1. U.S. Department of the Interior U.S. Geological Survey Accurate Projection of Small-Scale Raster Datasets 21 st International Cartographic Conference 10 – 16 Aug 2003 Durban, South Africa

2. Accurate Projection of Small-Scale Raster Datasets E. Lynn Usery, USGS, Mid-Continent Mapping Center, Rolla, MO Jeong Chang Seong, Northern Michigan University, Marquette, MI Dan Steinwand, Science Applications International Corp., EROS Data Center, Sioux Falls, SD Michael P. Finn, USGS, MCMC, Rolla

3. Outline Motivation Objectives Approach Methods Results Conclusions

4. Motivation – What is the Problem? Projection of global datasets with conventional GIS software results in error Errors affect global models and invalidate results

5. Objectives Develop a dynamic projection for raster data Determine methods to measure error and apply error correction Develop a better categorical resampler Develop an system to support map projection selection

6. Approach Empirical Testing Compute exact areas in spherical coordinates and replicate cell-by-cell in projected data Develop error theory using horizontal and vertical scale factors Develop a categorical resampler with user selection of output pixel on down-sampling Design and Implement a Decision Support System

7. Empirical Testing Multiple Datasets Global land cover, 30 arc-sec Global Life (ecological) Zones, ½ degree Global vegetation, 1 degree Multiple Projections Eckert IV Hammer Sinusoidal Mollweide Goode Homolosine Wagner IV Robinson (non-equal area)

8. Empirical Test Results Use of Commercial GIS Software Software is not always reliable for global projection Some projections do not run to completion Inverse projection results in extension of raster areas to 0-degree lines Repeat areas at edges of projection Computation times extensive

9. Mollweide from Commercial Software Michael P. Finn: Michael P. Finn:

10. Mollweide from USGS mapimg

11. Dynamic Projection of Raster Cells Compute areas of pixels in geographic coordinates Map each raster line to appropriate area Result is accurate for computation and analysis, but each raster line has different size

12. Areas of Single Pixels Computed from Spherical Coordinates (in meters 2 )

13. Error Theory and Modeling Best projection for global scale Criteria It shouldn’t lose pixel values when a local-scale dataset is projected to the global-scale projection It shouldn’t lose pixel values when a dataset in the global-scale projection is projected at a very accurate local-scale projection Efficient storage

14. Reprojection accuracies between global and local projections

15. Accuracy increase due to the change of skew angle

16. Error Theory and Modeling Summary Scale factor model explains most pixel value changes The change of pixel values occurs regardless of pixel resolutions Significant change as category numbers increase Significant change due to skewing

17. Categorical Resampling Down-sampling to larger pixel size aggregating multiple input pixels to one output pixel Nearest neighbor selects one pixel value Many pixels involved use simple statistical methods to determine output image pixels based on the area the pixel coverage in the input image

18. Extreme Downsampling and Reprojection with the Nearest Neighbor

19. Extreme Downsampling and Reprojection with the New Algorithm

20. Decision Support System for Map Projection Selection Global, continental, regional (10 ° min) Preserve shape, area, compromise Data type – raster or vector User input determines projection selection

23. Conclusions Projection of global raster data is a significant problem Area preservation in raster data is possible for computation and analysis, not for display A scale factor model accounts for most error and shows the sinusoidal projection to preserve areas better than others Categorical resampling with modal categories yields better results than nearest neighbor methods A Decision Support System is needed and now available

24. Addition Information Available at: http://mcmcweb.er.usgs.gov/carto_research/projection/index. html E-mail: mfinn@usgs.gov

25. U.S. Department of the Interior U.S. Geological Survey Accurate Projection of Small-Scale Raster Datasets 21 st International Cartographic Conference 10 – 16 Aug 2003 Durban, South Africa