1. A Brief Introduction to Groundwater Modeling
Karl Payne

2. Groundwater Modeling What is a groundwater model?
A groundwater model is a mathematical or analogue simulation of a groundwater flow or transport process.
“ As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” A. Einstein

3. Analytical Models & Numerical Models
Analytical models are mathematically exact solutions to the governing equations.

4. Hypothetical Aquifer

5. Questions

6. Mathematical Model

7. Analytical Solution

8. Answers

9. Analytical Models Simple to implement Require little input
Computationally undemanding
VERY LIMITED- simple homogeneous and isotropic systems
simple boundary conditions

10. Numerical Methods Approximate solutions to the governing equations.
Most widely used are finite-difference and finite-element methods.
These methods rely on discretization of the solution domain.

11. Finite Difference Method

12. Finite Difference Method

13. Numerical Solution

14. Applications of Groundwater Models
Groundwater Contamination:
Model could be used to estimate expected travel times
of contaminant plume.
Design of remedial program:
Model could be used determine optimum pumping rates
and placement of pumping wells of pump-and-treat
system.
Assessment of climate change impact on water
resources.

15. Modeling Protocol
Establish the Purpose
Develop a Conceptual Model
Selection of Computer Code
Model Design
Calibration
Model Verification

16. Model Purpose
Is the model being used for prediction or is it interpretive?
Example of predictive model would be a model used to investigate impact of climate change on water resources. One wants to predict how the freshwater/saltwater interface responds to changes in stresses.
Example of interpretation would be a sensitivity analysis-Identification of important system parameters.

17. Conceptual Model
A conceptual model is a pictorial representation of the groundwater system in the form of a block diagram or cross sections.
Hydrostratigraphy
System Boundaries
Hydrologic Stresses
Aquifer Parameters

18. Selection of Code

19. Model Design
The conceptual model is put into a form suitable for modeling. This step includes:
Designing the grid
Selecting time steps
Setting boundary and initial conditions
Selection of values for aquifer parameters and hydrologic stresses

20. Model Calibration

21. Model Calibration

22. Model Calibration

23. Model Verification Establish greater confidence in the model.
Verify the ability of the calibrated model to reproduce a second set of field data.

24. A Three-dimensional Saline Intrusion Model of Barbados using HydroGeoSphere
Karl Payne
07/09/2011

25. Introduction
Fig 1: Map of the Caribbean

26. Geology and Hydrogeology of Barbados
Barbados is composed of Pleistocene reef deposits up to 100 m thick
The Pleistocene limestone aquifer is underlain by low-permeability Tertiary sediments A B
Fig 2: Geology Map of Barbados

27. take place by diffuse infiltration through the soil or by
Fig 3: Cross-section through the line AB
Recharge to the Pleistocene limestone aquifer can
take place by diffuse infiltration through the soil or by
discrete infiltration through drainage wells and some sinkholes

28. The aquifer is divided into two hydrologic zones:
The streamwater zone which is the upland portion of the aquifer characterized by gravity-flow along the base of the limestone.
The sheetwater zone which is the freshwater lens portion of the aquifer that occurs in low-lying parts of the island.
Fig 4: Hydrogeologic map of Barbados

29. Conceptual Model Homogeneity and isotropy Unsaturated/Saturated Flow
Flow is three-dimensional
No vertical flow component across the contact between the Pleistocene limestone and the Tertiary stratum
Neglect the flux contribution from the Scotland District

30. Aquifer Parameters Hydraulic conductivity (K) of 10-4m/s
Porosity – 0.3
Recharge was taken to be 15% of average annual rainfall (1500mm/yr)

31. Model Selection
HydroGeoSphere(HGS)-Jointly developed by groundwater scientist at the University of Waterloo and Laval University, Canada.
A Three-dimensional numerical model describing fully-integrated subsurface and surface flow and solute transport.

32. HGS Features
2D overland/stream flow including stream/surface drainage network genesis.
3D variably-saturated flow in porous media.
3D variably-saturated flow in fractures and karst conduits.
Advective-dispersive transport, reactive solute/thermal transport in all continua.
Fully-coupled, simultaneous solution of surface/ subsurface flow and transport

33. Mesh Design Fig 5: Discretization of model domain
Fig 6: Land Surface Elevation

34. Saturation Animation

35. Results Fig 7: Freshwater lens in plan view
Fig 8: Pressure head distribution

36. Results

37. Model Calibration
PEST (Parameter Estimation) is the industry standard software package for parameter estimation and uncertainty analysis of complex environmental and other computer models.

38. Model Calibration
Fig 9: Delineation of model into K zones Fig 10: Sinkhole map of Barbados

39. Model Calibration
Fig 6: Calibration results

40. Modeling Approaches to Simulate Seawater Intrusion
Sharp interface vs Diffuse Interface

41. Density-dependent Transport
In coastal areas, there exists a body of sea water, often in the form of a wedge, underneath the freshwater lens.
Fresh water and salt water are miscible fluids and the zone of contact between them takes the form of a transition zone. (We saw this from geophysics)

42. t=0 yrs
t=100 yrs
t=50 yrs
Fig 8: Time evolution of the salinization process

43. Salinization Animation (Plan)

44. Salinization Animation (Cross-section)

45. Telescopic Mesh Refinement: Creating a LSM from RSM
Regional scale model used as BC to local scale

46. Example: Spring Hall Model

47. Questions?