foliage and branch biomass prediction an allometric approach

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.