Designs for estimating variability structure and implications for detecting watershed restoration effectiveness

1. Designs for estimating variability structure and implications for detecting watershed restoration effectiveness • David P. Larsen • Western Ecology Division, NHEERL, USEPA • 200 SW 35th St. Corvallis, OR 97333 • N. Scott Urquhart • Department of Statistics • Colorado State University • Ft. Collins, CO 80523

2. Topics • Linear trend detection • Applying the tools to restoration monitoring • Organizing variability • Expanding the linear trend detection model • Variance summary • Trend detection

3. A 2% per Year Linear Trend (each point is a regional mean value) For any patterned trend, there is an underlying linear component. 2% / yr Increase ( Slope = 0 ?)

4. A 2% per Year Linear Trend (each point is a regional mean value) Can we detect a difference is slope between “treated” and “untreated” systems? Treatment Reference

5. Linear trend detection • Hypothesis test: Slope = 0? • Power: If a trend is present, what is the likelihood of detecting it? • Hypothesis: Slope between treated and reference = 0 • Power: likelihood of detecting if different?

6. Linear trend detection • Power depends on: - magnitude of the trend (slope), - variability of our measurements, - number of sites, - the duration of the study (how long we can wait for the information).

7. Variance of a trend slope: How precisely can we estimate it?

8. Organizing Variability • Four major components: • Spatial • Site-to-site • Temporal (year to year) • Year • Site x Year Interaction • Residual

9. ----------Stream Size -----------> . “SITE” VARIANCE: Persistent Site-to-Site Differences due to Different Landscape/Historical Contexts Different Levels of Human Disturbance ------ Gradient -------->

10. Year variation • Concordant year-to-year variation across all sites • Caused by regional phenomena such as: • Wet/Dry years • Ocean conditions • Major volcanic eruptions

11. Interaction variation • Independent year-to-year variation among sites • Driven by local factors

12. Residual variation • The rest of it including: • Temporal or seasonal variation during sampling window • Fine scale spatial variation • Crew-to-crew differences in applying the protocol • Measurement error • …

13. Design framework • Multiple sites with revisits within and among years • Need a sample size of 30-50 to get reasonable estimate of variance, i.e., 30 – 50 sites; 30-50 revisits within year; at least 5 years with some sites visited annually, or at least in pairs of adjacent years.

14. AUGMENTED SERIALLY ALTERNATING SERIALLY ALTERNATING WITH CONSECUTIVE YEAR REVISITS

15. Variance of a trend slope(New sites each year) residual interaction year site Xi = Year ; Ns= Number of sites in region; Nv= Number of within-year revisits (Urquhart and Kincaid. 1999. J. Ag., Biol., and Env. Statistics 4:404-414)

16. residual interaction year Variance of a trend slope(Revisiting the same sites each year) Xi = Year ; Ns= Number of sites in region; Nv= Number of within-year revisits (See Urquhart & Kincaid, 1999)

17. Implications • Effect of site = 0 if sites are revisited across years • Year is not sensitive to “sample size”and its effect can become dominant • Residual is affected by within year revisits • Interaction and residual are affected by number of sites in survey, therefore other factors being equal, better to add sites to the survey rather than revisit sites

20. Some options(after adding sites doesn’t help) • Extend survey interval • Focus on subpopulations to manage variance • Monitor hypothesized covariates controlling “year”

21. Adaptations for Effectiveness Monitoring • Context • Comparing two watersheds

22. Adaptations for Effectiveness Monitoring • Context • Comparing multiple watersheds • Some treated ( ) • Some reference ( )

23. Power to detect a 2% per year “drift” from reference? Indicator Year

24. residual interaction site Variance of the difference in two trend slopes(New sites each Year) Xi = Year ; Ns= Number of sites in each region; Nv= Number of within-year revisits

25. residual interaction Variance of the difference in two trend slopes(Revisiting the same sites Each Year) Xi = Year ; Ns= Number of sites in each region; Nv= Number of within-year revisits

26. Denominator’s effect

27. Variance Summary(Large wood)

28. Design for power curves • Annual visits, # sites varies • Serially alternating design, with annual panel • Variance components values were selected as low and high for Log10(LW+0.1) • Alpha = 0.1

29. POWER YEAR POWER CURVES FOR LOW VALUES OF VARIANCE COMPONENTS

30. POWER YEAR POWER CURVES FOR HIGH VALUES OF VARIANCE COMPONENTS

31. POWER YEAR POWER CURVES FOR HIGH VALUES OF VARIANCE COMPONENTS; AUGMENTED ROTATING PANEL DESIGN

32. Summary • Characterization of spatial and temporal variation • Design framework for estimating components of variation • A framework for evaluating linear trend • How variation affects trend detection • Modifying the framework for evaluating restoration • An example using large wood as an indicator