A terrestrial reference system (TRS) is a reference system co-rotating with the Earth in its diurnal motion in space. In such a system, coordinates of points attached to the solid surface of the Earth are time-invariant, neglecting geophysical effects such as tectonic or tidal deformations.
Depending on its origin and orientation, a TRS may be geocentric, aka Earth-Centered Earth-Fixed (ECEF); or relative to a point on the Earth's surface, its zenith and meridian: either as local East-North-Up (ENU) or local North-East-Down (NED). TRS coordinates may be Cartesian or geodetic.
Figure: Terrestrial reference systems: Cartesian and Geodetic.Several organizations have designated spatial reference system identifiers (SRID) to uniquely identify commonly used terrestrial reference systems and derived coordinate systems (see Map Projections) for spatial referencing by coordinates (OGC 08-015r2):
epsg:4326
refers to WGS 84.Most definitions in this article are adapted from National Geodetic Survey's Geodetic Glossary.
The international terrestrial reference system (ITRS) is assimilated to the Geocentric Terrestrial Reference System (GTRS), historically the Conventional Terrestrial Reference System (CTRS), except for a slight difference in time evolution: {IERS Conventions, Chapter 4 Terrestrial reference systems and frames, 2010.}
A geodetic coordinate system (GCS, 大地坐标系) is a coordinate system consisting of an spheroid (ellipsoid of revolution) and a meridional plane through the polar axis, or equivalently a geodetic datum.
Datum (基准面) is a reference or basis for measuring. Geodetic datum (大地基准面), often use interchangeably with datum, is a coordinate system along with a reference ellipsoid that approximates the Earth's surface, specified by at least eight parameters: origin (3) and orientation (3) of the coordinate system, and dimensions (2) of the reference ellipsoid.
World Geodetic System 1984*
(WGS 84; EPSG:4326
; PROJ.4 +proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs
)
is the global geodetic datum of the U.S. Department of Defense and the Global Positioning System (GPS):
{EUROCONTROL and IfEN, 1998. WGS 84 Implementation Manual.}
1. Coordinate system (aligns with ITRS):
ω = 7.292115 x 10-5 rad/s
;
a = 6,378,137 m
;1/f = 298.257223563
;
GM = 398600.5 km3 s-2
;c̅_{20} = - 484.16685 x 10-6
;Besides WGS 84, geodetic datums with better local fit may be used in different regions, such as North American Datum of 1983 (NAD83) in North America, European Datum 1950 (ED50) and European Terrestrial Reference System 1989 (ETRS89) in Europe, and Ordnance Survey Great Britain 1936 (OSGB36). The WGS 84 datum is almost identical to the NAD83 datum and the ETRS89 datum.
North American Datum of 1927 (NAD27) is the first geodetic datum adopted for the United States.
NAD27 is referenced to the Meade’s Ranch Triangulation Station in Kansas (39°13’26.686″N, 98°32’30.506″W),
which is near the center of the contiguous United States (CONUS);
while NAD83 is geocentric, offset by about 2 meters.
NAD27 is uses the Clarke Ellipsoid of 1866:
a = 6,378,206.4 m
, 1/f = 294.98
(b = 6,356,583.8 m
);
while NAD83 uses the Geodetic Reference System (GRS80) Ellipsoid:
a = 6,378,137.0 m
, 1/f = 298.26
(b = 6,356,752.3 m
).
NAD27 and NAD83 may differ up to 100 meters in horizontal accuracy in CONUS,
see NAD27/83 datum shift.
You may use NGS Coordinate Conversion and Transformation Tool
for general datum shift query.
The coordinates of a point in a geodetic coordinate system are
longitude, latitude and altitude/elevation (λ, φ, h)
:
λ
: the azimuth (方位角) from the meridional plane, with range (−180°, +180°]
.φ
: the complementary angle of the polar angle of an ellipsoidal normal, with range [−90°, +90°]
.h
: the perpendicular distance of the point from the spheroid.Geodetic latitude are often confused with two other concepts of latitude.
Parametric latitude (β
), sometimes called reduced latitude,
is the point's parametric angle (离心角) on the meridional ellipse.
Parametric latitude is related to the geodetic latitude with $\tan \beta = b/a \tan \varphi$,
where a
and b
are the semimajor and semiminor axes of the ellipsoid.
Geocentric latitude, ψ
, is the angle from the center of the meridional ellipse.
There's no difference between geodetic longitude and geocentric longitude.
Geodetic longitude and latitude may be referred to as geographic coordinates (地理坐标),
which are often expressed in 60-based numbers:
an arcminute (arcmin, 角分, ′
) is 1/60 of a degree;
an arcsecond (arcsec, 角秒, ″
) is 1/3600 of a degree.
An arcsecond latitude (north/south) is approximately 30.87 meters (2500/81 m, -1.68‰),
which remains nearly constant due to the small flattening of the spheroid datum.
In comparison, the astronomic coordinates (天文坐标) for a point on the Earth's surface are the unique coordinates of the direction of the zenith at that point (天顶; opposite to the plumb line): the astronomic longitude is the angle to a selected celestial meridian; the astronomic latitude is the angle to the celestial Equator (天球赤道). Alternatively, the astronomic coordinates may be determined for the zenith orthogonal to the geoid, from the point vertically below. Difference between these two definitions may be significant.
Figure: Elevation, H; Geodetic height, h; and Geoidal height, N. Geoid undulation is h-H.Elevation (height, level; 海拔) is the distance of a point above a specified surface of constant potential, typically the geoid or its approximation, measured along the direction of gravity. As the true elevation is often impossible or extremely difficult to determine, most elevations are approximates, using mean sea level for example, which can differ from the geoid by up to a meter. Geodetic height (大地高), often used as height, is the distance between a point and a geodetic datum, measured along a perpendicular. GPS typically gives geodetic heights. Geoidal height (大地水准面高) is the geodetic height of a point on the geoid. Different from geoidal height, geoid undulation is the difference between elevation and geodetic height. Altitude is a generic term that cannot be technically defined, which casually means the distance of a location above a reference surface along a perpendicular, such as sea level or the physical surface of the Earth.
Established practice defines a location by combining its horizontal coordinates in one coordinate reference system and its vertical coordinate from another. A control station is a point on the ground whose horizontal or vertical location is used as a basis for obtaining locations of other points. By the kind of coordinates involved, control stations can be classified as horizontal or vertical control. Control datum refers to the datum used to specify locations of control stations.
Types of control datums:
The difference in coordinates between datums is commonly referred to as datum shift.