# Projected Coordinate System (PCS) : UTM, UPS, PLSS (Especially for GATE-Geospatial 2022)

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A projected coordinate system is defined on a flat, two-dimensional surface. Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions.

A projected coordinate system is always based on a geographic coordinate system that is based on a sphere or spheroid.

## Inverse and Forward Mapping Equations

In a projected coordinate system, locations are identified by coordinates on a grid, with the origin at the center of the grid. The value is given first and called easting, then the value is given and called northing.

The two values are called the x-coordinate and y-coordinate. Using this notation, the coordinates at the origin are and .

## Examples of Projected Coordinates System

Projected Coordinates System is following below:

- Rectangular Coordinates/Plane Coordinates
- UTM Grid system
- UPS Grid System
- PLSS Grid System
- State Plane Coordinates System

A grid system allows the location of a point on a map to be described in a way that is meaningful and universally understood.

## Details of Some Coordinate System

Out of these State Plane Coordinates System is most important and we will discuss these in next topic. Details of some others are:

**Transverse Mercator Projection (UTM)**: The transverse Mercator projection is often used for sections of the earth that are taller (south to north) than they are wide (west to east) . The Universal Transverse Mercator (UTM) coordinate systems use this projection. Many State Plane Coordinates Systems (SPCS) in the U. S. also use this projection. The transverse Mercator projection uses the following parameters for its projection equations:- Central Meridian
- False Easting
- False Northing
- Latitude of Origin
- Scale Factor

**Lambert Conformal Conic Projection**: The Lambert conformal conic projection is often used for sections of the earth that are wider (west to east) than they are tall (south to north) . Most state plane coordinate systems in the U. S. use this projection. The Lambert conformal conic projection uses the following parameters for its projection equations:- Central Meridian
- False Easting
- False Northing
- Latitude of Origin
- Standard Parallel 1
- Standard Parallel 2

**UPS Coordinate System**: Universal Polar Stereographic (UPS) coordinate system is a conformal projection for the polar regions. At the North pole, it extends latitudes 90°N – 83° 30′ N and 90°S – 79° 30 ′ s at the South pole to provide a 30′ overlap with UTM. This is because UPS coordinate system is usually used in conjunction with UTM coordinate system to locate positions on the earth ′ s surface. UTM coordinate system divides the earth into 60 zones each 6 degrees of longitude and extending from 84° North latitude to 80° South latitude. The polar regions are excluded. The origin of the UPS coordinate system are the poles (north or south) , where False easting (X) and false northing (Y) coordinate values are 2,000, 000 m. The X-axis lies along longitudes 90°E and 90°W. The Y-axis lies along longitudes 0° and 180°. For both the north and south zones, the scale factor at the pole is 0.994, and a parallel of true scale is created at 81º06 ′ 52.3 ″ . The system achieves the same accuracy (scale error of one unit in 2,500) as the UTM system. The UPS coordinate system extends a smaller area in the North pole because the UTM coordinate system was extended by 4° in the North pole to cover Greenland. Greenland is the largest island on Earth and is a self-governing overseas administrative division of Denmark.**Public Land Survey System (PLSS)**: The public land survey system is most often used on topographic maps published in the United States and has its roots in the early surveys of North America in the 1700՚s. The PLSS system differs from the coordinate systems described above in that it is more descriptive, and relies less on absolute measurements of location. It is a good way to give a quick approximation of a location, but the main drawback is its lack of accuracy. In each area early surveyors established a principal meridian running north-south, and a base line running east-west. Using the projection equations, geodetic locations on the surface of the earth (usually designated as degrees longitude and latitude) can be converted to coordinates (usually designated as eastings and northings, or x and y) in the planar system. Using the reverse projection equations, the coordinates on the planar system can be converted to locations on the surface of the earth.

## Important Aspects

- The coordinates in one planar system (PCS) do not usually align with the coordinates in a different planar system. To translate a coordinate from one PCS to another requires conversion from the coordinate from the first PCS to a geodetic location (longitude, latitude) on the surface of the earth and then project that location to a coordinate in the second PCS.
- Not all longitudes and latitude are the same. Each model of the earth (geographic coordinate system) will map locations on the surface of the earth to different longitudes and latitudes. Translating a longitude, latitude point from one geographic coordinate system to another is not a simple problem, so be aware that the underlying geographic coordinate systems may prevent you from translating the points from one PCS to another.