Topics covered in Hill and Tiedeman, 2007 (covered in class)

1. Topics covered in Hill and Tiedeman, 2007(covered in class) • Transient • Initial conditions • Transient observations • Transient parameters • Transport • Select processes to include • Define source geometry and concentrations • Scale issues • Numerical issues: model accuracy and execution time • Transport observations • Transport parameters • Recalibrating models – see book, p. 227-228

2. Transient: Initial conditions • Use results of a steady-state simulation • Ensures that transient response is the result of imposed transient characteristics • Often possible in ground-water, but not always possible in some fields. For example, atmospheric modeling • Use contoured measurements from a selected time.

3. Transient Observations • Processes behind measures transient response being simulated? • Yes: time-consistent observations • Often need to average high-frequency data for the long-time steps common to gw models • If unrepresented processes produce random errors with a mean of zero, they can be represented through the weighting.

4. Transient Observations: Differencing • As observations, use an initial value and the subsequent changes over time. • Differencing eliminates errors that produce an offset and emphasizes the transient response.

5. Transient Observations: Differencing Initial head Subsequent changes in head

6. Transient Observations: Weighting • Are the errors correlated or independent over time? • If errors are temporally correlated, it may be important to represent this. No one has investigated. • Differencing reduces the error, so results in larger weights on the subsequent changes (for example, the drawdowns)

7. Transport • Concentration observations • Selected articles • Highlights from three of the articles

8. Regression Using Concentration Observations • Often most efficient to first derive likely advective travel from the concentration measurements, and calibrate using a flow advective travel model (for example, MODFLOW and the ADV Package or MODPATH). It is easier to calibrate an advective-dispersive model once simulated flow directions approximate actual flow directions. • Use UCODE_2005, PEST, OSTRICH, etc. The flow and transport can be solved by the same computer program or by different programs. For example, MODFLOW and MT3DMS.

9. Selected Transport Articles • Anderman, Hill, Poeter, 1996, Ground Water. • Example of deriving and using an advective transport observation. Reproduced in the ADV documentation. • Barlebo, Hill, Rosbjerg, Jensen, 1998, Nordic Hydrology. • Example of transport model accuracy given calibration with head data only and with concentrations. • Mehl and Hill, 2001, Ground Water. • Compares the 4 solution methods in MT3D and one programmed by Steffen Mehl. Considers the how differences in the solution methods affect sensitivity analysis and parameter estimation. • Barth and Hill, 2005a,b, Journal of Contaminant Hydrology. • Uses the capabilities of MODFLOW and MT3DMS to represent processes important to viral transport. Investigates sensitivity and correlation of parameters, utility of observations, and effect of nonlinearity. • Tiedeman and Hill, 2006, chapter in Thangarayan (ed.) • Hill and Tiedeman, 2007, chapter 9.

10. From Barlebo +, 1998 Book, fig 15.12, p. 371. Presented as part of guideline 10. Book, fig 15.14, p. 372.

11. Importance of including confidence intervals in the comparison to reasonable values Here, the confidence intervals help show that the problem with an unreasonable estimate obtained using heads only is that the observation data provide inadequate information toward estimating this parameter value. Barlebo +, 1998, Grindsted landfill (Denmark) transport model Presented as part of guideline 10. Book, fig 15.14, p. 372.

12. From Mehl and Hill, 2001

13. Same parameters values. Different numerical methods. From Mehl and Hill, 2001

14. Same parameters values. Different numerical methods. With K parameters estimated From Mehl and Hill, 2001

15. Reactive-Transport Test Case[Barth and Hill, Journal of Contaminant Hydrology, 2005a,b; based on experimental results from Schijven et al., 1999] • Homogeneous. • Processes (to simulate virus transport): • advection • dispersion • sorption (to represent physical-chemical filtration) • reaction mechanisms (to represent virus inactivation)

16. Sensitivity analysis: How much information from all Observations for each Parameter? CSS • Observations • heads, flow, conservative transport moments, and virus transport • Numeric parameter • Transport time-step size CSS = [Sobs(w1/2 (y/b) b )2]1/2 Process parameters • Hydraulic • Conservative transport • Reactive transport

17. Sensitivity analysis: Are Parameter estimates unique? PCC PCC=cov(b1,b2)/[var(b1)1/2var(b2)1/2] COV(b) = s2(XTwX)

18. Different ways of using concentration data • Interpreted advective transport “observations” • Moments of the concentration data. • First moment = advective transport • Second moment=spread of plume • Interpreted time-concentration or space-concentration curves or contours. • Be careful about interpretation! • Concentration measurements scaled by maximum value or source value

19. Catchment zones figure contributed by Ruth Davison and Sascha Oswald

20. Tracing contamination pathways (especially in areas where gradient changes) • Cell size affects path line results Zheng, C., 1994, Analysis of particle tracking errors associated with spatial discretization, Ground Water.

21. Source characterization • There has been recent work on source characterization by, for example, Neupauer and Wilson (WRR) • Trying to estimate source concentrations makes it much harder to develop a transport model