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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. These are:

  • earth_radius

  • inverse_flattening

  • longitude_of_prime_meridian

  • prime_meridian_name

  • reference_ellipsoid_name

  • semi_major_axis

  • semi_minor_axis

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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/aea.html and http://geotiff.maptools.org/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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at http://geotiff.maptools.org/proj_list/azimuthal_equidistant.html and https://proj.org/operations/projections/aeqd.html.

Geostationary projection

grid_mapping_name = geostationary
Map parameters:

  • latitude_of_projection_origin

  • longitude_of_projection_origin

  • perspective_point_height

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

  • sweep_angle_axis

  • fixed_angle_axis

Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the standard_name attribute values projection_x_angular_coordinate and projection_y_angular_coordinate, respectively. It is assumed that the y-axis is aligned to the Earth’s N/S axis, whereas the x-axis aligns with the E/W axis. CF specified the standard names projection_x_coordinate and projection_y_coordinate for these coordinates prior to version 1.9, but that use is deprecated. In the case of this projection, the projection coordinates are the scanning angle of the satellite instrument.

Notes:

The geostationary projection assumes a hypothetical view of the Earth from a perspective above the Earth where the azimuth and elevation viewing angles are described using a hypothetical gimbal model. This model is independent of the physical scan principles of any observing instrument. The model consists conceptually of a set of two rotating circles with a colocated centre, whose axes of rotation are perpendicular to each other. The axis of the outer circle is stationary, while the axis of the inner circle moves about the stationary axis. This means that a given viewing angle described using this model is the result of matrix multiplications, which is not commutative, so that order of operations is essential in achieving accurate results. The two axes are conventionally called the sweep-angle and fixed-angle axes; we adhere to this terminology, although some find these terms confusing, for the sake of interoperability with existing implementations.

The algorithm for computing the mapping may be found at http://www.cgms-info.org/documents/pdf_cgms_03.pdf. This document assumes the point of observation is directly over the equator, and that the sweep_angle_axis is y.

Explanatory diagrams for the projection may be found on the PROJ website, as well as notes on using the PROJ software for computing the mapping.

The perspective_point_height is the distance to the surface of the ellipsoid.

The sweep_angle_axis attribute indicates the axis on which the view sweeps. It corresponds to the outer-gimbal (stable) axis of the gimbal view model. For example, the value = "y" corresponds to the Meteosat satellites, the value = "x" to the GOES satellites.

The fixed_angle_axis attribute indicates the axis on which the view is fixed. It corresponds to the inner-gimbal axis of the gimbal view model, whose axis of rotation moves about the outer-gimbal axis. If fixed_angle_axis is "x", sweep_angle_axis is "y", and vice versa. Only one of those the attributes fixed_angle_axis or sweep_angle_axis is mandatory, as they can be used to infer each other. Note also that the values "x" and "y" are not case-sensitive.

The use of projection_x_coordinate and projection_y_coordinate was deprecated in version 1.9 of the CF Conventions. The initial definition of this projection used these standard names to identify the projection coordinates even though their canonical units (meters) do not match those required for this projection (radians).

Lambert azimuthal equal area

grid_mapping_name = lambert_azimuthal_equal_area
Map parameters:

  • longitude_of_projection_origin

  • latitude_of_projection_origin

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/laea.html and http://geotiff.maptools.org/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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/lcc.html. and http://geotiff.maptools.org/proj_list/lambert_conic_conformal_1sp.html ("Lambert Conic Conformal (1SP)" or EPSG 9801) or http://geotiff.maptools.org/proj_list/lambert_conic_conformal_2sp.html ("Lambert Conic Conformal (2SP)" or EPSG 9802). For the 1SP variant, latitude_of_projection_origin=standard_parallel and the PROJ scale factor is 1.

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 (deprecated)

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software packages for computing the mapping may be found at https://proj.org/operations/projections/cea.html and http://geotiff.maptools.org/proj_list/cylindrical_equal_area.html ("Lambert Cylindrical Equal Area" or EPSG 9834 or EPSG 9835). Detailed formulas can be found in bibliography.adoc 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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software packages for computing the mapping may be found at https://proj.org/operations/projections/merc.html and http://geotiff.maptools.org/proj_list/mercator_1sp.html ("Mercator (1SP)" or EPSG 9804) or http://geotiff.maptools.org/proj_list/mercator_2sp.html ("Mercator (2SP)" or EPSG 9805).

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

Oblique Mercator

grid_mapping_name = oblique_mercator
Map parameters:

  • azimuth_of_central_line

  • latitude_of_projection_origin

  • longitude_of_projection_origin

  • scale_factor_at_projection_origin

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/omerc.html and http://geotiff.maptools.org/proj_list/oblique_mercator.html. The Rotated Mercator projection is an Oblique Mercator projection with azimuth = +90.

Orthographic

grid_mapping_name = orthographic
Map parameters:

  • longitude_of_projection_origin

  • latitude_of_projection_origin

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software packages for computing the mapping may be found at https://proj.org/operations/projections/ortho.html and http://geotiff.maptools.org/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 (EPSG 9829) or scale_factor_at_projection_origin (EPSG 9810)

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/ups.html and http://geotiff.maptools.org/proj_list/polar_stereographic.html.

The standard_parallel variant corresponds to EPSG Polar Stereographic (Variant B) (EPSG dataset coordinate operation method code 9829), while the scale_factor_at_projection_origin variant corresponds to EPSG Polar Stereographic (Variant A) (EPSG dataset coordinate operation method code 9810). As PROJ requires the standard parallel, [Snyder] formula 21-7 can be used to compute it from the scale factor if needed.

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 optional (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:

 

Sinusoidal

grid_mapping_name = sinusoidal
Map parameters:

  • longitude_of_projection_origin

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for computing the mapping may be found at https://proj.org/operations/projections/sinu.html and http://geotiff.maptools.org/proj_list/sinusoidal.html. Detailed formulas can be found in [Snyder], pages 243-248.

Stereographic

grid_mapping_name = stereographic
Map parameters:

  • longitude_of_projection_origin

  • latitude_of_projection_origin

  • scale_factor_at_projection_origin

  • false_easting - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for doing the calcuations may be found at https://proj.org/operations/projections/stere.html and http://geotiff.maptools.org/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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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 software package for doing the calcuations may be found at https://proj.org/operations/projections/tmerc.html and http://geotiff.maptools.org/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 - This parameter is optional (default is 0)

  • false_northing - This parameter is optional (default is 0)

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:

A general description of vertical perspective projection is given in [Snyder], pages 169-181.

The corresponding projection in PROJ is nsper. This should not be confused with the PROJ geos projection.

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

Table F.1. Grid Mapping Attributes
Attribute Type Description

azimuth_of_central_line

N

Specifies a horizontal angle measured in degrees clockwise from North. Used by certain projections (e.g., Oblique Mercator) to define the orientation of the map projection relative to a reference direction.

crs_wkt

S

This optional attribute may be used to specify multiple coordinate system properties in well-known text (WKT) format. The syntax must conform to the WKT format as specified in reference [OGC_WKT-CRS]. Use of the crs_wkt attribute is described in section 5.6.1.

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

Applied to all abscissa values in the rectangular coordinates for a map projection in order to eliminate negative numbers. Expressed in the unit of the coordinate variable identified by the standard name projection_x_coordinate. If false_easting is not provided it is assumed to be 0. The formula to convert from the coordinate value as written in the projection_x_coordinate (xf) to a value (x0) used in a transformation without false_easting, i.e. false_easting= 0, is: x0 = xf -false_easting

false_northing

N

Applied to all ordinate values in the rectangular coordinates for a map projection in order to eliminate negative numbers. Expressed in the unit of the coordinate variable identified by the standard name projection_y_coordinate. If false_northing is not provided it is assumed to be 0. The formula to convert from the coordinate value as written in the projection_y_coordinate (yf) to a value (y0) used in a transformation without false_northing, i.e. false_northing= 0, is: y0 = yf -false_northing

`fixed_angle_axis `

S

Indicates the axis on which the view is fixed in a hypothetical gimbal view model of the Earth, as used in the geostationary grid mapping. It corresponds to the inner-gimbal axis of the gimbal view model, whose axis of rotation moves about the outer-gimbal axis. This value can adopt two values, "x" or "y", corresponding with the Earth’s E-W or N-S axis, respectively. The counterpart to this attribute is sweep_angle_axis. If set to "x", sweep_angle_axis is "y", and vice versa. If one of the attributes fixed_angle_axis or sweep_angle_axis is provided, the other is not mandatory, as they can be used to infer each other.

geographic_crs_name

S

The name of the geographic coordinate reference system. Corresponds to a OGC WKT GEOGCS node name.

geoid_name

S

The name of the estimate or model of the geoid being used as a datum, e.g. GEOID12B. Corresponds to an OGC WKT VERT_DATUM name. The geoid is the surface of constant geopotential that the ocean would follow if it were at rest. This attribute and geopotential_datum_name cannot both be specified.

geopotential_datum_name

S

The name of an estimated surface of constant geopotential being used as a datum, e.g. NAVD88. Such a surface is often called an equipotential surface in geodesy. Corresponds to an OGC WKT VERT_DATUM name. This attribute and geoid_name cannot both be specified.

grid_mapping_name

S

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.

horizontal_datum_name

S

The name of the geodetic (horizontal) datum, which corresponds to the procedure used to measure positions on the surface of the Earth. Valid datum names and their associated parameters are given in https://github.com/cf-convention/cf-conventions/wiki/Mapping-from-CF-Grid-Mapping-Attributes-to-CRS-WKT-Elements (horiz_datum.csv, OGC_DATUM_NAME column) and are obtained by transforming the EPSG name using the following rules (used by OGR and Cadcorp): convert all non alphanumeric characters (including +) to underscores, then strip any leading, trailing or repeating underscores. This is to ensure that named datums can be correctly identified for precise datum transformations (see https://github.com/cf-convention/cf-conventions/wiki/OGC-WKT-Coordinate-System-Issues for more details). Corresponds to a OGC WKT DATUM node name.

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 (degrees_north) 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 (degrees_east) 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 (degrees_east) 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.

prime_meridian_name

S

The name of the prime meridian associated with the geodetic datum. Valid names are given in https://github.com/cf-convention/cf-conventions/wiki/Mapping-from-CF-Grid-Mapping-Attributes-to-CRS-WKT-Elements (prime_meridian.csv). Corresponds to a OGC WKT PRIMEM node name.

projected_crs_name

S

The name of the projected coordinate reference system. Corresponds to a OGC WKT PROJCS node name.

reference_ellipsoid_name

S

The name of the reference ellipsoid. Valid names are given in https://github.com/cf-convention/cf-conventions/wiki/Mapping-from-CF-Grid-Mapping-Attributes-to-CRS-WKT-Elements (ellipsoid.csv). Corresponds to a OGC WKT SPHEROID node name.

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 (degrees_east) to be oriented straight up from the North or South Pole. Domain: -180.0 <= straight_vertical_longitude_from_pole < 180.0

`sweep_angle_axis `

S

Indicates the axis on which the view sweeps in a hypothetical gimbal view model of the Earth, as used in the geostationary grid mapping. It corresponds to the outer-gimbal axis of the gimbal view model, about whose axis of rotation the gimbal-gimbal axis moves. This value can adopt two values, "x" or "y", corresponding with the Earth’s E-W or N-S axis, respectively. The counterpart to this attribute is fixed_angle_axis. If set to "x", fixed_angle_axis is "y", and vice versa. If one of the attributes fixed_angle_axis or sweep_angle_axis is provided, the other is not mandatory, as they can be used to infer each other.

towgs84

N

This indicates a list of up to 7 Bursa Wolf transformation parameters., which can be used to approximate a transformation from the horizontal datum to the WGS84 datum. More precise datum transformations can be done with datum shift grids. Represented as a double-precision array, with 3, 6 or 7 values (if there are less than 7 values the remaining are considered to be zero). Corresponds to a OGC WKT TOWGS84 node.

Notes:

  1. The various *_name attributes are optional but recommended when known as they allow for a better description and interoperability with WKT definitions.

  2. reference_ellipsoid_name, prime_meridian_name, horizontal_datum_name and geographic_crs_name must be all defined if any one is defined, and if projected_crs_name is defined then geographic_crs_name must be also.