# Section Six: Geographic Coordinate Systems

Up to this point, we've spent a lot of time looking at how we mathematically measure and model the Earth. We learned that:

1. the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." is the actual Earth surface upon which we walk;
2. a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." is a model of gravity, representing local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features to establish a proper zero point for elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface measurements;
3. reference ellipsoids comes in two varieties - local and global - and upon those reference ellipsoids a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. is drawn;
4. geographic grids require an Earth-centered, Earth-fixed coordinate system and an affine transformation;
5. Earth-centered, Earth-fixed coordinate systems require an angular unit of measure the selected units for measuring angles.  Choices include degree and radians.  and a principle meridian;
6. local reference ellipsoids fit inside the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." really great somewhere and really poorly everywhere else;
7. global reference ellipsoids fit everywhere inside a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , however, the fit pretty okay everywhere but not really great anywhere;
8. latitude also known as 'parallels' the east-west portion of a geographic grid measured with angles between 0 and 90° and longitude, which happen to use an Earth-centered, Earth-fixed coordinate system utilizing the Prime Meridian the name of the principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. in the latitude/longitude system as the principle meridian and degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° as the angular unit of measure the selected units for measuring angles.  Choices include degree and radians.  , is just one example (albeit the most common) of a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. ;
9. geographic grids are not, by themselves, a datum, nor a geographic coordinate system;
10. benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . are real world objects, found on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , which are the base of datums. These benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . allow for a series of points to connect the XY coordinates of a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid with the XY coordinates and Z values of the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . Once several benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . connect the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." to the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , all of the remaining control points can be found utilizing a Cartesian Coordinate System;
11. benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . are a real world objects that are converted into control points within the datum. Some, but not all, control points within a datums started out as benchmarks Benchmarks are real-world locations which have been carefully surveyed with locations to match a specific geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." . . The rest were mathematically derived;
12. datums, horizontal or vertical, are the product of connecting a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." to a chosen geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. via control points;
13. horizontal datums used to reference location on the Earth's surface, regardless of elevation (the focus of Introduction to GIS) contain only X and Y coordinates, assuming the entire world exists at an equal elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface ;
14. and vertical datums used to reference locations and distances above mean sea level; elevation. contain just Z values, while three-dimensional datums(used inside GPS receivers)are made up of XY and Z coordinates/values .

Geographic coordinate systems are the whole shabang - a datum connected paired with a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. - and their purpose in cartography, geodesy the science of measuring and monitoring the size and shape of the Earth and the location of points on its surface , GIS, and navigation is to represent all of the land and ocean masses graphically and give an "address" to every point on the Earth's surface. Much like grocery store down the street which has an address of 123 Bob Street, Boston Mass., it also has an address for it's location on the Earth's surface. This GCS address is measured not in an odd-even value/street name/city like it's Post Office address, but in - most commonly - latitude also known as 'parallels' the east-west portion of a geographic grid measured with angles between 0 and 90° and longitude, degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° , minutes "arc minute" 1/60th of a degree. Usually denoted by " , seconds arc minute. 1/60th of an arc minute; 1/3600 of a degree.  Usually denoted by ' . Long after the grocery store goes out of business and the street is demolished and replaced by a speed train track, the latitude also known as 'parallels' the east-west portion of a geographic grid measured with angles between 0 and 90° and longitude - the GCS address - will continue to be true. Since the point found on the GCS is tied to the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , even is if a huge hole or man-made mountain is put in place, the X and Y coordinates will never change (if we make a huge hole or mountain, the Z value will change - not to be confused with the gravitational pull, but the distance above local sea level).

Often, in Intro to GIS classes, datums and geographic coordinate systems are mixed up and the words used interchangeably, which is incorrect. Geographic coordinate systems require a complete and labeled geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. paired with a datum. The datum is, indeed, a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid connected to a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points, which are transferred from the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." to the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and mathematically derived via a temporary grid drawn on the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , but that without a complete geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. , it's still just a datum and not a Geographic Coordinate System. It's not until a datum is selected and a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. is "stretched" and "conformed" to match a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , using the control points of the datum as the "anchors" that a Geographic Coordinate System is created.

Every geographic coordinate system is based upon a datum and when you look at the properties of that GCS, you can find the name of the datum (as well as the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , for that fact). Knowing which datum a geographic coordinate system is based on (and how to look it up) is pretty important when it comes to accuracy (for now, we will leave it at that, as the full explanation will make more sense later). It is important to note that geographic coordinate systems are a stand alone thing - there is no need to move any further forward if your goal is to simply navigate around using GPS unit (as the job of a GPS unit is to find places in the real world on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." ). In the next section, we will learn what it takes to get the round earth to be a flat map utilizing a method where we project the data from a 3D object to a 2D object. This is necessary if we need to measure things such as area (since we think better in units like feet and meters squared instead of degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° squared) or wish to accurately navigate without drawing on a globe.

FIGURE 2.14: A Graphical Breakdown of the Parts of a Geographic Coordinate System
Geographic Coordinate Systems are a complete package: A datum with a specific geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. laid over the reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid . While it is important to understand how each part is made, this graphic is a simple breakdown of the parts and how they connect.

The Main Point...
Creating a Geographic Coordinate System:
Select a specific geodetic datum the result of attaching a "free-floating" reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a specifically measured geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points and benchmarks. (attaching a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." via control points) and match it to a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. (a labeled grid combining an Earth-Centered, Earth-Fixed coordinate system (a principle meridian and an angular unit of measure the selected units for measuring angles.  Choices include degree and radians.  ) and an affine transformation). The output is an a means to locate and label specific locations on the Earth’s surface. Once these places are labeled, tools such as GPS units can lead you right to them.

The term Geographic Coordinate System is often incorrectly used interchangeably with datum. While they seem similar, a geographic coordinate system is the whole package: a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. and a datum, while a datum is just the part which links a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid to a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." .