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Christie Staudhammer, Francisco Escobedo, and Luis Fernando Osorio School of Forest Resources and Conservation

Christie Staudhammer, Francisco Escobedo, and Luis Fernando Osorio School of Forest Resources and Conservation . Background. Accurate estimates of tree biomass are important to support research in carbon storage, bioenergy, harvest studies

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Christie Staudhammer, Francisco Escobedo, and Luis Fernando Osorio School of Forest Resources and Conservation

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  1. Christie Staudhammer, Francisco Escobedo, and Luis Fernando Osorio School of Forest Resources and Conservation

  2. Background • Accurate estimates of tree biomass are important to support research in carbon storage, bioenergy, harvest studies • Urban tree biomass is of interest to communities who have generated debris during wind and ice storms or are interested in the supply of green waste from tree maintenance and removal activities

  3. As part of a project to develop a predictive model for urban tree damage and debris related to hurricanes, we wanted to accurately quantifying urban forest biomass in hurricane-prone areas

  4. Background - 2 • Existing data: • Urban tree data from 5 communities across the southeastern US (SEUS) collected under the Urban Forestry Effects (UFORE) model sampling protocol • Post-hurricane sample data describing the state of urban trees subjected to the most severe winds from Hurricanes Rita, Ivan, and Katrina (2005) • Existing biomass equations: • Widely available, but… • Not applicable • Non-urban (i.e., natural forest-grown) trees • Based on trees sampled outside the SEUS • Estimates for some of the most prevalent species varied greaty (e.g., two estimates for Liquidambar styraciflua L. are 1343 tons/ha and 3.3 tons/ha)

  5. Study objectives and methods To better estimate the above-ground biomass of two common urban tree species in the SEUS: Quercus virginiana (live oak); and Quercus laurifolia (laurel oak) We measured 10 trees removed in and around the University of Florida campus and the city of Gainesville, FL Wet total tree weights (sub-samples dried) Randomized branch sampling (RBS) estimates for tree components

  6. Live oak Laurel oak

  7. Preliminary results • RBS substantially over-estimated actual tree weights in most trees • Biomass equations substantially under-estimated tree weights in all trees

  8. Objective of presentation • To investigate the effect of selection probability methodology on RBS bias • To explore the paradigms behind the RBS method which may be problematic for these species

  9. Methods - Data A non-random sample of 6 live oak and 4 laurel oak trees were obtained in and around the UF campus (north central Florida) • Oaks exhibit decurrent crowns, and are refractory species, i.e., they have widely spread crowns, and can endure high temperatures and pressures (Douglas fir is another refractory species) http://cruises.about.com/library/pictures/jekyll/bljekyll024.htm Champion live oak near Gainesville, Fl. Source: www.floridahikes.com

  10. Methods – Data Collection with Randomized Branch Sampling (RBS)

  11. Selection probabilities (qk) based on the pipe model: Using probability a D2, the probability of each choice in path for segment 2: q2=P(20cm segment)=0.138 q2=P(50cm segment)=0.862 Using probability a D2L: q2=P(20cm segment)=0.242 q2=P(50cm segment)=0.758 L=1 m D=20 cm L=0.5 m D=50 cm Note: q1=1.00

  12. For example, to choose segment 2 in path -> use D2 probabilities D q2 Q2 ------------------------------------------------------------------------------------------ 20 0.138 0.138 50 0.862 1.000 -> select a random number ~U[0,1] to choose Qk e.g., 0.54 -> select D=50 path -> Q2= 1.00 * 0.862 =0.862 L=1 m D=20 cm L=0.5 m D=50 cm

  13. Using qka D2: P(10cm segment)=0.11 P(28cm segment)=0.89 Cumulative probability along path: Q3= 0.86 * 0.89 = 0.76

  14. Using qka D2: P(10cm segment)=0.24 P(18cm segment)=0.76 Cumulative probability along path: Q4 = 0.76 * 0.76 = 0.68

  15. Using qka D2: P(6cm segment)=0.26 P(10cm segment)=0.74 Cumulative probability along path: Q5 = 0.68 * 0.74 = 0.56

  16. Q5 = inflation probability = 0.56 If leaves at end of path weigh 5.6 kg, then all leaves in tree weigh 5.6kg/0.56=10kg If branches<5cm at the end of that path weigh 11.2 kg, then all branches in tree<5cm weigh 11.2kg/0.56=20kg Note: example assumes no epicormic branches

  17. To arrive at the bole weight, each segment in the selected path is inflated, so that the path represents the entire tree. However… The weight of the stem is usually calculated by taking a disk, or ‘cookie’ at a selected point along the path using Importance sampling (Valentine, et al 1984).

  18. Imagine that this segment is cut into thin discs of known volume and thickness • We select a disc at random with probability a its volume • The inflated disc volume is then an unbiased estimate of the weight of the whole tree. • How to inflate? Consider the discrete case, where each segment in the selected path is inflated, so that the path represents the entire tree.

  19. Methods – Importance Sampling • Measure the taper along the path • Define a quantity a to the inflated cross-sectional area of the stem at a distance Ls from the butt: A(Ls) = D(Ls)2/Qk where: D(Ls)= Diameter of stem at Ls Qk = inflation probability of segment k • Fit an interpolation function S(L) to the values of A(Ls) using Smalian’s formula • Integrate this function over the length, l, of the path • V(l) will approximate a quantity a to the inflated volume of path

  20. Methods – Importance Sampling (cont’d) • A disc is cut at a random point Θalong the path, selected with probability a to S(L) • This point is found by solving V(Θ)=uV(l) where: u ~ U[0,1] • Determine the weight per unit thickness of the disc: B(Θ) • The inflated weight per unit thickness of disc is: B*(Θ)=B(Θ)/Qk • The estimated woody weight of the tree is then:

  21. Data collection goals • >= 10 trees • 6 paths per tree (two in bottom 1/3rd of tree, two in middle 1/3rd, two in last 1/3rd) • 5 cookies per tree

  22. In theory, our trees are simple… Reality is a…

  23. In reality, we were confronted with an average of 11 segments per path, with each path having 2-8 choices… Did this complication lead to our preliminary results?...

  24. Back to Preliminary Results The problem: We consistently over-estimate the weight of both the leaves and branches, and the stem of the tree The question: What makes urban oak trees so different that path selection probabilities are underestimated?

  25. Methods to accomplish presentation objectives • To investigate the effect of selection probability methodology on RBS bias • Investigate and describe how results vary with selection probability methodology • To explore the paradigms behind the RBS method which may be problematic for these species • Model bias as a function of tree and sample characteristics

  26. Methods & Results- selection probabilities • We investigated several post-hoc probability formulae, computing each Qkas if we had used: • D2 * L, D2, D2.67, D2.67 * L0.5 • RBS weight was computed for tree bole, and for leaves + branches • RBS weights were compared to actual tree weight, with bole weight % computed as a function of dbh (see Jenkins, et al. 2004) • Results • Worst bias with D2 * L • Best bias with D2, D2.67 , but still overestimated > 35%

  27. Path #2 Methods – path selection for disks Path #1 Question: What path (and therefore which selection probabilities) is used to inflate the segments in the interpolation function and obtain bole weight? Issue: When a disk is selected, it often is located along a part of several selected paths The answer to this question is obvious when there is a “main stem”, but not so when many paths appear to be “main”.

  28. Path #2 Path #1 Disk 1 Disk 2 Disk 3 For example: We could use the V(l) indicated by Path #1 or the V(l) indicated by Path #2 for disks 2 and 3. Issue: Which path is the most appropriate for those disks located along several paths, given a decurrent tree form?

  29. Example of bole weights obtained from 5 disks, using 6 paths on one tree Tree Qv-3 Actual bole wt = 1840 kg

  30. Methods – evaluation of path selection for disks and for other tree parts • 10 trees (6-live oak; 4- laurel oak) • 4-6 paths per tree, 2-5 disks per tree • Modeled RBS bias for bole and for leaves + branches • as a function of: • DBH, height of tree, crown area, species • height of disk (absolute and relative), strata (tree divided into thirds) • Explicit correlative structure to account for correlations within tree • NOT a random sample, so inference limited

  31. Results - bole • Significant interaction between strata (where path ended) and relative length associated with location of disk (length along path versus total tree height)

  32. Results – bole (continued) • Significant interaction between strata (where path ended) and tree DBH

  33. Results – leaves, branches, etc. • Significant interaction between tree DBH and relative length associated with the path (length along path versus total tree height)

  34. Discussion - What makes oak trees so different from other species of trees? Tyloses make live oaks wood much different from red oak; however, laurel and live oak did not show different biases Whereas total sapwood in pines is correlated with leaf biomass, in oaks, it is current sapwood In softwoods, specific gravity/wet weight decreases from bottom to top & pith to bark. In oaks, this may not follow - large branches with compression wood cause specific gravity/weight to vary depending of the location of the disk BUTOther forest grown oak species (e.g., red oak; Valentine and Hilton 1977 and Valentine, et al. 1984) were successfully estimated by RBS

  35. Discussion - What makes urban trees so different from forest-grown trees Degree of taper in stem due to pruning? Leaf aggregation due to pruning? Faster growth in stem due to light availability? BUT There are other urban species that are well-estimated by RBS, e.g., cherry and mulberry (Peper and McPherson 1998) Note: many RBS papers in the literature are “light” on methods

  36. Conclusions/opportunities (1 of 3) • Obviously, more investigation is required to make accurate RBS estimates with urban-grown Quercus • Random sample • Wider geographic area • Pruning histories • Results from this study indicate a decision framework for methods of estimating foliage versus bole weight…

  37. Conclusions/opportunities (2 of 3) • Possible decision framework for bole: • Disks should be associated with inflation probabilities of paths ending in the same strata of the tree as where they were cut from. • When trees are smaller (< 25 cm DBH), the best estimates are obtained using paths that end in the first third of the tree, and • When trees are larger (> 40cm DBH), the best estimates are obtained using paths that end in the last third of the tree.

  38. Conclusions/opportunities (3 of 3) • Possible decision framework for leaves/branches: • Paths that are about as long as the trees are tall provide the best estimates of leaf and branch weights, especially when trees are of moderate–large size (>30 cm DBH) • Questions/suggestions?

  39. Acknowledgements USDA Forest Service, Florida Division of Forestry, Wood to Energy (USDA grant) Grad students: Brian Roth, Alicia Lawrence, Ben Thompson Volunteers from UF-SFRC Natural Resources Sampling classes

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