1. GEOG 268: Cartography Ohio Northern University Winter 2001-2002 Hill 200

2. Geodesy  Mapping involves determining locations on earth, transforming positions onto flat map, graphically symbolizing those positions  Geographic locations determined by geographic coordinates  Latitude and Longitude  to establish a system of geographic coordinates, we first have to know the Earth’s size and shape

3. Designing base map & overlay  Generalizing process: Selection Classification: process in which objects are placed in groups with similar features Simplification: smoothing natural lines Symbolization:  replicative, or  abstract  where do we start?

4. Size and Shape of the Earth The development of a base map begins from a small model of the real earth. Cartographer needs knowledge of earth’s geographic grid as shown on perfect sphere to create projection Today?: irregular surface approximating an ellipsoid

5. Geodesy  Earth is very smooth geometrical figure  smoother than a bowling ball !  Cartography begins with approximating the Earth’s size and shape:  increasingly accurate approximations of Earth’s shape:  sphere  ellipsoid  geoid

6. Geodesy Earth’s shape? Pythagoras (6 th century BC), and Aristotle  round Earth (sailing ships) Earth’s size? Eratosthenes (250 BC):  Deep well in Aswan, sun overhead Solstice  Next solstice: angle of sun Alexandria  Circumference? 28,750 mi. (15% more)  Real circumference? ~ 24,000 miles

7. Spherical Earth Earth not perfect sphere but ellipsoidal cartographers use sphere with same surface area as ellipsoid:  authalic sphere: basic figure for mapping  3,959 mi. standard radius (WGS 84 ellipsoid)

8. Ellipsoidal Earth Until 1670s, Earth perfect sphere Newton: gravity causes flattening at poles  amount ~ 1/300th polar radius vs eq. Radius  satellite measurements = 1/298  3D fig. oblate ellipsoid (or oblate spheroid)  at least 11 different values used worldwide based on location.  Example: WGS 84 & GRS80 satellites  Example: Clarke 1866 ground observations

9. Geoidal Earth Even more accurate figure of the earth: Geoid (earth-like)  3D “equipotential” surface (mean sea level)  gravity everywhere = mean sea level gravity  geoid shape - irregular surface features  geoid deviates from ellipsoid because of  rock density & topography  deviates up to 300 ft. in certain places

10. Cartographic use of Sphere, Ellipsoid, Geoid All 3 are different approximations of the Earth’s surface Authalic sphere used as reference surface for small scale maps Ellipsoid used as a ref. for large scale mapping distances, directions and areas would be more correct at individual locations than sphere GPS compute lat/long and elevation using WGS 84 ellipsoid as reference surface Geoid  length of degree varies from equator to poles  used for local large scale ground based surveys