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Quantile top‐height age growth model and site classes
20/12/2011
1
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
Quantile top‐height age growth model and site classes
20/12/2011
2
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
Quantile top‐height age growth model and site classes
20/12/2011
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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
Quantile top‐height age growth model and site classes
20/12/2011
4
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
Quantile top‐height age growth model and site classes
20/12/2011
5
9
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
Quantile top‐height age growth model and site classes
20/12/2011
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11
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
Quantile top‐height age growth model and site classes
20/12/2011
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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
Quantile top‐height age growth model and site classes
20/12/2011
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15
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
Quantile top‐height age growth model and site classes
20/12/2011
9
17
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
Quantile top‐height age growth model and site classes
20/12/2011
10
19
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
)
Quantile site classes
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)
Quantile site classes
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
Quantile top‐height age growth model and site classes
20/12/2011
11
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
Quantile top‐height age growth model and site classes
20/12/2011
12
23
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
Quantile top‐height age growth model and site classes
20/12/2011
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25
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)
Quantile top‐height age growth model and site classes
20/12/2011
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27
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
Quantile top‐height age growth model and site classes
20/12/2011
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29
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
Quantile top‐height age growth model and site classes
20/12/2011
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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
Quantile top‐height age growth model and site classes
20/12/2011
17
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
I at 99%II at 95%III at 50%IV at 12%V 2%95%_LL95%_ULBoundries
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
I at 99%II at 95%III at 50%IV at 12%V 2%95%_LL95%_ULBoundries
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
Quantile top‐height age growth model and site classes
20/12/2011
18
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)
Quantile top‐height age growth model and site classes
20/12/2011
19
37
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
Quantile top‐height age growth model and site classes
20/12/2011
20
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 ‐
14 Q95_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 52.523 0.025 1.247 ‐ 9731 0.00 59.00 0.00 37.80 2679.436 0.82
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
17 Q75_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 52.303 0.022 1.202 ‐ 9731 0.00 59.00 0.00 37.80 7078.961 ‐
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 ‐
20 Q50_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 45.167 0.023 1.177 ‐ 9731 0.00 59.00 0.00 37.80 8843.946 0.70
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
25 Q25_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 44.858 0.021 1.183 ‐ 9731 0.00 59.00 0.00 37.80 7319.916 ‐
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 ‐
28 Q12_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 34.900 0.033 1.534 ‐ 9731 0.00 59.00 0.00 37.80 4734.130 0.58
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
33 Q05_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 29.355 0.041 1.837 ‐ 9731 0.00 59.00 0.00 37.80 2439.622 ‐
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 ‐
36 Q02_TOPH‐Age SS Y=b0(1‐exp(‐b2*x)**b3 26.543 0.046 2.070 ‐ 9731 0.00 59.00 0.00 37.80 1130.981 ‐
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
Quantile top‐height age growth model and site classes
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