Examining Clumpiness in FPS

1. Examining Clumpiness in FPS David K. Walters Roseburg Forest Products

2. Background • Clumpiness - described as the degree to which the trees on a given acre are dispersed in a less than uniform fashion • Example, • TPA estimated at 200, but there is a 0.2 acre hole…with no trees. The clumpiness would be ~80% and the trees would be growing at 200/.80 or 250tpa.

3. Motivation • Intuitively, FPS Clumpiness is a sensible variable in that the spatial orientation of trees should affect growth over time. However, the actual effect of a difference in clumpiness is not clearly known (at least it wasn’t to me). • It is common practice to “assign” a clumpiness index to “new” stands…0.85 is an oft suggested number for DF plantations. • Inherited data may or may not contain the information necessary to compute clumpiness.

4. Approach - A Computer Simulation • Using selected values of input variables, we can generate modeled outcomes

5. Choosing Input Variables • To maximize information about the model (system) response, inputs should? • cover the range of possible values efficiently • begin on the boundary of variable space

6. Methods of identifying the values for input variables... • Enumeration, consider the model: where only site class and age groups data are available,:

7. ...(continued) • Enumeration not possible with complex models • (e.g., a model requiring 10 continuous input variables means that 310 (59,049) cells would be required to generate a very coarse response surface) • Sampling... • simple random sampling (SRS) • stratified sampling (SS) will yield higher precision wrt estimation of response surface) • SS extensions such as Latin Hypercube Sampling (McKay et al., 1979)

8. Efficiency of LHS Example, V=a(Ha/D)b(D2H) where V is individual tree volume above 1.37m, H is tree height (m), and D is tree diameter at breast height (cm). Fitted to SW Oregon Douglas-fir tree data (Hann et al. 1987)

9. Efficiency of LHS Change in the estimate of the population mean Change in the estimate of the population variance

10. Efficiency - summary Relative efficiency (SRS to LHS) in estimating population mean is 8.1% (SESRS = 0.037, SELHS=0.003) in estimating population variance is 46% (If the methods were equally efficient, the relative efficiency would be 100 percent. )

11. Back to Clumpiness and FPS • Input Variables • Clumpiness • Site Index • Initial stocking • Output Variables • limit to DF Plantations • TPA, Basal Area, Volume trajectories and harvest values

12. Selecting Values of Input Variables • Site Index • 65, 85, 105, 125, 145 • Initial Stocking • 9x9 (538), 10x10 (436), 11x11 (360), 13x13 (258) • Clumpiness • what does it look like?

13. Clumpiness Variable Empirical Distribution - 3033 measured stands

14. Clumpiness, continued Empirical Distribution - 1021 DF Stands <80yrs old

15. What does Clumpiness Variable look like? Only DF>70%, <80yrs old (1021 stands) All Ages and Types (3033 stands)

16. What does Clumpiness Variable look like? 3003 stands DF, <80yrs (1021 stands)

17. Input Variables • Site Index (5) • 65, 85, 105, 125, 145 • Initial Stocking (4) • 9x9 (538), 10x10 (436), 11x11 (360), 13x13 (258) • Clumpiness (10) • Sample 10 Clumpiness Values between 0.3 and 1.0 using LHS from empirical pdf • 200 combinations

18. Experiment • Create 10 (clumpiness) x 5 (SI) x 4 (TPA0) or 200 initial starting conditions. Assuming Douglas-fir only. • “Grow” initial tree lists 100 years (only looking at first 60) using FPS, library 11 (Western Oregon Calibration).

19. Results • How do different clumpiness values affect growth trajectories and final harvest values?

20. Trees Per Acre - SI 65

21. Trees Per Acre - SI 85

22. Trees Per Acre - SI 105

23. Trees Per Acre - SI 125 9x9: 61, 81, 96,100,102 % 10x10: 71, 87, 97,100,102 % 11x11: 76, 89, 97,100,102 % 13x13: 83, 92, 98,100,101 %

24. Trees Per Acre - SI 145

25. BF/Acre - SI 65

26. BF/Acre - SI 85

27. BF/Acre - SI 105

28. BF/Acre - SI 125 9x9: 52, 73, 94,100,103 % 10x10: 55, 76, 94,100,103 % 11x11: 61, 79, 94,100,104 % 13x13: 70, 85, 96,100,102 %

29. BF/Acre - SI 145

30. TPA - SI 105, Spacing 11x11

31. BA - SI 105, Spacing 11x11

32. BF/Acre - SI 105, Spacing 11x11

33. BF/Acre - SI 105, Spacing 11x11

34. Age 50 Volumes

35. BF Reduction vs. Clumpiness 13x13 11x11 10x10 9x9

36. What to do? Stepwise Regression with Age, SI, QMD, BA, BF, TPA, %Spp, transformations yielded R2 approaching 18% Experience Table approach by Type/Size/Density classes may be less problematic

37. Summary and Conclusions • Clumpiness can have a huge impact on predicted stand and tree characteristics (50% or more volume reduction at rotation) • The effect of changing clumpiness is greater on higher sites. • The effect of changing clumpiness is greater on stands with more TPA • As Age increases, the observed clumpiness value increases (3000 stand sample). In FPS, clumpiness is static (except for re-inventory) • The effect of lowering clumpiness on volume (tpa,ba, etc.) is not linear. Have a rationale for the choice of clumpiness in young plantations, be careful about using a low number. • Clumpiness cannot be predicted well from stand characteristics. Avoid imputing it when possible

38. Questions?