Karen L. Ricciardi

1. The effects of uncertainty on a ground water management problem involving saltwater intrusion Karen L. Ricciardi Ann Mulligan Department of Mathematics University of Massachusetts in Boston Boston, MA, USA Karen.Ricciardi@umb.edu Woods Hole Oceanographic Institution Marine Policy Center Woods Hole, MA, USA amulligan@whoi.edu

2. Objective Determine a groundwater supply plan that: * meets the demands of the community * minimizes the risk of salt water intrusion Difficulties: * hydrologic parameters are uncertain * salt water interface responds nonlinearly to pumping changes  computational effort De

3. Lower CapeofMassachusetts(2004, Masterson)

4. 1 2 3 5 4 6 Truro, MA Pumping in 2004: 1. Knowles(2): 757 m3/d 2. S. Hollow(3/8): 2,158 m3/d 3. N. Truro Air Force Base 4: 312 m3/d 4. N. Truro Air Force Base 5: 312 m3/d 5. N. Unionfield: off 6. CCC-5: off Discharge in Provincetown. Total Supply Needs: 3,540 m3/d

5. Salt water Interface Modeling Using the Ghyben-Herzberg approximation (1:40), the SW interface is determined using the following iterative method. Pumping design Modflow Heads at cells SW interface Convergence criteria met? Yes No Update transmissivity

6. How does uncertainty affect the management of coastal water supply?

7. Uncertainty in Layers 1 and 2 Spatial variability (1992, Hess et al.; SGSIM) Modeler’s uncertainty

8. 1 2 3 5 4 6 Wells OFF (Modeler’s uncertainty) 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0

9. 1 2 3 5 4 6 Wells ON (Modeler’s uncertainty) 95% dryout 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0 0 0 0 1.5 3.0 4.5 6.0 0 1.5 3.0 4.5 6.0

10. [1] Only feasible in 5% of the scenarios

11. Management Model objective constraints

12. Results K1 = 656 m/d; K2 = 246 m/d 757 OFF 2,158  39 312  116 OFF  56 312  356 OFF  2,973

13. Modeler’s Uncertainty mean= 0 std= 0 mean= 43 std= 100 mean= 36 std= 38 Frequency Pumping (m3/d) mean= 518 std= 120 mean= 3 std= 9 mean= 2939 std= 204

14. Modeler’s Uncertainty

15. Modeler’s Uncertainty

16. 1 2 3 5 4 6 Modeler’s UncertaintyCorrelation Coefficients

17. 1 2 3 5 4 6 Modeler’s UncertaintyP-values (< 0.05 is significant)

18. Modeler’s Uncertainty NO UNCERTAINTY Well 1: off Well 2: 39 m3/d Well 3: 116 m3/d Well 4: 356 m3/d Well 5: 56 m3/d Well 6: 2,973 m3/d MEAN VALUES OF MULTIPLE SOLUTIONS Well 1: off Well 2: 43 m3/d Well 3: 36 m3/d Well 4: 518 m3/d Well 5: 3 m3/d Well 6: 2,939 m3/d

19. Risk (50% reliable)

20. Conclusions Uncertainty in the hydraulic conductivity should be considered when developing a management program where salt water intrusion may be an issue. Examining the solutions for the scenarios representing the uncertainty allows one to ascertain information about the correlation between wells. Examining modeler’s uncertainty using a multi-scenario approach provides a means by which it is possible to determine reliable management designs. There are multiple designs that provide reliable solutions to the management problem.

21. Current Work Equivalent solutions of the fixed supply problem Maximum supply problem. Spatial variability affects. Boundary affects: Single boundary problem. Well locations and numbers as a decision variable.

22. Thank you.

23. Truro, MA • 4 layers • 39x85 nodes/layer (2157 active) • Constant head at the oceans • Streams are modeled as drains with conductance = 149 m2/d, head = 0.6 m • MODFLOW 2000: water table on; convertible boundaries • Steady state • Recharge 0.0015 ft/d

24. Truro, Massachusetts

25. Truro, MA Head Results for Layer 1 • Mean head values used • Fixed pumping • SS not reached, no convergence of the iterative method 26 m 18 m 9 m 0 m

26. 1 1 2 2 3 3 5 5 4 4 6 6 Heads at wells when wells are OFF (100 spatially variable fields) Well 1 Well 2 Well 4 Well 3 Well 6 Well 5

27. 1 2 3 5 4 6 Wells ON(Spatially variable fields)

28. [2] Only feasible in 21% of the scenarios.

29. Management Model One perfectly homogeneous K field for each layer. well 1: off well 2: variable q well 3: off well 4: off well 5: variable q well 6: variable q total supply = 3,540 m3/d max head = 0.91 m (not 0.86 m as in the model) well 2: 1,076 m3/d well 6: 2,464 m3/d

30. Management Model Objective function is: • Piecewise linear • Not differentiable • Minimum head varies over different wells in the feasible region well 6 well 2 well 4

31. Management Model Constraints are: • Linear • Variable well dependence well 6 intrusion pumping well 2 intrusion well 1 intrusion

32. Constraints Too much pumping: If q1+q2+…+q5 > 3,540, then set q6 = q1+q2+…+q5+3,540. This will cause the drawdown to be much larger than it would be naturally. Salt water intrusion: If head at welli < 0.86 m then penalize the objective function by 1-eqi/1,000. This will increase the value of the objective function an amount related to the pumping at the well where there is a violation.

33. Pattern Search Solver 1997, Torczon 2003, Kolda and Torczon 2004, Gray and Kolda (APPSPACK)

34. Spatial Variability mean= 0 std= 0 mean= 57 std= 188 mean= 179 std= 130 Frequency Pumping (m3/d) mean= 385 std= 139 mean= 105 std= 165 mean= 2813 std= 419

35. Spatial Variability

36. Spatial VariabilityCorrelation Coefficients

37. 1 2 3 5 4 6 Spatial VariabilityP-values (< 5.0 E -2 is significant)