1. Uncertainty and Non-uniqueness
The calibrated model is always non-unique..

2. Traditional approach Two types of uncertainty analysis
Uncertainty in the calibration. This is
usually called a sensitivity analysis
Uncertainty in the prediction. This is usually
called an uncertainty analysis.

3. Steps in Transport Modeling
Traditional approach
Adjust parameter values
Calibration
sensitivity analysis
Prediction
(Zheng and Bennett)

4. Perform sensitivity analysis during calibration
New Paradigm
Perform sensitivity analysis during calibration
to help find the “best” solution.
Sensitivity coefficients
Assess uncertainty in the prediction during calibration.

5. New Paradigm Multi-model Analysis (MMA) Predictions and sensitivity
analysis are now inside
the calibration loop
From Hill and Tiedeman 2007

6. Case Study: Woburn, Massachusetts
Several equally plausible simulations
of TCE transport were developed based on estimates of
source locations, source concentrations, release times,
and retardation.
It cannot be determined which, if any, of the plausible scenarios
actually represents what occurred in the groundwater flow system
during this period, even though each of the plausible scenarios
closely reproduced measured values of TCE.

7. An example from John Doherty
Cattle Ck.

8. Cattle Creek Catchment

9. Soils and current land use

10. New Development
CANE EXPANSION
CURRENT

11. Model grid; fixed head and drainage cells shown coloured

12. Calibrated transmissivities

13. Modelled and observed water levels after model calibration.
14 different versions of the
conceptual model all showed
high water levels in the area of interest.

14. Monte Carlo
Analysis
Z&B

15. PDF
CDF
Z&B
Fig. 13.1

16. PDF
CDF
Z&B
Fig. 13.2

17. Hydraulic conductivity
Initial concentrations
(plume configuration)
Both
Z&B
Fig. 13.5

18. With inverse flow modeling
Reducing Uncertainty
Hypothetical
example
truth
Hard data only
Soft and hard data
With inverse flow modeling
Z&B
Fig. 13.6

19. “Truth lies at the bottom of a bottomless pit.”
J. Facher, attorney for Beatrice, Woburn Trial
“…knowledge competes with resolution…”
L.N. Hughes, Federal Judge
“One more run…”