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Strategies to improve
diameter distribution
modeling using LiDAR
data as auxiliary
variables
JOONGHOON SHIN
OREGON STATE UNIVERSITY
ADVISOR: DR. HAILEMARIAM TEMESGEN
Outline
1.
Why diameter distributions?
2.
How they have been studied?
3.
Preliminary analysis
4.
Future strategies to consider
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1. Why
diameter distributions?
Diameter Distribution

Required for stand table

Describes stand structure

Can estimate merchantable stand
volume & volume of wide range of
products (Van Laar and Akca 2007)

Important for forest management
planning
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2. How they have been
studied?
Two Aspects for Reviewing

Auxiliary Information

Modeling Methods
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Auxiliary Information

Stand attributes
: age, site quality, etc.

Remote sensing
: LiDAR
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Parametric Methods

Assumes underlying probability
distribution

Various probability density functions
(PDF): Weibull, beta, gamma,
Johnson’s SB, log-normal, etc.

Parameter prediction method (PPM)

Parameter recovery method (PRM)
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What to do with
multimodal or irregular

Truncated PDF

Mixture of PDFs

Non-parametric methods
(non-parametric PDF)
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Non-parametric Methods

Percentile prediction / diameter
classes prediction method

k-nearest neighbor imputation (kNN)
 Imputes
tree list itself
 Reference
population
data should represent
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3. Preliminary Analysis
Study Site

In Southwestern
Oregon covering
4 counties

1,609,292 acres

Average LiDAR
pulse density
8.1/m2

895 nested plots
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Methods / Response

Methods / Response variables
 PPM by Weibull and Johnson’s SB:
parameters of the PDFs
 Percentile prediction:
11 percentiles (0th, …, 100th)
 k-NN (MSN and RF):
tree lists
Auxiliary information

Predictor variables were selected from only
LiDAR height metrics
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Preliminary Results

Weibull
 Results
comparable to previous
findings (Bollandsås, et al. 2013)
 Did

not predict trees with large DBH
Johnson’s SB
 Hard
to estimate parameters:
310 out of 895 plots were estimated by
the method proposed by Wheeler
(1980)
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Preliminary Results

Percentile prediction
 Produced
some negative
percentiles (66 out of 895 plots)
 Need
a linear or non-linear system
of equations with constraint(s)

k-NN method
 Better
performance than others
 Getting
better as k increases
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Preliminary Results
- Comparison of methods
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The error index by Reynolds, et al. (1988)
𝑒=
𝑘
𝑖=1
𝑛𝑃𝑖 − 𝑛𝑂𝑖
× 100
𝑁
3-Weibull
Error
Index
53.5
SB
MSN
RF
Percentile
-
9.0 (k=1)
1.4 (k=3)
1.1 (k=5)
2.6 (k=1)
1.7 (k=3)
1.0 (k=5)
72.1
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4. Future Strategies to
Consider
Future Strategies
to Consider

Stand stratification
 Landsat
data
 Ecoregion
Service
data from EPA or Forest
 Combination
of LiDAR height and
intensity metrics
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Future Strategies
to Consider

Applying multiple PDFs to
characterize diameter distribution
at landscape level:
 Classification
 Regression
(PDF selection)
(PDF parameter)

Estimating small and large trees
separately (Mcgarrigle, et al. 2011)

Using LiDAR intensity as predictor
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Thank you! Any question?
References
1. Van Laar, A. and Akca, A. 2007 Forest mensuration. Springer
Science & Business Media.
2. Smalley, G.W. and Bailey, R.L. 1974. Yield Tables and Stand
Structure For Loblolly Pine Plantations In Tennessee, Alabama, and
Georgia Highlands. Res. Pap. SO-96. New Orleans, LA: U.S.
Department of Agriculture, Forest Service, Southern Forest
Experiment Station. 81 p.
3. Bollandsås, O.M., Maltamo, M., Gobakken, T. and Næsset, E.
2013 Comparing parametric and non-parametric modelling of
diameter distributions on independent data using airborne laser
scanning in a boreal conifer forest. Forestry 86:493–501.
4. Wheeler, R.E. 1980 Quantile Estimators of Johnson Curve
Parameters. Biometrika, 67 (3), 725-728.
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References
5. Reynolds, M.R., Burk, T.E. and Huang, W.-C. 1988 Goodness-ofFit Tests and Model Selection Procedures for Diameter Distribution
Models. Forest Science, 34 (2), 373-399.
6. Mcgarrigle, E., Kershaw, J.A., Lavigne, M.B., Weiskittel, A.R.
and Ducey, M. 2011 Predicting the number of trees in small
diameter classes using predictions from a two-parameter Weibull
distribution. Forestry, 84 (4), 431-439.
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