Date: 13/03/2015Training Reference: 2015 GIS_01

Document Reference: 2015GIS_01/PPT/L2Issue: 2015/L2/1/V1

Addis Ababa, Ethiopia

GIS

Coordinate Systems

Instructor: G. Parodi

Implementation of the Training Strategy of the Monitoring for Environment and Security in Africa

(MESA) Programme

  Name Responsibility

Contribution from Gabriel Parodi Lecturer ITC, University of Twente

Edited by Tesfaye Korme  Team Leader and Training Manager, Particip GmbH 

Reviewed by Martin Gayer  Project Manager, Particip GmbH 

Approved by Robert Brown Technical Development Specialist (TDS), TAT

GIS Trainer: Mr. Gabriel ParodiDepartment of Water Resources, Geo-Information Science and Earth Observation (ITC) at the University of Twente, Enschede, The Netherlands.

MESA Training Contractor: Particip-ITC-VITO Consortium

Consortium partners

Particip GmbHwww.particip.deMartin Gayer: martin.gayer@particip.de

ITC – Faculty of Geo-Information Science and Earth Observationwww.itc.nlChris Mannaerts: c.m.m.mannaerts@utwente.nl

VITO – Remote Sensing Unit Applications Teamwww.vito.beSven Gilliams: sven.gilliams@vito.be

Particip is the main Contractor

Short Introduction

Spatial referencing

(a) International Terrestrial Reference System: ITRS (b) International Terrestrial Reference Frame: ITRF

Two spatial referencing systems

Geographical coordinates Cartesian coordinates

Reference surfaces: Geoid & Ellipsoid

The Vertical datum : The Geoid

To describe height we need a imaginary zero surface. A surface where water doesn’t flow is a good

candidate. Geoid: Level surface that most closely approximates all

Earth’s oceans. Main ocean level was recorded locally, so there are

many parallel “vertical datums”.

Exaggerated illustrationof the geoid

Vertical datums

Altitudes (heights) are measured from the vertical datums Mean sea level (geoid) Different countries, different vertical datums. E.g.: MSLBelgium - 2.34 m = MSLNetherlands

Ellipsoids and horizontal datums

To describe the horizontal coordinates we also need a reference. To “project” coordinates in the plane we need a mathematical representation. The

geoid is only a physical model. The oblate ellipsoid is the simplest model that fits the Earth (also oblate spheroid) The ellipsoid is selected to fit the best mean local sea level. Then the ellipsoid is positioned and oriented with respect to the local mean sea level

by adopting a latitude, a longitude and a height of a fundamental point and an azimuth to an additional point.

Horizontal datums

Datum: ellipsoid with its location. The ellipsoid positions are modified by the datums.One datum is built for one ellipsoid, but one ellipsoid can be used by several datums!

Datum shifts (1)

Datum shifts (2)

Care: A wrong datum and you miss the point!!

Ellipsoid

semi-major axis

sem

i-min

or

axis

equatorialplane

Pole Mathematically describable rotational surface

Commonly used ellipsoids

Name Date a (m) b (m) UseEverest 1830 6377276 6356079 India, Burma, Sri Lanka

Bessel 1841 6377397 6356079 Central Europe, Chile,Indonesia

Airy 1849 6377563 6356257 Great brittainClarke 1866 6378206 6356584 North America, PhilippinesClarke 1880 6378249 6356515 France, Africa (parts)Helmert 1907 6378200 6256818 Africa (parts)International(or Hayford)

1924 6378388 6356912 World

Krasovsky 1940 6378245 6356863 Russia, Eastern EuropeGRS80 1980 6378137 6356752 North AmericaWGS84 1984 6378137 6356752 World (GPS measurements)

Datum transformations

It is mathematically straightforward.

It is a 3D transformation 3 origin shifts 3 rotation angles 1 scale factor

Δy

Δx

Δα

Translations (3 Parameters)

Movement of points along an Axis

X

Z

Y

Rotations (3 Parameters)

Movement of points around an Axis

Scale (1 Parameter)

Changing the distance between points

S

7 Parameters

XYZ

S Rxyz+

X’Y’Z’

=XYZ

3 Parameters

XYZ

+XYZ

X’Y’Z’

=

Classes of map projections

A map projection is a mathematical described technique of how to represent curved planet’s surface on a flat map.

There’s no way to flatten out a pseudo-spherical surface without stretching more some areas than others: compromising errors.

Secant projections

A transverse and an oblique projection

Azimuthal projection

Cylindrical projection

Conic projection

Properties of projections

Conformality Shapes/angles are correctly represented (locally)

Equivalence ( or equal-area )Areas are correctly represented

EquidistanceDistances from 1 or 2 points or along certain lines

are correctly represented

Conformal projection

Shapes and angles are correctly presented (locally). This example is a cylindrical projection.

Equivalent map projection

Areas are correctly represented. This example is a cylindrical projection.

Equidistant map projection

Distances starting one or two points, or along selected lines are correctly represented. This example is a cylindrical projection.

Compromise projection (Robinson)

Principle of changing from one into another projection

Comparison of projections (an example)

Universal Transverse Mercator: The UTM coordinate system

Transverse cylindrical projection: the cylinder is tangent along meridians

60 zones of 6 degrees Zone 1 starts at longitude 180° (in the Pacific

Ocean) Polar zones are not mapped X coordinates – six digits (usually) Y coordinates – seven digits (usually)

UTM-Zones

0oEquator

Central M

eridian

Greenw

ich

0o 6o

…. 29 30 31 32 …..

Two adjacent UTM zones

Classification of map projections

Class• Azimuthal• Cylindrical• Conical

Aspect• Normal• Oblique• Transverse

Property• Equivalent (or equal-area)• Equidistant• Conformal• Compromise

Secant or Tangent projection plane

( Inventor )