A Very Short Introduction to Geodesy

The science of the shape of the Earth

Brendan Harmon


A geodetic datum is a coordinate system and a reference surface. Important examples include:

  • World Geodetic System 1984 (WGS84)
  • North American Datum of 1983 (NAD83)
  • North American Vertical Datum 1988 (NAVD88)


A model of mean global sea level based on gravitational potential. The geoid represents mean sea level without winds, currents, and tides through both oceans and continents. The geoid is used as a vertical datum for measuring orthometric height above sea level.


NASA Scientific Visualization Studio

GRASS Commands

To map the geoid in GRASS GIS, download EGM08_25.prj and EGM08_25.tif. Then create a new GRASS location from EGM08_25.prj.

g.region n=90:00:00N s=90:00:00S e=360:00:00E w=00:00:00W
r.in.gdal -r input=EGM08_25.tif output=emg
r.colors map=emg color=viridis
r.relief input=emg output=relief zscale=500
r.shade shade=relief color=emg output=shade brighten=50
d.legend raster=emg at=5,35,2,3 font=Lato-Regular fontsize=16


The World Geodetic System 1984 (WGS84) uses the Earth Gravitational Model 1996 (EMG96) as its geoid reference. the Global Positioning System (GPS) uses WGS84 as its coordinate reference system (CRS)

Map Projections

A map projection transforms a globe into a planar map that can be measured.

Two-sided Azimuthal Polar Projections

Gott, Goldberg, & Vanderbei, 2021. Flat Maps that improve on the Winkel Tripel.

Universal Transverse Mercator

The Universal Transverse Mercator (UTM) coordinate system divides the world into 60 longitudinal zones and 20 latitudinal zones, 6 degrees wide and 12 degrees tall.

Universal Transverse Mercator

State Plane Coordinate System

The State Plane Coordinate System of 1983 is based on the North American Datum of 1983 (NAD 83). Each state in the US has at least one zone in either the Transverse Mercator, Lambert Conformal Conic, or Oblique Mercator projection. To reduce distortion, many states have multiple zones.

Course Datasets

Natural Earth


Governor’s Island

NY Long Island State Plane Feet