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Comparison of local grid refinement methods for MODFLOW
Abstract
Many ground water modeling efforts use a finite-difference method to solve the ground water flow equation, and many of these models require a relatively fine-grid discretization to accurately represent the selected process in limited areas of interest. Use of a fine grid over the entire domain can be computationally prohibitive; using a variably spaced grid can lead to cells with a large aspect ratio and refinement in areas where detail is not needed. One solution is to use local-grid refinement (LGR) whereby the grid is only refined in the area of interest. This work reviews some LGR methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. The first test case is two dimensional and heterogeneous; the second is three dimensional and includes interaction with a meandering river. Results include simulations using a uniform fine grid, a variably spaced grid, a traditional method of LGR without feedback, and a new shared node method with feedback. Discrepancies from the solution obtained with the uniform fine grid are investigated. For the models tested, the traditional one-way coupled approaches produced discrepancies in head up to 6.8% and discrepancies in cell-to-cell fluxes up to 7.1%, while the new method has head and cell-to-cell flux discrepancies of 0.089% and 0.14%, respectively. Additional results highlight the accuracy, flexibility, and CPU time trade-off of these methods and demonstrate how the new method can be successfully implemented to model surface water-ground water interactions.
... Using a large scale regional model to simulate the local scale groundwater problems can be inaccurate and not cost-beneficial [5] and it is common that the natural hydraulic boundary is located far from to the target local study area so that the extent of the model area becomes much larger than the area of interest [6]. In these situations, using unified global refined grids would be computationally expensive [7]. This issue can be solved using the emerging regional and local model coupling technique, which allows various grid size in one model domain. ...
... The unstructured grid could provide higher resolution keeping cell numbers relatively low by only refining around the wells. Some synthesis cases were analyzed to evaluate the accuracy and CPU time [7,30]. ...
... The LGR model can be run separately or jointly with the regional model. The simultaneous solution scheme provides feedback between the regional and local models [7], keeping consistent groundwater heads on the adjoining interface of the two models. ...
A coupled regional and local model is required when groundwater flow and solute transport are to be simulated in local areas of interest with a finer grid while regional aquifer boundary and major stresses should be retained with a coarser grid. The coupled model should also maintain interactions between the regional and local flow systems. In the Beijing Plain (China), assessment of managed aquifer recharge (MAR), groundwater pollution caused by rivers, capture zone of well fields, and land subsidence at the cone of depression requires a coupled regional and local model. This study evaluates three methods for coupling regional and local flow models for simulating MAR in the Chaobai River catchment in the Beijing Plain. These methods are the conventional grid refinement (CGR) method, the local grid refinement (LGR) method and the unstructured grid (USG) method. The assessment included the comparison of the complexity of the coupled model construction, the goodness of fit of the computed and observed groundwater heads, the consistency of regional and local groundwater budgets, and the capture zone of a well filed influenced by the MAR site. The results indicated that the CGR method based on MODFLOW-2005 is the easiest to implement the coupled model, capable of reproducing regional and local groundwater heads and budget, and already coupled with density and viscosity dependent model codes for transport simulation. However, the CGR method inherits shortcomings of finite difference grids to create multiple local models with inefficient computing efforts. The USG method based on MODFLOW-USG has the advantage of creating multi-scale models and is flexible to simulate rivers, wells, irregular boundaries, heterogeneities and the MAR site. However, it is more difficult to construct the coupled models with the unstructured grids, therefore, a good graphic user interface is necessary for efficient model construction. The LGR method based on MODFLOW-LGR can be used to create multiple local models in uniform aquifer systems. So far, little effort has been devoted to upgrade the LGR method for complex aquifer structures and develop the coupled transport models.
... MODFLOW-LGR solves these systems of equations iteratively: this ensures that the diagonal stencil of the MODFLOW coefficient matrix is preserved, so that the standard solvers of MODFLOW can be used to solve the resulting equation (Mehl and Hill 2005), and the errors observed for the TMR methods are reduced (Mehl and Hill 2002). However, the trade-off of using the iterative method is that it can be time consuming (Mehl et al. 2006) and that it requires relaxation to achieve convergence (Szekely 1998;Mehl and Hill 2002). MODFLOW-LGR offers two methods 5 to couple a parent model with a child model. ...
... Despite optimizing the LGR run times, these still exceed those of the GR model. This is contradictory toMehl et al. (2006)who found their LGR model to run faster than their GR model. This leaves an important question: When is it advantageous to use the MODFLOWLGR technique to increase local numerical discretization within regional-scale models instead of using a fine discretization for the entire model area? ...
... Considering this, attention was turned toward the size of the area of refinement. For the present test case, the area of the child model covers approximately a quarter of the parent-model area, whereas it only covers approximately one-tenth in the 3D case presented byMehl et al. (2006). For our test model, we tried to double the size of the GR, the GC, and the parent models, whereas the child-model area was left unchanged. ...
In this study the Local Grid Refinement (LGR) method developed for MODFLOW-2005 (Mehl and Hill, 2005) is utilized to describe groundwater flow in areas containing buried Quaternary valley structures. The tests are conducted as comparative analysis between simulations run with a globally refined model, a locally refined model, and a globally coarse model, respectively. The models vary from simple one layer models to more complex ones with up to 25 model layers. The comparisons of accuracy are conducted within the locally refined area and focus on water budgets, simulated heads, and simulated particle traces. Simulations made with the globally refined model are used as reference (regarded as ``true'' values). As expected, for all test cases the application of local grid refinement resulted in more accurate results than when using the globally coarse model. A significant advantage of utilizing MODFLOW-LGR was that it allows increased numbers of model layers to better resolve complex geology within local areas. This resulted in more accurate simulations than when using either a globally coarse model grid or a locally refined model with lower geological resolution. Improved accuracy in the latter case could not be expected beforehand because difference in geological resolution between the coarse parent model and the refined child model contradicts the assumptions of the Darcy weighted interpolation used in MODFLOW-LGR. With respect to model runtimes, it was sometimes found that the runtime for the locally refined model is much longer than for the globally refined model. This was the case even when the closure criteria were relaxed compared to the globally refined model. These results are contradictory to those presented by Mehl and Hill (2005). Furthermore, in the complex cases it took some testing (model runs) to identify the closure criteria and the damping factor that secured convergence, accurate solutions, and reasonable runtimes. For our cases this is judged to be a serious disadvantage of applying MODFLOW-LGR. Another disadvantage in the studied cases was that the MODFLOW-LGR results proved to be somewhat dependent on the correction method used at the parent-child model interface. This indicates that when applying MODFLOW-LGR there is a need for thorough and case-specific considerations regarding choice of correction method. References: Mehl, S. and M. C. Hill (2005). "MODFLOW-2005, THE U.S. GEOLOGICAL SURVEY MODULAR GROUND-WATER MODEL - DOCUMENTATION OF SHARED NODE LOCAL GRID REFINEMENT (LGR) AND THE BOUNDARY FLOW AND HEAD (BFH) PACKAGE " U.S. Geological Survey Techniques and Methods 6-A12
... MODFLOW-LGR solves these systems of equations iteratively: this ensures that the diagonal stencil of the MODFLOW coefficient matrix is preserved, so that the standard solvers of MODFLOW can be used to solve the resulting equation (Mehl and Hill 2005), and the errors observed for the TMR methods are reduced (Mehl and Hill 2002). However, the trade-off of using the iterative method is that it can be time consuming (Mehl et al. 2006) and that it requires relaxation to achieve convergence (Szekely 1998;Mehl and Hill 2002). ...
... Despite optimizing the LGR run times, these still exceed those of the GR model. This is contradictory to Mehl et al. (2006) who found their LGR model to run faster than their GR model. This leaves an important question: When is it advantageous to use the MODFLOW-LGR technique to increase local numerical discretization within regional-scale models instead of using a fine discretization for the entire model area? ...
... Considering this, attention was turned toward the size of the area of refinement. For the present test case, the area of the child model covers approximately a quarter of the parent-model area, whereas it only covers approximately one-tenth in the 3D case presented by Mehl et al. (2006). For our test model, we tried to double the size of the GR, the GC, and the parent models, whereas the child-model area was left unchanged. ...
This work studies costs and benefits of utilizing local-grid refinement (LGR) as implemented in MODFLOW-LGR to simulate groundwater flow in a buried tunnel valley interacting with a regional aquifer. Two alternative LGR methods were used: the shared-node (SN) method and the ghost-node (GN) method. To conserve flows the SN method requires correction of sources and sinks in cells at the refined/coarse-grid interface. We found that the optimal correction method is case dependent and difficult to identify in practice. However, the results showed little difference and suggest that identifying the optimal method was of minor importance in our case. The GN method does not require corrections at the models' interface, and it uses a simpler head interpolation scheme than the SN method. The simpler scheme is faster but less accurate so that more iterations may be necessary. However, the GN method solved our flow problem more efficiently than the SN method. The MODFLOW-LGR results were compared with the results obtained using a globally coarse (GC) grid. The LGR simulations required one to two orders of magnitude longer run times than the GC model. However, the improvements of the numerical resolution around the buried valley substantially increased the accuracy of simulated heads and flows compared with the GC simulation. Accuracy further increased locally around the valley flanks when improving the geological resolution using the refined grid. Finally, comparing MODFLOW-LGR simulation with a globally refined (GR) grid showed that the refinement proportion of the model should not exceed 10% to 15% in order to secure method efficiency.
... Finely discretized grids are needed to simulate such local areas of special complexity and rapid changes. However, using a fine grid over the entire model domain is computationally inefficient, and using variable spacing (finer in the area of interest) in a single MODFLOW-type finite-difference model is often inefficient and may generate errors (Mehl et al., 2006). Neither approach is suited to longwall subsidence configurations. ...
... Hunt and Steuer (2000) used TMR with Groundwater Vistas to connect a regional model (400-m spacing) to a site-scale model (100-m spacing), using the RM to assign constant-head boundary conditions for the refined model. Mehl et al. (2006) distinguish between traditional TMR without interactive feedback, and recent methods that involve numerical coupling of the local and coarse grids, either directly or iteratively. In this preliminary study, we are applying traditional approaches in which LM boundaries are defined non-interactively from the RM. ...
We are applying MODFLOW using Telescopic Mesh Refinement (TMR) to simulate hydrologic responses in the shallow aquifer system overlying longwall mining. The shallow system is separated from the deeper, heavily fractured zone by a confining zone and does not drain to the mine. Nevertheless, it presents special modeling problems due to rapid spatial and temporal changes in heads and hydraulic properties. TMR, in which a finer local model is embedded in a regional model, is a possible approach. For model development, we use a previous Illinois case study for which abundant data are available. In this preliminary study, we examine approaches to model boundaries, subsidence-induced changes in permeability and progression of the subsidence zone (in discrete stages), and head drops due to new fracture porosity (as sinks).
... An additional "local grid refinement" (LGR) option for MODFLOW 6 models allows for specification of an inset model that is dynamically linked (in both directions) to the parent model at a finer grid resolution. Unlike previous versions of LGR (e.g., Mehl et al., 2006;Vilhelmsen et al., 2012), this inset model formulation is coupled to the parent model at the matrix level (Langevin et al., 2017), making this an efficient option for simulating both regional flow and a detailed area of interest. To facilitate array resampling and dereferencing, currently; only uniform structured grids (that may be rotated) are supported. ...
In an age of both big data and increasing strain on water resources, sound management decisions often rely on numerical models. Numerical models provide a physics-based framework for assimilating and making sense of information that by itself only provides a limited description of the hydrologic system. Often, numerical models are the best option for quantifying even intuitively obvious connections between human activities and water resource impacts. However, despite many recent advances in model data assimilation and uncertainty quantification, the process of constructing numerical models remains laborious, expensive, and opaque, often precluding their use in decision making. Modflow-setup aims to provide rapid and consistent construction of MODFLOW groundwater models through robust and repeatable automation. Common model construction tasks are distilled in an open-source, online code base that is tested and extensible through collaborative version control. Input to Modflow-setup consists of a single configuration file that summarizes the workflow for building a model, including source data, construction options, and output packages. Source data providing model structure and parameter information including shapefiles, rasters, NetCDF files, tables, and other (geolocated) sources to MODFLOW models are read in and mapped to the model discretization, using Flopy and other general open-source scientific Python libraries. In a few minutes, an external array-based MODFLOW model amenable to parameter estimation and uncertainty quantification is produced. This paper describes the core functionality of Modflow-setup, including a worked example of a MODFLOW 6 model for evaluating pumping impacts to a lake in central Wisconsin, United States.
... Three major methods of local grid refinement are developed for finite difference models, which are the gradational mesh refinement (GMR), telescopic mesh refinement (TMR) and local grid refinement (LGR). The GMR is criticized for its numerical instabilities due to the large aspect ratio of cells [44]. TMR is a one-way coupling method, and requires modelers developing methods to assess and redress consistency of results along boundary interfaces, which could result in undetected errors [45]. ...
The suitable groundwater exploitation scheme in freezing-thawing agricultural areas under the well-canal conjunctive irrigation conditions is confronted with two major challenges, which are computationally expensive local grid refinements along wells, and the model suitability problem in the freezing-thawing period. In this study, an empirical method for groundwater level prediction in the freezing-thawing period was developed and integrated with the local grid refinement groundwater model MODFLOW-LGR for the groundwater process prediction. The model was then applied to estimate the suitable groundwater exploitation scheme, including the size of well-irrigated area and the irrigation area of single well. The results showed that suitable size of well-irrigated area should be smaller than 15 × 106 m2, and the recommended irrigation area of single well as 15 × 104 m2 to 19 × 104 m2. The recommended layout parameters of groundwater exploitation were further used to plan the well-canal conjunctive irrigation scheme in Yongji irrigation district located in northern China. This study provides an important pilot example of the conjunctive use of groundwater and surface water in arid irrigation areas with a seasonal freezing-thawing period.
... However, there are some models that require a fine-grid discretisation to obtain a better resolution and to get the correct answer to the problem. Unfortunately, this process is typically in line with a high computational cost [21]. This paper uses the Biebrza River to develop the research about the river and aquifer interaction. ...
The objective of the present paper is to develop a methodology that could allow the representation of the analytical hyporheic flux equation model (AHF) in a numerical model done in MODFLOW. Therefore, the scope of the research is to show the viability of the methodology suggested in a real case (Biebrza river, Poland, Europe). Considering that the model requires extensive manipulation in the creation of the packages, a test phase through the seepage package of MODFLOW is carried out with the aim of representing the river package of MODFLOW. FloPy is the tool chosen to develop this implementation due to the versatility of manipulating the packages available in MODFLOW through coding. The obtained results showed a correct implementation of the AHF model using the example of the Biebrza River. The results obtained will enable a better understanding regarding the modelling of the interaction between the river and the aquifer, considering streams with specific geometries where the depth is dimensionally higher than the width.
... Traditionally, LGR (Local Grid Refinement) methods are used to subdivide grid cells in corner-point grids, see e.g. Mehl et al. (2006). Corner-point grids are discussed in Section 3. ...
PhD thesis in Computational Geoscience at the Department of Energy Resources, Faculty of Science and Technology, University of Stavanger, Norway.
Abstract:
Development of numerical methods for effective updates of an earth model, with a particular focus on real-time decision support while drilling (geosteering). The methods include a) local updates of the geological structure in an earth model grid, b) multi-resolution management of both the geological structure and the grid enabling local control of their resolutions, and c) local-scale uncertainty management of the interpretation of the geological structure in the grid.
The aim is to pave the way for an always updated multi-realization 3D model at optimal resolution while drilling in complex formations, suitable for real-time decision support under uncertainty. The methods are general and could be improved to enable effective generation of earth model grids at fit-for-purpose resolution for any subsurface application.
... 等的模拟。此外，为了提高模拟精度，还可以使用 MODFLOW-LGR 对地下水水 分运动模型的网格进行局部细化 [18] 。在非饱和地下水模拟方面，Šimunek 等人开 发的 HYDRUS 模型则得到了较为广泛的应用，它可以用来模拟一维到三维非饱 和地下水中水分、热量和溶质的运移转化 [19] ，并且可以与 MODFLOW 耦合来研 究包气带和饱和地下水带之间的交互 [20] 。为了方便上述模型的构建和结果展示， ...
... Early TMR methods initiated with the work of Ward et al. (1987) and Duffield et al. (1987) in the late 1980s. Mehl et al. (2006) compares LGR methods in regards to computing requirements and percent discrepancy in a groundwater flow model. The study concluded that iteratively coupled LGR performed with higher accuracy than traditional TMR methods and was considered more efficient than the computationally intensive, yet highly accurate, global refinement and variably spaced grid methods. ...
Recent studies have concluded that stream reaches are not simply gaining or losing to
groundwater but are best described as a mosaic of exchanges that contrast between flow paths of
varying lengths and directions which inherently influence solute residence times. These residence
times directly affect chemical speciation of solutes such as salts, nitrate, selenium, and uranium and
have the opportunity to undergo microbial dissimilatory reduction in the shallow riparian zone and
the deeper sub-surface. To improve water quality and the overall health of these natural systems
requires engineering intervention supported by reliable data and calibrated models. A threedimensional
numerical flow model (MODFLOW-UZF2) is used to simulate unsaturated and
saturated groundwater flow, with linkage to a streamflow routing model (SFR2), for a 5-km reach
of the Arkansas River near Rocky Ford, Colorado. The reach-scale model provides increased
discretization of previous regional-scale models developed for the Arkansas River Basin, using 50 x
50 m grid cells and dividing the Quaternary alluvium that represents the unconfined aquifer into 10
layers. This discretization facilitates an enhanced view of groundwater pathways near the river
which is essential for future solute transport evaluation and for consideration of alternative best
management practices. Model calibration is performed on hydraulic conductivity (K) in the upper
three layers, K in the lower seven layers, and specific yield (Sy) of the entire aquifer by applying an
Ensemble Kalman Filter (EnKF) using observed groundwater hydraulic head and stream stage data.
The EnKF method accounts for uncertainty derived from field measurements and spatial
heterogeneity in parameters calibrated using a Monte-Carlo based process to produce 200
realizations in comparison to error-prone measurements of hydraulic groundwater hydraulic head
and stream stage as calibration targets. The calibrated transient model produced Nash-Sutcliffe
Efficiency (NSE) values of 0.86 and 0.99, respectively, for the calibration and evaluation periods for
calibration targets using the ensemble mean of realizations. Realizations of calibrated parameters
produced by the EnKF exhibit the equally-likely spatial distributions of aquifer flow and storage
characteristics possible in the area, while MODPATH simulations display the associated
groundwater flow paths possible under such conditions. The mean residence time of a streamdestined
fluid particle within the riparian zone was estimated as 1.8 years. Simulated flow paths to
the stream were highly variable given different geologic conditions produced by EnKF, with flow
paths to some stream reaches being traced to different groundwater sources and transit times
differing sometimes by decades. The simulated average annual groundwater return flow to the
stream was 70 m3 d-1. Simulated average annual return flow was highly variable along the study
reach and ranged from -250 to a little over 250 m3 d-1 with a CV of 1.4. The mean percentage of
shallow (within the top three model layers) groundwater return flow to flow in aquifer layers
beneath the stream was 27% with a CV of 0.58. Simulated groundwater flow paths were
superimposed upon a map of shallow shale units residing in the study region, demonstrating how
groundwater flow paths may interact with or contact regional seleniferous shale layers. Results
hold major implications for biogeochemical processes occurring in the sub-surface of the riparian
area and the hyporheic zone that have an important influence on solute concentrations. Results
may be used to aid decision makers in the implementation of best management practices and to
further understand contaminant sources and fate.
... The importance of the resolution of spatial discretization has been recognized before, particularly in studies on reactive transport (Mehl and Hill, 2002). In this field, grid telescoping, i.e., the modeling of a reactive transport problem using two grids, namely a coarse grid representing the whole catchment and a fine one representing the surrounding area of the contaminated plume, is relatively common (Mehl and Hill, 2002;Mehl et al., 2006). However, grid telescoping requires a well defined inner domain of interest and an outer domain from which conditions can be extracted and used as boundary conditions for the inner domain. ...
... This discretization process raises the question of appropriate scale, and how the trade-off of computational burden and model resolution is decided. It is also possible to vary the resolution, and to use a combination of fine and coarse resolutions (Mehl et al. 2006). No grid or set of elements will fully capture a conceptual model, so the trade-off is subjective in that a modeller and end-user have discretion to select a variety of alternative scales based on practical considerations, such as computational cost. ...
Models of groundwater systems help to integrate knowledge about the natural and human system covering different spatial and temporal scales, often from multiple disciplines, in order to address a range of issues of concern to various stakeholders. A model is simply a tool to express what we think we know. Uncertainty, due to lack of knowledge or natural variability, means that there are always alternative models that may need to be considered. This chapter provides an overview of uncertainty in models and in the definition of a problem to model, highlights approaches to communicating and using predictions of uncertain outcomes and summarises commonly used methods to explore uncertainty in groundwater management predictions. It is intended to raise awareness of how alternative models and hence uncertainty can be explored in order to facilitate the integration of these techniques with groundwater management.
... The behavior of a groundwater flow system may be described by techniques which have been developed to solve partial differential equations. In MODFLOW and FEFLOW, this is simulated by finite difference method and finite element method (FEM) (Mehl, Hill, and Leake 2006;Diersch 2014). ...
The method of fundamental solutions is a meshless method. Only boundary collocation points are needed during the whole solution process. It has the merits of mathematical simplicity, ease of programming, high solution accuracy, and others. In this paper, the method of fundamental solutions is applied to simulate 2D steady-state groundwater flow problems. The principle of superposition is used during the whole solution process. Numerical results are compared with the multiquadrics method and the mixed finite element method as well as analytical solutions. It is shown that the method of fundamental solutions is promising in dealing with steady groundwater flow problems.
... Huang et al. (16) developed a domain decomposition-based assembly model implemented in a parallel computing environment, which allows efficient simulation of large-scale ground water flow and transport problems using domain-wide grid refinement. Mehl et al. (17) reviewed some Local Grid Refinement methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. Safavi and Bahreini (18) investigated the surface water-ground water interactions by examining geological parameters and integrated their study to Najafabad semiarid plain. ...
Ground water is a significant part of the hydrological system and it has a strategical importance in protecting and developing water resources being depleted nowadays. As a natural resource, ground water plays a crucial role in water quality and water supply. Modelling ground water is an important part of sustainable water management. Therefore, the physical mechanism of the ground water should be determined by developing detailed hydrological and contaminant transport models. Furthermore, in order to establish accurate ground water models, surface/ground water interactions should be taken into account. While many studies cover ground water as a single system and therefore investigate pure ground water hydraulics and hydrology, studies related to surface/ground water interactions and the behavior of ground water by conducting a sensitivity analysis under different scenarios are exiguous in the literature. Therefore, in this research, surface water and ground water are considered as a unique system and the simulations are done accordingly. In this study, a conceptual stream-aquifer model is developed by using Visual MODular Finite-Difference FLOW (MODFLOW) which is a three-dimensional finite-difference ground water flow and contaminant transport simulation model. The effect of surface/ground water interactions on the hydrological behavior is investigated. Ground water level fluctuations and the flux between stream and aquifer are obtained with the hydrological model of the conceptual stream–aquifer system by conducting analyses under different flow boundary conditions and flow paths.
... The sediment layer is used as the sink/source of suspended sediment, and its thickness can be changed. Local grid refinement (LGR) can also be applied to arbitrary grid block domains (e.g., Mehl et al., 2006). ...
Simulation of the watershed-scale fate and transport of radionuclides is required in order to predict the consequences of contamination redistribution. Integrated watershed modeling is a suitable technique for this task, but it requires fully coupled investigation of radionuclide behavior in surface water, suspended sediment and subsurface aquifers. We developed a novel simulator for computing the spatiotemporal redistribution of fallout radionuclides in watersheds. The simulator was applied to an actual reservoir basin contaminated by fallout radionuclides from the Fukushima Dai-Ichi Nuclear Power Plant accident in 2011. As a result, the simulated 137Cs concentration in bottom sediment showed a reasonably close match with the measurement data. The distribution coefficient of 137Cs consistent with the latest measurement data was identified as being at least 400,000L/kg, and it was estimated that more than 90% of the total 137Cs distributed in the fallout remains in the catchment area.
... The importance of the resolution of spatial discretization has been recognized before, particularly in studies on reactive transport (Mehl and Hill, 2002). In this field, grid telescoping, i.e., the modeling of a reactive transport problem using two grids, namely a coarse grid representing the whole catchment and a fine one representing the surrounding area of the contaminated plume, is relatively common (Mehl and Hill, 2002;Mehl et al., 2006). However, grid telescoping requires a well defined inner domain of interest and an outer domain from which conditions can be extracted and used as boundary conditions for the inner domain. ...
Partial-differential-equation based integrated hydrological models are now regularly used at catchment scale. They rely on the shallow water equations for surface flow and on the Richards' equations for subsurface flow, allowing a spatially explicit representation of properties and states. However, these models usually come at high computational costs, which limit their accessibility to state-of-the-art methods of parameter estimation and uncertainty quantification, because these methods require a large number of model evaluations. In this study, we present an efficient model calibration strategy, based on a hierarchy of grid resolutions, each of them resolving the same zonation of subsurface and land-surface units. We first analyze which model outputs show the highest similarities between the original model and two differently coarsened grids. Then we calibrate the coarser models by comparing these similar outputs to the measurements. We finish the calibration using the fully resolved model, taking the result of the preliminary calibration as starting point. We apply the proposed approach to the well monitored Lerma catchment in North-East Spain, using the model HydroGeoSphere. The original model grid with 80,000 finite elements was complemented with two other model variants with approximately 16,000 and 10,000 elements, respectively. Comparing the model results for these different grids, we observe differences in peak discharge, evapotranspiration, and near-surface saturation. Hydraulic heads and low flow, however, are very similar for all tested parameter sets, which allows the use of these variables to calibrate our model. The calibration results are satisfactory and the duration of the calibration has been greatly decreased by using different model grid resolutions.
... (2) inclined model layers and variable cell thickness within the same layer; (3) specified concentration or mass flux boundaries; (4) the solute transport effects of external hydraulic sources and sinks, such as wells, drains, rivers, areal recharge, evapotranspiration; and (5) locally refined grids (Mehl et al., 2006). MT3DMS has been successfully applied to field problems with spatial scales ranging from laboratory, plot, and site scales (measured in meters) over a temporal scale of hours to days (e.g., Barth et al., 2001aBarth et al., , 2001bBianchi et al., 2011;Ma et al., 2010) to river basin scales (measured in kilometers) over a temporal scale of decades (e.g., Cao, 2011). ...
MT3DMS is a three-dimensional multi-species solute transport model for solving advection, dispersion, and chemical reactions of contaminants in saturated groundwater flow systems. MT3DMS interfaces directly with the U.S. Geological Survey finite-difference groundwater flow model MODFLOW for the flow solution and supports the hydrologic and discretization features of MODFLOW. MT3DMS contains multiple transport solution techniques in one code, which can often be important, including in model calibration. Since its first release in 1990 as MT3D for single-species mass transport modeling, MT3DMS has been widely used in research projects and practical field applications. This article provides a brief introduction to MT3DMS and presents recommendations about calibration and validation procedures for field applications of MT3DMS. The examples presented suggest the need to consider alternative processes as models are calibrated and suggest opportunities and difficulties associated with using groundwater age in transport model calibration. © 2012 American Society of Agricultural and Biological Engineers.
... A variety of refinement techniques have been developed for finite-difference models. Telescopic mesh refinement (Ward et al. 1987) or local grid refinement (Mehl and Hill 2006) allow for the development of submodels with a high grid resolution for more detailed well-stream interactions. MODFLOW-USG (Panday et al. 2013) uses an unstructured grid approach to the finite-difference formulation, which allows the construction of new models or adaptation of previous models in grids that are not rectangular, and hence allows for selective refinement next to surface water features and wells. ...
Regional finite-difference models often have cell sizes that are too large to sufficiently model well-stream interactions. Here, a steady-state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell-by-cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real-world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined “benchmark” MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost-effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite-difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady-state conditions.
... One interesting new approach might include embedded modeling approaches where local-scale, Biot-type 3D models could be embedded in a simpler regional-scale model. Recent advances in local grid refinement for MODFLOW (Mehl et al., 2006) and extension to embedding finite-element models in regional finite-difference models (Dickinson et al., 2007) suggest that an embedded approach is promising. ...
Regional aquifer-system compaction and land subsidence accompanying groundwater abstraction in susceptible aquifer systems in the USA is a challenge for managing groundwater resources and mitigating associated hazards. Developments in the assessment of regional subsidence provide more information to constrain analyses and simulation of aquifer-system compaction. Current popular approaches to simulating vertical aquifer-system deformation (compaction), such as those embodied in the aquitard drainage model and the MODFLOW subsidence packages, have proven useful from the perspective of regional groundwater resources assessment. However, these approaches inadequately address related local-scale hazardsground ruptures and damages to engineered structures on the land surface arising from tensional stresses and strains accompanying groundwater abstraction. This paper presents a brief overview of the general approaches taken by the U.S. Geological Survey toward understanding aquifer-system compaction and subsidence with regard to a) identifying the affected aquifer systems; b) making regional assessments; c) analyzing the governing processes; and d) simulating historical and future groundwater flow and subsidence conditions. Limitations and shortcomings of these approaches, as well as future challenges also are discussed.
... The models in this work were only loosely coupled by assigning calculated heads from the larger model as a Dirichlet boundary condition on the vertical boundaries of the smaller model. Other approaches are characterized by a higher degree of coupling to ensure continuity of fluxes and hydraulic heads at the contact of the two grids, for example Giudici et al. (2001), Mehl and Hill (2002), Romano et al. (2002), Keating et al. (2003) and Mehl et al. (2006). ...
This study investigates the effect of fine-scale clay drapes on tracer transport. A tracer test was performed in a sandbar deposit consisting of cross-bedded sandy units intercalated with many fine-scale clay drapes. The heterogeneous spatial distribution of the clay drapes causes a spatially variable hydraulic conductivity and sorption coefficient. A fluorescent tracer (sodium naphthionate) was injected in two injection wells and ground water was sampled and analyzed from five pumping wells. To determine (1) whether the fine-scale clay drapes have a significant effect on the measured concentrations and (2) whether application of multiple-point geostatistics can improve interpretation of tracer tests in media with complex geological heterogeneity, this tracer test is analyzed with a local three-dimensional ground-water flow and transport model in which fine-scale sedimentary heterogeneity is modeled using multiple-point geostatistics. To reduce memory needs and calculation time for the multiple-point geostatistical simulation step, this study uses the technique of direct multiple-point geostatistical simulation of edge properties. Instead of simulating pixel values, model cell edge properties indicating the presence of irregularly shaped surfaces are simulated using multiple-point geostatistical simulations. Results of a sensitivity analysis show under which conditions clay drapes have a significant effect on the concentration distribution. Calibration of the model against measured concentrations from the tracer tests reduces the uncertainty on the clay-drape parameters. The calibrated model shows which features of the breakthrough curves can be attributed to the geological heterogeneity of the aquifer and which features are caused by other processes.
... One interesting new approach might include embedded modeling approaches where local-scale, Biot-type 3D models could be embedded in a simpler regional-scale model. Recent advances in local grid refinement for MODFLOW (Mehl et al., 2006) and extension to embedding finite-element models in regional finite-difference models (Dickinson et al., 2007) suggest that an embedded approach is promising. ...
Regional aquifer-system compaction and land subsidence accompanying groundwater abstraction in susceptible aquifer systems in the USA is a challenge for managing groundwater resources and mitigating associated hazards. Developments in the assessment of regional subsidence provide more information to constrain analyses and simulation of aquifer-system compaction. Current popular approaches to simulating vertical aquifer-system deformation (compaction), such as those embodied in the aquitard drainage model and the MODFLOW subsidence packages, have proven useful from the perspective of regional groundwater resources assessment. However, these approaches inadequately address related local-scale hazards—ground ruptures and damages to engineered structures on the land surface arising from tensional stresses and strains accompanying groundwater abstraction. This paper presents a brief overview of the general approaches taken by the U.S. Geological Survey toward understanding aquifer-system compaction and subsidence with regard to a) identifying the affected aquifer systems; b) making regional assessments; c) analyzing the governing processes; and d) simulating historical and future groundwater flow and subsidence conditions. Limitations and shortcomings of these approaches, as well as future challenges also are discussed.
... This two-step calibration procedure requires the use of an advanced modeling package that allows for the effective manage- ment of highly variable geometrical aspect ratios, e.g., by the use of grid with a large difference in the element size and appropriate 1D FE representation of local constraints incorporated within the 3D mesh. This approach appears to be more convenient than alternative procedures existing in the groundwater modeling literature to address local analyses within a large-scale hydrogeologic system, e.g., the telescopic approach ͑Ward et al. 1987; Mehl and Hill 2004;Mehl et al. 2006͒ andthe hierarchical ͑Li and. Indeed, the greater FE flexibility relative to finite differences presently overcomes the need for using telescopic ͑or nested͒ grids. ...
To prevent erosion of polluted land and discharge of contaminated groundwater and surface water into the Venice Lagoon, a 57 km long cutoff wall has been designed by the Venice Water Authority and is currently under construction along the canal banks of the Venice, Italy industrial harbor. To predict the impact on the hydrologic regime and mitigate the related inundation hazard in the nearby urban areas, a complex three-dimensional finite-element model has been developed and implemented over the multiaquifer system down to a depth significantly larger than the wall bottom. The model is initially calibrated against the regional piezometry and then refined locally to reproduce the groundwater volume drained along a 5-km long bank of a harbor canal already bounded. Major results from the simulations show that after the wall completion the subsurface discharge into the lagoon is successfully abated by as much as 85% relative to the preexisting rate with, however, an expected 1-m increase of the water table in the inland city of Mestre, Italy thus pointing to the need for implementing a drainage trench upstream the wall to properly reduce the raised groundwater level. The model would also indicate that the shallowest aquifers may receive underground water from a large number of old deeper boreholes abandoned in the past and not properly sealed. From a more general perspective, the present study constitutes an important example where the reliable and sustainable design of a complex engineered structure bound to impact significantly on the surrounding environment can be much helped and improved by the use of advanced numerical models capable to capture the essential features of the underlying geohydrological processes.
... (2) inclined model layers and variable cell thickness within the same layer; (3) specified concentration or mass flux boundaries; (4) the solute transport effects of external hydraulic sources and sinks, such as wells, drains, rivers, areal recharge, evapotranspiration; and (5) locally refined grids (Mehl et al., 2006). MT3DMS has been successfully applied to field problems with spatial scales ranging from laboratory, plot, and site scales (measured in meters) over a temporal scale of hours to days (e.g., Barth et al., 2001aBarth et al., , 2001bBianchi et al., 2011;Ma et al., 2010) to river basin scales (measured in kilometers) over a temporal scale of decades (e.g., Cao, 2011). ...
The Ordos Basin is located in the arid northwest of China. The basin
encompasses parts of Shaanxi, Gansu, Shanxi and Inner Mongolia provinces
with a total area of 360,000 km2. The region has an abundant reserve of
coal and natural gas, hence it is a key energy base for China. However,
economic development in the region is hampered by severe water scarcity.
Sustainable management of limited groundwater resources is of major
concern. In this study, we applied a version of the MT3DMS solute
transport model to simulate the three-dimensional distribution of mean
groundwater ages in the confined Cretaceous sandstone aquifer in the
Ordos Basin. The groundwater age model was constrained by comparing the
simulated mean ages with carbon-14 age data collected at over 100
observation wells. Spatial distribution of groundwater ages in a large
basin simulated by a solute transport model and calibrated by
field-measured isotopic age data provides a unique opportunity to
analyze and quantify the sustainability of groundwater resources.
Younger groundwater represents a more dynamic system with a higher
capability for recharge and renewal. On the other hand, older
groundwater indicates a more stagnant system with a lower capability for
recharge and renewal. Thus, numerical simulation of groundwater ages can
be used as a valuable management tool to evaluate and ensure
sustainability of groundwater resources.
... In this study, the A&T aquifer was discretized into a finite-difference grid, comprising 187 rows and 232 columns oriented in the direction of regional groundwater flow. Cell sizes were set at 0.35 km per side but finer grid refinement was used around pumping wells, stream segments, and other model boundaries, where large variations in hydraulic gradients are expected over small spatial scales (see Mehl et al 2006). Vertically, the aquifer was divided into three model layers of variable thicknesses based on lithologic information from well logs as well as well-completion reports provided by the OWRB for the aquifer. ...
This paper uses Visual MODFLOW to simulate potential impacts of anthropogenic pumping and recharge variability on an alluvial
aquifer in semi-arid northwestern Oklahoma. Groundwater withdrawal from the aquifer is projected to increase by more than
50% (relative to 1990) by the year 2050. In contrast, climate projections indicate declining regional precipitation over the
next several decades, creating a potential problem of demand and supply. The following scenarios were simulated: (1) projected
groundwater withdrawal, (2) a severe drought, (3) a prolonged wet period, and (4) a human adjustment scenario, which assumes
future improvements in water conservation measures. Results indicate that the combined impacts of anthropogenic pumping and
droughts would create drawdown of greater than 12m in the aquifer. Spatially, however, areas of severe drawdown will be localized
around large-capacity well clusters. The worst impacts of both pumping and droughts will be on stream–aquifer interaction.
For example, the projected aquifer pumpage would lead to a total streamflow loss of 40%, creating losing stream system regionally.
Similarly, a severe drought would lead to a total streamflow loss of >80%. A post-audit of the model was also carried out
to evaluate model performance. By simulating various stress scenarios on the alluvial aquifer, this study provides important
information for evaluating management options for alluvial aquifers.
KeywordsNumerical modelling–northwestern Oklahoma–MODFLOW–alluvial aquifers–recharge variability–US Southern Great Plains–Hydrology–modelling–coupled systems–general/other
... The groundwater models are the most effective tools for predicting water levels in an aquifer based on existing or proposed parameters, assessing the effects of various pumping or injection well schemes on both surface and groundwater system simultaneously [1]. Recent studies have shown that the widely used U.S. Geological Survey (USGS) MODFLOW [2][3][4][5] and its precursors have included a "River" Package that could be generalized to represent a river as a constanthead source or sink of fixed areal extent overlying the aquifer. This paper presents an evaluation of the surface and groundwater relationship and the effect of Riverbed conductance in river valley aquifer. ...
Stream-aquifer interaction due to groundwater extraction has been analyized. Streamflow depletion in alluvial plain area at Sonhuajiang river valley, China, can be determined as a result of groundwater withdrawal. Three - dimensional transient numerical model technique based on hydrologic and hydrogeologic parameters was used to understand and quantify stream-aquifer interaction. Numerical model was setup based on the constructed conceptual model of the study area. The alluvial aquifer is shown to be of high transmissivity with the pumping stresses having a larger radius of influence, impacting both the aquifer water levels and the streamflow in the nearby Songhuajiang River, Jilin Province, China. Drawdown and recharge boundary effects were observed in all observation wells in the area. The alluvial aquifer exhibited a piezometric surface behavior and responded as semi-confined aquifer. A semi-confining clay layer less than 3 m thick and an additional recharge source from a nearby stream-alluvial system were the probable causes of the observed phenomena. Induced infiltration, reduced baseflow, river gaining, river losing, and the effect of riverbed conductance on river leakage were performed using visual MODFLOW model in the lower reach of the Songhuajiang River valley.
... Consequently, the perimeter conditions for the inset model may be in error. To resolve this problem, a local grid refinement package (LGR) has been developed for MODFLOW (Mehl andHill 2005, 2006) whereby the local refined grid is embedded in the regional model with shared nodes at their interface. Any changes in water withdrawals in the local model, therefore, are reflected in the entire regional model domain. ...
Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.
Multi-scale modeling of the localized groundwater flow problems in a large-scale aquifer has been extensively investigated under the context of cost-benefit controversy. An alternative is to couple the parent and child models with different spatial and temporal scales, which may result in non-trivial sub-model errors in the local areas of interest. Basically, such errors in the child models originate from the deficiency in the coupling methods, as well as from the inadequacy in the spatial and temporal discretizations of the parent and child models. In this study, we investigate the sub-model errors within a generalized one-way coupling scheme given its numerical stability and efficiency, which enables more flexibility in choosing sub-models. To couple the models at different scales, the head solution at parent scale is delivered downward onto the child boundary nodes by means of the spatial and temporal head interpolation approaches. The efficiency of the coupling model is improved either by refining the grid or time step size in the parent and child models, or by carefully locating the sub-model boundary nodes. The temporal truncation errors in the sub-models can be significantly reduced by the adaptive local time-stepping scheme. The generalized one-way coupling scheme is promising to handle the multi-scale groundwater flow problems with complex stresses and heterogeneity.
Increased groundwater withdrawals from confined aquifers in the Maryland Coastal Plain to supply anticipated growth at Fort George G. Meade (Fort Meade) and surrounding areas resulting from the Department of Defense Base Realignment and Closure Program may have adverse effects in the outcrop or near-outcrop areas. Specifically, increased pumping from the Potomac Group aquifers (principally the Patuxent aquifer) could potentially reduce base flow in small streams below rates necessary for healthy biological functioning. Additionally, water levels may be lowered near, or possibly below, the top of the aquifer within the confined-unconfined transition zone near the outcrop area.
A three-dimensional groundwater flow model was created to incorporate and analyze data on water withdrawals, streamflow, and hydraulic head in the region. The model is based on an earlier model developed to assess the effects of future withdrawals from well fields in Anne Arundel County, Maryland and surrounding areas, and includes some of the same features, including model extent, boundary conditions, and vertical discretization (layering). The resolution (horizontal grid discretization) of the earlier model limited its ability to simulate the effects of withdrawals on the outcrop and near-outcrop areas. The model developed for this study included a block-shaped higher-resolution local grid, referred to as the child model, centered on Fort Meade, which was coupled to the coarser-grid parent model using the shared node Local Grid Refinement capability of MODFLOW-LGR. A more detailed stream network was incorporated into the child model. In addition, for part of the transient simulation period, stress periods were reduced in length from 1 year to 3 months, to allow for simulation of the effects of seasonally varying withdrawals and recharge on the groundwater-flow system and simulated streamflow. This required revision of the database on withdrawals and estimation of seasonal variations in recharge represented in the earlier model. The calibrated model provides a tool for future forecasts of changes in the system under different management scenarios, and for simulating potential effects of withdrawals at Fort Meade and the surrounding area on water levels in the near-outcrop area and base flow in the outcrop area.
Model error was assessed by comparing observed and simulated water levels from 62 wells (55 in the parent model and 7 in the child model). The root-mean-square error values for the parent and child model were 8.72 and 11.91 feet, respectively. Root-mean-square error values for the 55 parent model observation wells range from 0.95 to 30.31 feet; the range for the 7 child model observation wells is 5.00 to 24.17 feet. Many of the wells with higher root-mean-square error values occur at the perimeter of the child model and near large pumping centers, as well as updip in the confined aquifers. Root-mean-square error values decrease downdip and away from the large pumping centers.
Both the parent and child models are sensitive to increasing withdrawal rates. The parent model is more sensitive than the child model to decreasing transmissivity of layers 3, 4, 5, and 6. The parent model is relatively insensitive to riverbed vertical conductance, however, the child model does exhibit some sensitivity to decreasing riverbed conductance.
The overall water budget for the model included sources and sinks of water including recharge, surface-water bodies and rivers and streams, general-head boundaries, and withdrawals from permitted wells. Withdrawal from wells in 2005 was estimated to be equivalent to 8.5 percent of the total recharge rate.
Aquifer characterization programs are usually performed with the objective of obtaining the data required to develop numerical groundwater models. Groundwater modeling starts with the development of a conceptual model, which is followed by the selection of a modeling code and model discretization. Initial values for the hydraulic and transport properties are then assigned to each model cell or element, which are subject to adjustment during the model calibration process. Predictive simulations are performed to evaluate the response of the aquifer to various stresses (e.g., groundwater pumping scenarios). A deterministic approach has been taken for most groundwater models, in which the goal is to obtain a single solution that represents a ‘best’ estimate of future conditions. The alternative stochastic approach involves running a large number of simulations in a probabilistic framework to explore the range of possible future conditions. The basic premise of stochastic modeling is that due to an incomplete knowledge of the spatial variability of parameters, the decision is made to analyze all (or least numerous) plausible representations of the aquifer. Stochastic modeling has high data requirements and is not a substitute for a robust aquifer characterization program.
Yeraltı suları bulunduğu bölgenin hidrolojik sisteminin önemli bir parçasıdır ve günümüzde tükenmekte olan su kaynaklarının korunması ve geliştirilmesi açısından stratejik bir rol oynamaktadır. Doğal bir kaynak olarak su kalitesi üzerinde ve su temininde önemli bir yere sahiptir. Su kaynakları dağılımının ve çevre kirlenmesinin bölgesel olarak değerlendirilmesi, su temini ve kalitesinin belirlenebilmesi için kaçınılmazdır. Bu nedenle yeraltı suyunun mekanizması, yapılan hassas hidrolojik modelleme çalışmaları ile belirlenmelidir. Bugüne kadar yapılan yeraltı suyu çalışmaları, yeraltı suyu hidroliğini ve hidrolojisini açıklayabilirken, yüzey suyu-yeraltı suyu etkileşimlerini kapsayan ve değişken parametreler ve farklı senaryolar altında yeraltı suyunun davranışını inceleyen çalışma literatürde oldukça kısıtlıdır. Genelde literatürde yüzey suyu ve yeraltı suyu ayrı formasyonlar olarak incelenirken, bu çalışmada yüzey ve yeraltı suyu tek bir sistem olarak ele alınmış ve simülasyonlar bu kabul çerçevesinde yapılmıştır. Bu çalışmada yeraltı suyu akımını modelleyen VISUAL MODFLOW bilgisayar programı ile kavramsal bir nehir-akifer modeli geliştirilmiş; yapılan simülasyonlar ile kavramsal olarak hazırlanmış nehir-akifer bölgesinin hidrolojik davranışı incelenmiş; ve yüzey suyu-yeraltı suyu etkileşimlerinin nehir-akifer formasyonunun hidrolojik davranışına olan etkisi araştırılmıştır. Yapılmış olan nehir-akifer hidrolojik modellemesi ile farklı nehir parametreleri için yeraltı su seviyesi dağılımı ve nehir-akifer arasında oluşan akım elde edilmiştir.
Groundwater is an important part of the hydrological system and it has a strategical place in protecting and developing water resources being depleted nowadays. As a natural resource, groundwater plays an important role in water quality and water supply. Regionally assessing the distribution of water resources and environmental pollution is inevitable for determining water supply and water quality. Therefore, the physical mechanism of the groundwater should be determined by developing detailed hydrological models. While many studies cover groundwater as a single system and therefore investigate pure groundwater hydraulics and hydrology, studies related to surface-groundwater interactions and the behavior of groundwater by conducting a sensitivity analysis under different scenarios are exiguous in the literature. Generally, surface and groundwater are examined separately in the literature; however, in this study they are considered as a unique system and the simulations are done accordingly. In this study, a conceptual stream-aquifer model is developed by using VISUAL MODFLOW computer program which is capable for simulations of groundwater flow. The hydrological behavior of the conceptual stream-aquifer region is observed and the effect of surface/groundwater interactions on the hydrological behavior of stream-aquifer region is investigated. Groundwater level fluctuations and the flux between stream and aquifer are obtained with the hydrological model of the conceptual stream–aquifer system by conducting sensitivity analyses for different stream parameters.
A generalized hierarchical approach with a water balance function is introduced to simulate stream-flow depletion in a complex groundwater system in Osceola County. The groundwater flow system at the site, because of the complex interaction between ambient streams, exhibits a unique multi-scale pattern that proves to be difficult to simulate using standard modelling tools. The hierarchical modelling system was first calibrated to water level measurements collected from monitoring wells. Afterwards, systematic hierarchical simulations and integrated water budget analyses were performed to evaluate the adverse resource impact of the ongoing water withdrawal. The multi-scale process-based results from this generic hierarchical modelling system provided critical storage and flux information that can be used to comprehensively assess the pros and cons of water resource development and management, such as artificial water withdrawal.
This research aims at improving the performance of regional groundwater models by incorporating high-resolution elevation data into the head-dependent packages of MODFLOW. Model code specific to the evapotranspiration package (EVT) of MODFLOW was modified to account for the variability in elevation data and to effectively delineate the evapotranspiration (ET) simulated region at user-specified digital elevation model (DEM) resolution. The regional groundwater model of the Rincon Valley-Mesilla Basins (NMOSE-2007 flow model) was improved and considered to evaluate and validate the developed code. The base DEM of the study area is smoothened and aggregated to various resampled resolutions that are integer divisors of NMOSE-2007 flow model resolution for use with ET simulation. A gradual decrease in ET outflow is observed when the variability in elevation is eliminated across the grid cell. Also, changes in cumulative ET outflow (as a fraction of total outflow) at different resampled grids followed a similar trend during the simulation. The computational cost is high for the models simulated at fine resolution, whereas the simulation accuracy is low for the models simulated at coarse resolution. To select the optimum resampled DEM resolution to simulate the ET component of groundwater for use with the NMOSE-2007 flow model, a chi-square test of homogeneity was performed at 5 and 10% significance levels by considering computational cost and simulation accuracy as the base parameters. Results of the statistical analysis concluded that simulating ET component at 80.467-m resolution and integrating the outflows to model cell (402.336 m) resolution would significantly improve the performance of the flow model without compromising on the computational cost. (C) 2014 American Society of Civil Engineers.
Ground water should be used efficiently and improved for sustainable water management plans. For this purpose, comprehensive ground water flow models are developed incorporating surface/ground water interactions. Typically, these models require a significant amount of hydrological parameters and the sensitivities of these parameters on interaction mechanisms need to be clarified. Therefore, in this study, the role of the geometric shape of the stream on stream/ground water interactions is investigated. First, an analytical solution for two-dimensional ground water flow is developed with sloping stream boundary in an isotropic and homogeneous aquifer. Then, ground water head distribution and hyporheic exchange flow between stream and aquifer are obtained by conducting sensitivity analyses with prototype models developed using Visual MODular Finite-Difference FLOW in order to observe individual effects of each stream property. Finally, by incorporating the highest possible stream/ground water interaction conditions into a conceptual stream-aquifer model, the combined effects of different stream shapes are interpreted. Results show that slope, abrupt slope change, and flow path of stream affect the interactions significantly. Moreover, interaction flow rates increase further under the combined effects of these stream properties. The outputs of this work will ultimately be used in site investigations and in forecasting ground water hydrology.
Many hydrogeology problems require predictions of hydraulic heads in a supply well. In most cases, the regional hydraulic response to groundwater withdrawal is best approximated using a numerical model; however, simulated hydraulic heads at supply wells are subject to errors associated with model discretization and well loss. An approach for correcting the simulated head at a pumping node is described here. The approach corrects for errors associated with model discretization and can incorporate the user's knowledge of well loss. The approach is model independent, can be applied to finite difference or finite element models, and allows the numerical model to remain somewhat coarsely discretized and therefore numerically efficient. Because the correction is implemented external to the numerical model, one important benefit of this approach is that a response matrix, reduced model approach can be supported even when nonlinear well loss is considered.
Society faces a future of unprecedented, extensive and rapid environmental change. The impacts of climate change and greater societal vulnerability will require far-reaching adaptations of behaviour and activity. To plan these, decision-makers require tools that will help them understand the extent and impact of natural hazards. These should take into account deterministic and probabilistic analyses of occurrence, impact, spatial distribution, background conditions and triggers that affect different hazards. Geographic information system (GIS)-based, 2D, models are easily understood by different users and are well suited to situations where data is plentiful, the historical record is relatively complete or where problems are simple. However, they have limitations. Advances in computer processing capacity have brought marked changes in how data can be manipulated and presented; this has allowed and driven an increasing desire to provide more detailed information about the spatial extent, temporal occurrence, triggers and impacts of geohazards. Future geohazard models based on 3D distributions of causative factors, including primary (e.g. precipitation) and secondary (e.g. groundwater) 4D processes, that determine the timing, scale and geographical distribution of events will rapidly evolve. They will increasingly integrate data from other disciplines, such as societal vulnerability, to develop risk models. Currently, geohazard models are constrained by inadequate data, a poor understanding of the interaction of processes, and cultural barriers such as inertia or intellectual property rights. The development of improved models, whether for planning purposes or management of crises, provides challenges, both in system development and in the communication of complexity and uncertainty with decision-makers.
Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.
Knowledge of the hydrological mechanisms behind habitat fragmentation of fen plant communities in intensively managed regions like The Netherlands is essential to improve currently utilized fen restoration and conservation strategies. In this study, we analysed the local and regional impact of anthropogenic drainage on the groundwater supply of fens. For this purpose, we developed fine-scale groundwater flow models and collected empirical data to analyse (1) the differences in groundwater supply between an anthropogenically drained fen and a poorly drained fen in The Netherlands, and (2) the local and regional effects of the elimination of drainage ditches on the groundwater supply of fens. Our results consistently indicated the presence of recently infiltrated precipitation on top of upwelling groundwater across the anthropogenically drained fen, and a mixing gradient of recently infiltrated precipitation and upwelling groundwater across the poorly drained fen. Furthermore, our results showed that the elimination of drainage ditches from the anthropogenically drained fen increased the area and the flux of groundwater supply of both the anthropogenically drained fen and the poorly drained fen. We conclude that anthropogenic drainage not only causes a lowering of groundwater tables, but also (1) enhances the infiltration of local precipitation across fens while simultaneously preventing upwelling groundwater from entering the fen root zone, and (2) reduces the groundwater supply of adjacent fens by intercepting groundwater that is potentially directed to downstream regions. These insights support the need to reconsider the current priorities in hydrological fen restoration strategies.
Ground-water models are commonly used to evaluate flow systems in areas that are small
relative to entire aquifer systems. In many of these analyses, simulation of the entire flow system
is not desirable or will not allow sufficient detail in the area of interest. The procedure of telescopic
mesh refinement allows use of a small, detailed model in the area of interest by taking boundary
conditions from a larger model that encompasses the model in the area of interest. Some previous
studies have used telescopic mesh refinement; however, better procedures are needed in carrying
out telescopic mesh refinement using the U.S. Geological Survey ground-water flow model,
referred to as MODFLOW. This report presents general procedures and three computer programs
for use in telescopic mesh refinement with MODFLOW. The first computer program, MODTMR,
constructs MODFLOW data sets for a local or embedded model using MODFLOW data sets and
simulation results from a regional or encompassing model. The second computer program,
TMRDIFF, provides a means of comparing head or drawdown in the local model with head or
drawdown in the corresponding area of the regional model. The third program, RIVGRID,
provides a means of constructing data sets for the River Package, Drain Package, General-Head
Boundary Package, and Stream Package for regional and local models using grid-independent data
specifying locations of these features. RIVGRID may be needed in some applications of telescopic
mesh refinement because regional-model data sets do not contain enough information on locations
of head-dependent flow features to properly locate the features in local models. The program is a
general utility program that can be used in constructing data sets for head-dependent flow packages
for any MODFLOW model under construction.
Recharge areas of spring systems can be hard to identify, but they can be critically important for protection of a spring resource. A recharge area for a spring complex in southern Wisconsin was delineated using a variety of complementary techniques. A telescopic mesh refinement (TMR) model was constructed from an existing regional-scale ground water flow model. This TMR model was formally optimized using parameter estimation techniques; the optimized "best fit" to measured heads and fluxes was obtained by using a horizontal hydraulic conductivity 200% larger than the original regional model for the upper bedrock aquifer and 80% smaller for the lower bedrock aquifer. The uncertainty in hydraulic conductivity was formally considered using a stochastic Monte Carlo approach. Two-hundred model runs used uniformly distributed, randomly sampled, horizontal hydraulic conductivity values within the range given by the TMR optimized values and the previously constructed regional model. A probability distribution of particles captured by the spring, or a "probabilistic capture zone," was calculated from the realistic Monte Carlo results (136 runs of 200). In addition to portions of the local surface watershed, the capture zone encompassed areas outside of the watershed--demonstrating that the ground watershed and surface watershed do not coincide. Analysis of water collected from the site identified relatively large contrasts in chemistry, even for springs within 15 m of one another. The differences showed a distinct gradation from Ordovician-carbonate-dominated water in western spring vents to Cambrian-sandstone-influenced water in eastern spring vents. The difference in chemistry was attributed to distinctive bedrock geology as demonstrated by overlaying the capture zone derived from numerical modeling over a bedrock geology map for the area. This finding gives additional confidence to the capture zone calculated by modeling.
The effluent from a former coal-carbonisation plant in Nottinghamshire has contaminated the underlying aquifer with ammonium and organic compounds. In terms of flow and contamination, the site has experienced a complex history. MODFLOW has been used to unravel the past flow directions and to provide a basis for solute transport and biodegradation modelling. The modelling has shown that a fine grid is required to represent local flows to prevent incorrect site interpretations. A telescopic mesh technique was essential for this study to enable the site features to be adequately represented while including the regional hydrogeological influences. The influence of grid size to numerical dispersion was investigated for the MT3D computer program. The 'method of characteristics' and 'hybrid method of characteristics' modules of MT3D were found to be relatively free from numerical dispersion for all the grid sizes investigated. However, the 'modified method of characteristics' suffered extensively, and a linear relationship between grid size and numerical dispersion was demonstrated for this complex model.
The available data base and hydrogeologic information for the Chem-Dyne
hazardous waste site, located in southwestern Ohio, are typical of many
Superfund sites. Data are localized because investigations conducted at
these sites are for the purpose of defining contaminant plumes. Little
or no data are available to characterize the regional flow systems which
impart a controlling influence on the rate and direction of contaminant
migration. To simulate groundwater flow and contaminant transport in
this setting, a telescopic mesh refinement (TMR) approach is
appropriate. This approach provides the means of accurately
incorporating regional controlling factors into smaller model domains
and also increased grid resolution in areas of critical importance. At
the Chem-Dyne site a finite-difference model was applied at three
scales: regional, local, and site. This application of TMR integrates
the regional and local flow system characteristics to analyze the
effectiveness of a proposed remedial action at the site scale. The TMR
modeling approach permits effective flow and transport model
construction and calibration to provide quantitative analysis of system
response to a groundwater extraction-injection well clean-up system.
Calibration of the flow models demonstrates the regional importance of
induced river infiltration to groundwater pumping centers and the
control of surface water features on the direction of plume migration.
The site-scale transport model reveals that a significant portion of the
volatile organic contaminants are not captured by the preliminary
proposed system.
Classical cell centered discretization of the reservoir simulation pressure equation on anh-adaptive grid results in anO(1/h) leading truncation error at the grid interface. A new flux continuous finite volume correction is presented together with an improved version of a previously proposed correction. While both corrections eliminate the leading error, the new correction exhibits the best convergence rates and has the following properties: the resulting matrix is in general symmetric positive definite, diagonally dominant for locally isotropic spatially varying coefficients, convergence toO(h) is demonstrated, and support of the standard approximation is retained, ensuring a fully implicit implementation. Results computed by the uncorrected classical scheme and both correction schemes are compared for two phase flow simulations with multilevel dynamic local grid refinement.
This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497–511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, “cage-shell” interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size—a coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.
This book combines two separate themes: a description of one of the links in the chain of the water cycle inside the earth's crust, i.e., the subsurface flow; and the quantification of the various types of this flow, obtained by applying the principles of fluid mechanics in porous media. The first part deals with the concept of water resources. The second part is necessary in order to quantify ground water resources. It points the way to other applications, such as solutions to civil engineering problems including drainage and compaction; and transport problems in porous media, including aquifer pollution by miscible fluids, multiphase flow of immiscible fluids, and heat transfer in porous media, i.e.e, geothermal problems.
The effluent from a former coal-carbonisation plant in Nottinghamshire has contaminated the underlying aquifer with ammonium and organic compounds. In terms of flow and contamination, the site has experienced a complex history. MODFLOW has been used to unravel the past flow directions and to provide a basis for solute transport and biodegradation modelling. The modelling has shown that a fine grid is required to represent local flows to prevent incorrect site interpretations. A telescopic mesh technique was essential for this study to enable the site features to be adequately represented while including the regional hydrogeological influences. The influence of grid size to numerical dispersion was investigated for the MT3D computer program. The ‘method of characteristics’and ‘hybrid method of characteristics’modules of MT3D were found to be relatively free from numerical dispersion for all the grid sizes investigated. However, the ‘modified method of characteristics’suffered extensively, and a linear relationship between grid size and numerical dispersion was demonstrated for this complex model.
A new method of local grid refinement for two-dimensional block-centered finite-difference meshes that uses an iteration-based feedback to couple two separate grids has been developed. Its convergence properties have been evaluated and comparisons with alternative methods have been completed (Mehl and Hill, in review a). This work further investigates a difficulty encountered with the traditional telescopic mesh refinement (TMR) methods that lack a feedback.Results indicate: (1) Coupling the coarse grid with the refined grid in a numerically rigorous way that allows for a feedback can improve the coarse grid results; this improvement is not possible using the TMR methods because there is no feedback. (2) The TMR methods work well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 6.8% and errors in cell-to-cell fluxes up to 7.1% for the case presented. (3) For the TMR methods, coupling using flux boundary conditions produces significant inconsistencies in the head distribution at the boundary interface. TMR inaccuracies can substantially effect parameter estimation (Mehl and Hill, in review b).
Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger-scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.
A numerical technique for spatial (lateral and vertical) zooming in finite-difference multiaquifer ground water flow models with a point-centered finite-difference scheme is presented. A composite, rectangular finite-difference mesh is used, allowing for different mesh resolutions and/or layering in hierarchically associated windows of the flow domain. An iterative procedure, called mesh interface simulator (MIS), is developed to link the parent and child meshes along their boundaries, referred to as interfaces. MIS equates the piezometric head along and the lateral flux across the interface. A numerical example of four interbedded meshes in a two-aquifer system with spatial zooming is evaluated. The results of numerical simulation are compared to an analytical solution to assess the overall approximation error of the numerical finite-difference and MIS procedures.
A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback.Results indicate: (1) The new method exhibits quadratic convergence for homogenous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%.
One of the main difficulties in transport modeling and calibration is the extraordinarily long computing times necessary for simulation runs. Improved execution time is a prerequisite for calibration in transport modeling. In this paper we investigate the problem of code acceleration using an adaptive grid refinement, neglecting subdomains, and devising a method by which the Courant condition can be ignored while maintaining accurate solutions. Grid refinement is based on dividing selected cells into regular subcells and including the balance equations of subcells in the equation system. The connection of coarse and refined cells satisfies the mass balance with an interpolation scheme that is implicitly included in the equation system. The refined subdomain can move with the average transport velocity of the subdomain. Very small time steps are required on a fine or a refined grid, because of the combined effect of the Courant and Peclet conditions. Therefore, we have developed a special upwind technique in small grid cells with high velocities (velocity suppression). We have neglected grid subdomains with very small concentration gradients (zero suppression). The resulting software, MODCALIF, is a three-dimensional, modularly constructed FORTRAN code. For convenience, the package names used by the well-known MODFLOW and MT3D computer programs are adopted, and the same input file structure and format is used, but the program presented here is separate and independent. Also, MODCALIF includes algorithms for variable density modeling and model calibration. The method is tested by comparison with an analytical solution, and illustrated by means of a two-dimensional theoretical example and three-dimensional simulations of the variable-density Cape Cod and SALTPOOL experiments. Crossing from fine to coarse grid produces numerical dispersion when the whole subdomain of interest is refined; however, we show that accurate solutions can be obtained using a fraction of the execution time required by uniformly fine-grid solutions.
Development and evaluation of local grid refinement methods for forward and inverse groundwater models
- Mehl
Mehl, S. 2003. Development and evaluation of local grid
refinement methods for forward and inverse groundwater
models. Ph.D. diss., Department of Civil, Environmental
and Architectural Engineering, University of Colorado,
Boulder.
MODGRID: Simultaneous solving of different groundwater flow models at various scales
- F Schaars
- P Kamps
Schaars, F., and P. Kamps. 2001. MODGRID: Simultaneous
solving of different groundwater flow models at various
scales. In Proceedings of MODFLOW 2001 and Other
Modeling Odysseys Conference. eds. Seo Poeter, Zheng
and Poeter. Colorado School of Mines, Golden, Colorado,
September 11-14, vol. 1, 38-44.
MODFLOW-2005, the U.S. geological survey modular ground-water model--Documentation of Local Grid Refinement (LGR) . USGS Techniques and Methods TM6-A12
- S Mehl
- M C Hill
Mehl, S., and M.C. Hill. 2005. MODFLOW-2005, the U.S. geological survey modular ground-water model--Documentation
of Local Grid Refinement (LGR). USGS Techniques and
Methods TM6-A12. Denver CO.