1. Strategies to improve diameter distribution modeling using LiDAR data as auxiliary variables
Joonghoon Shin
Oregon State University
Advisor: Dr. Hailemariam temesgen

2. Outline Why diameter distributions? How they have been studied?
Preliminary analysis
Future strategies to consider

3. 1. Why diameter distributions?

4. 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

5. 2. How they have been studied?

6. Two Aspects for Reviewing
Auxiliary Information
Modeling Methods

7. Auxiliary Information
Stand attributes : age, site quality, etc.
Remote sensing : LiDAR

8. 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)

9. What to do with multimodal or irregular
Truncated PDF
Mixture of PDFs
Non-parametric methods (non-parametric PDF)

10. Non-parametric Methods
Percentile prediction / diameter classes prediction method
k-nearest neighbor imputation (k- NN)
Imputes tree list itself
Reference data should represent population

11. 3. Preliminary Analysis

12. Study Site In Southwestern Oregon covering 4 counties 1,609,292 acres
Average LiDAR pulse density 8.1/m2
895 nested plots

13. Auxiliary information
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
Predictor variables were selected from only LiDAR height metrics
Auxiliary information

14. Preliminary Results Weibull Johnson’s SB
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)

15. Preliminary Results Percentile prediction k-NN method
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

16. Preliminary Results - Comparison of methods
The error index by Reynolds, et al. (1988)
𝑒= 𝑖=1 𝑘 𝑛 𝑃𝑖 − 𝑛 𝑂𝑖 𝑁 ×100
3-Weibull SB
MSN RF
Percentile
Error Index
53.5 -
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

17. 4. Future Strategies to Consider

18. Future Strategies to Consider
Stand stratification
Landsat data
Ecoregion data from EPA or Forest Service
Combination of LiDAR height and intensity metrics

19. Future Strategies to Consider
Applying multiple PDFs to characterize diameter distribution at landscape level:
Classification (PDF selection)
Regression (PDF parameter)
Estimating small and large trees separately (Mcgarrigle, et al. 2011)
Using LiDAR intensity as predictor

20. Thank you! Any question?

21. References
1. Van Laar, A. and Akca, A Forest mensuration. Springer Science & Business Media. 2. Smalley, G.W. and Bailey, R.L 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 Comparing parametric and non-parametric modelling of diameter distributions on independent data using airborne laser scanning in a boreal conifer forest. Forestry 86:493– Wheeler, R.E Quantile Estimators of Johnson Curve Parameters. Biometrika, 67 (3),

22. References
5. Reynolds, M.R., Burk, T.E. and Huang, W.-C Goodness-of- Fit Tests and Model Selection Procedures for Diameter Distribution Models. Forest Science, 34 (2), Mcgarrigle, E., Kershaw, J.A., Lavigne, M.B., Weiskittel, A.R. and Ducey, M Predicting the number of trees in small diameter classes using predictions from a two-parameter Weibull distribution. Forestry, 84 (4),