1. Gradient Nearest Neighbor (GNN) Method for Local-Scale Basal Area Mapping: FIA 2005 Symposium Interpolation Contest Kenneth B. Pierce Jr., Matthew J. Gregory* and Janet L. Ohmann Forestry Science Lab, 3200 SW Jefferson Way, Corvallis OR 97331

2. Why map? Why GNN? (Pacific Northwest perspective) Primary objective: supply missing data for analysis and modeling of forest ecosystems at the regional level Problem: basic information on current vegetation is needed to address a wide array of issues in forest management and policy. Increasingly, this information needs to be: –spatially complete (spatial pattern, small geographic areas) –consistent across large, multi-ownership regions –rich in floristic and structural detail –suitable for input to stand and landscape simulation models –flexible in meeting a variety of analytical needs Differs from other objectives which are concerned primarily with estimation

3. GNN Mapping in West Coast States Future GNN mapping: Wall-to-wall OR, CA, WA –Start Oct. ’05 in eastern OR –5-year mapping cycle –Coordinated with Region 6, Oregon Department of Forestry and other collaborators –Funded by FIA and the Western Wildlands Environmental Threat and Analysis Center ‘Ecological Systems’ for Gap Analysis Program (MZs 8 & 9) Includes non-forest mapping COLA CLAMS GNNFire Current GNN efforts

4. The Gradient Nearest Neighbor (GNN) Method for Vegetation Mapping A tool for: –Spatially explicit (wall-to-wall) vegetation data based on ‘interpolation’ of FIA plot data using an ecological (gradient) model –Inference of plot data to smaller geographic areas (e.g., 6 th -field HUCs) Imputation approach (as are kNN, MSN) provides: –Data that are regional in extent, yet rich in detail –Analytical flexibility for users

5. Components of GNN Imputation Statistical model = canonical correspondence analysis (CCA) (flexibility for redundancy analysis (RDA) and other methods): –Multivariate –Results in a weight for each of many spatial variables, based on its relationship with the multiple response variables –Any multivariate method can be specified (eg. PCA, CCorA) Distance measure (between map pixel and potential NN plots): –Euclidean distance for first n axes (usually 8, specified by user) –Axes weighted by their explanatory power (eigenvalues) Imputation method: –Single nearest neighbor (k=1, MSN-like) –Summary statistic of multiple neighbors (kNN-like) –Measures of variation based on multiple imputation (k>1)

6. Environmental and Disturbance Gradients (Explanatory Variables) Landsat TM (1996) Bands, transformations, texture ClimateMeans, seasonal variability Topography Elevation, slope, aspect, solar Disturbance Past fires, harvest, insects and disease LocationX, Y Ownership FS, BLM, forest industry, other private

7. Gradient Nearest Neighbor Method Plot data Climate Geology Topography Ownership Remote sensing PredictionSpatial data Plot locations Direct gradient analysis Plot assigned to each pixel Statistical model Imputation Pixel PSME (m 2 /ha) CanCov (%) Snags >50 cm (trees/ha) Old-growth index Etc... 11137.40.27... 279972.10.82...

8. (2) calculate axis scores of pixel from mapped data layers (3) find nearest- neighbor plot in gradient space Axis 2 (climate) gradient spacegeographic space Axis 1 (Landsat) (1) conduct gradient analysis of plot data field plots study area (4) impute nearest neighbor’s ground data to mapped pixel The imputation component of GNN

9. Accuracy assessment (‘obsessive transparency’) Local-scale accuracy (at plot locations) via cross-validation: –Confusion matrices –Kappa statistics –Correlation statistics Regional-scale accuracy: –distribution of forest conditions in map vs. plot sample –range of variation in map vs. plot sample Spatial depictions: –Variation among k nearest neighbors –Distance to nearest neighbor(s) (sampling sufficiency) Findings re. GNN map accuracy: –Excellent for regional patterns and amounts, imperfect for local sites –Mid-scales??? –Appropriate for regional planning and policy analysis

10. Bartlett Interpolation Contest Comparison between ‘control’ methods and GNN methods Effect of footprint size

11. Interpolation Contestants Kriging –best with intensive sampling and autocorrelated data Linear Model –perhaps best local predictions when a strong gradient / remote sensing link exists for the response Single neighbor GNN Imputation –best for multivariate responses and regional data, recaptures variation and attribute covariance Mean of 5 nearest GNN neighbors

12. ObservedKrigedLinearGNN1GNN5 Distributions Average3738374039 Maximum63544960 Variance173606412590 Models RMSE11.0712.4814.4113.29 Slope0.310.230.270.25 Y-intercept25.9329.0029.9129.62 Corr. coeff.0.530.370.320.34 R-square0.280.140.100.12 Model Comparisons

13. Plot scale accuracy assessment Predicted basal area (m 2 /ha) Observed basal area (m 2 /ha) ab cd a)Kriging b)Linear Model c)GNN1 d)GNN5

14. Quantile distributions Overprediction at lower basal areas / underprediction at higher basal areas Accentuated for linear model

15. Bartlett Study Area TM Leaf On 4|5|3

16. Bartlett Study Area TM Leaf On 4|5|3

17. Kriged Spatial Prediction 0.0 0.0 – 10.0 10.0 – 20.0 20.0 – 30.0 30.0 – 40.0 40.0 – 50.0 50.0 – 60.0 60.0 – 70.0 > 70.0 Basal area m 2 /ha 0.0 – 15.0 15.0 – 30.0 30.0 – 45.0 45.0 – 60.0 > 60.0

18. Linear Model Spatial Prediction 0.0 0.0 – 10.0 10.0 – 20.0 20.0 – 30.0 30.0 – 40.0 40.0 – 50.0 50.0 – 60.0 60.0 – 70.0 > 70.0 Basal area m 2 /ha 0.0 – 15.0 15.0 – 30.0 30.0 – 45.0 45.0 – 60.0 > 60.0

19. GNN 1 st Neighbor Spatial Prediction 0.0 0.0 – 10.0 10.0 – 20.0 20.0 – 30.0 30.0 – 40.0 40.0 – 50.0 50.0 – 60.0 60.0 – 70.0 > 70.0 Basal area m 2 /ha 0.0 – 15.0 15.0 – 30.0 30.0 – 45.0 45.0 – 60.0 > 60.0

20. GNN 5-Neighbor Mean Spatial Prediction 0.0 0.0 – 10.0 10.0 – 20.0 20.0 – 30.0 30.0 – 40.0 40.0 – 50.0 50.0 – 60.0 60.0 – 70.0 > 70.0 Basal area m 2 /ha 0.0 – 15.0 15.0 – 30.0 30.0 – 45.0 45.0 – 60.0 > 60.0

21. Effect of plot footprint size Studied to account for possible misregistration between plots and TM imagery Used two footprints at 30m cell resolution –1x1 and 2x2 (plot spacing is ~65m – 3x3 windows overlap) –Used for both extraction of spatial data and for mean basal area prediction at the cross-validation plots Imputation is still at a per-pixel level

22. ObservedGNN 1x1GNN 2x2 Distributions Average37.237.636.6 Maximum63.156.549.3 Variance172.2172.169.4 Models RMSE16.1512.65 Slope0.2290.230 Y-intercept29.128.0 Corr. coeff.0.230.36 GNN 1x1 Window GNN 2x2 Window

23. Summary – Bartlett Interpolation Inverse relationship between better model fits and maintaining sample variance between methods While kriging gives the highest degree of local scale agreement, it suffers from lack of spatial pattern Linear model and GNN imputation methods seem to maintain spatial pattern Plot footprint size made larger difference than anticipated

24. Strengths and limitations of GNN imputation Advantages: Recaptures most of variation in plot data Maintains multi-attribute covariance at a location Analytical flexibility: detailed vegetation data for post- mapping classification, analysis, and modeling Ability to map variability and assess sampling sufficiency Where strong gradients exist, can use other spatial environmental data to describe pattern Limitations: Map values are constrained to those at sampled locations Natural variability reduces local-scale prediction accuracy