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Abstract

The basic advantages of the multi-cell groundwater models are the parsimony, speed, and simplicity that make them ideal for hydrological applications, particularly when data are insufficient and/or repeated simulations are needed. However, the multi-cell models, in their basic version, are conceptual models and their parameters do not have physical meaning. This disadvantage may be overcome by the Narasimhan and Witherspoon’s integrated finite difference method, which, however, demands that the cells’ geometry conforms to the equipotential and no-flow lines. This restriction cannot be strictly satisfied in every application. Particularly in transient conditions, a mesh with static geometry cannot conform constantly to the varying flow kinematics. In this study, we analyse the error when this restriction is not strictly satisfied and we identify the contribution of this error to the overall error of a multi-cell model. The study is experimental based on a synthetic aquifer with characteristics carefully selected so as to be representative of real-world situations, but obviously the results of these investigations cannot be generalized to every type of aquifer. Nonetheless these results indicate that the error due to non-conformity to the aforementioned restriction plays a minor role in the overall model error and that the overall error of the multi-cell models with conditionally designed cells is comparable to the error of finite difference models with much denser discretization. Therefore the multi-cell models should be considered as an alternative option, especially in the cases where a discretization with a flexible mesh is indicated or in the cases where repeated model runs are required.

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... On the other hand, the calculation of the water balance of the discretization cells is intrinsic to the numerical methods. Depending on the discretization type, the numerical methods can be classified into finite element [28], finite difference [29], and finite volume [30]. In this Water levels vary with precipitation and water gate operation at the weir. ...
... On the other hand, the calculation of the water balance of the discretization cells is intrinsic to the numerical methods. Depending on the discretization type, the numerical methods can be classified into finite element [28], finite difference [29], and finite volume [30]. In this ...
... On the other hand, the calculation of the water balance of the discretization cells is intrinsic to the numerical methods. Depending on the discretization type, the numerical methods can be classified into finite element [28], finite difference [29], and finite volume [30]. In this study, we have used MODFLOW, a finite difference model [31], because we want to study the water balance of the aquifer and because of the simplicity of this method. ...
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The Juksan weir, installed in the Yeongsan river in South Korea from 2010 to 2012, has secured sustainable water resources and helped control flooding. However, low river flow velocities due to the weir have deteriorated the quality of the river water. For natural river restoration, the water gate was opened in 2017. In this study, the three-dimensional finite difference model Visual MODFLOW was used to analyze the effects of gate opening on stream–aquifer interactions. A conceptual model was developed to simulate the stream–aquifer dynamics caused by the operation of the water gate at the Juksan weir. Groundwater data were also analyzed to determine the impacts of weir operations on groundwater quality. Our results indicate that a lower river level due to the weir opening changed the groundwater flow, which then affected the water balance. The change in groundwater flow increased the variability of the groundwater quality which had homogenized because of induced recharge after the construction of the weir. This could affect groundwater use in agricultural areas near the weir. Therefore, further groundwater monitoring and hydrodynamic analyses are required to anticipate and address any potential issues.
... It should be noted that, in this study, the primary source of the mathematical formulation for groundwater flow arises from the multiple cell lumped-parameter models, also called a grey-box or compartmental model, that has been used by numerous researchers (e.g., Flores et al., 1978;Bear, 1979;Olin, 1995, Campana et al., 2001Kazumba et al., 2008;Roach and Tidwell, 2009;Rozos and Koutsoyiannis, 2010;Joodavi et al., 2016). In these models, the aquifer is divided into a number of cells that model the behavior of the groundwater system, and the mathematical formulation is derived by applying conservation of mass throughout the system of cells (Bear, 1979). ...
... Although the multi-cell models such as SMC developed in this study suffer from some disadvantages, they are attractive alternatives to numerical models that implement finite-element or finite-volume approaches, because they are fast and simple (Roach and Tidwell, 2009;Rozos and Koutsoyiannis, 2010). ...
Article
The optimization of spatially complex groundwater management models over long time horizons requires the use of computationally efficient groundwater flow models. This paper presents a new stochastic multi-cell lumped-parameter aquifer model that explicitly considers uncertainty in groundwater recharge. To achieve this, the multi-cell model is combined with the constrained-state formulation method. In this method, the lower and upper bounds of groundwater heads are incorporated into the mass balance equation using indicator functions. This provides expressions for the means, variances and covariances of the groundwater heads, which can be included in the constraint set in an optimization model. This method was used to formulate two separate stochastic models: (i) groundwater flow in a two-cell aquifer model with normal and non-normal distributions of groundwater recharge; and (ii) groundwater management in a multiple cell aquifer in which the differences between groundwater abstractions and water demands are minimized. The comparison between the results obtained from the proposed modeling technique with those from Monte Carlo simulation demonstrates the capability of the proposed models to approximate the means, variances and covariances. Significantly, considering covariances between the heads of adjacent cells allows a more accurate estimate of the variances of the groundwater heads. Moreover, this modeling technique requires no discretization of state variables, thus offering an efficient alternative to computationally demanding methods.
... The reliability of the ratio of the fluxes as an indicator of the compliance of a mesh was evaluated on the hypothetical non-homogeneous aquifer of Rozos and Koutsoyiannis (2010) study. The size of this aquifer was 50×50 km 2 , a constant uniform recharge was applied on it, a series of injecting wells with constant rate were deployed on the right half of its lower edge and a series of drains were deployed on the middle half of the upper edge. ...
... The original and the deformed meshes (shown left and right respectively in the figure below) were solved with the FVMSI model described in Rozos and Koutsoyiannis (2010) and the results of the solutions were compared against reference values obtained from the solution of the aquifer with MODFLOW. The RMSE of the solutions of these two meshes were found to be 5.32 and 6.46 m respectively. ...
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Poster
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... For example Frind and Germain (1986), Kinzelbach and Frind (1986), and Syriopoulou and Koussis (1991) have used principal directions (the crosssectional flow net) to efficiently simulate tracer transport. Natural coordinates, such as streamlines and their orthogonals, are similarly advantageous in the solutions of groundwater flow problems (Rozos and Koutsoyiannis, 2010). ...
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We present a high-efficiency method for simulating seawater intrusion (SWI), with mixing, in confined coastal aquifers based on uncoupled equations in the through-flow region of the aquifer. The flow field is calculated analytically and the tracer transport numerically, via spatial splitting along the principal directions (PD) of transport. Advection-dispersion processes along streamlines are simulated with the very efficient matched artificial dispersivity (MAD) method of Syriopoulou and Koussis and the system of discretized transverse-dispersion equations is solved with the Thomas algorithm. These concepts are embedded in the 2D-MADPD-SWI model, yielding comparable solutions to those of the uncoupled SWI equations with the state-of-the-art FEFLOW code, but faster, while 2D-MADPD-SWI achieves an at least hundredfold faster solution than a variable-density flow model. We demonstrate the utility of the 2D-MADPD-SWI model in stochastic Monte Carlo simulations by assessing the uncertainty on the advance of the 1,500 ppm TDS line (limit of tolerable salinity for irrigation) due to randomly variable hydraulic conductivity and freshwater flow rate.
... Our tests proved that running models in stochastic simulation mode can be a useful tool for their testing and validation since this augments information supplied by typical 8287 a "crash-test" for evaluating the model transposability in time, which is a necessary condition for their operational adequacy (Andréassian et al., 2009). Finally, through a proper representation of the varying character of climate and the related processes in stochastic terms, it ensures reliable estimation of the uncertainty and the long-term risk in hydrological studies and water resources management (Koutsoyiannis et al., 2007;Koutsoyiannis, 2010). This can also include the evaluation of extremes, which are not represented in the (usually limited) calibration data (Seibert, 2003). ...
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Preprint
This is the Discussion (Review) version of: Holistic versus monomeric strategies for hydrological modelling of human-modified hydrosystems Hydrology and Earth System Sciences 15(3):743-758 DOI: 10.5194/hess-15-743-2011
... Some studies suggest that the magnitude of this uncertainty does not justify such a level of detailed representation and simulation employed by groundwater models that numerically solve differential equations. Rozos and Koutsoyiannis (2010) suggested that multi-cell models should be considered as an alternative option in cases of increased uncertainty. This study extends that work by including solute transport in a multi-cell model that allows discretization of the flow domain using a low number of cells of flexible geometry. ...
... Alternatively, the multi-cell models, also called grey box or compartmental model, have been used by numerous researchers (e.g., Kazumba et al. 2008;Roach and Tidwell 2009;Rozos and Koutsoyiannis 2010) for modeling the behavior of groundwater systems. In these models, a large aquifer is divided into a number of cells and the mathematical formulation is derived by applying conservation of mass throughout the entire cells (Bear 1979). ...
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Estimation of groundwater recharge is essential for sustainable groundwater management planning in arid and semiarid areas. Accurate recharge estimation in a distributed scale is a great challenge, especially when multiple recharge sources exist and available data are limited and uncertain. There are various sophisticated direct and indirect methods such as water balance method to estimate this parameter. Conventional spatially and temporally lumped models cannot take into account spatial variation of hydraulic properties of an aquifer, land use, and hydrometeorological conditions in the water balance estimation. In this study, a semi-distributed hydrologic model is developed and applied in a complex alluvial-karst system in Firouzabad catchment (Iran) to estimate groundwater recharge from precipitation, subsurface inflow from adjacent karst aquifer, return flows, and riverbed infiltration. The proposed multi-compartment model considers groundwater balance in alluvial and karstic aquifers and surface soil layer. Furthermore, it contains a multi-cell aquifer model which is used to understand the macro mechanism of the alluvial aquifer. A parameter calibration procedure is implemented wherein groundwater head data are used in parameter estimation. The performance of the proposed model is assessed by evaluating the coefficient of determination (R 2) and the coefficient of efficiency. The results of the groundwater balance model are analyzed to quantify the seasonal long-term (16 years, from 1992 to 2008) groundwater recharge components. The proposed model is straightforward, efficient, and easy to apply, and its results are reasonable and acceptable.
... In a quasi-steady solution, a series of steady states substitutes the transient process, considering the physical system to evolve in abrupt steps from one steady state to the next one. This is a well-established concept in subsurface hydrology, dating back to Lembke (1887) and still in use (e.g., Verhoest and Troch (2000), Akylas et al. (2006) and Rozos and Koutsoyiannis, (2010)). Besides subsurface hydrology, Adams and Koussis (1980) have also analysed the response of cooling ponds to transient atmospheric forcing with the quasi-steady approach. ...
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... Some studies suggest that the magnitude of this uncertainty does not justify such a level of detailed representation and simulation employed by groundwater models that numerically solve differential equations. Rozos and Koutsoyiannis (2010) suggested that multi-cell models should be considered as an alternative option in cases of increased uncertainty. This study extends that work by including solute transport in a multi-cell model that allows discretization of the flow domain using a low number of cells of flexible geometry. ...
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Groundwater modelling is plagued by the increased uncertainty concerning the properties (hydraulic conductivity, porosity, geometry) and the conditions (boundary conditions, initial conditions, stresses) of aquifers. Some studies suggest that the magnitude of this uncertainty does not justify the detailed level of representation and simulation employed by groundwater models that numerically solve differential equations. Rozos and Koutsoyiannis (2010) suggested that multi-cell models should be considered as an alternative option in cases of increased uncertainty. This study extends that work by including solute transport in a multi-cell model that allows discretization of the flow domain using a low number of cells of flexible geometry. This method was tested in a case study that has analytical solution.
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Heat Transfer Calculations by Finite Differences, International Textbooks Effective and efficient global optimization for conceptual rainfall-runoff models
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