Chapter 03

Geodesy & Projections

Flattening a curved Earth is a mathematical impossibility. Learn why every map is a compromise and how to choose the right one for your work.

At a Glance

Prereqs: Chapters 01-02 Time: 25 min read + 25 min practice Deliverable: Projection choice memo

Learning outcomes

  • Distinguish datum, projection, and CRS in practical terms.
  • Predict and explain distortion patterns for common projections.
  • Select a CRS for measurement and justify the choice.

Key terms

CRS, datum, projection, EPSG, Web Mercator, UTM, distortion

Stop & check

  1. Why is Web Mercator a poor choice for area calculations?

    Answer: It distorts area (especially away from the equator).

    Why: It was designed for web mapping convenience, not measurement accuracy.

    Common misconception: If it looks right on screen, it must measure right.

  2. When is UTM a good default?

    Answer: For local/regional work within one UTM zone.

    Why: It preserves distance/area reasonably well locally in meters.

    Common misconception: UTM is a single global CRS; it is a zone system.

Try it (5 minutes)

  1. Pick one city-sized AOI and write the unit you want for distance (meters or degrees).
  2. Explain in one sentence why your unit choice matters for buffers.

Lab (Two Tracks)

Both tracks produce the same deliverable: a short memo (8-10 sentences) recommending a CRS for a stated task.

Desktop GIS Track (ArcGIS Pro / QGIS)

Reproject one layer and measure a distance/area. Compare results before/after and include one screenshot.

Remote Sensing Track (Google Earth Engine)

Load an AOI and compute a simple area/distance summary. Note the CRS/projection assumptions in your memo.

Common mistakes

  • Measuring distance/area in geographic coordinates (degrees).
  • Mixing layers with different CRS without noticing.
  • Assuming EPSG codes imply the same units everywhere.

Further reading: https://www.ucgis.org/site/gis-t-body-of-knowledge

The Fundamental Geodetic Challenge

The Earth is not a perfect sphere; it's an oblate spheroid (bulging at the equator) with a bumpy, geoid surface. To map it, we must first model it using a Datum.

The "Orange Peel" Problem: Try peeling an orange and flattening the skin. You'll find it impossible without tearing it or stretching the surface. Every map projection does exactly this to our planet.

Latitude, Longitude & The Graticule

To measure location on a varied sphere, we need a grid.

Latitude Longitude and Graticule
  • Latitude (Parallels): Measure North-South (0° at Equator to 90° at Poles). Lines never touch.
  • Longitude (Meridians): Measure East-West (0° at Prime Meridian to 180°). Lines converge at poles.

Interactive Projection Explorer

Toggle between different mathematical projections to see how the shapes and sizes of continents change. Watch Greenland closely, as it is the classic victim of map distortion!

🛑 Critical GIS: The Politics of Maps

For centuries, the Mercator projection was the standard for schools. Accused of "Colonialist Bias," it exaggerates the size of Europe and North America while shrinking Africa and South America. (Toggle between Mercator and Gall-Peters or Equal Area above to see the massive difference! Africa is actually 14 times larger than Greenland.)

Projection Surfaces

How do we flatten the globe? Imagine wrapping a piece of paper around a lightbulb (the translucent Earth). Where the paper touches the globe, distortion is minimal. As you move away from the point of contact, distortion increases.

Map Projection Surfaces
  • Cylindrical: Paper wrapped as a tube (Good for Equator, e.g., Mercator).
  • Conic: Paper formed as a cone (Good for Mid-Latitudes, e.g., US & Europe).
  • Planar (Azimuthal): Paper touching one point (Good for Poles).

🔦 The Lightbulb Analogy: Cylindrical Projection

Cylindrical projection shown as light from a bulb projecting through a globe onto a surrounding cylinder

A lightbulb inside a transparent globe projects features onto a surrounding cylinder

How it works:

  1. Imagine a transparent globe with continents drawn on it.
  2. Place a lightbulb at the center of the globe.
  3. Wrap a cylinder of paper around the globe, touching at the Equator.
  4. The light projects the shadows of the continents onto the cylinder.
  5. Unroll the cylinder—you have a flat map!
⚠️ The Catch:

Notice how features near the Equator (where the cylinder touches) are projected accurately. But features near the poles are stretched dramatically—the light rays hit the cylinder at increasingly steep angles, causing massive distortion. This is why Greenland looks enormous on a Mercator map!

The "Big Four" Distortions

When you flatten the Earth, you must sacrifice one or more of these properties. A projection can be:

  • Conformal: Preserves Shapes (essential for local surveying).
  • Equivalent: Preserves Area (essential for thematic maps of population).
  • Equidistant: Preserves Distance (measured from one or two points).
  • Azimuthal: Preserves Direction (important for flight paths).

Map Preprocessing

Projections are just the beginning. To make different datasets play nicely together, we often need to perform "housecleaning" tasks:

1. Georeferencing

Aligning a raw image (like a scanned map or aerial photo) to a known coordinate system. This is done by creating control points that link the pixels of the image to real-world coordinates.

World Files: Georeferencing often creates a small text file (e.g., .tfw or .jpw) containing the math to position the image.

2. Resampling

When you change a raster's projection or cell size, the grid must be recalculated. Common methods include:

  • Nearest Neighbor: Fast, keeps original values (good for discrete data like Land Use).
  • Bilinear Interpolation: Smoothes values (good for continuous data like Elevation).

3. Edge Matching

Stitching together adjacent maps (like tiles) to ensure features like roads connect seamlessly across boundaries.

State Plane Coordinate System (SPCS)

While UTM is global, the State Plane Coordinate System is purely American. It divides the U.S. into over 120 zones to minimize distortion for local surveying and engineering.

State Plane Coordinate System Map

Figure 3.6: The SPCS divides states like California into multiple horizontal belts (Zones) to maintain high precision.

  • The Goal: To allow surveyors to treat the earth as "flat" within a small zone with error rates of less than 1 part in 10,000.
  • The Zones:
    • North-South States: (like California) are often divided into horizontal strips using the Lambert Conformal Conic projection.
    • East-West States: (like Illinois) often use vertical strips based on the Transverse Mercator projection.
  • The Catch: It is a nightmare when your project crosses zone boundaries (e.g., a roadmap from San Francisco to Los Angeles crosses multiple zones).

Summary of Big Ideas

  • Geodesy is the science of measuring Earth's shape.
  • A Datum (like WGS84) is a mathematical reference for coordinates.
  • Coordinate Systems can be Geographic (lat/long) or Projected (meters/feet).
  • The Mercator projection is perfect for sailing but terrible for comparing country sizes.

Chapter 03 Checkpoint

1. Which projection is the "standard" used by most web maps (Google Maps, Leaflet)?

2. If you are making a map of "Total Forest Cover" where comparing sizes is crucial, which type of projection should you use?

Chapter Glossary

Geoid The hypothetical shape of the earth, coinciding with mean sea level and its imagined extension under (or over) land areas.
Standard Parallel The line of latitude where the projection surface touches the globe. Distortion is zero along this line.
Rhumb Line A line on a sphere that cuts all meridians at the same angle; the path taken by a ship or plane that maintains a constant compass direction.
← Chapter 02: Map Design Chapter 04: GNSS & Positioning →

BoK Alignment

Topics in the UCGIS GIS&T Body of Knowledge that support this chapter.