Spatial Reference, coordinate system, projection, elliptical body

Spatial references coordinate systems, projections, datums, ellipsoids-confusing?

People are often mixing the above as if they were one and the same, so here's a recap
Of them. One of the things you often find people saying is that "my data is in
WGS84 coordinate system ". This doesn't really make sense, but I will get back to this
Later.

This is a very confusing subject, and I might have gotten a few things wrong myself,
So please add a comment and I'll update it ASAP.

Coordinate systems

A coordinate system is simply put a way of describing a spatial property relative
To a center. There is more than one way of doing this:

• The Geocentric coordinate system is based on a normal (X, Y, Z) coordinate system
  The origin at the center of Earth. This is the system thatGPS
  
  
  Uses internally
  Doing it calculations, but since this is very unpractical to work with as a human
  Being (due to the lack of well-known concepts of east, north, up, down) it is rarely
  Displayed to the user but converted to another coordinate system.
• The Spherical coordinate system is probably the most well-known. It is based on angles
  Relative to a prime meridian and Equator usually as longpolling and Latitude. Heights
  Are usually given relative to either the mean sea level or the datum (I'll get back
  To the datum later ).
• The Cartesian coordinate system is defined as a "flat" coordinate system following
  The curvature of the earth. It's not flat in the sense that it usually follows
  The earth's curvature in one direction and has a known scale-error in the other direction
  Relative to the distance of the origin. The most well-known coordinate system is
  Universal Transverse Mercator (UTM), but surveyors define their own little local flat
  Coordinate systems all the time. It is very easy to work with, pretty accurate over
  Small distances making measurements such as length, angle and area very straightforward.
  Cartesian coordinate systems are stronugly connected to projections that I will cover
  Later.

 
 

Datums and ellipsoids

Some of the common properties of the above coordinate systems are that they are all
Relative to the center of Earth and has t the Geocentric coordinate system, uses
A height system relative to the surface of the earth.

This poses two immediate problems:

• Where is the center of the earth
• What is the shape of the earth?

By
Now most people shoshould know that the earth isn't flat (although there
Are still some who doubts it
). If we define the surface of Earth as being at
Mean sea level (often referred to as the Geoid), we don't get a spheroid or even
Ellipsoid. Because of gravitational changes often caused by large masses such as mountain
Ranges etc, Earth is actually very irregular with variations of +/-100 meters. Since
This is not very practical to work with as a model of earth, we usually use an ellipsoid
For approximation. The ellipsoid is defined by its semi-major axis, and either
Flattening of the semi-minor axis.

The center and orientation of the ellipsoid is what we call the datum. So the datum
Defines an ellipsoid and through the use of a set of points on the ground that we
Relate to points on the ellipsoid, we define the center of the Earth. This poses
Another problem, because continental drift moves the points used to define the points
Around all the time. This is why the name of a datum usually have a year in it, often
Referring to the position of those points January 1st of that year (although that
May vary ).

There are a vast amount of datums, some used for measurements all over the world,
And other local datums defined so they fit very well with a local area. Some common
Ones are: World Geodetic Data 1984
(WGS84), European
Data 1950
(ED50) and North American
Data 1983
(NAD83 ).

The most well-known is WGS84 used by the GPS systems today. It is a good approximation
Of the entire world and fix-points defined almost all over the world. When it was
Defined they forgot to include points in Europe though, so the Europeans now have
Their own ETRS89, which is usually referred to as the "realization of WGS84 in Europe ".
The problem here was solely because of continental drift, so they defined some points
Relative to WGS84 in 1989, and keeps track of the changes. In most use-cases it is
Of no real importance and you can use one or the other.

I mentioned earlier that people often refer to having their data in WGS84, and you
See now why this doesn't make sense. All you know from that is that the data is defined
Using the WGS84 datum, but you don't know which coordinate system it uses.

Projections

The earth isn't flat, and there is no simple way of putting it down on a flat paper
Map (or these days a flat screen), so people have come up with all sorts of ingenious
Solutions each with their pros and cons. Some preserves area, so all objects have
A relative size to each other, others preserve angles (conformal) like the Mercator
Projection, some try to find a good intermediate mix with only little distortion on
Several parameters etc. Common to them all is that they transform the world onto
Flat Cartesian coordinate system.

A common statement that I hear in GIS is the following "My map doesn't have a projection ",
But this is simply not possible (unless you have a good old globe). Often people are
Referring to data that is in longpolling/latitude and displayed on a map without applying
Any projection. What happens is that the system applies the simplest projection it
Can: Mapping longpolling directly to X and Latitude to Y. This results in an equirectangular
Projection, also called the "Plate Carree" projection. It results in very heavy distortion
Making areas look squashed close to the poles. The "opposite" of the Plate Carree
Is the Mercator projection which stretches areas close to the poles in the opposite
Direction, making them look very big. This is the type of projection you see used
On Live maps
,Google


Maps and Yahoo maps
, But as expected often mistakenly
Thinks, they do NOT use WGS84.

Spatial reference

The spatial reference is a combination of all the above. It defines an ellipsoid,
A datum using that ellipsoid, and either a geocentric, geographic or projection.
Projection also always has a geographic coordinate system associated with it. The European
Petroleum Survey Group
(EPSG) has a huge set of predefined spatial references,
Each given a unique ID. These ID's are used throughout the industry and you can download
An Access database with all them from their website, as well as some very good clients
On projection.

So when you hear someone saying they have their data in WGS84, you might as well assume
They have longpolling/latitude data in WGS84 projected using Plate Carree.
Spatial reference ID of this is EPSG: 4326.

Spatial References are often defined in a Well-known format defining all these parameters.
The Spatial Reference EPSG: 4326 can therefore also be written:

GEOGCS ["GCS_WGS_1984", DATUM ["D_WGS_1984", SPHEROID ["WGS_1984", 6378137,298.257223563], PRIMEM ["Greenwich", 0], UNIT ["Degree", 0.0174532925199433]

Live/Google/Yahoo maps use a Mercator projection, but although their datum is based
On WGS84, they use a sphere instead of an ellipsoid. This means that they use
Same center and orientation as WGS84, but without applying any flattening. The spatial
Reference string for their projection therefore becomes:

PROJCS ["Mercator", GEOGCS ["WGS84_Sphere", DATUM ["WGS84_Sphere ",
SPHEROID ["GRS 1980 Authalic Sphere", 6378137, Infinity, AUTHORITY ["EPSG", "7048"],
TOWGS84 [0, 0, 0, 0, 0, 0], PRIMEM ["Greenwich", 0, AUTHORITY ["EPSG", "8901"],
UNIT ["degree", 0.0174532925199433, AUTHORITY ["EPSG", "9102"], AXIS ["E", EAST], AXIS ["N ",
NORTH], PROJECTION ["Mercator_1SP"], PARAMETER ["False_Easting", 0], PARAMETER ["False_Northing ",
0], PARAMETER ["Central_Meridian", 0], PARAMETER ["Latitude_of_origin", 0], UNIT ["metre ",
1, AUTHORITY ["EPSG", "9001"], AXIS ["East", EAST], AXIS ["North", NORTH]