Basic Concepts in GIS
and Cartography
This is lecture 2
Lecture Outline
• There are two sections to today’s lecture
1) an introduction to spatial data
2) an introduction to thematic maps and
cartography
Spatial Data
• Spatial Data is a very broad topic that
includes the following:
• differentiation between map and database;
• continuous variation;
• attributes;
• scales of measurement; and
• scale and resolution.
Differentiating between the
map and the database
• There are two distinct aspects to GIS
– graphical output (which we see)
– underlying database (which contains all the
information that is converted to a map or many
maps).
• Analogy of iceberg
Model versus cartographic layer
• GIS relies on an underlying (hidden to
view) database (model layer)
• This layer provides information that is used
to present a visual or graphic output that we
call the map (cartographic layer).
From reality to 0s and 1s
• There is no obvious leap from everyday geographic
phenomena to strings of 0s and 1s in the computer.
• Every database or table contains digital
representations of geographic objects like roads,
forests, enemy armies and zip codes.
• These objects have counterparts in the real world.
They are features or discrete objects.
• The contents of a map are captured in a database by
turning map features into database objects, each of
which normally takes up one square or field in a data
table.
Fictitious features
• But many features shown on a map are
fictitious and do not exist in the real world.
• Contours do not really exist while houses
and lakes are real objects.
• Think of weather fronts - high or low
pressure systems - are they real objects?
Representing real and fictitious
objects on a map
• We get around some of these problems by creating
conventions or habits for spatial data
representation.
• There are many ways that things like weather
fronts could be represented but we try and use the
ways that people already understand.
• For instance, we always label water on maps in
italic. Bigger cities have a larger symbol than
small towns. Green represents sea level while
brown or orange represents higher elevations.
Short dashed lines on a weather map indicate rain.
Non discrete boundaries
• Many of the objects we portray on maps are discrete
objects (like houses, roads, underground pipelines and
mountains).
• There are things that don’t have fixed borders.
• One of the biggest problems is representing things, which
are spread out continuously, as discrete objects.
• For example, how do we represent changes in elevation or
forest cover? How do we represent ethnicity in a
population as, say, 40% White, 20% African-American,
20% Asian and 20% “other” when these things vary all
through both time and space?
• What we are dealing with is the problem of continuous
variation.
Continuous Variation
• Some characteristics vary continuously over
the earth’s surface (ex. Elevation,
atmospheric temperature and pressure,
natural vegetation or soil type).
• Yet, in order to store data spatially, we need
to assign discrete values to these entities.
• This is the process of discretization or
drawing crisp lines around fuzzy entities.
Methods of discretization
• We get around the problem of continuous variation by
using several conventions:
• 1.
Taking measurements at sample points like weather
stations; using traffic counters at intersections.
• 2.
By taking transects or cross-sections at intervals.
We than interpolate between sample sites. This is used in
geological sampling.
• 3.
Dividing the area into patches or zones, and
assuming the variable is constant within each zone. This is
how soil mapping works. It is also the principle behind
enumeration for census tracts.
• 4.
Drawing contours. This is done for elevations in
topographic mapping
Problems with discretization
• Each of these methods creates discrete objects.
• The objects in each case are points, lines or areas.
• But each method is approximate, capturing only
part of the real variation.
•
•
•
•
Problems:
a point sample misses variation between points
transects miss variation not on transects
zones pretend that variation is sudden at boundaries,
and that there is no variation within zones
• contours miss variation not located on contours
Tricks
• Tricks can be employed to try to improve
the success of each method.
- One example: map the boundaries as
fuzzy instead of sharp lines
• - We can also describe the zones as
mixtures instead of as single classes, e.g.
70% soil type A, 30% soil type B
Location and attributes
• For the purposes of GIS, spatial data always
has to have a location even if it is
continuous.
• Location is just the spatial attribute in the
database which leads to the question – what
is an attribute?
What are attributes?
Attributes:
• describe different characteristics of objects
• For example: a table showing the attributes of
objects is called an attribute table
• each object corresponds to a row of the table
• each characteristic or theme corresponds to a
column of the table
• thus the table shows the thematic and some of the
spatial modes
How to measure attributes and
spatial phenomena
• Need a way to create a numeric
correspondence between attributes and
database fields.
Scales of Measurement
• Many measurements of spatial data for use in GIS
are numerical.
• We use numbers because 1) they conform to the
digital architecture of the computer (i.e. easy for
the computer to digest); and 2) they allow us to
perform mathematical operations on data.
• Numerical values may be defined with respect to
nominal, ordinal, interval, or ratio scales of
measurement
• The different scales can be demonstrated using an
example of a marathon race:
Nominal
• On a nominal scale, numbers merely establish
identity
• For example: a phone number signifies only the
unique identity of the phone
• In the race, the numbers issued to racers which are
used to identify individuals are on a nominal scale
• these identity numbers do not indicate any order or
relative value in terms of the race outcome
Ordinal
On an ordinal scale, numbers establish order only
• The phone number 961-8224 is not more of
anything than 961-8049, so phone numbers are
not ordinal. (What are they?)
• In the race, the finishing places of each racer, i.e.
1st place, 2nd place, 3rd place, are measured on an
ordinal scale. The numbers mean something
relative to each other BUT
• We do not know how much time difference there
is between each racer
Interval
• On an interval scale, the difference (interval) between
numbers is meaningful, but the numbering scale does
not start at 0
• Subtraction makes sense but division does not
• For example, it makes sense to say that 200C is 100
degrees warmer than 100C, so Celsius temperature is
on an interval scale, but 200C is not twice as warm as
100C
• It makes no sense to say that the phone number 9680244 is 62195 more than 961-8049, so phone numbers
are not measurements on an interval scale
More on the interval scale
•
•
•
In the race, the time of the day that each racer
finished is measured on an interval scale.
If the racers finished at 9:10 GMT, 9:20 GMT
and 9:25 GMT, then racer one finished 10
minutes before racer 2, and the difference
between racers 1 and 2 is twice that of the
difference between racers 2 and 3.
However, the racer finishing at 9:10 GMT did
not finish twice as fast as the racer finishing at
18:20 GMT.
Ratio scale of measurement
• On a ratio scale, measurement has an absolute zero
and the difference between numbers is significant
• Division makes sense
• For example, it makes sense to say that a 50 kg
person weighs half as much as a 100 kg person, so
weight in kg is on a ratio scale.
• Clearly the same is true for pounds. A 150 #
person weighs half as much as a 300 pd person.
Ratio continued
The zero point of weight is absolute but the
zero point of the Celsius scale (used above)
is not
In our race, the first place finisher finished in
a time of 2:30, the second in 2:40 and the
450th place finisher took 5 hours
• The 450th finisher took twice as long as the
first place finisher (5/2.5 = 2)
Problems with measurement
systems
• These distinctions, though important, are
not always clearly defined.
• Is elevation interval or ratio? If the local
base level for a survey is 750 feet, then is a
mountain at 2000 feet twice as high as one
at 1000 feet when viewed from the valley?
Why you need to know what
measurement system is used
• Many types of geographical data used in
GIS applications are nominal or ordinal.
• Important to remember that even if the
program lets you, you can’t multiply lake x
pond.
• That is because nominal values establish the
order of classes, or their distinct identity,
but not intervals or ratios.
Things you cannot do
• Multiply soil type 2 by soil type 3 and get soil
type 6.
• Divide urban area by the ranking of a city’s crime
record to get a meaningful number.
• Subtract suitability class 1 from suitability class 4
to get 3 of anything
• (you use suitability classes to assess the best
locations for housing development or installation
of a shopping mall, or best place to drill for oil
etc).
Things you can do
•
Divide population by area (both ratio
scales) and get population density.
•
Subtract elevation at point a from
elevation at point b and get difference of
elevation.
The concept of scale
There is no best way to represent geographic
data in a database, and no matter how you
measure it you must deal with the
possibility of multiple representations.
But in order to do that we need to understand
the concept of scale.
Scale as a representative fraction
• the scale of a map is the ratio between distances
on the map and corresponding distances in the real
world
• if a map has a scale of 1:50,000, then 1 cm on the
map equals 50,000 cm or 0.5 km on the Earth's
surface
• the use of the terms "small scale" and "large scale"
is often confused, so it is important to be
consistent
Large vs small scale
• a large scale map shows great detail, small
features
• representative fraction is large, e.g. 1/10,000
• a small scale map shows only large features
• representative fraction is small, e.g. 1/250,000
• the scale controls not only how features are
shown, but what features are shown
• a 1:2,500 map will show individual houses and
lamp posts while a 1:100,000 will not
International scale
• different scales are used in different countries
• in the US, 1:100,000 is the largest scale at which
complete coverage of the continental states exists,
but there is limited coverage at 1:62,500 and
1:24,000
• in the UK, there is complete coverage at much
larger scales (1:1,250 to 1:10,000)
• In Canada, there is complete coverage at
1:100,000
Multiple resolutions and the
importance of scale
• The same phenomena may be represented in
different ways, at different scales and with
different levels of accuracy.
• For instance, at 1:5000 scale, a town might
be not a blob on a map but show every
building, street etc.
• At 1:2,000,000, that town is luck to be a dot
on the map
Changing scales
• Thus there may be multiple representations of the
same geographical phenomena. A church will be
represented differently in many different maps as will
roads, urban areas etc.
• It is difficult to convert from one representation to
another
• e.g. from a small scale (1:250,000) to a large scale
(1:10,000).
• This has to do with the types of objects enumerated
and the level of detail associated with them.
• NMAs sometimes maintain multiple databases with
different scales.
Question
• Is there scale inside the computer?
Scale and resolution
• Scale and resolution are intimately connected and
are both essential concepts in GIS and
cartography.
• Scale is the relationship between features on the
map and the real world.
• A scale of 1:5,000 means that a feature on the map
(or computer display) is 5000 times bigger in real
life.
• A road segment that measures 10 cm on a map
measures 50,000 cm (0.5 km) on the ground. Such
a scale is considered a large scale.
Small scale
• A small scale map, on the other hand, implies that
the fraction representing scale is very large.
• A map of the world that had a scale of
1:200,000,000 is small scale. A feature on the map
that measured a ½ inch would measure
100,000,000 inches (or 1578 miles) on the earth.
Resolution
• Resolution is the clarity of features on a
map or TV screen or remotely sensed
image.
• A high resolution usually implies a large
scale (i.e. features are big enough to be easy
to see).
• Low resolution implies a small scale (i.e.
features are small and hard to make out).
Example
• Imagine an airplane flies low to the ground over Burnaby
and takes an aerial photo. It would be easy to make out
shopping centers, major roads, perhaps even your home
from such an image. The aerial photo has good resolution
because it is large scale.
• Now imagine that you have a satellite which circles the
globe sending back remotely sensed images. It sends back
an image of Burnaby from high in the sky. It would be
hard to make out anything but the most prominent features
from the image.
• The resolution is lower (poorer) because the image is
small-scale.
Maps and cartography
• Maps are the main source of data for GIS.
• The traditions of cartography are
fundamentally important to GIS.
• GIS has roots in the analysis of information
on maps, and overcomes many of the
limitations of manual analysis.
Characteristics of a map
• Maps are often stylized, generalized or abstracted,
requiring careful interpretation
• Usually out of date
• Show only a static situation - one slice in time
• Often highly elegant/artistic
• Easy to use to answer certain types of questions such as:
how do I get there from here? Or what is at this point?
• Difficult or time-consuming to answer other types of
questions such as: what is the area of this lake? Or what
places can I see from this TV tower?
• These are things that are easy to determine from a GIS.
Types of Maps
• Two types of map:
• Topographic map - a reference tool, showing the
outlines of selected natural and man-made features
of the Earth
• Often acts as a frame for other information
• Thematic map - a tool to communicate
geographical concepts such as the distribution of
population densities, climate, movement of goods,
land use etc.
Thematic maps
• We deal mainly with thematic maps in GIS and
several types of thematic map are especially
important:
• A choropleth map uses reporting zones such as
counties or census tracts to show data such as
average incomes, percent female, or rates of
mortality. Remember that a chloropleth map is a
type of thematic map.
• the boundaries of the zones are established
independently of the data, and may be used to
report many different sets of data (ex. Census
tracts)
More thematic maps
• An area class map shows zones of constant
attributes, such as vegetation, soil type, or
forest species.
• The boundaries are different for each map
as they are determined by the variation of
the attribute being mapped, e.g. breaks of
soil type may occur independently of breaks
of vegetation.
Thematic maps continued
• An isopleth map shows an imaginary
surface by means of lines joining points of
equal value, "isolines" (e.g. contours on a
topographic map)
• Used for phenomena which vary smoothly
across the map, such as temperature,
pressure, rainfall or population density
The geographic grid
• The spherical coordinate system with latitudes and
longitudes used for determining the locations of
surface features.
• Parallels: east-west lines parallel to the equator.
• Meridians: north-south lines connecting the poles.
• The Geographic Grid
• Parallels are constantly parallel, and meridians
converge at the poles.
• Meridians and parallels always intersect at right
angles.