# Chapter 6 Part 1: Geodesy and Coordinate Systems

Uli Ingram

In this chapter you will learn about scale, geodesy and coordinate systems. The chapter will have examples and information about the aspects that make up coordinate systems. You will learn about the determining factors to consider when creating map projections, deformation and distribution of the projection, and how to determine which map projection to use for a project.

## 6.1: What is Geodesy?

Geodesy is the scientific discipline that deals with the measurement representation of the earth. Geodesists study the Earth’s gravitational field, motion of the Earth’s crust, tides, and the Earth’s rotation. In order to do this, geodesists have built national control networks that allow them to define and assign coordinates to physical locations on earth.

Three Approximations of Earth’s Shape: There are three commonly used approximations of the shape of the earth: sphere, ellipsoid, and geoid. The sphere is the simplest approximation of the earth’s shape as it is defined by a single radius. The ellipsoid is closer to the earth’s shape as defined by semi-major and semi-minor axes. The geoid is the closest approximation of the earth’s shape based on gravity measurements that help define global mean sea level. The reasons why the sphere and ellipsoid are still used are that they are much easier to use for calculations and when defined properly can be exceptionally accurate.

Figure 1: Sphere
Figure 2: Ellipsoid
Figure 3: Geoid

Ellipsoids: The ellipsoid is the most commonly used of the three approximations of the earth’s shape today. There is not a single ellipsoid that fits earth well; therefore, there have been many official ellipsoids throughout the 19th and 20th centuries. Different ellipsoids were adopted because different measurements were used in different countries when defining these ellipsoids, and geodetic surveys were isolated by large bodies of water. Because of this, and ellipsoid created by one country may approximate that portion of the earth very well, but may not be a suitable approximation for another portion of the earth.

Figure 4: Ellipsoid

Datums: There are three common datums that you will use in GIS: North American datum of 1927 (NAD 27), North American datum of 1983 (NAD 83), and World Geodetic System of 1984 (WGS 84).

According to the National Geodetic Survey, a datum is a set of constants specifying the coordinate system used for calculating coordinates of points on earth. Datums serve as starting points of reference for surveying and mapping as they link the physical earth to a mathematical coordinate. A datum is a reference surface for measuring locations on the earth. A datum has two major components: the specification of an ellipsoid, which is an ellipsoid that has been surveyed and defines the origin and orientation of latitudes and longitude lines. We cannot assign any coordinates to a location without first specifying a datum and linking that datum to the shape of the earth through field measurements.

NAD 27: The first datum we will discuss is the North American datum of 1927 also referred to as NAD 27. The NAD 27 datum is based on the Clarke 1866 ellipsoid which holds a fixed latitude and longitude in Kansas. The locations were adjusted based on about 26,000 measurements across North America. Quite a bit of GIS data is still available in NAD 27, however, more recent data should use North American datum of 1983.

NAD 83: It is worth mentioning that it is okay to use NAD 27 or NAD 83 data, however, when performing analysis you should convert all the data into a single datum for analysis purposes.

The North American datum of 1983, or NAD 83, is the successor of NAD 27, and uses an earth centered reference ellipsoid rather than a fixed station in Kansas. Additionally, 250,000 points were measured to adjust the latitude and longitude locations.

WGS 84: The third common datum is the World Geodetic System of 1984 commonly referred to as WGS 84. WGS 84 is based on satellite measurements and the WGS 84 ellipsoid which is similar to another ellipsoid named GRS 80. The major difference between the WGS 84 ellipsoid and the NAD 27 and NAD 83 datum is that the WGS 84 data has worldwide coverage, where NAD 27 and NAD 83 should only be used in North America. You should also note that the WGS 84 datum is used by the GPS system to report latitudes and longitudes.

Datums are not static and often see updates and adjustments throughout time. In fact, both NAD 83 and WGS 84 have been updated multiple times. Therefore it is very important that you read the documentation of the datasets that you are using in your GIS to determine exactly which datum was used in determining locations.

## 6.2: Coordinate Systems

As it pertains to Earth, we use 3-D coordinate systems which represent a sphere such as the earth. The important thing to note about the 3-D coordinate systems that we are going to discuss in this section is that it will not ignore the curvature of the earth, which makes it ideal for displaying locations, and measuring distances across long distances where the curvature of the earth will become a factor.

The 3-D coordinate system that we are going to discuss is going to use two angles of rotation commonly known as latitude and longitude, and a radius to specify the location. The angles of rotation will determine whether the location is north or south of the equator or east or west of the Prime Meridian and the radius will specify how far from the center of the earth that location is.

Longitude: Longitude, also known as Meridian, is the angle of rotation measured east and west around the globe. What may be confusing is that the lines of longitude run north-south from the North Pole to the South Pole. Lines of longitude will vary from positive 180° east to -180° west measured relative to the line of longitude of 0° which is known as the Prime Meridian.

The Prime Meridian runs through Greenwich, England. Lines of longitude west of Greenwich, England up to and including 180° are represented as a negative number or as a Western longitude. Lines of longitude east of Greenwich, England up to, and including 180°, is represented as a positive number or as an Eastern longitude.

Figure 5: Example of Longitude

Latitude: The second angle of rotation is known as latitude and is also referred to as a parallel. Parallels measure north to south on the globe, and the lines run in parallel to each other east and west from the North Pole to the South Pole. The equator is the latitude of 0°. Lines of latitude measure from positive 90° north, which is located at the North Pole, to -90° south, which is located at the South Pole.

Figure 6: Example of Latitude

2D Coordinate Systems: The 2-D Cartesian coordinate can represent many possible locations at many possible scales, and it is so flexible you can even create your own. However, there are two common representations that are widely used in North America, and the world. The first is the State Plane Coordinate System and the second being the Universal Transverse Mercator Coordinate System or UTM system.

State Plane: The state plane coordinate system is a set of 126 geographic zones that cover the United States of America. Each zone is designed specifically for the region of the United States of America that it covers. It is useful because it allows for simple calculations and is reasonably accurate within each zone. In the state plane coordinate system coordinates are always positive inside each zone. The state plane coordinate system can be based off of NAD 27 and NAD 83 datums, and the coordinates are represented and measured in feet.

Each state may have multiple state plane zones but this is not required. Each zone is strategically placed to minimize the amount of error within each zone. Additionally, each zone provides a common coordinate reference for horizontal coordinates over areas such as counties while limiting error to specified maximums. Depending on the shape of the state, the state plane zone can be based on two types of map projections, the Lambert Conformal Conic, or the Transverse Mercator.

Provided below is an illustration of the state plane zones in the 48 lower contiguous states of the United States of America. Notice that most states have multiple zones and that zones typically either run north to south, or east to west. Also note that most of the smaller states, particularly in the New England area, only have one state plane zone covering the entire state, while larger states such as California and Texas, have multiple zones so that the error can be minimized throughout the state. A notable exception to this is Montana. It is a large state but only has a single zone. State plane zones are typically designated with the name of the state followed by a section indicator, such as North, Central, and South, or combination of those, or, West, Central, and East. A notable exception is California which specifies each zone using a different number.

Figure 7: Example of State Plane Zones

Universal Transverse Mercator Coordinate System UTMCS: The Universal Transverse Mercator Coordinate System (UTMCS) is a worldwide 2-D coordinate system that splits the world into 60 zones. The Universal Transverse Mercator Coordinate System is useful because it provides for simple calculations and manages error within each zone. Unlike the state plane coordinate system which is measured in feet, the universal transverse Mercator coordinate system is specified and measured in meters.

This is an illustration of the state plane zones covering the world from 80° South 84° north. Note the line running along the equator, which splits as zones into north, and south.

Figure 8: State Plane Zones at 80°, 84° North

## Other Resources

### Readings

ArcGIS Blog Post about Coordinate Systems

### Module Audiovisual Resources

A Brief History of Geodesy (2 minute video)

Nine Impacts of Geodesy (5 minute video)

What is a datum (2 minute video)

## Summary

This chapter provided examples and information about Geodesy and Coordinate Systems.

## Credits

This work by the National Information Security and Geospatial Technologies Consortium (NISGTC), and except where otherwise noted, is licensed under the Creative Commons Attribution 3.0 Unported License.

Authoring Organization: Del Mar College

Written by: Richard Smith

Copyright: © National Information Security, Geospatial Technologies Consortium (NISGTC)

Development was funded by the Department of Labor (DOL) Trade Adjustment Assistance Community College and Career Training (TAACCCT) Grant No. TC-22525-11-60-A-48; The National Information Security, Geospatial Technologies Consortium (NISGTC) is an entity of Collin College of Texas, Bellevue College of Washington, Bunker Hill Community College of Massachusetts, Del Mar College of Texas, Moraine Valley Community College of Illinois, Rio Salado College of Arizona, and Salt Lake Community College of Utah.

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