GEOGRAPHIC INFORMATION SYSTEMS Lecture 09: Map Projections

Transcription

1 GEOGRAPHIC INFORMATION SYSTEMS Lecture 09: Map Projections Earth Ellipsoid and Horizontal Datums (cont d) Components of a Geographic Coordinate System Recognize that there are three components to a geographic coordinate system. 1) the units of the coordinate system (decimal degrees, latitude from 0 to ±90, longitude from 0 to ±180 ) 2) the orientation of the coordinate system (Equator is 0, Prime Meridian is 0,and north is up) 3) the datum (provides a reference framework for the coordinate system) a) the ellipsoid shape (defined by the semi-major and semi-minor axes and the flattening ratio) b) the ellipsoid origin (a reference point that defines how the ellipsoid is aligned to the geoid) - ellipsoid can be aligned to a land-based benchmark (e.g. the benchmark in NAD_27) - or the ellipsoid can be Earth-centered, as in the case of NAD_83 and WGS_84 For all Geographic Coordinate Systems, ArcMap assumes that the Equator is 0, the Prime Meridian is 0, north is up, latitude varies from +90 to -90, and longitude varies from +180 to -180 (as opposed to 0 to 360 ). Geographic Coordinate System: North American 1927 (GCS_NAD_27) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: North American Datum of 1927 (NAD_27) a) Ellipsoid: Clarke 1866 Ellipsoid Semi-major axis: 6,378,206.4 m Semi-Minor axis: 6,356,583.8 m Flattening Ratio: 1/ b) Ellipsoid Origin: NAD_27 benchmark on Meades Ranch, Kansas Geographic Coordinate System: North American 1983 (GCS_NAD_83) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: North American Datum of 1983 (NAD_83) a) Ellipsoid: Geodetic Reference System of 1980 (GRS_80) Semi-major axis: 6,378,137.0 m Semi-Minor axis: 6,356, m Flattening ratio: 1/ b) Ellipsoid Origin: Earth-centered Geographic Coordinate System: World Geodetic Reference System 1984 (GCS_WGS_84) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: World Geodetic Reference System of 1984 Datum (WGS_84) a) Ellipsoid: World Geodetic Reference System of 1984 Ellipsoid (WGS_84) Semi-major axis: 6,378,137.0 m Semi-Minor axis: 6,356, m Flattening ratio: 1/298, b) Ellipsoid Origin: Earth-centered Copyright Kevin Mulligan, Texas Tech University

2 Demonstration: Geographic Coordinate Systems in ArcMap - when we add a layer to ArcMap, the coordinate system information for the data layer is displayed in the Layer Properties dialog box > Source tab - in this case, counties,shp is using the GCS_North_American_1983 (the GCS referenced to NAD_83) - in ArcMap, it is also important to recognize that the data frame will take on the coordinate system properties of the first layer that is added - in the Data Frame Properties dialog box > Coordinate System tab, we see that the data frame properties have taken on the coordinate system of the counties.shp layer The Prime Meridian in Google Earth (and WGS_84) As a side note, the Prime Meridian in Google Earth does not run directly through the Royal Observatory in Greenwich. The Prime Meridian in Google Earth is located about 100m to the east. This discrepancy stems from the fact that the original Prime Meridian was based on the Airy Transit Circle (which was astronomically based) and Google uses WGS_84 (a different datum and ellipsoid). Given that GPS coordinates are also based on WGS_84, a GPS receiver will show the Prime Meridian at the Royal Observatory at about W. Copyright Kevin Mulligan, Texas Tech University

3 Distortion in Maps - all maps have some distortion in either: 1) area, 2) shape, 3) distance or 4) direction - the purpose of a map projection is to minimize the distortion in one or more of these properties - which map projection is most suitable depends upon: 1) the purpose of the map (e.g. navigation, atlas, general reference) 2) the area being mapped (including the size, shape and latitude) - the term map projection stems from the fact that the globe (latitude and longitude) is being projected mathematically onto a flat surface Classes of Map Projections - there are four general classes of map projections - cylindrical projections, pseudo-cylindrical projections, planar projections and conic projections 1) Cylindrical projections - geographic grid is mathematically projected onto a cylinder - cylinder touches the globe (minimize distortion) along a standard parallel or two standard parallels - can be used for world maps but often have severe distortion at high latitudes - best used to map low latitude tropical regions where the distortion in minimized - transverse cylindrical projections touch the globe (minimize distortion) along a central meridian Copyright Kevin Mulligan, Texas Tech University

4 2) Pseudo-cylindrical projections - pseudo-cylindrical projections are loosely based on a cylindrical projection but modified to make the world look correct or minimize the distortion in area on a world map - most widely used in atlases where the look of the map and relative areas are important 3) Conic projections - touches the globe along a standard parallel or two standard parallels in the mid-latitudes - not suitable for world maps (but can be used to map individual continents) - most often used to map mid-latitude regions (e.g. US, Europe, Russia, China) - also widely used to map US states (e.g. we most often use a conic projection to map Texas) 4) Planer projections - touches the globe at either pole or along a high-latitude standard parallel - not suitable for world maps (but can be used to map the northern or southern hemisphere) - most often used to map high-latitude regions (e.g. the Arctic and Antarctic) - lines of longitude radiate from the pole Copyright Kevin Mulligan, Texas Tech University

5 GIST 3300 / 5300 Map Projections Map Projections - getting the spherical Earth onto a flat map - minimizing the distortion on maps Types of Map Projections - cylindrical - pseudo-cylindrical - planer - conic

6 Ellipsoids and Datums (Cont d) Components of a Geographic Coordinate System There are three components to a GCS 1) the units of the GCS (decimal degrees, latitude 0 to ±90, long 0 to ±180 ) 2) the orientation of the GCS (Equator is 0, Prime Meridian is 0, north is up) 3) the datum (provides a reference framework for the GCS) - there are two components to a datum a) ellipsoid (defined by the flattening ratio) b) origin (how the ellipsoid is aligned to the Earth (geoid) Geographic Coordinate Systems GCS North American 1927 GCS North American 1983 GCS WGS 1984 These are the three most often used in the United States - but there are hundreds of other datums used by other countries - so there are hundreds of other Geographic Coordinate Systems

7 Prime Meridian Royal Observatory in Greenwich

8 Prime Meridian on Google Earth Prime Meridian Airy Transit Circle Prime Meridian WGS_84

9 - it is physically impossible to accurately represent a spherical surface (the Earth) on a flat piece of paper (a map) - there will always be some distortion in either: 1) shape 2) area 3) distance 4) direction

10 Greenland, 2,166,000 km 2 United States, 9,826,630 km 2 Canada, 9,984,670 km 2

11 Antarctica 14,000,000 km 2 United States, 9,826,630 km 2

12 - the purpose of a map projection is to minimize the distortion in one or more of the four map properties - either shape, area, distance, direction - which map projection is most suitable, depends upon: 1) the purpose of the map - e.g. navigation or general reference 2) the area being mapped - including the latitude, size and shape of the area - the term map projection stems from the fact that the globe (lat and long) is being projected mathematically onto a flat surface

13 - there are four general classes of projections 1) cylindrical projections - Earth projected onto a cylinder 2) pseudo-cylindrical projections - Earth projected onto a pseudo-cylinder 3) conic projections - Earth projected onto a cylinder 4) planer projections - Earth projected onto a flat plane

14 Cylindrical Projections - standard parallel(s) along a line of latitude One standard parallel Two standard parallels

15 Transverse Cylindrical Projection - standard meridian along a line of longitude

16 Conic Projections - standard parallel(s) along a line of latitude

17 Types of Map Projections Planer Projections - standard parallel along a line of latitude or at the pole