Exercise 3: Map Projections and Coordinate Systems

CE 394K GIS in Water ResourcesUniversity of Texas at AustinFall 2002

Prepared by Kristina Schneider and David R. Maidment

Contents

Projections of the World

Projections of the United States

Projections of Texas

Projections of Austin

Doing Projection in ArcToolbox

Map projection involves taking data whose spatial coordinates are defined in terms of latitude and longitude on a curved earth surface and transforming those data so that their spatial coordinates are defined in terms of Easting and Northing or (x, y) on a flat map surface. ARC/INFO and ArcToolbox permit the transformation of data into new projected coordinate systems. ArcMap permits data to be viewed in various map projections.

The intention of this exercise is to give you experience applying ArcMap to view maps in various commonly used projections, and to introduce you to the projection tool used to project maps from Geographic Coordinates to State Plane coordinates in ArcToolbox.

Step 1 / TheWorld in Geographic Coordinates
The files for this exercise are contained in the directory /class/maidment/giswr/mapproj in the LRC server. You can also download this file directly from this CD by clicking on mapproj.zip.
These data are built into a geodatabase called Mapproj.mdb which contains four feature datasets:
World: containing feature classes Cntry94 and World30 - countries and 30º meridians and parallels for the earth
USA: containing feature classes States, Countiesand Latlong - States and Counties of the US and a 5º grid of meridians and parallels
Texas: containing Quad75 and Onedegtx - a coverage of Texas showing a 1º gridand 7.5' quad map extents
Austin: containing Juris, Lakes, Roads - administrative boundaries of legal jurisdiction, lakes and roads in Austin, Texas.
All these feature datasets contain data in geographic coordinates defined on the NAD83 datum.
Download or link to these files now.
1. Start ArcMap. Click Add layers button and navigate to your Mapproj.mdb geodatabase, add in the World feature dataset layers. Drag World30 below the Cntry94 so that the layout of the countries is superimposed on the grid of 30-degree rectangles.
You want to make the layer World30 rectangles show just their outlines, so they can serve as the coordinate system, using their 30 degree mesh.
2. Right-click on the World30 layer and click Properties. Navigate to the Symbology tab and double click on Symbol to get the Symbol Selector window. Select the Hollow color and press OK. You should see the World in Geographic Coordinates.
3. Right-click on the Cntry94 layer and choose Label Features. You’ll see that the countries are named. If you don’t like the font and color of the label, right-click on the layer and select Properties. Navigate to the Label tab and press the Symbol button. Here you can choose the font, color, and style you would prefer. This option labels all the features in the layer. If you want to label the features using another attribute besides the country name, you can also do that using the Label Properties window.
4. To label just a few features, first right click on the Cntry94 layer and deselect Label Features. On the Draw Toolbar there is a Label button that allows you to label individual features. It is found underneath the big symbol in the Draw toolbar. If you don’t see the Draw Toolbar, use View/Toobars and click on Draw to make it visible.
Double click on the label button and keep the selections chosen by the computer. Close the screen just opened and click on the countries you would like to label. Be sure to have the Cntry94 feature class as the uppermost one in your legend, or you will get just numbers of the World30 boxes when you try to click on the countries to label them with names. Pretty cool!!

Move the cursor around on the view and you will see a pair of numbers above the view on the toolbar to the right of "scale" that alter as you move the cursor. These give the location of the cursor and from the values displayed you can see that these data are Latitude and Longitude displayed in Degrees, Minutes and Seconds.
If you find that the units displayed are decimal degrees but are described as “Unknown”, you can use Layer/Properties/General/Display to reset Unknown Units to “Degrees Minutes Seconds” .
5. Save the Map file as World.mxd
Questions:
  1. What is the spatial extent of the view shown in terms of degrees of latitude and longitude?
  2. Where is the point (0,0) latitude and longitude located on the earth's surface?
  3. If you draw a box around Australia, what is its extent (give the coordinates of lower left corner and upper right corner in degrees).

Step 2 / The World in Robinson Projection
The actual projection of the layers cntry94 and World30 is geographic, however these layers can be viewed in different projection systems. A common projection system for the World is the Robinson projection.
1. Create new Data Frame, using Insert/New Data Frame. Select View/Data Frame Properties… Select the General tab and name the data frame Robinson. Right click on the World30 feature class in Layers, select Copy, then Right click on the Robinson data frame and select Paste Layer. You’ll see the World30 feature class symbol appear in the Robinson data frame. Do the same for the Cntry94 feature class. Right click on the Robinson data frame and select Activate to display the data in this frame. Pretty cool!
To copy the two feature classes as a group, you can right click on a data frame in the table of contents (with Display tab active) and create a new Group Layer. Then individual layers can be dragged and dropped onto the new Group Layer. Then the entire group layer can be copied and pasted between data frames.

2. Right click on the Robinson data frame, and select the Coordinate System tab. Under the Select a Coordinate System box, choose the Predefined folder. Then select Projected Coordinate Systems/World/Robinson. Click OK. A warning may appear but we can ignore it for our purposes, so just click Yes. Ignore this message every time it appears throughout the exercise. You will see the World appear in a Robinson projection. The files themselves have not been projected permanently but are only displayed in the new projection.

The Robinson projection is a relatively new map projection for the earth designed to present the whole earth with a minimum of distortion at any location. If you move the cursor over this space, you'll see that the coordinates are now in a very different set of units, meters in the projected coordinate system.
3. Play with the different projections and explore the different shapes the world can take. Note that the data frame showing in the Data View is the one most recently created. If you want to view another data frame, Right click on the data frame name, and choose Activate.
You can create a layout that contains several different data frames. Switch to the Layout view, and you’ll see both data frames displayed.
You can resize and reposition these frames to create a map layout. Save the map file World.mxd
To be turned in: a Layout showing the World in Geographic Coordinates, in Robinson Projection, and a projection of your choosing.
Step 3 / United States in the Geographic Coordinates
You will now examine map projections used for the continental United States. We could continue adding data frames to the previous map file, but to simplify things, lets create a new map file. Use File/New/Blank document to create a new map file. Save the map file as USA.mxd.
1. Add the States and Latlong feature classes from the USA feature dataset of mapproj.mdb. Click on the Zoom in tool and zoom in to a view just of the continental United States, not including Alaska. Use the Pan toolto move the United States into the center of the view window if necessary.

Questions:
  1. What is the geographic extent of the United States? Give the East and West limits of longitude of the continental US and those for the Northern and Southern extent of the continent to the nearest degree.
  2. Which parallel defines much of the border between the United States and Canada?
  3. If we removed a vertical slice out of the world cut along the meridians defining the most Eastern and Western points in the continental United States, how much of the globe would we have cut out?

Step 4 / United States in Albers Equal Area Projection
The Albers Equal Area projection has the property that the area bounded by any pair of parallels and meridians is exactly reproduced between the image of those parallels and meridians in the projected domain. That is, the projection preserves the correct area of the earth although it distorts the direction, distance and shape somewhat.
1. Create a new Data Frame and copy and paste in the layers Latlong and States from the previous frame.To copy the layers you must make the old data frame active by right-clicking on the frame and selecting Activated. Then to Paste the layers you must make the new frame active in the same manner.
2. Rename the data frame as Albers Equal Area. Double Click on the data frame and go to the Coordinate System tab. Select the coordinate system Predefined/Projected Coordinate System/Continental/North America/USA Contiguous Albers Equal Area Conic projection. Zoom into the US without Alaska.

3. Compare the United States in geographic coordinates and in the Albers projection. You will see that in geographic coordinates the United States appears to be wider and flatter than it does in Albers Equal-Area Projection. This does not occur because Canada is sitting on the USA and squishing us! This effect occurs because as you go northward, the meridians converge toward one another while the successive parallels remain parallel to one another. When you reach the north pole, the meridians converge completely.
If you take a 5 degree box of latitude and longitude, such as one of those shown in the views, the ratio of the East-West distance between meridians to the North-South distance between parallels is Cos (latitude): 1. For example, at 30°N, Cos(30°) = 0.866, so the ratio is 0.866 : 1, at 45°N, Cos(45°) = 0.707, so the ratio is 0.707 : 1. In the projected Albers Equal Area frame the result is that square boxes of latitude - longitude appear as elongated quadrilaterals with a bottom edge longer than their top edge. In geographic coordinates, the effect of the real convergence of the meridians is lost because the latitude and longitude grid form a set of perpendicular lines, which is what makes the United States seem wider and flatter in geographic coordinates.
5. Save the USA.mxd project.
To be turned in: a Layout showing the United States in Geographic Coordinates and in the Albers Equal Area projection.
Step 5 / Texas in Geographic Coordinates
You will now examine the effect of various map projections up a map of the State of Texas.
1. Create a new map document, Texas.mxd. Add in the feature classes Counties and latlong from the USA feature dataset of the mapproj.mdb geodatabase. The feature class Counties is a counties layer of the United States, including Alaska and Hawaii.Rename the Layers data frame Texas in Geographic.
2. To make it easier to determine the counties located in Texas, go to the Counties / Properties and then to the Symbology tab. Choose to display the Counties by Categories with the Unique value of State_Name. Press the Add Values… button (don’t choose Add All Values!) and select Texas pressing OK. Deselect the check mark for <all other values>, which will leave only counties with the state_name as Texas to be shown.

3. Click OK, and you will see only the counties in Texas remain in the view. Zoom in to see the larger view of Texas counties.

The latitude/longitude grid displayed is at 5-degree intervals of latitude and longitude. You can determine what latitude or longitude a particular line represents by moving the cursor to any line and read the latitude and longitude number displayed on the right corner of the tool bar.
Questions:
  1. What is the geographic extent of Texas to the nearest degree in North, South, East and West?
  2. What meridian runs down the East side of the Texas Panhandle?

Step 6 / Texas in Lambert Conformal Conic projection
The Lambert Conformal Conic projection is a standard projection for presenting maps of land areas whose East-West extent is large compared with their North-South extent. This projection is "conformal" in the sense that lines of latitude and longitude, which are perpendicular to one another on the earth's surface, are also perpendicular to one another in the projected domain.
1. Create a new data frame, copy and paste Latlong and Counties to it from the previous view. Choose Properties for the data frame, rename the data frame as TX in Lambert projection.
2. Move to the Coordinate System tab and select Predefined/Projected Coordinate System/Continental/North America/USA Contiguous Lambert Conformal Conic projection. Click OK. Notice how the meridians now fan out from an origin at the center of rotation of the earth (a consequence of using a conic projection centered on the axis of rotation of the earth). The display shown is that produced by cutting the cone up the backside and unfolding the cone so that it lays flat on the table.

3. Zoom in to see the detailed Texas Counties in Lambert Conformal Conic projection.

Notice that Texas appears to be tilted to the right slightly. This occurs because the Central Meridian of the projection used is 96ºW, which would appear as a vertical line in the display if it were shown. Regions to the West of this meridian (most of Texas) appear tilted to the right while those to the East of this meridian appear tilted to the left.
Step 7 / Texas in the Texas Centric Mapping System
In order to present a pleasing map of Texas, and to minimize distortion of distance in State-wide maps, the Texas State GIS Committee, has approved a standard projection of Texas called the Texas Centric Mapping System (see for details. There are two variations on this projection, one in Lambert Conformal Conic coordinates and the other in Albers Equal Area coordinates. We’ll use the Albers Equal Area version since that works best for water resources computations that require true earth area to be preserved in map projections. The definition of this projection is:
Datum: North American Datum of 1983 (NAD83)
Ellipsoid: Geodetic Reference System of 1980 (GRS80)
Map units: meters
Central Meridian: 100°W (-100.0000)
Latitude of Origin: 18° N (18.0000)
Standard Parallel 1: 27° 30´ N (27.5000)
Standard Parallel 2: 35° N (35.0000)
False Easting: 1500000
False Northing: 6000000
This means the standard parallels where the cone cuts the earth's surface are located at about 1/6 of the distance from the top and bottom of the State, respectively, and that the origin of the coordinate system (at the intersection of the Central Meridian and the Reference Latitude) is to the South of Texas in the Gulf of Mexico, to which the coordinates (x, y) = (1500000, 6000000) meters is assigned so that the (x, y) coordinates of all locations in the State will be positive.
1. Create a new data frame, copy and paste Latlong and Counties to it from the previous view. Double-click on the data frame name and rename it Texas Centric 35.0. Click on the Coordinate System tab. With the <custom> folder highlighted select the New… button on the right to create a new Projected Coordinate System. Fill out the parameters with the values given above. You also have to select a Geographic Coordinate System to specify the earth datum. Select North American/North American Datum 1983.

2. Click both OKs in the two dialog box and you'll see the map of Texas transformed to a nice upright appearance, the Texas Centric Mapping System. Zoom into the state of Texas.

Step 8 / Texas in Universal Transverse Mercator (UTM) Projection
The Universal Transverse Mercator projection is actually a family of projections, each having in common the fact that they are Transverse Mercator projections produced by folding a horizontal cylinder around the earth. The term transverse arises from the fact that the axis of the cylinder is perpendicular or transverse to the axis of rotation of the earth. In the Universal Transverse Mercator coordinate system, the earth is divided into 60 zones, each 6° of longitude in width, and the Transverse Mercator projection is applied to each zone along its centerline, that is, the cylinder touches the earth's surface along the midline of each zone so that no point in a given zone is more than 3° from the location where earth distance is truly preserved.