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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. ______
Review The nature of spatial data and generalization • Spatial autocorrelation • Spatial sampling • Spatial interpolation (distance decay) Georeferencing
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
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. • Data:Geo-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)?
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.
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).
Georeferencing • Longitude and Latitude • UTM • Map projections
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 Earth’s rotation and center of mass, and the Greenwich Meridian
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.
Parallels Meridians Geographic Coordinates Prime Meridian Equator Prime Meridian
Oslo, Norway 59o56’ N. Latitude 10o45’ E. Longitude
NorthPole Equator Greenwich 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.
Definition of Latitude • Requires a model of the Earth’s 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 Earth’s axis in this case)
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
http://www.mentorsoftwareinc.com/CC/gistips/tips0698.htm • Datum: a single "known point", i.e. the mother of all known points. • When an existing datum’s 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 1980’s, 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 1980’s 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.
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.
Cartography • How can a flat map be used to describe locations on the earth’s curved surface?
Projections and Coordinates • There are many reasons for wanting to project the Earth’s 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, it’s impossible to create a raster on a curved surface • The Earth has to be projected to see all of it at once • It’s much easier to measure distance on a plane
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
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.
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.
Cylindrical Projections • Conceptualized as the result of wrapping a cylinder of paper around the Earth • The Mercator projection is conformal
Conic Projections • Conceptualized as the result of wrapping a cone of paper around the Earth • Standard Parallels occur where the cone intersects the Earth
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 The “Unprojected” Projection
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
Zones are each six degrees of longitude, numbered as shown at the top, from W to E
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
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
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
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
GIS Capability • A GIS package should be able to move between • map projections, • coordinate systems, • datums, and • ellipsoids.
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
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
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
Uncertainty • It is impossible to make a perfect representation of the world, so uncertainty about it is inevitable
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