Shape e o f f the e Earth

Transcription

1 1 Coordinate Systems & Projections

2 Coordinate Systems Two map layers are not going to register spatially unless they are based on the same coordinate system. 2

3 Contents Shape of the earth Datum Projections Coordinates / Coordinate Systems Scales 3

4 4 Shape of the Earth

5 Shape of the Earth Greek Scientists theory (BC): Using a circle's diameter as an axis and rotating the circle 360 degrees creates a perfect sphere. All locations on the sphere's surface are exactly the same distance from its center. English and Fresh scientists in 18 th Century: The earth is not a perfect sphere but an oblate ellipsoid. If it rotated about its major (longer) axis, it would be described as a prolate ellipsoid. 5

6 Shape of the Earth 6 The flattening is based on the difference between the semimajor axis a and the semiminor axis b.

7 Shape of the Earth We think of the earth as a sphere It is actually a spheroid, slightly larger in radius at the equator than at the poles 7

8 Shape of the Earth A spheroid is simply an ellipsoid that approximates a sphere. These examples are two common world spheroids used today with their values rounded to the nearest meter. For each spheroid, the difference between its major axis and its minor axis is less than 0.34 percent. Specific definitions for exactly what a spheroid is can vary, but the two most common definitions for a spheroid are: 1. An ellipsoid that approximates the shape of a sphere 2. An ellipsoid created by rotating an ellipse about either its major axis (called a prolate spheroid) or its minor axis (called an oblate spheroid) 8 WGS: World Geodetic System

9 Shape of the Earth Spheroids created using satellite information, such as GRS80, are starting to replace traditional groundmeasured spheroids, such as Clarke In this example, measurements for both spheroids have been rounded to the nearest meter. 9 GRS: Geodetic Reference System

10 10 Datums

11 11 EARTH SURFACES :Physical Models

12 Representations of the Earth Sea surface Ellipsoid Mean Sea Level is a surface of constant gravitational potential called the Geoid Earth surface 12 Geoid

13 Geodetic Datums Types of Geodetic Datums A Geocentric Datum is one which best approximates the size and shape of the Earth as a whole. The centre of its spheroid coincides with the Earth's centre of mass. Geocentric datums do not seek to be a good approximation to any particular part of the Earth. Rather, their application lies in projects or undertakings which have global application. 13 The Global Positioning System (GPS), which is operated by the United States Department of Defence, utilises a geocentric datum (WGS84 (WGS84)to )to express its positions because of its global extent. Geocentric Datum

14 Geodetic Datums Types of Geodetic Datums Geodetic datums are usually classified into two categories. These are known as local geodetic datums and geocentric datums. A Local Geodetic Datum is a datum which best approximates the size and shape of a particular part of the earth's sea--level surface. Invariably, sea the centre of its spheroid will not coincide with the Earth's centre of mass. Until very recently, most country's spatial information systems were based on local geodetic datums. 14 Local Datum

15 Map Projection (Basic Concepts) Coordinate system A method for specifying the location of real-world features on the surface of the earth. 15 Geographic coordinates GCS A measurement of a location on the earth's surface expressed in degrees of latitude and longitude. Projected coordinates A measurement of locations on the earth s surface expressed in a two-dimensional system that locates features based on their distance from an origin (0,0) along two axes, a horizontal x-axis representing east west and a vertical y-axis representing north south. A map projection transforms latitude and longitude to x,y coordinates in a projected coordinate system.

16 Map projection What is a Map Projection? Methods to convert the 3-D earth surface to a 2-D planar surface Can be used to represent the whole earth surface or only a portion of it based on different objectives Map projection process causes distortion. It will distort one or more of the following four spatial properties Shape Area Distance Direction 16

17 Map projection Map projections are systematic transformations of the spheroidal shape of the earth so that the curved, three dimensional shape of a geographic area on the earth can be represented in two dimensions, as x,y coordinates. Maps are flat, but the surfaces they represent are curved. Transforming three-dimensional space onto a two dimensional map is called projection. Projection formulas are mathematical expressions that convert data from a geographical location latitude and longitude on a sphere or spheroid to a representative location on a flat surface. 17

18 Map projection What is a Map Projection? For small areas, such as a city or county, the distortion will probably not be great enough to affect your map or measurements. If you re working at the national, continental, or global level, you ll want to choose a map projection that minimizes the distortion based on the requirements of your specific project 18

19 Map Projection (Basic Concepts) 19 When do you need a Map Projection? 1. If you are using measurements to make important decisions 2. To accurately compare the shape, area, distance, or direction of map features. 3. To correctly align a feature layer with an image layer in ArcView. 4. To transform different map projections of many GIS data sources to an unified map projection in a GIS database, 5. To adjust errors which occur at map digitization due to distortion of the map measured, 6. To produce geo-coded image by integrating GIS data and remote sensing imagery.

20 Map Projection (Basic Concepts) Classifying Clues Projections are commonly classified according to the geometric surface from which they are derived. These are called developable surfaces. The most common developable surfaces are the Cylinder, the Cone, and the Plane. 20

21 Types of projections Cylindrical projections Longitude lines are parallel and equally spaced Latitude lines are parallel and with varied space Azimuthal/Planar Projections Longitude lines appear as radial lines from the pole Latitude line appear as concentric circles Conic Projections Longitude lines appear as radial lines and meet at the conical apex Latitude lines appear as a set of rings 21

22 Map Projection (Basic Concepts) Minimizing Distortion A three-dimensional globe represents the Earth in such a way that area, distance, direction, and shape are all accurately represented. Unfortunately, it is impossible to preserve all of these properties on a flat surface. All map projections have only one important feature in common: positional accuracy. A map projection is therefore, a compromise! The extent to which these properties (area, distance, direction, and shape) are preserved provides another method of classifying projections: 22

23 Map Projection (Basic Concepts) Equal-Area or Equivalent Maps: (preserve area) When a map projection portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on Earth they represent. The creation of this projection results in shapes and angles being greatly distorted. This distortion increases with distance away from the point of origin. Equidistant Maps: (preserve distance) These projections portray distances from the center of the projection to any other place on the map. This projection maintains constant scale only from the centre of the projection or along great circles passing through this point. For example, a planar equidistant projection centered on Montreal would show the correct distance to any other location on the map, from Montreal only. This property is accomplished at the expense of distorting area and direction. 23

24 Map Projection (Basic Concepts) Azimuthal or Zenithal Maps: (preserve direction) A projection created when angles or compass directions from one central point are shown correctly to all other points on the map. However, to achieve this property, shapes, distances and areas are badly distorted. 24 Conformal Maps: (preserves local angles) A projection created when all angles at any point are preserved. Or, the scale at any point is the same in every direction. Lines of latitude and longitude intersect at right angles, and shapes are maintained for small areas. However, in the process of projection, the size of large areas is distorted.

25 The following table shows which pairs of properties can be combined in one projection Equal -Area Equidis tant Azimuthal Equal-Area -- No Yes No Equidistant No -- Yes No Azimuthal Yes Yes -- Yes Conformal No No Yes -- Conforma l 25

26 Map Projection (Choosing the Best Projection) some hints to help you choose the best projection for your map: When representing a very large area on a small map scale an Equal-Area map is preferable. This will result in a realistic representation of the relative size of different regions. 2. Equal-Area projections are also commonly used for landcover, landuse, or population density mapping. 3. For mapping circular regions or Polar Regions such as the whole of the Antarctic, an Azimuthal Planar projection is appropriate. This is because distortion will increase equally in all directions from the centre outwards. 4. Planar projections are capable of demonstrating "great circle routes" which are the shortest paths between two points on the Earth. This information is most useful in air navigation, because aircraft usually travel along great circle routes!

27 Map Projection (Basic Concepts) 27 For an elongated region, either a Conic or Cylindrical projection may be appropriate. The Mercator projection (now rarely used for world mapping) is a Cylindrical projection, but results in significant distortions of the relative size of continents. However, the Mercator projection is Conformal, therefore it is excellent for navigational purposes, but only preserves local shapes. 1. For East-West extended maps, a Conic projection is recommended since distortion will be at a minimum along lines of latitude. 2. Countries in the mid-latitudes are best represented by a Conical projection (places like North America, the Former Soviet Union, and Europe). The result is less overall distortion of land and water areas. The Lambert Conformal Conic projection is a commonly used Conic version.

28 The following table provides a examples of more common map projections, their properties, and their use: 28 Projection Type Properties Regional Use General Use Mercator cylindrical conformal true direction* Transverse Mercator Lambert conformal conic Azimuthal equidistant World*, equatorial, east-west extent, large and medium scale cylindrical conformal continents/oceans, equatorial/midlatitude, north-south extent, large and medium scale conic planar conformal true direction* equidistant* true direction* continents/oceans, equatorial/midlatitude, east-west extent, large and medium scale World*, hemisphere, equatorial/midlatitude, continents/oceans, regions/seas, polar, large scale* navigation large scale map series, U.S.G.S.** topographic large scale map series, N.T.S. and U.S.G.S. mapping countries of Canada and U.S.A., National Atlas of Canada 5th ed., I.M.W. (International Map of the World) navigation, topographic large scale map series, U.S.G.S.

29 What are coordinate systems? ArcInfo stores features using x,y coordinates. These coordinates are linked to real-world locations by a coordinate system. The coordinate system specifies a datum and a map projection. Datum: A datum is a mathematical representation of the shape of the earth s surface. A datum is defined by a spheroid, which approximates the shape of the earth and the spheroid s position relative to the center of the earth. There are many spheroids that represent the shape of the earth and many more datums based on them. 29

30 Coordinate systems Spherical coordinate systems Latitude & Longitude Sphere-like surface Cartesian coordinate system Using x, y coordinate values 2D, planar surface 30

31 Spheroid and Datum Spheroid A three-dimensional shape Similar to a sphere Not a perfect sphere Some standard spheroids Clarke 1866 GRS80 Datum A point of reference measuring locations on the earth surface Define the origin and orientation of the latitude and longitude Earth-centered and local datum Same Datums: NAD27 NAD83. 31

32 Latitude and Longitude Graticule N W + - Prime Meridian N E + + Lat and long measured in: degrees minutes seconds (60 =1 & 60 =1 ) 1 second= 30m. approx. (lat., or long. at equator) S W - - S E - + When entering data, be sure to include negative signs. Longitude sometimes recorded using 360 to avoid negatives. 32 Graticule: network of lines on globe or map representing latitude and longitude. Origin is at Equator/Prime Meridian intersection (0,0) Grid: set of uniformly spaced straight lines intersecting at right angles. (XY Cartesian coordinate system)

33 33 Scales

34 Map Scale Scale (MapDistance) (GroundDistance) Usually expressed as representative fraction 1:24,000 34

35 Map Scale 35 Common Mistake: Large Scale vs. Large Area People are often saying "large scale" map when they mean "large area". Map scale is often reported as a ratio, e.g., 1:100,000 scale. As a fraction this is A large scale map is one where the fraction is large. This happens when the second number is small. Example: 1 to 1 million map scale (1:1,000,000) expressed as a fraction is ; a 1:200 map scale, expressed as a fraction, is Which is the larger scale, , or 0.005? If you have two map sheets which are 10 inches across, the 1:1,000,000 map (which is small scale) covers a distance of 10,000,000 inches, which is about 158 miles when converted (10,000,000 inches * (1ft/12inches) * 1mile/5280 ft). The 1:200 map (large scale) covers about 200*10 inches which is only 0.03 miles. Remember, larger scale maps cover less area, but show more detail.

36 Example of Scales Larger scale, smaller area Smaller scale, Larger area 36 1:24,000 1:100,000 1:250,000

37 Measurement Scales Nominal Names as labels Ordinal Orders / ranks Interval Arbitrary start point Value relative to arbitrary origin Ratio Absolute zero as origin Angles from zero 37