Introduction to Cartography GEOG 2016 E

1. Introduction to CartographyGEOG 2016 E Lecture-2 Geodesy and Projections

2. What is Geodesy? • The science of geodesy determines: • Earth’s shape and • Interrelation of different points on earth’s surface • The true shape of the earth has been a topic of discussion for a long time • The problem gets complicated when this shape is projected on a flat surface to make a map • Projecting a curved surface on a flat surface distorts its features

3. Earth’s Shape • We all know that earth is not a perfectly symmetric sphere • Different shapes have been proposed: • Authalic Sphere: Has same surface area as an ellipsoid. It is used as the base figure for mapping • WGS 84 Ellipsoid: This is based on satellite orbital data • Clarke 1866 Ellipsoid: Based on ground measurements made in Europe, India, Peru, Russia and South Africa • Geoid: Closer to the real shape than any other shape. Obtained by approximating mean sea level in the oceans and the surface of a series of sea-level canals criss-crossing the continents

4. Geographic Uses of Different Shapes • Authalic Sphere: • Used for small scale map of countries and continents • Ellipsoid: • Used for large scale maps: topographic maps and nautical charts. GPS systems also assume ellipsoid shape. • Geoid: • Used as the reference surface for ground surveys for horizontal and vertical positions. Elevations are determined relative to mean sea level geoid.

5. Ellipsoid-Geoid Comparison

6. Map Projections • Earth’s surface is curved • How do we faithfully represent a curved surface on a flat surface? • Different methods have been proposed • None of them is perfect • Choice depends on application

7. Classification of Map Projections • Conformal Projections • Preserve local shape • Equal-Area Projections • Preserve area features – angle and/or scale may be distorted • Equidistant Projections • Preserve distances between certain points – scale is not maintained on the whole map • True-Direction Projections • Map great circles through the center point as straight lines

8. Alternative Classification of Map Projections • By geometric surface that the sphere is projected on: • Planar • Cylindrical • Conical • Each of these can be divided into subcategories depending on the position of the surface relative to the sphere

9. Planar Surface Projections • Also called azimuthal projections Planar Sphere touches the surface at only one point Secant Sphere touches the surface along a circle

10. Cylindrical Projections

11. Conical Projections Conic secant Cone touches the surface at a great circle and a small circle Conic surface Cone touches the surface at only one small circle

12. Mercator Projection • Mercator projection was first introduced by Belgian cartographer, Gerardus Mercator • It is a standard cylindrical projection.

13. Mercator Projection • Straight meridians and parallels that intersect at right angles • Scale is true at equator or at two standard parallels equidistant from the equator • Commonly used in marine navigation

14. Lambert Conformal Conic Projection • Directions are true in limited areas • Area and shape are distorted away from standard parallels

15. Albers Equal Area Conic Projection • Distorts scale and distance except along standard parallels • Directions are true in limited areas • Areas are proportional

16. Spatial Relationship between Projections