1. Annualized diameter and height growth equations for plantation grown Douglas- fir, western hemlock, and red alder Aaron Weiskittel 1, Sean Garber 1, Greg Johnson 2, Doug Maguire 1, & Robert A. Monserud 3 1 Department of Forest Science, Oregon State University 2 Weyerhaeuser Company 3 USDA Forest Service Pacific Northwest Research Station

2. Introduction Most regional individual tree growth & yield models operate on a 5-10 year time step It is commonly assumed that increasing the temporal resolution of the model will decrease overall precision Plot data are typically collected on a 2-10 year interval –makes estimating annual growth difficult and imprecise

3. Current state of regional models 1 (Cubic volume (ft 3 /acre) after 20 years of simulation) 1 Johnson, G. 2005. Growth model runoff II. Growth Model User Group Meeting. Vancouver, WA. 15 Dec. 2005. Available online: http://www.growthmodel.org/

4. Current state of regional models 1 (response to 200 lbs N/acre fertilization) 1 Johnson, G. 2005. Growth model runoff II. Growth Model User Group Meeting. Vancouver, WA. 15 Dec. 2005. Available online: http://www.growthmodel.org/

5. Current state of regional models 1 There is a wide range of responses to thinning, fertilization, and the combination of treatments for 6 commonly used models No one model adhered to all the general research findings on these treatments Results suggest that long model time steps may be inadequate for capturing growth dynamics following silvicultural treatment

6. Objectives/Justification Use the iterative method of Cao (2002; CJFR 32: 2051- 2059) to estimate annualized growth equations –Diameter and height for now, but crown recession and mortality in the future –Fit equations with maximum likelihood and multi-level mixed-effects –random effects were then correlated with installation physiographic features –Estimate parameters for 3 plantation species in western OR and WA (Douglas-fir, western hemlock, & red alder)

7. Methods Plantation data obtained from the Stand Management Cooperative, Swiss Needle Cast Cooperative, and Hardwood Silviculture Cooperative –Only control (untreated) plots used Hann et al. (2003; OSU FRL Res. Contrib. 40) model forms used Site indices used: –DF, Bruce (1981; For Sci 4: 711-725) –WH, Bonner et al. (1995; Can. For. Serv. Info Report BC-X-353) –RA, Nigh & Courtin (1998; New Forest 16: 59-70)

8. Methods: Model fitting technique Cao’s approach: –Requires no modification of the growth data (i.e. no interpolation to a common remeasurement length) –Constrains predicted periodic growth, which reduces the error associated with annually updating a tree list –Uses a simple do loop combined with a minimization function –Automatically weights longer remeasurement intervals more than short intervals.

9. Results Models fit the data well (r 2 ~ 0.5 – 0.9) and were consistent with biological expectations Multi-level mixed effects indicated significant installation and plot variation Diameter growth peaked at 30, 25, and 15 cm DBH for DF, WH, and RA respectively Hann et al. (2003) height growth equation worked well for DF, but modifications are required for WH and RA

10. Results Installation random effects provided a few interesting relationships for DF and RA, but fits were generally poor (r 2 < 0.35) WH showed no relationship with any physiographic variable EquationSignificant factors DF diameter growthElevation, slope, aspect, & soil water holding capacity DF height growthLatitude & aspect RA diameter growthLongitude, slope, & aspect RA height growthSlope & aspect

11. Results

12. Simulation 5 SMC control plots with varying site indices and the longest period of observation (>15 years) were selected Growth was simulated using the annualized growth equations combined with a previously fit annual mortality function and a static crown recession model Predictions were compared with SMC-variant of ORGANON v8

13. Simulation After 15 years of simulation, the annualized equations were comparable or in some cases, better than ORGANON predictions VariableAnnualizedORGANON Mean DBH bias (cm; n = 1118) 0.0731 1.2045 Absolute mean DBH bias (cm; n = 1118) 3.0692 3.3575 Mean HT bias (m; n = 152) -0.4738 -0.6319 Absolute mean HT bias (m; n = 152) 1.8496 1.5908 Mean HCB bias (m; n = 152) -0.9949 -2.1399 Absolute mean HCB bias (m; n = 152) 2.82282 3.2073

14. Simulation

15. Simulation: LOGS plots Similar degree of bias observed after 25-32 years of simulation on 6 LOGS control plots Height growth overpredicted on intermediate and suppressed individuals Mortality significantly overpredicted Degree of bias similar to a model with a much longer time step

16. Discussion We found systematic variation in growth across the landscape for DF and RA –south aspects were the poorest –DF growth increased with greater % slopes, while RA decreased The multi-level mixed effects model fits were poorer predictors than those obtained with maximum likelihood when applied to new locations, but the technique is useful for: –partitioning variation –updating tree lists on locations with previous measurements

17. Future plans Modify the WH and RA height growth equations –WH needs to be simplified to provide more stable parameter estimates –RA shows a bias across stand density Fit modifiers for thinning and fertilization Preliminary simulation code for R/SPLUS is available online (www.holoros.com/goab.htm) and an EXCEL/ACCESS interface is currently being developedwww.holoros.com/goab.htm

18. Conclusion Annualized equations offer an opportunity to improve the precision of growth projections, while providing several additional benefits: –Not restricted to a predetermined time interval (useful for updating inventories to the present) –Biologically justified (i.e. trees grow on an annual basis so should our models) –Improved chance of capturing the growth dynamics following intensive management –Opportunity to connect empirical equations with a process- based model (focus of my dissertation)

19. Acknowledgements USDA PNW Research Station for funding this work Stand Management Cooperative, Swiss Needle Cast Cooperative, Hardwood Silviculture Cooperative, and their supporting members for access to the data and maintenance of the plots Andy Bluhm, Randol Collier, David Hann, David Marshall, and Doug Mainwaring for assistance on creating the growth database