Lab: Projections for Cartography

Adapted from a blog post by: Andrew Klein, Texas A&M University; Christopher J. Sutton, Western Illinois University; Aileen Buckley, Esri.

One fundamental function of a Geographic Information System is its ability to translate spatial coordinates stored either as longitudes/latitudes or in a specific map projection into another. As with other modern GIS systems, ArcGIS presents the user to accomplish this in two ways. ArcMap and ArcGIS Pro have the ability to display geographic data stored in one geographic coordinate system into another without actually changing the underlying coordinate system. This is accomplished in real time and is often informally referred to as projecting “on the fly.”  GIS systems also provide a user the ability to permanently transform a geographic coverage from one map projection into another. Both of these approaches have their advantages and disadvantages.  This lab focuses on projecting “on the fly.”

Before you begin learning how to implement map projections in a GIS, a process which has gotten much easier and much better over time, a few pertinent points need to be made.

First and foremost, while a GIS can perform transform geographic coordinates from any number of map projections to another, it is up to the cartographer to understand the strengths/weaknesses of a particular map projection and appropriateness for its intended use.

The major point of the lab is to have you identify the suitability of a number of projections, and gain familiarity with how setting coordinate systems for the map frame work in ArcPro.

Within a GIS, spatial coordinates can be stored either in spherical coordinates (latitude/longitude) or in Cartesian coordinates (x,y within a particular map projection). Spatial information stored as latitude and longitude is often said to be unprojected, which ArcMap/ArcPro label as a geographic coordinate system (GCS). Conversely, spatial coordinates stored as Cartesian coordinates within a specified map projection are often said to be projected, labeled in ArcGIS as a projected coordinate system (PCS). In this lab, we will focus on selecting and modifying a specific PCS for a specific map purpose.

Because the mathematics of dealing with information in spherical and Cartesian coordinates differ greatly, it is essential when performing GIS analysis that the data be projected – or stored in a projected coordinate system. However, if the primary purpose is for visualization e.g., making a world map, it is also necessary to set the coordinate system in your map frame and project on the fly for map production.

GIS offers flexibility in creating maps with map projections tailored specifically to the problem at hand – unheard in old-fashioned pen and ink cartography. Take advantage of this technology, but be sure to use it correctly as a cartographer!

Setting coordinate systems and visualizing distortion

  1. Start by copying the Projections Lab files from the Google drive to your folder (ProjectionLab2019.zip). Open the included project, TissotsIndicatrix.aprx and take a minute to look at the layers.
    1. Countries: The countries of the world (source: Esri)
    2. ne10m_graticules_10: The graticule as a line feature, drawn every 10° (source: Natural Earth)
    3. ne_50m_populated_places_simple: Cities of the world (source: Natural Earth)
    4. TissotEllipses: The circles represent a Tissot’s Indicatrix placed every 30° in latitude and longitude (source: Esri)
    5. World_30: A 30° filled graticule that forms the ocean (source: Esri)

The Tissot Ellipses are a handy tool for visualizing distortion.  Their shape and size indicate the amount and type of distortion on the map at that location. You will be using these to help understand the distortions in the map projections you will examine as we go on.

Now let us turn our attention to map projections which is the focus of the lab.

  1. To display the current map projection used in the map frame, and later to modify it, it is necessary to open up the properties of our map frame (labeled Map in the Table of Contents). To do this, right click on Map and select Properties (at the bottom). This will bring up a dialog box entitled Map Properties. From the list at left, select Coordinate Systems. It should look something like this:
Map properties window
Figure 1. Map Properties
  1. Next to Current XY, click Details. This lists all the properties for this particular coordinate system. If it’s a projected coordinate system, you’ll see a line for Projection. When you manipulate the projections for the scenarios later on in lab, you will need include ALL of this information on your map.

Let’s examine the coordinate system information for a second. It should indicate the Current Coordinate System is GCS_WGS_1984 with a datum of D_WGS_1984. To someone familiar with ArcGIS, this indicates that ArcGIS is displaying the geographic information in an unprojected coordinate system (GCS in ArcGIS terminology) and the model of the earth it is employing is the WGS 1984 Datum. Once you become more familiar with ArcGIS you might guess this given that the geographic units it is displaying are in decimal degrees as these are the coordinates displayed in the bottom right of the map window.

If you remember your map projection lectures, it is almost never appropriate to display the spherical coordinates (latitudes/longitudes) in a map.

So what can we do to change this? It is actually quite easy. Underneath the Current XY box, you will notice the words XY Coordinate Systems Available. There are a number of options including Favorites, Layers, Geographic Coordinate Systems and Projected Coordinate Systems.

  1. Expand Projected Coordinate Systems, and since we have a world map you should expand Select one from the list that appears, click OK and see what happens.

In the example below, I have selected Eckert I and you can see how this projection displays the entire world.

Eckert I projection
Figure 2. Modifying the map projection to display the world in an Eckert projection
Eckert I map
Figure 3. Our world now displayed in an Eckert projection

It should be obvious how the borders of the world change as well as the continents. It might be slightly less obvious how the Tissot Ellipses change, but they provide important information about the distortions in shape and size at their locations. Notice in this projection that the center ellipse is circular (no change in shape) and as you move north and south the area of the ellipses increases which indicates an increase in area north and south. This means the map is not equal area. Also notice how the ellipses change shape – especially along the equator – this indicates the map is not conformal either. It is possible to use the Tissot Ellipses to see how dramatically the distortions are across the map both in magnitude and form.

  1. Now you should take time and examine the different map projections that ArcMap provides. As you are examining these projections you can refer to the USGS map projections page (or others) to understand the properties of the projections you are examining http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html
  2. The cartographers at Esri (the company that makes ArcGIS) have spent considerable time and effort creating a set of predefined projections that are very useful for both the world, various continents, countries, states etc. However, since you are a cartographer you may not want any of these ready-made projections, but instead want to set your own parameters.

There are several ways to create a custom map projection, but the easiest is to modify an existing one.

Projection modification window
Figure 4. Modifying the Eckert projection to have the central meridian run through the US rather than England
  1. Right click on the name of your projection in the list.
  2. Select Copy and Modify.

In the example below, I simply modified the existing world Eckert projection to move the central meridian from the Prime Meridian to the longitude of the center of the continental US (96° W). As you can see it is pretty easy to do and the resulting map displays the world according to ‘Merica. Note that not all projections are equally well suited to this particular modification – your results may vary.

Modified Eckert I
Figure 5. Modified Eckert I projection with the central meridian now positioned over the US

For the projection-curious, the Waterman does not currently exist in ArcGIS. If you want to see how it looks with Tissot’s Indicatrices, go here: https://www.jasondavies.com/maps/tissot/#waterman

General Assignment

Your job is to alter the map projections to visualize the impact on a map of China.  You will use a technique known as small multiples, which places multiple copies of a map at the same scale on a single page.  For more information on this technique, check out this post from Juice Analytics.

Making the Maps

  1. Insert a new map in to your project (Insert > New Map). Include the following layers from your geodatabase:
  • Countries
  • ne_50m_populated_places_simple
  • TissotEllipses
  • ne_10m_graticules_10
  1. Right click on the map frame and select Properties. Rename this first map to WGS1984.   While you’re in the Properties window, choose Coordinate System on the left and verify that it’s set to GCS WGS 1984.  This is the default behavior when you bring in unprojected data layers.

The next step is to isolate the desired features from your datasets.

  1. Use Select by Attributes to select China from Countries. You can launch this from the Attribute Table, or from the Map
  2. Click the + New expression button

    Select by Attributes window
    Figure 5: The Select by Attribute panel
  3. Set the Field to CNTRY_NAME, the condition to is Equal to, and the value to China.  Your clause should now read Where CNTRY_NAME is equal to China.
  4. At the bottom of the pane, click Run.

China should now be highlighted.  To get it all by itself, we need to export it to a new shapefile.

  1. On the Data ribbon, click Export Features. You can also launch this by right clicking on the layer in the Contents pane, selecting Data > Export Features, similar to the method for ArcMap.
  2. Name it something appropriate and save it in your working folder. Don’t forget to hit Run at the bottom of the pane.

Note: Saving the selection as a layer is not recommended, as layer files are very fragile, and more prone to break when moving files around.

  1. Remove the Countries layer from your map.
  2. Repeat this process with the ne_50m_populated_places_simple layer, selecting for Beijing.
  3. Remove the populated places layer from your map.
  4. Right click on your Beijing layer and select Label. Right click again and select Labeling Properties.
  5. In the pane that appears, select the Position tab, and under Placement, change the dropdown to Bottom left of point. This will keep the label clear of the borders.
  6. Symbolize China and Beijing as desired.

We need to make five more maps, but we’ll take advantage of some shortcuts to do so.

  1. Click the blue Project tab and select Options.
  2. Under Map and Scene, set the default basemap to None. (Note: this will only stick for this session if you are working on a lab computer.)
  3. Click OK and return to your map.
  4. Insert a new map. Rename it UTM Zone 50N, and set the coordinate system to Hong Kong 1980 UTM Zone 50N.  Check the Details and note that the Central Meridian is 117.0.
  5. Repeat this process as follows for the remaining four maps. For each of these, use the information you learned in the first part of this activity to set the Central Meridian to 117.
    1. Map frame: Mercator; CS: Mercator (World).
    2. Map frame: Albers Equal Area Conic; CS: Asia North Albers Equal Area Conic
    3. Map frame: Lambert Conformal Conic; CS: Asia North Lambert Conformal Conic.
    4. Map frame: Equidistant Conic; CS: Asia North Equidistant Conic

You should now have six map frames, labeled and set with six different coordinate systems.

  1. Return to the WGS84 map and highlight all the layers in the Contents pane (shift and click each one). Right click and select Copy.
  2. Choose the next map tab, right click on the map frame name (in Contents) and select Paste. All layers should now appear, with the same symbolization, but in the new CS.  Remember that this technique uses Arc’s project “on the fly” technique, and does not actually reproject the data.  For proper analysis, all layers would need to be reprojected using the Project tool.
  3. Repeat for the remaining maps.

Making the Layout

Your final layout will use only one scale bar and north arrow, placed unobtrusively on the page, and each individual map will be labeled with its projected coordinate system.  For this particular map, you will not need legends.

  1. Insert each map frame (6 in total). Resize them to 4” wide by 2.75” tall.
  2. Add page guides 0.25” from the edge to represent your print margins.
  3. Arrange your frames in a neat grid. Feel free to add extra page guides to help line them up.
  4. Once you have the frames arranged, remove the borders from the data frames.
  5. IMPORTANT: Verify that each map is at the same scale – 1:75,000,000 is recommended. Note that some projections may cause China to appear larger or smaller, so you must verify this with the scale settings at the bottom of the layout window. (This is how we get away with a single scale bar!)
  6. Next, label each frame with its coordinate system. Click each frame individually, and from Insert > Dynamic Text, select Map frame > Name.  In the Properties pane, you should see Name: followed by a tag [name], indicating that the frame’s name will be inserted here.  Remove the text before the tag, so that your frames are only labeled with their names.  Make sure the frame names are clean, with no typos or inappropriate abbreviations.  Do these one at a time, as the text drops in the middle of the page, and then move it to the correct map before inserting the next one.  Be very careful to apply the correct label to each map, and take advantage of page guides to align the labels.

The purpose of small multiples is to strip the maps down to the essentials for comparison, so all six maps should be symbolized the exact same way, and kept fairly simple.  You may also choose to experiment with your page layout, but bear in mind that small multiples are always in a grid pattern to help visualize differences more easily.

  1. Underneath your map set, add a short paragraph of text describing the distortions of each coordinate system, and its suitability for mapping (advantages/disadvantages). You may want to turn on the Tissot ellipses to help you visualize what’s happening, but don’t forget to turn them back off before exporting your final map.
  2. Add a title, source credits and your name and date. Your map doesn’t need to match the example below, but it should be somewhat similar in layout.  Export as a PDF.
Sample map of China in 6 coordinate systems
Figure 6: Small multiples layout comparing projections for China
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