Georeferencing Concepts

Transcription

1 Georeferencing Concepts 1 GIS differs from other information systems because they contain spatial data. Spatial data include coordinates defining location, shape and extent of geographic objects. To use GIS effectively requires an understanding of how coordinate systems are established 2 1

2 There are two major problems in mapping geographic features. What are they? 1. The Earth has an irregular shape which affects how we define coordinate systems used to represent geographic features in GIS Geodesy the science of measuring the shape of the Earth 2. A curved surface (e.g., portions of the earth) gets distorted when represented on a flat map Map projections transforming coordinates from a curved Earth to a flat map 3 So if we want to do a study that involves analysis of the location, shape or extent of geographic features we need to Model the shape of the Earth Develop an appropriate coordinate system for representing our area of interest on a flat map 4 2

3 There are five important components to model the shape of the Earth and to develop a coordinate system for a flat map. Does anyone know what these concepts might be? Ellipsoid Spherical or geographic coordinate system Datum Projection Units 5 What is an Ellipse? An Ellipsoid? Why is it needed? 6 3

4 Ellipsoids (Source: ESRI virtual campus) An ellipse is a 2-dimensional shape that is oval in shape. The shape is similar to a circle but flattened. An ellipsoid is actually a three-dimensional (mathematical) representation of an ellipse; it is created by rotating an ellipse about an axis. Ellipsoids (sometimes called spheroids) provide a model of the shape of the Earth. To georeference something in GIS, we need to define this 7 model. There are a number of standard ellipsoids (mathematical functions) used to describe the shape of the earth. Here is the WGS-84 ellipsoid. (Note: ArcView refers to this as a spheroid the terms ellipsoid and spheroid are sometimes used interchangeably even though ellipsoid is a special type of spheroid) b a Source: Peter Dana raphy/gcraft/notes/datum/datu m_f.html 8 4

5 Many different ellipsoid models of the Earth since 1830 Source: Peter Dana o.edu/geography/gcr aft/notes/datum/datu m_f.html Commonly used for North America: WGS 84 standard used in GPS systems Clarke 1866 WGS 72 WGS 84 GRS OK. Ellipsoids mathematically model the 3-D shape of the Earth. What s next? What is a Spherical or Geographic Coordinate System? Why is it needed? 10 5

6 What is a Spherical or Geographic Coordinate System? a reference system used to locate and measure geographic features on the surface of a sphere-like object, like the earth. We need to be able to place geographic features on the ellipsoid. What is arguably the most widely known geographic coordinate system? 11 Longitude/Latitude System (A Spherical System) (Source: ESRI virtual campus) Equator 0 o Latitude (Parallels) Prime meridian 0 o Longitude Latitude range from 0 to 90 in the northern hemisphere, goin g from the equator to the North Pole. In southern hemisphere, they range from 0 to -90, going from the equator to the South Pole. Longitude values range from 0 to 180 in the eastern hemisphere, beginning at the prime meridian in Greenwich, England, and traveling east across Europe, Africa, and Asia. In the western hemisphere, longitude values range from 0 to -180, starting at the prime meridian and traveling west across the Americas. 12 6

7 Longitude/Latitude System (Source: ESRI virtual campus) Spherical coordinate systems are measured in degrees, minutes, seconds (DMS) or degrees decimal (DD). How would you convert the above longitude into degrees decimal? DD = / /3600 = Why is DD useful? Because computers can do processing on them they can t in DMS format 13 Longitude/Latitude System (Source: ESRI virtual campus) The network of converging long/lat lines is called a graticule. It cannot be called a grid because the lines don t converge in right angles. 14 7

8 OK, now we ve got (1) a model of the Earth s shape and (2) a coordinate system for it. What is a datum? Why is this concept important? 15 Datum (Source: ESRI virtual campus) The geographic coordinate system (long, lat) is based on one longitude location the Greenwich observatory. Other long/lat locations need to be measured a Geodetic Survey. A geodetic datum is a set of control points whose geometric relationships are known, either through measurement or calculation (Dewhurst, 1990). From these measurements we know distance, area, direction, etc. between locations on the Earth. Datums have two components: The reference ellipsoid A set of survey points Both the shape of the spheroid and its position relative to the earth are important. Remember, the Earth is not a smooth sphere, (e.g., the Himalayan mountains and the flat deserts), so different datums work better in different places on the Earth. There are two types of datums: (1) Earth-centered and (2) Local. 16 8

9 NOTE: Some people use ellipsoid and spheroid interchangeably! Earth-centered Datum (Source: ESRI virtual campus) (this is really an ellipsoid) An earth-centered datum establishes the origin of the ellipsoid at the earth's currently known center of mass. Earth-centered datums define an X, Y, and Z, Cartesian coordinate system with respect to the center the reference ellipsoid The origin of the 1983 North American Datum (NAD83) is very close to the earth's center of mass and is the most commonly used datum for North America. The World Geodetic System of 1984 (WGS84) is the datum upon which GPS 17 measurements are based. Local Datum (Source: ESRI virtual campus) A local datum is aligned so that it closely corresponds to the earth's surface for a particular area. An example is the 1927 North American Datum (NAD27) which uses Meades Ranch, Kansas as the point of origin for all measurements

10 Earth-centered versus Local Datum (Source: ESRI virtual campus) Notice how the ellipsoid shifts, conceptually, with respect to the Earth s surface. 19 Various datums fit various locations of the Earth better See the list of datums at: t.html Datums use different ellipsoids. If 2 maps used for GIS input use different datums, you will run into compatibility problems because of the different ellipsoids used (what Bolstad calls datum shift ). For example, one dataset using the North American Datum 1927 and another using Indian datum 20 10

11 Peter Dana s website shows methods to convert data using one datum to another 21 datum.html#dconv Source: Peter Dana OK, we now have: 1. A earth model 2. A geographic coordinate system 3. A datum defining where these coordinates are on the model of the Earth What are Map Projections and why do we need them? 22 11

12 Why do we need map projections? (source: ESRI virtual campus) We want to represent locations identified in the geographic coordinate system and place them a flat surface (map). Map projections transfer the spherical Earth coordinates onto a twodimensional (planar) coordinate system. 23 What is the fundamental problem with wanting to represent a curved surface on a flat piece of paper? 24 12

13 The fundamental problem (source: ESRI virtual campus) Sphere graticule lines don t line up in right angles Cartesian coordinate system lines meet in right angles Converting a graticule to a grid results in some kind of distortion either shape, area, length, or direction). 25 Why do we need map projections? (source: ESRI virtual campus) Cartesian coordinate systems, such as: Universal Transverse Mercator (UTM) or State Plane Coordinate System (SPCS), are commonly used to locate features and are found on many maps. You convert spherical coordinates to Cartesian coordinates using a map projection

14 What are the ways we can project the curved Earth surface on a flat map? Using a cylinder (Cylindrical) Using a plane (Planar) Using a cone (Conic) 27 Cylindrical projections result from projecting a spherical surface onto a cylinder 28 14

15 Cylindrical Equal-Area projections (tangent to a line of latitude) They have straight meridians and parallels, the meridians are equally spaced, the parallels unequally spaced Area is true; Shape and scale get distorted near the upper and lower 29 regions of the map. (Anyone see the West Wing episode on this?) Transverse Mercator projections result from projecting the sphere onto a cylinder tangent to a meridian (line of longitude) 30 15

16 Equator The Universal Transverse Mercator (UTM) projection is used to define horizontal, positions world-wide by dividing the surface of the Earth into 6 degree zones, each mapped by the Transverse Mercator projection with a central 31 meridian in the center of the zone Question on UTM projection and Distortion UTM is a global coordinate system Common projection for data spanning large regions (e.g., several state plane zones) Many US federal gov data are in UTM because many agencies manage land spanning large areas and UTM is a well known, standard system UTM zones are 6 degrees wide so many studies will fit in this that would not fit in a state plane zone (for example) So UTM is a useful projection for broad study areas (larger than 1 state, or possibly crossing state boundaries) as long as it is within one UTM zone

17 Equator The Universal Transverse Mercator (UTM) projection is used to define horizontal, positions world-wide by dividing the surface of the Earth into 6 degree zones, each mapped by the Transverse Mercator projection with a central meridian in the center of the zone. If maps are limited to the thin, vertical region near the meridian of tangency they will be relatively free of distortion Mercator shapes are true, but area gets distorted (conformal). 33 Question on UTM projection and Distortion UTM is sometimes however not compatible for regional studies that cross UTM zones. This is because coordinate values are not continuous between zones. The coordinate system for UTM zone 15 is different than zone 16, for example. In other words, each UTM zone is its own projection. Combining will result in distortion in location and shape of the objects from a different zone than the one being used. UTM was designed to map areas within that particular zone 34 17

18 Planar Projections (tangent case) 35 An example of a planar projection (tangent) Often used for air route distances. Distances measured from the center are true. Distortion of other properties increases away from the center point

19 Conic Projections Generated by projecting a spherical surface onto a cone 37 Distorts scale and distance except along standard parallels. Areas are proportional and directions are true in limited areas. Used in the United States and other large countries with a larger east-west than north-south extent

20 Area, and shape are distorted away from standard parallels. Directions are true in limited areas. Used for maps of North America

21 Unprojected maps include those that are formed by considering longitude and latitude as a simple rectangular coordinate system. Scale, distance, area, and shape are all distorted with the distortion increasing toward the poles

22 State Plane Coordinates The State Plane Coordinate System (SPCS) uses a unique set of projection parameters for each of the 50 states Uses either a Transverse Mercator or Lambert s conformal conic projection Originally designed to provide a permanent record of land survey monuments in the United States. Zones, measured in feet, not meters. 43 Summary Geodesy science of modeling the shape of the earth Map projections transformation of coordinates from a curved Earth to a flat, paper map. Ellipsoid 3-D model of the earth (flattened) Spherical or geographic coordinate system system of locations on a 3-D ellipsoid (Long/Lat) Geodetic Datum set of measured or calculated points on the Earth. Provides a frame of reference for measuring locations on the Earth or places the geographic coordinate system on the ellipsoid. Map projections Systematic rendering of locations from a curved Earth to a flat map surface. The process of projecting will always distort one or more of four spatial properties: shape, area, distance, and direction

23 Summary (source -- ESRI Virtual campus) - The choice of map projection is important when you are working with small (broad) scale maps, like world maps - The choice of datum is important when working with large (fine) scale maps, such as city maps - When using map input for building GIS layers, you need to make sure they are in compatible map projections. 45 A final word on distortion 46 23

24 Suggestions from Theobald (1999: 42) on Selecting a Projection If you are making a fairly detailed map, for example a city, or requirements for accuracy is minimal, then you may not have to worry so much about which projection to use. If you are making a map of a regional to continental to global scale OR are interested in precise shape, area or distance measurements then you should choose carefully the projection. For many study areas there is already standard projects, such as State Plane for county or city governments or UTM for state governments. Three factors to consider related to accuracy: Latitude of area, extent and theme Latitude: Low-latitude areas (near equator) use a conical projection Polar regions use a azimuthal planar projection Extent Broad in East-West (e.g., the US) use a conical projection Broad in North-South (e.g., Africa) use a transverse-case cylindrical projection Thematic If you are doing an analysis that compares different values in different locations, typically an equal-area projection will be used