Examining Clumpiness in FPS
David K. WaltersRoseburg Forest Products
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
2
Background
Clumpiness - described as the degree to which the trees on a given acre are dispersed in a less than uniform fashion
Example,– TPA estimated at 200, but there is a 0.2 acre hole…
with no trees. The clumpiness would be ~80% and the trees would be growing at 200/.80 or 250tpa.
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Motivation
Intuitively, FPS Clumpiness is a sensible variable in that the spatial orientation of trees should affect growth over time. However, the actual effect of a difference in clumpiness is not clearly known (at least it wasn’t to me).
It is common practice to “assign” a clumpiness index to “new” stands…0.85 is an oft suggested number for DF plantations.
Inherited data may or may not contain the information necessary to compute clumpiness.
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Approach - A Computer Simulation
Using selected values of input variables, we can generate modeled outcomes
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Choosing Input Variables
To maximize information about the model (system) response, inputs should?– cover the range of possible values efficiently– begin on the boundary of variable space
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Methods of identifying the values for input variables...
Enumeration, consider the model:
where only site class and age groups data are available,:
B = 0.56 S A e0.8 0.4 -2.2 A-1
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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...(continued)
– Enumeration not possible with complex models (e.g., a model requiring 10 continuous input
variables means that 310 (59,049) cells would be required to generate a very coarse response surface)
Sampling... – simple random sampling (SRS)– stratified sampling (SS) will yield higher precision wrt
estimation of response surface)– SS extensions such as Latin Hypercube Sampling
(McKay et al., 1979)
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Efficiency of LHS
Example,
V=a(Ha/D)b(D2H)
where V is individual tree volume above 1.37m, H is tree height (m), and D is tree diameter at breast height (cm). Fitted to SW Oregon Douglas-fir tree data (Hann et al. 1987)
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Efficiency of LHS
Change in the estimate of the population mean
Change in the estimate of the population variance
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Efficiency - summary
Relative efficiency (SRS to LHS)in estimating population mean is 8.1%
(SESRS = 0.037, SELHS=0.003)
in estimating population variance is 46%
(If the methods were equally efficient, the relative efficiency would be 100 percent. )
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Back to Clumpiness and FPS
Input Variables– Clumpiness– Site Index– Initial stocking
Output Variables– limit to DF Plantations– TPA, Basal Area, Volume trajectories and
harvest values
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Selecting Values of Input Variables
Site Index– 65, 85, 105, 125, 145
Initial Stocking– 9x9 (538), 10x10 (436), 11x11 (360),
13x13 (258) Clumpiness
– what does it look like?
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Clumpiness VariableEmpirical Distribution - 3033 measured stands
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Co
un
t
0.00
0.02
0.04
0.06
0.08
0.10
0.12P
rop
ortio
n p
er B
ar
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Co
un
t
VIVIIIIII
SI_CLASS
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Co
un
t
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Clumpiness, continued
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Co
un
t
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18P
rop
ortio
n p
er B
ar
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Co
un
t
VIVIIIIII
SI_CLASS
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Co
un
t
Empirical Distribution - 1021 DF Stands <80yrs old
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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What does Clumpiness Variable look like?
Only DF>70%, <80yrs old (1021 stands)
All Ages and Types (3033 stands)
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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What does Clumpiness Variable look like?
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Cou
nt
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Proportion per B
ar
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Cou
nt
80+60- 8040- 6020- 400- 20
AGE_CLASS
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
100
200
300
400
Cou
nt
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Cou
nt
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Proportion per B
ar
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Cou
nt
60- 8040- 6020- 400- 20
AGE_CLASS
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0CLUMPINESS
0
50
100
150
200
Cou
nt
3003 stands DF, <80yrs (1021 stands)
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Input Variables
Site Index (5)– 65, 85, 105, 125, 145
Initial Stocking (4)– 9x9 (538), 10x10 (436), 11x11 (360),
13x13 (258) Clumpiness (10)
– Sample 10 Clumpiness Values between 0.3 and 1.0 using LHS from empirical pdf
200 combinations
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Experiment
Create 10 (clumpiness) x 5 (SI) x 4 (TPA0) or 200 initial starting conditions. Assuming Douglas-fir only.
“Grow” initial tree lists 100 years (only looking at first 60) using FPS, library 11 (Western Oregon Calibration).
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Results
How do different clumpiness values affect growth trajectories and final harvest values?
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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TPA vs Age, Site Index 65
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
Trees Per Acre - SI 65
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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TPA vs Age, Site Index 85
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
Trees Per Acre - SI 85
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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TPA vs Age, Site Index 105
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
Trees Per Acre - SI 105
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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TPA vs Age, Site Index 125
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
Trees Per Acre - SI 125
9x9: 61, 81, 96,100,102 %
10x10: 71, 87, 97,100,102 %
11x11: 76, 89, 97,100,102 %
13x13: 83, 92, 98,100,101 %
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Trees Per Acre - SI 145TPA vs Age, Site Index 145
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
200
400
600
ST
EM
S
0.950.90.850.750.65
CLUMP
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 65
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 65
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 85
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 85
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 105
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 105
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 125
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 125
9x9: 52, 73, 94,100,103 %
10x10: 55, 76, 94,100,103 %
11x11: 61, 79, 94,100,104 %
13x13: 70, 85, 96,100,102 %
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 145
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 145
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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TPA vs Age, Site Index 105, Spacing 11x11
0 20 40 60TOT_AGE
0
100
200
300
400
ST
EM
S
0.950.90.850.750.65
CLUMP
TPA - SI 105, Spacing 11x11
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60 80 100 120TOT_AGE
0
100
200
300
400
BA
0.950.90.850.750.65
CLUMP
BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60TOT_AGE
0
100
200
300
400
BA
0.950.90.850.750.65
CLUMP
BA - SI 105, Spacing 11x11
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60 80 100 120TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 105, Spacing 11x11
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60 80 100 120TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BA vs Age, Site Index 105, Spacing 11x11
0 20 40 60TOT_AGE
0
20000
40000
60000
80000
BF
0.950.90.850.750.65
CLUMP
BF/Acre - SI 105, Spacing 11x11
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Age 50 Volumes
Spacing9x9 10x10 11x11 13x13 9x9 10x10 11x11 13x13
Site Index 650.65 7,234 8,949 8,350 6,962 52.1% 76.0% 85.1% 97.8%0.75 11,140 10,681 9,629 7,042 80.2% 90.7% 98.1% 98.9%0.85 12,717 11,714 9,775 7,097 91.5% 99.5% 99.6% 99.7%0.9 13,893 11,775 9,815 7,117 100.0% 100.0% 100.0% 100.0%0.95 14,367 11,817 9,847 7,132 103.4% 100.4% 100.3% 100.2%
Site Index 850.65 14,411 15,196 14,940 12,501 62.4% 71.8% 81.2% 92.5%0.75 18,743 18,387 16,598 13,262 81.1% 86.9% 90.2% 98.1%0.85 22,490 20,081 18,068 13,448 97.3% 94.9% 98.2% 99.5%0.9 23,112 21,157 18,392 13,516 100.0% 100.0% 100.0% 100.0%0.95 23,543 21,828 18,530 13,565 101.9% 103.2% 100.8% 100.4%
Site Index 1050.65 19,011 21,856 22,951 22,765 50.2% 58.8% 68.2% 83.3%0.75 27,081 29,013 28,894 25,350 71.5% 78.1% 85.9% 92.8%0.85 34,097 34,710 32,330 26,795 90.1% 93.4% 96.1% 98.1%0.9 37,859 37,158 33,645 27,322 100.0% 100.0% 100.0% 100.0%0.95 38,880 38,670 34,071 27,780 102.7% 104.1% 101.3% 101.7%
Site Index 1250.65 24,116 27,676 31,574 31,675 51.6% 54.7% 65.6% 71.5%0.75 35,048 37,560 39,101 36,930 75.0% 74.2% 81.2% 83.4%0.85 43,912 47,619 46,141 43,074 94.0% 94.1% 95.9% 97.3%0.9 46,725 50,603 48,130 44,277 100.0% 100.0% 100.0% 100.0%0.95 49,175 52,433 49,888 44,831 105.2% 103.6% 103.7% 101.3%
Site Index 1450.65 26,282 31,093 35,086 40,076 50.1% 54.8% 60.9% 70.8%0.75 37,677 42,602 45,617 48,815 71.9% 75.1% 79.2% 86.2%0.85 49,260 54,013 56,805 54,913 94.0% 95.2% 98.6% 97.0%0.9 52,417 56,721 57,614 56,611 100.0% 100.0% 100.0% 100.0%0.95 54,338 60,254 58,968 58,294 103.7% 106.2% 102.3% 103.0%
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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BF Reduction vs. Clumpiness
13x13
11x1110x10
9x9
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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What to do?
SIZE/STOCKING Clumpyness HIGH HDWD %
SS/NON 0.5 0.45SS/LOW 0.65 0.6SSMED 0.71 0.66SS/HIGH 0.69 0.64POLE/NON 0.61 0.56POLE/LOW 0.62 0.57POLE/MED 0.72 0.67POLE/HIGH 0.78 0.73SAW/NON 0.75 0.7SAW/LOW 0.85 0.8SAW/MED 0.81 0.76SAW/HIGH 0.85 0.8LSAW/NON 0.83 0.78LSAW/LOW 0.87 0.82LSAW/MED 0.87 0.82LSAW/HIGH 0.87 0.82
Stepwise Regression with Age, SI, QMD, BA, BF, TPA, %Spp, transformations yielded R2 approaching 18%
Experience Table approach by Type/Size/Density classes may be less problematic
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
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Summary and Conclusions
Clumpiness can have a huge impact on predicted stand and tree characteristics (50% or more volume reduction at rotation)
The effect of changing clumpiness is greater on higher sites. The effect of changing clumpiness is greater on stands with more TPA As Age increases, the observed clumpiness value increases (3000
stand sample). In FPS, clumpiness is static (except for re-inventory) The effect of lowering clumpiness on volume (tpa,ba, etc.) is not
linear. Have a rationale for the choice of clumpiness in young plantations, be careful about using a low number.
Clumpiness cannot be predicted well from stand characteristics. Avoid imputing it when possible
Examining Clumpiness in FPS, Presented at GMUG on August 29, 2002
38
Questions?