Date: 13/03/2015 Training Reference: 2015 GIS_01 Document Reference: 2015GIS_01/PPT/L2 Issue: 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

NameResponsibility Contribution fromGabriel ParodiLecturer ITC, University of Twente Edited byTesfaye Korme Team Leader and Training Manager, Particip GmbH Reviewed byMartin Gayer Project Manager, Particip GmbH Approved byRobert BrownTechnical Development Specialist (TDS), TAT

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 illustration of the geoid

Vertical datums  Altitudes (heights) are measured from the vertical datums  Mean sea level (geoid)  Different countries, different vertical datums. E.g.:  MSLBelgium 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 an d 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 semi-minor axis equatorial plane Pole Mathematically describable rotational surface

Commonly used ellipsoids

Local and global datums  A global vertical and horizontal datum: GRS80-GRS84.  Local datums are still much in use: transformation is required during this transitional period.

Datum transformations  It is mathematically straightforward.  It is a 3D transformation  3 origin shifts  3 rotation angles  1 scale factor ΔyΔy ΔxΔx Δα

Datum transformations  It is mathematically straightforward.  Every point on Earth has 3 coordinates in the every datum.  Then the solution is to find the 3D transformation of the fundamental axis to match the point.  3 origin shifts  3 rotation angles  1 scale factor

Translations (3 Parameters) Movement of points along an Axis XX ZZ YY

Rotations (3 Parameters) Movement of points around an Axis   

Scale (1 Parameter) Changing the distance between points S

Differences Between Horizontal Datums  The two ellipsoid centers called  X,  Y,  Z  The rotation about the X,Y, and Z axes in seconds of arc  The difference in size between the two ellipsoids  Scale Change of the Survey Control Network  S Z Y X System 1 WGS-84 System 2 NAD-27 XX  Z  Y   

7 Parameters XYZXYZ S R xyz + X’ Y’ Z’ = XYZXYZ

3 Parameters XYZXYZ + XYZXYZ 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 Equidistance Distances 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 0o0o Equator Central Meridian Greenwich 0 o 6 o … …..

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 )