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
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Joaquin Meza and M. Levent Kavvas
EGUsphere, https://doi.org/10.31223/X5ND5B, https://doi.org/10.31223/X5ND5B, 2024
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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
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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
Preprint archived
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
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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
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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.
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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.
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
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...
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