Geodesy and map projections., Lecture notes of Environmental Science

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Geodesy and Map

Projections 2

Projected Coordinate Systems

• (^) Uses a rectangular or plane coordinate

system

• (^) A rectangular system is used to locate

positions on a flat map

• (^) Has a known point of origin called a

Reference Point.

• (^) Positions on the map can be specified in

terms of x and y coordinates, usually

measured in metres

• (^) This reference system is known as

Cartesian coordinate system.

Map Projections - Definition

• (^) Transferring information from a 3

dimentional (3D) spherical earth to a 2

dimentional (2D) surface e.g a plane sheet

of paper, a computer screen.

• (^) Also defined as a mathematical

transformation

Map Projections cont’d

• (^) Generally three ways to perform projections in GIS
  • (^) from a spherical geographic to a plane geographic system
  • (^) from a geographic to a projected coord system
  • (^) From a projected to a projected
• (^) When a feature lacks the projection, you have to specify the projection. In ArcGIS, this is done in the ArcTool box using the option “Define Projection”.
• (^) Features lack projections because their creator did not specify them at the beginning or it may be that the features lost their projections in the course of transfer.
• (^) However, when a converting from a geographic to a projected or from one projected coord system to another, in ArcGIS ArcToolbox, use the option called “Project”.

Projection Parameters

• (^) When performing map projections in GIS, the

following aspects or parameters should be

considered among others:

• (^) The projection or projection name
• (^) Spheroid (ellipsiod)
• (^) Central meridian (longitude of origin where

the projection begins)

• (^) Datum also known as the starting point of

measurement for the projection

• (^) Units e.g meters
• (^) Coordinate system (geographic or projected)

Datum

• (^) Defined as a point of reference used to measure locations on the surface of the earth. It defines the origin and orientation of the lines of latitude and longitude.
• (^) A datum is always related to a spheroid that simulates the shape of the earth.
• (^) Two types: Local and earth-centred (also called geocentric) datum.
• (^) A local datum is aligned so that it closely corresponds to the earth's surface for a particular area.
• (^) In local datum, earth’s centre does not fit the centre of the spheroid.
• (^) An earth-centered datum has its origin placed at the earth's currently known center of mass.

Datum cont’d

• (^) Local datum changes with natural causes (e.g earth quakes) or due to change in country or international mapping policies.
• (^) Current local datum in South Africa (since January
  1999. is the Hartebeesthoek 1994 situated near Pretoria. It uses the World Geodetic System 1984 (WGS84) spheroid (universal)
• (^) The old datum was called the Cape datum which had its origin point at Buffelsfontein near Port Elizabeth. It used the clarke 1880 spheroid (used only by a no. of countries).
• (^) Reason for change is due to change a universal ellipsoid for international

Classification of Map Projections

• (^) There a many classifications based on several factors, two classification types are here discussed.

1. Based on properties retained  (^) Equal area – preserve the area of objects, e.g. Albers’ equal area, Lambert’s equal area  (^) Conformal – preserve the shape of small objects, show correct direction, e.g. Mercator, Universal Transverse Mercator (UTM)  (^) Equidistant – preserve distances between objects and features, e.g Azimuthal equidistant, Equidistant conic and the Equidistant cylindrical.  (^) True-direction – Retains direction from one point to the other, e.g lambert Azimuthal equal-area projection

Classification cont’d

• (^) Cylindrical Projection e.g Transverse Mercator, Universal Transverse Mercator Mercator Transverse Mercator http://www.nationalatlas.gov

Classification cont’d

• (^) Planar projection e.g Aitoff, Azimuthal equal area projections http://www.nationalatlas.gov

Some Projections cont’d

• (^) Universal Transverse Mercator (UTM)
  • (^) Here, the whole world is divided into narrow

zones 6

o

apart within which features are projected

correctly.

• (^) Each 3 rd

longitude is the central meridian for each

zone.

• (^) Altogether 60 zones starting with zone 1 ( 180 o

o

W) to zone 60 ( 174

o

o

E).

• (^) The equator divides each zone into two halves

South and North e.g Durban is in zone 36S

Some Projections cont’d

• (^) Gauss Conformed System
  • (^) Also called the LO system
  • (^) LO stands for longitude of origin
  • (^) These are all the odd longitudes stretching across South Africa from west coast to the east coast e.g 17, 19 ......33.
  • (^) It projects areas correctly along these longitudes and both sides to the next even number meridian e.g the LO near Cape Town is 19, hence all areas along 19 and on both sides i.e 18 – 20 will be correctly projected.
  • (^) This projection is only used in South Africa
  • (^) It uses the Hartebeesthoek 1994 datum and the WGS ellipsoid

Deciding Which Projection to use

• (^) If the area extend horizontally over the whole country, it may be preferable to use Albers Equal Area Conic
• (^) If it extends elongated vertically but wide, may be use Transverse Mercator
• (^) If it is vertically narrower, maybe use UTM or LO system (Gauss Conformed)
• (^) When it comes to preserving shape, area, distance, etc see Classification based on properties retained above.

Other Map projections used Globally

• (^) See Pdf notes posted on //learning.ukzn.ac.za Entitled “Understanding map projections”