1. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 1 Self-referencing height versus age curves David M. Hyink Western/Southern Timberlands Research Weyerhaeuser Company June 22, 2004

2. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 2 History & Motivation: Self-referencing ht/age curves l Simultaneous estimation of ht/dbh coefficients across multiple re-measurements Avoid abiological crossings Temporally more consistent Stand-level attributes – Dominant height – Volume per acre l Tree-level attributes Height and height growth “Social position variables”

3. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 3 Periodic measured and predicted heights (x dbh) Age N 59 25 52 0 45 20 38 21 35 22 28 22 23 19 17 16 12 41 7 12

4. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 4 Tree #14: Measured and predicted heights (x dbh)

5. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 5 Annual height increment: Individual trees Red: M & MBlue: M & PBlack: P & P

6. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 6 Tree-level: Periodic measured heights by dbh

7. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 7 Tree-level: Periodic measured heights by age Sample Sizes: 12 41 16 19 22 22 21 20 0 25

8. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 8 Self-referencing curve form (3-parameter) A 1 d ( A 0 d R + k ) H 1 = (H 0 ) ------------------------ A 0 d ( A 1 d R + k ) Where: R = Z + (Z 2 + 2kH 0 / A 0 d ) 1/2 Z = H 0 – a And: A 0 = Age (years) at H 0 H 0 = Height @ A 0 (feet) A 1 = Age (years) at H 1 H 1 = Height @ A 1 (feet) a, k & d are parameters CJFR - 31:165-173 (2001)

9. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 9 Periodic measured and predicted heights

10. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 10 Methods Comparison: Ht(Dbh) vs. Ht(Age)

11. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 11 Methods Comparison: Ht(Dbh) vs. Ht(Age)

12. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 12 Methods Comparison: Ht(Dbh) vs. Ht(Age)

13. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 13 Methods Comparison: Ht(Dbh) vs. Ht(Age)

14. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 14 Tree-level: Periodic measured heights by age Sample Sizes: 12 41 16 19 22 22 21 20 0 25

15. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 15 Periodic measured and predicted heights ( x dbh) by age

16. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 16 Periodic measured and predicted heights ( x age) by age

17. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 17 Tree-level: Periodic measured heights by dbh

18. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 18 Periodic measured and predicted heights ( x dbh) by dbh

19. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 19 Periodic measured and predicted heights ( x age) by dbh

20. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 20 Method Comparison: Annual height increment Red: M & MBlue: M & PBlack: P & P

21. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 21 Method Comparison: Annual height increment Red: M & MBlue: M & PBlack: P & P

22. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 22 Method Comparison: Annual height increment - DF Red: M & MBlue: M & PBlack: P & PN=828955

23. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 23 Self-referencing Curves: Strub, et al.

24. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 24 Comparison of Models: Strub, et al.

25. Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR 25 Questions / Comments