Coordinate systems and spatial reference

Every spatial dataset lives in a coordinate system. Geographic coordinates (lat/lon in degrees) are the WGS84 / GPS standard but are NOT a Cartesian space — distances depend on latitude, and treating them as Cartesian distorts everything. Projected coordinates (UTM, state plane, Lambert Conformal) are designed for local Cartesian analysis but introduce distortion outside their valid zone. Choosing the right system is fundamental.

Geographic coordinates: NOT Cartesian

Latitude and longitude in degrees describe positions on the Earth's surface (an oblate spheroid, locally a sphere). One degree of LATITUDE is about 111 km everywhere. One degree of LONGITUDE is 111 × cos(latitude) km — 111 km at the equator, 0 km at the poles.

Treating (lat, lon) as Cartesian (equirectangular projection) means assuming 1° lon = 1° lat = same distance. This is fine within ~5° of the equator. AT MID-LATITUDES (30-60°), east-west distances are over-counted by factors of 1.5-2×. At high latitudes, the distortion is catastrophic.

Haversine distance: great-circle on a sphere

The Haversine formula computes the great-circle distance between two lat/lon points:

where φ is latitude, λ is longitude, R ≈ 6371 km. Use Haversine when working with raw lat/lon over distances > 10 km.

Projected coordinate systems

UTM, state plane, Lambert Conformal — each takes a region of the Earth and maps it to a 2D Cartesian plane with bounded distortion. UTM divides the world into 60 zones (6° wide). Within a zone, distances are nearly exact; across zones, distortion grows.

For geostatistical work in a SINGLE region (a basin, a country, an oil field), pick the right UTM zone or state plane and convert. Then use Euclidean distance freely. Most GIS tools (QGIS, ArcGIS, geopandas, shapely) automate this.

When to convert vs. when not

• Local field (< 50 km × 50 km): use local Cartesian or UTM. Euclidean distance valid.
• Regional study (state, basin): UTM if within a zone; state plane in US contexts.
• Continental study: use spherical / great-circle distance directly. Don't project — distortion accumulates.
• Global study (climate, oceanography): spherical / WGS84. Project only for visualisation.

Precision considerations

Real-world data have positioning error. GPS: ~3-10 m horizontal. RTK GPS: ~1-3 cm. Standard well-log: depths to 0.1 ft. Mapping coordinates rounded to nearest 100 m introduce systematic uncertainty that may exceed model precision; always document the positional precision alongside the data.

Try it

• Default centre latitude 40°. Look at the distance table. Haversine and UTM/local Cartesian agree closely (within ~0.2%). Equirectangular shows ~20% error on east-west pairs — significant in mid-latitudes.
• Move the centre latitude to 70° (Arctic Circle). Equirectangular error jumps to ~70% — 1° longitude is now only ~38 km, not 111 km. Cosine factor = cos(70°) = 0.34.
• Move to 0° (equator). Equirectangular error nearly vanishes; cos(0°) = 1.0; one degree lon ≈ one degree lat ≈ 111 km.
• Move to 85° (near pole). Catastrophic distortion in equirectangular. The widget's recommendation switches to "UNACCEPTABLE; use Lambert Conformal".
• For pure visualisation (display only, no distance calculations), equirectangular is OK. For variogram computation, kriging weights — ALWAYS use Haversine on geographic, or convert to a projection.

A geostatistical analyst imports global oceanographic data with lat/lon coordinates and uses Euclidean distance to compute variograms over the entire Pacific Ocean. Why is this a critical error, and what should they do instead?

What you now know

Geographic coordinates require special handling: Haversine for great-circle distances, or projection to a local Cartesian system. UTM is the standard projection for regional studies. The CHOICE OF COORDINATE SYSTEM affects every downstream geostatistical computation (variograms, kriging weights, neighbourhood selection). Get it right at the start; retro-fixing is painful. §0.5 turns to spatial sampling and the biases it introduces.

Mark section complete →

References

• Snyder, J.P. (1987). Map Projections — A Working Manual. USGS Professional Paper 1395. (The standard reference; free PDF.)
• Iliffe, J., Lott, R. (2008). Datums and Map Projections, 2nd ed. Whittles Publishing.
• OGC, "Coordinate Reference Systems (CRS) Vocabulary." Open Geospatial Consortium standards.
• Hofmann-Wellenhof, B., Moritz, H. (2006). Physical Geodesy, 2nd ed. Springer. (For deep understanding of geodetic datums.)
• Cressie, N., Wikle, C.K. (2011). Statistics for Spatio-Temporal Data. Wiley. (Chapter on coordinate systems and projections in geostatistics.)