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162 Husam Baalousha Figure 7. Discritization of the model domain into a finite element mesh. The finite element method has some disadvantages. The finite element mesh is not easy to build and consumes time, especially in complicated problems. Also, there is less documentation on the finite element method compared to finite difference method. Unlike the finite difference method, mass balance in the finite element method can be achieved for the entire domain but not for every element. The most well known finite element based groundwater models are Feflow (Wasy, 2005), Femwater (Lin, et. al. 1997), and MODFE (Torak 1993). Box 4: Finite element or finite difference Finite element Finite difference Model boundary Incorporates irregular and curved boundaries Difficult to incorporate irregular boundaries Nodes At vertices and flux boundary Nodes located at centre of cell Mesh/grid building Difficult to generate an efficient mesh Easy to build a finite difference grid Anisotropy Easily incorporated Difficult to incorporate Accuracy Acceptable accuracy More accurate especially in solute transport modelling Computation time Good and acceptable time requirement Computation time can be long in 3D problems.
6.0. Model Calibration Fundamentals of Groundwater Modelling 163 After the first run of a model, model results may differ from field measurements. This is expected because modelling is just a simplification of reality and approximations and computational errors are inevitable. The process of model calibration is aimed at fine-tuning the model results to match the measurements in the field. In a groundwater flow models, the resulting groundwater head is forced to match the head at measured points. This process requires changing model parameters (i.e. hydraulic conductivity or groundwater recharge) to achieve the best match. The calibration process is important to make the model predictive and it can also be used for inverse modelling. To illustrate the calibration process of a groundwater flow model, consider the groundwater head measurements (h ob ) i at the observation point i. The simulated head at the same point is (h sim ) i . The root mean square error of the residual is given by: n 1/ 2 ⎡1 2 ⎤ RMSE − Equation (11) = ⎢ ∑( h ob h sim ) ⎥ ⎣n i= 1 ⎦ Calibration involves an optimization process to minimize the RMSE given in Equation (11). To get a well-calibrated model, proper site characterisation and ample data are required. Otherwise, the calibrated model will only be valid for a set of conditions and not for any condition. Calibration can be manually done or automatically. Software like PEST (Doherty et. al. 1994) and UCODE (Poeter and Hill 1994) can be used for automatic calibration. Box 4: The calibrated model should satisfy: • A good match between measured and modelled head. • A good water mass balance. • The groundwater gradient from the model is similar to the observed gradient in the field. • Similar behaviour for any dataset. 7.0. Model Verification and Validation The term “validation” is not completely true when used in groundwater modelling. Oreskes et. al. (1994) asserted it is impossible to validate a numerical model because modelling is only approximation of reality. Model verification and validation is the next step after calibration. The objective of model validation is to check if the calibrated model works well on any dataset. Because the calibration process involves changing different parameters (i. e. hydraulic conductivity, recharge, pumping rate etc.) different sets of values for these parameters may produce the same solution. Reilly and Harbaugh (2004) concluded that good calibration did not lead to good prediction. The validation process determines if the resulting model is applicable for any
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GROUNDWATER: MODELLING, MANAGEMENT
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Copyright © 2009 by Nova Science P
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vi Chapter 8 Chapter 9 Chapter 10 C
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viii Luka F. König and Jonas L. We
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x Luka F. König and Jonas L. Weiss
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xii Luka F. König and Jonas L. Wei
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xiv Luka F. König and Jonas L. Wei
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SHORT COMMUNICATION
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4 Goloka Behari Sahoo and Chittaran
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Table 2. Number of Samples in Train
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12 Goloka Behari Sahoo and Chittara
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14 Goloka Behari Sahoo and Chittara
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In: Groundwater: Modelling, Managem
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GIS-Based Aquifer Modeling and Plan
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80 Sabrina Saponaro, Sara Puricelli
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100 Sabrina Saponaro, Sara Puricell
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Groundwater Management in the North
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232 Franco Cucchi, Giuliana Frances
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Table 1. Chemical and isotopical co
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Table 1. Continued Borehole ID Type
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Table 2. Univariate overview of the
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In: Groundwater: Modelling, Managem
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Analytical and Numerical Solutions.
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292 K.L. Katsifarakis 1. Introducti
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294 K.L. Katsifarakis fields with v
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296 K.L. Katsifarakis solution to t
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298 K.L. Katsifarakis The aforement
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300 K.L. Katsifarakis If applicatio
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302 K.L. Katsifarakis s w (50m) 96,
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304 K.L. Katsifarakis well coordina
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306 K.L. Katsifarakis injected in a
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308 K.L. Katsifarakis McKinney, D.C
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310 Nigel J. Cassidy 1.0. Introduct
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312 Nigel J. Cassidy separation). U
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314 Nigel J. Cassidy needed to char
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316 Nigel J. Cassidy resolution min
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318 Nigel J. Cassidy al., 2005; Eve
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320 Nigel J. Cassidy heat. As such,
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322 Nigel J. Cassidy substantially
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324 Nigel J. Cassidy 4.2. Conductiv
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326 Nigel J. Cassidy Figure 6. Prin
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328 Nigel J. Cassidy window is then
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330 Nigel J. Cassidy θ - volumetri
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332 Nigel J. Cassidy (2000). In gen
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334 Nigel J. Cassidy The influence
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336 Nigel J. Cassidy Figure 11. Sum
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338 Nigel J. Cassidy 2. An upper ae
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340 Nigel J. Cassidy upper sand lay
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342 Nigel J. Cassidy Bradford J. H.
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344 Nigel J. Cassidy Doolittle, J.
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346 Nigel J. Cassidy Jardani, A., D
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348 Nigel J. Cassidy Revil, A., Nau
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350 Nigel J. Cassidy Weiller, K. W.
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352 Nick Cartwright, Peter Nielsen,
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362 A. Akber, A. Mukhopadhyay, E. A
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392 Index Bangladesh, 188 banks, 11
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394 Index definition, 18, 20, 26, 1
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396 Index goals, 306 government, 19
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398 Index Miami, 349 migration, x,
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400 Index probability, 166, 295 pro
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402 Index specific heat, 90, 108 sp
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404 Index wetting, 86, 349 wind, 21
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