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Imputing plot-level tree attributes to pixels and
aggregating to stands in forested landscapes
Andrew T. Hudak, Nicholas L. Crookston, Jeffrey S. EvansUSDA Forest ServiceRocky Mountain Research StationMoscow, Idaho
Michael J. FalkowskiUniversity of IdahoDepartment of Forest ResourcesMoscow, Idaho
Brant Steigers, Rob TaylorPotlatch Forest Holdings, Inc.Lewiston, Idaho
Halli HemingwayBennett Lumber Products, Inc.Princeton, Idaho
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
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.
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
Regression
Airborne LiDAR and Satellite Image Data Acquisitions
(ALI = Advanced Land Imager)
LiDAR surveys collected summer 2003
Model Parameters Estimate Std. Error t value Pr(>|t|) Sig.(Intercept) -4.05E+01 2.04E+01 -1.981 0.049407 *Easting -1.23E-05 3.80E-06 -3.244 0.001448 **Northing 9.67E-06 4.32E-06 2.237 0.02675 *Elevation 1.04E-03 1.81E-04 5.713 5.67E-08 ***PANmean -9.18E-04 3.68E-04 -2.495 0.013675 *INTmean -2.39E-02 4.99E-03 -4.794 3.86E-06 ***HTmean 3.56E-02 1.02E-02 3.492 0.000628 ***HTstd 7.22E-02 1.75E-02 4.126 6.05E-05 ***HTmin 2.22E-02 9.46E-03 2.342 0.020454 *CCmean 1.74E-02 5.21E-03 3.342 0.001047 **CCstd 4.90E-02 1.56E-02 3.144 0.002006 **CCmin 8.45E-03 4.98E-03 1.695 0.092107 .CCmax -1.46E-02 6.06E-03 -2.407 0.017288 *---Significance codes: *** <0.001; ** <0.01; * <0.05; . <0.1---Regression sum of squares / d.f. 244.138 / 12Error sum of squares / d.f. 21.049 / 152Mean square error 0.1385Residual standard error 0.3721Multiple R-Squared 0.9206Adjusted R-squared 0.9144F-statistic 146.9 on 12 and 152 d.f., p-value: <2.20E-16
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.
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.
Multiple Linear Regression – Basal Area
Hudak et al. In pressCanadian J. Remote SensingAdjusted R2=0.91
N=13678 pixels
Height Distributions
LiDAR-Derived Predictor Variables
Predictor Variables
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)
Heights
Intensity
Predictor Variables, cont’d.
DENSITY - Percent vegetation returns measure of total canopy density
STRATUM0 - Percent ground returnsSTRATUM1 - Percent veg returns >0 and <=1mTXT – Standard deviation of returns >0 and <=1m
texture measure of ground clutterSTRATUM2 - Percent veg returns >1 and <=2.5mSTRATUM3 - Percent veg returns >2.5 and <=10mSTRATUM4 - Percent veg returns >10 and <=20mSTRATUM5 - Percent veg returns >20 and <=30mSTRATUM6 - Percent veg returns >30mPCT1 - Percent 1st returnsPCT2 - Percent 2nd returnsPCT3 - Percent 3rd returns
Canopy Density
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
Predictor Variables, cont’d.
randomForest
randomForest Model (Breiman 2001; Liaw and Wiener 2005)
• Generates a “Forest” of multiple classification trees
• Nonparametric bootstrap
• 30% out of bag (OOB) random sample
• Provides robust model fitting
• Freely available R package
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
Equivalency Plot
Equivalency Plot
Region of Similarity, Intercept
Equivalency Plot
No bias
Region of Similarity, Intercept
Equivalency Plot
Region of Similarity, Slope
Region of Similarity, Intercept
No bias
Equivalency Plot
No disproportionality
No bias
Region of Similarity, Slope
Region of Similarity, Intercept
Stand-Level Aggregation
552000 554000 556000 558000
5223
500
5225
000
5226
500
552000 554000 556000 558000
5223
500
5225
000
5226
500
Alternative virtual inventory approaches.
A systematic sample over a set of polygons
A separate systematic sample in each polygon.
Stand Subsamples
Triangular sample designCaptures spatial variation 150m spacingSystematic - offset rows
Aggregated LiDAR Basal Area Predictions
Aggregated LiDAR Basal Area Predictions
Stand Exam – Basal Area
(N = 50 stands)
Equivalency Plot
Slight disproportionality, not significant
Slight overpredictionbias, not significant
Imputation
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
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.
Total Basal Area (sqft / acre) mapped at 30 m resolution
Slight disproportionality, significant
Slight bias towardsoverprediction, insignificant
Equivalency Plot
Strong disproportionality,significant
Strong bias towardsoverprediction, significant
Equivalency Plot
Aggregated Regression vs. Imputation Predictions
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
• Funding:– Agenda 2020 Program
• Industry Partners:– Potlatch Land Holdings, Inc.– Bennett Lumber Products, Inc.
Acknowledgments
Questions?