Improving Decision Making Improving Decision Making in Choosing a Projection in Choosing a Projection

Michael Braymen Michael Braymen

OverviewOverview

ObjectiveObjective BackgroundBackground ProblemProblem Proposed SolutionProposed Solution ProcessProcess ObstaclesObstacles TimelineTimeline Literature Literature

ObjectiveObjective

•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.

BackgroundBackground

Early GIS adopters used common Early GIS adopters used common choices and local projections like choices and local projections like UTM and State planeUTM and State plane

Now easier and faster to project Now easier and faster to project Push to combine data into larger Push to combine data into larger

extentsextents

ProblemProblem

Organizations using GIS may not Organizations using GIS may not have expertise in-house to make have expertise in-house to make good decisions on projection choicegood decisions on projection choice

Example: USDA Forest Service Example: USDA Forest Service

Proposed SolutionProposed Solution

Create tools to assist the decision Create tools to assist the decision making processmaking process• Decision tree for common parameters Decision tree for common parameters

and characteristicsand characteristics• Graphic tool to display distortion of Graphic tool to display distortion of

selected characteristics with selected characteristics with quantifiable valuesquantifiable values

ProcessProcess

Two methods:Two methods:• Tissot’s indicatrixTissot’s indicatrix

• Grid of equal area polygonsGrid of equal area polygons

Tissot’s indicatrixTissot’s indicatrix The theory that at every point on a map The theory that at every point on a map

there is a pair of perpendicular lines that there is a pair of perpendicular lines that are also perpendicular on the earth are also perpendicular on the earth (Snyder 1987).(Snyder 1987).

Infinitely small circles on the earth always Infinitely small circles on the earth always project as perfect ellipses with the ratio of project as perfect ellipses with the ratio of the major and minor axis related to scale the major and minor axis related to scale and angular deformation. and angular deformation.

A statistical assessment of distortion can A statistical assessment of distortion can be done using a series of indicatrices for be done using a series of indicatrices for an area of interest.an area of interest.

Tissot’s indicatrixTissot’s indicatrix

Grid of equal area polygonsGrid of equal area polygons

1.1. Select equal area projection for Select equal area projection for area of interestarea of interest

2.2. Generate grid of equal area Generate grid of equal area polygonspolygons

3.3. Project grid to projection of interestProject grid to projection of interest

4.4. Calculate difference in area from Calculate difference in area from original, i.e. “true” areaoriginal, i.e. “true” area

5.5. Calculate statistics and displayCalculate statistics and display

Generate GridGenerate Grid

<graphic <graphic Examples>Examples>

Example for Pacific NWExample for Pacific NW

ObstaclesObstacles

Determining how to calculate Tissot’s Determining how to calculate Tissot’s indicatrix for any area of interest and indicatrix for any area of interest and projection.projection.

Assessing and minimizing additional Assessing and minimizing additional distortion due to point to point distortion due to point to point projection, e.g. lengths being shorter projection, e.g. lengths being shorter than they should be in a projection than they should be in a projection because a two vertex line should be a because a two vertex line should be a curve.curve.

Densify Arcs – Preliminary ResultsDensify Arcs – Preliminary Results

Original Arc length 10,000 metersOriginal Arc length 10,000 meters Add vertex every 100 metersAdd vertex every 100 meters Compare results of projection to Lambert Compare results of projection to Lambert

conformal conic for original and densified conformal conic for original and densified datadata

Single example –Single example –• 3 mm gap3 mm gap• Difference in perimeter = 0.008 metersDifference in perimeter = 0.008 meters• Difference in area = 48 square metersDifference in area = 48 square meters• Difference in computed error = 0.00005 %Difference in computed error = 0.00005 %

Estimated TimelineEstimated Timeline JULY - Document process for determining key JULY - Document process for determining key

characteristics and thresholdscharacteristics and thresholds AUGUST - Automate evaluation of area distortion AUGUST - Automate evaluation of area distortion

using equal area grid technique.using equal area grid technique. AUGUST - Analyze effect of vertex density on AUGUST - Analyze effect of vertex density on

projection distortion projection distortion SEPTEMBER - Automate evaluation of shape, scale SEPTEMBER - Automate evaluation of shape, scale

and area using Tissot’s indicatrixand area using Tissot’s indicatrix OCTOBER - Analyze sensitivity of analysis for OCTOBER - Analyze sensitivity of analysis for

continental and sub-continental extentscontinental and sub-continental extents NOVEMBER – Format and automate presentation of NOVEMBER – Format and automate presentation of

resultsresults ???? – Present Results???? – Present Results

LiteratureLiterature Adams, Oscar S. 1919, General Theory of Adams, Oscar S. 1919, General Theory of

Polyconic Projections: Washington, Government Polyconic Projections: Washington, Government Printing Office.Printing Office.

Deetz, Charles and Adams, Oscar S. 1945, Deetz, Charles and Adams, Oscar S. 1945, Elements of Map Projection with Applications to Elements of Map Projection with Applications to Map and Chart Construction: New York, Map and Chart Construction: New York, Greenwood Press. Greenwood Press.

Snyder, John Parr, 1987 Map Projections – A Snyder, John Parr, 1987 Map Projections – A Working Manual, US Geographical Survey Working Manual, US Geographical Survey Professional Paper 1395: Washington, Professional Paper 1395: Washington, Government Printing Office, ppg 20-21.Government Printing Office, ppg 20-21.

Tissot, Nicolas Auguste, 1881, Mémoire sur la Tissot, Nicolas Auguste, 1881, Mémoire sur la représentation des surfaces et les projections des représentation des surfaces et les projections des cartes géographiques: Paris, Gauthier Villars.cartes géographiques: Paris, Gauthier Villars.

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