1. Introduction to Cartography GEOG 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 surface Cone touches the surface at only one small circle Conic secant Cone touches the surface at a great circle and a 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