1. By Jay M. Ver Hoef Alaska Dept. of Fish and Game 1300 College Road Fairbanks, AK 99701 ffjmv@uaf.edu By Jay M. Ver Hoef Alaska Dept. of Fish and Game 1300 College Road Fairbanks, AK 99701 ffjmv@uaf.edu Some New Spatial Statistical Models for Stream Networks

2. Co-Authors Erin Poston Department of Geosciences, CSU David M. Theobald Natural Resources Ecology Lab, CSU Erin Poston Department of Geosciences, CSU David M. Theobald Natural Resources Ecology Lab, CSU

3. Stream Chemistry Example

4. Curriero, F. C. (1996). The Use of Non-Euclidean Distances in Geostatistics. Ph.D. Dissertation, Kansas State University. Little, L. S., Edwards, D., and Porter, D. E. (1997). Kriging in estuaries: as the crow flies, or as the fish swims? Journal of Experimental Marine Biology and Ecology 213:1-11. Rathbun, S. L. (1998). Spatial Modelling in Irregularly Shaped Regions: Kriging Estuaries. Environmetrics 9:109-129. Gardner, B., Sullivan, P. J., and Lembo, A. J. ( 2003). Predicting stream temperatures: geostatistical model comparision using alternative distance metrics. Canadian Journal of Aquatic Science 60:344-351. Yuan, L. L. (2004). Using Spatial Interpolation to Estimate Stressor Levels in Unsampled Streams. Environmental Monitoring and Assessment 94:23-38. Literature

5. Spatial Linear Model Prediction Estimation

6. Valid Models in 1-D

7. Valid Models for Linear Networks

8. Valid Models for Stream Networks + 1 layer + 2 layers+ 3 layers

9. Moving Average Construction

11. Valid Covariance

12. Moving Averages in 1-D

13. Barry, R.D. and Ver Hoef, J.M. 1996. Blackbox kriging: spatial prediction without specifying the variogram. Journal of Agricultural, Biological, and Environmental Statistics 1: 297 – 322. Ver Hoef, J.M. and R.D. Barry. 1998. Constructing and fitting models for cokriging and multivariable spatial prediction. Journal of Statistical Planning and Inference 69: 275 – 294. Cressie, N. and Ver Hoef, J.M. 2001. Multivariate geostatistics for precision agriculture (with discussion). Bulletin of the International Statistical Institute, Invited Papers Volume 59, Book 1, 407 – 410 Ver Hoef, J.M., N. Cressie, and R.P. Barry. 2003. Flexible Spatial Models for kriging and cokriging using moving averages and the Fast Fourier Transform (FFT). In Press in Journal of Computational and Graphical Statistics. Literature

14. Kriging on Streams Flow

15. Constructing a Valid Covariance Matrix  

16. Flow Matrix Example F 1 2 3 4 5 6 Flow

17. Choosing a Covariance Model Estimation

18. Estimating Fixed Effects Ikaluruk River Flow Estimation

19. Prediction

20. Discontinuity at Nodes Flow

21. Prediction Variances

22. Fish Example

23. Flow Pure Distance Models

24. Predictions