National Land Survey of Sweden - Reference systems, SWEREF 99 and RT 90

Swedish geodetic reference frames, SWEREF 99, RT 90 and RH 70

SWEREF 99
SWEREF 99 is a Swedish realisation of ETRS 89. The processing of the GPS data was performed according to the EUREF guidelines and was based on observations made on permanent reference stations in Sweden (SWEPOS), Denmark, Finland (FinnRef) and Norway (SATREF) during the GPS-weeks 1014-1019 (June-July 1999).

SWEREF 99 coincides with WGS 84[G730] and WGS 84[G873] within some decimeters. Coordinates can be transformed from SWEREF 99 to the Swedish coordinate datum RT 90, through a 7-parameter transformation given below (estimated accuracy 7 cm, 1 sigma, 2D).

The ellipsoid used with SWEREF 99 is GRS 80:
Semi-major axis a = 6378137
Inverse flattening 1/f = 298.257222101

SWEREF 99 replaces SWEREF 93 (the former realisation of ETRS 89).

For additional information concerning SWEREF 99, please refer to [1] and this report from the ETRS 89 proceedings in Tromsø (pdf)

RT 90, The National (Mapping) Coordinate Datum
RT 90 (Rikets koordinatsystem 1990) is a local geodetic datum. The coordinates emanate from the third triangulation of Sweden (1967-82). The Swedish national map series are based on a Transverse Mercator grid of this datum, denoted: RT 90 2.5 gon V 0:-15. For details about the grid system, see Swedish map projections

The ellipsoid used with RT 90 is Bessel 1841:
Semi-major axis a = 6377397.155
Inverse flattening 1/f = 299.1528128

RH 70, The National Height System 1970
RH 70 (Rikets höjdsystem 1970) is a normal height system resulting from the second precise levelling of Sweden (1951-1967). The system is connected to the NAP (Normaal Amsterdams Peil) via UELN 55 (United European Levelling Network 1955).

TRANSFORMATION PARAMETERS - SWEREF 99 -> RT 90
Coordinates measured by GPS in SWEREF 99 or WGS 84 can be transformed to RT 90 using the 7 parameters below.

= -414.0978567149 m = -0.8550434314 arcseconds

= -41.3381489658 m = +2.1413465185 arcseconds

= -603.0627177516 m = -7.0227209516 arcseconds

= 0.0 ppm (scale = 1.0)

Transformation Accuracy

TRANSFORMATION MODEL (Bursa Wolf)
The formula to be used in conjunction with the presented parameters is

where R is the rotation matrix defined by

INVERSE TRANSFORMATION
To transform from RT 90 to SWEREF 99 use the above given parameters together with the following strict inverse formula:

Where R^-1 is the mathematical inverse of the rotation matrix = the transposed matrix R^T.

PARAMETERS RT 90 -> SWEREF 99
If one does not have access to a strict inverse procedure, or for some other reason prefers to define a transformation in the direction RT 90 to SWEREF 99, use the following parameters with the forward formula

= +414.1055246174 m = +0.8551163377 arcseconds

= +41.3265500042 m = - 2.1413174055 arcseconds

= +603.0582474221 m = +7.0227298286 arcseconds

= 0.0 ppm (scale = 1.0)

WORKED EXAMPLE
Latitude, longitude and height above the ellipsoid GRS 80 in SWEREF 99:
= 58° 00' 00.000000" = 17° 00' 00.000000" h = 30.000
transformation to latitude, longitude and height above the ellipsoid Bessel 1841 in RT 90:
= 58° 00' 01.213296" = 17° 00' 11.683659" h = -5.3970
and projected to plane grid coordinates in RT 90 2.5 gon V 0:-15:
northing = 6431274.6309 m easting = 1570650.2449 m

Alternative transformation method using direct map projection from SWEREF 99 to RT 90 2.5 gon V 0:-15

A method has been developed at the National Land Survey of Sweden to compute projection parameters, which maps the latitudes and longitudes of one geodetic datum to Transverse Mercator northings and eastings of another datum, cf. [3].

The following projection parameters maps the latitudes and longitudes of SWEREF 99 to plane grid coordinates. The difference between coordinates obtained in this way and the original plane grid coordinates of RT 90 is less than 0.1 m in most parts of Sweden.

Please note that for applications where you strive for the highest possible accuracy, the official 7-parameter formula should be used.

PARAMETERS FOR DIRECT PROJECTION, SWEREF 99 -> RT 90 2.5 gon V 0:-15

Projection Transverse Mercator (Gauss-Krüger)

Ellipsoid GRS 80

Semi-major axis (a) 6378137

Inverse flattening (1/f) 298.257222101

Longitude of central meridian 15° 48' 22.624306" East Greenwich

Latitude of origin 0°

Scale along central meridian 1.00000561024

False Northing -667.711 m

False Easting 1500064.274 m

Note: the ellipsoid parameters for GRS 80 are used.

References:

[1] Jivall, Lotti: SWEREF 99 – New ETRS 89 Coordinates in Sweden, Analysis Report. LMV-rapport 2001:6

[2] Reit, B.-G: Swedish Coordinate Systems, Reports of the Finnish Geodetic Institute, No 95:4,pp. 145-150.

[3] Reit, B.-G: A simple way of introducing a global reference frame in surveying and mapping, Survey Review,Vol. 34, No 264, pp. 87-90.

The parameter values of the 7-parameter transformation is dependent on the order of multiplication of the rotation matrices. For parameters of other orders or for more information on Swedish geodetic reference systems, please contact:

Bo-Gunnar Reit
Lantmäteriverket
SE-801 82 Gävle
Tel: +46 26 63 37 35
E-mail: [email protected]

Transformation SWEREF 99RT 90 can be computed on this page:

Transformation Online
(Swedish language version only)