1. Modeling Crown Characteristics of Loblolly Pine Trees Harold E. Burkhart Virginia Tech

2. Outline • Importance of crown measures • Review two studies aimed at modeling loblolly pine crowns • Measurements • Modeling methods • Challenges and opportunities

3. Context Loblolly Pine Plantations Managed for Wood Production

4. Crown characteristics important for: • Making genetic selections • Crown width, branch size and angle • Estimating response to silvicultural treatments • Thinning, fertilizer • Quantifying wood quality • Number, size, location of branches

5. Loblolly pine crowns are highly variable Typically 2-5 whorls per year

6. Most commonly used crown variable crown ratio

7. Plot Measurements • Individual trees • Dbh • Total height • Height to base of crown Stand Age, site index, stand density, etc.

8. Model height to crown base or crown ratio CR = 1 – exp (-()) CR constrained between 0 and 1 () is a function of tree and stand attributes

9. Crown Development From: Liu, et al. 1995. For. Sci. 41:43-53.

10. Thinning Response Modifier I = BAa/BAb From: Liu, et al. 1995. For. Sci. 41:43-53.

11. More Detailed Descriptions of Tree Crowns Approximate with geometric shapes Model crown shape Model crown morphology (branch diameter, location, angle, and length)

12. Efforts to Model Loblolly Pine Crown Morphology Southern Global Change Project 1990s Subsequent work focused on wood quality modeling

13. Development of a Static Model of Loblolly Pine Crowns Southern Global Change Program • Quantify foliage distribution • Model number, size, location of branches • Provide link between G&Y and process model

14. Felled sample trees across a range of stand ages and densities 28 in Virginia Piedmont 40 in North Carolina Coastal Plain

15. Field Measurements Tree Characteristics • DBH and diameter at base live crown • Total height and height to base live crown • Stump age and age at base live crown • Crown class

20. Summary of Measurements Branch Characteristics • Height above ground to each branch • Diameter of each branch • Azimuth of each branch • Total length of the branch • Angle of the branch

21. Detailed measurements on a sample of branches

22. Mapping foliage distribution in X-Y-Z space

23. Foliage divided into inner, middle, and outer thirds

24. Modeling Branches • Total number of branches • Diameter distribution of branches • Vertical location of whorls • Number of branches per whorl • Circular location of branches in each whorl • Branch length • Branch angles

25. Analysis Total Number of Branches Recursive system involving number of whorls and number of branches No. whorls = 3.93 + 0.43 (dbh) + 0.94 (crown length) No. branches = 7.29 + 2.26 (No. whorls)

26. Diameter Distribution of Branches Model average, minimum, and maximum branch diameters as functions of dbh and whorl height Vertical Location of Branches Assumed fixed spacing of whorls

27. Number of Branches in a Whorl Utilize overall percentages and random assignment

28. Total branch length = Total Branch Length Model total branch length as a function of branch diameter

29. Branch Angle Model branch angle from vertical as a function of relative whorl height Branch angle = 64.7 – 28.47 (relative whorl height)2.73

30. Circular Patterns of Branches • Use circular statistics to examine rotational patterns of branches in consecutive whorls • Found for consecutive whorls with the same number of branches, a positive rotation exists

31. Doruska and Burkhart. 1994. CJFR 24:2362-2376.

32. Doruska and Burkhart. 1994. CJFR 24:2362-2376.

33. Foliage Weight and Surface Area Distributions From: Baldwin, et al. (1997) CJFR 27:918-927.

34. PTAEDA2 Growth & Yield Model MAESTRO Process Model Foliage Distribution Used inLinked Model From: Baldwin, et al. (2001) For. Sci. 47:77-82.

35. SI = b1 (log(A2) – log (A1)) + b2 (NPS2 – NPS1) + b3 (1/N2 – 1/N1)

36. Bias Observed Predicted No SI Adjustment SI Increase ft3/ac. m3/ha ft3/ac. m3/ha ft3/ac. m3/ha 4891 342.2 4284 299.8 4875 341.1

37. Dynamic Model of Knot Size, Frequency, and Distribution

38. Sampling of whorls Longitudinal data from a spacing study January 2005 • DBH • TH • Stem height and diameter of every visible whorl 214 whorl sections

39. Ring width Branch dissection Stem dissection technique Recovering information on knot morphology and branch development March-May 2005

40. Results • Vertical trend of branch diameters and location along and around the stem • Model of knot shape • Volume of knots (live/dead portions) • live branches • non-occluded dead branches • occluded dead branches • Branch model linked to growth and yield model (PTAEDA)

41. Model of Live Portion of Knots r = radius at length l R = maximum radius L = total length

42. From: Trincado and Burkhart. (2008) Wood and Fiber Sci. 40:634-646.

43. Branch Model From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

44. Number of Whorls Multicategory logistic regression (h) From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

45. From: Trincado and Burkhart. 2009. Can. J. For. Res. 39:566-579.

46. Location of Whorls No predictive equation possible Used observed relative mean location

47. Number of Branches per Whorl Stochastic procedure using double-truncated Poisson distribution with a,b = minimum and maximum number of branches per whorl observed

48. Branch Orientation around the Stem Adapted methods of Doruska and Burkhart (1994)

49. Angle of Branch Inclination Generated by sampling from a three-parameter Weibull distribution

50. Initial Branch Diameter Assigned from a three-parameter Weibull distribution