# Exercise 3 corse 2007 Advanced Track

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 Exercise 3 CORSE 2007 Advanced Track Referencing Data to Real World Locations

This exercise uses Module 3 of the ESRI course “Learning ArcGIS Desktop” Create a folder within your named folder called Projections and load the data for the You have already accessed and downloaded the course so all you have to do is download the Reference.exe file into the Projections folder and put the data into a folder called Reference
There are very important concepts in this Module. There is a problem, however, and that is that ESRI uses slightly different terms for the various projections, coordinate systems, and datums. The introductory textural material states that:
“There are two types of coordinate systems: geographic and projected. A geographic coordinate system is used to locate objects on the curved surface of the earth. A projected coordinate system is used to locate objects on a flat surface—a paper map or a digital GIS map displayed on a flat computer screen.”
Most GIS people consider coordinate systems to be State Plane or UTM and other methods of converting geographic coordinates of the globe as Projections. Thus discussions may be confusing at times.
As before the textural material herein is provided for reference and need not be read at this time, The important concepts and practices were covered in the PowerPoint for this topic.
Understanding coordinate systems
There are two types of coordinate systems: geographic and projected. A geographic coordinate system is used to locate objects on the curved surface of the earth. A projected coordinate system is used to locate objects on a flat surface—a paper map or a digital GIS map displayed on a flat computer screen.

Each of these coordinate systems attempts to model the earth and feature locations accurately, but, as you will learn, no system is completely accurate. In this topic, you will learn the basics of how geographic and projected coordinate systems work.

Geographic coordinate systems
A geographic coordinate system is a reference system for identifying locations and measuring features on the curved surface of the earth. It consists of a network of intersecting lines called a graticule. The intersecting lines of the graticule are probably familiar terms to you—longitude and latitude.
 The graticule is made up of vertical lines, called lines of longitude, and horizontal lines, called lines of latitude. Because the earth is spherical, these lines form circles.

In a geographic coordinate system, measurements are expressed in degrees, minutes, and seconds. A degree is 1/360th of a circle. Each degree can be divided into 60 minutes, and each minute can be divided into 60 seconds.

Lines of longitude are called meridians. Measures of longitude begin at the prime meridian (which defines the zero value for longitude) and range from 0° to 180° going east and from 0° to -180° going west.

Lines of latitude are called parallels. Measures of latitude begin at the equator and range from 0° to 90° from the equator to the north pole and from 0° to -90° from the equator to the south pole.

 The prime meridian (green line) is the starting point for longitude and has a value of 0. The equator (red line) is the starting point for latitude and has a value of 0. It runs midway between the north and south poles, dividing the earth into northern and southern hemispheres.

Longitude and latitude are actually angles measured from the earth's center to a point on the earth's surface. For example, consider the location referenced by the following coordinates:

Longitude: 60 degrees East (60° 00' 00")
Latitude: 55 degrees, 30 minutes North (55° 30' 00")

The longitude coordinate refers to the angle formed by two lines, one at the prime meridian and the other extending east along the equator. The latitude coordinate refers to the angle formed by two lines, one on the equator and the other extending north along the 60° meridian.

 Longitude and latitude are angles measured from the earth's center to a point on the earth's surface.

Understanding spheroids
A geographic coordinate system attempts to model the shape of the earth as accurately as possible. Many models of the earth's shape have been made over the years, and each has its own geographic coordinate system. All are based on degrees of latitude and longitude, but the exact latitude-longitude values assigned to individual locations will vary.

Two shapes that are commonly used to model the earth are a sphere and a spheroid.

 The shape of the earth can be approximated by a sphere or a spheroid.

Assuming that the earth is a sphere greatly simplifies mathematical calculations and works well for small-scale maps (maps that show a large area of the earth). A sphere does not provide enough accuracy, however, for large-scale maps (maps that show a smaller area of the earth in more detail). For those, it is preferable to use a spheroid.

A spheroid is a more accurate model of the earth, but it's not perfect.

More about the shape of the earth

Different spheroids are currently in use, in part because newer technology has provided more accurate measurements of the earth's shape. Some spheroids were developed to model the entire earth, while others were developed to model specific regions more accurately.

For example, the World Geodetic System of 1972 (WGS72) and World Geodetic System of 1984 (WGS84) spheroids are most commonly used to represent the whole world, while in North America, the Clarke 1866 and Geodetic Reference System of 1980 (GRS80) spheroids are most commonly used.

Why do you need to know about spheroids? Because ignoring deviations and using the same spheroid for all locations on the earth could lead to measurement errors of several meters or, in extreme cases, hundreds of meters.

Understanding datums
Now you know that a geographic coordinate system uses a spheroid (or less accurately a sphere) to model the earth. You also know that a spheroid doesn't describe the earth's shape exactly—a perfectly smooth spheroid does not reflect the undulations and other variations on the earth's surface. Because no single spheroid can model the bumpiness all over the earth's surface, there is more than one spheroid in use.

A geographic coordinate system needs a way to align the spheroid being used to the surface of the earth for the region being studied. For this purpose, a geographic coordinate system uses a datum. A datum specifies which spheroid you are using as your earth model and at which exact location (a single point) you are aligning that spheroid to the earth's surface.

 The red spheroid is aligned to the earth to preserve accurate measurements for North America. The blue spheroid is aligned to the earth to preserve accurate measurements for Europe.

A datum defines the origin of the geographic coordinate system. The origin is the point where the spheroid matches up perfectly with the surface of the earth and where the latitude-longitude coordinates on the spheroid are true and accurate. All other points in the system are referenced to the origin. In this way, a datum determines how your geographic coordinate system assigns latitude-longitude values to feature locations.

Just as there are different spheroids for different parts of the world, there are different datums to help align the spheroid to the surface of the earth in different regions.

Does changing datums affect your data?

 Does changing datums affect your data?

If you change the datum of the geographic coordinate system, you should know that the coordinate values of your data will also change. For example, consider a location in Redlands, California, that is based on the North American Datum of 1983 (also known as NAD 1983 or NAD83). The coordinate values of this location measured in degrees, minutes, and seconds (DMS) are:

–117° 12' 57.75961" (longitude)
34° 01' 43.77884" (latitude)

Now consider the same point on the North American Datum of 1927 (NAD 1927 or NAD27).

–117° 12' 54.61539" (longitude)
34° 01' 43.72995" (latitude)

The longitude value differs by about three seconds, while the latitude value differs by about 0.05 seconds.

 In both the NAD 1927 and the NAD 1983 datums, the spheroid matches the earth closely in one part of the world (North America) and is quite a bit off in others. Notice that the datums use different spheroids and different origins. For NAD 1927, the origin aligns the Clark 1866 spheroid with a point in North America. For NAD 1983, the origin (the center of the earth) aligns the center of the spheroid with the center of the earth. [Click to enlarge]

The most recently developed and widely used datum for locational measurement worldwide is the World Geodetic System of 1984 (WGS 1984). This datum is identical to NAD 1983 for most applications. The coordinates for the same location (Redlands, California) using WGS 1984 are:

–117° 12' 57.75961" (longitude)

34° 01' 43.778837" (latitude)
Projected coordinate systems
The surface of the earth is curved but maps are flat. To convert feature locations from the spherical earth to a flat map, the latitude and longitude coordinates from a geographic coordinate system must be converted, or projected, to planar coordinates.
 A map projection uses mathematical formulas to convert geographic coordinates on the spherical globe to planar coordinates on a flat map.

A projected coordinate system is a reference system for identifying locations and measuring features on a flat (map) surface. It consists of lines that intersect at right angles, forming a grid. Projected coordinate systems, which are based on Cartesian coordinates, have an origin, an x and a y axis, and a unit for measuring distance.
 Projected coordinate systems are based on Cartesian coordinates which use a grid. Feature locations are measured using x and y coordinate values from the point of origin.

The origin of the projected coordinate system (0,0) commonly coincides with the center of the map. This means that x and y coordinate values will be positive only in one quadrant of the map (the upper right). On published maps, however, it is desirable to have all the coordinate values be positive numbers.

To offset this problem, mapmakers add two numbers to each x and y value. The numbers are big enough to ensure that all coordinate values, at least in the area of interest, are positive values. The number added to the x coordinate is called a false easting. The number added to the y coordinate is called a false northing.

 By adding a large number to each x and y value, all coordinate values on the map are positive. In the graphic above, a false easting value of 7,000,000 was added to each x coordinate. A false northing value of 2,000,000 was added to each y coordinate.

Working with coordinate systems in ArcGIS
All geographic datasets have a geographic coordinate system (GCS). Some datasets also have a projected coordinate system (PCS). When you add a dataset to ArcMap™, ArcMap detects the geographic coordinate system and the projected coordinate system if there is one.

If all the data you want to display on a map is stored in the same geographic coordinate system, you can just add it to the map—the layers will overlay properly. If some of the datasets also have projected coordinate systems, even if they are different, you can also just add them to the map without data alignment worries—ArcMap will automatically make the layers overlay using a process called "on-the fly projection." The geographic coordinate system is the common language. ArcMap can convert the geographic coordinate system to any projected coordinate system and it can convert any projected coordinate system back to the geographic coordinate system.

An issue arises when you want to display datasets that have different geographic coordinate systems on the same map. The first layer you add to an empty data frame determines the coordinate system for the data frame. If that layer has a projected coordinate system, the data frame will have that same projected coordinate system. If you add a layer that has the same geographic coordinate system but a different projected coordinate system (or no projected coordinate system at all), ArcMap will perform an on-the-fly projection and convert the data to the data frame's projected coordinate system. The layers will overlay properly.

If, however, you try to add a layer that has a different geographic coordinate system, ArcMap will display a warning message telling you that it may not be able to properly align the data. ArcMap can still project the data on the fly, but it can no longer guarantee perfect alignment. (For perfect data alignment, you need to apply a transformation to make the geographic coordinate systems match—transformations are beyond the scope of this course.)

How do you know what coordinate system your data is stored in? You can view the coordinate system information for a dataset in ArcCatalog™, in its metadata. If a dataset has no coordinate system information in its metadata (it's missing), you may not be able to display the data in ArcMap. You may need to do some research to find out the coordinate system, then define the coordinate system using the ArcGIS tools provided. You will do this in the exercise coming up.

What happens when coordinate system information is missing?
When you add a dataset to ArcMap that is missing coordinate system information, ArcMap will try to read the coordinates of the data and determine whether they have been projected. If the coordinates are in the range of longitude-latitude values (x = ±180, y = ±90), ArcMap will add the data to the map and project it on the fly, although there may be inaccuracies because ArcMap cannot determine the geographic coordinate system for the data.

If the coordinates are not in the range of longitude-latitude values, ArcMap will display a warning. It will still add the data to the map, but it cannot project it on the fly. The result is usually that the data doesn't "fit" in the same coordinate space as the rest of the data, and either doesn't display or has serious alignment problems. In this case, you'll have to enter the necessary coordinate system information yourself in order to display the data properly on a map.

Map units are the units in which the coordinates for a dataset are stored. They are determined by the coordinate system. If the data is stored in a geographic coordinate system, the map units are usually decimal degrees (degrees, minutes, and seconds expressed as a decimal). If the data is stored in a projected coordinate system, the map units are usually meters or feet. Map units can be changed only by changing the data's coordinate system.

Display units are independent of map units—they are a property of a data frame. Display units are the units in which ArcMap displays coordinate values and reports measurements. You can set the display units for any data frame and change them at any time.

Recall that latitude and longitude coordinate values are actually angle measurements. Angles are measured in degrees. For latitude-longitude coordinates, degrees can be expressed two ways: as degrees, minutes, seconds (DMS) or as decimal degrees (DD). In a GIS, decimal degrees are more efficient because they make digital storage of coordinates easier and computations faster.

Below is an example of how to convert a coordinate location from DMS to DD.

The latitude of London expressed in DMS is 51° 29' 16" North. To convert this location to DD, follow these steps:

1. Divide each value by the number of minutes (60) or seconds (3600) in a degree:

29 minutes = 29/60 = 0.4833 degrees

16 seconds = 16/3600 = 0.0044 degrees

51° + 0.4833 ° + 0.0044 ° = 51.4877 DD