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 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

MinimumMaximum RangeMeanStandard DeviationCoefficient of VariationSkewness KurtosisAverage Absolute DeviationMedian Absolute Deviation5th, 25th, 50th, 75th, 95th PercentilesInterquartile RangeCanopy 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 InsolationTSRAI – 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?