What is a Geoid? The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level. In very simple terms, the geoid is, for all intents and purposes, the same as mean sea level (see vertical datum below). What is a Datum? The parameter or set of parameters that determine the location of the origin, the orientation and the scale of a coordinate reference system What is a Horizontal Datum? A datum is the mathematical model of the Earth we use to calculate the coordinates on any map, chart, or survey system. All coordinates reference some particular set of numbers for the size and shape of the Earth. From an implementation perspective, a Datum defines the position of the Coordinate Reference System origin plus a set of possible axes. However, the Datum does NOT define the axes order in which coordinates are recorded nor does it define the direction (sign) to be used for each coordinate axis. This information is provided by some database of coordinate reference system parameter information and is known as the coordinate system. What is a 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 average (or mean) sea level as the definition of 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. Definitions – Detailed as defined by ISO, EPSG, and the OGC – all based on standard best practices used in geodesy. Cartesian coordinate system: Coordinate system which gives the position of points relative to N mutually-perpendicular straight axes NOTE - In the context of geospatial coordinates the maximum value of N is three. Coordinate: one of a sequence of N numbers designating the position of a point in N-dimensional space. NOTE In a coordinate reference system, the coordinate numbers must be qualified by units. Coordinate reference system: coordinate system which is related to the real world by a datum. NOTE - For geodetic and vertical datums, it will be related to the Earth. Coordinate system: set of (mathematical) rules for specifying how coordinates are to be assigned to points NOTE 1 - One coordinate system may be used in many coordinate reference systems. NOTE 2 - The geometric properties of a coordinate space determine how distances and angles between points are calculated from the coordinates. For example, in an ellipsoidal (2D) space distances are defined as curves on the surface of the ellipsoid, whereas in a Euclidean plane as used for projected CRS distance is the length of a straight line between two points. The mathematical rules that determine distances and angles are calculated from coordinates and vice versa are comprised in the concept of coordinate system. Coordinate transformation: computational process of converting a position given in one coordinate reference system into the corresponding position in another coordinate reference system. NOTE 1 - A coordinate transformation can require and use the parameters of the ellipsoids associated with the source and target coordinate reference systems, in addition to the parameters explicitly associated with the transformation. NOTE 2 - The term ‘transformation’ is used only when the parameter values associated with the transformation have been determined empirically from a measurement / calculation process. This is typically the case when a change of datum is involved. Ellipsoid: Surface formed by the rotation of an ellipse about an axis. NOTE 1 - Sometimes the alternative word ‘spheroid’ is used in geodetic or survey practice to express the same concept. Although mathematically speaking incorrect the more common term in geodetic or survey practice is ‘ellipsoid’. NOTE 2 - An alternative term used in geodetic practice is ‘reference ellipsoid’ Elevation: distance of a point from a chosen reference surface along the direction of the gravity vector from the point to that surface. NOTE 1 - See ellipsoidal height and gravity-related height. It should be noted that ellipsoidal height is defined w.r.t. an ellipsoidal model of the shape of the earth. Ellipsoidal height is measured from the point along the line perpendicular to the ellipsoid’s surface. NOTE 2 - Height of a point outside the surface treated as positive; negative height is also named as depth. Geodetic coordinates: coordinates defined in a geocentric, geographic (2D or 3D) or projected coordinate reference system. Geodetic datum: datum describing the relationship of a 3D or 2D coordinate system to the Earth. NOTE In most cases, the geodetic datum includes an ellipsoid definition. Geographic coordinate reference system: coordinate reference system using an ellipsoidal coordinate system and based on an ellipsoid that approximates the shape of the Earth. NOTE 1 - A geographic coordinate system can be 2D or 3D. In a 3D geographic coordinate system, the third dimension is height above the ellipsoid surface Latitude (geodetic latitude, ellipsoidal latitude): Angle from the equatorial plane to the perpendicular to the ellipsoid through a given point, northwards treated as positive Longitude (geodetic longitude, ellipsoidal longitude): Angle from the prime meridian plane to the meridian plane of the given point, eastward treated as positive. Map projection: Conversion from a geodetic coordinate system to a planar surface Reference ellipsoid: ellipsoid used as the best local or global approximation of the surface of the geoid. Unit (unit of measure): Defined quantity in which dimensioned parameters are expressed. What is the WGS 84 Datum? The WGS84 (World Geodetic System 1984) datum consists of three-dimensional Cartesian coordinate system and an associated ellipsoid, so that WGS84 positions can be described as either XYZ Cartesian coordinates or latitude, longitude and ellipsoid height coordinates. The origin of the datum is the Geo-center (the center of mass of the Earth) and it is designed for positioning anywhere on Earth. In line with the definition of a datum given in section 3.2, the WGS84 datum is nothing more than a set of conventions, adopted constants and formulae. No physical infrastructure is included, and the definition does not indicate how you might position yourself in this system. The WGS84 definition includes the following items: * The WGS84 Cartesian axes and ellipsoid are geocentric; that is, their origin is the center of mass of the whole Earth including oceans and atmosphere. * The scale of the axes is that of the local Earth frame, in the sense of the relativistic theory of gravitation. * Their orientation (that is, the directions of the axes and, hence, the orientation of the ellipsoid equator and prime meridian of zero longitude) coincided with the equator and prime meridian of the Bureau Internationale de l'Heure at the moment in time 1984.0 (that is, midnight on New Year's Eve 1983). * Since 1984.0 the orientation of the axes and ellipsoid has changed such that the average motion of the crustal plates relative to the ellipsoid is zero. This ensures that the Z axis of the WGS84 datum coincides with the International Reference Pole, and that the prime meridian of the ellipsoid (that is, the plane containing the Z and X Cartesian axes) coincides with the International Reference Meridian. * The shape and size of the WGS84 biaxial ellipsoid is defined by the semi-major axis length meters and the reciprocal of flattening. This ellipsoid is the same shape and size as the GRS80 ellipsoid. Conventional values are also adopted for the standard angular velocity of the Earth, and for the Earth gravitational constant. The first is needed for time measurement and the second to define the scale of the system in a relativistic sense. There are a couple of points to note about this definition. Firstly, the ellipsoid is designed to best-fit the Geoid of the Earth as a whole. This means that it generally doesn't fit the Geoid in a particular country as well as the non-geocentric ellipsoid used for mapping that country. In Great Britain GRS80 lies about fifty meters below the Geoid and slopes from east to west relative to the Geoid, so the Geoid-ellipsoid separation is ten meters greater in the west than in the east. Our local mapping ellipsoid (the Airy 1830 ellipsoid) is a much better fit. Secondly, note that the axes of the WGS84 Cartesian system and, hence, all lines of latitude and longitude in the WGS84 datum, are not stationary with respect to any particular country. Due to tectonic plate motion, different parts of the world move relative to each other with velocities of the order of ten centimeters per year. The International Reference Meridian and Pole and, hence, the WGS84 datum, are stationary with respect to the average of all these motions. But this means they are in motion relative to any particular region or country. In Great Britain all WGS84 latitudes and longitudes are changing at a constant rate of about 2.5 centimeters per year in a north-easterly direction. Over the course of a decade or so, this effect becomes noticeable in large-scale mapping. Some parts of the world (for example, Hawaii and Australia) are moving at up to one meter per decade relative to WGS84. The full reference for WGS 84 can be found at ftp://164.214.2.65/pub/gig/tr8350.2/wgs84fin.pdf .