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

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

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

2. How they have been studied?

Two Aspects for Reviewing Auxiliary Information Modeling Methods

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

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)

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

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

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

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

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)

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

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

4. Future Strategies to Consider

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

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

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.

References 5. Reynolds, M.R., Burk, T.E. and Huang, W.-C. 1988 Goodness-of- Fit 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.