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Published on November 23, 2007

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Examining Clumpiness in FPS:  Examining Clumpiness in FPS David K. Walters Roseburg Forest Products Background:  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. Motivation:  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. Approach - A Computer Simulation:  Approach - A Computer Simulation Using selected values of input variables, we can generate modeled outcomes Choosing Input Variables:  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 Methods of identifying the values for input variables...:  Methods of identifying the values for input variables... Enumeration, consider the model: where only site class and age groups data are available,: ...(continued):  ...(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) Efficiency of LHS:  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) Efficiency of LHS:  Efficiency of LHS Change in the estimate of the population mean Change in the estimate of the population variance Efficiency - summary:  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. ) Back to Clumpiness and FPS:  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 Selecting Values of Input Variables:  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? Clumpiness Variable:  Clumpiness Variable Empirical Distribution - 3033 measured stands Clumpiness, continued:  Clumpiness, continued Empirical Distribution - 1021 DF Stands <80yrs old What does Clumpiness Variable look like?:  What does Clumpiness Variable look like? Only DF>70%, <80yrs old (1021 stands) All Ages and Types (3033 stands) What does Clumpiness Variable look like?:  What does Clumpiness Variable look like? 3003 stands DF, <80yrs (1021 stands) Input Variables:  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 Experiment:  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). Results:  Results How do different clumpiness values affect growth trajectories and final harvest values? Trees Per Acre - SI 65:  Trees Per Acre - SI 65 Trees Per Acre - SI 85:  Trees Per Acre - SI 85 Trees Per Acre - SI 105:  Trees Per Acre - SI 105 Trees Per Acre - SI 125:  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 % Trees Per Acre - SI 145:  Trees Per Acre - SI 145 BF/Acre - SI 65:  BF/Acre - SI 65 BF/Acre - SI 85:  BF/Acre - SI 85 BF/Acre - SI 105:  BF/Acre - SI 105 BF/Acre - SI 125:  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 % BF/Acre - SI 145:  BF/Acre - SI 145 TPA - SI 105, Spacing 11x11:  TPA - SI 105, Spacing 11x11 BA - SI 105, Spacing 11x11:  BA - SI 105, Spacing 11x11 BF/Acre - SI 105, Spacing 11x11:  BF/Acre - SI 105, Spacing 11x11 BF/Acre - SI 105, Spacing 11x11:  BF/Acre - SI 105, Spacing 11x11 Age 50 Volumes:  Age 50 Volumes BF Reduction vs. Clumpiness:  BF Reduction vs. Clumpiness 13x13 11x11 10x10 9x9 What to do?:  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 Summary and Conclusions:  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 Questions?:  Questions?

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