Two-dimensional systems - SWEREF 99, projections
The SWEREF 99 reference frame is a realization of ETRS 89, carried out in 1999 in accordance with the guidelines that were valid at that time. SWEREF 99 was approved as an official realization of ETRS 89 at the EUREF meeting in 2000.
Map projection
Because neither three-dimensional co-ordinates nor latitude and longitude are particularly useful for practical applications and technical use, there is a need for a map projection referred to SWEREF 99. Without entering into technical details, it can be stated that the Gauss conformal (Transverse Mercator) projection, which has been used in Sweden for geodetic and cartographic purposes during the last century, satisfies requirements regarding conformality and is also well-suited from other standpoints. On the projection plane (the mapping plane) a two-dimensional Cartesian co-ordinate system is used in which N (Northing) coordinates are measured northward from the Equator, which has an initial N value of 0 metres; and E (Easting) co-ordinates are measured from the central meridian, increasing eastwards.
Co-ordinates in SWEREF 99 TM.
SWEREF 99 TM
It is an advantage for many different applications at the national level if the whole Sweden can be mapped seamlessly, i.e. on one projection with position given in one co-ordinate system. A rigid application of, for example, UTM in Sweden would require a division into three zones.
The definition of a dedicated projection based on a meridian 15° E of Greenwich, with a scale factor of 0.9996, with the Equator as the origin for N co-ordinates and with E co-ordinates measured from the central meridian and increasing eastwards (the central meridian is assigned a value of 500 000 m to avoid negative values) will give consistency with UTM in the major part of the country.
SWEREF 99 dd mm
For applications on the local level, such as local authority technical activities, the projection must be designed in such a way that the inevitable deformations can, in most cases, be ignored. The most obvious deformation is variations in scale, which increase with distance from the central meridian. Scale changes can be kept at a reasonable level by limiting the area of validity for the projection both eastwards and westwards.
Zones for large scale applications.
The division of Sweden into 12 zones with a scale factor equal to 1 (one) will reduce scale errors to 50 mm/km in the major part of the country. The figure below illustrates the areas of validity for the different zones.
Positions in the zones are given in a co-ordinate system that is in conformity with the national system: the Equator is the origin for N co-ordinates and E co-ordinates are measured from the central meridian and increase eastwards (the central meridian is assigned a value of 150 000 m to avoid negative values)
Uniformity
In the future all information will be referred to SWEREF 99, although positions can be given in thirteen different plane co-ordinate systems. Transition between these systems is done by re-projection of latitude and longitude from N and E co-ordinates whereby new N and E co-ordinates can be determined by projection in the appropriate zone. The N co-ordinates in all systems will be a 7-digit number in the integer part and the E co-ordinates will be a number with a maximum of 6 digits in the integer part.
| System | Projection parameters | |||
|---|---|---|---|---|
| Central meridian, λ0 | Scale factor, k0 | N reduction (m) | E addition (m) | |
| SWEREF 99 TM | 15°00' E | 0.9996 | 0 | 500 000 |
| SWEREF 99 12 00 | 12°00' E | 1.0 | 0 | 150 000 |
| SWEREF 99 13 30 | 13°30' E | 1.0 | 0 | 150 000 |
| SWEREF 99 15 00 | 15°00' E | 1.0 | 0 | 150 000 |
| SWEREF 99 16 30 | 16°30' E | 1.0 | 0 | 150 000 |
| SWEREF 99 18 00 | 18°00' E | 1.0 | 0 | 150 000 |
| SWEREF 99 14 15 | 14°15' E | 1.0 | 0 | 150 000 |
| SWEREF 99 15 45 | 15°45' E | 1.0 | 0 | 150 000 |
| SWEREF 99 17 15 | 17°15' E | 1.0 | 0 | 150 000 |
| SWEREF 99 18 45 | 18°45' E | 1.0 | 0 | 150 000 |
| SWEREF 99 20 15 | 20°15' E | 1.0 | 0 | 150 000 |
| SWEREF 99 21 45 | 21°45' E | 1.0 | 0 | 150 000 |
| SWEREF 99 23 15 | 23°15' E | 1.0 | 0 | 150 000 |
