ADVANCED DIGITAL EARTH A. Earth Geometry and Geodesy Outline • Representaon of Earth (Latude and Longitude) • Determining Latude • Time Zones and the Longitude Problem • Maps • Map Projec)ons • Coordinate Systems • Map Scale • Georeferencing • Earth Shape: Sphere and Ellipsoid, Datum and Geoid Representa?ons of Earth What if you wanted to travel from San Diego to London, England? What path would you take? Which direc)on yields the shortest distance? The shortest distance between any two points is a straight line. But how do you draw a straight line on a globe? For that maer, how can you navigate upon a sphere, at all? Certainly, traveling to London, England is not as simple as saying, “Take a right turn at the Atlan)c Ocean.” The way that we have overcome this apparent problem is with the geographic grid. The geographic grid divides the world into both northern/ southern components (la-tude) and eastern/western components (longitude). The range of latude is from 0° (the Equator) to 90° North and South Latude. The range of longitude is from 0° (the Prime Meridian) to 180° (the Internaonal Date Line). Lines of latude are known as parallels. Lines of longitude are known as meridians. Every place on Earth has a geographic grid coordinate. For example, San Diego, California is located at 32° North Latude, 117° West Longitude. Diagram of Latude 90 degrees North Lat. = North Pole 90 degrees 0 degrees Lat. = Equator 45 degrees 45th Parallel 45 degrees South Latude North Pole 180°Longitude = Internaonal Date Line 90° West Longitude 180° 90° 90° East Longitude 0° Longitude = Prime Meridian View from above the North Pole (NP) 180 Long 135 West Long 135 East Long Diagram of Longitude 90 West Long NP 90 East Long 45 West Long 45 East Long 0 Long Please click on the following link to watch a video lecture that describes and explains Latude and Longitude: hNps://www.youtube.com/watch?v=9vfQM_M1Pec Determining Latude The use of the North Celes)al Pole star for navigaon purposes has been used for thousands of years. In par)cular, the posi)on of the North Star (Polaris) will tell you your latude (whereas a good clock will help you to determine your longitude). Finding Polaris Little Dipper Big Dipper Time Zones There are 24 )me zones in the world; each )me zone is separated by 15° (the world turns 360° per 24 hours = 15° rotaon per hour) (see Figure 3 on next slide). If you are west of the Prime Meridian (west of 0° Longitude), you are behind GMT (Greenwich Mean Time). If you travel east of the Prime Meridian, you are ahead GMT (remember, the Sun rises in the east and sets in the west due to Earth’s easterly – or, counterclockwise -- rotaon). In the example below, the )me for the person at the Prime Meridian is solar noon. For the person standing in the east, the )me is aernoon (no)ce the Sun is in the western, seng sky). For the person standing in the west, the )me is before noon (no)ce the Sun is in the eastern, rising sky). Direc)on of Sun (rises in the east and sets in the west) West Prime Meridian East If you cross the IDL (Internaonal Date Line = 180°) from the Western Hemisphere into the Eastern Hemisphere, you lose a day (set your calendar ahead a day). If you cross the IDL from the Eastern Hemisphere into the Western Hemisphere, you gain a day (set your calendar back a day). Figure 3 World Poli)cal Time Zones (adopted from Encarta Encyclopedia, 2000) -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 As you can see from the above )me zone map, the 15° rule is not always followed! Why not? Please click on the following link to watch a video lecture that describes and explains Time Zones: hNps://www.youtube.com/watch?v=OXuc84bP90k Early Voyage Problem: Longitude! How do you find East/West? Key = Time Just as you use longitudinal distance to calculate )me, you can also use )me difference to calculate your longitude! The relaonship between )me and longitude (1 hour = 15°) is the key. If you know the difference in )me between two places, and you know the longitude of one place, you can calculate the longitude of the other. For example, imagine you are a sailor and you need to know where you are (you don’t have a GPS unit!). You find your latude by no)cing the posi)on of the North Star above your horizon. To determine longitude, however, you must use a clock. Assume you leave San Diego. You set your clock to San Diego )me and set sail. Eventually, you want to determine your locaon. On your boat, you no)ce when the shadow is shortest on the mast (the Sun is at its highest point in the sky). It is solar noon. You check your clock. It reads 8 am. If it is noon for you and 8 am in San Diego, you are ahead of San Diego )me (you are east of San Diego) by 4 hours. 4 x 15 = 60°. Therefore, you are located 60° east of San Diego, which means you are at 120° - 60° = 60° West Longitude: In the Early days of sea voyages, determining longitude was a difficult task. Why? How do you read a pendulum clock at sea! A contest was created by England with the following results. We can thank John Harrison for our wristwatch. Chronometer #1: Finished in 1735 AD Chronometer #4: Finished in 1760 AD Please click on the following link to watch a video lecture that describes and explains The Longitude Problem: hNps://www.youtube.com/watch?v=s4hsI3Cz2tg Maps The map is the primary tool of the geographer….It can * fit in a pocket * give locaon * provide area data * be themac (such as weather maps, veg maps, soil maps…) Mapping: Projecons and Coordinates • There are many reasons for wan)ng to project the Earth’s surface onto a flat plane, rather than deal with the curved surface. – The paper used to output GIS maps is flat. – Flat maps are scanned and digi)zed to create GIS databases. – The Earth has to be projected to see all of it at once. – It’s much easier to measure distance on a plane. Projecons (cont.) • A transformaon of the spherical or ellipsoidal earth onto a flat map is called a map projec)on. • The map projec)on can be onto a flat surface or a surface that can be made flat by cung, such as a cylinder or a cone. • If the globe, aer scaling, cuts the surface, the projec)on is called secant. Lines where the cuts take place or where the surface touches the globe have no projec)on distor)on. From: hNp://naonalatlas.gov/ar)cles/mapping/a_projec)ons.html Projecons (cont.) • Projec)ons can be based on axes parallel to the earth's rotaon axis (equatorial), at 90 degrees to it (transverse), or at any other angle (oblique). • A projec)on that preserves the shape of features across the map is called conformal. • A projec)on that preserves the area of a feature across the map is called equal area or equivalent. • No flat map can be both equivalent and conformal. Most fall between the two as compromises. • To compare or edge-match maps in a GIS, both maps MUST be in the same projec)on. Distorons • Any projec)on must distort the Earth in some way • Two types of projec)ons are important in GIS – Conformal property: Shapes of small features are preserved: anywhere on the projec)on the distor)on is the same in all direcons. – Equal area property: Shapes are distorted, but features have the correct area. – Both types of projec)ons will generally distort distances. Map Projec?ons Flaen half of a rubber ball? No. Instead, features are projected onto one of three “developable” surfaces. Planar: a map projec)on Cylindrical: a map projec)on where the Conic: a map projec)on where the earth’s surface is resul)ng from the earth’s surface is projected onto a tangent projected onto a tangent or secant cone, which is conceptual projec)on of the or secant cylinder, which is then cut then cut from apex to base and laid flat earth onto a tangent or lengthwise and laid flat secant plane hNp://www.naonalatlas.gov/ar)cles/mapping/a_projec)ons.html#two 21" Conformal Projecon •! Cylindrical projecon •! Parallels and meridians at right angles. •! Angles and shapes of small objects preserved (at every point, east–west scale same as north–south scale). •! The size/shape/area of large Example: Mercator projec?on (1569) objects distorted. used for nau)cal purposes (constant •! Seldom used for world maps. courses are straight lines). 22" Equivalent Projec?on •! Conic projecon •! Preserves accurate area. •! Scale and shape are not preserved. Example: Albers Equal Area standard projec)on for US Geological Survey, US Census Bureau 23" Compromise Projecons •! Neither equivalent nor conformal. •! Meridians curve gently, avoiding extremes. •! Doesn’t preserve proper)es, but looks right. Example: Robinson projec?on (1961) • Good compromise projecon for ! viewing enre world. • Used by Rand McNally and the Naonal ! Geographic Society. 24" Cylindrical Projecons •! Conceptualized as the result of wrapping a cylinder of paper around the Earth. •! The Mercator projec)on is the best- known cylindrical projec)on. –! The cylinder is wrapped around the Equator. –! The projec)on is conformal. •! At any point scale is the same in both direc)ons.