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