site class growth and yield models for sitka spruce forest ... · site class growth and yield...

Quantile top‐height age growth model and site classes

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Coford Seminar, UCDCoford Seminar, UCD

Site class growth and yield models

15th December, 2011 15th December, 2011

Samuel Lekwadi, A. Nemesova and M. Mac Siúrtáin

g yfor Sitka spruce forest plantations

in Ireland

FORECAST Project, University College Dublin. Ireland

OutlineOutline

Quantile Top height-age site class growth models for Sitka spruce

New yield class models for Sitka spruce

2

Parameter database

Yield tables

Conclusion

Future Work


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Quantile Top height - Age site class growth modelsfor Sitka spruce forest plantations

in Ireland

3

Forest composition

Sitka Sitka ssprucepruce in Irelandin Ireland

33 tree species in Irish 33 tree species in Irish ForestryForestry

Sitka spr ceSitka spr ce

Introduction

Sitka spruce52%

32 Other

Species 48%

Sitka spruce:Sitka spruce:

Occupies Occupies 52%52% of the of the total forest areatotal forest area

Most Most commerciallycommercially growngrownspecies in Irelandspecies in Ireland

Forest Service (2007) Forest Service (2007)

species in Irelandspecies in Ireland


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55

Forest Site Classification Forest Site Classification

The quantification of forest site productivity potential to produce timber (Farrelly et al., 2007, Phillips, 2009)

Sit l ifi ti i f

Introduction

Site classification is necessary for:

Reliable forecasting of future timber supply

Effective silvicultural and forest management decision-makings

Forest sector industrial development and planning

6

Review of top height – age site class models

British Forestry Commission (FC) hand drawn top height – age curvesusing Imperial units

FC parameterized hand drawn top height age curves using

Introduction

FC parameterized hand drawn top – height age curves using orthogonal polynomials in metric units

Site index guide curve method:Anamorphic site index curves have the same shape Polymorphic site index curves have different shapes

Dynamic yield model for Sitka spruce – GROWFOR(Broad and Lynch, 2008)

Reparameterization of FC top – height age models using the Chapman-Richards function (Nemesova and Mac Siurtain, 2011) for use in a FORECAST parameter database


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7

Objectives:Objectives:

To develop reliable top height-age site class growth models with error structure error structure for the full range of Sitka spruce sitesusing Robust MethodologyRobust Methodologyusing Robust MethodologyRobust Methodology

To provide parameter estimates to FORECAST Project for the forecast of future timber supply in Ireland

Materials and Methods

8


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Data and experimental sites Silvicultural treatments were randomly

assigned to fixed permanent sample plots (PSPs) in each region

Repeated measurements of tree and

Sitka spruceSitka spruce

PSPPSPRepeated measurements of tree and stand variables were recorded from each PSP

Top height (m) and age (years) data were extracted for each PSP in each region

Data pooled to form national Data pooled to form national top height/age dataset

Coillte Coillte Teoranta Teoranta ((Irish Irish ForestForestry Board) ry Board)

10

MethodologyMethodology Site classification

Top height - age were used as a surrogate to classify forest site potential

Top height is: Closely related to cumulative volume production per hectare Independent of stocking density Easy to measure

Introduced Nonlinear Quantile Regression (NLQR) ((Koenker and Bassett, 1978) ForFor Objective forest site classification and growth modelling For For Objective forest site classification and growth modelling

More robust than Nonlinear Least Square (NLS) ((Roger and Hallock, 2001)

No strict distributional assumption about the error term


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Summary statistics of the pooled top height/age data

Variable N Mean Std Dev Min MaxTop height (m) 6043 14.23 8.70 0.20 47.00

Age (year) 6043 22.52 13.11 1.00 64.00

Methodology

Age (year) 6043 22.52 13.11 1.00 64.00

Assumptions:

Better forest site Better forest site will produce higher top height (m) at anygiven age (year) compared to a poorer site poorer site

Growth rate differs on different sites

Site class modelling

By modelling the conditional quantile conditional quantile distribution of the top height (response) given age (covariate)

U i Ch Ri h d li th d l

Methodology

(years) age

(mheight top observed

t =

) y =

where:

(1) + b)tb-e-(1 b=y i32

0 ε

Using Chapman-Richards nonlinear growth model

(Sajjaduzzaman et al., 2005)

12logarithms natural of base

termerror

inflection ofpoint the controlsconstant allometric

maximum its approachesheight top whichat rate

(m)height top attainable maximum asymptotic

(y )g

e =

= ε

= b

= b

= b

i

3

2

0


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13

Nonlinear quantile algorithm minimization

n

By sum of weighted absolute residuals (SWAR) using nlrq function in R

Methodology

1

( ( , ))minn

i i

i

y t

i

where :

τ = conditional quantiles in the interval (0,1)

ρ assigns a weight of τ to positive residuals y- ξ and 1-τ to negative residualsτξ(t ,β) is formulated as nonlinear parameters in (1)

β =parameter space

n =number of observations

All other terms as previously defined.

( ) ( ) ( )[ ]∑n

1=i _i,i+i,i btξ-yτ-1+btξ-yτ=SWAR

14

ResultsResults


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Parameter Estimate 95% CI Std. Error t value Pr(>|t|) Devianceτ = 0.99b0 53.573 (41.372, 65.781) 6.261 8.5571 0.0000 1583.428 Site I

b1 0.028 (0.016, 0.038) 0.006 4.6358 0.0000

b2 1.378 (1.136, 1.620) 0.124 11.1011 0.0000

τ = 0 95

Quantile parameter estimates for five site classes

τ = 0.95

b0 48.531 (44.808, 52.723) 1.909 25.4186 0.0000 4306.231 Site II

b1 0.026 (0.022, 0.030) 0.002 14.7527 0.0000

b2 1.319 (1.259, 1.380) 0.031 42.2163 0.0000

τ = 0.5b0 37.771 (36.457, 39.085) 0.674 56.0683 0.0000 5212.638 Site IIIb1 0.037 (0.035, 0.039) 0.001 28.7939 0.0000

b2 1.630 (1.564, 1.696) 0.034 48.5500 0.0000

τ = 0.12b0 35.739 (34.122, 37.356) 0.829 43.1271 0.0000 3982.713 Site IV

b1 0.039 (0.037, 0.041) 0.001 30.4335 0.0000

b2 1.860 (1.805, 1.915) 0.028 66.7162 0.0000

τ = 0.02b0 25.916 (24.434, 27.398) 0.760 34.1138 0.0000 1260.951 Site Vb1 0.060 (0.054, 0.066) 0.003 22.0277 0.0000

b2 2.660 (2.488, 2.8316) 0.088 30.2784 0.0000

P < 0.05P < 0.05

16

1.3701)0.0244t-e-48.2029(1=y

NLQR (0.5 quantile ) vs NLS (Guide curve) growth models

-0.038t 1.65y=37.393(1-e )

NLS Deviance = 31414

NLS (mean) growth model is influenced by the outliers. NLQR (0.5 quantile) growth model is less influenced by the outliers. NLQR gave the least deviance ( the smaller the better the model)

NLQR Deviance = 5121


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Site class growth models

Predicted top height (m) at 60 years:Predicted top height (m) at 60 years:

Toph (m) and 95% CIsToph (m) and 95% CIs

320

b)tbe(1byˆˆˆˆ -

τ -=

ResultsResults

Toph (m) and 95% CIsToph (m) and 95% CIsSite I (99%) => Site I (99%) => 42.6m ± 2.4%

Site II (95%) => Site II (95%) => 35.3m ± 2.9%

Site III (50%) => Site III (50%) => 30.4m ± 2.8%

Site IV (12%) => Site IV (12%) => 26.5m ± 2.9%

Polymorphic site growth curvesPolymorphic site growth curves

Site V (2%) => Site V (2%) => 21.4m ± 2.1%

18

Model Validation

Models overlaid on toph-age data from Coillte Non Research sites

Models validation using non Research observed top height-age

Data modelled by site classes II - V

20

30

40

Top h

eig

ht (

m)

classes II V

0 10 20 30 40 50 60

010

Age (years)

Quantile site classes

I at 99%II at 95%III at 50%IV at 12%V 2%95%_LL95%_ULBoundries


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Geospatial variability of site productivity in WicklowGeospatial variability of site productivity in Wicklow

40

Site growth curves on the observed top height and age for Wicklow Region

Wicklow Data modelled by site classes 1 – IV

1020

30

Top h

eig

ht (m

)


I at 99%II at 95%III at 50%IV at 12%

Evidence that all site classes in Wicklow are adequately modelled

0 10 20 30 40 50 60

0

Age (years)

V 2%95%_LL95%_ULBoundries

20

Geospatial variability of site productivity in CorkGeospatial variability of site productivity in Cork

40

10

20

30

To

p h

eig

ht (

m)


I at 99%II at 95%III at 50%IV at 12%V 2%

Cork Coillte PSP data are modelled by the site classes I, II, III Evidence that above average site classes in Cork are adequately modelled

0 10 20 30 40 50 60

0

Age (years)

95%_LL95%_ULBoundries


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21

Each site class growth model individually derived from a Chapman-Richards parametric function

NLQR parameter estimates will update the current FORECAST parameterd t b

Conclusions

database

Further work will improve the quantile top height – age site class growthmodels to cover the entire range of Coillte PSP and private top height – age data

The challenge we are facing is the scarcity of reliable privateforest data. We have made contacts with a number of potentialsources for the provision of private sector datap p

22

Yield models for Sitka spruce


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Forest yield models

The forest dynamics and variability as a function of age and site productivity under specified management regimes.

Forest yield models are used for: Routine forest management Forecasting future yields Forest and forest sector planning

24

Materials and Method


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For each region the following data were For each region the following data were extracted:extracted:

Top height (m)A ( )

PSP database supplied by Coillte (Irish Forestry Board) PSP database supplied by Coillte (Irish Forestry Board)

Age (year) Maincrop volume after thinning (V) (m3ha-1)Maincrop basal area after thinning (B) (m2ha-1)Maincrop Diameter after thinning (D) Thinning volume (TV) (m3ha-1)Thinning basal area (TB) (m2ha-1)g ( ) ( )

The extracted data were pooled to form the national PSP modellingdataset

26

Methodology

Yield variables computed:

Cumulative volume production (CVP)

CVPt = Vt +TVt-1 +Vt-2 +......TV0, (m3ha-1)

Cumulative basal area production (CBP)

CBAPt = Bt +TBt-1 +Bt-2 +......TB0 (m2ha-1)

Average growing stock (AGS)

AGSt = Vt + 0.5(TVt) (m3ha-1)


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0 1 2i

(b + b x+b lnx) + εy=e (2)

Yield Modelling

CVP, CBAP, AGS – top height model

i

i

y=e (2)

w here :

y = the com puted yield (C V P , C B A P A G S)

b = regression param eter

x = observed top height (m )

ln = natural log arithmln = natural log arithm

28

Transform predicted site class top height into yield

0 1 τ 2 τ(b + b y + b Iny )Vc = e

where :

C =

τ

i

V quantile estimated yields

y = τ predicted top heights

b = the estimated yield model parameters Eq. (2)

Parameterised yield vs age

- 2 3C 0

The CR function

b t b V = b (1- e ) (4)

Parameterised yield vs age


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Results

30

2.3981lnx)+0.05450x-(0.0946 e=y

CVP- top height model

Positive relationship

0

CVP vs Toph and 95% PI

R

R-square 82%

40

06

00

80

01

00

0

CV

P (

m3

/ha

)

R_square

81.7 %

An indication that top height is a reasonable predictor of CVP

10 15 20 25

20

0

Top height (m)

95%_ULFitted95%_LL


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31

Overlaid transformed CVP-age on observed CVP-age data

00

140

0

Reparameterized CVP vs age

- 2 30

b t bVc = b (1- e ) 20

040

0600

800

1000

120

CV

P (M

3/ha)

Site class

I at 99%II at 95%III at 50%IV t 12%

Transformed CVP - age modelled the observed CVP - age data reasonably well

0 10 20 30 40 50 60

02

Age (Year)

IV at 12%V at 2%Boundaries

32

Yield classes (m3 ha-1a-1)

Yield class = CAI and MAI Intersection

-1 -13c

δ CAI = f(V ) (m ha a )

δt

-1 -1c

3

i

v MAI = (m ha a )

t

Yield classes (m ha a )Site I - 29.6Site II - 27.5Site III - 25.7Site IV - 23.6Site V - 20.8Site VI - 18.3Site VII - 16.220

30

40

CVP CAI and MAI intersection

um

e (m

3/h

a/a)

Site class

I - 99%II - 97%III - 95%IV - 75%V - 50%X - 25%XI - 12%XII - 5%XIII - 2%

Site VIII - 14.4Site IX - 11.9

Site rotation age (year)32 – 48 yearsbest – worst sites0 10 20 30 40 50 60

01

0

Age (year)

Vo

lu

Curves

MAICAI


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33CBAP Models

60

80

10

01

20

14

0

CB

AP

(m

2/h

a)

CBAP vs Toph and 95% CI

R_square

60.87 %

6080

100

120

140

CB

AP

(m

2/h

a)

Quantile CBAP vs Toph and 95% CI

quantile site classes


10 15 20 25 30

20

40

Top height (m)

95%_ULFitted95%_LL

0 5 10 15 20 25 30 35

020

40

Top height (m)

00

120

140

Reparameterized CBAP vs age

4

CBAP CAI and MAI intersection

Site class

I - 99%II - 97%III - 95%IV - 75%

0 10 20 30 40 50 60

020

40

60

80

10

Age (Year)

CB

AP

(m

2/h

a)

Site class

I at 99%II at 95%III at 50%IV at 12%V at 2%Boundaries

0 10 20 30 40 50 60

01

23

Age (year)

Volu

me (m

2/h

a)

V - 50%X - 25%XI - 12%XII - 5%XIII - 2%

34AGS Models

600

800

1000

120

0140

0

AG

S (m

3/ha

)

Quantile AGS vs Toph and 95% PI

quantile site classes


600

800

1000

1200

AG

S (m

3/h

a)

AGS vs Toph and 95% PI

R_square

80.98 %

0 5 10 15 20 25 30 35

020

040

0

Top height (m)

00120

01400

Reparameterized AVGS vs age

25

AVGS CAI and MAI intersection

Site class

I - 99%II - 97%III - 95%IV - 75%V - 50%X - 25%

10 15 20 25 30 35

0200

400

Top height (m)

95%_ULFitted95%_LL

0 10 20 30 40 50 60

020

0400

600

800

100

Age (Year)

AVG

S (M

3/h

a)

Site class

I at 99%II at 95%III at 50%IV at 12%V at 2%Boundaries

0 10 20 30 40 50 60

05

10

1520

Age (year)

Vol

ume (m

3/h

a)

%XI - 12%XII - 5%XIII - 2%

AGS increases with sites classes


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35

0

Maincrop Volume - Toph

Site class

I - 99%II - 95%V - 50%XI - 12%6

00

MC Volume -Toph

R-Square %

85.69

Main crop Volume – Toph model

Other yield variables for Yield Tables

200

40

06

00

Vo

lum

e m

3ha

1

XI 12%XIII - 2%Boundaries

0200

300

400

500

Vo

lum

e m

3ha

1

10 15 20 25

0Toph (m)

10 15 20 25

100

Top height(m)

36

1.5

Main crop Mean volume-Age

Site class

I - 99%II - 95%III - 50%XI - 12%XIII 2%

Main crop Mean Volume

0.5

1.0

Vo

lum

e m

3ha

1

XIII - 2%Boundaries

10 15 20 25

0.0

age(years)


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Volume for No-Thinning stands

38

YC 29. 5 at 30yrs Cumulative YC 29. 5 at 30yrs YC 3.51 at 13yrs YC 22.21 at 45yrs YC 0.92 at 19yrs

Maincrop After Thinning yields from Thinning Production Vol CBA AGS Toph

Age Toph Trees Mean DB BA ±E_BA Mean_Vol Vol ±E_Vol Trees Mean_DBBA ±E_BA Mean_Vol Vol ±E_Vol BA Vol MAI CAI MAI CAI AGS MAI CAI MAI CAI

yrs m m2

m2ha

‐1m

2ha

‐1m

3m

3ha

‐1m

3ha

‐1m

2m

2ha

‐1m

2ha

‐1m

3m

3ha

‐1m

3ha

‐1m

2ha

‐1m

3ha

‐1m

3ha

‐1a‐1m

3ha

‐1a‐1

m2ha

‐1a‐1m

2ha

‐1a‐1

m3ha

‐1m

3ha

‐1a‐1m

3ha

‐1a‐1

ma‐1

ma‐1

10 8.9 2607 10.1 20.7 1.85 0.008 21.5 16.2 2616 12.4 31.4 3.1 0.03 85 11.4 35.0 138.4 13.73 30.82 3.5 3.71 108.48 10.99 19.98 0.89 0.98

11 9.9 2518 10.6 22.2 1.7 0.011 28.2 19.79 2449 12.6 30.7 2.8 0.04 88 10.3 38.7 170.4 15.4 33.35 3.52 3.65 129.24 11.87 21.22 0.9 0.98

12 10.8 2432 11.1 23.7 1.52 0.015 35.8 23.33 2293 12.9 30.1 2.5 0.04 90 9.3 42.3 204.6 16.99 35.47 3.53 3.58 151.21 12.69 22.32 0.9 0.98

13 11 8 2349 11 7 25 1 1 33 0 019 44 5 26 65 2147 13 2 29 5 2 3 0 04 93 8 3 45 9 240 8 18 48 37 19 3 53 3 5 174 24 13 47 23 3 0 91 0 9713 11.8 2349 11.7 25.1 1.33 0.019 44.5 26.65 2147 13.2 29.5 2.3 0.04 93 8.3 45.9 240.8 18.48 37.19 3.53 3.5 174.24 13.47 23.3 0.91 0.97

14 12.8 2269 12.2 26.4 1.12 0.024 54.1 29.61 2010 13.5 28.9 2.0 0.05 95 7.4 49.4 278.5 19.86 38.52 3.52 3.42 198.2 14.2 24.16 0.91 0.96

15 13.7 2192 12.7 27.8 0.9 0.030 64.8 32.08 1882 13.8 28.3 1.8 0.05 97 6.6 52.8 317.3 21.14 39.49 3.51 3.34 222.97 14.89 24.91 0.92 0.96

16 14.7 2117 13.2 29.1 0.67 0.036 76.3 33.94 1762 14.2 27.7 1.6 0.06 99 5.8 56.1 357.0 22.31 40.13 3.5 3.26 248.44 15.54 25.56 0.92 0.95

17 15.6 2045 13.8 30.4 0.43 0.043 88.8 35.13 1650 14.5 27.2 1.4 0.06 101 5.2 59.4 397.1 23.37 40.46 3.48 3.17 274.49 16.15 26.11 0.92 0.94

18 16.6 1976 14.3 31.7 0.18 0.052 102.1 35.61 1545 14.8 26.6 1.2 0.07 102 4.7 62.5 437.5 24.32 40.52 3.46 3.08 301.02 16.71 26.56 0.92 0.93

19 17.5 1908 14.8 33.0 0.08 0.061 116.2 35.38 1446 15.2 26.1 1.0 0.07 104 4.3 65.5 477.8 25.17 40.34 3.44 3 327.96 17.24 26.94 0.92 0.91

20 18.4 1843 15.4 34.2 0.34 0.071 131.0 34.46 1354 15.5 25.6 0.9 0.08 106 4.1 68.5 517.9 25.92 39.95 3.42 2.91 355.2 17.73 27.23 0.92 0.9

21 19.3 1781 15.9 35.4 0.61 0.082 146.4 32.94 1268 15.9 25.1 0.8 0.09 107 4.0 71.3 557.5 26.58 39.37 3.39 2.82 382.68 18.19 27.46 0.92 0.89

22 20.2 1720 16.5 36.6 0.88 0.094 162.5 30.92 1187 16.2 24.6 0.8 0.09 109 4.2 74.1 596.4 27.14 38.64 3.36 2.74 410.32 18.62 27.61 0.92 0.88

23 21 1661 17.0 37.8 1.15 0.108 179.0 28.55 1112 16.6 24.1 0.8 0.10 110 4.5 76.8 634.7 27.62 37.78 3.33 2.65 438.05 19.01 27.71 0.91 0.86

24 21.9 1605 17.6 39.0 1.43 0.122 196.0 26.02 1041 17.0 23.6 0.9 0.11 112 4.9 79.4 672.0 28.03 36.82 3.3 2.57 465.83 19.37 27.75 0.91 0.85

25 22.7 1550 18.2 40.2 1.71 0.138 213.4 23.57 974 17.4 23.1 0.9 0.12 113 5.3 81.9 708.3 28.36 35.77 3.27 2.49 493.59 19.71 27.73 0.91 0.84

26 23.6 1497 18.7 41.3 1.99 0.154 231.1 21.44 912 17.8 22.6 1.1 0.13 114 5.9 84.3 743.6 28.62 34.65 3.24 2.41 521.28 20.02 27.67 0.91 0.82

27 24 4 1446 19 3 42 4 2 27 0 172 248 9 19 91 854 18 2 22 2 1 2 0 14 116 6 5 86 7 777 7 28 82 33 48 3 21 2 33 548 87 20 3 27 56 0 9 0 8127 24.4 1446 19.3 42.4 2.27 0.172 248.9 19.91 854 18.2 22.2 1.2 0.14 116 6.5 86.7 777.7 28.82 33.48 3.21 2.33 548.87 20.3 27.56 0.9 0.81

28 25.2 1397 19.9 43.6 2.55 0.191 267.0 19.15 800 18.6 21.7 1.3 0.15 117 7.1 89.0 810.7 28.97 32.28 3.18 2.25 576.31 20.55 27.42 0.9 0.8

29 26 1349 20.5 44.7 2.84 0.211 285.1 19.16 749 19.0 21.3 1.4 0.16 118 7.7 91.2 842.5 29.06 31.05 3.14 2.18 603.56 20.79 27.24 0.9 0.78

30 26.8 1303 21.2 45.8 3.12 0.233 303.3 19.81 701 19.5 20.9 1.5 0.17 120 8.4 93.3 873.1 29.11 29.81 3.11 2.1 630.6 21 27.02 0.89 0.77

31 27.5 1259 21.8 46.9 3.41 0.255 321.4 20.84 656 19.9 20.4 1.6 0.18 121 9.1 95.3 902.4 29.11 28.58 3.08 2.03 657.4 21.19 26.78 0.89 0.76

32 28.3 1216 22.4 48.0 3.7 0.279 339.5 22.02 615 20.4 20.0 1.7 0.20 122 9.7 97.3 930.5 29.07 27.34 3.04 1.96 683.93 21.36 26.51 0.88 0.74

33 29 1175 23.1 49.0 3.99 0.304 357.4 23.19 575 20.8 19.6 1.8 0.21 123 10.4 99.2 957.4 29 26.13 3.01 1.9 710.16 21.51 26.21 0.88 0.73

34 29.7 1135 23.7 50.1 4.28 0.330 375.0 24.28 539 21.3 19.2 1.9 0.23 124 11.1 101.1 983.0 28.9 24.93 2.98 1.83 736.09 21.65 25.89 0.87 0.72

35 30.4 1096 24.4 51.1 4.57 0.358 392.4 25.3 504 21.8 18.8 2.0 0.25 125 11.7 102.9 1007.5 28.77 23.76 2.94 1.77 761.68 21.76 25.56 0.87 0.7


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Parameter Database

Parameter Database

Model_name Species Model b0 b2 b3 R_sqr N Min(X) Max(X) Min(Y) Max(Y) Deviance GYC

1 NLS_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 50.117 0.021 1.197 ‐ 9731 0.00 59.00 0.00 37.80 60494.486 ‐

2 NLS_TOPH‐Age SS U95%_CI) 53.504 0.023 1.242 ‐ 9731 0.00 59.00 0.00 37.80 60494.486 ‐

3 NLS_TOPH‐Age SS L95%_CI 46.730 0.018 1.152 ‐ 9731 0.00 59.00 0.00 37.80 60494.486 ‐

4 Q99_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 62.917 0.023 1.251 ‐ 9731 0.00 59.00 0.00 37.80 600.824 0.90

5 Q99_TOPH‐Age SS U95%_CI) 75.082 0.016 1.160 ‐ 9731 0.00 59.00 0.00 37.80 600.824 0.90

6 Q99_TOPH‐Age SS L95%_CI 50.751 0.016 1.160 ‐ 9731 0.00 59.00 0.00 37.80 600.824 0.90

7 Q99 TOPH Age SS U95% CI) 75 082 0 016 1 160 9731 0 00 59 00 0 00 37 80 600 824 0 907 Q99_TOPH‐Age SS U95%_CI) 75.082 0.016 1.160 ‐ 9731 0.00 59.00 0.00 37.80 600.824 0.90

8 Q99_TOPH‐Age SS L95%_CI 50.751 0.016 1.160 ‐ 9731 0.00 59.00 0.00 37.80 600.824 0.90

9 Q97_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 60.259 0.023 1.248 ‐ 9731 0.00 59.00 0.00 37.80 1540.716 ‐

10 Q97_TOPH‐Age SS U95%_CI) 70.989 0.016 1.153 ‐ 9731 0.00 59.00 0.00 37.80 1540.716 ‐

11 Q97_TOPH‐Age SS L95%_CI 49.528 0.016 1.153 ‐ 9731 0.00 59.00 0.00 37.80 1540.716 ‐

12 Q97_TOPH‐Age SS U95%_CI) 70.989 0.016 1.153 ‐ 9731 0.00 59.00 0.00 37.80 1540.716 ‐

13 Q97_TOPH‐Age SS L95%_CI 49.528 0.016 1.153 ‐ 9731 0.00 59.00 0.00 37.80 1540.716 ‐


15 Q95_TOPH‐Age SS U95%_CI) 58.765 0.020 1.169 ‐ 9731 0.00 59.00 0.00 37.80 2679.436 0.82

16 Q95_TOPH‐Age SS L95%_CI 46.281 0.020 1.169 ‐ 9731 0.00 59.00 0.00 37.80 2679.436 0.82


18 Q75_TOPH‐Age SS U95%_CI) 57.110 0.019 1.154 ‐ 9731 0.00 59.00 0.00 37.80 7078.961 ‐

19 Q75_TOPH‐Age SS L95%_CI 47.495 0.019 1.154 ‐ 9731 0.00 59.00 0.00 37.80 7078.961 ‐


21 Q50_TOPH‐Age SS U95%_CI) 47.998 0.020 1.137 ‐ 9731 0.00 59.00 0.00 37.80 8843.946 0.70

22 Q51_TOPH‐Age SS L95%_CI 42.337 0.020 1.137 ‐ 9731 0.00 59.00 0.00 37.80 8843.946 0.70

23 Q50 TOPH‐Age SS U95% CI) 47.998 0.020 1.137 ‐ 9731 0.00 59.00 0.00 37.80 8843.946 0.70Q _ g _ )

24 Q51_TOPH‐Age SS L95%_CI 42.337 0.020 1.137 ‐ 9731 0.00 59.00 0.00 37.80 8843.946 0.70


26 Q25_TOPH‐Age SS U95%_CI) 49.532 0.017 1.125 ‐ 9731 0.00 59.00 0.00 37.80 7319.916 ‐

27 Q25_TOPH‐Age SS L95%_CI 40.185 0.017 1.125 ‐ 9731 0.00 59.00 0.00 37.80 7319.916 ‐


29 Q12_TOPH‐Age SS U95%_CI) 39.005 0.026 1.408 ‐ 9731 0.00 59.00 0.00 37.80 4734.130 0.58

30 Q12_TOPH‐Age SS L95%_CI 30.794 0.026 1.408 ‐ 9731 0.00 59.00 0.00 37.80 4734.130 0.58

31 Q12_TOPH‐Age SS U95%_CI) 39.005 0.026 1.408 ‐ 9731 0.00 59.00 0.00 37.80 4734.130 0.58

32 Q12_TOPH‐Age SS L95%_CI 30.794 0.026 1.408 ‐ 9731 0.00 59.00 0.00 37.80 4734.130 0.58


34 Q05_TOPH‐Age SS U95%_CI) 31.132 0.037 1.737 ‐ 9731 0.00 59.00 0.00 37.80 2439.622 ‐

35 Q05_TOPH‐Age SS L95%_CI 27.579 0.037 1.737 ‐ 9731 0.00 59.00 0.00 37.80 2439.622 ‐


37 Q02_TOPH‐Age SS U95%_CI) 29.506 0.038 1.859 ‐ 9731 0.00 59.00 0.00 37.80 1130.981 ‐

38 Q02_TOPH‐Age SS L95%_CI 23.581 0.038 1.859 ‐ 9731 0.00 59.00 0.00 37.80 1130.981 ‐

40

Conclusions

Model parameters will improve the FORECAST parameter databaseparameter database

The model parameters will enable forecast of futureyield

Challenges: Obtaining data from private sector sectorsector


20/12/2011

21

Quantile top-height age growth model and site

classes

41

Developing thinning and spacing specific yield models

Future work

42

AcknowledgementsAcknowledgements

Ted Lynch, Coillte, for providing PSP dataTed Lynch, Coillte, for providing PSP data

COFORD COFORD -- DAFF funding under the DAFF funding under the National Development PlanNational Development Plan

site class growth and yield models for sitka spruce forest ... · site class growth and yield...

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