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Workshop on Applied Statistics in Ecological and Environmental Science
Freiburg, November 7-9, 2012
NW-FVA
Using shape constrained additive
models (SCAM)
to quantify climate and site effects
on forest productivity
Dr. Matthias Albert and Dr. Matthias Schmidt,
Abt. Waldwachstum, NW-FVA
Outline
1. Motivation
2. Comparison first model approach and new method
3. Data base
4. Model formulation
5. Sensitivity analysis and first results
6. Conclusions, challenges and open questions
Forest Growth – Climate Change
change = dynamics = static models have to be replaced
Principle of constant site conditions is not valid anymore even for medium term periods
10 20 30 40 50 60 70 80 90 100
h [m]
hg100[m]
age
25
40
35
30
25
40
35
30
ih1 … ih6
hi
simulation periode 2011 - 2040
1. Motivation 3/16
Developing mitigation and adaptation strategies
site-productivity
relationship = f
climate
change
1. Motivation
?
4/16
Developing mitigation and adaptation strategies
site-productivity
relationship = f
climate
change
1. Motivation
?
4/16
2. First Model Approach
hg100i=1+nutiTβ+f1(tempi)+f2(cwbi)+f3(asmi)+f4(Ndepi)+f5(loni,lati)+i
εi = N(0,σ2)
-GAM, parameterized with nationwide data set
-Climate variables modeled with WETTREG
-Mean values for climate normal period 1961 to 1990
Norway spruce
effect
[m]
temp in GS [°C]
Norway spruce
effect
[m]
cwb in GS [mm]
spruce: R² = 0.44 se = 3.1 m
5/16
library mgcv 1.6-0
R version 2.10.0
2. First Model Approach effect
[m]
temp in GS [°C] effect
[m]
cwb in GS [mm]
Scots pine Scots pine
6/16
2. New Method
Hope for improvement
-measured climate values (DWD data)
-dynamic reference period for each stand: time of establishment to inventory date
-SCAM technology to prevent unplausible effect curves
-logarithmic transformation, i.e. exponential multiplicative combination of explanatory
variables
7/16
library mgcv 1.7-12
R version 2.14.1
library scam 1.1-1
3. Data base
Yield data: - inventory data of National Forest Inventory and Lower Saxony Forest Enterprise Inventory - site index (modeled) (Schmidt, 2008)
Site parameters: - soil nutrients from site mapping (6 classes) - available field capacity (mapped) - nitrogen deposition (modeled)
Climate parameters: temperature, precipitation and evapotranspiration in growing season
-based on measured data at 2336 meteorological stations by German Weather Service -regionalization on 200x200 m scale using WASIM-ETH (Schulla, 1997; Spekat et al., 2006)
-mean values for stand wise reference period
(Alveteg et al., 1997; Ahrends et al., 2007; Gauger et al., 2008)
8/16
for spruce: N=57,096
4. Model Formulation
log(E[hg100i])=1+f1(Tempi)+f2(Arii)+i; E[hg100i]~Gamma
Norway spruce R²=0.42; se=3.2 m
Stage 1
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.0430 0.1312 23.2 <2e-16 ***
Approximate significance of smooth terms:
edf Ref.df F p-value
s(tempsum) 4.903 4.903 974.82 < 2e-16 ***
s(ari) 1.017 1.017 66.16 2.53e-16 ***
Stage 2
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.460414 0.182703 7.993 1.34e-15 ***
nut314 0.027679 0.002772 9.985 < 2e-16 ***
nut321 -0.101653 0.003688 -27.560 < 2e-16 ***
nut322 -0.005868 0.002643 -2.220 0.0264 *
nut323 0.037575 0.002409 15.595 < 2e-16 ***
Approximate significance of smooth terms:
edf Ref.df F p-value
s(ndep) 5.966 5.966 2377.9 <2e-16 ***
s(mod_nFK) 3.938 3.938 154.2 <2e-16 ***
s(lon,lat) 171.837 171.837 141.0 <2e-16 ***
Model stage 1
log(E[hg100i])=1+nutiTβ+ )ˆ)(ˆ
i2i1 (ArifTempf +f3(asm)+f4(Ndepi)
+f5(loni,lati)+i; E[hg100i]~Gamma
Model stage 2
monotone increasing P-splines bs="mpi"
9/16
4. Model Formulation partial effect
temp in GS [°C]
partial effect
ari in GS [mm/°C]
partial effect
asm [mm/C°] Ndep [eq/a/ha]
partial effect
10/16
5. Sensitivity and Results hg100 [m]
temp in GS [°C]
22
20
18
16
14
12
10
aridity index
poor site conditions
hg100 [m]
temp in GS [°C]
good site conditions
2.1
3.0
3.1
4.5
the partial effect of one variable is not constant
with varying other variables;
thus a more dynamic and biologically plausible
model behaviour is possible
11/16
5. Sensitivity and Results
8.7
9.5
5.6
6.2
hg100 [m]
ari in GS [mm/°C]
hg100 [m]
ari in GS [mm/°C]
poor site conditions good site conditions
2500
2300
2100
1900
1700
1500
temp
12/16
5. Sensitivity and Results
Status quo
GAM SCAM
I.5 yield class (and better)
I.5 to II.5 yield class
II.5 yield class (and worse)
13/16
5. Sensitivity and Results
2011 – 2040
GAM SCAM
> 7,5 %
2,5 % to 7,5 %
-2,5 % to 2,5 %
-2,5 % to -7,5 %
< -7,5 %
projection WETTREG2010,
scenario A1B, var05
13/16
5. Sensitivity and Results
2041 - 2070
GAM SCAM
> 7,5 %
2,5 % to 7,5 %
-2,5 % to 2,5 %
-2,5 % to -7,5 %
< -7,5 %
13/16
5. Sensitivity and Results
2071 - 2100
GAM SCAM
> 7,5 %
2,5 % to 7,5 %
-2,5 % to 2,5 %
-2,5 % to -7,5 %
< -7,5 %
13/16
6. Conclusions, challenges, questions
GAM formulation shows more dynamics over time, SCAM indicates servere
change in first period, rather few changes in following predictions
Which behaviour is more realistic, i.e. best represents projected climate change?
Status quo Status quo
temperature aridity
<8
8-10
10-12
12-14
14-16
16-18
18-20
>20
<1800
1800-2000
2000-2200
2200-2400
2400-2600
>2600
14/16
6. Conclusions, challenges, questions
GAM formulation shows more dynamics over time, SCAM indicates servere
change in first period, rather few changes in following predictions
Which behaviour is more realistic, i.e. best represents projected climate change?
temperature
2011 - 2040 2011 - 2040
aridity
<8
8-10
10-12
12-14
14-16
16-18
18-20
>20
<1800
1800-2000
2000-2200
2200-2400
2400-2600
>2600
14/16
6. Conclusions, challenges, questions
GAM formulation shows more dynamics over time, SCAM indicates servere
change in first period, rather few changes in following predictions
Which behaviour is more realistic, i.e. best represents projected climate change?
temperature
2041 - 2070 2041 - 2070
aridity
<8
8-10
10-12
12-14
14-16
16-18
18-20
>20
<1800
1800-2000
2000-2200
2200-2400
2400-2600
>2600
14/16
6. Conclusions, challenges, questions
GAM formulation shows more dynamics over time, SCAM indicates servere
change in first period, rather few changes in following predictions
Which behaviour is more realistic, i.e. best represents projected climate change?
temperature
2071 - 2100 2071 - 2100
aridity
<8
8-10
10-12
12-14
14-16
16-18
18-20
>20
<1800
1800-2000
2000-2200
2200-2400
2400-2600
>2600
14/16
6. Conclusions, challenges, questions
Max = 2695
Min = 10.07
Parameterization data temp
Parameterization data ari
2011 - 2040 2071 - 2100
2011 - 2040 2071 - 2100
15/16
partial effect
temp in GS [°C]
?
6. Conclusions, challenges, questions 16/16
SCAM formulation has a severe extrapolation problem; fit an approximation function
Is there any chance to better discriminate between effects of correlated
predictors?
One conclusion, one challenge …
One question …
Thank you for your attention
Special thanks to: Hermann Spellmann and Jürgen Nagel
Johannes Sutmöller, Robert Nuske and Bernd Ahrends