USEFUL DEFINITIONS

Coordinate System – A system of mathematical and geodetic constants that defines how a geographic location can be expressed using numerical values.

Latitude – The North/South component of the spherical coordinates system, defined as the angle between: 1) a line perpendicular to the Earth ellipsoid from the geographic location and 2) the equatorial plane.

Longitude – The East/West component of the spherical coordinates system, defined as the distance, in degrees of arc, from the prime meridian (Greenwich Meridian). Longitude lines are essentially circles that pass through the North and South poles and intersect the equator.

Easting/Northing – The coordinate values on the x and y axes of Cartesian systems, representing the distance between the geographic location and the origin of the coordinate system.

Projection – The representation of the Earth’s spherical surface onto a plane. Mathematical method to convert spherical coordinates to a Cartesian coordinates.

Cylindrical Projection – The spherical Earth is projected onto a cylinder wrapping the globe. It may be used in the traditional way, with the cylinder tangent to the globe in the equator, or transversely, in which case the cylinder is tangent to the central meridian.

Conic Projection – The earth surface is mathematically projected onto a cone, with origin, or vertex, perpendicular to the pole of the hemisphere being represented. This projection can be used with the cone touching the Earth surface at a single parallel (standard parallel), or mathematically inserting the cone onto the planet,

creating an intersection in two standard parallels.

Implemented Projections:

Albers Equal-Area ConicLambert Conformal ConicTransverse Cassini/SoldnerTransverse Mercator/Gauss-Krüger

Predefined Systems:

Argentina Coordinate System - Transverse MercatorAustralia Coordinate System - AlbersAustralia Coordinate System - LambertAustralia Coordinate System - Transverse MercatorAustria Coordinate System - LambertAustria Coordinate System - Transverse MercatorBelgian Coordinate System - LambertBritish Coordinate System - Transverse MercatorFrench Coordinate System - LambertGermany Coordinate System - LambertGermany Coordinate System - Transverse MercatorIrish Coordinate System - Transverse MercatorItalian Coordinate System - Transverse MercatorJapanese Coordinate System - Transverse MercatorNorth American Coordinate System - AlbersNorth American Coordinate System - LambertNorth American State Plane Coordinate SystemPortuguese Coordinate System - Transverse MercatorSwedish Coordinate System - Transverse MercatorUniversal Transverse Mercator - UTM

Each system contains subsystems (zones) for different regions. For example, the Universal Transverse Mercator system is divided into 120 subsystems (60 zones for the north hemisphere and 60 for the south hemisphere). In this release, the pre-defined systems, including all subsystems or zones, make a total of 315 different setting combinations.

Each coordinate system/zone is described by the projection, standard ellipsoid, origin point, scale factor or standard parallels, and translation constants. The selection of the system, zone, and ellipsoid only transfers predefined values to the conversion parameters.

CelPlanner also provides a user-defined option, which allows users to define their own parameters. An example of an implementation of this option follows.

Earth Semi-Major Axis – Equatorial radius of the planet. With the flattening factor, it defines the reference ellipsoid for the coordinate system.

Earth Flattening Factor – Factor obtained from the relation between the equatorial and polar radius. Along with the equatorial radius, it defines the reference ellipsoid for the coordinate system.

Central Scale Factor – Factor used to reduce distortion in cylindrical projections. It acts on imaginary cylinder dimensions, reducing the distance between the cylinder and the planet in areas that are far from the central meridian. For example, in UTM systems, this value is specified as 0.9996.

Latitude/Longitude Origin – Location at which the projection calculations (for x and y axes) result in zero for the Cartesian coordinates system, before application of false easting and false northing.

Northern/Southern Standard Parallel – In the conic projection system, the lines that show parallels (or latitude) where an imaginary cone touches the planet surface.

False Easting/Northing – Values usually added to coordinates on the x and y axes to produce coordinate systems with positive values only.

Earth Semi-Major Axis (6,000,000 to 7,000,000 m)

Earth Flattening Factor (200 to 400)Central Scale Factor (0.5 to 2.0)Latitude Origin (-90 to 90°)Longitude Origin (-180 to 180°)Northern Standard Parallel

(-90 to 90°)

Southern Standard Parallel

(-90 to 90°)

False Easting (-20,000,000 to 20,000,000 m)

False Northing (-20,000,000 to 20,000,000 m)

Datum – Set of data defining coordinate systems, encapsulating the ellipsoid specification (planet’s size and format) and the standard origin location.

A single fixed point on the Earth can be represented by a different coordinate for each datum. Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters.

Different nations and agencies use different datum as the basis for coordinate systems. The technological advancements that have made global positioning measurements with sub-meter accuracies possible require careful datum selection and conversion.

The datum can be horizontal or vertical. A horizontal datum is the base reference for a coordinate system. The vertical datum is a base measurement point from which all elevations are determined.

Horizontal Datum

The horizontal datum definition contains three key elements: the parameters defining the shape of an ellipsoid that models the surface of the earth at the point of interest, the location of the ellipsoid origin point, and the orientation of the ellipsoid. This ellipsoid provides a mathematical surface for location calculation.

The parameters of the datum’s ellipsoid determine its shape in three-dimensional space. The origin point ties this ellipsoid down in two dimensions; however the ellipsoid can still rotate around this point, requiring a third element to define its orientation.

An ellipsoid is defined by two parameters: the semi-major and semi-minor axii (sometimes given as a ratio called flattening factor). Because the Earth is irregularly shaped, these parameters can have a number of different values depending on where they are measured. Therefore, practically every country in the world has created its own datum system. Approximately 140 different systems are in use throughout the world. The release notes appendix provides a list of some datum types used today along with their corresponding parameters.

The World Geodetic System 1984 (WGS-84) is the Department of Defense standard datum and is the global positioning system (GPS) reference. The WGS-84 is a global geodetic system. Unlike traditional systems that are referenced to an origin point on the surface of the earth, this system uses a highly accurate satellite determined position for the center of the earth. The Z axis passes through the pole of rotation, the X axis is the perpendicular to it and passes through the prime meridian (Greenwich). The Y axis is orthogonal to the other two axii.

Coordinates values resulting from interpreting latitude, longitude, and height values

based on one datum as though they were based in another datum can cause position errors

in three dimensions of up to one kilometer. The example in Figure 1 shows how a datum

mismatch looks graphically.

Figure 1

The difference between different datum can vary as much as one kilometer. Table 1 compares the shift (in meters) from WGS-84 to other datum. The coordinates presented in the table were used in the regions where each datum predominates.

Table 1

Location Datum Shift

18Q VT 81170149(US)

NAD27201 meters

52S BS 84457638(Japan)

TOKYO754 meters

29°18’12.7”N47°46’57.9”E

(Europe)ED-50

176 meters

01°18’18.4”S15°46’56.6”E

(Africa)ARC-50

296 meters

Map dated 1989 WGS-84

Map dated 1957NAD-27

15S WN443015S WC4330

Vertical Datum

The zero surface to which elevations or heights are referred is called a vertical datum.

Traditionally, surveyors and mapmakers have tried to simplify the task by using the mean

sea level as the definition for zero elevation because the sea surface is available

worldwide. The mean sea level (MSL) is determined by continuously measuring the rise

and fall of the ocean at “tide gauge stations” on seacoasts for a period of about 19 years.

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 mean sea level

then is defined as the zero elevation for a local or regional area. The MSL is a close

approximation of the geoid, which is the true zero surface for measuring elevations. The

geoid represents the earth’s surface of equal gravitational potential

The diagram in Figure 2 shows a phenomenon known as deviation of the vertical. The red line is perpendicular to the mathematical calculation surface, the ellipsoid. The green line is perpendicular to the geoid. Because the ellipsoid and the geoid are not necessarily parallel, this may cause problems when surveying with instruments referenced to the horizontal plane of gravity, because measurements are made in relation to the geoid but calculated on the ellipsoid.

Figure 2

Ellipsoid Normal, Perpendicular to Ellipsoid Surface

Earth Surface

Geoid: Surface of Equal Gravitational

Potential

Ellipsoid

Geoid Separation

Deviation of the vertical

Height, or elevation, can be calculated using any zero as a starting point, including the center of the Earth. Figure 3 shows the relationship among different height systems.

Figure 3

The mean sea level elevation is roughly equivalent to the orthometric height (H). Geoid height (N) is the separation between the geoid and the ellipsoid. Ellipsoid height (h), or geodetic height, is the distance above or below the ellipsoid.