Scale
Representing Scale on Maps
Definition:
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
maps
• 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
detail
• 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
distortion
– 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
(aggregating)
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
change
– 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
area?
– 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
1:24000
• Using such a map to plan a hike, you
determine that the trail is 11 3/8 inches
long
• 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
cm-to-km?
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-
miles?
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
resolution
– 1 mile ~ 1.61 km
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?
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
Examples
• 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
park.
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
create
• 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
research
• 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
accurate)
• 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