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GISI Foundation: Spatial Reference Systems, Projections, and Coordinate Geometry

GISI Foundation · Work through your exam, one topic at a time.

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Spatial Reference Systems, Projections, and Coordinate Geometry

This domain carries most of the calculation and "why is my map wrong" marks. You must distinguish a coordinate system from a projection, know what each projection family preserves, and be able to reason about the error introduced when you measure on a plane.

Geographic versus projected

  • A geographic coordinate system (GCS) is a datum plus angular units; positions are latitude/longitude. EPSG:4326 is WGS 84 geographic; EPSG:4269 is NAD83 geographic.
  • A projected coordinate system (PCS) applies a map projection to that datum and uses linear units, for example EPSG:32633 (WGS 84 / UTM zone 33N).
  • A datum is an ellipsoid plus its tie to the Earth. NAD27 to NAD83 shifts can reach roughly 100 m or more in North America; NAD83 to WGS 84 differences are around a metre or two in CONUS. Always apply a published transformation rather than assuming identity.

What each projection family preserves

  • Conformal (Mercator, Lambert Conformal Conic, Transverse Mercator): preserves local angles and shape; area is distorted, badly at high latitude.
  • Equal-area (Albers, Mollweide, sinusoidal): preserves area; shapes shear.
  • Equidistant: true distance only from the centre point or along standard lines, never everywhere.
  • Azimuthal: true direction from the centre.
  • UTM has 60 zones, each 6 degrees wide, transverse Mercator with a central-meridian scale factor of 0.9996; distortion grows toward zone edges, which is why large study areas often use a state plane or custom Albers system.

Worked example

Two points in UTM zone 33N yield a planar Euclidean distance of 1,000.00 m near the zone edge, where the local scale factor is about 1.0008. The true ground distance is roughly 1,000.00 / 1.0008 = 999.2 m, an over-estimate of about 0.8 m (0.08%). Reasoning: planar distance equals ground distance only along the line where the scale factor is 1; at the central meridian that is 0.9996, so a small correction applies. For cadastral work the correction matters; for regional screening it does not.

Traps that cost marks

  • Calling EPSG:4326 a projection. It is a geographic coordinate system; Web Mercator (EPSG:3857) is the projected one.
  • Assuming on-the-fly reprojection rewrites your data; it only changes display, and analysis still runs in the data frame's coordinate system.
  • Mixing layers with different datums without a transformation.