The use of climate in individual tree growth models, an example from the Sierra Nevada ecoregion

1. 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

2. Acknowledgments • 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

3. Presentation Outline • Objectives • Model Structure • Data • Modeling • Results • Implementation in FVS • Evaluation • Projections • Conclusions

4. 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

5. Forest Growth Models • 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)

6. “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)

7. Model Forms Nonlinear Linear, Log-Linear CACTOS (Wensel and Robards 1989) FVS-ICASCA (Dixon 1999) FVS-SORNEC (Dixon 2005)

8. General Model Structure

9. Data • Fit data • Climate data • PRISM • Monthly • 4x4 km grid • Evaluation data

10. 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

11. Log Bias Correction • Ratio of the Means (Snowdon 1991)

12. Residuals: ponderosa pine example

13. Results: Common Variables

14. Functional Form DBH Height

15. Crown Ratio Diameter Growth Height Growth

16. Competition Index Diameter Growth Height Growth

17. Latitude Diameter Growth Height Growth

18. Results: Climate & Topography

19. Climate Variables Only red fir growth entirely negative to temperature increases More precipitation => more growth Degree-day variables generally better than straight temperature Height Growth

20. PP Ht growth Topography Stage and Salas (2007) formulation highly adaptable Requires wide range of data Requires high tolerance for insignificant parameter estimates DF Diam. growth

21. Implementation in FVS • 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 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

22. 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)

23. Projections to Test Model Behavior

24. Douglas-fir, Flat Ground, No PCT

25. Douglas-fir, SW Aspect, No PCT

26. 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)

27. Mid-Sierra Transect

28. Winter Precipitation, A2, DF Site

29. Winter Mean Max Temperature, A2, DF Site

30. Mature Douglas-fir Stand, TNF, A2

31. Douglas-fir Plantation, TNF, A2

33. Conclusions 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?

34. Questions Tim Robards tim.robards@fire.ca.gov 916.445.5342 Angora Fire, S. Lake Tahoe, 2007