How we understand the world is dependent on our scale of observation. Consider Map 2.4.1 that displays the median household income for the United States as collected by the U.S. Census Bureau (select “Legend” in the top-right of the map to see the income categories represented by each color). What do you notice about the spatial distribution of income at the scale of the entire country? One prominent observation is that major cities such as Seattle, San Francisco, Austin, New York, or Boston are locations with relatively high household income. Now, what happens when you change the scale your scale of observation. To find out, type in the name of one of the major cities in the search box and observe how the spatial distribution of household income changes. You should notice that income is not evenly distributed across the city. In fact, most cities display some form of a “clustered” pattern of income, where low-income households are clustered in one area while relatively high-income households are clustered in another area. It is evident from this example that we cannot necessarily transfer our observations about the world at one scale to another. In this module we learn why scale is so important to think about when talking about space and spatial patterns.
Map 2.4.1
2.4.1 Zooming In and Zooming Out
Let’s take a look at the concept of scale by examining your neighborhood in Map 2.4.2. Click on the Find my location icon (the circle icon on the left side of the map) to have the blue dot appear in your current location. In the bottom-left hand corner of the map you will see a scale bar that indicates how distance on the map relates to distance in the real world. Now click on the zoom in button. What happens to the units in the scale bar? Click on the zoom in button again and observe how the units in the scale bar change. You should notice that the units on the scale bar decrease (the numbers become smaller) as you continue to zoom in. Why is this?
Map 2.4.2
As you zoom into the map, the actual size of the scale bar on your display does not change. If you were to take a ruler, tape measure, or even your finger and put it up to the scale bar, you will see that the length of the bar remains the same no matter how far you zoom in or zoom out. Let’s say that the length of this scale bar is 1 inch (roughly 2.5 centimeters). This means that 1 inch on our map is equivalent to whatever number is given on the right side of the scale bar, and therefore half an inch is equivalent to the number given in the middle of the scale bar. When you selected the Find my location button, you likely saw that the length of the scale bar represents 0.2 miles, which means that, at that scale, 1 inch = 0.2 miles. As you zoom in you should see that 1 inch = 600 feet, and as you zoom in further you should see that 1 inch = 300 feet. Intuitively, if you could continue to zoom in indefinitely, the space on your map would be so large that 1 inch on the map would be equivalent to 1 inch in the real world. Each time we zoom in we receive a finer scale map because we can observe finer (or more) details about the world.
It should now be obvious that as we zoom out in a map the distance represented by the scale bar increases. In doing so, we are provided with a coarser scale map. You can understand this by simply zooming out in Map 2.4.2, but let’s jump to a coarser geographic scale by entering “Australia” in the search box. When the country Australia appears in your display, you will notice that the distance covered by the scale bar is 200 miles. Now click on the Home icon in the right side of the map and you will be taken to a coarser-scale map of the world where the scale bar represents a distance of 600 miles. This analysis shows us that our scale bar represents a greater distance on the surface of the earth the further we zoom out, and less distance on the surface of the earth as we zoom in.
2.4.2 Representative Fraction
Knowing the distance on the surface of the earth that is covered by a specific distance on a map allows us to create something called a representative fraction, or RF. The RF on a map is a ratio that describes the equivalent number of units between two points on a map versus the number of units between two points on the ground. An example RF is 1:10,000, which means that 1 unit (such as an inch or a centimeter), is equivalent to 10,000 of the same units on the ground. Let’s dive into map 2.4.2 to explore how this works.
Clicking on the Find my location button in map 2.4.2, we know that 1 inch = 0.2 miles at the scale the map is presented. Next, we want to have both sides of the = sign in the same units. To do this, we simply multiply the right side of the equals (=) sign by the number of inches in a single mile, which is 63360. The equation to calculate the RF looks like this:
RF = 1: 0.2 x 63,360
= 1:12,672
Thus, 1 unit on the map covers a distance of 12672 identical units on the ground. Sometimes cartographers or other individuals making professional maps will adjust the scale of the map in order to have a rounded RF, such as 1:12,500, that is much easier to communicate.
2.4.3 Complications with Scale
At this point you may be asking why we use the terms fine and coarse to describe spatial scale. Most of us are likely more familiar with hearing small scale versus large scale when referring to space. However, the terms small and large mean something different depending on if you’re a scientist or planner verses if you’re a cartographer who specializes in making maps. To the scientist/planner, scale typically refers to the spatial extent of a geographic area under study. Therefore, a small-scale map would refer to something like the neighborhood map you examined above, while a large-scale map would represent a map of the world. Conversely, cartographers talk about the neighborhood map as a large-scale map because it is represented by a large ratio of what’s on the map versus what’s on the ground. In other words, the neighborhood map is represented by a large representative fraction. Cartographers would thus refer to the world map as a small-scale map that is represented by a small representative fraction. In order to avoid this confusion, we, like others before us (Longely et al. 2011), use the terms “fine” and “coarse” to discuss scale.
2.4.3 Why Scale Matters
The importance of scale is much more than simply selecting how much of the world you can fit onto a map. Everything in the world happens at a particular scale. Consider human migration, natural disturbances like earthquakes or tsunamis, crime in urban areas, or the spread of invasive species in the wild. If we do not look at these processes at the right scales we risk ignoring important information that would help us develop plans to address these issues. Let us look at a couple of examples. Imagine you are a transportation planner for the city of Los Angeles who has been charged with the task of reducing the city’s traffic problems. This could include increasing the amount of public transportation opportunities for commuters or increasing the number of locations from where people can car pool together. At what scale do you address this problem? Map 2.4.3 shows low automobile traffic volume in the Los Angeles area and the density of people per square mile. The downtown area is indicated by the large gray point, while the information on traffic volume and population density can be examined in the legend. Is this an appropriate scale at which to address traffic congestion?
Map 2.4.3
If you consider that hundreds of thousands of commuters travel an average of almost 30 minutes to their place of employment in the city, you should conclude that the scale of our observation in Map 2.4.3 is too fine to adequately address traffic congestion. Zoom out and you will see the underlying population layer (deselect the traffic layer to get a better look) where you can observe relatively large populations living quite far from Los Angeles’ downtown core (represented by the large circle). Let’s assume that a significant proportion of the commuting population travel 40 miles to work downtown. How can you figure out the appropriate scale for your study? To find out the answer to this question, let’s perform a basic spatial analysis (you will be performing more advanced analyses later). Select View Larger Map from under Map 2.4.3, which will open this map in ArcGIS Online. Select “Content” to the left of the map, and then select the dropdown arrow next to the “Downtown L.A.” layer. Next, select “Perform Analysis” and click on the “Points” option. Then, select “Use Proximity Analysis” and “Create Drive Time Areas”. Select a driving distance of 40 miles and click “Run Analysis” at the bottom of the window. Once the analysis is complete, you will see the area over which commuters travel 40 miles to get to work in Los Angeles’ downtown core. Analyze the various data in the map and determine what is a suitable RF at which to analyze traffic in order to improve the city’s transportation system?
2.4.4 Scale Dependence
The term scale dependence explains that the scale at which we conduct our observations influences our knowledge about some event or phenomenon in the world. Go back to Map 2.4.1 that displays average household income across the U.S. We made an observation at the beginning of this module that major cities are locations with relatively high household income. When you type in any major city into the search box you zoom into the city and can observe that household income varies. Zoom in further and you will notice further clustering of low and high household income area. Again, our knowledge about the spatial distribution of income in the U.S. is explicitly tied to the scale of our observations, and applying information from one scale or area to another scale or area is considered a fallacy – or, in other words, is not acceptable. There are two types of fallacies when it goes to scale.
First, we cannot take an observation made at the scale of the country and apply it to every location within each city. In other words, we cannot assume that every household in each city enjoys above average income. If we did use national level observations to make assumptions about what happens within cities, we would be committing what is called an ecological fallacy. Second, we cannot take an observation made at the scale of a city or neighborhood and apply it to the entire country. Doing so would mean that we are committing an individualistic fallacy, because we are taking information on an individual and applying it to a much broader scale. A third type of fallacy exists when it comes to space and geospatial data: cross-level fallacy. This occurs when we take the observations in one city and assume that it will be consistent for every other city as some cities have more income inequality than others.
In summary, scale is incredibly important when describing the world. We need to know the scale at which events take place, and how observations changes as we embark on finer or courses scales. Finally, we need to ensure that we are not making mistakes by assuming that observations made at specific scales can be readily applied at other scales. Having knowledge about how scale operates allows us to make informed and intelligent decisions about how to address pressing issues regarding spatial phenomena.