Geographic Coordinate Systems

Coordinates are the values used to express a precise position on the earth's surface or on a map. There are multiple coordinate systems based on the various reference surfaces used to represent locations. When using a plane as a reference surface (for example, a map), the coordinates can be planar, projected, or 2D. (Two-dimensional). The term “two-dimensionality" refers to how each point on a map, for example, requires two values to establish its location (x, y). We are dealing with spatial coordinates or three- dimensional (or 3D) coordinates when we use a sphere or an ellipsoid as a reference surface, in which the height of the point must be added from the reference surface as a third dimension to determine its exact location, that is, we need to know the three values (x, y, and Z) for each location. In the case of the sphere, the coordinates are called Spherical Coordinates, while in the case of the ellipsoid they are called Geodetic Coordinates, Geographic Coordinates, or Ellipsoidal Coordinates. There are also one-dimensional (or 1D) coordinates, which often just reflect the point's height from the surface of the reference form utilized. There are four-dimensional (or 4D) coordinates in high-precision geodetic and geophysical applications where the location is determined by the point at a specific time so that its coordinates are (x, y, z, t), where the fourth dimension "t" expresses the time of measuring these coordinates for this location.

Locating on the Sphere

Centuries ago, scientists developed a technique for representing the position of any point on the Earth's crust (assuming the Earth is spherical) by:

·        The horizontal baseline is that great circle (that is, the one that passes through the center of the Earth), which is located in the middle of the distance between the two poles and is called the equator.

·        The vertical baseline was taken to be the semi-circle that connects the North and South poles and passes through Greenwich, England.

·        The equator was divided into 360 equal sections, and 360 semi-circles (imaginary or conventional) were drawn on the earth's surface, connecting the two poles and passing through one of the equator's division points. Longitude is the name given to each semi-circle. Because 360 degrees correspond to 360 divisions, dividing two adjacent angles equals one degree. The Greenwich longitude was numbered zero, and the longitudes adjacent to it from the east side were 1 degree east, 2 degree east,... to 180 degree east, and the same for the lines west of Greenwich, 1 degree west to 180 degree west. The longitude angle is the angle located in the plane of the equator between two sides, one of which passes through the Greenwich longitude while the other passes through the longitude of the same point.

·        The main longitude (Greenwich) was divided into 180 equal sections, and imaginary minor circles were drawn on the ground parallel to the equator (the small circle is the one that does not pass through the center of the Earth), with each circle passing through one of the points dividing the Greenwich longitude. Thus, the angle in the center of the globe between two consecutive division points is equal to 1 degree because 180 degrees correspond to 180 divisions, and these circles were named latitude circles, including 90 circles north of the equator circle and 90 circles south of the equator circle. Similarly, the circle of the equator was numbered zero, and the circle of latitude adjacent to it from the north side was 1 degree north, then 2 degrees north … to 90 degrees north, and the circles located south of the equator circled from 1 degree south to 90 degrees south. The latitude angle is defined as an angle in the plane of a circle of longitude, with its vertex at the center of the circle and its primary side passing through the plane of the equator and the other side crossing through a circle of latitude.

Types of Geographic Coordinate System

For geographic data, there are two primary types of coordinate systems: geodetic coordinate systems based on map projections and geographic coordinate systems based on latitude and longitude. The fundamental distinction is that projected geodetic coordinates are Cartesian coordinates with two orthogonal axes that are equally sized. Distances and areas determined in these units are comparable around the world. Geographic coordinates, on the other hand, are polar coordinates defined by two angles and a distance (the radius of the Earth) (between a given location and the equator and between this location and the prime meridian). Because the spacing between longitude lines diminishes from the equator to the poles, they are ineffective for comparing distances or regions around the world. They are, nevertheless, helpful as a full global system free of the distortion difficulties associated with map projections.

Geographical or Geodetic Coordinates

One of the coordinate systems whose center is the Earth's center and whose axes revolve with the Earth is a geodetic coordinate system. As a result, it's known as an earth-centered earth-fixed system, or ECEF for short. The system's center is in the earth's center of gravity, and its vertical z-axis coincides with the axis of rotation. On Earth, the first horizontal x-axis is perpendicular to the Greenwich meridian, and the second horizontal y-axis is perpendicular to the x-axis.

Any point in this system is represented by three values or three coordinates, indicating that it is 3D:

·        Longitude is symbolized by the Latin symbol (ʎ), and it is the angle measured in the plane of the equator between the Greenwich meridian (which is the longitude that is internationally used to be the number zero) and the longitude of the required point.

·        Latitude is symbolized by the Latin symbol (ɸ), which is the angle in the vertical plane formed by the perpendicular direction passing through the required point with the plane of the equator (the vertical direction on the surface of the ellipsoid does not pass through the center of the ellipsoid, whereas the perpendicular to the surface of the sphere does).

·        The height above the surface of the ellipsoid is represented by the symbol h and is called the Geodetic or Ellipsoidal Height.

There are several systems of units used to express latitude and longitude, the most well-known of which is the sexagesimal system of units, in which the full circle is divided into 360 degrees (the degree symbol isº) and the degree is divided into 60 parts, each of which is called a minute (the minute symbol isʹ), and then the minute is divided into 60 parts, each of them is called a second (the second symbol is "). For example, a longitude of 30º 45ʹ 52.3ʺ means that the location of this point is at 30 degrees, 45 minutes, and 52.3 seconds. The longitude lines are either east of the Greenwich meridian (symbolized by adding the letter E) or west of Greenwich (symbolized by adding the letter W). As for the latitude circles, they are either north of the equator (symbolized by adding the letter N) or south of the equator (symbolized by adding the letter S).

Spherical Coordinates

The spherical coordinate system is similar to the geodetic or geographic coordinate system, with only one difference: the reference surface here is the sphere, not the ellipsoid. The vertical direction on the surface of the sphere passes through its center, as opposed to the ellipsoid, where the vertical direction does not pass through its center.

Cartesian Geodetic Coordinates

It is a coordinate system having the same definition as the geodetic coordinate system, except that its three coordinates are longitudinal (i.e. in meters or kilometers) rather than curved (in degrees), making it easier to deal with, especially in calculations. Descartes, a French scientist, devised it in the seventeenth century. The center of the earth is the origin point of the Geodetic Cartesian Coordinates system, and its first axis, X, is formed by the intersection of the meridian plane passing through Greenwich with the plane of the equator. Its second axis, Y, is perpendicular to the X axis, and its third (vertical) axis, Z, is the earth's rotating axis, passing through its center and both poles. Each point's location is represented by three coordinates: Z, Y, and X.