Exercise 3: Map Projections and Coordinate Systems


Contents

Projections of the World

Projections of the United States

Projections of Texas

Projections of Austin

Doing Projection in ArcView


           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 permits transformation of data into new projected coordinate systems. ArcView GIS permits data to be viewed in various map projections and vector data can be projected to new coordinate systems.A Projection Utility Wizard is provided with the standard ArcView GIS software. 

           The intention of this exercise is to give you experience applying ArcView to view maps in various commonly used projections, and to introduce you to a sample projection script used to project maps from Geographic Coordinates to State Plane coordinates.


Step 1 
The World in Geographic Coordinates
The files for this exercise are contained in the directory /class/maidment/giswr/mapproj in the LRC server. They are also available at  ftp.crwr.utexas.edu in /pub/gisclass/mapproj as a zip file called mapproj. You can also download this file directly from this CD by clicking on mapproj.zip.

These data include: 

Cntry94.shp and World30.shp - countries and 30º meridians and parallels for the earth 

States.shp, Counties.shp  and Latlong.shp - States and Counties of the US and a 5º grid of meridians and parallels 

75quad, Onedegtx - a coverage of Texas showing 7.5' quad maps and a 1º grid 

Jurisgeoc, Lakegeoc, Roadgeoc - administrative boundaries, lakes and roads in Austin, Texas. 

Download or link to these files now. We'll suppose that they are in the folder projectiondata

Start ArcView and open a new View. Click Add themes button  and navigate to your projectiondata directory, hold down the shift-key and add in both Cntry94.shp, and World30.shp themes. Drag World30.shp below the Cntry94.shp so that the layout of the countries is superimposed on the grid of 30 degree rectangles. 

You want to make the theme World30.shp rectangles show just their outlines, so they can serve as the coordinate system, using their 30 degree mesh. 

Make the World30.shp theme active, then double click the legend symbol to open the Legend Editor. In the Legend Editor, double click the symbol again to open the Fill Palette. In the Fill Palette, click the clear rectangle  in the top left corner, the symbol in the Legend Editor should become clear. Click Apply. You should see the World in Geographic Coordinates. 

Highlight the Cntry94.shp theme. Choose Auto-label from Theme menu, use the default setting, and click OK. If you don't like the font and color of the label, choose Select All Graphics from the Edit menu, then choose Show Symbol Palette from the Window menu, choose the font you prefer. Then click on the Color Palette button  , change the Foreground next to Color to Text, then choose the color you prefer. If you want to remove some of the labels, you can click on the label and delete them individually. 

From the View menu, choose Properties, and rename the View1 as World in Geographic Coordinates. 

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 displayed in Decimal Degrees of Latitude and Longitude. 

Highlight both the Cntry94.shp theme and the World30.shp theme and use Copy Themes from the Edit menu to put these themes on the clipboard. 

Save the Project .apr file! 

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? 
Step 2 
The World in Robinson Projection
The actual projection of the themes cntry94.shp and World30.shp is geographic, however these themes can be viewed in different projection systems. A common projection system for the World is the Robinson projection. 

Double click on the View icon in the project window to open a new view. Use Paste from the Edit menu to place the themes cntry94.shp and World30.shp in this view from the clipboard. If you don't see them go back to the View World in Geographic Coordinates and use Edit/Copy Themes with both themes highlighted to first put the themes on the clipboard. 

Choose Properties from View menu, in the View Properties window, rename the View1 as World in Robinson Projection, then click the Projection button to open Projection Properties dialog box. Keep the Category as Projections of the World, but scroll down the dropdown list of Type, and choose Robinson. 

Click both OK to return to the View. Turn on both themes, you will see the World appear in a Robinson projection.

Save the Project. 
 

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. 

Step 3 
Viewing the World from Space
Create another new View by the same procedure as used previously, copy the themes Cntry94.shp and World30.shpfrom the previous view and paste them into the new view. 

Choose Properties from the View menu and rename the view as Viewing the World from Space. Click the Projection button, and choose "the World from Space" under projection Type (the last option in the Category "Projections of the World"). You'll see a nice 3-D view of the globe as seen from a viewpoint above Massachusetts. 

If you want to see how the world looks when viewed from above Austin, Texas, go back to the projection selection window, click on "Custom" and then type -97 for the Central Meridian and 31 for the reference latitude. And there is the world centered on Austin, Texas! 
 

You may wish to try looking at the world from a few other places. You can get the coordinates of locations on the earth by viewing earth in the geographic projection. Play around a bit and have some fun! 

Save the project! 

To be turned in: a Layout showing the World in Geographic Coordinates, in Robinson Projection, and as Viewed from Space. 

You can now close all the views and the layout dealing with display of the world.

Step 4 
United States in the Geographic Coordinates
You will now examine map projections used for the continental United States. 

Create new View and rename it as United States in Geographic Coordinates. Add in States.shp and latlong.shp from your data directory. These are an outline of the United States and a 5-degree grid of latitude and longitude as a line theme. Click on the Zoom in tool  and zoom in to a view just of the continental United States, not including Alaska. Use the Pan tool  to 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 5 
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. 

As you did previously, create a new View, and copy and paste in the themes Latlong and States.shp from the previous View, United States in Geographic coordinates. 

Choose Properties from the View menu, and rename the View as United States in Albers Equal Area Projection. Change the Map Units from unknown to Decimal Degrees since the View that you are looking at is in Geographic Coordinates. 

Click the Projection button, change the Category to Projections of the United States, and among the choices offered, select the Albers Equal-Area (Conterminous U.S.) as the Type of the projection. Make a note of the Spheroid and the projection parameters used here. Click both OK's and return to the view. You will see the United States appear in Albers Equal Area Projection. 
 

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 view (View2), the result is that square boxes of latitude - longitude appear as elongated quadrilaterals with a bottom edge 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. 

To be turned in: a Layout showing the United States in Geographic Coordinates and in the Albers Equal Area projection. 

You can now close the Views and Layout of the United States. 

Save the project.

Step 6 
Texas in Geographic Coordinates
You will now examine the effect of various map projections up a map of the State, Texas. 

Create a new view and add in the themes Counties.shp and latlong.shp. The theme Counties.shp is a counties theme of the United States, including Alaska and Hawaii. 

Since you will only work on Texas, you will use theme definition to only show the counties of Texas. Make the Counties.shp theme active, choose Properties from the Theme menu. In the Theme Properties dialog box, click the Query Builder tool  . In the Query Builder dialog box, double click [State_name], click equal button  , then double click "Texas". You will see the Query is built in the scratch pad. Click OK. In your Theme Properties dialog box, you will see the theme now have the definition of "([State_name]="Texas")". This means only the counties with the state_name as Texas will show up in the view. 

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 7 
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. 

Create a new View, copy and paste Latlong and Counties to it from the previous view. Choose Properties from the View menu, rename the View as Texas in Lambert Conformal Conic projection. Set the map units to Decimal Degrees, then click on the Projection button. In the Projection Properties dialog box, select Category: Projections of the United States, and Type: Lambert Conformal Conic (Conterminous U.S.). Click OK to the two dialog boxes to transform the view to the Lambert Conformal Conic projection. 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 which would be produced by cutting the cone up the back side and unfolding the cone so that it lays flat on the table. 

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 8 
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 http://tgic.state.tx.us/standards/tgic-s06.doc 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) 
Reference Latitude: 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. 

Create a new View, copy and paste Latlong and Counties to it from the previous view. Make the Counties.shp theme active, choose Properties from the View menu, rename the View as Texas in Texas Centric Mapping System. Set the map units to Decimal Degrees, then click on the Projection button. In the Projection Properties dialog box, check the Custom radio button at the up-left corner. Choose Projection as Albers Equal-Area Conic, and choose GRS 80 from Spheroid scroll bar, then type the parameters given above into the boxes beside each of the parameters in the form. 
 

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. 

 

Step 9 
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. 

Create a new View, copy and paste Latlong and Counties to it from the previous view. 

Make the Counties.shp theme active, choose Properties from the View menu, rename the View as Texas in Universal Transverse Mercator (UTM) Projection. Set the map units to Decimal Degrees, then click on the Projection button. In the Projection Properties dialog box, under Category, select UTM, and under Type, select Zone 14. You will see a standard set of projection parameters displayed in the dialog box. 

These parameters mean that the Central Meridian of Zone 14 is at 99°W so that it covers from 96°W to 102°W; the Reference Latitude is 0.0000 (the equator, which is 0°N); the origin of the coordinate system is at the intersection of the Central Meridian with the Reference Latitude and thus is at (0°N, 99°W), where the coordinates are (x, y) = (500,000, 0) m. The false Easting of 500,000m is to ensure that all points in the zone have positive x coordinates. The y-coordinates are always positive in the Northern hemisphere because 0 is at the equator. In the Southern Hemisphere, a false Northing of 10,000,000m is applied to ensure that the y-coordinate is always positive. 

The Scale Factor of 0.9996 means that along the Central Meridian, the true scale of 1.0 is reduced slightly so that at locations off the true meridian the scale factor will be more nearly 1.0 (the Transverse Mercator projection distorts distance positively as you move away from the Central Meridian). 

Click both OKs to see the projection applied. The pattern of meridians and parallels looks strange, converging at top and bottom of the picture, which correspond to the North and South Poles, respectively. 

Zoom in on Texas, the map of the State looks much as it did in the Texas State Mapping System using the Lambert Conformal Conic projection. 

Questions:
1. How many UTM zones does it take to cover Texas? 
2. Which zone applies in West Texas? Central Texas? East Texas? 

To be turned in: A Layout showing Texas in Geographic, Lambert Conformal Conic and UTM projections

Step 10 
Austin in Geographic Coordinates
You have viewed the effect of different projections on different scales from the World, Country and State level. In the next few steps, you will take a look at the City of Austion and the effect of two map projections upon a map of the City. 

Create a new view and add in the themes Jurisgeoc, Lakegeoc, Roadgeoc, 75quad, and Onedegtx from your data directory. The theme Jurisgeoc is a coverage of the legal jurisdictions of the City of Austin. The themes Lakegeoc and Roadgeoc are coverages of the lakes and main roads of the Austin area respectively. The theme 7.5quad is a mesh of 7.5 minute quadrangles for Texas with map sheet names in each quad, and the theme Onedegtx is a line theme with lines each one degree of latitude and longitude so you can see where Austin is located geographically. All these themes are in geographic coordinates. 

Choose Properties from View menu, rename the view as Austin in Geographic Coordinates, then change the Map Unit to decimal degrees. 

Turn on the themes. Make the Jurisgeoc theme active, then click on the Zoom to Active Theme button  to zoom in on Austin. 

Drag the Onedegtx.shp theme down to just above the 75quad.shp theme, and make 75quad.shp clear, with only outline. (See instructions in Step 1) 

You can get a better picture of Austin by using the Legend editor to classify the roads by Size (Size = 1 is the largest road for IH-35 and the Mopac expressway), and the Jurisdictions by Name. The names give the locations of surrounding cities and 2 mile and 5 mile buffer zones around the Austin City Limits called Extra Territorial Jurisdictions, or ETJ's. 

Double click the Legend symbol of the Jurisgeoc theme and open the Legend Editor. Change Legend Type from Single Symbol to Unique Value, and choose Name for Values Field. Change the Color Schemes to Pastels. 

Click Apply. You will see the City of Austin classified by legal jurisdictions. 

Double click on the legend symbol of Roadgeoc.shp. In the Legend Editor, change Legend Type to Graduated Color, and choose Size for Classification Field. Click on Classify button, change the Number of classes to 9, and click OK. You should see color get darker when the number increase. Click the Flip Color Ramp button  , and you will see the colors are ramped from dark to light with the Value increase. So the largest street with the smallest value has the darkest color. 
 

Click Apply. You should see the City of Austin in Geographic Coordinates. 

The 75quad theme is the 7.5 Minute Quadrangle Sheet Coverage. Make the 75quad theme active and zoom to the extent of the active theme so that you see all of Texas laid out in 7.5 min quadrangle sheets. 

Questions:
1. How many 7.5' quadrangle sheets are there in a 1 degree by 1 degree box? 
2. How many 7.5' quadrangle sheets are needed to cover Texas? 

  • Just Southwest of Austin there is the intersection of a 1º parallel and a 1º meridian . What is the latitude and longitude of this location?
  • Make a list of the names of the 1:24,000 scale map sheets (7.5' quads) that are needed to cover Austin. (There is a neat automated way in which you can prepare this list of map sheet names without copying anything by hand). 
Step 11 
Austin in State Plane - 1927 Projection
The State Plane - 1927 projection is a standardized projection that is used for definition of legal boundaries in Austin. Texas has five zones in the State Plane coordinate system, each defined using the Lambert Conformal Conic projection, with different projection parameters depending on which zone you are in. Austin is in the Texas Central Zone. The 1927 refers to the NAD 27 datum. 

With the view Austin in Geographic Coordinates still open, hold down the shift key and make all of the themes active. Choose Copy Themes from Edit menu. 

Create a new view and from Edit menu, choose Paste. You will see all of the themes copied in the new view, already classified. 

Choose Properties from the View menu, rename it as Austin at State Plane - 1927, and change the Map Units to decimal degrees. Click the projection button, under Projection Category, choose State Plane - 1927, and under Type, choose Texas, Central. You'll see the projection parameters appear on the window. Click both OKs and see the projection applied. 

To be turned in: A Layout showing Austin in Geographic coordinates and in State Plane Coordinates.

Step 12 
Projection in ArcView
Projection is usually performed in ARC/INFO. ArcView GIS 3.2 allows map projection using a Projection Utility Wizard. Before you can use the Projector wizard, you have to choose menu File/Extensions. The dialog that appears lists all the available extensions. Click the check box next to Projection Utility Wizard and press OK. 

Create a new view and copy the themes from the view Austin in Geographic Coordinates as described in Step 11. Rename the View as Projection in ArcView, and change the Map Units to decimal degrees. Make the Jurisgeoc theme active, and click on Zoom to active theme button to zoom in on Austin. Choose Hide/Show Legend from the Theme menu to hide the legend of the Jurisgeoc theme. Before you change a projection, you have to set up the current Map Units first. Choose menu View/Properties, change the Map Units from Unknown to decimal degrees. Click OK. 

While the Jurisgeoc theme is active, choose File/Projection Utility Wizard, and wait for the Wizard to initialize. Choose Jurisgeoc.shp as the theme to be projected. For current coordinate system, choose Geographic Coordinates, NAD 27 (North American Datum of 1927)

say Yes, to the question of storing the current coordinate system on the Jurisgeo.shp file.For the new coordinate system, choose the NAD 27, Texas State Plane, Central Zone with units in Feet:

Save the new file as Jurisstp.shp, and add the new shape file as a theme to a new View. Make the new theme Jurisstp.shp active, then click on Zoom to active theme button. You will see the new theme shown in the view, and the numbers on the up-right corner are not latitude and longitude any more. They are in the units of the State Plane coordinates - feet. 

If you want, you can project the 7.5 quadrangle map, the roads, the lakes and the one degree boxes similarly, and add them to the new View. Verify that it looks the same as the View you got by using the View Properties Projection button earlier. 

Question: the area over which the City of Austin has "Full Purpose" jurisdiction is the area in the center of this map. The areas around this are areas in which the City has limited jurisdiction or areas which lie within surrounding cities. Over what % of the area shown in the jursstip.shp polygons does the City of Austin have "Full Purpose" jurisdiction? Briefly explain how you got the answer.

Step 13 
Save your project in ArcView 
You're done!!

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