Modeling Tree Growth Under Varying Silvicultural Prescriptions
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Modeling Tree Growth Under Varying Silvicultural Prescriptions Leah Rathbun University of British Columbia Presented at Western Mensurationists 2010
description
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 - PowerPoint PPT Presentation
Transcript of Modeling Tree Growth Under Varying Silvicultural Prescriptions
Modeling Tree Growth Under Varying Silvicultural Prescriptions
Leah RathbunUniversity of British Columbia
Presented at Western Mensurationists 2010
Location• Coastal Western Hemlock
(CWH) BEC zone• Temperatures - 5.2 to 10.5˚
C • Second growth uneven-
and even-aged multi-species stands regenerated naturally and from plantings.
• Western hemlock, Douglas-fir, western redcedar, red alder, Sitka spruce and yellow cedar
Box-Lucas Model
Developed from Von Bertalanffy function
Flexible model form
dbhfdbhfff
fkDinc 12
21
11 expexpˆ
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
Douglas fir:
Cedar:
Hemlock:
dbhfdbhfff
fkDinc 12
21
11 expexpˆ
)lnexp 8654101 SpHaRDBHaGEAaSIa(dbh)a(af
))ln(exp( 876543102 SpHbCurtisRDbRDBHbGEAbSIbBALbdbhbbf
))ln(exp( 6532101 RDBHaGEAaBALaGadbhaaf
))ln(exp( 65102 RDBHbGEAbdbhbbf
))ln(exp( 653101 RDBHaGEAaBALadbhaaf
)SpHbRDBHbGEAbGb)dbhln(bbexp(f 8652102
Untreated trees
Douglas-fir
Hemlock
Cedar
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
• 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
dbhfdbhfff
ffDinc 3443
35 expexpˆ
F924 time
Fbexpff
FtimeFaff 913 exp
FtimeFckf 15
Fertilization Effects
For Douglas fir and cedar:
And for hemlock:
FtimeFaff 913 exp
FtimeFbff 924 exp
15 kf
FtimeFckf 15
Fertilized
Douglas-fir
Hemlock
Cedar
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
Hemlock
Cedar
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
Fertilized & Thinned
Douglas-fir
Hemlock
Cedar
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
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 hemlockPredicted 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
heightfheightfff
fkH 1incP 1221
1 expexp
)SIadbhadbha(aexpf 3dtransforme2101 )SIbdbhbdbhb(bexpf 3dtransforme2102
Potential height
Douglas-fir
Western hemlock
Western redcedar
• Douglas-fir
• Cedar
• Hemlock
Average Height ModelGrowth Potential Dependent
incPinc H*MH
CurtisRDcRDBHcGEAcSIcBALcGccM 7654320
CurtisRDcSIcBALcGcdbhccM 743210
CurtisRDcRDBHcGEAcSIcBALcGcdbhccM 76543210
Average Height ModelGrowth Potential Independent
Douglas fir:
Cedar:
Hemlock:
dbhfdbhfff
fkDinc 12
21
11 expexpˆ
)lnexp 8654101 SpHaRDBHaGEAaSIa(dbh)a(af
))ln(exp( 876543102 SpHbCurtisRDbRDBHbGEAbSIbBALbdbhbbf
))ln(exp( 6532101 RDBHaGEAaBALaGadbhaaf
))ln(exp( 65102 RDBHbGEAbdbhbbf
))ln(exp( 653101 RDBHaGEAaBALadbhaaf
)SpHbRDBHbGEAbGb)dbhln(bbexp(f 8652102
Average height
Douglas-fir
Hemlock
Cedar
Fertilization Effects
• 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
dbhfdbhfff
ffDinc 3443
35 expexpˆ
F924 time
Fbexpff
FtimeFaff 913 exp
FtimeFckf 15
FertilizedDouglas-fir
a)Low site quality, low density
b)High site quality, low density
c)High site quality, high density
FertilizedHemlock
a)Low site quality, low densityb)Low site quality, high densityc)High site quality, low densityd)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
ThinnedDouglas-fir
a)Low site quality, low densityb)Low site quality, high densityc)High site quality, low densityd)High site quality, high density
ThinnedCedar
a)Low site quality, low density
b)High site quality, low density
c)High site quality, high density
ThinnedHemlock
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 & ThinnedDouglas-fir
a)Low site quality, low densityb)Low site quality, high densityc)High site quality, low densityd)High site quality, high density
a)Low site quality, low densityb)Low site quality, high densityc)High site quality, low densityd)High site quality, high density
Fertilized & Thinned
Hemlock
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
