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Scale Scale Representing Scale on Maps Definition The scale


   Representing Scale on Maps
   The scale of a map is the ratio between distances on the
   map and the corresponding distances in the real world.
                 Map Scale
• Scale representation on the map:
  – Representative fraction (RF): “1:100,000”,
    “1 to 100,000”, or “1/100,000”
  – Verbal: 1 inch is equal to 50 miles
  – Graphic: Scale bar          10 miles
         Map scale is a ratio
• It is unit-independent
• 1/1000 > 1/100,000
  – (1/100 is greater than 1/100,000)
• Thus 1:1000 is a large scale map, showing
  a smaller region but magnified
• 1/100,000 is a small scale map, showing a
  larger region
              Point of confusion
• Scale in most other contexts, even in geography, is not used
  as a ratio
   • e.g., data, area, processes, government, & economies

• For example: Large scale data (e.g., global temperature
  distribution), affects large scale processes (e.g., ocean
  circulation patterns), but this data is shown on small scale

• Often we circumvent confusion by using terms like “regional
  scale” or “hill slope scale”, but confusion can still occur if we
  ask “which is larger?”

• Take home message: if/when I ask about “map scale” on an
  exam I mean the ratio (i.e., small scale = large area),
  otherwise scale means what you think it should
General Classification of Map Scale
• Notions of small and large are reversed from our
  conventional thinking when we talk about map scale
   large scale refers to looking at a small area in
• Here are some scale guidelines:
   – Large scale map  1:400 to 1:50,000
   – Intermediate scale map  1:50,000 to 1:250,000
   – Small scale map  1:250,000 and beyond
   Map Scale and Map Projections
• The representative fraction of a map does not tell
  us the scale everywhere on the map
• Transformations due to projecting maps introduce
  – The representative fraction (and the scale bar) is only
    accurate along standard lines or points
For Example
                  Scaling Up
• Data created for local areas can be used
  for larger (regional or national) areas
  – Note: now we are talking about scale in common
    terms (not map scale), so “up” implies larger areas
   Maps and GIS - Scaling Up

•The river network shown here on a national scale was
produced at a much finer scale, and it contains a great
deal of detail that cannot be seen at this map scale
Maps and GIS - Scaling Up
                             This level of detail is not
                             necessary or useful at the
                             national scale.

     All the detail that is
     encoded in this river
     network data is really
     only visible and useful
     when operating at more
     local scales.

Vector data such as this river may need to be smoothed for scaling up.
       Maps and GIS - Scaling Up
                         Scale Effect on Mapping

         White                                     White
         pine       wheat                          pine       wheat
                                  Scaling up

       Lodgepole                                  Lodgepole
       pine           rice                        pine         rice

                                   What should we call these cells?

Raster data may need to be generalized. An aggregation algorithm must be chosen.
 Maps and GIS - Scaling Down
• Small scale data contains more detail
  than large scale data
• Using large scale data for analysis at a
  smaller scale can cause problems
 Maps and GIS - Scaling Down

Here we can see a national scale coastline (shown in red)
superimposed over local scale data, we can clearly see the
generalization and lack of detail
                Vertical Scale
• As with horizontal scales, vertical scale is related
  to the level of detail of the information conveyed
  by the map
• Contour lines are often used to define the
  vertical scale
• Contour intervals are usually provided as “X
  feet” or “X meters” meaning a contour line will be
  placed on the map marking the X vertical
   – For example: “Contour interval 80 feet”
• Contour lines are also frequently used in
  meteorology (e.g., temperature and air pressure)
      Vertical Scale: Contour Lines
What is the
contour interval for
this example?
Vertical Scale: Contour Lines
          Scale Question 1
• Which map has a larger map scale and
  which map covers a larger geographic
  – 1:1,000,000 or 1:12,000
         Scale Question 2
• On a map with a scale of 1:100,000 how
  much distance is represented by 2 cm?
           Scale Question 3
• USGS topographic maps (commonly
  called quadrangles) have a scale of
• Using such a map to plan a hike, you
  determine that the trail is 11 3/8 inches
• How far will you be hiking?
           Scale Question 4
• Given the representative fraction
  1:1,000,000, what is the verbal scale (i.e.,
  the word statement that conveys scale) in
          Scale Question 5
• Given the representative fraction 1:62,500,
  what is the verbal scale (i.e., the word
  statement that conveys scale) in inches-to-
          Scale Question 6
• How many pixels (a.k.a. raster or GRID
  cells) from a Landsat image are required
  to cover a square mile?

  – Landsat pixels have 30-meter spatial
  – 1 mile ~ 1.61 km
Scale Questions 7 - 9
                        how much
                        elevation did
                        we gain on
                        this hike?
                        how far did we
                        hike in
                        how far did we
                        hike in actual
                 Scale Questions 7 - 9

•   Approximately how much elevation did we gain on this hike?
•   Approximately how far did we hike in straight-line distance?
•   Approximately how far did we hike in actual distance?

Panoramic photo taken at sunrise from ~1000 ft below the below the summit
            Choosing a scale
•   The scale of your data should be chosen
    according to:
    1. Your data needs
    2. The intended use of the existing data
•   Your data options are:
    –   Landsat TM data (30 meter resolution)
    –   SPOT satellite imagery (5 meter resolution)
    –   Ikonos satellite data (1 meter resolution)
• What data source do you use when:
1. You’re building a nuclear power plant on a site near a
   lake, and need to plan the location of each component
   of the plant
2. Some illegal cutting of small patches of forest is going
   on in a national park in the Brazilian Amazon. We want
   to map where the cuts have occurred throughout the
            Using scale in practice
•       Reading scale
    –     Know how to determine distance using scale bars,
          representative fractions, and verbal statements of scale
•       Choosing a scale for display
    –     Important for effectively conveying the information to map
          users, this is also related to the size of the map that will be
          produced (e.g., poster size vs. a figure in a paper)
    –     Remember to include scale information on all maps that you
•       Scale and accuracy
    –     Data are accurate only for the scale at which they are
          collected and for larger areas (scaling up)
    –     Extrapolating information to smaller areas can produce
          ecological fallacies
     Scale & Accuracy Example
• Here is an example of scale and accuracy from my own

• I study environmental controls on the alpine treeline
  ecotone (i.e., the transition zone between closed-canopy
  subalpine forests and the tundra, ice, snow, and rock
  that lies above)

• In addition to controls like temperature and precipitation,
  I wanted to include species composition in my analysis
  because tree species respond differently to stress
         Scale & Accuracy Example
•   The original paper maps were published in 4 books by E.L. Little in the 1970s, and
    did NOT include minimum mapping units (a.k.a. the scale for which they are

•   Here is what the metadata say
     –   "At least 90% of the points tested on hard copy printout are within 1/50 inch (0.5mm) of the
         source data.”
     –   "In some instances, data for the United States portions of the maps were derived from source
         maps at 1:10,000,000 scale and the portions outside the United States were derived from
         sources at approximately 1:27,000,000 scale. The coverages were checked for node,
         intersection, and duplication errors and corrected when necessary. All polygons were
         snapped closed at nodes."

•   My determination
     –   There is no alternative dataset, so it’s this or nothing
     –   0.5 mm on a 1:10,000,000 scale map is equal to 5 km of error due to the digitization process
     –   The accuracy of maps is almost certainly much worse (imagine drawing a range map on a
         map where 1mm = 10 km)
     –   Therefore single species composition values should be taken at the study-site level because
         analysis, at larger scales is too problematic considering the limitations of this dataset

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