foliage and branch biomass prediction an allometric approach
TRANSCRIPT
Foliage and Branch Biomass Prediction
an allometric approach
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)
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 .
Virtual Foliage Density Distribution
lH
hh
0
Where r=density
H=total tree height,
l=crown length,
h=the distance from tree top, and
h=distance increment.
r
•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
Candidates
Weibull
Maxima
flexibility symbolicsolution
appliedbefore
Yes
Yes
N/A
Yes
Yes
N/A
Distribution Function SelectedMaxima Function
hβαher Where and are the coefficients
Distribution & Foliage Biomass
Assume that
dhπrF 2B
Where FB is foliage biomass.
Foliage Biomass Function(Integration)
l
0
hγ22l
0
2hβB dhehkαdh)hek(αF
Where 2βγ
k is the transition coefficient.
Foliage Biomass Equation
]2)ell(γγ)e[2(1γ
kαF lγlγ
3
2
B
= an adjustment term of crown length
)e2(1 lγ = the assimilation rate according to the Lambert-Beer’s law
lγ2)ell(γγ
Foliage Biomass & Sapwood area
According to the pipe model theory, foliage
biomass is proportional to the sapwood area at
breast height:
2A ηdbhS
Where SA = sapwood area is the proportionality coefficient
Foliage Biomass & Age
Foliage biomass was affected by age and a
proposed function relationship is:
τB AF
Where A is tree age is a coefficient
Constant Transition Method
Let k (in foliage biomass equation) be equal to:
τ2Aηdbh
Foliage Biomass Equation(revised)
τlγlγ3
22
B ]A2)ell(γγ)e[2(1γ
αηdbhF
or:
τlγlγ2B ]A2)ell(γγ)e[2(1ξdbhF
Where is a coefficient
Branch Biomass Equation
A linear relationship exists between foliage
biomass and branch biomass, that is:
BB ζFB
Where BB is branch biomass
is a coefficient
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.
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.
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.
•H - complete vegetation control
•F- annual fertilization
•HF- both H and F
•C- check plot
Treatments
• 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.
Foliage and Branch Samples
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
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.
Estimates (the Piedmont)
Parameter Estimate STD LCL UCLRegion (the piedmont) 0.0639 0.0064 0.0514 0.0764
0.6385 0.0386 0.5623 0.7142
f 0.6913 0.0416 0.6096 0.7730
0.8224 0.0358 0.7521 0.8928
f 0.8785 0.0360 0.8078 0.9492
2.2533 0.0640 2.1277 2.3790
Estimates (the Lower Coastal Plain)
Parameter Estimate STD LCL UCL
Region (the lower coastal plain)
0.0449 0.0063 0.0565 0.0813
0.6385 0.0386 0.5623 0.7142
f 0.6913 0.0416 0.6096 0.7730
0.8224 0.0358 0.7521 0.8928
f 0.8785 0.0360 0.8078 0.9492
2.5846 0.0640 2.1277 2.3790
Fit Statistics
Model Efficiency RMSE
FB 0.9636 0.6836 (kg)
BB 0.9648 1.6492 (kg)
Predictions & Observationsfoliage biomass in the Piedmont
0
1
2
3
4
5
5 10 12
Age
Dry
Fo
liag
e B
iom
ass (
kg
)
F=0
F=1
F=0 (ob)
F=1 (ob)
Predictions & Observationsfoliage biomass in the Lower Coastal Plain
0
1
2
3
4
5
6 10 12
Age
Dry
Fo
liag
e B
iom
ass
(kg
)
F=0
F=1
F=0 (ob)
F=1 (ob)
Predictions & Observationsbranch biomass in the Piedmont
0
1
2
3
4
5
6
7
8
9
10
11
5 10 12
Age
Dry
Bra
nch
Bio
mas
s (k
g)
F=0
F=1
F=0 (ob)
F=1 (ob)
0
1
2
3
4
5
6
7
8
9
10
11
6 10 12
Age
Dry
Bra
nch
Bio
mas
s (k
g)
F=0
F=1
F=0 (ob)
F=1 (ob)
Predictions & Observationsbranch biomass in the Lower Coastal Plain
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.
Dry Foliage Biomasssame dbh (18 cm), the Piedmont
0
1
2
3
4
5 6 7 8 9 10
Crown Length (m)
Dry
Fo
liag
e B
iom
ass (
kg
) F=1
F=0
Dry Foliage Biomasssame dbh (18 cm), the Lower Coastal Plain
0
1
2
3
4
5
5 6 7 8 9 10
Crown Length (m)
Dry
Fo
liag
e B
iom
ass (
kg
)
F=1
F=0
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.
Position of the Maximum Density
Let the first order derivation of the virtual
density r
)βheα(edh
dr hβhβ
be zero, i.e.,
0dh
dr
Position of the Maximum Density
That is,
Where r reaches the maximum value.
β
1h
Position of the Maximum Density
For unfertilized trees
For fertilized trees
treeoftopthefrommeters1.570.6385
1h
treeoftopthefrommeters1.450.6913
1h
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.
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.
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.