## Standard Horizontal Coordinate Transforms

This page documents the horizontal coordinate transforms that are standard in CDM. Most follow the CF-1.0 Conventions, where they are called grid_mappings. They are also often called projections, because most emply projective geometry.

To follow CF, typically one creates a transform definition variable, whose purpose is to contain attributes whose values are the parameters of the transform. Typically the variable does not contain any real data, and so a scalar variable is used. Each data variable that uses the transform has an attribute with name grid_mapping whose value is the name of the transform variable. The projection coordinate variables are also required.

For example:

``````  float data(y0, x0);
data:grid_mapping = "Lambert_Conformal";

double x0(x0=640);
x0:standard_name = "projection_x_coordinate";
x0:long_name = "x distance on the projection plane from the origin";
x0:units = "km";

double y0(y0=440);
y0:standard_name = "projection_y_coordinate";
y0:long_name = "y distance on the projection plane from the origin";
y0:units = "km";

char Lambert_Conformal;
Lambert_Conformal:grid_mapping_name = "lambert_conformal_conic";
Lambert_Conformal:standard_parallel = 38.5; // double
Lambert_Conformal:longitude_of_central_meridian = 262.5; // double
Lambert_Conformal:latitude_of_projection_origin = 38.5; // double
``````

In this example, the Lambert_Conformal variable defines the projection and the data variable references it with the grid_mapping attribute. The x0 and y0 are coordinate variables, and the CF convention standard_name attribute is used to identify them unambiguously as projection x and y coordinates. The defaullt unit is km, but any units that can be converted to km can be used. The value of the coordinates must be the correct geolocation for your data. The projection that you specify is then used to calculate the correct (lat, lon) point. All projections have the form:

`````` Projection: (x, y) -> (lat, lon)
ProjectionInverse: (lat, lon) -> (x, y)
``````

where the x,y values in this equation are the ones that you put into the x and y projection coordinate variables.

_To summarize, in order for CF Horizontal transforms to work in the CDM, you must:

1. define x and y projection coordinate variables, using the correct projection units, typically km on the projection plane.
2. define your projection dummy variable which has an attribute “grid_mapping_name”
3. refer to the projection in your data variables with the “grid_mapping” attribute._</b>

### Standard Horizontal Transforms (Projections)

The following are the currently implemented transforms.

Required attributes are in bold, optional in bold italics. Attribute names follow the CF Conventions Appendix F (Grid Mappings). See that document for details on the meanings of the formula terms. The projection algorithms are mostly taken from John Snyder, Map Projections used by the USGS, Bulletin 1532, 2nd edition (1983). Some of the ellispoidal forms are corrected versions of com.jhlabs.map.proj.

In some cases, the earth radius may be specified, which uses a spherical earth for the projection. This is indicated by the presence of the earth_radius attribute.

In some cases, the ellipsoidal form of the projection may be used. This is indicated by the presence of the semi_major_axis, and either the semi_minor_axis or inverse_flattening attributes. Note that not all projections have an ellipsoidal implementation.

When neither earth_radius or semi_major_axis is allowed or specified, the projection will be spherical with a default earth radius of 6371.229 km.

The units of earth_radius, semi_major_axis, semi_minor_axis must be in meters.

The optional false_easting, and false_northing should match the units of the x and y projection coordinates. Alternatively, the attribute “units” may be specified on the dummy Coordinate Transform Variable (this is CDM standard, not CF). When they are not present in the documentation below, they are not used. Contact us if you have a real sample where they are non-zero.

#### albers_conical_equal_area

``````   char Albers_Projection;
:grid_mapping_name = "albers_conical_equal_area";
:standard_parallel = 20.0, 60.0; // one or two
:longitude_of_central_meridian = -32.0;
:latitude_of_projection_origin = 40.0;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
``````

This uses a spherical or ellipsoidal earth. See Snyder, p 98.

#### azimuthal_equidistant

``````char azimuthal_equidistant;
:grid_mapping_name = "azimuthal_equidistant";
:semi_major_axis = 6378137.0; // double
:inverse_flattening = 298.257223563; // double
:longitude_of_prime_meridian = 0.0; // double
:false_easting = 0.0; // double
:false_northing = 0.0; // double
:latitude_of_projection_origin = -37.0; // double
:longitude_of_projection_origin = 145.0; // double
``````

Adapted from proj4 jhlabs. See Snyder, p 191.

#### flat_earth

``````   char Flat_Earth;
:grid_mapping_name = "flat_earth";
:longitude_of_projection_origin = -132.0;
:latitude_of_projection_origin = 40.0;
``````

This is not a standard CF projection. It is used when a “flat earth” assumption is acceptable.

#### geostationary

``````   char Geostationary;
:grid_mapping_name = "geostationary";
:longitude_of_projection_origin = -97.0;
:latitude_of_projection_origin = 0.0;
:perspective_point_height= 33.0, 45.0;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
:sweep_angle_axis= 33.0, 45.0;
:fixed_angle_axis= 33.0, 45.0;
``````

This uses an ellipsoidal earth. Notes from CF:

• The “perspective_point_height” is the distance to the surface of the ellipsoid. Adding the earth major axis gives the distance from the centre of the earth.
• The “sweep_angle_axis” attribute indicates which axis the instrument sweeps. The value = “y” corresponds to the spin-stabilized Meteosat satellites, the value = “x” to the GOES-R satellite.
• The “fixed_angle_axis” attribute indicates which axis the instrument is fixed. The values are opposite to “sweep_angle_axis”. Only one of those two attributes are mandatory.

See CF adding geostationary. This projection covers both Eumetsat GEOS and US GOES-R satellites.

#### lambert_azimuthal_equal_area

``````   char Lambert_azimuth_Projection;
:grid_mapping_name = "lambert_azimuthal_equal_area";
:longitude_of_projection_origin = -32.0;
:latitude_of_projection_origin = 90.0;
:false_easting = 0.0; // km
:false_northing = 0.0; // km
``````

This uses a spherical earth. See Snyder, p 184.

#### lambert_conformal_conic

``````   char Lambert_Conformal;
:grid_mapping_name = "lambert_conformal_conic";
:standard_parallel = 33.0, 45.0;   // one or two
:longitude_of_central_meridian = -97.0;
:latitude_of_projection_origin = 40.0;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
``````

This uses a spherical or ellipsoidal earth. See Snyder, p 104.

#### lambert_cylindrical_equal_area

``````char lambert_cylindrical_equal_area;
:grid_mapping_name = "lambert_cylindrical_equal_area";
:semi_major_axis = 6378137.0; // double
:inverse_flattening = 298.257223563; // double

:longitude_of_central_meridian = 145.0; // double
:false_easting = 0.0; // double
:false_northing = 0.0; // double
:standard_parallel = -37.0; // double
``````

Adapted from proj4 / jhlabs. See Snyder, p 76. As of version 4.3.10

#### mcidas_area

``````   char McIDAS_Projection;
:grid_mapping_name = "mcidas_area";
:AreaHeader = 33.0, 45.0, ...;   // an integer array
:NavHeader = -97.0, ...;     // an integer array
``````

This is not a standard CF projection. The headers are read from a McIDAS Area file, and placed in the attributes as int arrays.

#### mercator

``````  char Mercator_Projection;
:grid_mapping_name = "mercator";
:longitude_of_projection_origin = 110.0;
:latitude_of_projection_origin = -25.0;
:standard_parallel = 0.02;
``````

This uses a spherical earth and default radius. See Snyder, p 47.

Used for MSG (METEOSAT 8 onwards) data.

``````   char Space_View_Perspective_or_Orthographic;
:longitude_of_projection_origin = 0.0; // double
:latitude_of_projection_origin = 0.0; // double
:semi_major_axis = 6356755.5; // double
:semi_minor_axis = 6378140.0; // double
:height_from_earth_center = 4.2163970098E7; // double
:scale_x = 35785.830098; // double
:scale_y = -35785.830098; // double
``````

This is not a standard CF projection. This uses an ellipsoidal earth. See this document. Note there is a bug in some versions of Eumetsat GRIB encoding, per Simon Eliot 1/18/2010, in which the “apparent diameter of earth in units of grid lengths” is incorrectly specified. We do a correction for this in ucar.nc2.iosp.grid.GridHorizCoordSys when we read the GRIB file.

#### orthographic

``````  char Orthographic_Projection;
:grid_mapping_name = "orthographic";
:longitude_of_projection_origin = 110.0;
:latitude_of_projection_origin = -25.0;
``````

This is not a standard CF projection. This uses a spherical earth and default radius. See Snyder, p 145.

#### polar_stereographic

``````   char Polar_Stereographic;
:grid_mapping_name = "polar_stereographic";
:straight_vertical_longitude_from_pole = -32.0;
:latitude_of_projection_origin = 90.0;
:scale_factor_at_projection_origin = 0.9330127018922193;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
``````

The Polar Stereographic is the same as the Stereographic projection with origin at the north or south pole. It can use a spherical or ellipsoidal earth.

The polar stereographic will accept these alternate parameter names:

``````   char Polar_Stereographic;
:grid_mapping_name = "polar_stereographic";
:longitude_of_projection_origin = -32.0;
:latitude_of_projection_origin = 90.0;
:standard_parallel = 0.9330127018922193;
``````

If the standard_parallel is specified, this indicates the parallel where the scale factor = 1.0. In that case the projection scale factor is calculated as

`````` double sin = Math.abs(Math.sin( Math.toRadians( stdpar)));
scale = (1.0 + sin)/2;
rotated_pole
char rotated_pole;
:grid_mapping_name = "rotated_latitude_longitude";
:grid_north_pole_latitude = 37.0f; // float
:grid_north_pole_longitude = -153.0f; // float
``````

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

`````` float rlat(rlat=84);
:standard_name = "grid_latitude";
:long_name = "rotated latitude";
:units = "degrees";
:_CoordinateAxisType = "GeoY";
float rlon(rlon=90);
:standard_name = "grid_longitude";
:long_name = "rotated longitude";
:units = "degrees";
:_CoordinateAxisType = "GeoX";
``````

The rotated longitude coordinate must be in the range [-180,180] (so there will be a problem when it crosses the dateline). Code contributed by Robert Schmunk.

#### rotated_latlon_grib

Grib 1 projection 10 and Grib 2 projection 1. This is not a standard CF projection.

`````` char rotated_pole;
:grid_mapping_name = "rotated_latlon_grib";
:grid_south_pole_latitude = 37.0f; // float
:grid_south_pole_longitude= -153.0f; // float
:grid_south_pole_angle= 0.0f; // float
``````

Contributed by Tor Christian Bekkvik.

#### sinusoidal

``````   char SinusoidalProjection;
:grid_mapping_name = "sinusoidal";
:longitude_of_central_meridian = 0.0; // required
:false_easting = 0.0;
:false_northing = 0.0;
``````

Spherical earth. See CF adding sinusoidal.

This projection is one of those selected by the ​ESA Climate Change Initiative, which will be reanalysing the MERIS, MODIS and SeaWiFS time series and producing netcdf-CF files.

#### stereographic

``````   char Stereographic;
:grid_mapping_name = "stereographic";
:longitude_of_projection_origin = -32.0;
:latitude_of_projection_origin = 90.0;
:scale_factor_at_projection_origin = 0.9330127018922193;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
``````

This uses a spherical or ellipsoidal earth. See Snyder, p 153.

#### transverse_mercator

``````   char Transverse_mercator;
:grid_mapping_name = "transverse_mercator";
:longitude_of_central_meridian = -32.0;
:latitude_of_projection_origin = 40.0;
:scale_factor_at_central_meridian = 0.9330127018922193;
:false_easting = 0.0;
:false_northing = 0.0;
:semi_major_axis =  6378.137;
:semi_minor_axis =  6356.752;
:inverse_flattening =   298.257;
:_CoordinateTransformType = "Projection";
:_CoordinateAxisTypes = "GeoX GeoY";
``````

This uses a spherical or ellipsoidal earth. See Snyder, p 53.

#### UTM (Universal Transverse Mercator)

``````   char UTM_Projection;
:grid_mapping_name = "universal_transverse_mercator";
:utm_zone_number = 22;
:semi_major_axis = 6378137;
:inverse_flattening = 298.257;
:_CoordinateTransformType = "Projection";
:_CoordinateAxisTypes = "GeoX GeoY";
``````

This is not a standard CF projection. UTM uses an ellipsoidal earth. Code contributed from the GeoTransform package by Dan Toms, SRI International. Note that semi_major_axis is in meters.

#### vertical_perspective

``````   char vertical_perspective_Projection;
:grid_mapping_name = "vertical_perspective";
:longitude_of_projection_origin = -97.0;
:latitude_of_projection_origin = 40.0;
:height_above_earth = 23980.0; // km