examining clumpiness in fps david k. walters roseburg forest products

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.


3

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.


4

Approach - A Computer Simulation

Using selected values of input variables, we can generate modeled outcomes


5

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


6

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


7

...(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)


8

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)


9

Efficiency of LHS

Change in the estimate of the population mean

Change in the estimate of the population variance


10

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. )


11

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


12

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?


13

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


14

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


15

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


16

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)


17

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


18

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).


19

Results

How do different clumpiness values affect growth trajectories and final harvest values?


20

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


21


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



22


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



23


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


9x9: 61, 81, 96,100,102 %

10x10: 71, 87, 97,100,102 %

11x11: 76, 89, 97,100,102 %

13x13: 83, 92, 98,100,101 %


24

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


25

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


26


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


27


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


28


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 %


29


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


30

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


31

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


0 20 40 60TOT_AGE

0

100

200

300

400

BA

0.950.90.850.750.65

CLUMP

BA - SI 105, Spacing 11x11


32


0 20 40 60 80 100 120TOT_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, Spacing 11x11


33


0 20 40 60 80 100 120TOT_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, Spacing 11x11


34

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%


35

BF Reduction vs. Clumpiness

13x13

11x1110x10

9x9


36

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


37

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


38

Questions?

examining clumpiness in fps david k. walters roseburg forest products

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