Improving Decision Making in Choosing a Projection

1. Improving Decision Making in Choosing a Projection Michael Braymen

2. Overview • Objective • Background • Problem • Proposed Solution • Process • Obstacles • Timeline • Literature

3. Objective • To facilitate decision making in choosing projections. • Expand the common decision process for choosing projections • Create a tool that will allow comparison of different projections • Display distortion of various characteristics of projections both graphically and quantifiably. • The audience for the tool would be GIS professionals • Prepare results in form for non-GIS professional.

4. Background • Early GIS adopters used common choices and local projections like UTM and State plane • Now easier and faster to project • Push to combine data into larger extents

5. Problem • Organizations using GIS may not have expertise in-house to make good decisions on projection choice • Example: USDA Forest Service

6. Proposed Solution • Create tools to assist the decision making process • Decision tree for common parameters and characteristics • Graphic tool to display distortion of selected characteristics with quantifiable values

7. Process • Two methods: • Tissot’s indicatrix • Grid of equal area polygons

8. Tissot’s indicatrix • The theory that at every point on a map there is a pair of perpendicular lines that are also perpendicular on the earth (Snyder 1987). • Infinitely small circles on the earth always project as perfect ellipses with the ratio of the major and minor axis related to scale and angular deformation. • A statistical assessment of distortion can be done using a series of indicatrices for an area of interest.

9. Tissot’s indicatrix B. A. C. D.

10. Grid of equal area polygons • Select equal area projection for area of interest • Generate grid of equal area polygons • Project grid to projection of interest • Calculate difference in area from original, i.e. “true” area • Calculate statistics and display

11. Generate Grid • <graphic Examples>

13. Example for Pacific NW

14. Obstacles • Determining how to calculate Tissot’s indicatrix for any area of interest and projection. • Assessing and minimizing additional distortion due to point to point projection, e.g. lengths being shorter than they should be in a projection because a two vertex line should be a curve.

15. Densify Arcs – Preliminary Results • Original Arc length 10,000 meters • Add vertex every 100 meters • Compare results of projection to Lambert conformal conic for original and densified data • Single example – • 3 mm gap • Difference in perimeter = 0.008 meters • Difference in area = 48 square meters • Difference in computed error = 0.00005 %

16. Estimated Timeline • JULY - Document process for determining key characteristics and thresholds • AUGUST - Automate evaluation of area distortion using equal area grid technique. • AUGUST - Analyze effect of vertex density on projection distortion • SEPTEMBER - Automate evaluation of shape, scale and area using Tissot’s indicatrix • OCTOBER - Analyze sensitivity of analysis for continental and sub-continental extents • NOVEMBER – Format and automate presentation of results • ???? – Present Results

17. Literature • Adams, Oscar S. 1919, General Theory of Polyconic Projections: Washington, Government Printing Office. • Deetz, Charles and Adams, Oscar S. 1945, Elements of Map Projection with Applications to Map and Chart Construction: New York, Greenwood Press. • Snyder, John Parr, 1987 Map Projections – A Working Manual, US Geographical Survey Professional Paper 1395: Washington, Government Printing Office, ppg 20-21. • Tissot, Nicolas Auguste, 1881, Mémoire sur la représentation des surfaces et les projections des cartes géographiques: Paris, Gauthier Villars.

18. Questions?