Report

Modeling Tree Growth Under Varying Silvicultural Prescriptions Leah Rathbun University of British Columbia Presented at Western Mensurationists 2010 Location • Coastal Western Hemlock (CWH) BEC zone • Temperatures - 5.2 to 10.5˚ C • Second growth unevenand even-aged multispecies stands regenerated naturally and from plantings. • Western hemlock, Douglas-fir, western redcedar, red alder, Sitka spruce and yellow cedar Box-Lucas Model Dˆ inc k1 f1 exp f 2 dbh exp f1dbh f1 f 2 Developed from Von Bertalanffy function Flexible model form Database for Diameter Growth • • • • • Permanent Sample Plot (PSP) data 1,455 untreated plots 0.008 to 0.806 ha 1932 to 2003 Varying intervals - 1 to 17 years, average of 5.0 years • 13 to 11,750 live trees per hectare • Site Index values from 6.2 to 52.8 m • Average basal area per hectare value of 38.7 m2/ha Parameter Prediction Approach • Data was subset to obtain estimates for f1 and f2 for a species • Subset defined from untreated data containing at least 4 measurement periods. • Different combinations of predictor variables were used, based upon correlation values • Linear, log-linear, and nonlinear equations • AIC values were used to select model forms • Box-Lucas model was refit using the resultant parameter estimates as starting values. Variable Selection Tree size and stage of development, site productivity, and inter-tree competition were considered: •dbh, height, and diameter increment •Site index and growth effective age •Curtis’ relative density and basal area per hectare •Basal area of larger, stems per hectare, relative dbh, crown competition factor of larger Selected Diameter Model Dˆ inc k1 f1 exp f 2 dbh exp f1dbh f1 f 2 Douglas fir: f1 exp(a0 a1 ln (dbh) a4 SI a5GEA a6 RDBH a8 SpH) f 2 exp(b0 b1 ln(dbh) b3 BAL b4 SI b5GEA b6 RDBH b7CurtisRD b8 SpH) Cedar: f1 exp(a0 a1 ln(dbh) a2G a3 BAL a5GEA a6 RDBH) f 2 exp(b0 b1 ln(dbh) b5GEA b6 RDBH) Hemlock: f1 exp(a0 a1 ln(dbh) a3 BAL a5GEA a6 RDBH) f 2 exp(b0 b1 ln( dbh) b2G b5GEA b6 RDBH b8 SpH ) Untreated trees Douglas-fir Cedar Hemlock Fertilization Effects • 85 plots received fertilization • Majority received one application of nitrogen ranging in concentration from 50 to 400 kg/ha • A few plots additionally received ammonium phosphate. Fertilization Effects Dˆ inc f 5 f3 exp f 4 dbh exp f 3dbh f3 f 4 F f 3 f1 exp a9 time F F f 4 f 2 exp b9 tim eF F f 5 k1 c tim eF • All three parameters were modified individually • Each possible combination of the three parameters were modified • Akaike’s Information Criteria (AIC) values used to select final model Fertilization Effects F f 3 f1 exp a9 time F F f 4 f 2 exp b9 tim eF For Douglas fir and cedar: f 5 k1 And for hemlock: F f 5 k1 c tim eF Fertilized Douglas-fir Cedar Hemlock Thinning Effects • 419 plots received a thinning event • Average basal area cut was 8.2 m2/ha • Average of 892 trees per hectare was removed • Original model was fit using parameter estimates found from untreated data • State variables changed immediately following a thin Thinned Douglas-fir Cedar Hemlock Fertilized and Thinned Effects • 93 plots received a combination of a thinning followed by fertilization • Fertilization was applied within the measurement period following thinning • Fertilized model was fit using parameter estimates found from fertilized data • State variables changed immediately following a thin Douglas-fir Cedar Hemlock Fertilized & Thinned Database for Height Growth • • • • 1,316 untreated plots 0.008 to 0.253 ha 1932 to 1996 Varying intervals - 1 to 30 years, average of 4.8 years • 222 to 11,750 live trees per hectare • Site Index values from 10.7 to 52.8 m • Average basal area per hectare value of 38.1 m2/ha Potential Height Model • Data selection – Binning by dbh (90th and 99th percentiles) – Predicted values approach • Box-Lucas model fit using dbh and a transformation of dbh in a linear model for f1 and f2 • Predict 90th and 99th percent confidence interval, upper value • Fit Box-Lucas model using dbh and a transformation of dbh in a linear model for f1 and f2 Potential Height Model ˆ H P inc k1 f1 exp f 2 height exp f1height f1 f 2 f1 exp(a0 a1dbh a2 dbhtransforme d a3 SI ) f 2 exp(b0 b1dbh b2 dbhtransforme d b3 SI ) Binning approach: - f1: dbh0.5 for Douglas-fir and ln(dbh) for cedar and hemlock - f2: dbh2 for Douglas-fir and cedar and ln(dbh) for hemlock Predicted values approach: - f1: dbh2 for Douglas-fir and ln(dbh) for cedar and hemlock - f2: dbh2 for Douglas-fir and cedar and ln(dbh) for hemlock Potential height Douglas-fir Western redcedar Western hemlock Average Height Model Growth Potential Dependent ˆ M* H ˆ H inc P inc • Douglas-fir M c0 c2G c3 BAL c4 SI c5GEA c6 RDBH c7 CurtisRD • Cedar M c0 c1dbh c2G c3 BAL c4 SI c7 CurtisRD • Hemlock M c0 c1dbh c2G c3 BAL c4 SI c5GEA c6 RDBH c7 CurtisRD Average Height Model Growth Potential Independent Dˆ inc k1 f1 exp f 2 dbh exp f1dbh f1 f 2 Douglas fir: f1 exp(a0 a1 ln (dbh) a4 SI a5GEA a6 RDBH a8 SpH) f 2 exp(b0 b1 ln(dbh) b3 BAL b4 SI b5GEA b6 RDBH b7CurtisRD b8 SpH) Cedar: f1 exp(a0 a1 ln(dbh) a2G a3 BAL a5GEA a6 RDBH) f 2 exp(b0 b1 ln(dbh) b5GEA b6 RDBH) Hemlock: f1 exp(a0 a1 ln(dbh) a3 BAL a5GEA a6 RDBH) f 2 exp(b0 b1 ln( dbh) b2G b5GEA b6 RDBH b8 SpH ) Average height Douglas-fir Cedar Hemlock Fertilization Effects Dˆ inc f 5 f3 exp f 4 dbh exp f 3dbh f3 f 4 F f 3 f1 exp a9 time F F f 4 f 2 exp b9 tim eF F f 5 k1 c tim eF • 82 plots received fertilization • All three parameters were modified individually • Each possible combination of the three parameters were modified • Akaike’s Information Criteria (AIC) values used to select final model Fertilized Douglas-fir a)Low site quality, low density b)High site quality, low density c)High site quality, high density Fertilized Hemlock a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density Thinning Effects • 388 plots received a thinning event • Average basal area cut was 7.6 m2/ha • Average of 988 trees per hectare was removed • Original model was fit using parameter estimates found from untreated data • State variables changed immediately following a thin Thinned Douglas-fir a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density Thinned Cedar a)Low site quality, low density b)High site quality, low density c)High site quality, high density Thinned Hemlock a)Low site quality, low density b)High site quality, low density c)High site quality, high density Fertilized and Thinned Effects • 92 plots received a combination of a thinning followed by fertilization • Fertilization was applied within the measurement period following thinning • Fertilized model was fit using parameter estimates found from fertilized data • State variables changed immediately following a thin Fertilized & Thinned Douglas-fir a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density Fertilized & Thinned Hemlock a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density Conclusions • Box-Lucas model works well • Silvicultural treatments applied to managed stands, not experimentally designed study • The adjustments added for fertilization worked well • Modification of state variables only modeled the effects of thinning well for Douglas-fir • Separate models are recommended for potential and average height Acknowledgements • • • • • • Dr. Valerie Lemay Dr. Nick Smith Dr. Peter Marshall Dr. Lori Daniels Ken Epps and Island Timberlands FVS group at the U.S. Forest Service