Faculty of Applied Engineering and Urban Planning

1. Faculty of Applied Engineering and Urban Planning Civil Engineering Department Introduction to Geodesy and Geomatics Position, Positioning Modes, and the Geodetic Models Lecture 2 Week 3 2nd Semester 2008/2009

2. Positioning in Geodesy Geodesy is interested in positioning points on the surface of the earth. • Simply “Position” means where something is!! • In geodesy, it has a more detailed meaning and involves several technical and mathematical considerations… • In geodesy, a position is a result of a measurement method on the surface of the earth based on a certain coordinate system and a reference model for the earth’s surface.

3. Coordinate System and Reference Model • A position cannot be expressed using a single quantity. • It is expressed in two or more quantities or parameters, called the “coordinates” of a point. • The coordinates of a point is based upon a certain coordinate system. • In geodesy, there are several coordinate systems being used from which the position of a point on the surface of the earth is being referred.

4. Coordinate Systems and Reference Model A coordinate system is then needed to be “put-on” a model that closely fits the surface of the earth. • In geometric geodesy, the earth is represented by an ellipsoid of revolution whose dimensions fits closely the surface of the earth. • This ellipsoid of revolution is known as the reference ellipsoid (other older literature termed this as “spheroid”). • The coordinate system and the reference system are the essential components of a reference framework.

5. Different Positioning in Geodesy • There are several positioning modes in the realm if geodesy: • Point Positioning • Relative Positioning • Kinematic Positioning/Navigation • Each positioning mode can be done using one or more surveying operations/methods by terrestrial, celestial, or orbital flatform.

6. Point Positioning • Point Positioning is the determination of the coordinates of points based on a fixed object not lying on the terrestrial surface. • It is not possible to determine either 3D or 2D (horizontal) positions of isolated points on the earth surface by terrestrial means. • For point positioning we must be looking at celestial objects, meaning that we must be using either optical techniques to observe stars (geodetic astronomy), or electronic/optical techniques to observe earth’s artificial satellites (satellite positioning).

7. Relative Positioning • It is the process of positioning of a point with respect to an existing point or points. • This mode of positioning is the preferred mode in geodesy. • The classical terrestrial techniques for 2D relative positioning make use of angular (horizontal) and distance measurements, which always involve two or three points.

8. Kinematic Positioning • As we have seen so far, classical geodetic positioning deals with stationary points (objects). • In recent times, however, geodetic positioning has found its role also in positioning moving objects, such as ships, aircraft and cars. • This application became known as kinematic positioning, and it is understood as being the real-time positioning part of navigation.

9. Kinematic Positioning and Navigation • The velocity vector can be measured on the moving vehicle in relation to the surrounding space, or in relation to an inertial coordinate system by an inertial positioning system.

10. Spatial reference systems and frames • The geometry and motion of objects in 3D Euclidean space are described in a reference coordinate system. • A reference coordinate system is a coordinate system with well-defined origin and orientation of the three orthogonal, coordinate axes. We shall refer to such a system as a Spatial Reference System (SRS).

11. Spatial reference systems and frames • A spatial reference system is a mathematical abstraction. • It is realized (or materialized) by means of a Spatial Reference Frame (SRF). • We may visualize an SRF as a catalogue of coordinates of specific, identifiable point objects, which implicitly materialize the coordinate axes of the SRS. • Object geometry can then be described by coordinates with respect to the SRF. • An SRF can be made accessible to the user, an SRS cannot.

12. Spatial reference systems and frames • Several spatial reference systems are used in the Earth sciences. • The most important one for the GIS community is the International Terrestrial Reference System (ITRS). The ITRS has itsorigin in the centre of mass of the Earth. The Z-axis points towards a mean Earth north pole. The X-axis is oriented towards a mean Greenwich meridian and is orthogonal to the Z-axis. The Y -axis completes the right-handed reference coordinate system

13. Spatial reference systems • Several spatial reference systems are used in the Earth sciences. • The most important one for the GIS community is the International Terrestrial Reference System (ITRS). The ITRS has itsorigin in the centre of mass of the Earth. The Z-axis points towards a mean Earth north pole. The X-axis is oriented towards a mean Greenwich meridian and is orthogonal to the Z-axis. The Y -axis completes the right-handed reference coordinate system

14. Spatial reference systems • The ITRS is realized through the International Terrestrial Reference Frame (ITRF), a catalogue of estimated coordinates (and velocities) at a particular epoch of several specific, identifiable points (or stations). • These stations are more or less homogeneously distributed over the Earth surface. They can be thought of as defining the vertices of a fundamental polyhedron , a geometric abstraction of the Earth’s shape at the fundamental epoch.

15. Spatial reference systems • Maintenance of the spatial reference frame means relating the rotated, translated and deformed polyhedron at a later epoch to the fundamental polyhedron. • Frame maintenance is necessary because of geophysical processes (mainly tectonic plate motion) that deform the Earth’s crust at measurable global, regional and local scales. • The ITRF is ideally suited to describe the geometry and behaviour of moving and stationary objects on and near the surface of the Earth.

16. Spatial reference systems and frames • Global, geocentric spatial reference systems, such as the ITRS, became available only recently with advances in extra-terrestrial positioning techniques. • The centre of mass of the Earth is directly related to the size and shape of satellite orbits (in the case of an idealized spherical Earth it is one of the focal points of the elliptical orbits), observing a satellite (natural or artificial) can pinpoint the centre of mass of the Earth, and hence the origin of the ITRS.

17. Modern Implementation of the ITRF in a region • It means: • First, a regional densification of the ITRF polyhedron through additional vertices to ensure that there are a few coordinated reference points in the region under consideration. • Secondly, the installation at these coordinated points of permanently operating satellite positioning equipment and communication links. Assignment 1 Check out this link and summarize the paper in not more than 200 words. http://www.gisqatar.org.qa/conf97/links/b3.html

18. Modern Implementation of the ITRF in a region The ITRF continuously evolves as new stations are added to the fundamental polyhedron. As a result, we have different realisations of the same ITRS, hence different ITRFs. A specific ITRF is therefore codified by a year code. One example is the ITRF96. ITRF96 is a list of geocentric coordinates (X, Y and Z in metres) and velocities (δX/δt, δY/δt and δZ/δt in metres per year) for all stations, together with error estimates. The station coordinates relate to the epoch 1996.0. To obtain the coordinates of a station at any other time (e.g., for epoch 2000.0) the station velocity has to be applied appropriately.

19. International Earth Rotation and Reference Systems Service (IERS) Established in 1987 (started Jan. 1, 1988) by IAU and IUGG to realize/maintain/provide: • The International Celestial Reference System (ICRS) • The International Terrestrial Reference System (ITRS) • Earth Orientation Parameters (EOP) • Geophysical data to interpret time/space variations in the ICRF, ITRF & EOP • Standards, constants and models (i.e., conventions) http://www.iers.org/

20. International Terrestrial Reference System (ITRS) Adopted by IUGG in 1991 for all Earth Science Applications • Realized and maintained by ITRS Product Center of the IERS • Its Realization is called International Terrestrial Reference Frame (ITRF) • Set of station positions and velocities, estimated by combination of VLBI, LLR, SLR, GPS and DORIS individual TRF solutions More than 800 stations located on more than 500 sites Available: ITRF88, 89,…,97, 2000 Latest: ITRF2005 http://itrf.ensg.ign.fr/GIS/index.php

21. Assignment 2 • Check out the web site: • http://itrf.ensg.ign.fr/GIS/index.php • What are the ITRF network stations that exist in occupied Palestine??! • What are the techniques used? • Search the following techniques: • GPS • DORIS • SLR • VLBI

22. ITRF2005 results • Polar Motion • Origin (Geocenter) and Scale time variations • Geophysical results • Plate motions • Post Glacial Rebound • Geocenter Motion • Surface Loading ==> Seasonal variation

23. Polar Motion Y(mas) X (mas)

24. ITRF2005 and Plate motion:Horizontal Site velocities

25. Vertical Velocities

26. The geoid and the vertical datum In first instance, we tend to describe our environment in two dimensions. Hence, we need a simple 2D curved reference surface upon which the complex 2D Earth topography can be projected for easier 2D horizontal referencing and computations. We humans, also consider height an add-on coordinate and charge it with a physical meaning. We state that point A lies higher than point B, if water can flow from A to B. Hence, it would be ideal if this simple 2D curved reference surface could also serve as a reference surface for heights with a physical meaning.

27. The geoid and the vertical datum To describe heights, we need an imaginary surface of zero height. Each level surface is a surface of constant height. However, there are infinitely many level surfaces. The most obvious choice is the level surface that most closely approximates all the Earth’s oceans. We call this surface the geoid.

28. The ellipsoid and the horizontal datum Can we also use the mean sea level surface to project upon it the rugged Earth topography? In principle yes, but in practice no. The mean sea level is everywhere orthogonal to the direction of the gravity vector. A surface that must satisfy this condition is bumpy and complex to describe mathematically. The mathematical shape that is simple enough and most closely approximates the local mean sea level is the surface of an oblate ellipsoid.

29. The ellipsoid and the horizontal datum Can we also use the mean sea level surface to project upon it the rugged Earth topography? In principle yes, but in practice no. The mean sea level is everywhere orthogonal to the direction of the gravity vector. A surface that must satisfy this condition is bumpy and complex to describe mathematically. The mathematical shape that is simple enough and most closely approximates the local mean sea level is the surface of an oblate ellipsoid.

31. The ellipsoid and the horizontal datum Can we also use the mean sea level surface to project upon it the rugged Earth topography? In principle yes, but in practice no. The mean sea level is everywhere orthogonal to the direction of the gravity vector. A surface that must satisfy this condition is bumpy and complex to describe mathematically. The mathematical shape that is simple enough and most closely approximates the local mean sea level is the surface of an oblate ellipsoid.

32. Local datum Historically, the ellipsoidal surface has been realized locally, not globally. An ellipsoid with specific dimensions — a and b as half the length of the major, respectively minor, axis — is chosen which best fits the local mean sea level. Then the ellipsoid is positioned and oriented with respect to the local mean sea level by adopting a latitude (φ) and longitude (λ) and height (h) of a so-called fundamental point and an azimuth to an additional point.

33. Local datum Historically, the ellipsoidal surface has been realized locally, not globally. An ellipsoid with specific dimensions — a and b as half the length of the major, respectively minor, axis — is chosen which best fits the local mean sea level. Then the ellipsoid is positioned and oriented with respect to the local mean sea level by adopting a latitude (φ) and longitude (λ) and height (h) of a so-called fundamental point and an azimuth to an additional point.

34. The ellipsoid and the horizontal datum The local horizontal datum is implemented through a so-called triangulation network. A triangulation network consists of monumented points forming a network of triangular mesh elements. The angles in each triangle are measured in addition to at least one side of a triangle; the fundamental point is also a point in the triangulation network. The implementation of the datum enables easy user access. The users do not need to start from scratch in order to determine the geographic coordinates of a new point.

35. Coordinate Systems • Recall… • • Position of a point is described by two or more coordinates based on a certain coordinate system… • • According to the previous discussion, there are general types of coordinates systems: • According to the parameters used: • 1. Rectilinear Type of Coordinate System • 2. Curvilinear type of Coordinate System • According to the surface/space dimension used: • 1. Linear (One-Dimension) Coordinate System • 2. Planar (Two-Dimensional) Coordinate System • 3. Space (Three-Dimensional) Coordinate System

36. Coordinate Systems • In geodesy, we are concern on positioning points on the three-dimensional surface of the earth which can be represented in a two-dimensional or three-dimensional geodetic models. • In the study of geodesy, coordinate system is under both rectilinear and curvilinear type on a planar or three dimensional surface.

37. Coordinate Systems • In studying Geometric Geodesy, three coordinate systems are commonly in use: • The Cartesian-Space Rectangular Coordinate System • The Geodetic Coordinate System • The Map-Grid Coordinate System

38. Cartesian-Space Rectangular Coordinate System a rectilinear type of coordinate system on a three-dimensional surface where the position of the points is expressed as coordinates of a righthanded orthogonal system whose origin coincides with the center of the ellipsoid, XZ-plane defines the zero meridian and XY plane defines the equator Uses (X,Y,Z) as its coordinate components

39. Geodetic Coordinate System (Geographic Coordinate System) a curvilinear type of coordinate system on three-dimensional space which uses a an surface to define the position of point on the earth. This coordinate system also uses three parameters to define the position of a point: 1. Geodetic latitude (φ): the angle between the ellipsoid normal through the point and the equator. (0≤ φ ≤ 90N or S) 2. Geodetic Longitude (λ): the angle in the equatorial plane between the zero meridian and the meridian of the point. (0 ≤ λ ≤180E or W) 3. Ellipsoidal height (h): the distance along the normal from the surface of the ellipsoid to point P.

40. Geodetic Coordinate System

41. Map-Grid Coordinate System (Projected Coordinate system) A rectilinear type of coordinate system on a planar surface where the horizontal position of a point is defined. The idea of which is to make the curved surface of the Earth by some mathematical transformation (map projection) into a plane. It uses basically two parameters to define the position of a point: Northing, N (or y) Easting, E (or x) • The third component of the position of a point which is the Elevation becomes an attribute in this coordinate system