Stepwise Modeling
Perhaps the most practical advantage of the analytic element method is its operational efficiency. In the absence of a mesh or element network, the hydrologist is concerned only with entering hydrologic features in the model. Representing streams by strings of straight line elements and lakes by polygones is a rather intuitive task. Also, for initial modeling runs, a limited set of surface water features may be introduced. Later, when insight into the groundwater flow regime increases, more data may be added to locally refine the modeling. This stepwise modeling is not new. For example, Ward applied what he calls a "telescopic mesh refinement modeling approach" to the Chem-Dyne hazardous waste site in southwestern Ohio (Ward et al., 1987). However, Ward had to use three different computer models for the three different scales at which he was modeling. Conditions on the grid boundary of the "local scale" were obtained from the "regional scale" modeling results, while similarly the conditions on the grid boundary of the "site scale" were obtained from the "local scale" modeling results. In contrast, the analytic element method allows these different scales to be treated within the same model by locally refining the input data, thus avoiding transfer of conditions along artificial boundaries from one model into the other. When necessary, even three-dimensional flow features can be included, see "Analytic Element Modeling of Groundwater Flow" by Henk Haitjema, Academic Press, 1995.

While uniquely suitable for groundwater flow modeling at different scales current generation analytic element models have some limitations. For instance, both transient flow and three-dimensional flow are only partially implemented in analytic element models. Gradually varying aquifer properties cannot be represented in analytic element models. GFLOW also does not support multi-aquifer flow. Depending on circumstances and on the purpose of the modeling, however, these phenomena may be important. The GFLOW graphical user interface allows the user carry the modeling beyond the limitations of the analytic element method. This may be done in two different ways:

First, by extracting a MODFLOW model out of a GFLOW model, transferring the internal boundaries (streams, wells, lakes) and the domains with differing aquifer properties as defined in GFLOW directly to the finite difference grid. The GFLOW steady state groundwater flow solution is used to define either head or discharge specified conditions on the grid perimeter, and to precondition the MODFLOW solution procedure with heads at each cell center from the GFLOW solution. This procedure of extracting a MODFLOW model is quick and easy using the "grid" menu option in GFLOW. In this manner, the stepwise modeling procedure within the analytic element model is extended to modeling groundwater flow with MODFLOW and, when needed, contaminant transport with e.g. MT3D.

Second, a hybrid GFLOW-MODFLOW model may be constructed using the "Leakage from MODFLOW" option on the "grid" menue. The idea is to use the gridless analytic element model GFLOW to represent the upper layer(s) of a MODFLOW model to better represent surface water-groundwater interactions. This feature is often used to model detailed well-stream interactions that are not possible to represent in the original (coarse) MODFLOW model (Haitjema et al. 2010, Abrams et al. 2015).


  • Abrams, D.B., H.M. Haitjema, D.T. Feinstein and R.J. Hunt. Field Test of a Hybrid Finite-Difference and Analytic Element Regional Model. Groundwater, DOI: 10.111/gwat.12319, 2015
  • Haitjema, H.M. (1995). Analytic Element Modeling of Groundwater Flow. Academic Press, Inc.
  • Strack, O.D.L., "Groundwater Mechanics" Prentice Hall, 1989.
  • Haitjema, H.M., D.T. Feinstein, R.J. Hunt and M.A. Gusyev. A Hybrid Finite-Difference and Analytic Element Groundwater Model. Groundwater, 48, no.4: 538-448, 2010
  • Ward, D.S., D.R. Buss, J.W. Mercer and S.S. Hughes. Evaluation of a groundwater corrective action at the Chem-Dyne hazardous waste site using a telescoping mesh refinement modeling approach. Water Resources Research 23, no.4: 603-617, 1987