Converts between geographical latitude and longitude coordinates and UTM eastings and northings (D.B. Baird).

### Options

`CONVERTTO` = string token |
Whether to convert to UTM eastings and northings from geographical latitude and longitude coordinates, or to geographical coordinates from UTM (`geographical` , `utm` ); default `utm` |
---|---|

`DATUM` = string token |
The datum to use when constructing the grid for eastings and northings (`WGS84` , `NAD83` , `GRS80` , `OSGB36` ,`WGS72` , `AUSTRALIAN1965` , `KRASOVSKY1940` , `NORTHAMERICAN1927` , `INTERNATIONAL1924` , `HAYFORD1909` , `CLARKE1880` , `CLARKE1866` , `AIRY1830` , `BESSEL1841` , `EVEREST1830` ); default `WGS8` |

`CENTRALMERIDIAN` = scalar |
Central meridian in degrees for the UTM coordinates |

`SINGLEZONE` = string token |
Whether to convert to easting and /northings in a single zone (`yes` , `no` ); default `no` |

`EORIGIN` = scalar |
False origin for easting; default 500000 |

`NORIGIN` = scalar |
False origin for northing; default 0 |

### Parameters

`LATITUDE` = scalars or variates |
Latitudes |
---|---|

`LONGITUDE` = scalars or variates |
Longitudes |

`DIRECTION` = string tokens |
Directions of the angles of latitude and longitude coordinates (`NE` , `NW` , `SE` , `SW` ); default `NE` |

`EASTING` = scalars or variates |
UTM easting grid references |

`NORTHING` = scalars or variates |
UTM northing grid references |

`ZONE` = scalars or variates |
UTM zones |

### Description

`UTMCONVERSION`

converts geographical latitude and longitude coordinates to the Universal Transverse Mercator (UTM) coordinate system which uses eastings and northings to represent a point on the earth’s surface. These easting and northing coordinates are given on a 1 metre scale, so the distance between two points can be calculated by Pythagoras’ theorem in the usual way.

The UTM system is made up of 60 zones which each cover 6 degrees of longitude. It divides the surface of Earth between latitudes 80°S and 84°N into 60 zones (numbered from 1 to 60), each 6° of longitude in width and centred over a meridian of longitude. Zone 1 is bounded by longitude 180° to 174° W and is centred on the 177th West meridian. Zone numbering increases in an easterly direction. Each of the 60 longitude zones in the UTM system is based on a transverse Mercator projection, which is capable of mapping a region of large north-south extent with a low amount of distortion. By using narrow zones of 6° (up to 800 km) in width, and reducing the scale factor along the central meridian by only 0.0004 (to 0.9996, a reduction of 1:2500) the amount of distortion is held below 1 part in 1,000 inside each zone. Distortion of scale increases to 1.0010 at the outer zone boundaries along the equator. In each zone 500,000 is used as the origin of the easting coordinate, at the central meridan.

By default `UTMCONVERSION`

converts from geographical latitude and longitude coordinates to UTM eastings and northings. However, you can set option `CONVERTTO=geographical`

to convert from UTM to geographical coordinates instead.

The `LATITUDE`

parameter specifies or saves the latitudes, and the `LONGITUDE`

parameter specifies or saves the longitudes. These can be scalars to convert a single coordinate, or variates for several. By default the latitudes and longitudes are assumed to have a north, east orientation, with the latitudes giving the angle from the equator between the North and South poles in the range -90 and 90, and the longitudes giving the angle east or west around the earth from the Greenwich UK Meridian in the range -180 to 180. However, you can specify other orientations using the `DIRECTION`

parameter. This may be a single text value (`NE`

, `NW`

, `SE`

or `SW`

) if all angles have the same orientation, or a text compatible with `LATITUDE`

if the orientation varies over the units. The angles must be given as decimal numbers. You can convert from degrees, minutes and seconds, with the calculation

`Angle = degrees + minutes/60 + seconds/3600`

The UTM eastings and northings are saved or specified by the `EASTINGS`

and `NORTHINGS`

parameters, respectively, and the UTM zone by the `ZONE`

parameter. If you are unsure of the zone when converting to latitudes and longitudes, you should convert a latitude and longitude within your set of points not its zone.

Distortion of scale increases as you approach the boundaries between the UTM zones. However, it is often convenient or necessary to measure a series of locations on a single grid, even when some are located in two adjacent zones. Ideally, the coordinates of each position should be measured on the grid for the zone in which they are located. However, as the scale factor is still relatively small near zone boundaries, it is possible to overlap measurements into an adjoining zone when necessary. By setting `SINGLEZONE=yes`

you can force all the points to be mapped into a common zone (the one in which the mean of the longitudes lies).

Historically, several different constants have been used in the UTM projection calculations. By default, `UTMCONVERSION`

uses the standard WGS84 system, which is the same as the NAD83 system. However, you can use the `DATUM`

option to request alternative sets of constants.

The `CENTRALMERIDIAN`

option specifies the central meridian for the UTM coordinates (i.e. the longitude of the UTM origin). If this is unset, the central meridian is taken from the standard UTM zone that is closest to the mean longitude of the data. The `EORIGIN`

option specifies a false origin for easting i.e. the value for the UTM easting along the central meridian; default 500000. Similarly the `NORIGIN`

option specifies a false origin for northing i.e. the value for the UTM northing along the equator (latitude zero); default 0.

Options: `CONVERTO`

, `DATUM`

, `SINGLEZONE`

, `CENTRALMERIDIAN`

, `EORIGIN`

, `NORIGIN`

.

Parameters: `LATITUDE`

, `LONGITUDE`

, `DIRECTION`

, `EASTING`

, `NORTHING`

, `ZONE`

.

### Method

`UTMCONVERSION`

uses the 1973 US Army calculations, which are accurate to within less than a metre within each given zone.

### Action with `RESTRICT`

`UTMCONVERSION`

takes account of restrictions on any of the input variates.

### Reference

Dutch, S. Converting UTM to Latitude and Longitude (or vice versa)

### See also

Procedure: `GBGRIDCONVERSION`

.

### Example

CAPTION 'UTMCONVERSION example',\ 'Calculate and plot New Zealand UTM coordinates.';\ STYLE=meta,plain SPLOAD '%GENDIR%/Examples/NZPlaces.gsh' CALCULATE Lat = Lat_Deg + Lat_Sec/60 & Long = Long_Deg + Long_Sec/60 UTMCONVERSION [SINGLEZONE=yes] LATITUDE=Lat; LONGITUDE=Long; DIRECTION='SE';\ EAST=Easting; NORTH=Northing; ZONE=Zone PRINT Place,Lat,Long,Easting,Northing,Zone; FIELD=*,5(10) XAXIS 3; action=hide YAXIS 3; action=hide FRAME 3; SCALING=xyequal; BOX=omit PEN 1...3; METHOD=point; SYMBOL=14; COLOUR='black','blue','green';\ CFILL='black','blue','green'; LABELS=Place; SMLABEL=0.4 DGRAPH [TITLE='New Zealand'; WINDOW=3; KEY=0]\ Y=Northing; X=Easting; PEN=Feature