appf.adoc

Appendix A: Grid Mappings

Each recognized grid mapping is described in one of the sections below. Each section contains: the valid name that is used with the grid_mapping_name attribute; a list of the specific attributes that may be used to assign values to the mapping’s parameters; the standard names used to identify the coordinate variables that contain the mapping’s independent variables; and references to the mapping’s definition or other information that may help in using the mapping. Since the attributes used to set a mapping’s parameters may be shared among several mappings, their definitions are contained in a table in the final section. The attributes which describe the ellipsoid and prime meridian may be included, when applicable, with any grid mapping.

We have used the FGDC "Content Standard for Digital Geospatial Metadata" [FGDC] as a guide in choosing the values for grid_mapping_name and the attribute names for the parameters describing map projections.

Albers Equal Area

grid_mapping_name = albers_conical_equal_area

Map parameters:

• standard_parallel - There may be 1 or 2 values.

• longitude_of_central_meridian

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software package for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/albers_equal_area_conic.html.

Azimuthal equidistant

grid_mapping_name = azimuthal_equidistant

Map parameters:

• longitude_of_projection_origin

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software package for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/azimuthal_equidistant.html.

Lambert azimuthal equal area

grid_mapping_name = lambert_azimuthal_equal_area

Map parameters:

• longitude_of_projection_origin

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software package for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/lambert_azimuthal_equal_area.html.

Lambert conformal

grid_mapping_name = lambert_conformal_conic

Map parameters:

• standard_parallel - There may be 1 or 2 values.

• longitude_of_central_meridian

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software package for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/lambert_conic_conformal_2sp.html.

Lambert Cylindrical Equal Area

grid_mapping_name = lambert_cylindrical_equal_area

Map parameters:

• longitude_of_central_meridian

• Either standard_parallel or scale_factor_at_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute value projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/cylindrical_equal_area.html ("Lambert Cylindrical Equal Area" or EPSG 9834 or EPSG 9835). Detailed formulas can be found in [Snyder] pages 76-85.

Latitude-Longitude

grid_mapping_name = latitude_longitude

This grid mapping defines the canonical 2D geographical coordinate system based upon latitude and longitude coordinates on a spherical Earth. It is included so that the figure of the Earth can be described.

Map parameters:

None.

Map coordinates:

The rectangular coordinates are longitude and latitude identified by the usual conventions ([latitude-coordinate] and [longitude-coordinate]).

Mercator

grid_mapping_name = mercator

Map parameters:

• longitude_of_projection_origin

• Either standard_parallel (EPSG 9805) or scale_factor_at_projection_origin (EPSG 9804)

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute value projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/mercator_1sp.html ("Mercator (1SP)" or EPSG 9804) or http://www.remotesensing.org/geotiff/proj_list/mercator_2sp.html ("Mercator (2SP)" or EPSG 9805).

More information on formulas available in [OGP-EPSG_GN7_2].

Orthographic

grid_mapping_name = orthographic

Map parameters:

• longitude_of_projection_origin

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute value projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/orthographic.html ("Orthographic" or EPSG 9840).

More information on formulas available in [OGP-EPSG_GN7_2].

Polar stereographic

grid_mapping_name = polar_stereographic

Map parameters:

• straight_vertical_longitude_from_pole

• latitude_of_projection_origin - Either +90. or -90.

• Either standard_parallel or scale_factor_at_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software package for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/polar_stereographic.html.

Rotated pole

grid_mapping_name = rotated_latitude_longitude

Map parameters:

• grid_north_pole_latitude

• grid_north_pole_longitude

• north_pole_grid_longitude - This parameter is option (default is 0).

Map coordinates:

The rotated latitude and longitude coordinates are identified by the standard_name attribute values grid_latitude and grid_longitude respectively.

Notes:

 

Stereographic

grid_mapping_name = stereographic

Map parameters:

• longitude_of_projection_origin

• latitude_of_projection_origin

• scale_factor_at_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Formulas for the mapping and its inverse along with notes on using the PROJ.4 software package for doing the calcuations may be found at http://www.remotesensing.org/geotiff/proj_list/stereographic.html . See the section "Polar stereographic" for the special case when the projection origin is one of the poles.

Transverse Mercator

grid_mapping_name = transverse_mercator

Map parameters:

• scale_factor_at_central_meridian

• longitude_of_central_meridian

• latitude_of_projection_origin

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Formulas for the mapping and its inverse along with notes on using the PROJ.4 software package for doing the calcuations may be found at http://www.remotesensing.org/geotiff/proj_list/transverse_mercator.html.

Vertical perspective

grid_mapping_name = vertical_perspective

Map parameters:

• latitude_of_projection_origin

• longitude_of_projection_origin

• perspective_point_height

• false_easting

• false_northing

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute value projection_x_coordinate and projection_y_coordinate respectively.

Notes:

Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/geos.html. These notes assume the point of perspective is directly over the equator. A more general description of vertical perspective projection is given in [Snyder], pages 169-181.

In the following table the "Type" values are S for string and N for numeric.

Table F.1. Grid Mapping Attributes

Attribute	Type	Description
earth_radius	N	Used to specify the radius, in metres, of the spherical figure used to approximate the shape of the Earth. This attribute should be specified for those projected coordinate reference systems in which the X-Y cartesian coordinates have been derived using a spherical Earth approximation. If the cartesian coordinates were derived using an ellipsoid, this attribute should not be defined. Example: "6371007", which is the radius of the GRS 1980 Authalic Sphere.
false_easting	N	The value added to all abscissa values in the rectangular coordinates for a map projection. This value frequently is assigned to eliminate negative numbers. Expressed in the unit of the coordinate variable identified by the standard name projection_x_coordinate.
false_northing	N	The value added to all ordinate values in the rectangular coordinates for a map projection. This value frequently is assigned to eliminate negative numbers. Expressed in the unit of the coordinate variable identified by the standard name projection_y_coordinate.
grid_mapping_name	N	The name used to identify the grid mapping.
grid_north_pole_latitude	N	True latitude (degrees_north) of the north pole of the rotated grid.
grid_north_pole_longitude	N	True longitude (degrees_east) of the north pole of the rotated grid.
inverse_flattening	N	Used to specify the inverse flattening (1/f) of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth. The flattening (f) of the ellipsoid is related to the semi-major and semi-minor axes by the formula f = (a-b)/a. In the case of a spherical Earth this attribute should be omitted or set to zero. Example: 298.257222101 for the GRS 1980 ellipsoid. (Note: By convention the dimensions of an ellipsoid are specified using either the semi-major and semi-minor axis lengths, or the semi-major axis length and the inverse flattening. If all three attributes are specified then the supplied values must be consistent with the aforementioned formula.)
latitude_of_projection_origin	N	The latitude chosen as the origin of rectangular coordinates for a map projection. Domain: -90.0 <= latitude_of_projection_origin <= 90.0
longitude_of_central_meridian	N	The line of longitude at the center of a map projection generally used as the basis for constructing the projection. Domain: -180.0 <= longitude_of_central_meridian < 180.0
longitude_of_prime_meridian	N	Specifies the longitude, with respect to Greenwich, of the prime meridian associated with the geodetic datum. The prime meridian defines the origin from which longitude values are determined. Not to be confused with the projection origin longitude (cf. longitude_of_projection_origin, a.k.a. central meridian) which defines the longitude of the map projection origin. Domain: -180.0 <= longitude_of_prime_meridian < 180.0 decimal degrees. Default = 0.0
longitude_of_projection_origin	N	The longitude chosen as the origin of rectangular coordinates for a map projection. Domain: -180.0 <= longitude_of_projection_origin < 180.0
north_pole_grid_longitude	N	Longitude (degrees) of the true north pole in the rotated grid.
perspective_point_height	N	Records the height, in metres, of the map projection perspective point above the ellipsoid (or sphere). Used by perspective-type map projections, for example the Vertical Perspective Projection, which may be used to simulate the view from a Meteosat satellite.
scale_factor_at_central_meridian	N	A multiplier for reducing a distance obtained from a map by computation or scaling to the actual distance along the central meridian. Domain: scale_factor_at_central_meridian > 0.0
scale_factor_at_projection_origin	N	A multiplier for reducing a distance obtained from a map by computation or scaling to the actual distance at the projection origin. Domain: scale_factor_at_projection_origin > 0.0
semi_major_axis	N	Specifies the length, in metres, of the semi-major axis of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth. Commonly denoted using the symbol a. In the case of a spherical Earth approximation this attribute defines the radius of the Earth. See also the inverse_flattening attribute.
semi_minor_axis	N	Specifies the length, in metres, of the semi-minor axis of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth. Commonly denoted using the symbol b. In the case of a spherical Earth approximation this attribute should be omitted (the preferred option) or else set equal to the value of the semi_major_axis attribute. See also the inverse_flattening attribute.
standard_parallel	N	Specifies the line, or lines, of latitude at which the developable map projection surface (plane, cone, or cylinder) touches the reference sphere or ellipsoid used to represent the Earth. Since there is zero scale distortion along a standard parallel it is also referred to as a "latitude of true scale". In the situation where a conical developable surface intersects the reference ellipsoid there are two standard parallels, in which case this attribute can be used as a vector to record both latitude values, with the additional convention that the standard parallel nearest the pole (N or S) is provided first. Domain: -90.0 <= standard_parallel <= 90.0
straight_vertical_longitude_from_pole	N	The longitude to be oriented straight up from the North or South Pole. Domain: -180.0 <= straight_vertical_longitude_from_pole < 180.0