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

3

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)

5

“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

Nonlinear Linear, Log-Linear

Model Forms

CACTOS (Wensel and Robards 1989) FVS-ICASCA (Dixon 1999)

FVS-SORNEC (Dixon 2005)

7

General Model Structure

0 1 2 3 4

5 6 7 8

9 10

11

212 13

214

PBAL[ln(GR)] ln(dbh) (dbh) CRln(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

215

216 17 18 19

P) SL ELEV sin(ASP)

ELEV ELEV Albrx Albry ik

b

b b b b e e

8

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

9

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

10

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

11

Residuals: ponderosa pine example

10 20 30 40 50 60 70

0.0

0.5

1.0

DBH

Res

idua

ls

12

Results: Common Variables

DBH THT

CR PBAL Index

Latitude

13

DBH Height

Functional Form14

DBH (Inches)

Dia

met

er G

row

th M

ultip

lier

2

4

6

8

10

12

20 40 60 80

SpeciesPonderosa pineSugar pineIncense-cedarDouglas-firWhite f irRed f ir

Tree Height (feet)

Hei

ght G

row

th M

ultip

lier

5

10

15

50 100 150 200

SpeciesPonderosa pineSugar pineIncense-cedarDouglas-f irWhite firRed 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-firWhite 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-firWhite f irRed fir

15

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-firWhite 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 fir

16

Diameter Growth Height Growth

Latitude17

UTM-Y

Dia

met

er G

row

th M

ultip

lier

0

5

10

4000 4200 4400 4600

Species, AreaIncense-cedar, East of 540Ponderosa pine, East of 540Red f ir, Statew ideSugar pine, Statew ideWhite f ir, East of 540

UTM-Y

Hei

ght G

row

th M

ultip

lier

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 & TopographyWinter Precip (10/12)

Winter Temp (10/12)

Many seasonal variables

Climate

Full specification (11/12)

WF height (ELEV)

Topography

18

Climate VariablesOnly red fir growth entirely negative to temperature increases

More precipitation => more growth

Degree-day variables generally better than straight temperature Degree Days

Hei

ght G

row

th M

ultip

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-f ir, spring, Max 5Douglas-f ir, summer, Min 10White fir, annual, Max 5Red f ir, w inter, Max 10

Height Growth

19

TopographyStage and Salas (2007) formulation highly adaptable

Requires wide range of data

Requires high tolerance for insignificant parameter estimates

PP Htgrowth

DF Diam.growth

20

Hei

ght G

row

th M

ultip

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)

Cou

nt

0500

10001500

4000 6000 8000

Dia

met

er G

row

th M

ultip

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)

Cou

nt

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

21

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)

22

Projections to Test Model BehaviorFactor 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)

23

Douglas-fir, Flat Ground, No PCThe

ight

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

stem

s

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

24

Douglas-fir, SW Aspect, No PCThe

ight

50

100

150

20 40 60 80 100

Climate Curves

50

100

150

10 20 30 40

Height-Dbh

stem

s

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

25

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)

26

Mid-Sierra Transect27

Winter Precipitation, A2, DF Site

CCSM3

Decade (1950 - 2090)

Pre

cipi

tatio

n (m

m)

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

cipi

tatio

n (m

m)

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

cipi

tatio

n (m

m)

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

cipi

tatio

n (m

m)

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

28

Winter Mean Max Temperature, A2, DF Site

CCSM3

Decade (1950 - 2090)

Mea

n D

aily

Max

imum

Tem

pera

ture

(C)

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CNRM

Decade (1950 - 2090)

Mea

n D

aily

Max

imum

Tem

pera

ture

(C)

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

GFDL

Decade (1950 - 2090)

Mea

n D

aily

Max

imum

Tem

pera

ture

(C)

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

PCM1

Decade (1950 - 2090)

Mea

n D

aily

Max

imum

Tem

pera

ture

(C)

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

29

Mature Douglas-fir Stand, TNF, A2

Year

Tota

l Cub

ic F

oot V

olum

e pe

r Acr

e

9000

10000

11000

12000

13000

14000

1950 2000 2050 2100

GC ModelPCM1GFDLCRM3CCSMFVSFVSAVG

30

Douglas-fir Plantation, TNF, A2

Year

Tota

l Cub

ic F

oot V

olum

e pe

r Acr

e

0

2000

4000

6000

8000

1950 2000 2050 2100

GC ModelPCM1GFDLCRM3CCSMFVSFVSAVG

31

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

32

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

Tim Robardstim.robards@fire.ca.gov916.445.5342

34

Angora Fire, S. Lake Tahoe, 2007