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Unification of the Georeferencing Systems of GIS Spatial Data Infrastructure
Dr Kamal Abdellatif Abdalla
Surveying and Mapping Directorate,
Al Ain Town Planning Department
P. O. Box 1339, Al Ain, UAE
Email: drka@alainplanning.gov.ae
1. Introduction
Technological advancements in GPS positioning and GIS implementations and processing have provided the ability to perform precise georeferencing and produce high quality spatial data infrastructure. This ability, together with the applications of continuously operating reference stations (CORS) and the expanding use of geodetic control in support of spatial information systems, demands the adoption of reliable procedures to support georeferencing of spatial data and GIS activities. The continuing evolution of GPS and GIS hardware and software as well necessitate the adoption of standards and specifications in planning, methodologies, and implementation of both systems.
The impact of GPS on geodetic control surveying, assisted the geomatics community with a powerful tool for the establishment of precise geodetic control. This evolution has brought with it reduction in cost and an increased demand for geodetic control services. GIS users and spatial data developers rely on georeferencing and on the standards and specifications adopted to ensure the given level of product consistency. In order to produce or update spatial data a geodetic network is necessary. Such a network consists of a number of points spread across the area under consideration, these points are usually in the form of monuments established and placed in the ground, along with a high-accuracy positional value for each point. Traditionally, there have been completely separate networks for horizontal and vertical control, but some and recent networks combine the two on common monuments. By referencing spatial data to such a network, the resulting data and information from multiple local survey activities can be accurately connected.
The diversity of datums in use today and the technological advancements that have made possible global positioning measurements requires careful datum selection and careful conversion between coordinates in different datums. It is well known that the current, and growing, trend towards the use of satellite positioning systems and global satellite mapping systems to produce position-based products in a global reference frame can introduce serious practical difficulties if the results need to be related to older maps and/or digital data. Special problems arise, for instance, in the fields of updating, map revision, cadastral surveying and geomatics operations to support spatial data production. The difficulty fundamentally arises because of the need to transform the data into the coordinate systems used to describe the older data. In principle, coordinate transformations are straightforward mathematical procedures but in practice they can cause serious problems.
The required accuracy for a control survey depends primarily on its purpose. Factors that affect accuracy are type and condition of equipment used, field procedures adopted, and the experience and capabilities of personnel employed. Through years different sets of detailed standards of accuracy and specifications for geodetic control are published.
2. Earth Surfaces and Models
Geodesy deals with the earth surface and the other surfaces used for computation of control points and representation of spatial data, namely the ellipsoid and geoid surfaces. These surfaces can be defined as follows.
(a) The earth has a highly irregular and constantly changing surface. Models of the surface of the earth are used in navigation, surveying and mapping. Topographic and sea level models attempt to model physical variations of the surface, while gravity models and geoids are used to represent local variations in gravity that change the local definition of a level . The topographical surface of the earth is the actual surface of the land and sea at some moment in time. Sea level is the average surface of the oceans. Tidal forces and gravity differences from location to location cause even this smoothed surface to vary over the globe by hundreds of meters. Gravity models attempt to describe in detail the variations in the gravity field. The importance of this effort is related to the idea of leveling. Local variations in gravity, caused by variations in the earth’s core and surface materials, cause this gravity surface to be irregular. Future trends of GIS may focus in representing and analyzing the physical and geophysical information an important spatial data infrastructure.
(b ) The ellipsoid is generated by the revolution of an ellipse about its minor axis;. The ellipsoid is considered to represent simplified figure of the earth and used as the fundamental reference surface for horizontal coordinates. This figure is flattened towards the earth's poles (Figure 2). The size of the ellipsoid is defined by its semi-major axis (a) and minor axis (b); its geometrical shape is defined by the flattening (f=1-b/a), while reference ellipsoids are usually defined by the semi-major axis and the flattening .
Figure 1. The relation between the earth surface, ellipsoid and geoid
Figure 2. An ellipsoid with semi-major axis a and semi-minor axis b
(c) The geoid (Figure 1) is the equipotential surface of the earth's gravity field, which corresponds most closely with mean sea level and extends continuously through the continents and used as zero reference for orthometric heights. However, the geoid is a geometrically and mathematically complicated surface, which is impractical to use for mapping purposes. The knowledge of the geoid is necessary for automatic transformation of the ellipsoidal heights to orthometric heights and vice versa.
The ellipsoidal height (Figure. 1) is a purely geometrical quantity, the length of the normal to the reference ellipsoid between the ellipsoid and the point of interest. The orthometric height, on the other hand, is defined as the length of the line that is always normal to the equipotential surface of the gravity field, between the geoid and the point of interest and is related to the gravity field of the earth. The relationship between the orthometric height, h, the ellipsoidal height, H, and the geoidal height, N can be given by the following approximation:
h = H + N (1)
Regional ellipsoids have generally been established using astronomical observations to define the deflection of the vertical (difference between geoidal and ellipsoidal normals) to be zero at an origin point. The orientation and scale of the ellipsoid is defined using further geodetic observations. Once the best fitting regional ellipsoid has been defined, it is adopted as the reference surface for geodetic positions in that region. The available geodetic observations are then adjusted, applying the least squares technique, to form the regional datum based on that reference ellipsoid.
A global ellipsoid (such as WGS84) corresponds to a best fit to the geoid over the entire earth. Early attempts to define the global ellipsoid used both gravity and arc measurements. The first internationally recognized global ellipsoid was the 1924 International Ellipsoid. The advent of satellite-derived geodetic data enabled improved determinations of the global ellipsoids. Furthermore, such ellipsoids are geocentric, which means that their geometrical centre corresponds with the earth's centre of mass. The orientation of the ellipsoid is achieved by aligning its minor axis with the earth's mean spin axis at a particular time. The next internationally recognized global geocentric ellipsoid, which was derived with the inclusion of refined and superseded by the Geodetic Reference System 1980 (GRS80), which is also geocentric, with a=6378137 metres and f=1/298.257222101 (Moritz, 1980).
In addition to defining the geometrical size and shape of the earth, physical parameters are associated with global ellipsoids. These are the product of the Newtonian gravitational constant and the mass of the earth (GM), the angular velocity of the earth's rotation, and the dynamical form factor. This factor is used to derive the flattening of the ellipsoid (Heiskanen and Moritz, 1967; Moritz, 1980). These additional physical parameters allow a model gravity field to be computed. The most recent and widely used global geocentric ellipsoid is the World Geodetic System 1984 (WGS84), which based on the GRS80 ellipsoid, but with f=1/298.257223563.
In georeferencing system the study of the gravity field is usually taken into account.
Gravity anomalies can be derived from land observations or satellite radar altimeter data, and can be used for geoid determination and gravity anomaly maps production.
3. Geodetic Coordinate Systems
Geodesy is interested in positioning points on the surface of the earth. For this task a well-defined coordinate system is needed. Many coordinate systems are being used in georeferencing, mainly local and geocentric coordinate systems. The coordinates systems use both Cartesian and curvilinear coordinates. The geocentric systems have their z-axis aligned with the instantaneous spin axis of the earth and became more useful, with the advent of satellite positioning. The non-geocentric systems are used for local coordinate systems, in such case their origin would be located at a point on the surface of the earth.
Both the geocentric and local geodetic coordinate systems are used together with reference ellipsoids. These reference ellipsoids are taken to be geocentric or near geocentric, with the axis of revolution coinciding with the z-axis of the coordinate system. The basic idea behind using the reference ellipsoids is that they fit the real shape of the earth, as described by the geoid. Basically, reference ellipsoids are the horizontal surfaces to which the geodetic latitude and longitude are referred. As well the ellipsoid is associated with the Cartesian coordinate system, and must be fixed with respect to the earth. Such an ellipsoid is often called a horizontal datum. The horizontal geodetic coordinates (Latitude, f, and longitude, l), together with the ellipsoidal height, H, make the basic curvi-linear coordinates system. They are related to their associated Cartesian coordinates X, Y and Z by the following expression:
Where
v : The radius of curvature of reference ellipsoid,
a : Semi major axis of the reference ellipsoid.
E : the eccentricity. And
H : the ellipsoidal height.
In recent years, the International Terrestrial Reference System (ITRS), is fixed to the earth through several permanent stations whose horizontal velocities are monitored and recorded. The fixing is done at realization of the ITRS by means of coordinates of some selected points is called the International Terrestrial Reference Frame (ITRF). Transformation parameters needed for transforming coordinates from one epoch to the next are produced by International Earth Rotation Service (IERS), which keep track of the time evolution of the positions.
Many organizations recommend that the coordinate system used for the Framework should meet the criteria of global consistency. This is most convenient when the GIS spatial data expand beyond the extent of national boundaries, using global datums.
Global Coordinate Systems are coordinate systems to specify locations on the surface of the earth and have defined three-dimensional positions with respect to the center of mass of the reference ellipsoid. The Z-axis points toward the North Pole; The X-axis is referenced to the intersections plane defined by the prime meridian and the equatorial plane. The Y-axis completes a right-handed orthogonal system by a plane 90 º east of the X-axis and its intersection with the equator.
4. Geodetic Datums and Reference Systems
The datum can be defined, in simple terms, as a mathematical model of the earth or a reference surface consisting of five quantities: the latitude and longitude of an initial point, the azimuth of a line from the point, and two constants necessary to define the reference ellipsoid. It forms the basis for the computation of horizontal control surveys. In general it is a geometric reference system defined by one or more known positions that serve as a basis for computation of other positions. While the geodetic reference system is defined by an expression of the gravity field, the scale, geoid and ellipsoid. Usually the geographical coordinates of known points in the region to be mapped comprise the datum. Therefore, there is a distinction between the ellipsoid and the datum: The ellipsoid is a geometrical reference surface, whereas the datum is the adopted coordinate set, which is based on a particular ellipsoid. Therefore, not all geographical latitudes and longitudes of the same surface location are equal, but depend upon the ellipsoid and coordinate datum to which they are referenced. Control points are locations that have coordinates, which are derived from a reference frame. Reference frames may take many forms, including assumed coordinates for local reference systems. However in order to be able to share information among various GIS agencies for the same area, it is important to have a common frame of reference. This common reference system is the national geodetic reference system for the country and can be called National Spatial Reference System.
Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications that completely describe the size, shape, orientation, gravity field, and angular velocity of the earth. Referencing geodetic coordinates to the wrong datum can result in position errors. Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems and for precise positioning systems.
A horizontal datum references the location and a vertical datum references elevations. International GPS Service, IGS, was established in 1994 by the International Association of Geodesy, IAG, to support the International earth Rotation Service (IERS) by collecting GPS observations from global networks of continuously operating reference stations. The IERS maintains two primary reference systems: celestial and terrestrial. The celestial reference system provides the context for the Earth-Centered, Earth-Fixed terrestrial reference system. Realization of this system is made by three technologies in addition to GPS: Very Long Baseline Interferometry (VLBI), Doppler Orbitography by Radiopositioning Integrated on Satellite (DORIS), and Satellite Laser Ranging. The International GPS Service (IGS) network of GPS reference stations form global baselines which are periodically least squares adjusted to a set of coordinates and reported annually as the International Terrestrial Reference Frame, ITRF. However, since there are tools to convert data between the ITRF and other coordinate systems, GIS data can be pre-processed for conformance with ITRF. Further, commonly available software supporting the viewing of geographic coordinate-based data supports the dynamic projection of this data for interactive distance determinations and map production.
The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). Parameters for simple XYZ conversion between many datums and WGS-84 are computed and published. Datum conversions are accomplished by various methods. Complete datum conversion is based on seven parameter transformations that include three translation parameters, three rotation parameters and a scale parameter, an example for such transformation is given by Molodensky model as follows:
where
XD, YD, ZD : 3- d coordinates in Datum D,
XS, YS, ZS : 3- d coordinates of control in Datum S.
DX, DY, DZ : Translation parameters in X, Y, Z directions between datum D and S.
Rx, Ry, Rz : Rotations around X, Y, and Z axes between datum D and S.. DL : difference in scale factor.
The Standard Molodensky formulas can be used to convert latitude, longitude and ellipsoid height from one geocentric datum to anther datum.
A regional or geocentric datum comprises geographical coordinates that are referenced to the surface of a particular reference ellipsoid. As illustrated above, a single ground point can have different geographical coordinates by virtue of the datum and the ellipsoid used, and the regional reference ellipsoid is chosen so as to fit the geoid, as closely as possible, over the area to be mapped. This approach enables subsequent geodetic and spatial data, which are collected on the physical surface of the earth, to be reduced to the surface of the ellipsoid..
5. Horizontal Control of Spatial Data
Horizontal geodetic control networks can be established by a number of different methods, however GPS has become the most widely used method due to its efficiency and superior results. These networks provide positional information with reference to the adopted horizontal datum
In order to place spatial data into a large spatial context, a geodetic control network will be used. Such a network consists of a number of monumented points, spread across the area, along with a high-accuracy positional value for each point. By referencing field measurements to such a network, the resulting data and information from multiple local survey projects can be accurately connected. A control network itself is established by highly precise surveying methods followed by a statistical adjustment to reconcile all of the measurements. For each monument the result is a published positional value along with a stated accuracy level. While control surveying work may be carried out incrementally over time, with the new measurements adjusted to the existing network. The control point established some years ago might have multiple positional values, each successive value published as part of a fresh adjustment.
Actually, geodetic control is typically separated into two components: horizontal (latitude/longitude) and vertical (elevation). This is because latitude/longitude and elevation are based on completely different concepts and measurement methods. Even today, GPS can provide extremely high-accuracy horizontal results, a more traditional method is required to establish vertical control. While a network point may have geodetic-quality values for both horizontal and vertical, the methods of determining these values will still be different.
The horizontal geodetic networks of national extent, sometimes called national control networks, have been the main tools for positioning needed for spatial data acquisition and in mapping, boundary demarcation, and other geodetic applications. The national networks are usually interconnected to create continental networks. The transformation between coordinates must take into account the errors in both coordinates sets. A transformation of coordinates thus consists of two distinct components: the transformation between the corresponding coordinate systems as described above, plus a model for the difference between the errors in the two coordinate sets.
6. Vertical Control
Vertical control networks are a series of points on which precise heights, or elevations, have been established. Vertical control stations are typically called Bench Marks (BM) as part of a vertical information network, the benchmark's elevation is known relative to a vertical datum, usually approximating the mean sea level. The vertical accuracy standard is usually referenced to the standard specifies a linear value within which the true or theoretical location of the point falls 95 percent of the time. Once the levelled height difference is obtained from field observations, one has to add to it a small correction based on gravity values along the way, to convert it to either the orthometric, dynamic or normal height difference. Geodetic levelling is probably the most accurate geodetic relative positioning technique. Modern techniques are inherently three-dimensional: simultaneous observations at two points yield three-dimensional coordinate differences that can be added directly to the coordinates of the known point to get the required coordinates of the unknown point.
The zero surface to which elevations or heights are referred is called a vertical datum, which is associated with the Mean Sea Level (MSL). The mean sea level (MSL) is determined by continuously measuring the rise and fall of the ocean at tide gauge stations. This averages out the highs and lows of the tides caused by the changing effects of the gravitational forces from the sun and moon which produce the tides. The MSL then is defined as the zero elevation for a local or regional area. MSL is a close approximation to the geoid, which is the true zero surface for measuring elevations. Heights obtained from geodetic leveling are known as orthometric heights (Figure 1). The orthometric heights are usually reflect local variations in gravity as well as changes in topography.
As stated, GPS, on the other hand, produces a much different kind of height. Whether one uses point, differential, or differenced carrier phase positioning, one obtains a set of XYZ coordinates that depend upon locations of base stations and satellite positions. These three-dimensional, geometric relationships, in contrast to geodetic leveling, do not depend on local gravity variations. Since XYZ coordinates do not directly express ellipsoidal or orthometric heights, it is necessary to transform them into a different coordinate system. Typically, XYZ are transformed into geodetic latitude, longitude and ellipsoidal height (see equation 3 ).
The justification of a global vertical datum adopting unification approach, can be summarized (Heck and Rummel, 1990), as follow:
7. Georeferencing and GIS Spatial Data
Geographic Information Systems require georeferencing of spatial data for a variety of reasons, such as: collection and processing of spatial data, establishing of mapping relationship to other existing data, updating, discovering and potentially reconciling discrepancies between conflicting data sets; providing a reference coordinate system for GIS applications, to reduce mapping errors as new data are created , to constrain mapping errors within a geographic area, to improve the spatial accuracy of existing data sets; conversion of maps into digital format for GIS. Georeferencing is fundamental in data sharing and in the integration of spatial data from various sources into a single consistent data set. This is often achieved using a single common geodetic reference frame, or datum. A number of factors have led to an increasing need to georeferencing and to base spatial data products on a common reference frame that extends across the whole globe. These factors include growing reliance on satellite positioning systems and development of satellite based mapping systems affording increasingly higher resolution. Another major influence is the trend to spatial data infrastructures with national, regional and even global coverage.
To handle most of the problems of spatial data, there is a need for a good understanding of the definition and realization of georeferencing. A practical approach to georeferencing implementation is the need to be in accordance with agreed standards and guidelines addressed by several international organizations. As well the information describing coordinate reference frames, often referred to as coordinate system metadata that used by the industry and many national and international standards organizations as well as industry are categorized as standards for geometics and non-geomatics activities. Beginning in the 1980s, national standards for spatial data infrastructure and geographic information have been drafted in several countries and international organizations.
Practically spatial coordinates based on local or global reference systems are usually converted to a map projection system for both spatial representation and map production. The projections are not defining ellipsoid or geodetic datum. The most common projection used for spatial data to high accuracy is the Universal Transverse Mercator projection (UTM), which is usually adopting the required reference system and practically suited to maps of north south extent. In the future, it is more likely that spatial data is to be drawn on the surface of global ellipsoid based on latitude and longitudes rather than UTM grids. Airborne and space borne georeferencing techniques are likely to include 4- dimensional approach, and be integrated with georeferencing systems in conjunction with aerial or space frames for digital photogrammetric and remote sensing mapping.
Unification and georeferencing will help in increasing the quantity and quality of data sharing and integration capabilities of GIS networks, and can be used for studying the physical phenomena (Cmbrinck et. Al, 2003), that related to spatial data as a function of time, such as crustal dynamics and movements, tide effects, gravity fields, magnetic fields and ionospheric mapping. This will also help in initiating regional geoids and gravity anomaly maps production.
Different sets of detailed standards of accuracy and specifications for geodetic surveys are to be considered to get reliable georeferencing of spatial data. Many GIS systems handle high quality vector and raster data and digital terrain models (DTM) from a wide variety of sources including, satellite imagery, aerial photography and Ladar scanning, the quality of their end product depends very much on the accuracy of georeferencing..
The revolution in GPS has not been confined to the surveying community, but has extended into mapping, spatial data infrastructure, and Geographic Information System (GIS). Now widespread integration between GIS and GPS are available, in various activities of GIS applications including mobile GIS, monitoring and tracking activities. Many of these applications require accurate positioning, and, a common requirement is the transformation of GPS heights into heights above mean sea level or the geoid. The adoption of georeferencing system will enable the production of a homogeneous series of maps and spatial data, which will meet user requirements. However, this change will also have far-reaching implications for the users and producers of maps and spatial information systems all around the world. However, georeferencing deals with positioning which is the fundamental element of GIS base maps and spatial data in terms of usage, analysis, and features location accuracy and the reliability of any information derived from the GIS system. Georeferencing will also, help in ensuring that all maps or layers in GIS database overlay accurately and the data set is georeferenced to a common coordinate system, and it playing a major role in constructing, displaying and analyzing different GIS layers and giving more abilities to the GIS system in using spatial data for analysis and measurements of length, size, area and shape.
9. Conclusions
Georeferencing can be considered as a common geospatial data item to many GIS applications and provides key elements for integration and sharing of spatial data and thematic information. The unification and implementation of global reference systems will lead to: better accuracy in connection with national and regional datums; removal of systematic regional biases in gravity anomaly data; enhancing, and converting national and regional datums to global reference systems.
The paper recommended that future spatial data representation should focus on the surface of reference ellipsoids; and the planning for unification of georeferencing systems should incorporate IGS stations at national and regional levels. Global or regional spatial reference systems should be initiated to provide national and global framework for spatial data. It should be characterized by accuracies compatible with modern positioning technologies and facilitate sharing of geospatially referenced data between various governments and spatial data users. Georeferencing is important as it relate the global reference systems to the time dimension. This time dimension will give another angle of view to the spatial data that represent a region geometry and spatial topology at certain time.
References
Unification of the Georeferencing Systems of GIS Spatial Data Infrastructure
Dr Kamal Abdellatif Abdalla
Surveying and Mapping Directorate,
Al Ain Town Planning Department
P. O. Box 1339, Al Ain, UAE
Email: drka@alainplanning.gov.ae
1. Introduction
Technological advancements in GPS positioning and GIS implementations and processing have provided the ability to perform precise georeferencing and produce high quality spatial data infrastructure. This ability, together with the applications of continuously operating reference stations (CORS) and the expanding use of geodetic control in support of spatial information systems, demands the adoption of reliable procedures to support georeferencing of spatial data and GIS activities. The continuing evolution of GPS and GIS hardware and software as well necessitate the adoption of standards and specifications in planning, methodologies, and implementation of both systems.
The impact of GPS on geodetic control surveying, assisted the geomatics community with a powerful tool for the establishment of precise geodetic control. This evolution has brought with it reduction in cost and an increased demand for geodetic control services. GIS users and spatial data developers rely on georeferencing and on the standards and specifications adopted to ensure the given level of product consistency. In order to produce or update spatial data a geodetic network is necessary. Such a network consists of a number of points spread across the area under consideration, these points are usually in the form of monuments established and placed in the ground, along with a high-accuracy positional value for each point. Traditionally, there have been completely separate networks for horizontal and vertical control, but some and recent networks combine the two on common monuments. By referencing spatial data to such a network, the resulting data and information from multiple local survey activities can be accurately connected.
The diversity of datums in use today and the technological advancements that have made possible global positioning measurements requires careful datum selection and careful conversion between coordinates in different datums. It is well known that the current, and growing, trend towards the use of satellite positioning systems and global satellite mapping systems to produce position-based products in a global reference frame can introduce serious practical difficulties if the results need to be related to older maps and/or digital data. Special problems arise, for instance, in the fields of updating, map revision, cadastral surveying and geomatics operations to support spatial data production. The difficulty fundamentally arises because of the need to transform the data into the coordinate systems used to describe the older data. In principle, coordinate transformations are straightforward mathematical procedures but in practice they can cause serious problems.
The required accuracy for a control survey depends primarily on its purpose. Factors that affect accuracy are type and condition of equipment used, field procedures adopted, and the experience and capabilities of personnel employed. Through years different sets of detailed standards of accuracy and specifications for geodetic control are published.
2. Earth Surfaces and Models
Geodesy deals with the earth surface and the other surfaces used for computation of control points and representation of spatial data, namely the ellipsoid and geoid surfaces. These surfaces can be defined as follows.
(a) The earth has a highly irregular and constantly changing surface. Models of the surface of the earth are used in navigation, surveying and mapping. Topographic and sea level models attempt to model physical variations of the surface, while gravity models and geoids are used to represent local variations in gravity that change the local definition of a level . The topographical surface of the earth is the actual surface of the land and sea at some moment in time. Sea level is the average surface of the oceans. Tidal forces and gravity differences from location to location cause even this smoothed surface to vary over the globe by hundreds of meters. Gravity models attempt to describe in detail the variations in the gravity field. The importance of this effort is related to the idea of leveling. Local variations in gravity, caused by variations in the earth’s core and surface materials, cause this gravity surface to be irregular. Future trends of GIS may focus in representing and analyzing the physical and geophysical information an important spatial data infrastructure.
(b ) The ellipsoid is generated by the revolution of an ellipse about its minor axis;. The ellipsoid is considered to represent simplified figure of the earth and used as the fundamental reference surface for horizontal coordinates. This figure is flattened towards the earth's poles (Figure 2). The size of the ellipsoid is defined by its semi-major axis (a) and minor axis (b); its geometrical shape is defined by the flattening (f=1-b/a), while reference ellipsoids are usually defined by the semi-major axis and the flattening .
Figure 1. The relation between the earth surface, ellipsoid and geoid
Figure 2. An ellipsoid with semi-major axis a and semi-minor axis b
(c) The geoid (Figure 1) is the equipotential surface of the earth's gravity field, which corresponds most closely with mean sea level and extends continuously through the continents and used as zero reference for orthometric heights. However, the geoid is a geometrically and mathematically complicated surface, which is impractical to use for mapping purposes. The knowledge of the geoid is necessary for automatic transformation of the ellipsoidal heights to orthometric heights and vice versa.
The ellipsoidal height (Figure. 1) is a purely geometrical quantity, the length of the normal to the reference ellipsoid between the ellipsoid and the point of interest. The orthometric height, on the other hand, is defined as the length of the line that is always normal to the equipotential surface of the gravity field, between the geoid and the point of interest and is related to the gravity field of the earth. The relationship between the orthometric height, h, the ellipsoidal height, H, and the geoidal height, N can be given by the following approximation:
h = H + N (1)
Regional ellipsoids have generally been established using astronomical observations to define the deflection of the vertical (difference between geoidal and ellipsoidal normals) to be zero at an origin point. The orientation and scale of the ellipsoid is defined using further geodetic observations. Once the best fitting regional ellipsoid has been defined, it is adopted as the reference surface for geodetic positions in that region. The available geodetic observations are then adjusted, applying the least squares technique, to form the regional datum based on that reference ellipsoid.
A global ellipsoid (such as WGS84) corresponds to a best fit to the geoid over the entire earth. Early attempts to define the global ellipsoid used both gravity and arc measurements. The first internationally recognized global ellipsoid was the 1924 International Ellipsoid. The advent of satellite-derived geodetic data enabled improved determinations of the global ellipsoids. Furthermore, such ellipsoids are geocentric, which means that their geometrical centre corresponds with the earth's centre of mass. The orientation of the ellipsoid is achieved by aligning its minor axis with the earth's mean spin axis at a particular time. The next internationally recognized global geocentric ellipsoid, which was derived with the inclusion of refined and superseded by the Geodetic Reference System 1980 (GRS80), which is also geocentric, with a=6378137 metres and f=1/298.257222101 (Moritz, 1980).
In addition to defining the geometrical size and shape of the earth, physical parameters are associated with global ellipsoids. These are the product of the Newtonian gravitational constant and the mass of the earth (GM), the angular velocity of the earth's rotation, and the dynamical form factor. This factor is used to derive the flattening of the ellipsoid (Heiskanen and Moritz, 1967; Moritz, 1980). These additional physical parameters allow a model gravity field to be computed. The most recent and widely used global geocentric ellipsoid is the World Geodetic System 1984 (WGS84), which based on the GRS80 ellipsoid, but with f=1/298.257223563.
In georeferencing system the study of the gravity field is usually taken into account.
Gravity anomalies can be derived from land observations or satellite radar altimeter data, and can be used for geoid determination and gravity anomaly maps production.
3. Geodetic Coordinate Systems
Geodesy is interested in positioning points on the surface of the earth. For this task a well-defined coordinate system is needed. Many coordinate systems are being used in georeferencing, mainly local and geocentric coordinate systems. The coordinates systems use both Cartesian and curvilinear coordinates. The geocentric systems have their z-axis aligned with the instantaneous spin axis of the earth and became more useful, with the advent of satellite positioning. The non-geocentric systems are used for local coordinate systems, in such case their origin would be located at a point on the surface of the earth.
Both the geocentric and local geodetic coordinate systems are used together with reference ellipsoids. These reference ellipsoids are taken to be geocentric or near geocentric, with the axis of revolution coinciding with the z-axis of the coordinate system. The basic idea behind using the reference ellipsoids is that they fit the real shape of the earth, as described by the geoid. Basically, reference ellipsoids are the horizontal surfaces to which the geodetic latitude and longitude are referred. As well the ellipsoid is associated with the Cartesian coordinate system, and must be fixed with respect to the earth. Such an ellipsoid is often called a horizontal datum. The horizontal geodetic coordinates (Latitude, f, and longitude, l), together with the ellipsoidal height, H, make the basic curvi-linear coordinates system. They are related to their associated Cartesian coordinates X, Y and Z by the following expression:
Where
v : The radius of curvature of reference ellipsoid,
a : Semi major axis of the reference ellipsoid.
E : the eccentricity. And
H : the ellipsoidal height.
In recent years, the International Terrestrial Reference System (ITRS), is fixed to the earth through several permanent stations whose horizontal velocities are monitored and recorded. The fixing is done at realization of the ITRS by means of coordinates of some selected points is called the International Terrestrial Reference Frame (ITRF). Transformation parameters needed for transforming coordinates from one epoch to the next are produced by International Earth Rotation Service (IERS), which keep track of the time evolution of the positions.
Many organizations recommend that the coordinate system used for the Framework should meet the criteria of global consistency. This is most convenient when the GIS spatial data expand beyond the extent of national boundaries, using global datums.
Global Coordinate Systems are coordinate systems to specify locations on the surface of the earth and have defined three-dimensional positions with respect to the center of mass of the reference ellipsoid. The Z-axis points toward the North Pole; The X-axis is referenced to the intersections plane defined by the prime meridian and the equatorial plane. The Y-axis completes a right-handed orthogonal system by a plane 90 º east of the X-axis and its intersection with the equator.
4. Geodetic Datums and Reference Systems
The datum can be defined, in simple terms, as a mathematical model of the earth or a reference surface consisting of five quantities: the latitude and longitude of an initial point, the azimuth of a line from the point, and two constants necessary to define the reference ellipsoid. It forms the basis for the computation of horizontal control surveys. In general it is a geometric reference system defined by one or more known positions that serve as a basis for computation of other positions. While the geodetic reference system is defined by an expression of the gravity field, the scale, geoid and ellipsoid. Usually the geographical coordinates of known points in the region to be mapped comprise the datum. Therefore, there is a distinction between the ellipsoid and the datum: The ellipsoid is a geometrical reference surface, whereas the datum is the adopted coordinate set, which is based on a particular ellipsoid. Therefore, not all geographical latitudes and longitudes of the same surface location are equal, but depend upon the ellipsoid and coordinate datum to which they are referenced. Control points are locations that have coordinates, which are derived from a reference frame. Reference frames may take many forms, including assumed coordinates for local reference systems. However in order to be able to share information among various GIS agencies for the same area, it is important to have a common frame of reference. This common reference system is the national geodetic reference system for the country and can be called National Spatial Reference System.
Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications that completely describe the size, shape, orientation, gravity field, and angular velocity of the earth. Referencing geodetic coordinates to the wrong datum can result in position errors. Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems and for precise positioning systems.
A horizontal datum references the location and a vertical datum references elevations. International GPS Service, IGS, was established in 1994 by the International Association of Geodesy, IAG, to support the International earth Rotation Service (IERS) by collecting GPS observations from global networks of continuously operating reference stations. The IERS maintains two primary reference systems: celestial and terrestrial. The celestial reference system provides the context for the Earth-Centered, Earth-Fixed terrestrial reference system. Realization of this system is made by three technologies in addition to GPS: Very Long Baseline Interferometry (VLBI), Doppler Orbitography by Radiopositioning Integrated on Satellite (DORIS), and Satellite Laser Ranging. The International GPS Service (IGS) network of GPS reference stations form global baselines which are periodically least squares adjusted to a set of coordinates and reported annually as the International Terrestrial Reference Frame, ITRF. However, since there are tools to convert data between the ITRF and other coordinate systems, GIS data can be pre-processed for conformance with ITRF. Further, commonly available software supporting the viewing of geographic coordinate-based data supports the dynamic projection of this data for interactive distance determinations and map production.
The Global Positioning system is based on the World Geodetic System 1984 (WGS-84). Parameters for simple XYZ conversion between many datums and WGS-84 are computed and published. Datum conversions are accomplished by various methods. Complete datum conversion is based on seven parameter transformations that include three translation parameters, three rotation parameters and a scale parameter, an example for such transformation is given by Molodensky model as follows:
where
XD, YD, ZD : 3- d coordinates in Datum D,
XS, YS, ZS : 3- d coordinates of control in Datum S.
DX, DY, DZ : Translation parameters in X, Y, Z directions between datum D and S.
Rx, Ry, Rz : Rotations around X, Y, and Z axes between datum D and S.. DL : difference in scale factor.
The Standard Molodensky formulas can be used to convert latitude, longitude and ellipsoid height from one geocentric datum to anther datum.
A regional or geocentric datum comprises geographical coordinates that are referenced to the surface of a particular reference ellipsoid. As illustrated above, a single ground point can have different geographical coordinates by virtue of the datum and the ellipsoid used, and the regional reference ellipsoid is chosen so as to fit the geoid, as closely as possible, over the area to be mapped. This approach enables subsequent geodetic and spatial data, which are collected on the physical surface of the earth, to be reduced to the surface of the ellipsoid..
5. Horizontal Control of Spatial Data
Horizontal geodetic control networks can be established by a number of different methods, however GPS has become the most widely used method due to its efficiency and superior results. These networks provide positional information with reference to the adopted horizontal datum
In order to place spatial data into a large spatial context, a geodetic control network will be used. Such a network consists of a number of monumented points, spread across the area, along with a high-accuracy positional value for each point. By referencing field measurements to such a network, the resulting data and information from multiple local survey projects can be accurately connected. A control network itself is established by highly precise surveying methods followed by a statistical adjustment to reconcile all of the measurements. For each monument the result is a published positional value along with a stated accuracy level. While control surveying work may be carried out incrementally over time, with the new measurements adjusted to the existing network. The control point established some years ago might have multiple positional values, each successive value published as part of a fresh adjustment.
Actually, geodetic control is typically separated into two components: horizontal (latitude/longitude) and vertical (elevation). This is because latitude/longitude and elevation are based on completely different concepts and measurement methods. Even today, GPS can provide extremely high-accuracy horizontal results, a more traditional method is required to establish vertical control. While a network point may have geodetic-quality values for both horizontal and vertical, the methods of determining these values will still be different.
The horizontal geodetic networks of national extent, sometimes called national control networks, have been the main tools for positioning needed for spatial data acquisition and in mapping, boundary demarcation, and other geodetic applications. The national networks are usually interconnected to create continental networks. The transformation between coordinates must take into account the errors in both coordinates sets. A transformation of coordinates thus consists of two distinct components: the transformation between the corresponding coordinate systems as described above, plus a model for the difference between the errors in the two coordinate sets.
6. Vertical Control
Vertical control networks are a series of points on which precise heights, or elevations, have been established. Vertical control stations are typically called Bench Marks (BM) as part of a vertical information network, the benchmark's elevation is known relative to a vertical datum, usually approximating the mean sea level. The vertical accuracy standard is usually referenced to the standard specifies a linear value within which the true or theoretical location of the point falls 95 percent of the time. Once the levelled height difference is obtained from field observations, one has to add to it a small correction based on gravity values along the way, to convert it to either the orthometric, dynamic or normal height difference. Geodetic levelling is probably the most accurate geodetic relative positioning technique. Modern techniques are inherently three-dimensional: simultaneous observations at two points yield three-dimensional coordinate differences that can be added directly to the coordinates of the known point to get the required coordinates of the unknown point.
The zero surface to which elevations or heights are referred is called a vertical datum, which is associated with the Mean Sea Level (MSL). The mean sea level (MSL) is determined by continuously measuring the rise and fall of the ocean at tide gauge stations. This averages out the highs and lows of the tides caused by the changing effects of the gravitational forces from the sun and moon which produce the tides. The MSL then is defined as the zero elevation for a local or regional area. MSL is a close approximation to the geoid, which is the true zero surface for measuring elevations. Heights obtained from geodetic leveling are known as orthometric heights (Figure 1). The orthometric heights are usually reflect local variations in gravity as well as changes in topography.
As stated, GPS, on the other hand, produces a much different kind of height. Whether one uses point, differential, or differenced carrier phase positioning, one obtains a set of XYZ coordinates that depend upon locations of base stations and satellite positions. These three-dimensional, geometric relationships, in contrast to geodetic leveling, do not depend on local gravity variations. Since XYZ coordinates do not directly express ellipsoidal or orthometric heights, it is necessary to transform them into a different coordinate system. Typically, XYZ are transformed into geodetic latitude, longitude and ellipsoidal height (see equation 3 ).
The justification of a global vertical datum adopting unification approach, can be summarized (Heck and Rummel, 1990), as follow:
- The implementation of a global vertical datum will lead to a better accuracy in the connection of national and continental datums.
- Removal of the systematic regional biases in gravity anomaly data banks, due to referencing heights to different level surfaces in different vertical datum zones, requires the definition of a global vertical datum, in such case the gravity anomalies can refer to one unique geopotential surface.
- Discrepancies in results obtained by geodetic levelling and oceanographic procedures, used for the determination of sea surface slopes, need a consistent vertical datum.
7. Georeferencing and GIS Spatial Data
Geographic Information Systems require georeferencing of spatial data for a variety of reasons, such as: collection and processing of spatial data, establishing of mapping relationship to other existing data, updating, discovering and potentially reconciling discrepancies between conflicting data sets; providing a reference coordinate system for GIS applications, to reduce mapping errors as new data are created , to constrain mapping errors within a geographic area, to improve the spatial accuracy of existing data sets; conversion of maps into digital format for GIS. Georeferencing is fundamental in data sharing and in the integration of spatial data from various sources into a single consistent data set. This is often achieved using a single common geodetic reference frame, or datum. A number of factors have led to an increasing need to georeferencing and to base spatial data products on a common reference frame that extends across the whole globe. These factors include growing reliance on satellite positioning systems and development of satellite based mapping systems affording increasingly higher resolution. Another major influence is the trend to spatial data infrastructures with national, regional and even global coverage.
To handle most of the problems of spatial data, there is a need for a good understanding of the definition and realization of georeferencing. A practical approach to georeferencing implementation is the need to be in accordance with agreed standards and guidelines addressed by several international organizations. As well the information describing coordinate reference frames, often referred to as coordinate system metadata that used by the industry and many national and international standards organizations as well as industry are categorized as standards for geometics and non-geomatics activities. Beginning in the 1980s, national standards for spatial data infrastructure and geographic information have been drafted in several countries and international organizations.
Practically spatial coordinates based on local or global reference systems are usually converted to a map projection system for both spatial representation and map production. The projections are not defining ellipsoid or geodetic datum. The most common projection used for spatial data to high accuracy is the Universal Transverse Mercator projection (UTM), which is usually adopting the required reference system and practically suited to maps of north south extent. In the future, it is more likely that spatial data is to be drawn on the surface of global ellipsoid based on latitude and longitudes rather than UTM grids. Airborne and space borne georeferencing techniques are likely to include 4- dimensional approach, and be integrated with georeferencing systems in conjunction with aerial or space frames for digital photogrammetric and remote sensing mapping.
Unification and georeferencing will help in increasing the quantity and quality of data sharing and integration capabilities of GIS networks, and can be used for studying the physical phenomena (Cmbrinck et. Al, 2003), that related to spatial data as a function of time, such as crustal dynamics and movements, tide effects, gravity fields, magnetic fields and ionospheric mapping. This will also help in initiating regional geoids and gravity anomaly maps production.
Different sets of detailed standards of accuracy and specifications for geodetic surveys are to be considered to get reliable georeferencing of spatial data. Many GIS systems handle high quality vector and raster data and digital terrain models (DTM) from a wide variety of sources including, satellite imagery, aerial photography and Ladar scanning, the quality of their end product depends very much on the accuracy of georeferencing..
The revolution in GPS has not been confined to the surveying community, but has extended into mapping, spatial data infrastructure, and Geographic Information System (GIS). Now widespread integration between GIS and GPS are available, in various activities of GIS applications including mobile GIS, monitoring and tracking activities. Many of these applications require accurate positioning, and, a common requirement is the transformation of GPS heights into heights above mean sea level or the geoid. The adoption of georeferencing system will enable the production of a homogeneous series of maps and spatial data, which will meet user requirements. However, this change will also have far-reaching implications for the users and producers of maps and spatial information systems all around the world. However, georeferencing deals with positioning which is the fundamental element of GIS base maps and spatial data in terms of usage, analysis, and features location accuracy and the reliability of any information derived from the GIS system. Georeferencing will also, help in ensuring that all maps or layers in GIS database overlay accurately and the data set is georeferenced to a common coordinate system, and it playing a major role in constructing, displaying and analyzing different GIS layers and giving more abilities to the GIS system in using spatial data for analysis and measurements of length, size, area and shape.
9. Conclusions
Georeferencing can be considered as a common geospatial data item to many GIS applications and provides key elements for integration and sharing of spatial data and thematic information. The unification and implementation of global reference systems will lead to: better accuracy in connection with national and regional datums; removal of systematic regional biases in gravity anomaly data; enhancing, and converting national and regional datums to global reference systems.
The paper recommended that future spatial data representation should focus on the surface of reference ellipsoids; and the planning for unification of georeferencing systems should incorporate IGS stations at national and regional levels. Global or regional spatial reference systems should be initiated to provide national and global framework for spatial data. It should be characterized by accuracies compatible with modern positioning technologies and facilitate sharing of geospatially referenced data between various governments and spatial data users. Georeferencing is important as it relate the global reference systems to the time dimension. This time dimension will give another angle of view to the spatial data that represent a region geometry and spatial topology at certain time.
References
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- Geodetic Survey Division (1996). Accuracy standard for Positioning version.1, Geomatics Canada, Survey Division, Ontario.
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