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

2. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 2 Background n Clumpiness - described as the degree to which the trees on a given acre are dispersed in a less than uniform fashion n 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 3 Motivation n 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). n It is common practice to “assign” a clumpiness index to “new” stands…0.85 is an oft suggested number for DF plantations. n Inherited data may or may not contain the information necessary to compute clumpiness.

4. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 4 Approach - A Computer Simulation n Using selected values of input variables, we can generate modeled outcomes

5. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 5 Choosing Input Variables n 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 6 Methods of identifying the values for input variables... n Enumeration, consider the model: where only site class and age groups data are available,:

7. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 7...(continued) – Enumeration not possible with complex models (e.g., a model requiring 10 continuous input variables means that 3 10 (59,049) cells would be required to generate a very coarse response surface) n 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 8 Efficiency of LHS Example, V=a(Ha/D) b (D 2 H) 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 9 Efficiency of LHS Change in the estimate of the population mean Change in the estimate of the population variance

10. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 10 Efficiency - summary Relative efficiency (SRS to LHS) in estimating population mean is 8.1% (SE SRS = 0.037, SE LHS =0.003) in estimating population variance is 46% (If the methods were equally efficient, the relative efficiency would be 100 percent. )

11. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 11 Back to Clumpiness and FPS n Input Variables – Clumpiness – Site Index – Initial stocking n Output Variables – limit to DF Plantations – TPA, Basal Area, Volume trajectories and harvest values

12. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 12 Selecting Values of Input Variables n Site Index – 65, 85, 105, 125, 145 n Initial Stocking – 9x9 (538), 10x10 (436), 11x11 (360), 13x13 (258) n Clumpiness – what does it look like?

13. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 13 Clumpiness Variable Empirical Distribution - 3033 measured stands

14. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 14 Clumpiness, continued Empirical Distribution - 1021 DF Stands <80yrs old

15. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 15 What does Clumpiness Variable look like? Only DF>70%, <80yrs old (1021 stands) All Ages and Types (3033 stands)

16. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 16 What does Clumpiness Variable look like? 3003 stands DF, <80yrs (1021 stands)

17. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 17 Input Variables n Site Index (5) – 65, 85, 105, 125, 145 n Initial Stocking (4) – 9x9 (538), 10x10 (436), 11x11 (360), 13x13 (258) n Clumpiness (10) – Sample 10 Clumpiness Values between 0.3 and 1.0 using LHS from empirical pdf n 200 combinations

18. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 18 Experiment n Create 10 (clumpiness) x 5 (SI) x 4 (TPA 0 ) or 200 initial starting conditions. Assuming Douglas-fir only. n “Grow” initial tree lists 100 years (only looking at first 60) using FPS, library 11 (Western Oregon Calibration).

19. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 19 Results n How do different clumpiness values affect growth trajectories and final harvest values?

20. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 20 Trees Per Acre - SI 65

21. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 21 Trees Per Acre - SI 85

22. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 22 Trees Per Acre - SI 105

23. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 24 Trees Per Acre - SI 145

25. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 25 BF/Acre - SI 65

26. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 26 BF/Acre - SI 85

27. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 27 BF/Acre - SI 105

28. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 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. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 29 BF/Acre - SI 145

30. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 30 TPA - SI 105, Spacing 11x11

31. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 31 BA - SI 105, Spacing 11x11

32. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 32 BF/Acre - SI 105, Spacing 11x11

33. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 33 BF/Acre - SI 105, Spacing 11x11

34. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 34 Age 50 Volumes

35. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 35 BF Reduction vs. Clumpiness 13x13 11x11 10x10 9x9

36. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 36 What to do? Stepwise Regression with Age, SI, QMD, BA, BF, TPA, %Spp, transformations yielded R 2 approaching 18% Experience Table approach by Type/Size/Density classes may be less problematic

37. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 37 Summary and Conclusions n Clumpiness can have a huge impact on predicted stand and tree characteristics (50% or more volume reduction at rotation) n The effect of changing clumpiness is greater on higher sites. n The effect of changing clumpiness is greater on stands with more TPA n As Age increases, the observed clumpiness value increases (3000 stand sample). In FPS, clumpiness is static (except for re-inventory) n 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. n Clumpiness cannot be predicted well from stand characteristics. Avoid imputing it when possible

38. Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002 38 Questions?