LiDAR Analysis of Mixed-Species, Multi-Cohort Stands Dr. John A. Kershaw, Jr. Western Mensurationists June 20, 2016

Topics for Western Mensurationists Influence of Data Sources and Model Approaches on Predictions from LiDAR Influence of Cell Size on model predictions and forest-level estimates Stand Typing using “shape-based” metrics Individual Tree Segmentation Copula-Based Diameter Prediction Model

Collaborators Graduate Students Faculty Research Scientists Charles McPhee, UNB Hunter Roberts, UNB Rei Hache, UMaine Elias Ayrey, UMaine Faculty Dr. Aaron Weiskittel, Umaine Dr. Mark Ducey, UNH Prof. Jasen Golding, UNB Research Scientists Dr. Mike Lavigne, Can For Service Elizabeth McGarrigle, NS DNR

Boots Off-the-Ground?

Noonan Research Forest 1500 ha Softwood, Intol. Hardwood, Mixedwood Stands Many degraded stand structures 100 m sample grid Angle count sample at each grid intersection (2M BAF) Every 10 years 1480 ACS points “Lam” Plots 110 fixed-area PSPs 11.28 m radius 50 X 50 mapped plots Mixed HW/SW multistrata stand Pure BS single strata Pure EH single strata

Penobscot Experimental Forest 1619 ha Softwood and mixedwood stands 50 years of silvicultural study 117 permanent sample plots Nested design 15.95 m radius OS plot 7.98 m radius Sapling plot

First Principles Own your Work (con)FUSION doesn’t give me much flexibility or confidence in the metrics extracted Wrote my own R code Canopy extractor Ground extractor Flexible metric generator As did my grad students for their work I’m a systems kind of guy If you can’t explain you model have you really developed a model or merely summarize data?

First Principles

LiDAR – A New Paradigm in Forest Mensuration Data-Rich Source of Information Lots of Interest/Effort on Various Aspects of LiDAR and Forest Mensuration Dominated by Imputation-Based Data Summary Approaches Many Paradigms/Myths being Generated randomForest Imputation Fixed-Area Plots Coregistration Requirements

but,….We Need a Few Curmudgeons to ask some Critical, Hard Questions

Influence of Data Sources and Model Approach on Predictions from LiDAR (Hache, Kershaw, Weiskittel) Two Data Sources Noonan Research Forest, UNB Penobscot Experimental Forest, Umaine Same Forest Types Different underlying ground data LiDAR acquisition differed in pulse density Questions? LiDAR data extraction Fitting of randomForest vs NLME Predictions of randomForest vs NLME Fixed-area vs Angle Count Samples What factors influence model performance?

LiDAR data NRF PEF Leaf-off condition Riegl LMS Q680i laser scanner 724 m altitude 28-degree scan angle 50% overlap 6 pulses/m2 PEF Partial leaf-off condition Optech Gemini 246 sensor 1982 m altitude 20-degree scan angle 25% overlap 1 pulse/m2

Models randomForest LiDAR extraction radii NLME Stand Type (HW, SW,MW) q45LiDAR q50Canopy LiDAR extraction radii 10, 15, 20, 25, 30 m about sample point NLME Random effects on b0 and b1 Stand Type as random factor

Goodness-of-fit with Local Data Data Source Fit NLME   Random Forest Model Test Statistic 10 15 20 25 30 NRF R2 0.68 0.67 0.64 0.63 0.61 0.85 0.84 0.83 0.82 RMSE 33.4 34.4 35.5 36.4 37 22.8 23.5 24.3 24.9 25.5 Mean Bias -0.3 -0.2 -0.1 -0.11 -0.07 -0.05 -0.01 Abs Error 25.9 26.8 27.8 28.5 29.1 17.7 18.2 19.1 19.6 PEF 0.43 0.53 0.54 0.8 45.4 41 40.6 40.8 41.1 26.7 24.7 23.8 0.33 -0.5 -0.6 0.16 0.08 0.15 0.34 32.2 31.8 31.7 18.7 16.6 17.3 16.7 17.1

Equivalence of Local Prediction Equivalence Test   LiDAR Extraction Radius 10 15 20 25 30 Field NLME{N/N+P/P} H{0} Reject Mean Diff. -0.26 -0.28 -0.25 -0.21 -0.18 Std Dev 34.5 34.95 35.92 36.74 37.37 Region of Sim 15% 10% RF{N/N+P/P} -0.10 -0.05 -0.04 0.01 -0.07 23.09 23.57 24.36 24.83 23.58 NLME(N/N+P/P) 0.16 0.22 0.21 0.11 14.96 14.84 14.87 15.18 15.41 25% 20%

Goodness-of-fit with Nonlocal Data Data Source Fit NLME   Random Forest Model Test Statistic 10 15 20 25 30 NRF PEF R2 0.4 0.48 0.47 0.46 0.35 0.37 0.39 RMSE 46.3 43.2 43.1 43.6 44.1 48.3 47.5 46.7 46.6 Mean Bias 3.56 5.36 7.12 6.93 7.84 14.4 14.51 15.03 14.52 14.36 Abs Error 36.2 32.7 32.4 32.9 36 35.4 35.2 0.64 0.58 0.59 0.62 0.57 0.53 0.51 0.49 35.8 38.7 38.1 38.5 36.6 38.9 40.7 41.8 42.5 5.42 11.7 8.2 7.42 -5.39 -11.9 -14.1 -15.4 -15.5 27.8 29.7 29.4 29.8 28.9 31.4 33.5 34

Equivalence of Prediction Nonlocal Data Equivalence Test   LiDAR Extraction Radius 10 15 20 25 30 Field NLME{N/P+P/N} H{0} Reject Mean Diff. 5.27 11.21 8.12 7.38 6.45 Std Dev 36.34 37.41 37.66 38.23 38.72 Region of Sim 25% 40% 30% RF{N/P+P/N} -3.87 -9.86 -11.89 -13.01 -13.24 38.43 39.44 40.07 40.78 20% 35% 45% NLME{N/N+P/P} Not rej. 5.54 11.06 8.37 7.59 6.62 10.91 10.08 9.66 50% ≤50% -3.60 -9.59 -11.63 -12.89 -13.07 13.34 17.99 17.92 18.15 RF{N/N+P/P} -5.38 -11.27 -8.16 -7.38 -6.51 17.94 19.31 18.24 18.21 18.14 -9.14 -21.07 -20.00 -20.48 -19.69 18.04 21.42 20.78 20.22 19.45 -3.77 -9.81 -11.85 -13.11 -13.17 19.84 20.51 20.59 21.24

Fixed-Area versus ACS

So what factors influenced model performance?

Effect of Cell Size on Area-Based Estimates Total Volume as the response variable NLME and RF models 3 variables: maxCanHT, q45Height, and Height of Max LiDAR Density Fitted to the 100 m grid ACS plots on Noonan Applied to LiDAR cells 2, 4, 5, 10, 20, 25, 50, and 100 m squares Summed to stand levels Total and 95% CI based on var between stands

100 m Grid Map

2 m grid Map

Forest-Level Totals

Broad Forest Typing with LiDAR Hunter Roberts interested in detecting hemlock groves Small patches, mostly .02 - .1 ha in size Detect and map these across Noonan Used LiDAR height and intensity distributions Weibull shape and scale parameters Skewness Broad Types: EH, Sp-Fir, Mix HD, HD/SW, SW, Water, Other (Meadows, CCs, young PCT)

T14 Map

A Canopy View

Individual Tree Segmentation From the canopy view it is clear that individual trees can be “seen” Several methods to extract or “segment” individual trees have been proposed Two approaches Crown profile probabilities Layer Staking

Crown Profile Probabilities

Crown Profile Probabilities Develop a library of crown profile parameters for species of interest Start with highest LiDAR point – assume this marks a tree Look at next highest point Fit a crown profile through the two points and compare shape parameter with library Estimate the probability that shape belongs in library Decide based on minimum probability if the two points belong to the same tree of two different trees Assign point to a tree Calculate crown radius and assign all points below to that tree Repeat until all points assigned to trees

Noonan 50X50 plot 1

Noonan 50X50 plot 2

Results 60% of trees in mixed-species, multi-cohort stand 78% of trees in dense, spruce-dominated single cohort stand Algorithm slow 8 hours on my mini-supercomputer Can’t detect subcanopy trees Could apply a density filter to identify “hotspots” of LiDAR returns to possibly segment these trees Requires another pass through all points (16 hours for 50 X 50 m plot)

So what? What’s this all good for? Tree segmentation gives us tree height distributions Ground-based data gives us a copula of H-D Inverting the copula, we can take the LiDAR-derived height distribution and sample to obtain a predicted diameter distribution

LiDAR-derived H-D Distribution

Noonan DBH Distribution

Summary of Pros/Cons PROS CONS Coregistration not required Area-based dbh distributions quite good Mean tree volume equivalent Intensive computational resources required About 60% of tree extracted Total volume underestimated by about 15% Not species-specific

Questions?