Imputing plot-level tree attributes to pixels and aggregating to stands in forested landscapes

1. Imputing plot-level tree attributes to pixels and aggregating to stands in forested landscapes Andrew T. Hudak, Nicholas L. Crookston, Jeffrey S. Evans USDA Forest Service Rocky Mountain Research Station Moscow, Idaho Michael J. Falkowski University of Idaho Department of Forest Resources Moscow, Idaho Brant Steigers, Rob Taylor Potlatch Forest Holdings, Inc. Lewiston, Idaho Halli Hemingway Bennett Lumber Products, Inc. Princeton, Idaho

2. Outline • LiDAR for Precision Forest Management • Regression-based basal area prediction • LiDAR-derived predictor variables • randomForest-based basal area prediction • Aggregating to the stand level • Imputation-based basal area prediction

3. LiDAR Project Areas Hudak et al. (2006), Regression modeling and mapping of coniferous forest basal area and tree density from discrete-return lidar and multispectral satellite data. Canadian Journal of Remote Sensing 32: 126-138.

4. Field Sampling • Plots randomly placed within strata defined by: • Elevation • Solar insolation • NDVIc (satellite image-derived indicator of Leaf Area Index) • 3 (elevation) x 3 (insolation) x 9 (NDVIc) = 81 strata / study area • 1/10 acre plots in Moscow Mountain study area • 1/5 acre plots in St. Joe Woodlands study area • Fixed radius plot for all trees >5” dbh, circumscribed by variable radius plot for large trees

5. Regression

6. Airborne LiDAR and Satellite Image Data Acquisitions LiDAR surveys collected summer 2003 (ALI = Advanced Land Imager)

7. Predicted Basal Area (ln-transformed) regression model Hudak et al. (2006), Regression modeling and mapping of coniferous forest basal area and tree density from discrete-return lidar and multispectral satellite data. Canadian Journal of Remote Sensing 32: 126-138.

8. Hudak et al. (2006), Regression modeling and mapping of coniferous forest basal area and tree density from discrete-return lidar and multispectral satellite data. Canadian Journal of Remote Sensing 32: 126-138.

9. Multiple Linear Regression – Basal Area N=13678 pixels Hudak et al. In press Canadian J. Remote Sensing Adjusted R2=0.91

10. Height Distributions

13. LiDAR-Derived Predictor Variables

14. Predictor Variables Heights Minimum Maximum Range Mean Standard Deviation Coefficient of Variation Skewness Kurtosis Average Absolute Deviation Median Absolute Deviation 5th, 25th, 50th, 75th, 95th Percentiles Interquartile Range Canopy Relief Ratio • (mean – min) / (max – min) Intensity

15. Predictor Variables, cont’d. Canopy Density DENSITY - Percent vegetation returns • measure of total canopy density STRATUM0 - Percent ground returns STRATUM1 - Percent veg returns >0 and <=1m TXT – Standard deviation of returns >0 and <=1m • texture measure of ground clutter STRATUM2 - Percent veg returns >1 and <=2.5m STRATUM3 - Percent veg returns >2.5 and <=10m STRATUM4 - Percent veg returns >10 and <=20m STRATUM5 - Percent veg returns >20 and <=30m STRATUM6 - Percent veg returns >30m PCT1 - Percent 1st returns PCT2 - Percent 2nd returns PCT3 - Percent 3rd returns

16. Predictor Variables, cont’d. SLP – Slope (degrees) SLPCOSASP – Slope * cos(Aspect) SLPSINASP – Slope * sin(Aspect) INSOL – Solar Insolation TSRAI – Topographic Solar Radiation Aspect Index • (1 - cos((pi / 180)(Aspect - 30))) / 2 Topography

17. randomForest

18. randomForest Model (Breiman 2001; Liaw and Wiener 2005) • Generates a “Forest” of multipleclassification trees • Nonparametric bootstrap • 30% out of bag (OOB) random sample • Provides robust model fitting • Freely available R package

19. Importance Plot – Basal Area 26 Variables in final model 30% Out of bag sample 10,000 Bootstrap iterations 100 Node permutations Random variable subsets 89.97% variation explained

20. Equivalency Plot

21. Equivalency Plot Region of Similarity, Intercept

22. Equivalency Plot Region of Similarity, Intercept No bias

23. Equivalency Plot Region of Similarity, Slope Region of Similarity, Intercept No bias

24. Equivalency Plot Region of Similarity, Slope No disproportionality Region of Similarity, Intercept No bias

25. Stand-Level Aggregation

26. Alternative virtual inventory approaches. • A systematic sample over a set of polygons • A separate systematic sample in each polygon.

27. Stand Subsamples Triangular sample design Captures spatial variation 150m spacing Systematic - offset rows

28. Aggregated LiDAR Basal Area Predictions

29. Aggregated LiDAR Basal Area Predictions

30. Stand Exam – Basal Area

31. Equivalency Plot Slight disproportionality, not significant Slight overprediction bias, not significant (N = 50 stands)

32. Imputation

33. yaImpute package (Crookston and Finley, in prep) • Eight options for k-NN imputation • including MSN, GNN, randomForest • Comparative plotting functions • Mapping capability • Freely available R package

34. Twelve lidar-derived predictor variables (X’s) used to impute and map Basal Area of 11 conifer species (Y’s) with the yaImpute package Hudak et al. (In Review), Nearest neighbor imputation modeling of species-level, plot-scale structural attributes from LiDAR data. Remote Sensing of Environment.

35. Total Basal Area (sqft / acre) mapped at 30 m resolution

36. Equivalency Plot Slight disproportionality, significant Slight bias towards overprediction, insignificant

37. Equivalency Plot Strong disproportionality, significant Strong bias towards overprediction, significant

38. Aggregated Regression vs. Imputation Predictions

41. Conclusions: • LiDAR metrics provide detailed structure information • Our sampling design based on a spectral data-derived LAI index may have inadequately stratified our landscapes based on basal area variation • Stand exams may not represent an unbiased sample of the full range of conditions in these landscapes, which is problematic for landscape-level inferences • The R packages randomForest and yaImpute hold much promise for modeling and mapping, as regression and imputation tools • Necessary next step is to impute tree lists from the LiDAR predictor variables for input into FVS

42. Questions? Acknowledgments • Funding: • Agenda 2020 Program • Industry Partners: • Potlatch Land Holdings, Inc. • Bennett Lumber Products, Inc.