western mensurationists’ meeting – june 20-22, 2004 – warm springs, or 1 self-referencing...
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Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Self-referencing height versus age curvesSelf-referencing height versus age curves
David M. HyinkDavid M. Hyink
Western/Southern Timberlands ResearchWestern/Southern Timberlands Research
Weyerhaeuser CompanyWeyerhaeuser Company
June 22, 2004June 22, 2004
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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History & Motivation: Self-referencing ht/age curves
Simultaneous estimation of ht/dbh coefficients across multiple re-measurements• Avoid abiological crossings
• Temporally more consistent
• Stand-level attributes
– Dominant height
– Volume per acre
Tree-level attributes• Height and height growth
• “Social position variables”
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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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
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Tree #14: Measured and predicted heights (x dbh)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Annual height increment: Individual trees
Red: M & M Blue: M & P Black: P & P
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Tree-level: Periodic measured heights by dbh
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Tree-level: Periodic measured heights by age
Sample Sizes:
12 41 16 19 22 22 21 20 0 25
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Self-referencing curve form (3-parameter)
A1d ( A0
d R + k )
H1 = (H0 ) ------------------------
A0d ( A1
d R + k )
Where:
R = Z + (Z2 + 2kH0 / A0d )1/2
Z = H0 – a
And:
A0 = Age (years) at H0
H0 = Height @ A0 (feet)
A1 = Age (years) at H1
H1 = Height @ A1 (feet)
a, k & d are parameters
CJFR - 31:165-173 (2001)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Periodic measured and predicted heights
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Methods Comparison: Ht(Dbh) vs. Ht(Age)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Methods Comparison: Ht(Dbh) vs. Ht(Age)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Methods Comparison: Ht(Dbh) vs. Ht(Age)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Methods Comparison: Ht(Dbh) vs. Ht(Age)
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Tree-level: Periodic measured heights by age
Sample Sizes:
12 41 16 19 22 22 21 20 0 25
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Periodic measured and predicted heights (xdbh) by age
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Periodic measured and predicted heights (xage) by age
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Tree-level: Periodic measured heights by dbh
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Periodic measured and predicted heights (xdbh) by dbh
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Periodic measured and predicted heights (xage) by dbh
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Method Comparison: Annual height increment
Red: M & M Blue: M & P Black: P & P
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Method Comparison: Annual height increment
Red: M & M Blue: M & P Black: P & P
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Method Comparison: Annual height increment - DF
Red: M & M Blue: M & P Black: P & P N=828955
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Self-referencing Curves: Strub, et al.
0
10
20
30
40
50
60
70
80
90
0 5 10 15dbh
ht
age 15
age 18
age 21
age 24
age 27
age 30
age 33
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Comparison of Models: Strub, et al.
model SSe R squareCurtis DBH 1534784 93.78Curtis constrained DBH 1630093 93.39self-referencing DBH 1579491 93.60self-referencing Age 668465 97.29
Western Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, ORWestern Mensurationists’ Meeting – June 20-22, 2004 – Warm Springs, OR
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Questions / Comments