Transcript Individual Tree Growth Models for the Sierra Nevada

The use of climate in individual tree
growth models, an example from the
Sierra Nevada ecoregion
TIMOTHY ROBARDS, PH.D.
UNIVERSITY OF CALIFORNIA, BERKELEY
CAL. DEPT. OF FORESTRY & FIRE PROTECTION,
FIRE & RESOURCE ASSESSMENT PROGRAM
Western Mensurationists Meeting
June 23, 2009
Acknowledgments
2
 Prof. John Battles, UC Berkeley
 Prof. Greg Biging, UC Berkeley
 Prof. Kevin O’Hara, UC Berkeley
 Prof. Peter Berck, UC Berkeley
 Dr. Martin Ritchie, USDA Forest Service, PSW
 Mr. Guido Franco, Cal. Energy Commission
 Dr. Adrian Das, USGS
 Dr. William Stewart, UC Extension
Presentation Outline
3
 Objectives
 Model Structure
 Data
 Modeling
 Results
 Implementation in FVS
 Evaluation
 Projections
 Conclusions
Objectives
4
 Climate-sensitive forest growth simulator
 Accurate projections for adaptation and mitigation research
 Use best available data
 Six species: PP, SP, IC, DF, WF, RF
 Component of bi-annual climate change report
 Evaluate climate change impacts to forest productivity
 Mortality
 FVS modified variant
 Use available add-ons (FFE, pests)
 Take advantage of work already done (volume, imputation)
 Work with LMS or FVS carbon add-on for carbon projects
Forest Growth Models
5
 Forest Yield Models/Empirical (Monserud 2003)

CRYPTOS, CACTOS, FVS, Conifers, PPYMod, PPSIM
 Ecological Gap Models
 Process/Mechanistic Models

Stand-BGC (Milner et al. 2003)
 Ecological Compartment Models

Process model of fluxes
 Vegetation Distribution Models

MC1 (Lenihan et al. 2006), DGVMs: plant functional types
 Hybrid Models

3-PG (Landsberg and Waring 1997), BIOMOVE (Hannah et al. 2009)
“With growing concern over potential climate
change, the most useful models will be sensitive to
key effects of climate change on tree and stand
development over long time periods. This will be
fundamental to addressing questions of
sustainability of forest management.”
(Monserud 2003)
6
Model Forms
7
Nonlinear
CACTOS (Wensel and Robards 1989)
FVS-SORNEC (Dixon 2005)
Linear, Log-Linear
FVS-ICASCA (Dixon 1999)
General Model Structure
8
 PBAL 
E[ln(GR)]  b0  b1ln(dbh)  b2 (dbh)  b3CR  b4 

 ln(dbh+1) 
b5 PRECIP  b6 TEMP  b7SL+b8SL[cos(ASP)] 
b9SL[sin(ASP)]  b10SL  ln(ELEV+1)  
b11SL  ln(ELEV+1)  cos(ASP) 
b12SL  ln(ELEV+1)  sin(ASP)  b13SL  ELEV  
2
b14SL  ELEV  cos(ASP)  b15SL  ELEV  sin(ASP) 
2
2
b16 ELEV  b17 ELEV 2  b18 Albrx  b19 Albry  eik  e
Data
9
 Fit data
Years
No. of
No. of
No. of
No. of
Covered No. of No. of Diameter
Diameter Height
Height
Data Source (approx.) Plots Trees Increments Remeas. Increments Remeas.
NCStem
1965-1980
105 5,465
4,639
0
2,436
0
NCPlot
1961-1998
622 31,807
3,725
39,741
2,991
44,025
DolphMC
1958-1988
397 3,232
4,436
284
1,417
150
DolphRF
1964-1987
254 1,955
3,564
0
1,296
0
 Climate data
 PRISM
 Monthly
 4x4 km grid
 Evaluation data
Modeling
10
 Linear mixed effects model


Random: temporal, spatial
Fixed: everything else
 R statistical software




LME4 library (Bates 2007)
GRID Graphics (Murrell 2006)
Equivalence library (Robinson 2007)
Bakuzis matrix library (modified from Johnson (2007))
 Criteria



AIC
Parameter significance (topography exception)
Residuals
Log Bias Correction
11
 Ratio of the Means (Snowdon 1991)
Species
Diameter
Height
Ponderosa pine
1.163
1.231
Sugar pine
1.093
1.195
Incense-cedar
1.197
1.254
Douglas-fir
1.201
1.216
White fir
1.289
1.194
Red fir
1.087
1.107
Residuals: ponderosa pine example
0.5
0.0
Residuals
1.0
12
10
20
30
40
DBH
50
60
70
Results: Common Variables
13
DBH
THT
PBAL
Index
CR
Latitude
Functional Form
14
Height
DBH
12
15
8
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
Red fir
6
4
Height Growth Multiplier
Diameter Growth Multiplier
10
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
Red fir
10
5
2
20
40
DBH (Inches)
60
80
50
100
Tree Height (feet)
150
200
Crown Ratio
15
Height Growth
Diameter Growth
5
8
6
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
Red fir
4
Height Growth Multiplier
Diameter Growth Multiplier
4
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
Red fir
3
2
2
1
0.0
0.2
0.4
0.6
Crown Ratio
0.8
1.0
0.0
0.2
0.4
0.6
Crown Ratio
0.8
1.0
Competition Index
16
Height Growth
Diameter Growth
1.0
1.0
0.9
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
Red fir
0.6
Height Growth Multiplier
Diameter Growth Multiplier
0.8
0.8
Species
Ponderosa pine
Sugar pine
Incense-cedar
Douglas-fir
White fir
0.7
0.6
0.4
0.5
0.2
0
200
400
Plot Basal Area Larger Scaled by DBH (PBALI)
600
0
200
400
Plot Basal Area Larger Scaled by DBH (PBALI)
600
Latitude
17
Height Growth
Diameter Growth
0.15
Species, Area
Incense-cedar, East of 540
Ponderosa pine, East of 540
Red fir, Statew ide
Sugar pine, Statew ide
White fir, East of 540
5
Height Growth Multiplier
Diameter Growth Multiplier
10
0.10
Species, Area
Incense-cedar, Statewide
Ponderosa pine, East of 540
Red fir, Statewide
Sugar pine, East of 540
White fir, East of 540
0.05
0
4000
4000
4200
4400
UTM-Y
4600
4200
4400
UTM-Y
4600
Results: Climate & Topography
18
Climate
Topography
Winter
Precip
(10/12)
Full
specification
(11/12)
Winter
Temp
(10/12)
WF height
(ELEV)
Many
seasonal
variables
19
Climate
Variables
More precipitation =>
more growth
Degree-day variables
generally better than
straight temperature
2.0
Height Growth Multiplier
Only red fir growth
entirely negative to
temperature increases
2.5
Species, Season, Degree C
Ponderosa pine, w inter, Max 10
Ponderosa pine, spring, Max 5
Ponderosa pine, summer, Max 10
Sugar pine, w inter, Min 10
Sugar pine, spring, Min 5
Incense-cedar, w inter, Min 5
Incense-cedar, spring, Max 5
Douglas-fir, spring, Max 5
Douglas-fir, summer, Min 10
White fir, annual, Max 5
Red fir, w inter, Max 10
1.5
1.0
0.5
0
100
200
Degree Days
Height Growth
300
Slope, Aspect
PP Ht
growth
0
Mid, N
Mid, E
Height Growth Multiplier
20
Topography
0.4
0.3
0.2
Count
4000
6000
DF Diam.
growth
8000
1500
1000
500
0
4000
6000
8000
Slope, Aspect
Elevation
(feet)
0
Mid, N
Mid, E
Mid, S
Mid, W
Steep, N
Steep, E
Steep, S
Steep, W
Diameter Growth Multiplier
12
10
8
6
4
2
2000
Count
Requires high tolerance
for insignificant
parameter estimates
Steep, E
Steep, S
Steep, W
0.1
Stage and Salas (2007)
formulation highly
adaptable
Requires wide range of
data
Mid, S
Mid, W
Steep, N
3000
4000
5000
6000
1000
500
0
2000
3000
4000
Elevation (feet)
5000
6000
Implementation in FVS
21
 Source Code from USDA Forest Service, Forest Management





Service Center, Ft Collins, CO
Lahey-Fujitsu Express ver. 7.1 Fortran Compiler
Additional input file for climate data
Annual time steps, maximum of 80
Height and diameter growth models for 6 species
No changes to outputs
YEAR
1
2
3
4
5
6
7
8
9
PRE_W
10600
12189
12138
8022
13785
8199
10522
4300
11346
PRE_P
5739
2801
1363
3801
2507
5864
3045
2692
4333
PRE_S PRE_WP PRE_PS
7640 16339
6503
11030 14990
3904
4730 13500
1835
0470 11823
3848
9070 16291
3413
2960 14063
6160
2710 13567
3316
2140
6992
2906
8900 15679
5223
MAXT5D
365
365
365
365
365
365
365
365
365
MAXT5D_W
151
151
151
151
151
151
151
151
151
MAXT5D_P
92
92
92
92
92
92
92
92
92
MAXT5D_S
122
122
122
122
122
122
122
122
122
MINT5D_W
31
31
31
31
31
31
Evaluation
22
 Equivalence test using nonparametric bootstrap
regression method (Robinson et al. 2005)



559 diameter, 167 height measurements
± 25%, 100 iterations
Rejected null hypothesis that model and data different
 Model behavior evaluated using modified and
reduced Bakuzis Matrix




Forest Types: PP, MC, DF, WF, RF
10 x 10 spacing to 20 years in Conifers (Ritchie 2008)
PCT and no PCT
Flat ground, NE and SW aspects (30% slope)
Projections to Test Model Behavior
23
Factor
No. of
Classes
Forest Type 5
Density
2
Topography 3
Climate
6
Values of Classes
 Ponderosa pine, elevation of 3,500 feet
 Mixed Conifer, elevation of 4,000 feet
 Douglas-fir, elevation of 4,000 feet
 White fir, elevation of 5,000 feet
 Red fir, elevation of 6,500 feet
 Thinned: each stand will start with a 20 by 20 foot spacing (109 trees
per acre) at age 10.
 Dense: each stand will start with a 10 by 10 foot spacing (436 trees
per acre) at age 0.
 Flat ground
 30% slope, NE aspect
 30% slope, SW aspect
 Average precipitation and temperature from model data
 Hot (average precipitation, 75th percentile of temperature)
 Dry and hot (25th percentile of precipitation, 75th percentile of
temperature)
 Dry and cold (25th percentile of precipitation, 25th percentile of
temperature)
 Wet and hot (75th percentile of precipitation, 75th percentile of
temperature)
 Wet and cold (75th percentile of precipitation, 25th percentile of
temperature)
Douglas-fir, Flat Ground, No PCT
24
height
Climate Curves
Height-Dbh
140
140
120
120
100
100
80
80
60
60
40
40
20
40
60
80
Bakuzis Matrix
Leary's Triangular Form, Reduced
version 2.0
100
5
10
stems
Sukachev Effect
15
20
25
Reineke
400
400
300
300
200
200
100
100
LEGEND
Climate Scenario
20
40
60
80
100
5
10
15
20
Average
DryCold
DryHot
Hot
WetCold
WetHot
25
qmd
volume
Yield Curves
Eichorn's Rule
Yield-Density Effect
15000
15000
15000
10000
10000
10000
5000
5000
5000
0
0
20
40
60
age
80
100
0
40
60
80
100
height
120
140
100
200
stems
300
400
Douglas-fir, SW Aspect, No PCT
25
height
Climate Curves
Height-Dbh
Bakuzis Matrix
150
150
100
100
Leary's Triangular Form, Reduced
50
50
version 2.0
20
40
60
80
100
10
Sukachev Effect
30
40
Reineke
400
stems
20
LEGEND
400
300
300
200
200
100
100
20
40
60
80
Climate Scenario
100
10
20
30
Average
DryCold
DryHot
Hot
WetCold
WetHot
40
qmd
volume
Yield Curves
Eichorn's Rule
Yield-Density Effect
25000
25000
25000
20000
20000
20000
15000
15000
15000
10000
10000
10000
5000
5000
5000
0
0
20
40
60
age
80
100
0
50
100
height
150
100
200
stems
300
400
Projections
26
 100-year projections
 Downscaled climate (Scripps Institute, UCSD)
A2: CO2 850ppm max; self-reliance; population increases
 B1: CO2 550 ppm max; global solutions; population plateaus
 4 GCMs


Elevational transect (Tahoe National Forest)
Mid-Sierra Transect
27
Winter Precipitation, A2, DF Site
28
GFDL
2500
Precipitation (mm)
Precipitation (mm)
CCSM3
2000
1500
1000
500
2500
2000
1500
1000
500
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
1
2
3
4
Decade (1950 - 2090)
5
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
CNRM
PCM1
2500
Precipitation (mm)
Precipitation (mm)
6
2000
1500
1000
500
2500
2000
1500
1000
500
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
Winter Mean Max Temperature, A2, DF Site
CCSM3
18
16
14
12
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Mean Daily Maximum Temperature (C)
Mean Daily Maximum Temperature (C)
29
GFDL
18
16
14
12
1
2
3
4
CNRM
18
16
14
12
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
6
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
Mean Daily Maximum Temperature (C)
Mean Daily Maximum Temperature (C)
Decade (1950 - 2090)
5
PCM1
18
16
14
12
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Decade (1950 - 2090)
Mature Douglas-fir Stand, TNF, A2
30
Total Cubic Foot Volume per Acre
14000
13000
GC Model
12000
PCM1
GFDL
CRM3
CCSM
FVS
FVSAVG
11000
10000
9000
1950
2000
2050
Year
2100
Douglas-fir Plantation, TNF, A2
31
Total Cubic Foot Volume per Acre
8000
6000
GC Model
PCM1
GFDL
CRM3
CCSM
FVS
FVSAVG
4000
2000
0
1950
2000
2050
Year
2100
Forest Type
Policy Period
Measure
PCM1
GFDL
Ponderosa
Pine
A2
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
50-Yr Yield
MAI
10,602
212.04
10,972
219.44
11,471
229.42
10,722
214.44
12,076
241.52
10,993
219.86
6,824
136.48
7,000
140
7,299
145.98
6,846
136.92
7,402
148.04
7,004
140.08
4,358
87.16
4,391
87.82
4,695
93.9
4,342
86.84
5,105
102.1
4,357
87.14
6,074
121.48
6,167
123.34
6,361
127.22
6,004
120.08
6,367
127.34
6,469
129.38
10,712
214.24
11,277
225.54
10,617
212.34
10,712
214.24
12,339
246.78
10,324
206.48
6,863
137.26
7,127
142.54
7,082
141.64
6,863
137.26
7,588
151.76
6,885
137.7
4,290
85.8
4,544
90.88
4,355
87.1
4,290
85.8
5,254
105.08
4,153
83.06
6,351
127.02
6,509
130.18
6,243
124.86
6,351
127.02
6,436
128.72
6,120
122.4
1951-2000
2001-2051
2050-2099
B1
1951-2000
2001-2051
2050-2099
A2
1951-2000
Douglas-fir
2001-2051
2050-2099
B1
1951-2000
2001-2051
2050-2099
Mixed
Conifer
A2
1951-2000
2001-2051
2050-2099
B1
1951-2000
2001-2051
2050-2099
A2
1951-2000
Red Fir
2001-2051
2050-2099
B1
1951-2000
2001-2051
2050-2099
32
CRM3
10,420
208.4
13,024
260.48
12,591
251.82
10,359
207.18
12,525
250.5
12,225
244.5
6,766
135.32
7,674
153.48
7,579
151.58
6,760
135.2
7,451
149.02
7,413
148.26
4,275
85.5
5,452
109.04
5,188
103.76
4,248
84.96
5,144
102.88
4,882
97.64
6,356
127.12
6,504
130.08
6,436
128.72
6,342
126.84
6,599
131.98
6,736
134.72
CCSM
10,633
212.66
10,780
215.6
12,255
245.1
10,655
213.1
10,539
210.78
11,826
236.52
6,804
136.08
7,025
140.5
7,547
150.94
6,808
136.16
7,038
140.76
7,327
146.54
4,308
86.16
4,280
85.6
5,046
100.92
4,314
86.28
4,351
87.02
4,912
98.24
6,339
126.78
6,165
123.3
6,183
123.66
6,346
126.92
6,445
128.9
6,388
127.76
FVS-Avg
5,428
108.56
5,428
108.56
5,428
108.56
5,428
108.56
5,428
108.56
5,428
108.56
4,301
86.02
4,301
86.02
4,301
86.02
4,301
86.02
4,301
86.02
4,301
86.02
2,534
50.68
2,534
50.68
2,534
50.68
2,534
50.68
2,534
50.68
2,534
50.68
5,987
119.74
5,987
119.74
5,987
119.74
5,987
119.74
5,987
119.74
5,987
119.74
FVS
7,390
147.8
7,390
147.8
7,390
147.8
7,390
147.8
7,390
147.8
7,390
147.8
7,252
145.04
7,252
145.04
7,252
145.04
7,252
145.04
7,252
145.04
7,252
145.04
5,490
109.8
5,490
109.8
5,490
109.8
5,490
109.8
5,490
109.8
5,490
109.8
2,263
45.26
2,263
45.26
2,263
45.26
2,263
45.26
2,263
45.26
2,263
45.26
Mean
GCM
Volume
Change
211.8
230.3
8.7%
234.7
10.8%
212.2
237.4
11.9%
226.8
6.9%
136.3
144.1
5.8%
147.5
8.3%
136.4
147.4
8.1%
143.1
5.0%
86.2
93.3
8.3%
96.4
11.9%
86.0
99.3
15.5%
91.5
6.5%
125.6
126.7
0.9%
126.1
0.4%
125.2
129.2
3.2%
128.6
2.7%
Conclusions
33
Work so far
Next steps
 Traditional empirical




models can be
expanded to include
climate & topography
 Feasible to use existing
simulators and data
 Growth impacts may be
positive in future
Incorporate snow
Incorporate soil
Examine interactions
Examine competition,
model form, parsimony
 Coast model?
 FVS/Stand-BGC
simulations?
 Annual/seasonal growth
using increment data from
perm plots?
Questions
34
Tim Robards
[email protected]
916.445.5342
Angora Fire, S. Lake Tahoe, 2007