LiDAR-AGB Draft Tables and Figures

Building blocks for the LiDAR-AGB manuscript…

Lucas Johnson
2022-03-21

LiDAR Coverages Map

GPO-LiDAR region component coverages, colored by year of acquisistion and labeled by ID numbers in Table 1.

Figure 1: GPO-LiDAR region component coverages, colored by year of acquisistion and labeled by ID numbers in Table 1.

LiDAR Coverage Summary

Table 1: Component LiDAR coverage metadata. IDs for cross figure correspondence; Year of acquisition; Area covered; Pulse density (PD) in pulses per m\(^2\); Number of FIA plots in calibration and assessment datasets. Area of Applicability (AOA) in percent of LiDAR coverage pixels considered inside of the predictor space area of applicability. AOA computation conducted after initial LCMAP masking.
ID Name Year Area (ha) PD AOA Calibration Assessment
1 Erie, Genesee & Livingston 2019 555,853 2.04 97.72 11 19
2 Fulton, Saratoga, Herkimer & Franklin 2018 557,421 1.98 99.61 39 36
3 Southwest B 2018 560,675 1.73 98.06 28 39
4 Cayuga & Oswego 2018 438,201 2.78 96.89 25 31
5 Southwest 2017 432,841 1.73 98.53 33 37
6 Franklin & St. Lawrence 2017 1,014,527 2.69 99.24 104 116
7 Oneida Subbasin 2017 303,986 2.1 96.02 15 24
8 Allegany & Steuben 2016 333,590 1.69 97.77 32 37
9 Columbia & Rensselaer 2016 248,839 1.69 98.19 17 31
10 Clinton, Essex & Franklin 2015 677,727 2.23 98.7 115 118
11 Warren, Washington & Essex 2015 618,275 2.78 99.37 106 111
12 Madison & Otsego 2015 478,939 2.13 99.24 56 75
13 3 County 2014 768,203 2.04 96.12 92 137
14 Long Island 2014 315,542 2.04 94.77 22 82
15 Schoharie 2014 275,154 2.04 95.12 31 51
16 NYC 2014 83,269 1.54 90.4 2 25
17 Great Lakes 2014 574,551 2.04 98.47 73 105
Total 8,237,594 98.12 801 1,074

AGB x LCMAP Summary

Table 2: Summary of reference data and LINMOD mapped predictions by LCPRI landcover classes. Mean AGB values in Mgha\(^{-1}\). Total AGB values in millions of metric tons. Area in hectares. AOA in percent of LCMAP classified pixels considered inside of the predictor space area of applicability.
LCPRI Num Plots Mean Ref. AGB Area Mean Map AGB Total Map AGB AOA
Barren 1 0.00 23,372 13.35 0.31 94.38
Developed 4 0.00 587,505 52.37 30.77 92.84
Grass/Shrub 12 30.68 198,487 45.95 9.12 98.17
Water 17 0.00 176,963 21.22 3.76 92.68
Wetland 36 115.13 615,190 74.30 45.71 97.64
Cropland 132 1.98 1,750,531 14.21 24.87 98.25
Tree cover 599 137.97 4,236,729 127.97 542.16 98.13

AGB Maps

a) LINMOD AGB prediction surfaces reflecting a temporal patchwork of conditions; b) Warren, Washington \& Essex LINMOD AGB (2015); c) Cayuga \& Oswego LINMOD AGB (2018).

Figure 2: a) LINMOD AGB prediction surfaces reflecting a temporal patchwork of conditions; b) Warren, Washington & Essex LINMOD AGB (2015); c) Cayuga & Oswego LINMOD AGB (2018).

Riemann Assessment Metrics

Table 3: Map accuracy results for select scales (in ha) and the LINMOD ensemble prediction surface. Dist = distance between hex centroids in km; PPH = plots per hex; n = number of comparison units (plots or hexagons);RMSE, MAE, MBE in Mgha\(^{-1}\). All accuracy metrics as defined in section XStandard errors in parentheses. R\(^2\) standard errors excluded here as they were all < 0.01.
Scale Dist n PPH % RMSE RMSE MAE MBE R2
Plot Pixel 709 33.28 37.23 (0.05) 26.39 (0.99) 0.40 (1.40) 0.78
8660 10 514 1.38 32.21 35.55 (0.07) 25.12 (1.11) 0.12 (1.57) 0.79
54126 25 191 3.71 25.58 28.06 (0.18) 18.53 (1.53) -1.24 (2.03) 0.82
216506 50 68 10.43 17.14 18.47 (0.24) 13.03 (1.60) -1.18 (2.25) 0.90

Riemann Assessment 1:1 Plot

1:1 plots comparing modeled predictions to FIA estimates across selected scales, represented by distances between hexagon centroids (rows). Geometric Mean Functional Regression trend line shown with dashed (orange) line, and 1:1 line shown with solid (red) line.

Figure 3: 1:1 plots comparing modeled predictions to FIA estimates across selected scales, represented by distances between hexagon centroids (rows). Geometric Mean Functional Regression trend line shown with dashed (orange) line, and 1:1 line shown with solid (red) line.

Riemann Metrics x Aggregation Unit Size

Summary assessment metrics (as defined in section X) comparing LINMOD mapped predictions to FIA estimates as a function of aggregation unit size (described by distances between hexagon centroids). Red trend lines produced using LOESS method.

Figure 4: Summary assessment metrics (as defined in section X) comparing LINMOD mapped predictions to FIA estimates as a function of aggregation unit size (described by distances between hexagon centroids). Red trend lines produced using LOESS method.

Standard FIA Hexagon Comparison

Comparison of mapped LINMOD predictions to FIA estimates and associated 95% confidence interval within standardized aggregation hexagons. FIA estimates of AGB are scaled by the proportion of forest cover indicated by LCMAP 2016 tree cover, wetland, croplands and grasslands classified pixels. FIA estimates exceeding 425 Mg/Ha (max plot level observation in our training data) were excluded from the analysis as they are artifacts of the forest cover scaling procedure. Observations are sorted by increasing FIA estimates along the x-axis. RMSE, MAE, MBE in Mgha$^{-1}$ as defined in section X; % RMSE computed as RMSE divided by the mean FIA standard estimates across standard hexagons. % Outside reflects the percentage of FIA standard hexagons where our aggregate predictions fell outside the FIA 95% confidence interval.

Figure 5: Comparison of mapped LINMOD predictions to FIA estimates and associated 95% confidence interval within standardized aggregation hexagons. FIA estimates of AGB are scaled by the proportion of forest cover indicated by LCMAP 2016 tree cover, wetland, croplands and grasslands classified pixels. FIA estimates exceeding 425 Mg/Ha (max plot level observation in our training data) were excluded from the analysis as they are artifacts of the forest cover scaling procedure. Observations are sorted by increasing FIA estimates along the x-axis. RMSE, MAE, MBE in Mgha\(^{-1}\) as defined in section X; % RMSE computed as RMSE divided by the mean FIA standard estimates across standard hexagons. % Outside reflects the percentage of FIA standard hexagons where our aggregate predictions fell outside the FIA 95% confidence interval.

Spatial Error

LINMOD plot to pixel residuals summarized at units spaced 50km apart. Hexagons with only one reference plot removed. a) Max of FIA plot-level AGB estimates Mgha$^{-1}$ b) Standard Deviation of FIA plot-level AGB estimates Mgha$^{-1}$ c) MBE Mgha$^{-1}$ d) RMSE Mgha$^{-1}$ e) Hex-level MBE as a function of max reference value within each hex f) Hex-level RMSE as a function of Hex-level standard deviation. Red trend lines in e & f produced with least squares regression. MBE and RMSE as defined in section X.

Figure 6: LINMOD plot to pixel residuals summarized at units spaced 50km apart. Hexagons with only one reference plot removed. a) Max of FIA plot-level AGB estimates Mgha\(^{-1}\) b) Standard Deviation of FIA plot-level AGB estimates Mgha\(^{-1}\) c) MBE Mgha\(^{-1}\) d) RMSE Mgha\(^{-1}\) e) Hex-level MBE as a function of max reference value within each hex f) Hex-level RMSE as a function of Hex-level standard deviation. Red trend lines in e & f produced with least squares regression. MBE and RMSE as defined in section X.

Supplements

Predictors

Table 4: Definitions of predictors used for model fitting.
Predictor Definition Group
H0, H10, … H100, H95, H99 Decile heights of returns, in meters, as well as 95th and 99th percentile return heights. LiDAR
D10, D20… D90 Density of returns above a certain height, as a proportion. After return height is divided into 10 equal bins ranging from 0 to the maximum height of returns, this value reflects the proportion of returns at or above each breakpoint. LiDAR
N Number of returns at a given plot or pixel LiDAR
ZMEAN, ZMEAN_C Mean height of all returns (ZMEAN) and all returns above 2.5m (ZMEAN_C) LiDAR
Z_KURT, Z_SKEW Kurtosis and skewness of height of all returns LiDAR
QUAD_MEAN, QUAD_MEAN_C Quadratic mean height of all returns (QUAD_MEAN) and all returns above 2.5m (QUAD_MEAN_C) LiDAR
CV, CV_C Coefficient of variation for heights of all returns (CV) and all returns above 2.5m (CV_C) LiDAR
L2, L3, L4, L_CV, L_SKEW, L_KURT L-moments and their ratios as defined by Hosking (1990), calculated for heights of all returns LiDAR
CANCOV Ratio of returns above 2.5m to all returns (Pflugmacher et al. 2012) LiDAR
HVOL CANCOV * ZMEAN (Pflugmacher et al. 2012) LiDAR
RPC1 Ratio of first returns to all returns (Pflugmacher et al. 2012) LiDAR
TMIN, TMIN, PRECIP Climate variables in the form of 30 year normals (1980-2010) for minimum and maximum annual temperature (C) and average annual precipitation (mm) from Daly (2008) Climate
ELEV, SLOPE, ASPECT, TWI Topographic variables computed from a 30m DEM downloaded using the terrainr package (Mahoney 2021) Topography
TAX_CODE_* Individual tax code classifications as defined by NYS Department of Taxation and Finances (2019) Tax
TAX_CATEGORY_* Broad grouping of tax codes as defined by NYS Department of Taxation and Finances (2019) Tax

Model Performance Metrics (Holdout Data)

Table 5: Model performance metrics (as defined in section X) against 30% holdout partition (n = 171; RMSE, MBE in Mgha\(^{-1}\)).
RF GBM SVM LINMOD
RMSE 40.55 41.02 41.63 41.07
% RMSE 37.34 37.78 38.34 37.82
MBE 3.14 1.05 -1.90 3.10
R\(^2\) 0.75 0.74 0.73 0.74

Model Performance 1:1 (Holdout Data)

Predicted vs observed scatter plot and 1:1 line for four component models against the holdout portion of the calibration dataset. AGB values in Mgha$^{-1}$.

Figure 7: Predicted vs observed scatter plot and 1:1 line for four component models against the holdout portion of the calibration dataset. AGB values in Mgha\(^{-1}\).

Riemnann Metrics - All Models

Table 6: Map accuracy results for select scales (in ha) and all models. Dist = distance between hex centroids in km; PPH = plots per hex; n = number of comparison units (plots or hexagons); RMSE, MAE, MBE in Mgha\(^{-1}\). All metrics as defined in section X. Standard errors computed via bootstrap resampling in parentheses. R\(^2\) standard errors excluded here as they were all < 0.01.
Scale Dist n PPH Model % RMSE RMSE MAE MBE R2
Plot Pixel 709 RF 33.52 37.49 (0.05) 26.85 (0.98) 0.52 (1.41) 0.77
GBM 33.42 37.38 (0.05) 26.70 (0.98) -0.83 (1.40) 0.77
SVM 34.51 38.60 (0.06) 26.47 (1.06) -4.62 (1.44) 0.76
LINMOD 33.28 37.23 (0.05) 26.39 (0.99) 0.40 (1.40) 0.78
8660 10 514 1.38 RF 32.32 35.67 (0.06) 25.50 (1.10) 0.32 (1.57) 0.78
GBM 32.07 35.40 (0.07) 25.10 (1.10) -1.14 (1.56) 0.79
SVM 33.58 37.06 (0.08) 25.34 (1.19) -5.03 (1.62) 0.77
LINMOD 32.21 35.55 (0.07) 25.12 (1.11) 0.12 (1.57) 0.79
54126 25 191 3.71 RF 25.01 27.44 (0.17) 18.57 (1.47) -1.15 (1.99) 0.83
GBM 25.81 28.31 (0.19) 18.97 (1.52) -2.36 (2.05) 0.82
SVM 27.76 30.45 (0.21) 19.85 (1.67) -6.42 (2.16) 0.79
LINMOD 25.58 28.06 (0.18) 18.53 (1.53) -1.24 (2.03) 0.82
216506 50 68 10.43 RF 16.73 18.03 (0.22) 13.05 (1.52) -0.95 (2.20) 0.91
GBM 17.54 18.91 (0.24) 13.55 (1.61) -2.01 (2.30) 0.90
SVM 20.27 21.85 (0.30) 15.44 (1.89) -6.54 (2.55) 0.86
LINMOD 17.14 18.47 (0.24) 13.03 (1.60) -1.18 (2.25) 0.90

Riemann Assessment 1:1 Plot - All models

1:1 plots comparing modeled predictions to FIA estimates across selected scales, represented by distances between hexagon centroids (rows), and all models (columns). Geometric Mean Functional Regression trend line shown with dashed (orange) line, and 1:1 line shown with solid (red) line.

Figure 8: 1:1 plots comparing modeled predictions to FIA estimates across selected scales, represented by distances between hexagon centroids (rows), and all models (columns). Geometric Mean Functional Regression trend line shown with dashed (orange) line, and 1:1 line shown with solid (red) line.

Spatial Autocorrelation of Mapped Residuals

Global spatial autocorrelation (Moran's I) of LINMOD mapped residuals as a function of search radius. Red dashed upper and lower envelopes represent the 95% interval computed from 1000 bootstrap iterations of randomly re-assigning plot locations.

Figure 9: Global spatial autocorrelation (Moran’s I) of LINMOD mapped residuals as a function of search radius. Red dashed upper and lower envelopes represent the 95% interval computed from 1000 bootstrap iterations of randomly re-assigning plot locations.

Model-based Prediction Uncertainty

Smoothed kernel density estimates of model-based bootstrap standard errors for LINMOD aggregate predictions across six size groupings. Aggregate predictions and estimates of standard error were computed for 1000 randomly sampled polygons with sizes from 1-500 hectares.

Figure 10: Smoothed kernel density estimates of model-based bootstrap standard errors for LINMOD aggregate predictions across six size groupings. Aggregate predictions and estimates of standard error were computed for 1000 randomly sampled polygons with sizes from 1-500 hectares.

Model-based Bootstrap Bias

Bootstrap bias summaries comparing the original model aggregate prediction to the average aggregate prediction across all bootstrap iterations for six size groupings. Aggregate predictions and estimates of bootstrap bias were computed for 1000 randomly sampled polygons with sizes from 1-500 hectares.

Figure 11: Bootstrap bias summaries comparing the original model aggregate prediction to the average aggregate prediction across all bootstrap iterations for six size groupings. Aggregate predictions and estimates of bootstrap bias were computed for 1000 randomly sampled polygons with sizes from 1-500 hectares.

Corrections

If you see mistakes or want to suggest changes, please create an issue on the source repository.

Citation

For attribution, please cite this work as

Johnson (2022, March 21). CAFRI Labs: LiDAR-AGB Draft Tables and Figures. Retrieved from https://cafri-labs.github.io/acceptable-growing-stock/posts/lidar-agb-draft-tables-and-figures/

BibTeX citation

@misc{johnson2022lidar-agb,
  author = {Johnson, Lucas},
  title = {CAFRI Labs: LiDAR-AGB Draft Tables and Figures},
  url = {https://cafri-labs.github.io/acceptable-growing-stock/posts/lidar-agb-draft-tables-and-figures/},
  year = {2022}
}