Foliage and Branch Biomass Prediction

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Foliage and Branch Biomass Prediction

• an allometric approach

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Problem

• The prediction of crown biomass (foliage and
  branches) is more difficult to make because of
• sophisticated structures, and
• irregular distributions (not continuous and less
  uniform)

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Virtual Density

• Assume that crown biomass distributes uniformly
  on crown cross-area and continuously along crown
  depth and thus continuous functions can be
  applied for describing density variation .

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Virtual Foliage Density Distribution
r
h
?h
0
l
H
Where rdensity Htotal tree height,
lcrown length, hthe
distance from tree top, and
?hdistance increment.
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• the value of the density should be zero at the
  top of tree
• the density increases along crown depth until it
  reaches a maximum and then decreases

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Candidates
symbolic solution
applied before
flexibility
Weibull
Yes
N/A
Yes
Maxima
Yes
Yes
N/A
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Distribution Function SelectedMaxima Function
Where ? and ? are the coefficients
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Distribution Foliage Biomass
Assume that
Where FB is foliage biomass.
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Foliage Biomass Function(Integration)
Where
k is the transition coefficient.
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Foliage Biomass Equation
the assimilation rate according to the
Lambert-Beers law
an adjustment term of crown length
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Foliage Biomass Sapwood area
According to the pipe model theory, foliage
biomass is proportional to the sapwood area at
breast height
Where SA sapwood area ? is the
proportionality coefficient
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Foliage Biomass Age
Foliage biomass was affected by age and a
proposed function relationship is
Where A is tree age ? is a
coefficient
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Constant Transition Method
Let k (in foliage biomass equation) be equal to
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Foliage Biomass Equation(revised)
or
Where ? is a coefficient
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Branch Biomass Equation
A linear relationship exists between foliage
biomass and branch biomass, that is
Where BB is branch biomass ? is a
coefficient
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Fertilization Impact
Fertilization significantly increased foliage
biomass. The distribution of leaf biomass could
be shifted higher for fertilized trees.
Therefore, the distribution coefficient should be
adjusted for fertilized trees.
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Region Impact
Physiographic region is also a factor that
affects foliage and branch biomass. Thus,
parameters ? and ? in both biomass prediction
models should differ by region.
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Data
Data came from the Consortium for Accelerated
Pine Plantation Studies (CAPPS), which was
initiated in 1987 and maintained by the School of
Forest Resources, University of Georgia.
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Treatments

• H
• - complete vegetation
  
  control
• F
• - annual fertilization
• HF
• - both H and F
• C
• - check plot

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Foliage and Branch Samples

• In the winter of 1999, 192 trees were harvested
  in the lower coastal plain of Georgia for
  research on foliage, branches, and stem biomass.
• In the winter of 2000, the same amount trees were
  harvested in the piedmont of Georgia for the same
  purpose.

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Data Analysis

• complete vegetation control did not significantly
  affect foliage biomass
• fertilization significantly increased foliage
  biomass.
• age is a significant predictor of foliage biomass
• foliage and branch biomass differ significantly
  by region

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Model Fitting

• Nonlinear mixed-effects system modeling method
  was employed in order to obtain consistent and
  unbiased estimates.
• Calculated foliage biomass were applied for an
  independent variable in the branch biomass
  prediction model fitting to eliminate
  simultaneous equation bias.

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Estimates (the Piedmont)
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Estimates (the Lower Coastal Plain)
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Fit Statistics
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Predictions Observationsfoliage biomass in the
Piedmont
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Predictions Observationsfoliage biomass in the
Lower Coastal Plain
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Predictions Observationsbranch biomass in the
Piedmont
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Predictions Observationsbranch biomass in the
Lower Coastal Plain
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Growth Trend

• Foliage and branch biomass growth of fertilized
  trees keep from dropping until age 12 in both
  regions.
• Foliage and branch biomass growth of unfertilized
  trees drop from age 10 in the piedmont.

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Dry Foliage Biomasssame dbh (18 cm), the Piedmont
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Dry Foliage Biomasssame dbh (18 cm), the Lower
Coastal Plain
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Fertilized vs Unfertilized

• Dry foliage biomass of a unfertilized tree is
  more than the fertilized tree with the same dbh.
• A plausible explanation- a tree in unfertilized
  stands may be more dominant than the fertilized
  tree with the same dbh.

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Position of the Maximum Density
Let the first order derivation of the virtual
density r
be zero, i.e.,
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Position of the Maximum Density
That is,
Where r reaches the maximum value.
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Position of the Maximum Density
For unfertilized trees
For fertilized trees
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Position of the Maximum Density
The average crown length is 6.98 meters for
unfertilized trees and 7.47 meters for fertilized
trees. The position is at about upper 78
(100(1-1.57/6.98)) tree crown for unfertilized
trees and upper 81 (100(1-1.45/7.47)) tree crown
for fertilized trees.
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Age Foliage Biomass
If a tree reaches larger size at younger age, it
should gain more foliage biomass. The foliage
biomass of a fertilized tree with dbh 18 cm and
crown length 8 m at age 10 is about 5 kg, versus
a unfertilized tree with the same dbh and crown
length at age 12, 4.75 kg. That is, the younger
fertilized trees gained more than 5 foliage
biomass.
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Number of Parameters
The allometric approach significantly reduced the
number of parameters to be estimated. The
developed foliage and branch biomass prediction
models used only four parameters, compared with
the empirical models, where eight parameters were
used for the same purpose.
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