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A. Manglik - One of the best experts on this subject based on the ideXlab platform.
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Modeling Water Table Fluctuations in Anisotropic Unconfined Aquifer Due to Time Varying Recharge from Multiple Heterogeneous Basins and Pumping from Multiple Wells
Water Resources Management, 2015Co-Authors: A. ManglikAbstract:Prediction of water table fluctuations in response to proposed schemes of recharging and pumping is important to make judicious selection of an appropriate scheme out of many schemes to achieve the preset objective of sustainable management of Groundwater resources without compromising the regional water balance. This is achieved by solving Groundwater Flow Equation with suitable initial and boundary conditions, aquifer parameters, and recharge/pumping parameters. Earlier, analytical solutions were developed to predict water table fluctuations in aquifer due to time varying recharge rate from multiple basins considering spatially uniform recharge rate for the entire basin area. However, the recharge rate may vary spatially within a single basin due to many factors such as variation in the height of water column above the base of the basin, degree of siltation of the base of the basin etc. In the present work, we develop an analytical solution for modeling of water table fluctuations in an anisotropic aquifer due to intermittently applied spatio-temporally varying rate of recharge from multiple basins and pumping from multiple wells arbitrarily distributed within the model domain. In the present solution, wells are treated as point sources, which helps in reducing numerical artifacts. Some earlier obtained analytical solutions are the special cases of the present solution.
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A Generalized Predictive Model of Water Table Fluctuations in Anisotropic Aquifer Due to Intermittently Applied Time-Varying Recharge from Multiple Basins
Water Resources Management, 2013Co-Authors: A. Manglik, V. S. SinghAbstract:Mathematical models play a key role in assessing the future behavior of a Groundwater system in response to various schemes of ground water resources development such as artificial recharging and in selecting an appropriate one out of many proposed schemes for its sustainable development. This paper presents an analytical solution of Groundwater Flow Equation for unconfined, anisotropic, 2-D rectangular aquifer under the Boussinesq approximation to predict water table fluctuations in the aquifer in response to general time-varying intermittent recharge from multiple rectangular infiltration basins of different spatial dimensions. The horizontal anisotropy incorporated in the model is such that the principal axes of the hydraulic conductivity tensor are oriented parallel to the rectangular sides of the aquifer. The time-varying recharge rate is approximated by a series of line elements of different lengths and slopes depending on the nature of variation of recharge rate. The solution is obtained by using extended finite Fourier sine transform. Application of the solution is demonstrated with the help of synthetic examples. Numerical results of the analytical solutions are verified by comparison with the results obtained from MODFlow. Numerical results indicate significant effect of anisotropy in hydraulic conductivity on the nature of water table variation.
Abdon Atangana - One of the best experts on this subject based on the ideXlab platform.
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Analysis of exact Groundwater model within a confined aquifer: New proposed model beyond the Theis Equation
European Physical Journal Plus, 2018Co-Authors: Mashudu Clifford Mathobo, Abdon AtanganaAbstract:The aim of this work was to develop the exact Groundwater Flow model within a confined aquifer. We argued that, the Theis Groundwater Flow model is an approximation of the real formulation of the model as Theis removed some components of the Equation to have a simple model. Initially, we derived an exact Groundwater Flow Equation for a confined aquifer so as to include all high order terms that were removed by Theis and also to take into account the assumptions that were used during the derivation of the Groundwater Flow by Theis. Thereafter, we proved that the new Groundwater Flow Equation has a unique solution. We then derived a new numerical scheme for a singular partial differential Equation that combines the Mellin transform and the Lagrange approximation of a continuous function. The Mellin transform was used to remove the singularity in the newly developed exact Groundwater Flow Equation for a confined aquifer. The Equation became ordinary, wherein we used the Adam Bashforth method to the ordinary differential Equation in the Mellin space. The inverse of Mellin was then used to get the exact numerical scheme in real space. We present the stability analysis of the new numerical scheme using the von Neumann method. Lastly, numerical simulations using experimental field data are presented. Our solution is compared to that of Theis. Our simulations show the importance of the scaling factor which was removed from the Theis Groundwater Flow Equation. The simulations also show that the change in drawdown dependdepends on the scaling factor.
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New Groundwater Flow Equation with its exact solution
Scientia Iranica, 2016Co-Authors: Abdon Atangana, Canan UnluAbstract:A new model of Groundwater Flowing within a confined aquifer was proposed using the concept of local derivative with fractional order. The derivative used in this model obeys all the properties of a local derivative and has a fractional order. The new Groundwater Flow Equation was solved analytically via three different analytical methods. The first method is the well-known method of separation of variable. The problem with this method is the introduction of the Eigen-value that does not have physical meaning. The second method was achieved using novel integral Equation called Atangana-transform and this method yields exact solution. An alternative method based on the modified Boltzmann transformation also yields to exact solution. Some numerical simulations were done to express the efficiency of the model
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On the modified Groundwater Flow Equation: analytical solution via iteration method
Hydrological Processes, 2015Co-Authors: Abdon Atangana, Ernestine AlabaraoyeAbstract:To take into account the variability of the medium through which the Groundwater Flow takes place, we presented the Groundwater Flow Equation within a confined aquifer with prolate coordinates. The new Equation is a perturbed singular Equation. The perturbed parameters is introduced and can be used as accurately replicate the variability of the aquifer from one point to another. When the perturbed parameter tends to zero, we recover the Theis Equation. We solved analytically and iteratively the new Equation. We compared the obtained solution with experimental observed data together with existing solutions. The comparison shows that the modified Equation predicts more accurately the physical problem than the existing model. Copyright © 2015 John Wiley & Sons, Ltd.
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A possible modification of Groundwater Flow Equation using coordinate transformations
Water Science & Technology: Water Supply, 2014Co-Authors: Abdon Atangana, Ernestine AlabaraoyeAbstract:We described a Groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water Flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified Equation collapsed to the ordinary Groundwater Flow Equation. We proposed an analytical solution to the standard version of Groundwater as a function of time, space and uncertainty factor α . Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified Equation by means of the Adomian decomposition and variational iteration methods.
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Exact solution of the time-fractional Groundwater Flow Equation within a leaky aquifer Equation
Journal of Vibration and Control, 2014Co-Authors: Abdon AtanganaAbstract:The concern of this work was first to extend the model describing the Groundwater Flowing within a leaky aquifer to the scope of the fractional order derivative. We first derive the solution of the...
Luk Peeters - One of the best experts on this subject based on the ideXlab platform.
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estimating seepage flux from ephemeral stream channels using surface water and Groundwater level data
Water Resources Research, 2014Co-Authors: Saskia Noorduijn, Margaret Shanafield, Mark A Trigg, Glenn A Harrington, Peter G Cook, Luk PeetersAbstract:Seepage flux from ephemeral streams can be an important component of the water balance in arid and semiarid regions. An emerging technique for quantifying this flux involves the measurement and simulation of a flood wave as it moves along an initially dry channel. This study investigates the usefulness of including surface water and Groundwater data to improve model calibration when using this technique. We trialed this approach using a controlled Flow event along a 1387 m reach of artificial stream channel. Observations were then simulated using a numerical model that combines the diffusion-wave approximation of the Saint-Venant Equations for streamFlow routing, with Philip's infiltration Equation and the Groundwater Flow Equation. Model estimates of seepage flux for the upstream segments of the study reach, where streambed hydraulic conductivities were approximately 101 m d−1, were on the order of 10−4 m3 d−1 m−2. In the downstream segments, streambed hydraulic conductivities were generally much lower but highly variable (∼10−3 to 10−7 m d−1). A Latin Hypercube Monte Carlo sensitivity analysis showed that the flood front timing, surface water stage, Groundwater heads, and the predicted streamFlow seepage were most influenced by specific yield. Furthermore, inclusion of Groundwater data resulted in a higher estimate of total seepage estimates than if the flood front timing were used alone.
Peter G Cook - One of the best experts on this subject based on the ideXlab platform.
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estimating seepage flux from ephemeral stream channels using surface water and Groundwater level data
Water Resources Research, 2014Co-Authors: Saskia Noorduijn, Margaret Shanafield, Mark A Trigg, Glenn A Harrington, Peter G Cook, Luk PeetersAbstract:Seepage flux from ephemeral streams can be an important component of the water balance in arid and semiarid regions. An emerging technique for quantifying this flux involves the measurement and simulation of a flood wave as it moves along an initially dry channel. This study investigates the usefulness of including surface water and Groundwater data to improve model calibration when using this technique. We trialed this approach using a controlled Flow event along a 1387 m reach of artificial stream channel. Observations were then simulated using a numerical model that combines the diffusion-wave approximation of the Saint-Venant Equations for streamFlow routing, with Philip's infiltration Equation and the Groundwater Flow Equation. Model estimates of seepage flux for the upstream segments of the study reach, where streambed hydraulic conductivities were approximately 101 m d−1, were on the order of 10−4 m3 d−1 m−2. In the downstream segments, streambed hydraulic conductivities were generally much lower but highly variable (∼10−3 to 10−7 m d−1). A Latin Hypercube Monte Carlo sensitivity analysis showed that the flood front timing, surface water stage, Groundwater heads, and the predicted streamFlow seepage were most influenced by specific yield. Furthermore, inclusion of Groundwater data resulted in a higher estimate of total seepage estimates than if the flood front timing were used alone.
Mark A Trigg - One of the best experts on this subject based on the ideXlab platform.
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estimating seepage flux from ephemeral stream channels using surface water and Groundwater level data
Water Resources Research, 2014Co-Authors: Saskia Noorduijn, Margaret Shanafield, Mark A Trigg, Glenn A Harrington, Peter G Cook, Luk PeetersAbstract:Seepage flux from ephemeral streams can be an important component of the water balance in arid and semiarid regions. An emerging technique for quantifying this flux involves the measurement and simulation of a flood wave as it moves along an initially dry channel. This study investigates the usefulness of including surface water and Groundwater data to improve model calibration when using this technique. We trialed this approach using a controlled Flow event along a 1387 m reach of artificial stream channel. Observations were then simulated using a numerical model that combines the diffusion-wave approximation of the Saint-Venant Equations for streamFlow routing, with Philip's infiltration Equation and the Groundwater Flow Equation. Model estimates of seepage flux for the upstream segments of the study reach, where streambed hydraulic conductivities were approximately 101 m d−1, were on the order of 10−4 m3 d−1 m−2. In the downstream segments, streambed hydraulic conductivities were generally much lower but highly variable (∼10−3 to 10−7 m d−1). A Latin Hypercube Monte Carlo sensitivity analysis showed that the flood front timing, surface water stage, Groundwater heads, and the predicted streamFlow seepage were most influenced by specific yield. Furthermore, inclusion of Groundwater data resulted in a higher estimate of total seepage estimates than if the flood front timing were used alone.
