modeling framework
HESS Opinions: Unsaturated infiltration – the need for a reconsideration of historical misconceptions
Sigmoidal water retention function with improved behaviour in dry and wet soils
The challenges of an in situ validation of a nonequilibrium model of soil heat and moisture dynamics during fires
Anatomy of the 2018 agricultural drought in the Netherlands using in situ soil moisture and satellite vegetation indices
Beyond Perrault's experiments: repeatability, didactics and complexity
Mechanisms of consistently disjunct soil water pools over (pore) space and time
Energy states of soil water – a thermodynamic perspective on soil water dynamics and storage-controlled streamflow generation in different landscapes
Hydrological characterization of cave drip waters in a porous limestone: Golgotha Cave, Western Australia
Soil water stable isotopes reveal evaporation dynamics at the soil–plant–atmosphere interface of the critical zone
Soil water migration in the unsaturated zone of semiarid region in China from isotope evidence
A thermodynamic formulation of root water uptake
Soil–aquifer phenomena affecting groundwater under vertisols: a review
How effective is river restoration in re-establishing groundwater–surface water interactions? – A case study
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
Averaged water potentials in soil water and groundwater, and their connection to menisci in soil pores, field-scale flow phenomena, and simple groundwater flows
Nana He, Xiaodong Gao, Dagang Guo, Yabiao Wu, Dong Ge, Lianhao Zhao, Lei Tian, and Xining Zhao
Hydrol. Earth Syst. Sci., 28, 1897–1914, https://doi.org/10.5194/hess-28-1897-2024, https://doi.org/10.5194/hess-28-1897-2024, 2024
Short summary
Short summary
Deep-layer soil desiccation (DSD) can restrict the sustainability of deep-rooted plantations in water-limited areas. Thus, we explored the extreme effects of DSD based on mass data published and measured on the Loess Plateau and found that the permanent wilting point is a reliable indicator of the moisture limitation of DSD, regardless of tree species, with the corresponding maximum root water uptake depth varying among climatic zones. These dimensions increased the risk of planted trees' death.
Andre Peters, Sascha C. Iden, and Wolfgang Durner
Hydrol. Earth Syst. Sci., 27, 4579–4593, https://doi.org/10.5194/hess-27-4579-2023, https://doi.org/10.5194/hess-27-4579-2023, 2023
Short summary
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.
Tobias Karl David Weber, Lutz Weihermüller, Attila Nemes, Michel Bechtold, Aurore Degré, Efstathios Diamantopoulos, Simone Fatichi, Vilim Filipović, Surya Gupta, Tobias L. Hohenbrink, Daniel R. Hirmas, Conrad Jackisch, Quirijn de Jong van Lier, John Koestel, Peter Lehmann, Toby R. Marthews, Budiman Minasny, Holger Pagel, Martine van der Ploeg, Simon Fiil Svane, Brigitta Szabó, Harry Vereecken, Anne Verhoef, Michael Young, Yijian Zeng, Yonggen Zhang, and Sara Bonetti
EGUsphere, https://doi.org/10.5194/egusphere-2023-1860, https://doi.org/10.5194/egusphere-2023-1860, 2023
Short summary
Short summary
Pedotransfer functions (PTFs) are used to predicts parameters of models describing the hydraulic properties of soils. The appropriateness of these predictions critically rely on the nature of the datasets for training the PTFs as well the physical comprehensiveness of the models. This roadmap papers is addressed at PTF developers and users, and critically reflects the utility and future of PTFs. To this end, we present a manifesto aiming at a paradigm shift in PTFs research.
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
Short summary
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
Hydrol. Earth Syst. Sci., 27, 895–915, https://doi.org/10.5194/hess-27-895-2023, https://doi.org/10.5194/hess-27-895-2023, 2023
Short summary
Short summary
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
Short summary
Short summary
This paper presents a new analytical concept to answer long-lasting questions of the cosmic-ray neutron sensing community, such as
what is the influence of a distant area or patches of different land use on the measurement signal?or
is the detector sensitive enough to detect a change of soil moisture (e.g. due to irrigation) in a remote field at a certain distance?The concept may support signal interpretation and sensor calibration, particularly in heterogeneous terrain.
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
Short summary
Short summary
The way soils capture infiltrating water affects crops and natural vegetation as well as groundwater recharge. This retention of soil water is captured by a mathematical function that covers all water contents from very dry to water-saturated. Unfortunately, data in the dry range are often absent or unreliable. I modified an earlier function to be more robust in the absence of dry-range data, and present a computer program to estimate the parameters of the new function.
Nurit Goldberg-Yehuda, Shmuel Assouline, Yair Mau, and Uri Nachshon
Hydrol. Earth Syst. Sci., 26, 2499–2517, https://doi.org/10.5194/hess-26-2499-2022, https://doi.org/10.5194/hess-26-2499-2022, 2022
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Cited articles
Baumer, B. and Meerschaert, M. M.: Fractional diffusion with two time scales, Physica A, 373, 237–251, 2007.
Baumer, B., Benson, D., and Meerschaert, M. M.: Advection and dispersion in time and space, Physica A, 350, 245–262, 2005.
Bear, J.: Hydraulics of groundwater, McGraw-Hill Inc., New York, 1979.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: Application of a fractional advection-dispersion equation, Water Resour. Res., 36, 1403–1412, 2000a.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: The fractional-order governing equation of Levy motion, Water Resour. Res., 36, 1413–1423, 2000b.
Brooks, R. H. and Corey, A. T.: Hydraulic properties of porous media, Hydrol. Pap. no. 3, Colorado State University, Fort Collins, CO, 1964.
Cushman, J. H., O'Malley, D., and Park, M.: Anomalous diffusion as modeled by a nonstationary extension of Brownian motion, Phys. Rev. E., 79, 032101, https://doi.org/10.1103/PhysRevE.79.032101, 2009.
Darcy, H.: Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856.
El-Abd, A. E.-G. and Milczarek, J. J..: Neutron radiography study of water absorption in porous building materials: anomalous diffusion analysis, J. Phys. D Appl. Phys., 37, 2305–2513, 2004.
Ferguson, H. and Gardner, W. H.: Diffusion theory applied to water flow data obtained using gamma ray absorption, Soil Sci. Soc. Am. Pro., 27, 243–246, 1963.
Freeze, R. A. and Cherry, J. A.: Groundwater, Prentice-Hall, N.J, 1979.
Gerolymatou, E., Vardoulakis, I., and Hilfer, R.: Modelling infiltration by means of a nonlinear fractional diffusion model, J. Phys. D Appl. Phys., 39, 4104–4110, 2006.
Guerrini, I. A. and Swartzendruber, D.: Soil water diffusivity as explicitly dependent on both time and water content, Soil Sci. Soc. Am. J., 56, 335–340, 1992.
He, J.-H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Method. Appl. Mech., 167, 57–68, 1998.
Levy, M. and Berkowitz, B.: Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, J. Contam. Hydrol., 64, 203–226, 2003.
Li, M.-F., Ren, J. R., and Zhu, T.: Series expansion in fractional calculus and fractional differential equations, arXiv: 0910.4819v2 [math-ph], 2009.
Meerschaert, M. M., Benson, D. A., and Baumer, B.: Multidimensional advection and fractional dispersion, Phys. Rev. E, 59, 5026–5028, 1999.
Meerschaert, M. M., Benson, D. A., Scheffler, H. P., and Baumer, B.: Stochastic solution of space-time fractional diffusion equations, Phys. Rev. E, 65, 041103-1–04113-4, 2002.
Meerschaert, M. M., Mortensen, J., and Wheatcraft, S. W.: Fractional vector calculus for fractional advection-dispersion, Physica A, 367, 167–181, 2006.
Nielsen, D. R., Biggar, J. W., and Davidson, J. M.: Experimental consideration of diffusion analysis in unsaturated flow problem, Soil Sci. Soc. Am. Pro., 26, 107–111, 1962.
Odibat, Z. M. and Shawagfeh, N. T.: Generalized Taylor formula, Appl. Math. Comput., 186, 286–293, 2007.
Pachepsky, Y., Timlin, D., and Rawls, W.: Generalized Richards' equation to simulate water transport in unsaturated soils, J. Hydrol., 272, 3–13, 2003.
Peaudecerf, G. and Sauty, J.-P.: Application of a mathematical model to the characterization of dispersion effects on groundwater quality, Prog. Water Technol., 10, 443–454, 1978.
Podlubny, I.: Fractional Differential Equations, Academic Press, San Diego, 340 pp., 1999.
Rawlins, S. L. and Gardner, W. H.: A test of the validity of the diffusion equation for unsaturated flow of soil water, Soil Sci. Soc. Am. Pro., 27, 507–511, 1963.
Schumer, R., Benson, D. A., Meerschaert, M. M., and Wheatcraft, S. W.: Eulerian derivation for the fractional advection-dispersion equation, J. Contam. Hydrol., 48, 69–88, 2001.
Schumer, R., Meerschaert, M. M., and Baumer, B.: Fractional advection-dispersion equations for modeling transport at the earth surface, J. Geophys. Res., 114, F00A07, https://doi.org/10.1029/2008JF001246, 2009.
Sidle, C., Nilson, B., Hansen, M., and Fredericia, J.: Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark, Water Resour. Res., 34, 2515–2527, 1998.
Silliman, S. E. and Simpson, E. S.: Laboratory evidence of the scale effect in dispersion of solutes in porous media, Water Resour. Res., 23, 1667–1673, 1987.
Sudicky, E. A., Cherry, J. A., and Frind, E. O.: Migration of contaminants in groundwater at a landfill: a case study. 4. A natural-gradient dispersion test, J. Hydrol., 63, 81–108, 1983.
Sun, H., Meerschaert, M., Zhang, Y., Zhu, J., and Chen, W.: A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media, Adv. Water Resour., 52, 292–295, 2013.
Usero, D.: Fractional Taylor series for Caputo fractional derivatives. Construction of numerical schemes, http://www.fdi.ucm.es/profesor/lvazquez/calcfrac/docs/paper_usero.pdf (last access: February 2017), 2008.
Zhang, Y., Benson, D. A., Meerschaert, M. M., and Labolle, E. M.: Space-fractional advection-dispersion equations with variable parameters: diverse formulas, numerical solutions, and application to the macrodispersion experiment site data, Water Resour. Res., 43, W05439, https://doi.org/10.1029/2006WR004912, 2007.
Zhang, Y. and Benson, D. A.: Lagrangian simulation of multidimensional anomalous transport at the MADE site, Geophys. Res. Lett., 35, L07403, https://doi.org/10.1029/2008GL033222, 2008.
Zhang, Y., Benson, D. A., and Reeves, D. M.: Time and space nonlocalities underlying fractional-derivative models: distinction and literature review of field applications, Adv. Water Resour., 32, 561–581, 2009.
Short summary
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.
In this study dimensionally consistent governing equations of continuity and motion for...
Special issue