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Modeling Biomass and
Timber Volume by Using an
Allometric Growth Model from
Landsat TM Images
Qingmin Meng, Chris Cieszewski
D. B. Warnell School of Forest Resources
University of Georgia
Introduction
Ground truthing vs. remote sensing data.
Remote sensing.
Direct exploration of the multispectral data.
Using vegetation index, such as VI, TVI, or NDVI.
Kth nearest neighbor estimation.
Introduction
Uncertainty of the expansion from a pixel
scale to a regional scale.
Can we improve it ?
A method provides information of pixels and
possesses the space information.
Objectives
Mixed-effects models will be employed and
regional differences will be considered.
Build new indices, surface area and volume of
NDVI.
Model selection.
Analyze the spatial difference of forest biomass
and timber volume according to the fitted
models.
Methodology
NDVI, NDVIsa, and NDVIvol.
Allometric growth model
Y Y0 M b
Methodology (cont’d)
General equation of allometric growth law
y ax b
What is the general law of allometric growth?
Methodology (cont’d)
Linear fixed-effects model
Y X
Linear mixed-effects model
Y X Zb
Methodology (cont’d)
GIS and RS techniques
Geometric correction, data transformation,
mask, triangular irregular network function,
3-D model, and NDVIsa and NDVIvol
extraction ( in Imagine and ArcView).
Study area and data
Georgia regions
Ridge and valley
Mountain
Piedmont
Upper coastal plain
Lower coastal plain
Figure 1. Five study regions in GA.
Study area and data (cont’d)
Image boundary
County boundary
Figure 2. Study areas covered by images.
Study area and data (cont’d)
The 2001 data for six county-level
dependent vaiables.
biomass of all, all live merchantable biomass, volume
of all live trees, volume of growthing stock, volume of
sawtimber, and volume of the sawlog portion.
NDVIsa and NDVIvol are extracted from
Landsat TM images.
Results
Table 1. Fixed vs. mixed effects models using NDVIvol as predictor
Model Residual Adjusted
Loglik-
AIC* BIC* standard p-value R-square R-square
Response # lihood
error
1 108.39 125.91 -48.19 0.3174
Biomass
2 106.64 118.32 -49.32 0.3229 0.325
of all trees 0.4954
3 147.29 156.05 -70.65 0.3936 <.0001 0.4991
1 112.48 130.00 -50.24 0.3222
M erchanatable
2 110.54 122.22 -51.27 0.3276 0.3572
biomass
3 151.88 160.63 -72.94 0.4002 <.0001 0.4887 0.4849
1 111.60 129.12 -49.80 0.3213
Volume of all
2 109.84 121.52 -50.92 0.3272 0.3271
live trees 3 147.73 156.49 -70.87 0.3942 <.0001 0.5012 0.4976
1 127.24 144.76 -57.62 0.3409
Growing stock
2 124.46 136.17 -58.23 0.3451 0.5451
volume 3 164.71 173.47 -79.35 0.4194 <.0001 0.4739 0.4701
1 212.29 229.81 -100.15 0.4695
Sawtimber
2 208.55 220.22 -100.27 0.4704 0.8849
volume
3 240.55 249.31 -117.28 0.5532 <.0001 0.3061 0.3010
Volume of 1 202.49 220.02 -95.25 0.4526
sawlog 2 198.91 210.59 -95.45 0.4537 0.8146
portion 3 233.94 242.70 -113.97 0.5400 <.0001 0.3142 0.3092
Results (cont’d)
Table 2. Fixed vs. mixed effects model using NDVIsa as predictor
Model Residual Adjusted
Loglik- p- R-
AIC* BIC* standard R-square
Response # lihood value square
error
1 154.17 171.69 -71.09 0.3746
Biomass
2 162.90 174.58 -77.45 0.3987 0.0017
Of all trees
3 189.58 198.34 -91.79 0.4590 <.0001 0.3188 0.3139
1 157.24 174.76 -72.62 0.3789
Merchanatable 2 165.39 177.08 -78.69 0.4024 0.0023
biomass
3 192.88 201.64 -93.44 0.4645 <.0001 0.3112 0.3062
1 157.99 175.52 -72.99 0.3803
Volume of all 2 166.67 178.35 -79.99 0.4047 0.0018
live trees 3 191.09 199.85 -92.55 0.4615 <.0001 0.3164 0.3114
1 171.75 189.27 -79.87 0.4006
Growing stock 2 177.86 189.54 -84.93 0.4215 0.0064
volume 3 204.44 213.19 -99.22 0.4845 <.0001 0.2979 0.2928
1 237.75 255.26 -112.87 0.5166
Sawtimber
2 234.15 245.83 -112.07 0.5176 0.8172
volume 3 260.53 269.29 -127.27 0.5946 <.0001 0.1982 0.1924
Volume of 1 226.13 243.65 -107.06 0.4905
sawlog 2 226.92 238.60 -109.46 0.5037 0.0911
portion 3 255.29 264.05 -124.65 0.5833 <.0001 0.1997 0.1938
Results
Table 3. The best models
Model
Estimation Region
Intercept Slope
1 -2.1443069 0.9755356
Biomass 2 -6.9357346 1.1892055
Of all trees 3 -9.1793452 1.2557426
4 -2.9403983 1.0022634
5 -0.8259313 0.9267044
1 -2.1920545 0.9695219
2 -6.9057884 1.1803815
Merchanatable 3 -9.3062054 1.2531440
biomass 4 -3.2558101 1.0064089
5 -0.7418328 0.9158308
1 -5.698310 0.9636407
2 -10.031518 1.1589341
Volume of all live 3 -13.292529 1.2665148
trees 4 -6.937340 1.0082550
5 -4.061954 0.9038428
Results (cont’d)
Table 3. The best models (cont’d)
1 -7.112829 1.0151401
2 -10.415131 1.1704217
Growing stock 3 -13.253895 1.2614818
volume 4 -8.301378 1.0560060
5 -5.545369 0.9558549
1 -7.620637 1.077952
Sawtimber 2 -11.065563 1.245154
volume 3 -8.614393 1.126178
4 -6.998769 1.047766
5 -7.610956 1.077485
1 -9.173880 1.073298
2 -13.618008 1.279459
Volume of sawlog
portion 3 -10.394362 1.129898
4 -8.293959 1.032473
5 -9.137134 1.071600
Conclusions (cont’d)
The allometric growth model is suitable for the
assessment of biomass and timber volume at a large
scale.
The linear mixed-effects models can more accurately
estimate biomass and timber volume than the linear
fixed-effects models.
NDVIsa and NDVIvol both contain the pixel
information and area information.
NDVIvol is more suitable than NDVIsa in predictions.
Conclusions (cont’d)
Regional characteristics of allometry of
biomass and timber volume.
In the ridge and valley region and the lower
coastal plain region, the overall indices, biomass of all,
et al. have negative allometric characteristics.
In the mountain region and piedmont region, the
overall indices of biomass and volume have positive
allmoteric characteristics.
In the upper coast plain region, however, the
overall index of biomass and volume have neutral
allometric characteristics
The end.
Thank you.
