Today’s Lecture: Grid design/boundary conditions and parameter selection. Thursday’s Lecture: Uncertainty analysis and Model Validation

Using a regional model to set boundary conditions for a site model Telescopic Mesh Refinement (TMR) (USGS Open-File Report ); a TMR option is available in GW Vistas. Analytic Element Screening Model 

Analytical Solutions Numerical Solutions Hybrid (Analytic Element Method) (numerical superposition of analytic solutions) Review Types of Models

Analytical Solutions Toth solution Theis equation etc… Continuous solution defined by h = f(x,y,z,t) Review Types of Models

Numerical Solutions Discrete solution of head at selected nodal points. Involves numerical solution of a set of algebraic equations. Review Types of Models Finite difference models (e.g., MODFLOW) Finite element models (e.g., MODFE: USGS TWRI Book 6 Ch. A3) See W&A, Ch. 6&7 for details of the FE method.

Finite Elements: basis functions, variational principle, Galerkin’s method, weighted residuals Nodes plus elements; elements defined by nodes Nodes located on flux boundaries Flexibility in grid design: elements shaped to boundaries elements fitted to capture detail Easier to accommodate anisotropy that occurs at an angle to the coordinate axis Able to simulate point sources/sinks at nodes Properties (K,S) assigned to elements

Involves superposition of analytic solutions. Heads are calculated in continuous space using a computer to do the mathematics involved in superposition. Hybrid Analytic Element Method (AEM) The AE Method was introduced by Otto Strack. A general purpose code, GFLOW, was developed by Strack’s student Henk Haitjema, who also wrote a textbook on the AE Method: Analytic Element Modeling of Groundwater Flow, Academic Press, Currently the method is limited to steady-state, two-dimensional, horizontal flow

How does superposition work? Example: The Theis solution may be added to an analytic solution for regional flow without pumping to obtain heads under pumping conditions in a regional flow field. Theis solution assumes no regional flow. (from Hornberger et al. 1998)

Solution for regional flow. Apply principle of superposition by subtracting the drawdown calculated with the Theis solution from the head computed using an analytic solution for regional flow without pumping. (from Hornberger et al. 1998)

Trout Lake km N Example: An AEM screening model to set BCs for a site model of the Trout Lake Basin Outline of the site we want to model

Outline of the Trout Lake MODFLOW site model Analytical element model of the regional area surrounding the Trout Lake site Analytic elements outlined in blue & pink represent lakes and streams.

Flux boundary for the site model Results of the Analytic Element model using GFLOW

Water table contours from MODFLOW site model using flux boundary conditions extracted from analytic element (AE) model Trout Lake Flux boundaries

Particle Tracking east of Trout Lake Lake derived Simulated flow paths Allequash Lake Big Muskellunge Lake Terrestrial (Pint et. al, 2002)

Things to keep in mind when using TMR or an AEM screening models to set boundary conditions for site models If you simulate a change in the site model that reflects changed conditions in the regional model, you should re-run the regional model and extract new boundary conditions for the site model.

Example: Simulating the effects of changes in recharge rate owing to changes in climate Flux boundary for the site model needs to be updated to reflect changed recharge rates.

Things to keep in mind when using TMR or an AEM screening models to set boundary conditions for site models If transient effects simulated in the site model extend to the boundaries of the site model, you should re-run the regional model under those same transient effects and extract new boundary conditions for the site model for each time step. Example: Pumping in a site model such that drawdown extends to the boundary of the site model.

Treating Distant Boundaries General Head Boundary Condition Telescopic Mesh Refinement Analytic Element Regional Screening Model

TMR is increasingly being used to extract site models from regional scale MODFLOW models. For example: Dane County Model Model of Southeastern Wisconsin RASA models Also there is an AEM model of The Netherlands that is used for regional management problems.

Curvature of the water table Vertical change in head Variability of aquifer characteristics (K,T,S) (Kriging vs. zonation) Variability of hydraulic parameters (R, Q) Considerations in selecting the size of the grid spacing Desired detail around sources and sinks (e.g., rivers)

Grid Design and Boundary Conditions Regular vs irregular grid spacing Distant boundary conditions Irregular spacing may be used to obtain detailed head distributions in selected areas of the grid. Finite difference equations that use irregular grid spacing have a higher associated error than FD equations that use regular grid spacing.