timothy robards, ph.d. university of california, berkeley cal. dept. of forestry & fire...
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TIMOTHY ROBARDS, PH.D.
UNIVERSITY OF CALIFORNIA, BERKELEY
CAL. DEPT. OF FORESTRY & FIRE PROTECTION, FIRE & RESOURCE ASSESSMENT PROGRAM
The use of climate in individual tree growth models, an example
from the Sierra Nevada ecoregion
Western Mensurationists MeetingJune 23, 2009
Acknowledgments
Prof. John Battles, UC BerkeleyProf. Greg Biging, UC BerkeleyProf. Kevin O’Hara, UC BerkeleyProf. Peter Berck, UC BerkeleyDr. Martin Ritchie, USDA Forest Service,
PSWMr. Guido Franco, Cal. Energy CommissionDr. Adrian Das, USGSDr. William Stewart, UC Extension
2
Presentation Outline
ObjectivesModel StructureDataModelingResultsImplementation in FVSEvaluationProjectionsConclusions
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Objectives
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
4
Forest Growth Models
Forest Yield Models/Empirical (Monserud 2003) CRYPTOS, CACTOS, FVS, Conifers, PPYMod, PPSIM
Ecological Gap ModelsProcess/Mechanistic Models
Stand-BGC (Milner et al. 2003)Ecological Compartment Models
Process model of fluxesVegetation Distribution Models
MC1 (Lenihan et al. 2006), DGVMs: plant functional typesHybrid Models
3-PG (Landsberg and Waring 1997), BIOMOVE (Hannah et al. 2009)
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“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)
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Nonlinear Linear, Log-Linear
Model Forms
CACTOS (Wensel and Robards 1989) FVS-ICASCA (Dixon 1999)
FVS-SORNEC (Dixon 2005)
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General Model Structure
0 1 2 3 4
5 6 7 8
9 10
11
2
12 13
2
14
PBAL[ln(GR)] ln(dbh) (dbh) CR
ln(dbh+1)
PRECIP TEMP SL+ SL[cos(ASP)]
SL[sin(ASP)] SL ln(ELEV+1)
SL ln(ELEV+1) cos(ASP)
SL ln(ELEV+1) sin(ASP) SL ELEV
SL ELEV cos(AS
E b b b b b
b b b b
b b
b
b b
b
2
15
216 17 18 19
P) SL ELEV sin(ASP)
ELEV ELEV Albrx Albry ik
b
b b b b e e
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Data
Fit data
Climate data PRISM Monthly 4x4 km grid
Evaluation data
Data Source
Years Covered (approx.)
No. of Plots
No. of Trees
No. of Diameter Increments
No. of Diameter Remeas.
No. of Height Increments
No. of Height Remeas.
NCStem 1965-1980 105 5,465 4,639 0 2,436 0NCPlot 1961-1998 622 31,807 3,725 39,741 2,991 44,025DolphMC 1958-1988 397 3,232 4,436 284 1,417 150DolphRF 1964-1987 254 1,955 3,564 0 1,296 0
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Modeling
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
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Log Bias Correction
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
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Residuals: ponderosa pine example
10 20 30 40 50 60 70
0.0
0.5
1.0
DBH
Re
sid
ua
ls
12
Results: Common Variables
DBH THT
CR PBAL Index
Latitude
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DBH Height
Functional Form14
DBH (Inches)
Dia
me
ter
Gro
wth
Mu
ltip
lier
2
4
6
8
10
12
20 40 60 80
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-firWhite f irRed fir
Tree Height (feet)
He
igh
t Gro
wth
Mu
ltip
lier
5
10
15
50 100 150 200
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite f irRed f ir
Diameter Growth Height Growth
Crown Ratio
Crown Ratio
Dia
met
er G
row
th M
ultip
lier
2
4
6
8
0.0 0.2 0.4 0.6 0.8 1.0
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite f irRed f ir
Crown Ratio
Hei
ght G
row
th M
ultip
lier
1
2
3
4
5
0.0 0.2 0.4 0.6 0.8 1.0
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite f irRed f ir
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Diameter Growth Height Growth
Competition Index
Plot Basal Area Larger Scaled by DBH (PBALI)
Dia
met
er G
row
th M
ultip
lier
0.2
0.4
0.6
0.8
1.0
0 200 400 600
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite f irRed f ir
Plot Basal Area Larger Scaled by DBH (PBALI)
Hei
ght G
row
th M
ultip
lier
0.5
0.6
0.7
0.8
0.9
1.0
0 200 400 600
SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite f ir
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Diameter Growth Height Growth
Latitude17
UTM-Y
Dia
me
ter
Gro
wth
Mu
ltip
lier
0
5
10
4000 4200 4400 4600
Species, AreaIncense-cedar, East of 540Ponderosa pine, East of 540Red fir, Statew ideSugar pine, Statew ideWhite f ir, East of 540
UTM-Y
He
ight
Gro
wth
Mu
ltipl
ier
0.05
0.10
0.15
4000 4200 4400 4600
Species, AreaIncense-cedar, StatewidePonderosa pine, East of 540Red fir, StatewideSugar pine, East of 540White fir, East of 540
Results: Climate & Topography
Winter Precip (10/12)
Winter Temp (10/12)
Many seasonal variables
Climate
Full specification (11/12)
WF height (ELEV)
Topography
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Climate Variables
Only red fir growth entirely negative to temperature increases
More precipitation => more growth
Degree-day variables generally better than straight temperature
Degree Days
He
igh
t Gro
wth
Mu
ltip
lier
0.5
1.0
1.5
2.0
2.5
0 100 200 300
Species, Season, Degree CPonderosa pine, w inter, Max 10Ponderosa pine, spring, Max 5Ponderosa pine, summer, Max 10Sugar pine, w inter, Min 10Sugar pine, spring, Min 5Incense-cedar, w inter, Min 5Incense-cedar, spring, Max 5Douglas-fir, spring, Max 5Douglas-fir, summer, Min 10White f ir, annual, Max 5Red fir, w inter, Max 10
Height Growth
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Topography
Stage and Salas (2007) formulation highly adaptable
Requires wide range of data
Requires high tolerance for insignificant parameter estimates
PP Htgrowth
DF Diam.growth
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He
igh
t Gro
wth
Mu
ltip
lier
0.1
0.2
0.3
0.4
4000 6000 8000
Slope, Aspect0Mid, NMid, E
Mid, SMid, WSteep, N
Steep, ESteep, SSteep, W
Elevation (feet)
Co
un
t
0500
10001500
4000 6000 8000
Dia
me
ter
Gro
wth
Mu
ltip
lier
2
4
6
8
10
12
2000 3000 4000 5000 6000
Slope, Aspect0Mid, NMid, E
Mid, SMid, WSteep, N
Steep, ESteep, SSteep, W
Elevation (feet)
Co
un
t
0
500
1000
2000 3000 4000 5000 6000
Implementation in FVS
Source Code from USDA Forest Service, Forest Management Service Center, Ft Collins, CO
Lahey-Fujitsu Express ver. 7.1 Fortran CompilerAdditional input file for climate dataAnnual time steps, maximum of 80Height and diameter growth models for 6 speciesNo changes to outputsYEAR PRE_W PRE_P PRE_S PRE_WP PRE_PS MAXT5D MAXT5D_W MAXT5D_P MAXT5D_S MINT5D_W 1 10600 5739 7640 16339 6503 365 151 92 122 31 2 12189 2801 11030 14990 3904 365 151 92 122 3 12138 1363 4730 13500 1835 365 151 92 122 4 8022 3801 0470 11823 3848 365 151 92 122 31 5 13785 2507 9070 16291 3413 365 151 92 122 31 6 8199 5864 2960 14063 6160 365 151 92 122 31 7 10522 3045 2710 13567 3316 365 151 92 122 31 8 4300 2692 2140 6992 2906 365 151 92 122 9 11346 4333 8900 15679 5223 365 151 92 122 31
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Evaluation
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)
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Projections to Test Model Behavior
Factor No. of Classes
Values of Classes
Forest Type 5 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
Density 2 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.
Topography 3 Flat ground 30% slope, NE aspect 30% slope, SW aspect
Climate 6 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)
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Douglas-fir, Flat Ground, No PCTh
eig
ht
40
60
80
100
120
140
20 40 60 80 100
Climate Curves
40
60
80
100
120
140
5 10 15 20 25
Height-Dbh
ste
ms
100
200
300
400
20 40 60 80 100
Sukachev Effect
qmd
100
200
300
400
5 10 15 20 25
Reineke
age
volu
me
0
5000
10000
15000
20 40 60 80 100
Yield Curves
height
0
5000
10000
15000
40 60 80 100 120 140
Eichorn's Rule
stems
0
5000
10000
15000
100 200 300 400
Yield-Density Effect
Bakuzis Matrix
Leary's Triangular Form, Reduced
version 2.0
LEGENDClimate Scenario
AverageDryColdDryHot
HotWetColdWetHot
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Douglas-fir, SW Aspect, No PCTh
eig
ht
50
100
150
20 40 60 80 100
Climate Curves
50
100
150
10 20 30 40
Height-Dbh
ste
ms
100
200
300
400
20 40 60 80 100
Sukachev Effect
qmd
100
200
300
400
10 20 30 40
Reineke
age
volu
me
0
5000
10000
15000
20000
25000
20 40 60 80 100
Yield Curves
height
0
5000
10000
15000
20000
25000
50 100 150
Eichorn's Rule
stems
0
5000
10000
15000
20000
25000
100 200 300 400
Yield-Density Effect
Bakuzis Matrix
Leary's Triangular Form, Reduced
version 2.0
LEGENDClimate Scenario
AverageDryColdDryHot
HotWetColdWetHot
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Projections
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)
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Mid-Sierra Transect27
Winter Precipitation, A2, DF Site
CCSM3
Decade (1950 - 2090)
Pre
cip
itatio
n (
mm
)
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
CNRM
Decade (1950 - 2090)
Pre
cip
itatio
n (
mm
)
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
GFDL
Decade (1950 - 2090)
Pre
cip
itatio
n (
mm
)
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
PCM1
Decade (1950 - 2090)
Pre
cip
itatio
n (
mm
)
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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Winter Mean Max Temperature, A2, DF Site
CCSM3
Decade (1950 - 2090)
Me
an
Da
ily M
axi
mu
m T
em
pe
ratu
re (
C)
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
CNRM
Decade (1950 - 2090)
Me
an
Da
ily M
axi
mu
m T
em
pe
ratu
re (
C)
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
GFDL
Decade (1950 - 2090)
Me
an
Da
ily M
axi
mu
m T
em
pe
ratu
re (
C)
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
PCM1
Decade (1950 - 2090)
Me
an
Da
ily M
axi
mu
m T
em
pe
ratu
re (
C)
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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Mature Douglas-fir Stand, TNF, A2
Year
To
tal C
ub
ic F
oo
t Vo
lum
e p
er
Acr
e
9000
10000
11000
12000
13000
14000
1950 2000 2050 2100
GC ModelPCM1GFDLCRM3CCSMFVSFVSAVG
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Douglas-fir Plantation, TNF, A2
Year
To
tal C
ub
ic F
oo
t Vo
lum
e p
er
Acr
e
0
2000
4000
6000
8000
1950 2000 2050 2100
GC ModelPCM1GFDLCRM3CCSMFVSFVSAVG
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Forest Type Policy Period Measure PCM1 GFDL CRM3 CCSM FVS-Avg FVSMean GCM
Volume Change
A2 1951-2000 50-Yr Yield 10,602 10,712 10,420 10,633 5,428 7,390 MAI 212.04 214.24 208.4 212.66 108.56 147.8 211.8
2001-2051 50-Yr Yield 10,972 11,277 13,024 10,780 5,428 7,390 MAI 219.44 225.54 260.48 215.6 108.56 147.8 230.3 8.7%
2050-2099 50-Yr Yield 11,471 10,617 12,591 12,255 5,428 7,390 MAI 229.42 212.34 251.82 245.1 108.56 147.8 234.7 10.8%
B1 1951-2000 50-Yr Yield 10,722 10,712 10,359 10,655 5,428 7,390 MAI 214.44 214.24 207.18 213.1 108.56 147.8 212.2
2001-2051 50-Yr Yield 12,076 12,339 12,525 10,539 5,428 7,390 MAI 241.52 246.78 250.5 210.78 108.56 147.8 237.4 11.9%
2050-2099 50-Yr Yield 10,993 10,324 12,225 11,826 5,428 7,390 MAI 219.86 206.48 244.5 236.52 108.56 147.8 226.8 6.9%
A2 1951-2000 50-Yr Yield 6,824 6,863 6,766 6,804 4,301 7,252 MAI 136.48 137.26 135.32 136.08 86.02 145.04 136.3
2001-2051 50-Yr Yield 7,000 7,127 7,674 7,025 4,301 7,252 MAI 140 142.54 153.48 140.5 86.02 145.04 144.1 5.8%
2050-2099 50-Yr Yield 7,299 7,082 7,579 7,547 4,301 7,252 MAI 145.98 141.64 151.58 150.94 86.02 145.04 147.5 8.3%
B1 1951-2000 50-Yr Yield 6,846 6,863 6,760 6,808 4,301 7,252 MAI 136.92 137.26 135.2 136.16 86.02 145.04 136.4
2001-2051 50-Yr Yield 7,402 7,588 7,451 7,038 4,301 7,252 MAI 148.04 151.76 149.02 140.76 86.02 145.04 147.4 8.1%
2050-2099 50-Yr Yield 7,004 6,885 7,413 7,327 4,301 7,252 MAI 140.08 137.7 148.26 146.54 86.02 145.04 143.1 5.0%
A2 1951-2000 50-Yr Yield 4,358 4,290 4,275 4,308 2,534 5,490 MAI 87.16 85.8 85.5 86.16 50.68 109.8 86.2
2001-2051 50-Yr Yield 4,391 4,544 5,452 4,280 2,534 5,490 MAI 87.82 90.88 109.04 85.6 50.68 109.8 93.3 8.3%
2050-2099 50-Yr Yield 4,695 4,355 5,188 5,046 2,534 5,490 MAI 93.9 87.1 103.76 100.92 50.68 109.8 96.4 11.9%
B1 1951-2000 50-Yr Yield 4,342 4,290 4,248 4,314 2,534 5,490 MAI 86.84 85.8 84.96 86.28 50.68 109.8 86.0
2001-2051 50-Yr Yield 5,105 5,254 5,144 4,351 2,534 5,490 MAI 102.1 105.08 102.88 87.02 50.68 109.8 99.3 15.5%
2050-2099 50-Yr Yield 4,357 4,153 4,882 4,912 2,534 5,490 MAI 87.14 83.06 97.64 98.24 50.68 109.8 91.5 6.5%
A2 1951-2000 50-Yr Yield 6,074 6,351 6,356 6,339 5,987 2,263 MAI 121.48 127.02 127.12 126.78 119.74 45.26 125.6
2001-2051 50-Yr Yield 6,167 6,509 6,504 6,165 5,987 2,263 MAI 123.34 130.18 130.08 123.3 119.74 45.26 126.7 0.9%
2050-2099 50-Yr Yield 6,361 6,243 6,436 6,183 5,987 2,263 MAI 127.22 124.86 128.72 123.66 119.74 45.26 126.1 0.4%
B1 1951-2000 50-Yr Yield 6,004 6,351 6,342 6,346 5,987 2,263 MAI 120.08 127.02 126.84 126.92 119.74 45.26 125.2
2001-2051 50-Yr Yield 6,367 6,436 6,599 6,445 5,987 2,263 MAI 127.34 128.72 131.98 128.9 119.74 45.26 129.2 3.2%
2050-2099 50-Yr Yield 6,469 6,120 6,736 6,388 5,987 2,263 MAI 129.38 122.4 134.72 127.76 119.74 45.26 128.6 2.7%
Ponderosa Pine
Douglas-fir
Mixed Conifer
Red Fir
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Conclusions
Work so far
Traditional empirical models can be expanded to include climate & topography
Feasible to use existing simulators and data
Growth impacts may be positive in future
Next steps
Incorporate snowIncorporate soilExamine interactionsExamine competition,
model form, parsimonyCoast model?FVS/Stand-BGC
simulations?Annual/seasonal growth
using increment data from perm plots?
33
Questions
34
Angora Fire, S. Lake Tahoe, 2007