Today

1
Todays Lecture Grid design/boundary
conditions and
parameter selection.
Thursdays Lecture Uncertainty analysis and
Model Validation
2
Using a regional model to set boundary
conditions for a site model
?

• Telescopic Mesh Refinement (TMR)
• (USGS Open-File Report 99-238)
• a TMR option is available in GW Vistas.
• Analytic Element Screening Model

3
Review Types of Models

• Analytical Solutions
• Numerical Solutions
• Hybrid (Analytic Element Method)
• (numerical superposition of analytic
  solutions)

4
Review Types of Models

• Analytical Solutions
• Toth solution
• Theis equation
• etc
• Continuous solution defined by h f(x,y,z,t)
  

5
Review Types of Models

• Numerical Solutions
• Discrete solution of head at selected nodal
  points.
• Involves numerical solution of a set of
  algebraic
• equations.

Finite difference models (e.g., MODFLOW)
Finite element models (e.g., MODFE USGS
TWRI Book 6 Ch. A3) See WA, Ch. 67
for details of the FE
method.
6
Finite Elements basis functions, variational
principle, Galerkins method,
weighted residuals

• Nodes plus elements elements defined by nodes

• Properties (K,S) assigned to elements

• Nodes located on flux boundaries

• Able to simulate point sources/sinks at nodes

• 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

7
Hybrid Analytic Element Method (AEM)
Involves superposition of analytic solutions.
Heads are calculated in continuous space using a
computer to do the mathematics involved in
superposition.
The AE Method was introduced by Otto Strack. A
general purpose code, GFLOW, was developed
by Stracks student Henk Haitjema, who also wrote
a textbook on the AE Method Analytic Element
Modeling of Groundwater Flow, Academic Press,
1995.
Currently the method is limited to
steady-state, two-dimensional, horizontal flow
8
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)
9
Solution for regional flow.
(from Hornberger et al. 1998)
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.
10
Example An AEM screening model to set BCs for a
site model of the Trout Lake Basin
Trout Lake
Outline of the site we want to model
N
11
Analytical element model of the regional area
surrounding the Trout Lake site
Outline of the Trout Lake MODFLOW site model
Analytic elements outlined in blue pink
represent lakes and streams.
12
Results of the Analytic Element model using GFLOW
Flux boundary for the site model
13
Water table contours from MODFLOW site model
using flux boundary conditions extracted from
analytic element (AE) model
Flux boundaries
Trout Lake
14
Particle Tracking east of Trout Lake
Allequash Lake
Big Muskellunge Lake
Lake derived
Terrestrial
Simulated flow paths
(Pint et. al, 2002)
15
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.

16
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.
17
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.
18
Treating Distant Boundaries
Analytic Element Regional Screening Model
Telescopic Mesh Refinement
General Head Boundary Condition
19
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.
20
Considerations in selecting the size of the grid
spacing
Variability of aquifer characteristics (K,T,S)
(Kriging vs. zonation)
Variability of hydraulic parameters (R, Q)
Curvature of the water table
Vertical change in head
Desired detail around sources and sinks (e.g.,
rivers)
21
Grid Design and Boundary Conditions

• Distant boundary conditions

• Regular vs irregular grid spacing

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.