Steffen W. Mehl

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

Abstract 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%.

Evaluation of a local grid refinement method for steady-state block-centered finite-difference groundwater models

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).

MODFLOW–LGR—Documentation of ghost node local grid refinement (LGR2) for multiple areas and the boundary flow and head (BFH2) package

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Sustainable Capture: Concepts for Managing Stream‐Aquifer Systems

Most surface water bodies (i.e., streams, lakes, etc.) are connected to the groundwater system to some degree so that changes to surface water bodies (either diversions or importations) can change flows in aquifer systems, and pumping from an aquifer can reduce discharge to, or induce additional recharge from streams, springs, and lakes. The timescales of these interactions are often very long (decades), making sustainable management of these systems difficult if relying only on observations of system responses. Instead, management scenarios are often analyzed based on numerical modeling. In this paper we propose a framework and metrics that can be used to relate the Theis concepts of capture to sustainable measures of stream-aquifer systems. We introduce four concepts: Sustainable Capture Fractions, Sustainable Capture Thresholds, Capture Efficiency, and Sustainable Groundwater Storage that can be used as the basis for developing metrics for sustainable management of stream-aquifer systems. We demonstrate their utility on a hypothetical stream-aquifer system where pumping captures both streamflow and discharge to phreatophytes at different amounts based on pumping location. In particular, Capture Efficiency (CE) can be easily understood by both scientists and non-scientist alike, and readily identifies vulnerabilities to sustainable stream-aquifer management when its value exceeds 100%.

NEW GHOST-NODE METHOD FOR LINKING DIFFERENT MODELS WITH VARIED GRID REFINEMENT

A flexible, robust method for linking grids of locally refined models that may be constructed using different types of numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method based on the iterative method of Mehl and Hill (2002, 2004). It is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that facilitates clear analysis of typical problems. The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM. Results indicate that when the grids are matched spatially so that nodes and control volume boundaries are aligned, the new coupling technique has approximately twice the error as coupling using two MODFLOW models. When the grids are non-matching; model accuracy is slightly increased over matching grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models.

River Seepage Conductance in Large‐Scale Regional Studies

Flow exchange between surface and groundwater is of great importance be it for beneficial allocation and use of water resources or for the proper exercise of water rights. In large-scale regional studies, most numerical models use coarse grid sizes, which make it difficult to provide an accurate depiction of the phenomenon. In particular, a somewhat arbitrary leakance coefficient in a third type (i.e., Cauchy, General Head) boundary condition is used to calculate the seepage discharge as a function of the difference of head in the river and in the aquifer, whose value is often found by calibration. A different approach is presented to analytically estimate that leakance coefficient. It is shown that a simple equivalence can be deduced from the analytical solution for the empirical coefficient, so that it provides the accuracy of the analytical solution while the model maintains a very coarse grid, treating the water-table aquifer as a single calculation layer. Relating the empirical leakance coefficient to the exact conductance, derived from physical principles, provides a physical basis for the leakance coefficient. Factors such as normalized wetted perimeter, degree of penetration of the river, presence of a clogging layer, and anisotropy can be included with little computational demand. In addition the river coefficient in models such as MODFLOW, for example, can be easily modified when grid size is changed without need for recalibration.

Advective transport observations with MODPATH-OBS--documentation of the MODPATH observation process

The MODPATH-OBS computer program described in this report is designed to calculate simulated equivalents for observations related to advective groundwater transport that can be represented in a quantitative way by using simulated particle-tracking data. The simulated equivalents supported by MODPATH-OBS are (1) distance from a source location at a defined time, or proximity to an observed location; (2) time of travel from an initial location to defined locations, areas, or volumes of the simulated system; (3) concentrations used to simulate groundwater age; and (4) percentages of water derived from contributing source areas. Although particle tracking only simulates the advective component of conservative transport, effects of non-conservative processes such as retardation can be approximated through manipulation of the effective-porosity value used to calculate velocity based on the properties of selected conservative tracers. This program can also account for simple decay or production, but it cannot account for diffusion. Dispersion can be represented through direct simulation of subsurface heterogeneity and the use of many particles. MODPATH-OBS acts as a postprocessor to MODPATH, so that the sequence of model runs generally required is MODFLOW, MODPATH, and MODPATH-OBS. The version of MODFLOW and MODPATH that support the version of MODPATH-OBS presented in this report are MODFLOW2000/2005 or MODFLOW-LGR, and MODPATH or MODPATH-LGR. MODFLOW-LGR is derived from MODFLOW-2005, MODPATH 5, and MODPATH 6 and supports local grid refinement. MODPATH-LGR is derived from MODPATH 5. It supports the forward and backward tracking of particles through locally refined grids and provides the output needed for MODPATH-OBS. MODPATH-LGR and MODPATH-OBS simulations can use nearly all of the capabilities of MODFLOW-2005 and MODFLOW-LGR; for example, simulations may be steady-state, transient, or a combination. Though the program name MODPATH-OBS specifically refers to observations, the program also can be used to calculate model prediction of observations. MODPATH-OBS is primarily intended for use with separate programs that conduct sensitivity analysis, data needs assessment, parameter estimation, and uncertainty analysis, such as UCODE_2005, and PEST. In many circumstances, refined grids in selected parts of a model are important to simulated hydraulics, detailed inflows and outflows, or other system characteristics. MODFLOW-LGR and MODPATH-LGR support accurate local grid refinement in which both mass (flows) and energy (head) are conserved across the local grid boundary. MODPATH-OBS is designed to take advantage of these capabilities. For example, particles tracked between a pumping well and a nearby stream, which are simulated poorly if a river and well are located in a single large grid cell, can be simulated with improved accuracy using a locally refined grid in MODFLOW-LGR, MODPATH-LGR, and MODPATHOBS. The locally-refined-grid approach can provide more accurate simulated equivalents to observed transport between the well and the river. The documentation presented here includes a brief discussion of previous work, description of the methods, and detailed descriptions of the required input files and how the output files are typically used.

MODPATH-LGR; documentation of a computer program for particle tracking in shared-node locally refined grids by using MODFLOW-LGR

MODPATH-LGR is a particle tracking post-processing program for computing three-dimensional flow paths for steady-state and transient groundwater flow in models with local-grid refinement (sometimes called embedded models). Locally refined grids consist of a larger regional-scale parent model and one or more smaller embedded local-scale child models. This program uses output produced by MODFLOWLGR, in which child grids in parent grids are refined by using the Shared-Node Local Grid Refinement (LGR) package of the three-dimensional finite-difference groundwater-flow model MODFLOW published by the U.S. Geological Survey (USGS). The particle tracking scheme is based on MODPATH, which uses an analytical expression for particle movement within each finite-difference cell. Particles are tracked among cells until discharged through model boundaries, weak sinks, or other designated discharge zones. MODPATHLGR tracks particles between the parent and child models by using flows calculated at the interface boundaries. Flows calculated by MODFLOW-LGR are modified to account for fractional finite-difference cells along the shared-node interface between parent and child models. Required program input includes standard MODPATH input files for the parent and child models and a MODPATH-LGR control file. This documentation describes how particles are transferred between parent and child models and demonstrates program operation with two hypothetical steady-state xsimulations.