Coordinate System

What is Coordinate System?

A Coordinate Reference System (CRS) is a framework used to represent the locations of geographic features, imagery, or observations. It enables spatial data to be accurately positioned and interpreted in relation to the Earth.

Each CRS is defined by the following elements:

1. Measurement Framework

   • Geographic: Coordinates measured on a spherical or ellipsoidal surface (latitude and longitude, referenced to the Earth’s center).
   • Projected: Coordinates projected onto a two-dimensional (planar) surface, typically using a mathematical transformation (map projection).

2. Unit of Measurement

   • Geographic CRS: Uses decimal degrees for latitude and longitude.
   • Projected CRS: Uses linear units such as meters or feet.

3. Map Projection Definition (for Projected CRS)

   • Specifies how the three-dimensional surface of the Earth is translated onto a two-dimensional plane. This includes the mathematical projection method and its parameters.

4. Other System Properties

   • Includes the reference ellipsoid (spheroid), geodetic datum, and projection parameters such as standard parallels, central meridian, and false easting/northing (x and y shifts).

Types of Coordinate System

There are two common types:

Geographic Coordinate Reference System (Geographic CRS)

A Geographic CRS uses latitude and longitude to specify locations on the Earth’s surface, referencing positions on a three-dimensional spherical or ellipsoidal model of the planet. It is defined by:

• An angular unit of measurement: Typically degrees for both latitude and longitude.
• A prime meridian: The zero-longitude line from which other longitudes are measured (commonly the Greenwich Meridian).
• A geodetic datum: A mathematical model of the Earth’s shape (based on a spheroid or ellipsoid) that provides a frame of reference for the coordinates.

Projected Coordinate Reference System (Projected CRS)

A Projected CRS transforms the Earth’s curved surface (as defined by a geographic CRS) onto a flat, two-dimensional Cartesian plane using a map projection. Every projected CRS is based on an underlying geographic CRS (including its datum and spheroid). Locations in a projected CRS are identified by:

• X and Y coordinates: These represent positions on a grid, measured in linear units (such as meters or feet).
• Grid origin: The origin (0,0) of the coordinate system, which may or may not be at the center of the projection area, depending on the specific projection parameters chosen.

Cartesian Coordinate Plane

A Cartesian plane assumes:

1. Right-angle (orthogonal) x and y axes
2. Uniform scale throughout the plane
3. Locations are measured relative to an origin (0,0)

Shape of the Earth (geodesy)

Concept of Spheroid and Datum

• Spheroid is a shape that approximates the shape of the earth.

• Datum is a mathematical model that defines the position of the spheroid relative to the center of the Earth. Datum describes how coordiate system is alligned with the Earth.

• There are two main types of Datum

  • Geodetic (or geographic) datum : defines origin and orientation of latitude and longitude.
  • Vertical datum : defines elevation or depth (sea level)

• Datum includes 2 things: A Spheroid and Reference Point

• Locations CRS changes depending on which datum and spheroid are used to describe locations.

Three Main Datums

Basically each datum has slightly different shape of the earth ellipsoid and the reference point.

Datum	Spheroid	Semi-major axis (m)	Flattening	Reference Point	Notes
WGS84	WGS84 Ellipsoid	6,378,137.0	1/298.257223563	Earth’s center of mass	Standard for GPS
NAD83	GRS80 Ellipsoid	6,378,137.0	1/298.257222101	Earth’s center of mass	Used for US/Canada; similar to WGS84, not identical.
NAD27	Clarke 1866 Ellipsoid	6,378,206.4	1/294.9786982	Meades Ranch, Kansas, USA	Local reference; older maps.

Next blog will describe and compare few main polar projections.