SIG/GIS: Systèmes d Information Géographiques Geographical Information Systems. Principles

Transcription

1 SIG/GIS: Systèmes d Information Géographiques Geographical Information Systems Principles GEOREFERENCING

2 Outlines 1- Representing Geography 2- The nature of Geographic Data 3- Geo-referencing 4-Uncertainty 2

3 Learning Objectives Geo-referencing Know the requirements for an effective system of georeferencing; Be familiar with the problems associated with place-names, street addresses, and other systems used every day by humans; Know how the Earth is measured and modeled for the purposes of positioning; Know the basic principles of map projections, and the details of some commonly used projections; Understand the principles behind GPS, and some of its applications. 3

4 outlines 4 Introduction Place-names Postal addresses and postal codes IP addresses Linear referencing systems Cadasters and the US Public Land Survey System Measuring the Earth: latitude and longitude Projections and coordinates Measuring latitude, longitude, and elevation: GPS Converting geo-references Geotagging and mashups Geo-registration Summary

5 Introduction an atomic element of geographic information: a triple of location, optionally time, and attribute 5 Geographic location is the element that distinguishes geographic information from all other types, so methods for specifying location on the Earth s surface are essential to the creation of useful geographic information.

6 Introduction Time is optional element for geographic information but location is essential. Location is important The ability to map To tie different kinds of information together because refer to same place To measure distances and areas 6 Without location, data is said aspatial (non spatial)

7 Introduction Several terms are used to describe the act of assigning locations including geo-reference, geolocate, geocode, or tag with location. Authors use geo-reference in this chapter 7

8 Introduction A primary requirements for a georeferenced system it must be unique, Only one location associated with a given georeference, No confusion Its meaning can be shared among all of the people who wish to work with the information Must be persistent through time, because it would be very confusing if georeferences changed frequently Many georeferencing systems are unique within an area or domain 8 Add more information to ensure the uniqueness(domain name)

9 Introduction 9

10 Introduction While some georeferences are based on simple names, others are based on various kinds of measurements, called metric georeferences Essential to any kind of numerical analysis Provide the potential of infinitely fine resolution Allow distances to be calculated Other geo-refencing systems order locations Facilitates mail delivery (sorting, estimate distances) 10

11 Introduction 11

12 Introduction 12

13 Place-names Simplest form of geo-referencing First developed Any distinctive feature can serve as a point of reference for sharing information Each country has an authorized naming systems Many commonly used placenames have meanings that vary between people, and with the context in which they are used. Mount Everest (Chomolungma for Tibetians) 13

14 Place-names placenames are of limited use as georeferences 14 often have very coarse spatial resolution. Asia covers over 43 million km 2, Only certain place-names are officially authorized by national or subnational agencies The meaning of certain placenames can become lost through time.

15 Web user-generated content Place-names Alternative to Top-down system of naming let s describe the whole world Individuals can assign names independently of officialdom Volunteered Geographic Information (VGI) 15

16 Postal addresses and postal codes Introduced after the development of mail delivery in the 19th century. They rely on several assumptions Every dwelling and office is a potential destination for mail; Dwellings and offices are arrayed along paths, roads, or streets, and numbered accordingly; Paths, roads, and streets have names that are unique within local areas; Local areas have names that are unique within larger regions; and Regions have names that are unique within countries 16

17 Postal addresses and postal codes 17 Postal addresses fail in locating anything that is not a potential destination for mail, such as a natural feature Canadian Forward Sortation Areas FSAs(6 characters), US ZIP code areas and UK postcodes can be changed whenever the post office decides. However, they are sufficiently constant to be used for many purposes

18 Postal addresses and postal codes 18 Outward Codes for the Southend-on-Sea, UK, Local Delivery Offices (LDOs). Outward codes form the first two, three, or four characters of the UK postal code and are separated from the three characters that identify the Inward Codes (Map courtesy of Maurizio Gibin)

19 Postal addresses and postal codes 19

20 IP addresses Every device (computer, printer, etc.) connected to the Internet has a unique IP (Internet Protocol) address The IP address of the user s computer is provided whenever the computer is used to access a Web site, allowing the operators of major sites to determine the user s location Ex:

21 Web services IP addresses Conversion IP address vs. geographic coordinates to north and west 21 Allows search engines to order the results of the search by proximity to the users loctaions

22 Linear referencing systems A linear referencing system identifies location on a network by measuring distance from a defined point of reference along a defined path in the network Linear referencing systems are widely used in managing transportation infrastructure and in dealing with emergencies OnStar system installed in Cadillac ( most prestigious brand of General Motors) 22 Radio the position of the vehicle automatically as soon as it is involved in an accident

23 Linear referencing systems 23

24 Linear referencing systems However, there may be difficulties in defining distances along the network accurately, especially 24 if roads include steep sections where horizontal distance is different from three-dimensional distance # limited number of intersections

25 Cadasters and the US Public Land Survey System The cadaster is defined as the map of land ownership in an area, maintained for the purposes of taxing land, or of creating a public record of ownership The US Public Land Survey System (PLSS) defines land ownership over much of western North America, and is a useful system of georeferencing. 25

26 Cadasters and the US Public Land Survey System PLSS 26 Need to survey and distribute the vast land resources Its simplicity and regularity make it useful for many purposes Its geometric regularity satisfy the metric requirement

27 Cadasters and the US Public Land Survey System To implement the PLSS in an area, - a surveyor first lays out an accurate north south line or prime meridian. - Rows are then laid out six miles apart and perpendicular to this line, to become the townships of the system. - Then blocks or ranges are laid out in six mile by six mile squares on either side of the prime meridian - Each square is referenced by township number, range number, whether it is to the east or to the west, and the name of the prime meridian. - Thirty-six sections of one mile by one mile are laid out inside each township, and numbered using a standard system (note how the numbers reverse in every other row). - Each section is divided into four quarter-sections of a quarter of a square mile, or 160 acres, the size of the nominal family farm or homestead - The process can be continued by subdividing into four to obtain any level of spatial resolution. 27

28 Portion of the Township and Range system (Public Lands Survey System) widely used in the western United States as the basis of land ownership (B). Townships are laid out in 6 mile squares on either side of an accurately surveyed Principal Meridian. The offset shown between T16 N and T17 N is needed to accommodate the Earth s curvature (shown much exaggerated). The square mile sections within each township are numbered as shown in (A).

29 Measuring the Earth: latitude and longitude The system of latitude and longitude is often called the geographic system of coordinates Most powerful system It allows the computation of the distance between any two points 29

30 Measuring the Earth: latitude and longitude 30 Definition of the ellipsoid, formed by rotating an ellipse about its minor axis (corresponding to the axis of the Earth s rotation)

31 Measuring the Earth: latitude and longitude first identify the axis of the Earth s rotation. The Earth s center of mass lies on the axis, and the plane through the center of mass perpendicular to the axis defines the Equator Slices through the Earth parallel to the axis, and perpendicular to the plane of the Equator, define lines of constant longitude 31

32 Measuring the Earth: latitude and longitude 32

33 Measuring the Earth: latitude and longitude it is more conventional to refer to longitude by degrees East or West, so longitude ranges from 180 degrees West to 180 degrees East. West is negative and East is positive; we store parts of degrees using decimals rather than minutes and seconds 33

34 Measuring the Earth: latitude and longitude definition of latitude requires that we know something about the shape A much better approximation of the Earth s shape is the ellipsoid of rotation (spheroid ) The difference between the ellipsoid and the sphere is measured by its flattening, or the reduction in the minor axis relative to the major axis. Flattening is defined as: f = (a b)/a where a and b are the lengths of the major and minor axes respectively 34

35 Measuring the Earth: latitude and longitude 35 The ellipsoid known as WGS84 (the World Geodetic System of 1984) is now widely accepted, Actual flattening of the Earth = 1/300 NAD83 (North America Datum 1983) : R = m f= 1/ longitude pass 100m east Greenwich

36 Measuring the Earth: latitude and longitude 36 The Earth is slightly flattened, such that the distance between the Poles is about 1 part in 300 less than the diameter at the Equator. Definition of the latitude of Point A, as the angle between the equator and a line drawn perpendicular to the ellipsoid

37 Measuring the Earth: latitude and longitude latitude, and varies from 90 South to 90 North. south latitudes are negative numbers and north latitudes as positive. Latitude symbolized by (φ) and longitude by (λ), A line of constant latitude is termed a parallel. Ignoring the flattening, two points on the same north south line of longitude and separated by one degree of latitude are 1/360 of the circumference of the Earth, or about 111 km, apart. 37

38 Measuring the Earth: latitude and longitude One minute of latitude corresponds to 1.86 km, 38 One second of latitude corresponds to about 30 m. Given latitude and longitude it is possible to determine distance between any pair of points The length of this arc on a spherical Earth of radius R is given by: R arccos[sin φ1 sin φ2 + cos φ1 cos φ2 cos(λ1 λ2)]

39 Measuring the Earth: latitude and longitude For example, the distance from a point on the Equator at longitude 90 East (in the Indian Ocean between Sri Lanka and the Indonesian island of Sumatra) and the North Pole Evaluation the equation for φ1 = 0, λ1 = 90, φ2 = 90, λ2 = 90. It is best to work in radians (1 radian is degrees, and 90 degrees is π/2 radians). The equation evaluates to R arccos 0, or R π/2, or one quarter of the circumference of the Earth. Using a radius of 6378 km this comes to km, or close to km 39 The French originally defined the meter in the late 18th century as one ten millionth of the distance from the Equator to the Pole).

40 Projections and coordinates Projections are needed because many technologies for working with geographic data are flat, paper printing, Raster Earth when seen from space The Cartesian coordinate system assigns two coordinates to every point on a flat surface, by measuring distances from an origin parallel to two axes drawn at right angles. 40

41 Projections and coordinates 41

42 Projections and coordinates We often talk of the two axes as x and y, and of the associated coordinates as the x and y coordinate, respectively 42 The coordinates of a projection on a flat sheet are often termed easting and northing A map projection transforms a position on the Earth s surface identified by latitude and longitude (φ, λ) into a position in Cartesian coordinates (x, y).

43 Projections and coordinates Every recognized map projection can be represented as a pair of mathematical functions: x = f (φ,λ) y = g(φ, λ) 43

44 Projections and coordinates For example, the Mercator projection uses the functions: x = λ y = ln tan[φ/2 + π/4] where ln is the natural log function The inverse function λ = x φ = 2 arctan e y π/2 44

45 Projections and coordinates 45 A projection must satisfy one of The conformal property ensures that the shapes of small features on the Earth s surface are preserved on the projection The equal area property ensures that areas measured on the map are always in the same proportion to areas measured on the Earth s surface. Useful for analyses involving areas Major classes of physical models used are cylindrical, azimuthal(planar) and conic

46 The basis for three types of map projections cylindrical, planar, and conic. In each case a sheet of paper is wrapped around the Earth, and positions of objects on the Earth s surface are projected onto the paper. The cylindrical projection is shown in the tangent case, with the paper touching the surface, but the planar and conic projections are shown in the secant case, where the paper cuts into the surface. (Reproduced by permission of Peter H. Dana)

47 Examples of some common map projections. The Mercator projection is a tangent cylindrical type, shown here in its familiar equatorial aspect (cylinder wrapped around the equator). The Lambert Conformal Conic projection is a secant conic type. In this instance, the cone onto which the surface was projected intersected the Earth along two lines of latitude: 20 North and 60 North. (Reproduced by permission of Peter H. Dana)

48 Projections and coordinates Examples of projections 1- The Plate Carrée or Cylindrical Equidistant projection 48 The simplest of all projections maps longitude as x and latitude as y, and for that reason is also known informally as the unprojected projection. Very odd-looking Earth results. The projection is not conformal(small shapes are distorted)

49 (A) The so-called unprojected or Plate Carrée projection, a tangent cylindrical projection formed by using longitude as x and latitude as y. (B) A comparison of three familiar projections of the United States. The Lambert Conformal Conic is the one most often encountered when the United States is projected alone and is the only one of the three to curve the parallels of latitude, including the northern border on the 49th Parallel. (Reproduced by permission of Peter H. Dana)

50 Projections and coordinates For all projections types 50 Where the developable surface coincides with the surface of the Earth, the scale of the projection is 1 Tangent projections are where the developable surface coincides with the surface of the Earth along only one line (or at one point) Secant projections attempt to minimize distortion by allowing the paper to cut through the surface, so that scale can be both greater and less than 1 The grid of latitude and longitude is known as the graticule

51 Projections and coordinates 2- The Universal Transverse Mercator projection UTM 51 Most used in military applications and datasets with global coverage It is based on Mercator projection but in transverse rather than Equatorial aspect

52 Projections and coordinates Mercator Projection The cylinder is wrapped around the poles rather than the equator 52 There are 60 zones in the system, zone = 6 degrees wide Zone1 : from 180w to 174w with the half cylinder wrapped along 177w (zone10???)

53 Projections and coordinates 53 The projection is conformal Scale is at the central meridian and at the edges of the zone The UTM system is secant, with lines of scale 1 located some distance out on both sides of the central meridian.

54 The system of zones of the Universal Transverse Mercator system. The zones are identified at the top. Each zone is six degrees of longitude in width (Reproduced by permission of Peter H. Dana)

55 Home work Projections and coordinates Study what is meant by false easting and false northing 55

56 Measuring Latitude, Longitude and Elevation: GPS First time for people to know almost exactly where they are anywhere on the Earth s surface 56 GPS Global Positioning System (America) GLONASS (Russia) GALILEO (Europe)

57 Measuring Latitude, Longitude and Elevation: GPS GPS 24 satellites Orbiting the earth in 12 hours Distinct orbits At height 20200km Transmit radio pulses at timed intervals To determine position a receiver makes calculations 57 The signals The known positions of the satellites The velocity of light

58 Measuring Latitude, Longitude and Elevation: GPS GPS Three dimensions (latitude, longitude, elevation) : at least 4 satellites Accuracy depends on # satellites Simple GPS, 10 m accuracy Accuracy degrades Tall buildings Trees Indoors Under bridges 58

59 Converting Georeferences GIS allow conversion between # systems Old method : gazeteer(placenames to lat,long) Importance Converting list of customers addresses to coordinates for mapping or analysis (geocoding) Combining datasets that use different systems of georeferencing Converting to projections that have desirable properties for analysis Searching internet for data about specific location Positioning GIS map display by recentering on places of interest 59

60 Converting Georeferences Examples of Gazeteers 60 Alexadria Digital Library gazeteer: U.S. Geographic Names Information System: Detect place-names in text and convert them to georeferences:

61 It is possible now to Geotagging and Mashups Take a mailing list containing street addresses Geocode them Create maps 61 Mashup: joining two or more online services that neither was able to do on its own. Ex: Combines property listing from with cartographic data maps.google.com

62 Geotagging and Mashups Geotags: georeferences embedded in text (Wikipedia) Codes representing latitude, longitude in compressed form 62 At home, see and

63 Georegistration During the process of assembling database when two datasets use different or unkown coordinate systems The standard approach is to find a number of points that can serve as a registration points (tics) Using them find equations to do the conversion 63

64 We have seen Conclusion The complex ways the human refer to specific locations 64 Any form of geographic information must involve a georeference Many benefits of GIS rely on accurate georeferencing