1. Subsurface Hydrology Unsaturated Zone Hydrology Groundwater Hydrology (Hydrogeology )

2. Water Table R = P - ET - RO P E ET RO R / P = ? R Groundwater

3. Processes we might want to model Groundwater flow calculate both heads and flow Solute transport – requires information on flow (velocities) calculate concentrations v = K I / n

4. Types of Models Physical (e.g., sand tank) Analog (electric analog, Hele-Shaw) Mathematical

5. Hele-Shaw Model

6. Types of Models Physical (e.g., sand tank) Analog (electric analog, Hele-Shaw) Mathematical

7. Components of a Mathematical Model Governing Equation (Darcy’s law + water balance eqn) with head (h) as the dependent variable Boundary Conditions Initial conditions (for transient problems)

8. Toth Problem Impermeable Rock Groundwater divide Groundwater divide Laplace Equation 2D, steady state

9. Conceptual Model A descriptive representation of a groundwater system that incorporates an interpretation of the geological & hydrological conditions. Generally includes information about the water budget.

10. Types of Solutions of Mathematical Models Analytical Solutions: h= f(x,y,z,t) (example: Theis eqn.) Numerical Solutions Finite difference methods Finite element methods Analytic Element Methods (AEM)

11. Topo-Drive Finite element model of a version of the Toth Problem for regional flow in cross section.

12. Finite difference models may be solved using: a computer programs (e.g., a FORTRAN program) a spreadsheet (e.g., EXCEL)

13. MODFLOW  USGS code  Finite Difference Model MODFLOW 88 MODFLOW 96 MODFLOW 2000

14. Steps in Groundwater Modeling 1. Model Design 2. Calibration (History matching) 3. Prediction (head)