1. Mapping Chemical Contaminants in Oceanic Sediments Around Point Loma’s Treated Wastewater Outfall Kerry Ritter Ken Schiff N. Scott Urquhart Dawn Olson Ami Groce Tim Stebbins

2. Overview Motivation Problems with current methods Kriging offers a more sophisticated statistical alternative Provides predictions as well as prediction errors Allows for a cost-efficiency analyses for any sampling density or configuration

3. Maps are useful tools for understanding and managing resources Spatial patterns are recognized more easily with visual displays Can quickly locate disturbance, assess its relative magnitude and extent, and weigh risk to neighboring areas Maps are effective and efficient media for communicating information to the public

4. How do we design the “optimal” sampling grid? Depends on goals of the study Samples closer together tend to be more alike than samples farther apart Placing samples to far apart may make extrapolation to non-sampled locations suspect Placing samples too close together may be redundant and waste resources

5. Current maps Often based on sparse data (< 30 sites) Use simple interpolation methods – Spline smoothing – Triangulation – Linear interpolation Do not provide measures of uncertainty Cannot determine how dense a sampling grid is optimal

6. Core Grid Core Grid + Phase I

7. What is kriging? A statistical tool used to create maps Predictions = weighted average of neighbors Weights based on the strength of spatial correlation Provides estimate of confidence Optimal Available in many mapping or statistical software packages

8. Kriging Predictions (Core + Phase I) Kriging Errors (Core + Phase I)

9. For kriging understanding the spatial variablity is key Determines weighting factors for kriging Provides estimates of kriging errors – Confidence intervals – Cost-efficiency analyses for future studies

10. How do we model spatial variability? Variogram= variance of paired sample differences as a function of distance between pairs Measure of spatial correlation Apply statistical models for fitting variogram – Spherical – Gaussian – Exponential – Linear Use method of least squares to fit parameters

11. 2 km8 km4 km variogram Distance b/t sampling sites Variogram fit for lead (spherical)

12. Variorgram provides estimates of prediction errors that… Do not depend on the data Do not depend on location *Depend only on distance between sites

13. Link variogram to cost efficiency Can determine prediction error for any grid spacing/configuration Can weigh the cost of increasing sampling effort with benefit of precision

14. Percent error v. density Core4km2.5km1km0.5km Percent Core Error Sampling density

15. Kriging Predictions (Core + Phase I) Kriging Errors (Core + Phase I)

16. Summary Kriging offers a more sophisticated statistical alternative for creating maps Provides predictions as well as prediction errors Errors are independent of data, but depend only on distance between sampling sites Modeling the variogram is key Allows for a cost-efficiency analyses for any sampling density or configuration – Uneven allocation of resources, targeted sampling