Overview

Welcome to Lesson 3! In previous lessons, we discussed and designed several types of thematic maps, including proportional symbol, dot, and choropleth maps. Here, we discuss a more specialized type of thematic map - flow maps. In this lesson, we'll integrate our knowledge of visual variables, map symbolization, and levels of measurement into our discussion of these flow maps: maps that show movement between locations. 

Before diving into our flow map discussion, however, we introduce another topic integral to cartography: map projection. We explore the different ways in which we define locations on Earth's surface, the process of creating a map projection, and how our choice of projection alters readers' interpretations of our maps. By the end of this lesson, you should understand the different classes and cases of projections, as well as popular map projections and their characteristics. In Lab 3, we use this knowledge to create custom projections for flow map-based advertisements - a twist intended to emphasize the vast variety of clients and audiences for whom cartographers design thematic maps.

Learning Outcomes

By the end of this lesson, you should be able to:

• explain the relationship between the geoid, a reference ellipsoid, and a datum, as well as the importance of these elements in cartography;
• classify projections based on their class, case, and aspect;
• describe projection properties and their respective utility for different mapping tasks;
• integrate knowledge of a map’s purpose, scale, and location into the projection selection process;
• describe the use of visual variables and levels of measurement in flow maps.

Lesson Roadmap

Questions?

If you have questions, please feel free to post them to the Have a question about Lesson 3? Ask here! forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

From a young age, we are generally taught that Earth is a sphere. Images such as those taken from space (e.g., Figure 3.1.1) reinforce this idea. Yet, this is an oversimplification—Earth's actual shape is far more complicated as it appears to be. This poses an issue for cartographers, because our job often requires us to use measurements of the Earth to represent it accurately. So, short of going out and measuring every nook and cranny of the Earth’s surface, what tools can we use to create a faithful model of our very non-spherical planet?

Figure 3.1.1: The Earth from space.

Credit: NASA [2]

Due to the centrifugal force created by Earth’s rotation, Earth bulges outwards slightly at the middle—it is wider around the equator than from pole to pole. Because of this, a better way to describe Earth’s shape is as an ellipsoid. Ellipsoids which closely resemble spheres (also referred to as spheroids)—and as Earth is wider in the East-West direction, the most precise word to describe the approximation of Earth's shape is oblate ellipsoid (or oblate spheroid). In the literature about this topic, the terms ellipsoid and spheroid are often used interchangeably. Which term you use is less important than your understanding of the general concepts involved.

Figure 3.1.2: An example of an oblate spheroid.

Credit: USGS [3]

Many scientific fields are concerned with determining heights across Earth’s surface. In order to establish an accurate height, a zero-surface needs to be established. While the equator and prime meridian offer convenient zero-references for horizontal positions (a horizontal datum), heights (or the vertical component) is more challenging. To determine accurate heights (or elevation), a vertical datum is needed.

Elevation can be described as the distance of a point above a specified zero-surface of constant potential (usually gravity or gravitation). This distance is measured along the direction of gravity between the point in question on Earth’s surface and the specified zero-surface. To start this measurement, a suitable surface must be selected. Many surfaces exist such as an equipotential surface (i.e., a level surface of constant potential energy). Meyer (2010) explains that, in theory, on a level surface, there is no change in gravity potential and water does not flow across said surface. Water only flows between different equipotential surfaces due to forces that arise from the differences in potential energy.

Earth possesses an infinite number of equipotential surfaces. Deakin (1996) described that a cross-section of Earth’s equipotential surfaces would appear as an infinite number of thin onion skins that are not parallel to one another, are continuous, have smoothly varying radii of curvature, and are spaced closer together at the poles than at the equator with verticals as curved lines intersecting each surface at right angles. This convergence is a consequence of Earth’s physical oblate shape, to a first order and that gravity is stronger at the poles.

One particularly important zero-surface of the Earth is mean sea level (MSL), or the average height of the ocean’s surface. Historically, MSL was calculated simply by measuring the height of the ocean over time at fixed points. Mean sea level is affected by Earth’s gravity as gravity across Earth’s surface is not constant. Earth’s gravity is different in Lincoln, NE than it is in Los Angeles, CA, and if the ocean existed in both locations, its surface would be at different heights due, in part, to the influence of gravity. In places where the ocean is not found (like Lincoln, NE) it is difficult to measure MSL. Historically, estimates of MSL for interior locations were created by extending MSL based, in part, on long-term computations from tidal gauge stations located along the coasts. This process created a vertical datum called the Sea Level Datum of 1929 (which was later renamed to the National Geodetic Vertical Datum of 1929 in 1973). Unfortunately, the surveys used to create this datum introduced error into this geodetic height network.

Despite best intentions, MSL does not accurately represent Earth’s true shape. Estimates of MSL are fraught with accounting for forces such as winds, tides, currents that complicate the estimation process. A different zero-surface, known as the geoid, helps address these complications. In conceptual terms, the geoid is a level surface that the world’s ocean would assume if Earth’s rotation, winds, tides, and currents stopped, and its waters freely flowed over land conforming to Earth’s gravity field. In a general sense, MSL approximates the geoid, after a least squares adjustment is made. Van Sickle (2017) offers that these environmental forces cause MSL to deviate from the geoid up to 2 meters implying that MSL does not exactly follow the geoid. It is important to remember that the geoid does not represent the terrain of the Earth. However, the surfaces are related, for example, as rock masses have an effect on local gravitational forces and can help shape the geoid.

Figure 3.1.3 illustrates a geoid model. Overall, this geoid model is bumpy but these undulations are not visible to our eyes. In the figure, magenta hues indicate places of greater mass and stronger gravity (MSL is higher) while cyan hues represent lower mass and weaker gravity (MSL is lower). Some of Earth’s surface topography, reflected by the geoid undulations, can be visualized in this figure such as the Pyrenees Mountains and the Himalayans. Other undulations cannot and are attributed to, for example, different rock densities (such as observed in the basin in the Indian Ocean).

Figure 3.1.3: A graphic depiction of the geoid. This visualization is nicknamed “The Potsdam Gravity Potato.”

Credit: NASA [4]

Figure 3.1.4: The Geoid’s relationship with Earth’s surface and the reference Ellipsoid.

Credit: USGS [3]

The geoid is constantly changing—due both the ever-changing nature of Earth’s surface (e.g., from continental shifts, melting glaciers, etc.), and because technological advancements have allowed for more and more precise gravitational calculations over the years. The dynamics of Earth and the imprecision of measurement techniques mean that any model of the geoid is only an approximation (just as MSL is an approximation for Earth’s gravitational (and height) surface), in reality.

Ellipsoids and geoids are both ways to model the Earth, and thus there are multiple ways to “fit” these models to our physical planet. We do this by choosing a set of reference points, and using these reference points create a geodetic network called a datum. There are many different datums from which to choose. Each datum can be composed of unique ellipsoid and geoid models.

Horizontal datums denote locations using a system of longitude and latitude. The network of latitude and longitude lines that appears on a map is called the graticule. Horizontal datums are based primarily on a specified reference ellipsoid. We have already addressed the idea of a vertical datum, which is used to specify heights from a zero-surface (i.e. the geoid). Both horizontal and vertical datums are important for designing cartometric maps, as was mentioned in Types of Maps. But in order to get the most accurate horizontal measurements of a particular area of concern, one must select a horizontal datum that accurately models the geographic location in question.

The two illustrations in Figure 3.2.1 below demonstrate how datums differ in their design based on their intended purpose. On the left, the reference ellipsoid is aligned to closely fit the geoid in one part of the world (Australia). This is a local datum developed for use in Australia, and though the ellipsoid fits other parts of the world poorly, this is acceptable given the datum's intended use. On the right, the reference ellipsoid more closely fits the geoid overall. This is a geocentric datum, which is ideal for global mapping projects. The reference ellipsoid on the right is also centered at the center of Earth’s mass, which is important for GPS positioning.

Figure 3.2.1: The Australian Geodetic Datum (AGD84) (left), and the Geocentric Datum of Australia (GDA94) (right).

Credit: Intergovernmental Committee on Surveying and Mapping, Australia [5]

The three most popular horizontal datums used in North America are the North American Datum of 1927 (NAD27), the North American Datum of 1983 (NAD83), and the World Geodetic System (WGS84), which is actually considered to be a terrestrial reference frame (which expresses both horizontal and vertical datums all rolled into one standard. NAD27 was the first standardized connected system of location points in North America. It was based on the Clarke Ellipsoid of 1866—measurements were made and recorded based on the relative positioning of all locations from Meade’s Ranch in Kansas. NAD83 is the modernized replacement of NAD27 and sought to improve positional accuracy as a result of adding thousands of new benchmarks. NAD83 replaced NAD27 in 1983; its increase in accuracy came from the addition of more benchmarks compared to NAD27. Still, NAD83, relied on human measurement of triangulation from control points. The National Geodetic Survey (NGS) has been working to replace NAD83 with a terrestrial reference frame that will encompass the entirety of the United States and its territories. Known as the North American Terrestrial Reference Frame of 2022 (NATRF22), this will combine the geometric and geopotential aspects into a single product that will rely primarily on Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), as well as on a gravimetric geoid model resulting from NGS’ Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project. The intended accuracy of heights relative to MSL in the geopotential component of NATRF2022 will be 2 centimeters over any distance, where possible. The magnitude of change with NATRF2022 will vary depending on your geographic location. NATRF2022 will change latitude and longitude positioning and ellipsoid height between 1 and 4 meters. In the conterminous United States (CONUS), NATRF2022 will change heights on average 50 centimeters, with approximately a 1-meter tilt towards the Pacific Northwest.

The World Geodetic System (WGS84), designed by the National Geospatial-Intelligence Agency, developed alongside GPS technology, was the first datum suitable for general worldwide use. WGS84 is the standard datum used by GPS technologies today, though NAD83 remains popular for non-GPS-based mapping activities in North America. As mentioned, a new geometric and geopotential datum for North America, NATRF2022, will soon be realized and available for use. More information on this and other new datums is available from the National Geodetic Survey [6].

Historical maps and data often reference the now-outdated NAD27 datum; it is important to be aware of the datum which was used to designate the locations of your spatial data. Datum transformation is the process of re-calculating coordinate locations or heights based on a different datum and may be necessary if you are combining datasets that were specified using different datums (e.g., NAD27 vs. NAD83), or if you are hoping to map historical data using a more up-to-date system.

As noted previously, modeling the earth as an ellipsoid or geoid is necessary for Cartometric mapping—mapping that involves the taking of precise measurements from maps. Current GIS software tools (and the computers they run on) are now powerful enough to create projections based on an ellipsoidal Earth without much difficulty. For most thematic mapping purposes, however, conceptualizing Earth as a sphere is close enough.

For the rest of this lesson, we will discuss Earth’s shape as if it were spherical, despite this being an oversimplification. The reason for this is that to create a map—that is, a two-dimensional (flat) rendering of Earth’s surface—we need to represent a three-dimensional object on a two-dimensional plane. And even with a simple sphere, this is no simple task. In addition, the thematic maps that are created in this class do not have a high accuracy measurement requirement; thus, a spherical Earth assumption is sufficient for thematic map purposes.

Unlike Earth, maps are flat. Though Earth can also be represented as a globe, globes are inconvenient, expensive, and challenging to design. Maps are much more convenient: they are easier both to produce and to reproduce, and when you are mapping detailed data at a relatively large scale, the Earth appears to be more or less flat anyway. So when you want to transform latitude and longitude values from the three-dimensional Earth onto a two-dimensional surface (a map), you will use a process called map projection.

Figure 3.3.1: Conceptualizing map projection.

Credit: Wikimedia Commons [10]

In the past, cartographers were tasked with projecting maps by hand, necessitating relatively complex mathematical calculations. Fortunately, GIS software such as ArcGIS is now able to perform this task of projection for us automatically. Though deriving a map projection through manual methods is uncommon today, map projections are still being refined and invented– as one example, Bojan Šavrič (Esri), Tom Patterson (US National Park Service), and Bernhard Jenny (Monash University) released the Equal Earth Projection in 2017.

To create a map, cartographers transfer a model of the earth as it appears on a reference globe to a developable surface.

A reference globe is a model of Earth, including landmasses, oceans and the graticule (lines of latitude and longitude), at some chosen scale, which is the final scale of the map to be created (Slocum et. al 2023). This projected map is thus modeled from an imaginary scaled-down version of Earth.

A developable surface is a mathematically-definable surface onto which landmasses and the graticule are projected (Slocum et. al 2023). In simpler terms, a developable surface is any surface that can be “unrolled” flat and thus, create a two-dimensional map. Typically, this surface is described as a cone, a plane (flat surface), or a cylinder. In this next section, we discuss how the choice of a developable surface—among other factors—influences a map projection's characteristics.

Like ellipsoids, geoids, and datums, there are many projections to choose from, as well as many options for customizing the projection you choose. Before you decide, it will help to understand the characteristics of different projections. Projections are generally defined by their class, case, and aspect. All three of these characteristics refer to the way in which the developable surface relates to the reference globe.

A projection’s class refers to which developable surface was used to create the projection. Was the developable surface a cone (conic class), plane (planar class/azimuthal), or cylinder (cylindric class)?

Figure 3.4.1: Developable surfaces and their use in map projection: Cylinder (left), Cone (middle), and Plane (right).

Credit: Data Source: ICSM.gov.au [11]

The projection class you use will depend, among other factors, on the location of the region you intend to map. Planar projections, for example, are often used for polar regions.

As shown by the figure below (Figure 3.4.2), a map will contain no distortion at the location where the reference globe touches the developable surface, and distortion increases with distance from this location.

Figure 3.4.2: An illustration of map distortion levels.

Credit: Data Source: ICSM.gov.au [11]

Even among projections of the same class, there is more than one way to create a projection with the selected developable surface. A projection’s case refers to how this surface was positioned on the reference globe. If the developable surface touches the globe at only one point or line, this is called a tangent projection. If it touches at two, this is called a secant projection.

Figure 3.4.3: Creating a conic projection of the tangent (left), and secant (right) case.

Credit: ICSM.gov.au [11]

Aspect refers to where the developable surface is placed on the globe. If it is placed over one of the Poles (North or South), this is called a polar aspect projection. If the center is along the equator, this creates an equatorial projection. If the developable surface is placed anywhere else, we call this an oblique projection.

Figure 3.4.4: An illustration of a planar projection (azimuthal equidistant) in the polar (left), equatorial (center), and oblique aspect. Conic and cylindrical maps can similarly be positioned at various location on Earth’s surface

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

No matter what its class, case, and aspect, the projection process always creates distortion. Different projections, however, have different types of distortion. In the next section, we discuss these differences.

All map projections distort landmasses (and waterbodies) on Earth’s surface in some way. Even so, projections can be designed to preserve certain types of relationships between features on maps. These include equivalent projections (which preserve areal relationships), conformal

All map projections distort landmasses (and waterbodies) on Earth’s surface in some way. Even so, projections can be designed to preserve certain types of relationships between features on maps. These include equivalent projections (which preserve areal relationships), conformal projections (angular relationships), azimuthal projections (directional relationships), and equidistant projections (distance relationships). The projection you choose will depend on the characteristics most important to be preserved, given the purpose of your map.

Eqvivalent

Equivalent projections preserve areal relationships. This means that comparisons between sizes of land-masses (e.g., North America vs. Australia) can be properly made on equal area maps. Unfortunately, when areal relationships are maintained, shapes of landmasses will inevitably be distorted—it is impossible to maintain both.

In Figure 3.5.1 below, shape distortion is most pronounced near the top and bottom of the map. This is because the poles of Earth (North and South) are represented as lines of the same length as the equator. Recall that lines of longitude on the globe converge at the poles. When these convergence points are instead mapped as lines, landmasses are stretched East-West, which means that to maintain the same area, landmasses must be compressed in the opposite direction. In the map below, Russia (and other landmasses) are represented at the proper size (compared to other landmasses on the map) but their shapes are significantly distorted.

Figure 3.5.1: The Albers equal area projection.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

The property of equivalence is perhaps best understood by contrasting the appearance of landmasses on an equivalent projection with a popular projection that greatly distorts area—the Mercator projection (Figure 3.5.2).

Figure 3.5.2: The Mercator Projection.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

The Mercator projection results in a significant distortion of areas far from the equator. In order to maintain local angles, parallels (lines of latitude) are placed further and further apart as you depart from the equator. The website thetruesize.com [12] demonstrates this effect.

Despite this, the Mercator is useful for some purposes. It has historically been used for navigation—it is efficient for routing as any straight line drawn on the map represents a route with a constant compass bearing (e.g., due West). This line of constant compass bearing is commonly referred to as a rhumb line or loxodrome. The Mercator is a conformal projection.

Conformal

Conformal projections preserve local angles. Though the scale factor (map scale) changes across the map, from any point on the map, the scale factor changes at the same rate in all directions, therefore maintaining angular relationships. If a surveyor were to determine an angle between two locations on Earth’s surface, it would match the angle shown between those same two locations on a conformal projection.

Figure 3.5.3: The Lambert Conformal Conic Projection, a popular conformal projection.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

Although the Mercator projection simplifies navigation, rhumb lines do not show the shortest distance between two points. The shortest point between two points on Earth is called a great circle route. Unlike rhumb lines, such lines appear curved on a conformal projection (Figure 3.5.4). Of course, the literal shortest path from Providence to Rome is actually a straight line: but you'd have to travel beneath Earth's surface to travel it. When we talk about the shortest distance between two points on Earth, we are talking in a practical sense of traveling across or above Earth's surface.

Figure 3.5.4: Rhumb line (constant compass bearing) vs. great circle (shortest distance; shown in yellow) between Providence, Rhode Island and Rome, Italy as shown on the Mercator projection.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

Azimuthal

The gnomonic map projection has the interesting property that any straight line drawn on the projection is a great circle route. The gnomonic projection is an example of an azimuthal projection.

Figure 3.5.5: A gnomonic projection centered on the North Pole.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

Azimuthal projections are planar projections on which correct directions from the center of the map to any other point location are maintained. The stereographic projection is another example of an azimuthal projection. Though only on the gnomonic projection is every straight line a great circle route, a straight line drawn directly from the map’s center is a great circle on any azimuthal projection.

Figure 3.5.6: A stereographic projection, centered on the North Pole.

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

The most common types of azimuthal projections are the gnomonic, stereographic, Lambert azimuthal equal area, and orthographic projections. The primary difference between azimuthal projection types is the location of the point of projection. In Figure 3.5.7 below, a gnomonic projection occurs when the point of projection is Earth’s center. Stereographic maps have a point of projection on the side of Earth opposite the plane’s point of tangency; the point of projection for an orthographic map is at infinity.

Figure 3.5.7: Changing the point of projection. Gnomonic (left), Stereographic (center), Orthographic (right).

Credit: USGS.gov [13]

Equidistant

Equidistant projections are often useful as they maintain distance relationships. However, they do not maintain distance at all points across the map. Instead, an equidistant projection displays the true distance from one or two points on the map (dependent on the projection) to any other point on the map or along specific lines.

Figure 3.5.8: Azimuthal Equidistant (left); Two-Point Equidistant (right)

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

In the azimuthal equidistant projection (Figure 3.5.8, left) distance can be correctly measured from the center of the map (shown by the black dot) to any other point. In two-point Equidistant projection (Figure 3.5.8, right), correct distance can be measured from any two points to any other point on the map (and, thus, to each other). In the example above, those two points are (30⁰S, 30⁰W) and (30⁰N, 30⁰E). These values were supplied as parameters to GIS software while projecting the map. However, you can customize the parameters that better suit the map's purpose, the geographic area to be mapped, and the map’s purpose.

Figure 3.5.9: Cylindrical Equidistant with Standard Parallel at the Equator (Plate Carrée).

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

Not all equidistant maps are circular in shape. The cylindrical equidistant projection, for example, is equidistant in that correct distances can be measured along any meridian. When the cylindrical equidistant projection uses the Equator as its standard parallel, the graticule appears to be composed of grid squares, and it is called the Plate Carrée, a popular map projection due to its simplicity and utility.

So far, we have discussed maps that preserve areal (equivalent), angular (conformal), distance (equidistant), and directional (azimuthal) relationships. As demonstrated by the previous examples, maps that preserve certain properties do so at the expense of others. It is impossible to preserve angular relationships, for example, without significantly distorting feature areas. For this reason, another class of projections exists—compromise projections.

Compromise

Compromise projections do not entirely preserve any property but instead provide a balance of distortion between the various properties. A frequently-used example is the Robinson Projection, shown in Figure 3.5.10 below. Note on this projection how the landmasses appear more similar in shape and size to what is seen on a globe compared to their appearance on a projection that preserves a specific property entirely (e.g., The Mercator).

Figure 3.5.10: The Robinson Projection

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

Interruption is not a projection property, but a characteristic of a projection. Specifically, interrupted projections can be useful in some mapping contexts. Interrupted maps, such as the Goode homolosine interrupted projection (Figure 3.5.11), are reminiscent of an “orange-peel” pressed against a flat surface, a common metaphor for map projections. In the same way that peeling an orange allows you to make the rind flatter, interruption allows cartographers to represent landmasses with generally less distortion.

Figure 3.5.11: The Goode homolosine interrupted projection.

Credit: NASA Goddard Institute for Space Studies (GISS) [14]

The interrupted nature of this projection severely distorts (by dividing) water bodies, and so would not be useful for maps related to oceanic data, or those intending to visualize routes across Earth’s (connected) surface. These distortions, however, allow the map to display a more accurate representation of landmasses’ sizes and shapes at the expense of accurate proximity. Note that while the divisions on the projection shown in Figure 3.5.11 are over water, divisions over land are also possible, though not as popular.

Many projections are available in ArcGIS and other software, some of which are imaginative and fun (e.g., the Berghaus star; Figure 3.5.12) and all of which can be customized to suit a map’s location and purpose. We will talk more about how to select an appropriate map projection in the next section.

Figure 3.5.12: The Berghaus Star Projection

Credit: Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

projections (angular relationships), azimuthal projections (directional relationships), and equidistant projections (distance relationships). The projection you choose will depend on the characteristics most important to be preserved, given the purpose of your map.

There are many factors to keep in mind when choosing a projection for your map. The number of projections available can sometimes seem overwhelming, and as there is no distortion-free map, the selection of any projection involves a trade-off between different properties.

When selecting a projection for your map, your map’s purpose, geographic scale, and location should be at the forefront of your decision-making process. Many cartographers have proposed guidelines or tools to assist map-makers in choosing an appropriate projection.

Slocum et al. (2023) provide five suggestions for choosing a projection for a thematic map:

1. The cartographer should aim to select the projection with the least distortion.
2. Distortion can be kept to a minimum by aligning the location of the map with the location of the standard line(s) or point(s)—where the reference globe meets the developable surface.
3. As the amount of geographic area covered by the map increases, distortion becomes more of an issue—projection selection is much less consequential with large-scale “zoomed-in” detailed maps.
4. Some projections are popular and in widespread use—this does not necessarily mean they are the best choice for your map.
5. Projection influences the overall look of your map design—this has been less studied and is generally less quantifiable than other factors, but it’s still important to consider.

Frederick Pearson (1984), also proposed a simple set of guidelines for map projection selection based on the latitude of the area to be mapped. If the map was of an equatorial region, he suggested a cylindric projection. If it was mid-latitude, a conic projection, if it was polar, a planar projection (Pearson 1984). While this is a good starting point, one must consider these guidelines in the context of a map’s purpose. One must also then choose between the many projections that exist of each type (e.g., there are many different conic projections).

Some online tools have been developed to help in the projection selection process. One such tool is Projection Wizard [15], developed by Bojan Šavrič (Šavrič, Jenny, and Jenny 2016). It is a web-based tool that suggests projections based on user input of only the intended distortion property (e.g., equal-area), and the location of the map (input via an adjustable map frame).

Figure 3.6.1: Projection Wizard, developed by Dr. Bojan Šavrič.

Credit: Projection Wizard [16]

Projection Wizard is based largely on projection selection guidelines developed by John Snyder (1987), guidelines which are also discussed in detail by Slocum et al. (2023). These sources are listed in the recommended readings for this section—highly suggested if you would like to learn more about this topic.

As noted by Slocum et al. (2023), selecting an appropriate projection requires thinking not only about its objective utility, but about its overall design and what your map’s readers will think of it. Recent research has investigated user responses to map projections. Battersby and Kessler (2012) investigated novice and experienced map-readers’ strategies for comprehending distortion on maps, and found that both groups struggled to correctly specify distortion on maps. Šavrič et al. (2015) focused on user preference and found that many readers tend to favor the Robinson (and similar) projections, and that general map-readers have somewhat different preferences for map projections overall than experienced cartographers.

In addition to attending to projection guidelines and anticipating reader responses, it is often helpful simply to experiment with different projections. The following tools are good resources to explore projection properties and distortion:

• Map Projection Transitions [17] - a cool interactive visualization of spinning map projections
• Projection Compare [18] - visually compare two map projections overlaid on top of each other
• Map Projection Playground [19] - explore map projection parameters
• Mercator Puzzle [20] - a fun game with map projections

Two map projections that you will notice are frequently used in the United States are the Lambert conformal conic and transverse Mercator. The Lambert conformal conic, as its name suggests, is a conformal (preserves local angles) projection that uses a cone as its developable surface. The name “Lambert” is from its inventor—Swiss scientist Johann Heinrich Lambert. Conic projections are particularly useful for mid-latitude regions with primarily East-West extent, such as the United States.

Figure 3.7.1: Lambert conformal conic, with a standard parallel at 60N.

Credit: Map by Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

The transverse Mercator projection is a slight alteration of the Mercator projection. Where the Mercator uses the equator as its line of tangency, the transverse Mercator uses a meridian. Figure 3.7.2 below uses the prime meridian as its standard line.

Figure 3.7.2: The Transverse Mercator Projection.

Credit: Map by Cary Anderson, The Pennsylvania State University; Data Source: Natural Earth.

These two projections are used in the State Plane Coordinate System (SPCS), a coordinate system designed for use in the United States. The SPCS is useful for some mapping tasks such as local government planning, as these coordinate systems have been designed to be highly accurate within each zone. Problems can occur, however, when areas of interest cross a zone boundary: this requires that at least one set of data be transformed so that proper GIS analysis can be conducted.

Figure 3.7.3: Projections used in US State Plane Reference Systems.

Credit: Cary Anderson, Penn State University, Data Source: Esri. After this graphic by Radical Cartography [22].

As shown, the transverse Mercator is used in states with a primarily North-South extent (e.g., Vermont, New Jersey) or in locations where the state is usefully divided into multiple North-South extent (e.g., New York). The Lambert conformal conic projection is similarly used for East-West extents. Some states, such as Florida, use both (Lambert conformal conic is used for the Florida panhandle). The oblique Mercator is used only in one case—the Alaska panhandle—as this region has an extent that is neither North-South nor East-West.

Another coordinate system that you will see frequently (once you start paying attention to these things) is the Universal Transverse Mercator (UTM). The system divides the world into 60 zones, each of which covers six degrees of longitude. The set of zones that covers the US is shown in Figure 3.7.4.

Figure 3.7.4: The UTM grid for the US.

Credit: Data Source: USGS [23]

Each UTM zone uses a secant transverse Mercator projection with unique parameters based on the longitudes of its bounds. As the Mercator is a conformal projection, local angles are maintained. Areas and distances are distorted, but the use of secant projections and the somewhat small size of the zones keeps this distortion low – at about 1 part in 1,000. The larger size of these zones means that they are more likely than SPCS zones to cover the entirety of a local area of interest, though recommendations exist for adjusting maps in cases where a mapped area overlaps multiple zones. UTM's worldwide coverage also makes it useful for creating maps that are shared around the world, and it is widely used in military applications.

Choosing an appropriate projection is important for all mapping tasks. Consider, for example, a proportional symbol map. You would not want to use a projection that significantly distorts area—as the intention of such a map is to compare the size of the symbol to the size of its underlying area, this would be misleading.

A map type that we haven’t yet discussed, and to which projection choice can be integral, is a flow map. A flow map is a map that visualizes movement between places—often across large regions, even the entire globe.

Figure 3.8.1: A map of net migration to and from California by the US Census Bureau.

Credit: Census.gov [25]

Flow maps can be classified into two main types: those that represent origins and destinations, and those that map routes. Origin-destination flow maps (sometimes called OD maps) show the general or exact start and end points (and often the direction) of flows, but do not map out a precise route. An example is shown in Figure 3.8.1. Flow arrows show the direction and magnitude of migration flows, but the route paths are not meaningful, or even necessarily accurate. Note, for example, the placement of a large red arrow showing migration from many locations to California. This indicates that many people migrated from these places to California during that time period, but we can imagine that their actual movement covered various routes. Their journeys also surely ended in more places than just north-central California, but the purpose of the map is to show flows between states, so exact origins and destinations are not important.

Other flow maps show meaningful routes, such as the flow of traffic, or stream flows. Figure 3.8.2 is an example—instead of focusing on the starts and ends of flows, it maps out a route network (notice, also, that the network itself provides sufficient visual information for readers to orient themselves spatially without the need for a basemap–a very cool design idea) . Size is used to visually encode the amount of truck traffic, and color represents the percent change of traffic compared to the previous year.

Figure 3.8.2: A map visualizing traffic flows in Hong Kong.

Credit: South China Morning Post [26].

Possibly the most famous flow map ever designed was drawn by Charles Minard; it represents the French army’s travel and suffering during the Russian campaign of 1812 (Figure 3.8.3). Edward Tufte, in his influential book The Visual Display of Quantitative Information, described this work as perhaps the best statistical graphic that had ever been created (Tufte 2001).

Figure 3.8.3: Minard’s Map the successive losses in men of the French Army in the Russian campaign 1812-1813

Credit: Martin Grandjean [27] (CC BY-SA 3.0 [28]), from Wikimedia Commons [29] (click link for larger image!)

Figure 3.8.4: A modern re-drawing of Minard’s map, translated into English.

Credit: DkEgy (CC BY-SA 4.0 [30]) from Wikimedia Commons [31] (click link for larger image!)

Another map by Minard (Figure 3.8.5) is more reminiscent of modern flow maps. It illustrates migration flows across the world using multiple visual variables. The achromatic continent fills and boundaries place emphasis on the flowlines as the more important component of the map.

Figure 3.8.5: Minard’s 1858 Map of World Migration.

Credit: (CC-BY-SA Freely reusable with link to the original post, Digitized by Martin Grandjean, martingrandjean.ch [32] (click link for larger image!)

Figure 3.8.5, as well as Figure 3.8.3 (and 5.8.4) above, are examples of aggregating flows to create a more comprehensible map. Figure 3.8.5 shows the magnitude of migration flow between Europe and America, for example, but it does not show the many routes these people likely traveled. Figure 3.8.6 below is an example of the opposite design choice—all origins and destinations are mapped. This is appropriate for some mapping purposes, but if there are many routes, this makes the map more challenging to read.

Figure 3.8.6: All scheduled flights in June 2009.

Credit: NASA - Wikipedia user Jpatokal [33], CC BY-SA 3.0 [28]

Figure 3.8.6 also differs from the other flow maps shown above in that it does not visualize any data except the flight origins and destinations. When creating flow maps, whether you map precise routes or just origins and destinations, and whether you chose to visually encode additional data, such as with size or color hue, will depend on the intended purpose of your map.

Flow maps can also be combined with other types of thematic maps, such as proportional symbol or choropleth maps, to show multiple sets of data. Figure 3.8.7, for example, combines a qualitative choropleth map with directional flows.

Figure 3.8.7: A combined choropleth and flow map.

Credit: Cary Anderson. Data Source: United Nations Office on Drugs and Crime, World Drug Report 2015 (United Nations publication, Sales No. E.15.XI.6). Data courtesy of Gabriel Tamariz, The Pennsylvania State University.

Critique #2

During this course, we will be completing five map-based critiques of your colleagues' maps. In Week One, you completed the first of five critiques of a map produced by a professional organziation. For Critique #2, you will complete a peer-to-peer review (or peer review) of one of your colleague's maps. In this activity, you will be assigned to critique a colleague's map from Lesson 2 Lab: Lettering and Layouts. During that lab, you put significant thought and effort into symbolizing terrain, seleting colors for the basemap information and selecting labels - now you will appraise another's work instead of your own. This new perspective is likely to be beneficial to you both while you are writing the critique, and later, when you review the feedback provided to you by one of your peers. Participating in these peer-review critiques will improve both how you think about cartographic design skills and your ability to critically evaluate the map design of others.

Your peer review assignment includes writing up a 300+ word critique of one of your colleague’s Lesson 2 Lab. 

In your written critique please describe:

• three (3) things about the map design that you think works well and why.
• three (3) suggestions you have for improvement of the map design and why these improvements would be helpful.

According to the two prompts above, a map critique is not just about finding problems, but about reflecting on a map in an overall context. Your critique should focus on the map design that works well as much as it does on suggestions for design improvements. In your discussion, you should connect your ideas back to what we learned in the previous lessons.

Remember, your critique should be as much about reflecting upon design ideas well-done as it is about suggesting improvements to the design. In your discussion, connect your ideas to concepts from previous lessons where relevant.

You may find these two resources helpful as you write your critiques:

• Daniel Huffman’s 2020 blog post on how to “Critique with Empathy [34]"
• Ordnance Survey’s (Wesson, Glynn and Naylor, 2013) list of effective cartographic design principles [35] 

Grading Criteria

A rubric is posted for your review.

Submission Instructions

Flow Mapping with Customized Projections

In Lesson 3, we discussed map projections and projection characteristics. We also discussed how to choose a map projection based on your map's intended location, scale, and purpose. It can be challenging, however, to really understand how the choice of a projection alters your map without trying it out for yourself. In Lab 3, we will be creating three map layouts that visualize flight data as flowlines. This ties together both of the topics in Lesson 3 (map projections and flow mapping), and provides a practical demonstration of the influence of map projections in small-scale thematic mapping.

For good measure, we will design each of these map layouts as advertisements: encouraging creative design and adding emphasis to the importance of map purpose and audience in choosing projections for maps. Recall from this week's required reading, Mark Monmonier's discussion of Maps that Advertise. Your challenge this week is to create map layouts that are both scientifically-appropriate and engaging to your intended customers - the readers of your maps.

This lab, which you will submit at the end of Lesson 3, will be reviewed/critiqued by one of your classmates in Lesson 4 (critique #2).

Lab Objectives

• Create three advertisements for London Heathrow Airport (LHR) using flight origin-destination data.
• Select and customize map projections based on each map’s purpose and overall design.
• Use appropriate visual variables to symbolize background data and flowlines.
• Create well-designed layouts with appropriate legends and text elements.

Overall Lab Requirements

For Lab 3, you will use the provided data to create three (3) different map layouts, each of which is an advertisement for LHR airport.

• For each map, you should choose and customize an appropriate map projection.
  • Each layout must use a different projection. For layout #2, which contains four maps, you may use the same projection for all maps.
• Include a written reflection (250+ words); use the following questions to guide your writing:
  • For each map layout, which projection did you choose, how did you customize it, and why?
  • Include a screenshot of the projection customization window (Visual Guide Figure 3.18) for each map layout (3 screenshots in total).

Map Requirements

Layout One: Highlight the distance a flight from Heathrow can take you

• Create a map that highlights distance – how far a customer can go via Heathrow’s non-stop flights.
• Classify and visualize flight paths based on their length (e.g., short haul vs. long haul). Use sensible units and at least three classes.

Layout Two: Highlight that Heathrow can fit anyone’s schedule

• Use the flight path data that has been pre-segmented into time blocks: Morning (7am-noon), Afternoon (noon-5pm), Evening (5pm-10pm), and Night (10pm-7am).
• Design with category and hierarchy; visualize daily counts of flights during each time block.
• Combine these four maps (one per time block) into one balanced layout with an appropriate legend.

Layout Three: Highlight that Heathrow flies to desirable locations

• Create a world map that shows all flight paths to and from London Heathrow (LHR). Symbolize as appropriate.
• Add and symbolize tourism data (included as its own layer) to demonstrate that flights from LHR take customers to popular tourist destinations.
  • Instead of using the tourism data, you may symbolize a relevant field from the Natural Earth (boundary file) data on your map.

Lab Instructions

1. Registered students can download the Lab 3 zipped [38] file (475 KB). It contains:
   • A project (.aprx) file to be opened in ArcGIS Pro.
     • This file contains boundary, flight, and tourist data – the focus here is on design; you will not need to upload any new data of your own.
     • Flight data coordinates use the datum WGS 1984.
   • Data Sources:
     • Arrival/Departure flight data source: Flightradar24 [39]
     • Boundary data source: Natural Earth
     • Tourism Data: UNWTO (World Tourism Organization)
2. Extract the zipped folder, and double-click the blue (.aprx) file to open ArcGIS Pro.
   • You should see the starting file, with all data included. See the Lab 4 Visual Guide for additional guidance.

Grading Criteria

A rubric is posted for your review.

Ready to Begin?

Further instructions are available in the Lesson 3 Lab Visual Guide.

Summary

Welcome to the end of Lesson 3! In this lesson, we discussed the complex process of modeling Earth's surface, and how concepts such as reference ellipsoids and datums relate to the map projections used by cartographers every day. During our discussion of characteristics of map projections, we focused on the appropriateness of various map projections for different mapping tasks: based on a map's location, scale, and purpose. Finally, we connected these ideas to a new thematic mapping technique - flow mapping. Though projection choice is often particularly consequential in flow map design—due to the nature of the data visualized, and to the large regions such maps often depict—it is an important consideration in many mapping projects. You will often have to select an appropriate map projection when making other kinds of thematic maps, including proportional symbol, dot density, and choropleth maps.

In Lab 3, we explored the effect of projection selection on small-scale thematic map design while creating map-based advertisements for London Heathrow Airport (LHR). We designed these maps using prior knowledge of visual variables and symbols on maps, and put together neat, useful layouts intended to appeal to our map readers. Prepare for another creative real-world mapping experience in Lab 4!

Reminder - Complete all of the Lesson 3 tasks!

You have reached the end of Lesson 3! Double-check the to-do list on the Lesson 3 Overview [41] page to make sure you have completed all of the activities listed there before you begin Lesson 4.