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Examining Clumpiness in FPS David K. Walters Roseburg Forest Products

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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.

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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.

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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

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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

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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,:

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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)

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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)

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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

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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. )

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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

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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?

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

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

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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)

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

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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

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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).

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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?

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

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

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

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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 %

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

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

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

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

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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 %

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

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

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

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

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

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

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

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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

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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

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

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