Annualized diameter and height growth equations for plantation grown Douglas-fir, western hemlock, and red alder

Aaron Weiskittel1, Sean Garber1, Greg Johnson2, Doug Maguire1, & Robert A.

Monserud3 1Department of Forest Science, Oregon State University2Weyerhaeuser Company3USDA Forest Service Pacific Northwest Research Station

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

Current state of regional models1

(Cubic volume (ft3/acre) after 20 years of simulation)

1Johnson, G. 2005. Growth model runoff II. Growth Model User Group Meeting. Vancouver, WA. 15 Dec. 2005. Available online: http://www.growthmodel.org/

Current state of regional models1

(response to 200 lbs N/acre fertilization)

1Johnson, G. 2005. Growth model runoff II. Growth Model User Group Meeting. Vancouver, WA. 15 Dec. 2005. Available online: http://www.growthmodel.org/

Current state of regional models1

• 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

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)

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)

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.

Results• Models fit the data well (r2 ~ 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

Results• Installation random effects provided a few

interesting relationships for DF and RA, but fits were generally poor (r2 < 0.35)

• WH showed no relationship with any physiographic variable

Slope & aspect

Results

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Douglas-fir diameter growth rate

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

Simulation• After 15 years of simulation, the annualized

equations were comparable or in some cases, better than ORGANON predictions

3.2073

Simulation

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

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

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 developed

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)

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