Robust Representation of Dry Cells in Single‐Layer MODFLOW Models

Abstract

Dewatered or "dry" grid cells in the USGS ground water modeling software MODFLOW may cause nonphysical artifacts, trigger convergence failures, or interfere with parameter estimation. These difficulties can be avoided in two dimensions by modifying the spatial differencing scheme and the iterative procedure used to resolve nonlinearities. Specifically, the spatial differencing scheme is modified to use the water level on the upstream side of a pair of adjacent cells to calculate the saturated thickness and hence intercell conductance for the pair. This makes it possible to explicitly constrain the water level in a cell to be at or above the cell bottom elevation without introducing nonphysical artifacts. Thus constrained, all initially active cells will remain active throughout the simulation. It was necessary to replace MODFLOW's Picard iteration method with the Newton-Raphson method to achieve convergence in demanding applications involving many dry cells. Tests using a MODFLOW variant based on the new method produced results nearly identical to conventional MODFLOW in situations where conventional MODFLOW converges. The new method is extremely robust and converged in scenarios where conventional MODFLOW failed to converge, such as when almost all cells dewatered. An example application to the Edwards Aquifer in south-central Texas further demonstrates the utility of the new method.

Simulating Seepage into Mine Shafts and Tunnels with MODFLOW

“…This numerical artifact of MODFLOW could have been avoided by applying an upstream weighting of transmissivities (e.g., Painter et al 2008) at the cell faces representing dewatered shaft, that is, T M 1/2 = T 1 = K z. MODFLOW interface transmissivity, T M 1/2 , is usually calculated as a harmonic or arithmetic mean of the transmissivities in the adjacent cells, that is, T 0 and T 1 .…”

Crossing boundaries, the influence of groundwater model boundaries and a method to join and split MODFLOW models

“…This may be achieved via 'engineering out' the problems of drying by modifying the model (e.g. thickening of layers), altering the source code to remove the potential for drying (Hydrogeologic 1996;Doherty 2001;Painter et al 2008;Keating & Zyvoloski 2009) and/or by reducing the frequency or effect of rewetting by alteration of resaturation or solver-based parameters (McDonald et al 1991). A composite of these methods was useful in the development of the joined NEAC groundwater model.…”

MODFLOW‐NWT: Robust Handling of Dry Cells Using a Newton Formulation of MODFLOW‐2005

“…The first versions of the widely used groundwater flow model MODFLOW (McDonald and Harbaugh 1988) had a sure but inflexible way of handling unconfined finite‐difference aquifer cells where the water table dropped below the bottom of the cell—these “dry cells” were turned inactive for the remainder of the simulation. Problems with this formulation were easily seen, including the potential for inadvertent loss of simulated recharge in the model (Doherty 2001; Painter et al 2008), and rippling of dry cells through the solution that unacceptably changed the groundwater flow system (Juckem et al 2006). Moreover, solving problems of the natural world often required the ability to reactivate dry cells when the water table rose above the cell bottom.…”

“…Early attempts at “re‐wetting” dry cells in MODFLOW, such as BCF2 (McDonald et al 1992) were found to work for some, but not all, MODFLOW models. Re‐wetting of dry cells was often numerically unstable and prevented model convergence (Doherty 2001; Painter et al 2008). When BCF2 did have a stable solution, the resulting runtimes were appreciably longer, the effort to select suitable BCF2 settings was often large, and the solution did not robustly handle input perturbations of parameter estimation (Doherty 2001).…”

“…Moreover, there were still large numbers of groundwater flow problems that remained unstable even with this modification (Doherty, written communication, 2012). Thus, even though some proprietary versions of MODFLOW had better handling of dry cells, many modelers substituted shortcuts within MODFLOW; shortcuts such as assuming all layers were confined, artificially lowering cell bottoms, and large convergence criteria—non‐physical adjustments that “could raise questions about the accuracy and reliability of the model results” (Painter et al 2008).…”