Individual Tree Taper, Volume and Weight for Loblolly Pine

1. Individual Tree Taper, Volume and Weightfor Loblolly Pine Bruce E. Borders Western Mensurationists Fortuna, CA June 18-20, 2006

2. Current Models • Compatible total/merchantable tree volume/weight/taper functions • Fitted separately by physiographic region (LCP, UCP, Piedmont) • Large number of sample trees used in fit – however the range of data is limited in stem size (approximately 1500 trees largest DBH = 14” class) • Problems using ratios low on the stem • Implied Taper functions not very realistic (taper function derived from ratio volume equation)

3. Need More Data and Better Models! • Large stumpage value drop for pulpwood in many areas of the South (about 2000) have resulted in more interest in solid wood production • Hence, more users are finding the need to merchandise stems into products that require estimates for stem sections found in the lower stem – current models do not work well

4. Other Data Sources • CAPPS Destructively Sampled Trees • Age 6, 10, 12 years – data will be added to PMRC individual tree database • Wood Quality Consortium Destructively Sampled Trees – 272 trees distributed across southern U.S. • U.S. Forest Service – FIA unit has a relatively large database with volume, weight and taper information available

5. Data Used to Fit Functions - 2005

6. Data Used to Test Functions - 2005 NOTE – all data will be combined for final model fits

7. Existing Model Form Where: V/W = cubic volume or weight to a top dob of Dm inches H = total height (ft); D = dbh (inches) Pienaar, L.V., T.R. Burgan and J.W. Rheney. 1987. Stem volume, taper and weight equations for site-prepared loblolly pine plantations. PMRC Technical Report 1987-1.

8. Existing Model Forms • Simple models – a lot of appeal for ease of use • Models fitted separately by LCP, UCP, Piedmont • Predict cubic volume inside/outside bark • Predict green weight inside/outside bark • Predict dry weight with and without bark

9. Existing Model Forms • These models were developed for use in estimating volume or weight to a given top diameter • However, the model form has limited flexibility in reflecting stem form realistically and it was fitted by Pienaar et al. (1987) with data bases structured to have Dm values of 6” and smaller • Today – users require capability to merchandise stems into various products that may be found anywhere within the stem

12. Existing Model Form • NOTE – the functions did not perform any better when fitted to the new database

13. New Functions – Taper/Volume • Objective – provide two sets of functions • Simple and easy to implement (e.g. a ratio volume/weight equation and associated taper function) – realize that weaknesses will exist – fitted and evaluated model forms suggested by Bailey (1994), Zhang et al. (2002) and Fang et al. (2000) – only present results for Fang (2000) model • Sophisticated and very flexible system that should provide very accurate estimates of stem volume and weight for any stem segment – realize that implementation will require thorough understanding of the functions to be programmed (based on work of Clark, A. III, R.A. Souter and B. Schlaegel. 1991)

14. New Functions - Weight • Weights will be predicted using a per cubic foot density measure (lbs of wood and bark per cubic foot of wood) • Thus, to determine the green weight of wood and bark in any specific stem section we will calculate the cubic foot volume of wood and multiply by lbs of wood and bark per cubic foot of wood • These densities have been studied extensively by Alex Clark and others. Estimates currently available for different regions by age classes.

15. Simple Models • Function flexibility and complexity increase from Bailey (1994), Zhang et al. (2002) to Fang et al. (2000). • Of course, stem shape is complex and therefore it is not surprising the Fang et al. performed best of these three alternatives • Fang, Z., B.E. Borders, and R.L. Bailey. 2000. Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. For. Sci. 46(1)

16. Simple Approach – Alternative 3 • In this work the stem profile was modeled with 3 segments each with its own form factor • The join points of the segments were estimated as parameters • The model was derived to insure that the taper function integrated to a total volume that was consistent with a total stem volume prediction equation that was fitted simultaneously

17. Revised Fang et al. Model • I have revised the model as follows: • First join point is at 4.5 feet • Taper function is constrained to go through DBH • No constraint to insure taper function integrates to a given total volume equation (as in the original paper) • Form factors and upper join point vary with tree dbh and height

18. Revised Fang et al. Model

19. Revised Fang et al. Model

26. Revised Fang Model

27. Revised Fang Model

28. Not So Simple Approach (Because Tree Shapes Are Not So Simple!!)Clark, Souter and Schlaegel 1991Souter and Clark 2001 • Clark, A. III, R.A. Souter and B. Schlaegel. 1991. Stem profile equations for southern tree species. Research Paper SE-282. Asheville, NC. USDA Forest Service, Southeastern For Exp Sta. 113 pp. • Souter, R.A. and A. Clark III. 2001. Taper and volume prediction in southern tree species. USDA For. Serv. Southern Research Station. FIA Work Unit Administrative Report.

29. Souter & Clark Model • Three segment stem profile equation used to define stem shape from ground line to total height – each segment is fitted independently of one another and are constrained to be continuous at the join points of 4.5’ and 17.3’ • The first segment is divided into two sub-segments to allow for more flexibility • The topmost segment is divided into three sub-segments to allow for more flexibility

30. Souter & Clark Model • Function uses dbh, diameter at 17.3’ (Girard form class (GFC) height), and total tree height • Recall GFC = dib @ 17.3’/dbh • Note – functions are provided to predict dbhib from dbh and to predict dob and dib at 17.3 as a function of dbh and total height

34. Souter & Clark Taper Function

37. Souter & Clark Taper FunctionVolume Equation

38. Souter & Clark Taper FunctionVolume Equation

39. Souter & Clark Taper FunctionVolume Equation

40. Souter & Clark Taper FunctionHeight Prediction for Given Top Diameter

41. Souter & Clark Taper FunctionAuxiliary Variable Prediction

42. Souter & Clark Taper FunctionAuxiliary Variable Prediction

43. Souter & Clark Taper FunctionAuxiliary Variable Prediction • To implement – predict dbhib from dbh (eq. 1); predict dib17.3 from dbh (eq. 4); predict dob17.3 from dib17.3 (eq. 3) – do not use eq. 2 or 5. • Any parameters shown in equations above that do not appear in the parameter estimate lists below should be set to 0

44. Weight Density • Clark, A. III, R.F. Daniels and B.E. Borders. 2005. Effect of rotation age and physiographic region on weight per cubic foot of planted loblolly pine. Southern Silvicultural Confernce. Memphis, TN. March 2005.

45. Weight Density • All individual tree weight data from the PMRC, WQC and U.S. Forest Service was used for this work • Loblolly plantations were separated into two regions – Atlantic and Gulf Coastal Plains combined and Piedmont, Upper Coastal Plain and Hilly Coastal Plain (Inland) combined

46. Weight Density

47. Weight Density • Three age classes • 10 to 18 years • 19 to 27 years • > 27 years

48. Weight Density • Green weight of wood and bark per cubic foot of wood – can use in conjunction with inside bark cubic volume functions shown above to obtain estimated weight of wood and bark

49. Weight Density • Coastal Plains – 68.12 lbs wood and bark/cubic foot of wood (66.91 to 69.33) • Inland – 66.61 lbs wood and bark/cubic foot of wood (65.89 to 67.32)

50. Weight Density • Lbs wood and bark/cubic foot of wood