1. Two-Phase Sampling Approach for Augmenting Fixed Grid Designs to Improve Local Estimation for Mapping Aquatic Resources Kerry J. Ritter Molly Leecaster N. Scott Urquhart Ken Schiff

2. Project Funding The work reported here was developed under the STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by EPA. The views expressed here are solely those of the presenter and STARMAP, the Program they represent. EPA does not endorse any products or commercial services mentioned in this presentation. Southern Californian Coastal Water Research Project (SSCWRP)

3. Background Maps of sediment condition are important for making decisions regarding pollutant discharge Maps in marine systems are rare Special study by San Diego Municipal Wastewater Treatment Plant Objective : To build statistically defensible maps of chemical constituents and biological indices around two sewage outfalls –Point Loma –South Bay

4. Point Loma and South Bay Outfalls

5. TYPICAL DESIGN SITUATION Many features of the real situation are unknown. –Here: The nature of the semivariogram Multiple Responses –  What is a good solution for one response may not be a good design for another! Time constraint –Answer was required by this past Monday

6. Two-Phase Approach Phase I: Model spatial variability at various spatial scales (eg. Variogram) –This summer Phase II: Use information from Phase I to design survey that meets accuracy requirements –next summer = 2005

7. How Should We Add Sites to Existing Grid in Order to Estimate Variogram? What is best design configuration? More sites with less intensity or fewer sites with more intensity? Shorter sample spacing or larger sample spacing?

8. Variogram } NUGGET=> SILL=> RANGE 

9. Empirical Variograms (Point Loma 2000 Regional Survey)

10. Design Considerations for Modeling the Variogram Sufficient replication at various spatial scales –Variogram model –Parameter estimates Adequate spatial coverage –Stationarity –Isotropy vs. Anisotropy –Strata Allow for multiple responses

11. Choosing the Best Design Case Study: Point Loma Three design configurations –S, STAR, and S with satellites Two sets of lag classes –Shorter vs. larger sample spacing Compare lag distributions Simulation study –Simulate response –Consider different models of spatial variability Compare relative performance of designs for estimating parameters

12. “STAR” and “S” Cluster Designs

13. “S” and “S with Satellites” Design

14. Sample Allocation StarSS with Satellites Grid Stations =12 5 “STAR” Clusters of Size 17 3 grid station 2 sites of interest 1 “S” Cluster of Size 9 11 “S” Clusters of Size 9 5 grid stations 6 sites of interest 8 “S” Clusters of Size 9 8 Satellites added to 3 S” 4 grid stations 4 sites of interest Field duplicates=9Field duplicates=6Field duplicates=8 Total Samples = 12+3*(17-1) +2*(17)+9+9=112 Total Samples = 12+5*(9-1)+6*(9)+6=112 Total Samples = 12+4*(9-1) +6*(9)+6=112

15. “Star” Cluster Design

16. “S” Cluster Design Lag = 0.05, 0.10, 0.20, 0.50Lag = 0.05, 0.25, 1.00, 3.00

17. “S” Cluster with Satellites

18. Omnidirectional Lag Dist. Lag = 0.05, 0.10, 0.20, 0.50 Lag = 0.05, 0.25, 1.00, 3.00

19. Directional Lag Dist Lag = 0.05, 0.10, 0.20, 0.50 { Lag = 0.05, 0.25, 1.00, 3.00 is similar}

20. Simulation Study 3 Grid Enhancements: S, STAR, S with Satellites Two sets of lag classes of size 4 –0.05, 0.10, 0.20, 0.50 (km) –0.05, 0.25, 1, 3 (km) Spherical variogram –Range = 1, 2, 4, 6 –Nugget = 0.00, 0.10 –Sill = 1 1000 sims Fit using automated procedure in Splus –This may have introduced artifacts

21. Percent Difference from Target Range (Median Range) S=1, N= 0.10 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50

22. Percent Difference from Target Sill (Median Sill) S=1, N= 0.10 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50

23. Percent Difference from Target Nugget (Median Nugget) S=1, N= 0.10 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50

24. Summary STAR- performed better than S and S with Satellites for estimating variogram parameters - robust to different lag classes S – lacks sufficient information at short distances for estimating nugget S with Satellites- better than S design for estimating nugget, not as good as STAR Larger lag classes generally did better than shorter lag classes

25. Further Research Choose another variogram model –Exponential Choose another variogram fitting algorithm –REML Simulate anisotropy Investigate robustness to model misspecification Explore other designs

26. END OF PLANNED PRESENTATIONS Questions and suggestions are welcome

27. Note Note that rest of slides show simulation results for N=0, S=1. They will not be included in presentation

28. Percent Difference from Target (Median Range) S=1, N= 0 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50Lag = 0.05, 0.25, 1.00, 3.00

29. Percent Difference From Target (Median Sill) S=1, N=0 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50

30. Difference from Target (Median Nugget) S=1, N= 0 Lag = 0.05, 0.25, 1.00, 3.00Lag = 0.05, 0.10, 0.20, 0.50

31. “S” Cluster Design 12 grid stations12 11 “S” Clusters of Size 9 99-5 = 94 –5 grid stations –6 sites of interest (some old stations, some Bight stations, some new) 6 field duplicates 6 Total samples = 112 112

32. “STAR” Cluster Design 12 grid stations12 5 “STAR” Clusters of Size 16 (17)80 –3 grid stations –2 site of interest (one Bight station, one old station) 2 1 “S” Cluster of Size 8 (9) 9 –new station 9 field duplicates 9 Total samples = 112112

33. “S” Cluster with Satellites 12 grid stations12 8 “S” Clusters of Size 8 (9) –4 grid stations (8) 32 –4 sites of interest (some old stations, some Bight stations, some new) (9) 36 8 Satellites added to 3 Clusters24 8 field duplicates 8 Total samples = 112 112