Cartography: the science of map making Locating yourself on a Globe • You need a frame of reference • That is the purpose of Latitude and Longitude • Defining these parameters: – Earth rotates on an imaginary axis ~ North and South Poles • Equator: is a great circle that lies equidistant between them. Great Circles: • ..are imaginary circles of the surface of the earth who's plane passes through the center of the earth. • The circumference of the earth is 25,000 miles of 40,000 km • "Great" because it is the largest possible circle Great Circles: • 1) cut the earth in half and each half is known as a hemisphere • 2) are the circumference of the earth • 3) provide the shortest routes of travel on the earth's surface. – ** Planes travel in great circles. – ** We were always taught a line is the shortest distance between two points - Not True. • Small circles: circles whose planes do not pass through the center of the earth. Latitude • Latitude: is the angular distance north or south of the equator. • 1° of latitude = 112 km 360°/40,000 km • 1 degree = 60 minutes • 1 minute = 60 seconds 36°49'52" N • ArcView uses: Decimal Degrees • Sextant measures the angular distance between 2 points (sun & horizon) • **So it easy to determine latitude. Longitude: • Longitude: no natural reference point • In 1884 by International Agreement Greenwich England was the chosen starting point. • This is called the prime meridian or zero degrees and everything is east or west of that. – (angular distance from Greenwich, England) The global grid: • Parallels: lines of latitude, only the equator is a great circle all other parallels are small circles (they never meet) • Meridians: these are line of longitude and when joined with its mate half way around the globe form great circles • * the distance between meridians will vary with latitude Global Coordinate System • Longitude and Latitude – Degrees, minutes, seconds – 1o latitude = 110.5 km (equator) – 1o longitude = 111.3 cos(latitude) • Meridian • Parallel • Great and Small Circles How the Earth is Divided • Hemispheres: Northern, Southern, Eastern, Western Time Zones • Solar noon: most towns used this, defined as when a vertical stake cast the shortest shadow. • By the 19th century transportation and communications (namely railroads and telegraph) connected towns and cities, the adopt of a standard time was necessary. Time Zones (continued) • 1884 at the International Meridian Conference 24 time zones were established. • Greenwich Mean Time (GMT) = Universal time = Zulu time • 360°/24 = 15° for each time zone, however for convenience many time zones follow state and country lines. • International Date Line: where each new day begins 180th meridian • Chronometer Time Zones Globes • The Globe is a nearly perfect representation of the earth, it shows the shape and spatial relationships of land and water. • Problem: Can only look at 1/2 at a time. • However globes can not show detail and are big and clumsy. Benefits of Maps • Maps: are the geographers most important tool. • Benefits: – – – – – reproduced easily and inexpensive different scales can put an enormous amount of information on a map roads, buildings, property lines, vegetation, topography distribution of land forms Map Features important in GIS • Areas • Lines – width exaggeration • Points – size exaggeration On a globe four properties are true: • • • • 1) parallels of latitude are always parallel 2) parallels are evenly spaced 3) meridians of longitude converge at the poles 4) meridians and parallels cross everywhere at right angles Map Projection: • A map projection is a mathematical formula for representing the curved surface of the earth on a flat map. Think of a light bulb Distortions • • • • distance area shape direction You must make a choice between: • Equivalence: equal area relationship throughout the map, however you get distorted shapes. • Conformal: shapes are true and meridians and parallels are at right angles, however land masses are greatly enlarged at high latitudes. • Except for very small areas Conformality and Equivalence are mutually exclusive. • There are over 1000 different projections. Other types of considerations • Equidistant projections – However scale is not maintained correctly by any projection throughout an entire map • True-direction projections or azimuthal projections, maintain some of the great circle arcs. (The shortest distance between 2 points on a globe is the great circle route.) Map Projection • Distortions are inherent in maps – Earth is round, map is flat • Projection is the term used to describe the process of mapping a round surface to flat paper – wide variety of projections possible – each projection causes different distortions to information 13 Map Projections Types Planar Projection Conical Projection Cylindrical Projection 14 Cylindrical Projection: example: Mercator • Tangent to the globe at the equator. No distortions at the equator but it increases moving North or South. Nice rectangular grid. • Why are they used in Navigation? *A straight line drawn anywhere on a Mercator projection is a true compass heading: this is called a rhumb line. • However, the distance along this line may vary. Variations on Cylindrical Projection Azimuthal Projection example: Many Polar projections • Plane is tangent to the globe at some point N or S of the equator or one point on the equator. No distortion at the point of tangency but it increases moving away. All directions from the center are accurate. It is like a view from space. Can only see half the world at once. • All great circles passing through the point of tangency appear as straight lines. • Good for knowing the great circle path (I.e. shortest distances, important to navigators. Variations of Azimuthal Projections Conic: example:Lambert Conformal Conic Projection • One or more cones tangent to one or more parallels. Best for mid-latitudes in an E-W direction (U.S.) • A straight line is almost a perfect great circle route (planes use this) • Can be conformal or equivalent Variations on conic projections Transformations • The conversion between projections involving mathematical formulas. • Good GIS packages can do this. • Overlaying different projections is not possible.