Imputing plot level tree attributes to pixels and aggregating to stands in forested landscapes
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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. Evans USDA Forest Service Rocky Mountain Research Station Moscow, Idaho Michael J. Falkowski University of Idaho

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

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

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


Outline

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

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

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

Regression


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

Airborne LiDAR and Satellite Image Data Acquisitions

LiDAR surveys collected summer 2003

(ALI = Advanced Land Imager)


Predicted basal area ln transformed regression model

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.


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

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

Multiple Linear Regression – Basal Area

N=13678 pixels

Hudak et al. In press

Canadian J. Remote Sensing

Adjusted R2=0.91


Height distributions

Height Distributions


Lidar derived predictor variables

LiDAR-Derived Predictor Variables


Predictor variables

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


Predictor variables cont d

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


Predictor variables cont d1

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


Randomforest

randomForest


Randomforest model breiman 2001 liaw and wiener 2005

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


Importance plot basal area

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


Equivalency plot1

Equivalency Plot

Region of Similarity, Intercept


Equivalency plot2

Equivalency Plot

Region of Similarity, Intercept

No bias


Equivalency plot3

Equivalency Plot

Region of Similarity, Slope

Region of Similarity, Intercept

No bias


Equivalency plot4

Equivalency Plot

Region of Similarity, Slope

No disproportionality

Region of Similarity, Intercept

No bias


Stand level aggregation

Stand-Level Aggregation


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

  • Alternative virtual inventory approaches.

  • A systematic sample over a set of polygons

  • A separate systematic sample in each polygon.


Stand subsamples

Stand Subsamples

Triangular sample design

Captures spatial variation

150m spacing

Systematic - offset rows


Aggregated lidar basal area predictions

Aggregated LiDAR Basal Area Predictions


Aggregated lidar basal area predictions1

Aggregated LiDAR Basal Area Predictions


Stand exam basal area

Stand Exam – Basal Area


Equivalency plot5

Equivalency Plot

Slight disproportionality,

not significant

Slight overprediction

bias, not significant

(N = 50 stands)


Imputation

Imputation


Yaimpute package crookston and finley in prep

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


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

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

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


Equivalency plot6

Equivalency Plot

Slight disproportionality,

significant

Slight bias towards

overprediction,

insignificant


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

Equivalency Plot

Strong disproportionality,

significant

Strong bias towards

overprediction,

significant


Aggregated regression vs imputation predictions

Aggregated Regression vs. Imputation Predictions


Conclusions

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


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

Questions?

Acknowledgments

  • Funding:

    • Agenda 2020 Program

  • Industry Partners:

    • Potlatch Land Holdings, Inc.

    • Bennett Lumber Products, Inc.


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