GIST 3300 / 5300 Last Time Ellipsoids and Datums Today Map Projections Map Projections Today we will build on the concepts of Geographic Coordinate Systems, Ellipsoids and Datums and add the concepts of Map Projections - getting the model of the spherical Earth onto a flat map - minimizing the distortion on maps Types of Map Projections - cylindrical - pseudo-cylindrical - planer - conic 1
Map Projections - 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 Map Projections Greenland, 2,166,000 km 2 United States, 9,826,630 km 2 Canada, 9,984,670 km 2 2
Map Projections Antarctica 14,000,000 km 2 United States, 9,826,630 km 2 Map Projections - 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 3
Map Projections - 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 (in many strips) 3) conic projections - Earth projected onto a cone 4) planer projections - Earth projected onto a flat plane Map Projections 4
The Globe A physical model not a map projection Shapes true Areas true Distances true Directions - true Map Projections Cylindrical Projections - standard parallel(s) along a line of latitude - Good for mapping low latitude tropical regions One standard parallel Two standard parallels 5
Mercator Projection (cylindrical) Directions are true used for navigation Directions do not provide the shortest route between two locations Polar areas north or south of 85 o are not present Miller Cylindrical Projection (cylindrical) Similar to Mercator but directions are not true not used for navigation Polar areas north or south of 85 o are present Poles are shown as a straight line 6
Map Projections Transverse Cylindrical Projection - standard meridian along a line of longitude Transverse Mercator Projection (cylindrical) Distortion is minimized along a central meridian The UTM coordinate system uses a transverse Mercator projection Also, useful for mapping areas with a long north-south extent 7
Map Projections Conic Projections - standard parallel(s) along a line of latitude - Good for mapping mid-latitude regions Albers Equal Area Conic Projection (conic projection) Areas are true Used to map areas in the mid latitudes (e.g. contiguous United States) 8
Lambert Conformal Conic Projection (conic projection) Shapes are true (conformal) Used to map areas in the mid latitudes (e.g. contiguous United States) Types of Map Projections Planer Projections - standard parallel along a line of latitude or at the pole - Good for mapping polar regions 9
Stereographic Projection (planer projection) Shapes are true (conformal) Directions are true extending from the map center Used to map polar areas of the world Orthographic Projection (planer projection) Perspective view from space 10
Types of Map Projections Pseudocylindrical Projections - Trade off shape to preserve area - Strips of cylinders are tangent to different standard parallels Sinusoidal Projection - Infinitely many strips - Equal area Robinson Projection (pseudo-cylindrical) Some distortion in shape, area, distance and direction It looks good used in atlases 11
Sinusoidal Equal Area Projection (pseudo-cylindrical) Areas on the map are proportional to those on a globe 12
GEOGRAPHIC INFORMATION SYSTEMS Lecture 08: 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) 2) the orientation of the coordinate system (Prime Meridian 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 As a side note, for Geographic Coordinate Systems, ArcMap assumes that the Equator 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 NAD27) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: North American Datum of 1927 (NAD_27) Ellipsoid: Clarke 1866 Ellipsoid Semi-major axis: 6,378,206.4 m Semi-Minor axis: 6,356,583.8 m Flattening Ratio: 1/294.978698214 Ellipsoid Origin: NAD_27 benchmark on Meades Ranch, Kansas Geographic Coordinate System North American 1983 (GCS NAD83) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: North American Datum of 1983 (NAD_83) Ellipsoid: Geodetic Reference System of 1980 (GRS_80) Semi-major axis: 6,378,137.0 m Semi-Minor axis: 6,356,752.3141 m Flattening ratio: 1/298.257222101 Ellipsoid Origin: Earth-centered Geographic World Geodetic Reference System of 1984 (very similar to GCS NAD83) 1) Angular Units: Degrees 2) Prime Meridian: Greenwich 3) Datum: World Geodetic Reference System of 1984 Datum (WGS_84) Ellipsoid: World Geodetic Reference System of 1984 Ellipsoid (WGS_84) Semi-major axis: 6,378,137.0 m Semi-Minor axis: 6,356,752.314245 m Flattening ratio: 1/298,257.223563 Ellipsoid Origin: Earth-centered Copyright 2015, Kevin Mulligan, Texas Tech University
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 Copyright 2015, Kevin Mulligan, Texas Tech University
Map Projections 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 2015, Kevin Mulligan, Texas Tech University
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 2015, Kevin Mulligan, Texas Tech University