“Best” permutation for each model type determined by ranking RMSE, variance ratio, bias, and R2 (Table 5). Arizona favored less complex variable permutations (except for certain regression tree methods).

Likely due to stronger empirical relationships between biomass and Landsat spectral data compared to Minnesota data.

Compared the “best” permutation across model types using same four criteria. Regression tree methods yielded the lowest error for both AZ and MN. GNN best preserved variance in Arizona. RMA best preserved variance in Minnesota. RMA and SGB were the least biased in Arizona. GNN was the least biased in Minnesota.

Overall, RF was the best model type for optimizing all four criteria, and was superior to other methods at minimizing prediction error.

Empirical Modeling Data divided into model (2/3) and validation (1/3) sets. Empirical biomass models developed for each of six modeling techniques and eight variable permutations. Eight variable permutations based on four categories of predictor variables (Table 4).

1. RAW: Raw Landsat bands only (1)2. RAW.SPECT: Raw Landsat bands + Derived spectral indices (1 + 2)3. RAW.30: Raw Landsat bands + Derived spectral variables + Topographic variables (1 + 2 + 3)4. RAW.ALL: Raw Landsat + Derived spectral indices + Topographic variables + Climate Variables (1 + 2 + 3 + 4)5. TC: Tasseled Cap bands only (Brightness, Greenness, Wetness)6. TC.SPECT: TC bands + Derived spectral indices (TC Bands + 2)7. TC.30: TC bands + Derived spectral indices + Topographic variables (TC Bands + 2 + 3)8. TC.ALL: TC bands + Derived spectral indices + Topographic variables + Climate Variables (TC Bands + 2 + 3 + 4)

Biomass predictions for each model type/permutation validated in terms of RMSE, variance ratio, bias, and observed v. predicted R2. Performance of each permutation ranked to determine “best” permutation per model type and per sample scene. RMA, GNN, and TC models selected for creation of 20+ year biomass trajectories that were smoothed with LanDTrenDR. Biomass trajectories validated using biomass change data derived from successively remeasured FIA data.

Introduction and Background North American Carbon Program (NACP) and Forest Inventory and Analysis (FIA) goals:

Improve methods for quantification of forest disturbance and regrowth processes (Goward et al., 2008). Characterize forest disturbance and regrowth dynamics by integrating FIA data and Landsat time-series data to model aboveground forest biomass dynamics.

Many approaches for empirical modeling of biomass using optical remote sensing data, but little consensus on best method. Little is known about multi-temporal prediction of biomass.

Three study objectives: 1. Evaluate a suite of six statistical techniques for modeling biomass.

Reduced Major Axis (RMA) regression Orthogonal regression technique. Maintains data variance structure.

Generalized Additive Models (GAMs) Generalization of multiple regression. Useful for detecting non-linear relationships.

Gradient Nearest Neighbor (GNN) imputation Assigns plot attributes to each unmapped pixel based upon a multivariate distance in gradient space. Maintains co-variance structure among response variables.

Cubist Regression tree technique. Fits a multivariate linear model to each rule.

Stochastic Gradient Boosting (SGB) Refinement of traditional regression tree analysis. Potentially less sensitive to outliers or unbalanced data and more resistant to over-fitting.

Random Forests (RF) Ensemble regression tree approach. Constructs numerous small regression trees from which predictions are averaged.

2. Evaluate the effect of inclusion of ancillary predictor variables. Spectral variables, derived spectral indices, topographically-derived variables, and climate variables.

3. Assess how the choices of model/predictor variables affect predictions of biomass change.Limitations to empirical modeling of biomass using optical remote sensing data are well known.

Solution hinges upon leveraging the temporal information contained within the Landsat time-series (Kennedy et al., 2007). Trends across 20+ year trajectories of biomass are noteworthy, especially in instances of forest disturbance or regrowth. Smoothing biomass trajectories with a curve-fitting algorithm enables a more accurate evaluation of biomass dynamics (Figure 1). The algorithm, Landsat Detection of Trends in Disturbance and Recovery (LanDTrenDR) uses segmentation rules to summarize the temporal progression of any spectral or derived spectral index (e.g. biomass) of Landsat imagery (Kennedy et al, in prep.). Captures both abrupt and slow disturbance as well as diverse sequences of disturbance and regrowth.

Comparison of methods to model aboveground biomass for derivation of 20+ year trajectories Powell, S.L1, Kennedy, R.E.2, Healey, S.P.3, Pierce, K.B.4, Cohen, W.B.1, Moisen, G.G.3, Ohmann, J.L.1

1 U.S.D.A. Forest Service, Pacific Northwest Research Station, Corvallis, OR 973312 Dept. of Forest Science, Oregon State University, Corvallis, OR 97331

3 U.S.D.A. Forest Service, Rocky Mountain Research Station, Ogden, UT 844014 WA Dept. of Fish and Wildlife, Olympia, WA 98501

Landsat data development Biennial Landsat time-series stacks acquired for two sample scenes (Table 1).

Arizona and Minnesota (Figure 2). Geometrically corrected and radiometrically calibrated to surface reflectance with the LEDAPS algorithm (Masek et al., 2006). Relative radiometric normalization to a common reference image (noted by * in table) using the Multivariate Alteration Detection (MAD) method (Canty et al., 2004).

Stat. AZ MN

n 136 978

Mean 47 64

Stdev 59 46

Min 0 0

Max 320 230

Arizona Minnesota

06/21/1985 06/28/1984

07/26/1986 08/21/1986

07/02/1989 09/14/1989

06/19/1990 07/31/1990

06/22/1991 08/19/1991

06/27/1993 08/24/1993

06/14/1994 08/14/1995

06/22/1997 09/04/1997

06/25/1998 08/06/1998

06/14/2000* 07/24/1999

06/12/2002 07/05/2001

07/09/2003 09/05/2003*

08/31/2005 08/06/2004

09/03/2006 09/13/2006

Model Type AZ MN

RMA TC TC.SPECT

GAMS TC.SPECT TC.ALL

GNN TC RAW.ALL

CUBIST RAW.ALL TC.ALL

SGB TC TC.ALL

RF TC.ALL RAW.ALL

State Meas. Yrs. Inventory Type Use # Plots

AZ 1995 Periodic Cycle 2 Remeasure Validation

36

2001-2004 Annual Cycle 3 Model 136

MN 1998-2003 Annual Cycle 12 Model 978

2003-2005 Annual Cycle 13 Remeasure Validation

285

Table 3. Biomass summary statistics for AZ Cycle 3 and MN Cycle 12 inventories.

Table 2. Summary of field measurement years, inventory type, how the data were used, and number of plots for each of the four FIA inventories used in this study.

Figure 2. Arizona (Landsat path/row 37/35) and Minnesota (Landsat path/row 27/27) study scenes.

Table 1. Landsat time-series stacks for two sample scenes, with normalization reference images noted by *.

FIA data development Plot-level estimates of live aboveground tree biomass developed for four inventories (Table 2). Only used homogenous “single condition plots”. Calculated biomass change for a subset of plots that were remeasured between successive inventories. Summary biomass statistics for the model building inventories shown in Table 3.

Table 4. Four groups of predictor variables used to construct the eight predictor variable permutations for empirical modeling. Climate variables were 18-year mean annual values derived from DAYMET (Thornton et al., 1997). Disturbance Index from Healey et al., 2005. Potential Relative Radiation from Pierce et al., 2005.

1. Raw Landsat Bands (28.5 m)

2. Derived Spectral Indices (28.5 m)

3. Topographic Variables

(28.5 m)

4. Climate Variables

(1 km)

Band 1 NDVI Elevation Temperature

Band 2 Tasseled-cap Brightness Slope Growing Degree Days

Band 3 Tasseled-cap Greenness Potential Relative Radiation Water Vapor Pressure

Band 4 Tasseled-cap Wetness Precipitation

Band 5 Tasseled-cap Angle

(TCG/TCB)

Shortwave Radiation

Band 7 Tasseled-cap Distance

(sqrt(TCB2+TCG2))

Disturbance Index

Results and Discussion

Methods

Accuracy of biomass predictions varied by model type and variable permutation. In terms of RMSE (Figure 4) the differences between model types were generally smaller than the differences between variable permutations within a model type. Regression tree methods (Cubist, SGB, and RF) generally favored more complex variable permutations to achieve the lowest error among model types (Figure 4). Other methods (RMA, GNN, and GAMS) tended towards less complex variable permutations and had slightly higher error rates. In Arizona:

All model types and permutations fared poorly with respect to preservation of variance (Figure 5). Nearly all model types and permutations were biased towards under prediction (Figure 6).

In Minnesota: All model types and permutations deflated the prediction variance with the exception of RMA (Figure 5). Virtually no differences between model types and permutations with respect to bias (Figure 6).

RMA

GNN

RF

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OBS BIO CHANGE (MG/HA)

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(M

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A)

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OBS BIO CHANGE (MG/HA)

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(M

G/H

A)

AZ – Pre-Fit AZ – Post-Fit

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A)

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OBS BIO CHANGE (MG/HA)

PR

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(M

G/H

A)

-200

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0

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OBS BIO CHANGE (MG/HA)

PR

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BIO

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AN

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(M

G/H

A)

-200

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0

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OBS BIO CHANGE (MG/HA)

PR

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(M

G/H

A)

-200

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0

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-200 -150 -100 -50 0 50 100 150 200

OBS BIO CHANGE (MG/HA)

PR

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(M

G/H

A)

-200

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0

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OBS BIO CHANGE (MG/HA)

PR

ED

BIO

CH

AN

GE

(M

G/H

A)

MN – Pre-Fit MN – Post-Fit

Table 5. “Best” variable permutation for each model type and sample scene.

Figure 4. RMSE by sample scene, model type, and permutation.

AZ: RMSE by Model Type and Permutation

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rma cubist gnn sgb gams rf

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Figure 5. Variance ratio by sample scene, model type, and permutation.

AZ: Bias by Model Type and Permutation

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Figure 6. Bias by sample scene, model type, and permutation.

Figure 7. Observed biomass change (from remeasured FIA inventories) vs. biomass change predictions pre- and post-fit by LanDTrenDR curve-fitting.

0

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clearcut fit

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FIA Plot Measurements

Figure 1 . Sample biomass trajectories demonstrating the effect of curve-fitting (solid lines) on raw biomass predictions (dashed lines) for two recently disturbed FIA plots (plot-level biomass observations shown as stars).

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Figure 8. Effect of LanDTrenDR on biomass change RMSE for AZ (left) and MN (right) model types.

AZ MN

For all model types, the error in predicted biomass change was greatly reduced by curve-fitting with LanDTrenDR (Figure 7). GNN and RMA exhibited the greatest improvements in Arizona and Minnesota respectively (Figure 8). RF exhibited the least improvement, but was the most accurate model for predicting biomass change. All model types were similarly affected by curve-fitting, with an overall reduction in the range of biomass predictions.

Funded provided by NASA’s Carbon Cycle Science Program

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