Geographic Information Systems GIS SGO1910

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Geographic Information Systems (GIS)SGO1910
SGO4930 Fall 2005
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Announcements

• Graduate Students taking SGO4910 for 10 credits,
  see me at the break!
• Lab opening times (Hallvard)
• Mid-term Quiz 30 questions - up to (and not
  including) ch6
• Multiple Choice
• Which of the following does NOT describe raster
  data
• a) each cell can contain a single value
• b) lines are captured as points
• c) remote sensing satellites are a source of data
• d) cells are called pixels
• e) every cell must contain a value
• True-False
• The vector data model represents features using a
  grid of cells. ______

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Review

• The nature of spatial data and generalization
• Spatial autocorrelation
• Spatial sampling
• Spatial interpolation (distance decay)
• Georeferencing

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Georeferences as Measurements

• Some georeferences are metric
• They define location using measures of distance
  from fixed places
• E.g., distance from the Equator or from the
  Greenwich Meridian
• Others are based on ordering
• E.g. street addresses in most parts of the world
  order houses along streets
• Others are only nominal
• Placenames do not involve ordering or measuring

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Something to think about

• Objective To study combined effects of natural
  resource endowments as well as spatial inequality
  in terms of welfare and conflict at the
  sub-national level.
• Hypothesis Areas with low levels of social
  welfare relative to the rest of the country are
  especially prone to conflict.
• DataGeo-referenced survey data from DHS
  (Demographic and Health Surveys).
• Question How to make use of this information
  (i.e., aggregate or convert it) so that it
  represents education levels for regions (or for
  grids of some size)?

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The data

• The DHS surveys are based on clustered sampling.
  For each dataset the actual country is divided
  into between 100 and 521 areas, and 25 households
  are randomly drawn from each area and surveyed
  with a household questionnaire.

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• Do the data need to be generalized? If not, then
  maybe they should be left alone. And why
  different samples in different districts? You get
  into trouble when you try to generalize -
  depending on how the data were collected (in this
  case, through clustered sampling and random
  surveying).

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Georeferencing

• Longitude and Latitude
• UTM
• Map projections

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Latitude and Longitude

• The most comprehensive and powerful method of
  georeferencing
• Metric, standard, stable, unique
• Uses a well-defined and fixed reference frame
• Based on the Earths rotation and center of mass,
  and the Greenwich Meridian

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Geographic Coordinates

• Geographic coordinates are the earth's latitude
  and longitude system, ranging from 90 degrees
  south to 90 degrees north in latitude and 180
  degrees west to 180 degrees east in longitude.
• A line with a constant latitude running east to
  west is called a parallel.
• A line with constant longitude running from the
  north pole to the south pole is called a
  meridian.
• The zero-longitude meridian is called the prime
  meridian and passes through Greenwich, England.
• A grid of parallels and meridians shown as lines
  on a map is called a graticule.

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Geographic Coordinates
Prime Meridian
Equator
Prime Meridian
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Geographic Coordinates as Data
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Oslo, Norway

• 59o56 N. Latitude
• 10o45 E. Longitude

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Definition of longitude. The Earth is seen here
from above the North Pole, looking along the
Axis, with the Equator forming the outer circle.
The location of Greenwich defines the Prime
Meridian. The longitude of the point at the
center of the red cross is determined by drawing
a plane through it and the axis, and measuring
the angle between this plane and the Prime
Meridian.
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Definition of Latitude

• Requires a model of the Earths shape
• The Earth is somewhat elliptical
• The N-S diameter is roughly 1/300 less than the
  E-W diameter
• More accurately modeled as an ellipsoid than a
  sphere
• An ellipsoid is formed by rotating an ellipse
  about its shorter axis (the Earths axis in this
  case)

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Earth Shape Sphere and Ellipsoid
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Ellipsoids and Datums

• Because the Earth is not shaped precisely as an
  ellipsoid, initially each country felt free to
  adopt its own measure as the most accurate
  approximation to its own part of the Earth
• Today an international standard has been adopted
  known as WGS 84
• Its US implementation is the North American Datum
  of 1983 (NAD 83)
• Many US maps and data sets still use the North
  American Datum of 1927 (NAD 27)
• Differences can be as much as 200 m

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http//www.mentorsoftwareinc.com/CC/gistips/tips06
98.htm

• Datum a single "known point", i.e. the mother of
  all known points.
• When an existing datums accuracy is inconsistent
  with the precision of the surveying practices
  currently in use, its time to think about a new
  datum. Thus, in the late 1980s, the North
  American Datum of 1927 gave way to the North
  American Datum of 1983. The 250,000 (or so)
  "known points" are still in the same physical
  location, but they have new numbers assigned to
  them. Surveyors no longer need to downgrade high
  precision measurements to accommodate a
  (relatively) imprecise datum.
• How much of difference is there? The differences
  can be significant. When reworking one datum to
  produce a new datum (as described last month),
  several issues come into play. One is the
  ellipsoid in use. NAD27 was based on the Clarke
  1866 ellipsoid. By the 1980s a more accurate
  ellipsoid had been established with the
  assistance of satellites and other sophisticated
  technology. (More about ellipsoids in a future
  issue of the Casual Cartographer.) Thus the
  switch from NAD27 to NAD83 also includes the
  switch from the Clarke 1866 ellipsoid to the
  GRS1980 ellipsoid. This has lead to some
  substantial differences way beyond what one would
  expect. That is, if the only difference between
  NAD27 and NAD83 was limited to very small
  differences in measurements, one would expect the
  difference between the two datums to be rather
  small. However, since a change in ellipsoids was
  also included, the shift from NAD27 to NAD83 is
  as large as 100 meters (325 feet) in portions of
  California.

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Cartography and GIS

• Understanding the way maps are encoded to be used
  in GIS requires knowledge of cartography.
• Cartography is the science that deals with the
  construction, use, and principles behind maps.

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Cartography

• How can a flat map be used to describe locations
  on the earths curved surface?

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Projections and Coordinates

• There are many reasons for wanting to project the
  Earths surface onto a plane, rather than deal
  with the curved surface
• The paper used to output GIS maps is flat
• Flat maps are scanned and digitized to create GIS
  databases
• Rasters are flat, its impossible to create a
  raster on a curved surface
• The Earth has to be projected to see all of it at
  once
• Its much easier to measure distance on a plane

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Distortions

• Any projection must distort the Earth in some way
• Two types of projections are important in GIS
• Conformal property Shapes of small features are
  preserved anywhere on the projection the
  distortion is the same in all directions
• Equal area property Shapes are distorted, but
  features have the correct area
• Both types of projections will generally distort
  distances

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Map Projections

• A transformation of the spherical or ellipsoidal
  earth onto a flat map is called a map projection.
• The map projection can be onto a flat surface or
  a surface that can be made flat by cutting, such
  as a cylinder or a cone.
• If the globe, after scaling, cuts the surface,
  the projection is called secant. Lines where the
  cuts take place or where the surface touches the
  globe have no projection distortion.

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Map Projections (ctd)

• Projections can be based on axes parallel to the
  earth's rotation axis (equatorial), at 90 degrees
  to it (transverse), or at any other angle
  (oblique).
• A projection that preserves the shape of features
  across the map is called conformal.
• A projection that preserves the area of a feature
  across the map is called equal area or
  equivalent.
• No flat map can be both equivalent and conformal.
  Most fall between the two as compromises.
• To compare or edge-match maps in a GIS, both maps
  MUST be in the same projection.

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no flat map can be both equivalent and
conformal.
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Cylindrical Projections

• Conceptualized as the result of wrapping a
  cylinder of paper around the Earth
• The Mercator projection is conformal

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Conic Projections

• Conceptualized as the result of wrapping a cone
  of paper around the Earth
• Standard Parallels occur where the cone
  intersects the Earth

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The Unprojected Projection

• Assign latitude to the y axis and longitude to
  the x axis
• A type of cylindrical projection
• Is neither conformal nor equal area
• As latitude increases, lines of longitude are
  much closer together on the Earth, but are the
  same distance apart on the projection

• Also known as the Plate Carrée or Cylindrical
  Equidistant Projection

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The Universal Transverse Mercator (UTM) Projection

• A type of cylindrical projection
• Implemented as an internationally standard
  coordinate system
• Initially devised as a military standard
• Uses a system of 60 zones
• Maximum distortion is 0.04
• Transverse Mercator because the cylinder is
  wrapped around the Poles, not the Equator

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Zones are each six degrees of longitude, numbered
as shown at the top, from W to E
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Implications of the Zone System

• Each zone defines a different projection
• Two maps of adjacent zones will not fit along
  their common border
• Jurisdictions that span two zones must make
  special arrangements
• Use only one of the two projections, and accept
  the greater-than-normal distortions in the other
  zone
• Use a third projection spanning the jurisdiction
• E.g. Italy is spans UTM zones 32 and 33

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UTM Coordinates

• In the N Hemisphere define the Equator as 0 mN
• The central meridian of the zone is given a false
  Easting of 500,000 mE
• Eastings and northings are both in meters
  allowing easy estimation of distance on the
  projection
• A UTM georeference consists of a zone number, a
  six-digit easting and a seven-digit northing
• E.g., 14, 468324E, 5362789N

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State Plane Coordinates

• Defined in the US by each state
• Some states use multiple zones
• Several different types of projections are used
  by the system
• Provides less distortion than UTM
• Preferred for applications needing very high
  accuracy, such as surveying

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Converting Georeferences

• GIS applications often require conversion of
  projections and ellipsoids
• These are standard functions in popular GIS
  packages
• Street addresses must be converted to coordinates
  for mapping and analysis
• Using geocoding functions
• Placenames can be converted to coordinates using
  gazetteers

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GIS Capability

• A GIS package should be able to move between
• map projections,
• coordinate systems,
• datums, and
• ellipsoids.

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Part I Uncertainty
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Can a Database be Perfect?

• The real world is infinitely complex
• a perfect description would have to be infinitely
  large and complex
• A geographic database must always approximate,
  generalize, abstract, or simplify
• we have many ways of doing this in GIS

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How Hilly is Denmark?

• Denmark is relatively flat compared say to
  Norway, or Switzerland, or Nepal
• people often think of it as flat
• Suppose the slope attribute in a database is
  given the value 0 for an object representing the
  country of Denmark
• this is a crude approximation
• (lowest point Lammefjord -7 m) (highest
  point Yding Skovhoej 173 m)
• it is much simpler than recording the slope at
  30m intervals across the country
• it may be good enough for some purposes

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GIS Compresses the Real World

• Representations are almost always lossy (i.e.,
  you lose information)
• It is important to know how much loss has
  occurred
• by measuring the difference between the data and
  the real world
• we term this uncertainty, or the degree to which
  data leave us uncertain about the real world

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Uncertainty

• It is impossible to make a perfect representation
  of the world, so uncertainty about it is
  inevitable

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Sources of Uncertainty

• Measurement error different observers, measuring
  instruments
• Specification error omitted variables
• Ambiguity, vagueness and the quality of a GIS
  representation
• A catch-all for incomplete representations or a
  quality measure

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