The map coordinate system

4. The map coordinate system

As the Earth is round, when positions on the Earth are to be established, those positions must be transferred from the real-world locations to the map via a coordinate system. The map coordinate system is a reference of global positions on a flat map. The origins of coordinates are on the Earth’s surface. It is a rectangular coordinate system originated from intersection of at least two axes. There are two types of coordinate systems, which are two-dimensional and three-dimensional coordinate systems. These coordinates are references of the global positions with geographic coordinate systems.

1.  Geographic coordinate systems

The Geographic coordinate systems establish positions on the Earth by referencing the longitude and latitude values measured from the angular distances from the origins of latitude and longitude. The origin of latitude is established from the point where it intersects the Earth’s center and is perpendicular to the rotation axis. That originating plane is called an equator which divides the globe into northern and southern hemispheres. Latitude values are measured relatively to the equator and range from –90 degrees at the South Pole to +90 degrees at the North Pole. As such, the reference of latitude values to indicate positions on the Earth will be measured by Degrees Minute Second, and marked with the letters to indicate North or South directions, such as Latitude 30 degrees 20 minutes 15 seconds North.

The origin of longitude, meanwhile, is established from the vertical plane in line with the globe’s axis where it passes the astronomical tower in Greenwich, UK. This origin is called the Prime Meridian which divides the Earth into the Eastern and Western hemispheres.

Longitude values are measured relatively to the prime meridian. They range from -180 degrees when travelling west to 180 degrees when travelling east. The measurement unit of longitude values are the same as that of the latitudes, except the direction’s marks which indicate the west or south azimuth, such as Longitude 90 degrees 20 minutes 45 seconds West.

2. UTM coordinate systems

UTM coordinate systems are adapted from Transverse Mercator map projection to maintain conformality property by using a cylinder to intersect the globe between Latitude 84 degrees north and 80 degrees south. The radius of a cylinder is shorter than that of the globe and the cylinder cuts through two meridian lines—inward and outward—which are called “Secant”, allowing more accuracy especially at both sides of the Central Meridian.

This type of coordinate systems were used by the US Army in 1946 to make maps with more accurate details. The systems are obtained from azimuthal and conformal map projections, and also come with standard regulations for worldwide application. Distances are measured by meters. Presently, the UTM coordinate systems are commonly used in both military and civil affairs. For Thailand, the Thai and US governments had agreed to make national maps in 1950 by using the Transverse Mercator projections, with UTM coordinate systems.

The global space between Latitude 80 degrees south and Latitude 84 degrees north is divided into 60 zones, each zone covering 6 degrees, on the longitudes. All the zones are numbered 1-60 respectively. Zone 1 is located between longitude 180 degrees west and 174 degrees west. Zone 2 is located next to Zone 1 on the east, followed by the remaining zones. Zone 60, the last one, lies between longitude 174 degrees east and 180 degrees east, adjacent to Zone 1. Each zone has its own central meridian. For example, Zone 1, between longitude 180-174 degrees west, will get the longitude 177 degrees west as its central meridian. Such features are found in every zone.

The space in each zone is divided into squares by parallels of latitude. Each parallel spacing is angled at 8 degrees, starting from latitude 80 degrees south, continuing with the 8-degree intervals passing the equator up to latitude 72 degrees north. Then from latitude 72-84 degrees north, the space is divided into 20 squares, each angled at 12 degrees. These squared space is called “Grid zone”. There are totally 1,200 grid zones. Dividing the space with this method will create rectangular grids of 6 x 8 degrees, except the area between latitude 72-84 degrees north which has the grid size of 6 x 12 degrees. After the division, the Roman alphabet from C to X (except I and O) are written on the divided space, starting with letter C from latitude 80 degrees south.

The grid table is inscribed with numbers and alphabet which are called UTM Grid zone destination. The numbers are read right up. For example, “47 Q” refers to the 47th vertical zone and the horizontal zone Q.  Letters A, B and Y, Z are used for the Universal Polar Stereographic in both polar regions.

Distances in UTM coordinate systems are measured by meters. In each zone, the the central meridian intersects the equator at the right angle. The intersection point is called the zone origin of UTM coordinate systems. The direction that is parallel to the central meridian and heading northward is called “Grid north”. The eastern coordinates are set with Easting 500,000 meters from the false origin, while the northern coordinates for the equator are plotted in two cases, including Northing 0 meter from the equator and Northing 10,000,000 meters from the false origin. Therefore, the coordinates of zone origin of UTM system are E 500,000 m ; N 0 m for the northern hemisphere, and E 500,000 m ; N 10,000,000 m for the southern hemisphere. In addition, the use of UTM coordinate values can overlap that of adjacent zones with 40-km distance for convenient use at the periphery of each zone.

3. ระบบพิกัดแผนที่ GLO (General Land Office grid system)

This is another type of coordinate systems that helps for the division of  surveyed areas to make geographic maps. It is commonly used for reading and making geological maps. In this coordinate system, the space is partially divided with each part being defined as follows:

• Base line and Township line Any referred latitude in the surveyed area is called “base line”, and the parallels above and below the base line in every 6-mile spacing are Township lines.
• Principal meridian and Range line The longitude referred to in a survey is called the principal meridian. The point of intersection with a base line is called Initial point. The lines parallel to the principal meridian on the east and west in every 6-mile spacing is the range line.
• Township area is a square space of 6 x 6 miles, rounded with township lines and range lines. This area of 36 square miles is established by using distant positions from the base line and principal meridian. For example, 2N., R.1W is on the second township line above the 1st base line and range line on the west of the principal meridian.
• Section The 36- square mile area of the township line is divided into 36 squares, each square covering 1 square mile which is called “section”.
• Quadrangle A geographic map which is divided in accordance with this system is normally in rectangular shape. The space of rectangular map is framed with longitudes in the east and west, and latitudes in the north and south. The rectangular map is named after important cities or distinguished geographical features in the map. The quadrangle maps used in the US are classified by the distance between surrounding longitudes and latitudes into four types, which are:

The map of 1 Degree series, using a 1:250,000 scale
The map of 30 Minute series, using a 1:125,000 scale
The map of 15 Minute series, using a 1:62,500 scale
The map of 7.5 Minute series, using a 1:24,000 scale

How to read coordinates from the GLO maps

- Find the number attached to the section where the place is located. For example, 21 is read Sec.21.
- Find the township position on the township line where the place is located from the left or right periphery of the map, such as T.1N.
- Find the Range position on the Range line where a place is located at the top or bottom of the map, such as R.2W.
- To identify positions within the section, the space must be divided to determine the azimuth where the subsection is located and the scale comparing subsection with the pre-divided space.                                                                        These indicators are placed before the read position of the section, such as NE ¼ SW ¼ Sec.21 T.1N R.2W

Military grid

Because finding position by the degree-minute-second measurement is difficult and slow, a new method was invented to be used in army affairs. This method is called “military grid” which is a rectangular coordinates system comprising a group of lines that are parallel and almost in the north-south direction, used for measuring distance on the east of the origin, as well as a group of parallels that are almost in the east-west direction and also intersecting and perpendicular to the first group of lines. This second group is used for measuring distance above the origin. The intersection of these two groups of lines create squares, which are printed on the map. They are called “grid squares”, which are displayed together with numbers written at the map peripheries, showing distance from the origin. Normally, the distance from the origin is represented with numbers only once at the left bottom of the map. Of those numbers indicating distance from the false origin of other lines, the last 3 or 4 digits of the full number are omitted. This also depends on the size of grid intervals. For instance, the L7017 and L7018 map series will have grid distance of 1,000 meter. Therefore, the last three digits that will be omitted are 000, which are shown in the military grid.

In fact, the UTM map projection and the military grid are not different. The military grid or grid coordinates are tools for reading maps with UTM projection. Both are relevant to each other. Military grid is the part that clearly depicts the positions referred to with UTM projection, making it better understood. Therefore, the geographic map created by the Royal Thai Survey Department has used military grid to identify positions on the map, as the system is easy to understand and also enables quick and efficient use of the map.
A tip for writing or reading grid values used in military affairs is to “read right up”. The lower left intersection point is the grid coordinate value of that particular square.
The geographic coordinates system is therefore important for determining positions on the map, to indicate the positions in the real-world geography. It is the system that every map user needs to understand and know the correct method to read it, so the map can be used practically and efficiently.