U.S. Department of the Interior U.S. Geological Survey Projecting Global Raster Databases July 11, 2002 Joint International Symposium on GEOSPATIAL THEORY, PROCESSING AND APPLICATIONS, Ottawa, Canada

Projecting Global Raster Databases E. Lynn Usery Michael P. Finn Douglas Scheidt U.S. Geological Survey 1400 Independence Road Rolla, Missouri 65401

Outline Motivation Objectives Approach Methods – Empirical Testing Results Conclusions

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

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

Approach Empirical Testing Design and Implement a Decision Support System for map projection selection Compute exact areas in spherical coordinates and replicate cell-by-cell in projected data

Empirical Testing Multiple Datasets Global land cover, 30 arc-sec Global elevation, 30 arc-sec Global population, 30 arc-sec Global temperature, ½ degree Global precipitation, ½ degree Global vegetation, 1 degree Down-sample 30 arc-sec data to 1,4,8,16,25,50 kilometers

Empirical Testing Multiple Projections – Primarily Equivalent Eckert IV Hammer Sinusoidal Mollweide Lambert Equal Area Cylindrical Wagner IV Robinson (non-equal area)

Empirical Test Results Use of Commercial GIS Software Commercial GIS software is unreliable for global projection; variety of problems Projections do not complete Work at some resamplings, but not others Inverse projections result is extension of raster areas to 0-degree lines Repeat areas at edges of projection Computation times extensive (100 to 200 hours on high end computers) May not use exact projection equations

Hammer from Commercial Software

Hammer from USGS Mapimg

Mollweide from Commercial Software

Mollweide from Mapimg

Sinusoidal from USGS Mapimg

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

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 For 30 arcsec data, a cell at equator is approximately 1 km x 1 km, cell area = 1 km 2 Near poles, a cell is 1 km x m, cell area = 6 m 2

Area Calculation for Equiangular Pixels in Spherical Coordinates

Latitude30 Arcsec0.5 Degree1.0 Degree 0 858,6313,091,035,69212,363,671, ,6312,982,220,44811,970,315, ,6282,670,171,82110,761,202, ,1882,176,155,4088,818,730, ,3701,533,837,6096,275,272, ,291786,991,3183,304,173, (-1 unit) 6313,487,417107,896,706 Pixel Areas Computed from Spherical Coordinates (in meters 2 )

Conclusions Projection of global raster data is a significant problem Commercial GIS software is not reliable for global projection Users need guidance and software that works correctly for raster data

Conclusions A Decision Support System is needed and now available Area preservation in raster data is possible for computation and analysis, not for display

U.S. Department of the Interior U.S. Geological Survey Projecting Global Raster Databases July 11, 2002 Joint International Symposium on GEOSPATIAL THEORY, PROCESSING AND APPLICATIONS, Ottawa, Canada