This article is a brief description of the Finnish horizontal coordinate systems. The list of the coordinate systems below in table 1.

Table 1, Finnish horizontal coordinate systemsIDName in FinnishName in EnglishUsed in map productionCommentVVJ Helsingin järjestelmä Helsinki system -1970 Still used in some cities ED50 (National) European Datum 1950 European Datum 1950 Never (National) = national adjustment 1966 KKJ Kartastokoordinaattijärjestelmä Finnish National Coordinate System 1970-2005 Based on ED50 EUREF-FIN EUREF-FIN EUREF-FIN 2003- Nautical charts, 2005- Topographic maps ETRS89 realization in Finland

Finnish version of this article can be found from: Suomalaiset koordinaatistot

If you have any comments, questions or suggestions regarding this article, please don't hesitate to contact me: eino.uikkanen@iki.fi

VVJ, Helsinki system, also known in Finnish as 'Vanha valtion järjestelmä', is the predecessor of the current KKJ coordinate system. The transition from VVJ to KKJ started in 1970, but VVJ is still in use in some cities.

KKJ is not based on VVJ, but KKJ was defined so, that it optimally fits to it's predecessor VVJ. Therefore VVJ coordinates can be handled as if they were KKJ coordinates, noting however following differences in values and representation of VVJ- and KKJ-coordinates:

- The difference between VVJ and KKJ coordinates is 2 meters on average, the maximum difference being appr. 10 meters.
- VVJ y-coordinate is represented without the preceding zone number, but possibly preceded by central meridian value, e.g. if KKJ y-coordinate is 3511666 then VVJ y-coordinate represented as 511666 or 27°511666
- The VVJ coordinates are often represented without thousands or even hundreds of kilometers in the coordinate value.

In Finland the European Datum 1950 (ED50) is based on the National Adjustment of the first order triangulation network in 1966, in which the initial coordinates were taken from the European adjustment (Korhonen, 1967). The result of this adjustment, national ED50, is never used for mapping purposes directly. The national ED50 is however important, because it is the base of the Finnish National Coordinate System KKJ.

KKJ is derived from the Finnish national adjustment (1966) of the ED50 (European Datum 1950) coordinate system by shifting and rotating ED50 plane coordinates so, that they optimally fit to KKJ's predecessor VVJ, Helsinki System.

KKJ-coordinates can be presented in geographical (latitude, longitude) or in rectangular grid-coordinates (northing, easting). Very often simple name KKJ without reference to the coordinate type is used to refer to rectangular grid-coordinates. In fact, it's quite a common misunderstanding, that KKJ means only the grid-coordinates. Because KKJ is 2D-coordinate system, it does not contain any definition of the height system. If, however, the height of a point is given in connection with the horizontal coordinates, it is always orthometric height in the national height system (e.g. N60).

The reference ellipsoid used with KKJ is International 1924 ellipsoid, also known as Hayford ellipsoid. The parameters of this ellipsoid are represented in table 2. Since the parameters of the reference ellipsoids are in often expressed as delta values between WGS84 and the appropriate ellipsoid, also delta values (DA, DF) are represented in the table.

Table 2, International 1924 and WGS84 ellipsoidsParameterDescriptionUnitWGS84International 1924WGS84-International 1924A, DA Semi major axis meter 6378137 6378388.0 -251 F, DF Flattening 1/298.257223563 1/297 -0.1419270 Gauss-Krüger projection formula is used to convert between KKJ-geographical and KKJ-grid-coordinates. KKJ-grid consists of six zones, each 3 degrees wide. Very often only zones 1-4 are represented, because these zones almost cover the entire Finland. This grid system with six 3 degrees wide zones is called 'Basic Coordinate System', in Finnish 'Peruskoordinaatisto'. Parameters for zone 3 are also used countrywide and is then called 'Uniform Coordinate System', in Finnish 'Yhtenäiskoordinaatisto' or YKJ. In topographic maps the Basic Coordinate Systems grid-lines are printed black and Uniform Coordinate Systems grid-lines are printed red.

Table 3, KKJ Basic Coordinate System, KKJ peruskoordinaatistoProjectionEllipsoidZoneCentral MeridianFalse EastingScale factor at Central MeridianZone widthKKJ International 1924 0 18 500000 1.000 3 KKJ International 1924 1 21 1500000 1.000 3 KKJ International 1924 2 24 2500000 1.000 3 KKJ International 1924 3 27 3500000 1.000 3 KKJ International 1924 4 30 4500000 1.000 3 KKJ International 1924 5 33 5500000 1.000 3

Table 4, KKJ Uniform Coordinate System, KKJ yhtenäiskoordinaatisto YKJProjectionEllipsoidZoneCentral MeridianFalse EastingScale factor at Central MeridianZone widthYKJ International 1924 3 27 3500000 1.000 Country wide An easy way of thinking of how KKJ-grid-coordinates are derived is as follows:

- Go from the point to the central meridian along the shortest way - the length of the trip is the starting value for the y-coordinate. On the western side of the central meridian this value is negative and on the eastern side positive. E.g. y=45107.
- Continue from this point to the equator along the central meridian - the length of the trip is the value of the x-coordinate. E.g. x=6717563.
- Add 500000 meters to the value of y-coordinate to make all y-coordinate values positive. This value is called False Easting. E.g. y=545107.
- Put the number of the zone in front of the y-coordinate. Now the value of the y-coordinate tells also the zone number and coordinate values of different zones are easy to distinguish. E.g. y=2545107.
- The final values of grid-coordinates are: x=6717563 and y=2545107

Points 3 and 4 are normally covered with one parameter, which is called False Easting. In the example above the False Easting would then be 2500000 meters (500000 meters + 2 in front of the coordinate-value).

Below sample values of different coordinate types:

Table 5, Sample coordinate valuesCoordinate typeLatitudeLongitudeWGS84 geographical 60.566077 24.819210 KKJ geographical 60.565894 24.822422 xyKKJ-grid, zone 2 6717563 2545107 KKJ-grid, zone 3/Uniform 6719258 3380581

Conversion between ETRS89(WGS84) and KKJ - datum conversion

The best values for three and seven parameter similarity transformations from KKJ to ETRS89/WGS84 are described in the table 6. More accurate (than similarity transformation) transformation methods between EUREF-FIN(WGS84) and KKJ are described in Public Recommendation 154 (JHS 154, JUHTA - Advisory Committee on Information Management in Public Administration).

The parameters for the seven parameter similarity transformation (column 1) are calculated by Finnish Geodetic Institute (FGI) for KKJ-ETRS89 conversion using least square method and based on 90 points, for which both ETRS89-coordinates measured by Finnish Geodetic Institute and KKJ-coordinates are known. Therefore these parameters give at least nearly as good result as a similarity transformation ever can give. Because of the distortion of both scale and orientation in the current KKJ-system, this similarity transformation still leaves residual errors of maximum two meters.

The parameters for three parameter similarity transformations (columns 2-4) I have calculated myself using the 90 points used by Finnish Geodetic Institute to calculate KKJ-ERTS89- transformation parameters. This way the measurements made by Finnish Geodetic Institute made it possible to calculate new more accurate parameters for three parameter similarity transformations too. I made the calculations simply by minimizing the arithmetic averages of the errors in 3D-cartesian-coordinate values X, Y and Z. Then I rounded the values to the nearest integers, because I calculated these values mainly for use in handheld GPS-devices and most handheld GPS-devices accept only integer values for DX, DY and DZ. Parameters, which are calculated to be used anywhere in Finland, are listed in column 2. The parameters which I calculated to give the best fit in southern Finland (latitude <65 degrees) and northern Finland (latitude >65 degrees) are listed in columns 3 and 4.

In column 5 (gray column) I have presented also the parameters, which are in use in many computer programs and most handheld GPS-devices, where the transformation between KKJ and WGS84 is predefined. These parameters are calculated by Jukka Varonen from Finnish Maritime Administration in 1989. These parameters were calculated for use in the sea area only (covering appr. Southern Finland), but are still well applicable for the entire Finland.

Average and maximum errors for all parameter sets I have calculated myself. Error-values for the three parameter sets I have calculated for rounded values. N/B, that these error-values are average and maximum values of errors within selected sets of points. These sets of points represent the selected areas very well, but still, the error values represent errors within these sets of points only, not average and maximum errors in general.

Table 6, Parameters for similarity transformation between KKJ and WGS84 (ETRF89)ParameterDescriptionUnit12345Latitudes of the applied area <65 >65 DX Shift along X-axis meter -96.062 -75 -74 -76 -78 DY Shift along Y-axis meter -82.428 -230 -229 -232 -231 DZ Shift along Z-axis meter -121.754 -89 -88 -91 -97 rx Rotation around X-axis second -4.801 ry Rotation around Y-axis second -0.345 rz Rotation around Z-axis second +1.376 m Scale factor = (scale-1)*10^6 +1.496 Average error meter 0.8 1.6 1.4 0.8 1.8 Maximum error meter 2 3.3 2.5 1.8 3.4 Before applying these parameters one should check, how his program or GPS-device expects the units of measures and signs of rotation angles (rotation directions) to be given. Below the formula, for which the parameters in this article are calculated. Most programs and GPS-devices use this formula, but there are exceptions.

Table 7, 3D-similarity transformation formula, for which the parameters are calculated |X2| |DX| | 1 Rz -Ry | |X1||Y2| = |DY| + (1+m/10^6) * |-Rz 1 Rx | * |Y1||Z2| |DZ| | Ry -Rx 1 | |Z1|

Finland is in the middle of the transition period, during which the current national coordinate system KKJ will be replaced by pan-European coordinate system ETRS89.

Finnish Geodetic Institute has created reference frame called EUREF-FIN, which is fixed to European-wide EUREF89 reference frame. EUREF89 is a realization of ETRS89. EUREF-FIN coincides with WGS84 at meter level (diff. 2012 appr.80 cm) and therefore for all mapping and charting purposes EUREF-FIN and WGS84 can be considered the same.

The realization of the pan-European coordinate system ETRS89 in Finland (EUREF-FIN) is defined in the Public Recommendation 153 (JHS 153, JUHTA - Advisory Committee on Information Management in Public Administration). In national mapping and spatial information services it is recommended to use ETRS89 (EUREF-FIN) instead of the current KKJ coordinate system.

The map projections and plane coordinates used with EUREF-FIN as well as accurate datum transformation methods and parameters between EUREF-FIN and KKJ coordinates are defined in the Public Recommendation 154 (JHS 154, JUHTA - Advisory Committee on Information Management in Public Administration).

In country wide use it is recommended to use pan-European ETRS89-TMnn -projection (UTM, nn = zone number). In Finland projection ETRS-TM35 is used country wide and is therefore called ETRS-TM35FIN, where FIN is for the non-standard zone width.

In local mapping and spatial information services it is possible to use Gauss-Krüger -projection called ETRS-GKn, where n is the (closest) central meridian.

Table 8 describes the projection parameters for the grid coordinates used in Finland. For comparison purposes also KKJ projection parameters are included.

Table 8, Projection parameters for grid coordinates used in FinlandProjectionEllipsoidCentral MeridianFalse EastingScale factor at Central MeridianZone widthETRS-TM35FIN GRS80 27 500000 0.9996 13 ETRS-TMn, n=34,35,36 GRS80 21,27,33 500000 0.9996 6 ETRS-GK GRS80 19,20,...,31 n500000, n=19,20,...,31 1.0000 1 KKJ International 1924 18,21,24,27,30,33 n500000, n=0,1,...,5 1.0000 3

GRS80 reference ellipsoid used in conversion between 3D X,Y,Z -coordinates and geodetic coordinates. The difference between GRS80 and WGS84 ellipsoids is so small, that it can be ignored in most applications. In table 9 however the parameters for both ellipsoids and comparison between parameters.

Table 9, GRS80 and WGS84 ellipsoidsParameterDescriptionUnitWGS84GRS80WGS84-GRS80A, DA Semimajor axis meter 6378137 6378137 0 F, DF Flattening 1/298.257223563 1/298.257222101 -0.000000164423..

New mapsStarting from 2003 have all new nautical charts been published in EUREF-FIN (appr. WGS 84). These new nautical charts apply international INT chart symbols. Because shallow waters are printed in blue according the INT symbols, the new nautical charts are called "blue nautical charts" while the old nautical charts are called "green nautical charts" based on the green color of the land areas. The transition period, during which the new and old nautical charts are used parallel, will be 4 to 5 years long.

Starting from 2005 National Land Survey of Finland produces new topographic maps in EUREF-FIN. The transition period, during which the new and old topographic maps are used parallel will be several years long. In the new maps ETRS-TM35FIN-grid is printed with black crosses, three UTM-grids TM34, TM35 and TM36 are printed in red and geographical coordinates are printed in blue. ETRS-GK-grids are not printed on basic maps.

## Using Finnish maps with GPS-devices and electronic maps

When Finnish maps are used with GPS-devices or mapping/navigation programs, the respective datum- and/or grid-parameters may need to be selected or set up according to the table 10. An empty cell means, that you can apply general default parameters; datum=WGS84/EUREF-FIN, ellipsoid=WGS84/GRS80 or close.

Table 10, Datum- and grid-conversions needed with Finnish mapsMap typeCoordinate typeDatum conversionEllipsoidGrid conversionOld topographic maps, KKJ, 1970-2005 Geographic KKJ <> EUREF-FIN International 1924 Grid KKJ <> EUREF-FIN International 1924 KKJ1-KKJ5 / YKJ Old "green" nautical charts, KKJ, -2002 Geographic KKJ <> EUREF-FIN International 1924 New topographic maps, EUREF-FIN, 2005- Geographic Grid ETRS-TM35FIN / ETRS-GK(n) New "blue" nautical charts, EUREF-FIN, 2003- Geographic

A datum conversion between KKJ and WGS84/EUREF-FIN is predefined in many GPS-devices and electronic mapping programs. These predefined conversions include both 3D-similarity transformation (datum-conversion) conversion between 3D-cartesian coordinates and geographic coordinates (ellipsoidal conversion). The problem here is, that KKJ has many aliases in different GPS-devices; KKJ, KKJ3, KKJ27, Finnish Grid, Finnish Nautical Chart etc.

In many GPS-devices the grid parameters for YKJ uniform coordinate system are predefined (but named KKJ, KKJ3, Finnish grid, seldom YKJ). The grid parameters for other KKJ zones (basic coordinate system) are very seldom predefined. If the KKJ-grid parameters are predefined, selecting KKJ-grid parameters selects normally automatically the KKJ-datum parameters too.

It is also normally possible to enter the grid parameters as user defined parameters. In that case take the parameters from tables 3, 4 or 8. Please note, that Central Meridian is also called Longitude of Origin. The value for false northing is 0 in all cases (new and old grids).

## Conversion flow, formulae and parameters

Table 11 describes the entire conversion flow from KKJ grid-coordinates to EUREF-FIN grid-coordinates with respective formulae and parameters. This conversion flow is quite general and hence applicable to many similar cases by substituting the parameters or projected coordinate formula with respective parameters or formula.

Table 11, conversion flow KKJ-grid-coordinates > ETRS-based grid coordinates > KKJ-grid-coordinatesFromToConversionFormulaParametersKKJ grid-coordinates KKJ geographic Transverse Mercator projection (Gauss-Krüger) JHS154, app. 1 KKJ-grid-coordinates, table 3 KKJ geographic KKJ 3D-X,Y,Z-coordinates Geographic > 3D-X,Y,Z JHS153, 5.2 Hayford ellipsoid, table 2 KKJ 3D-X,Y,Z-coordinates EUREF-FIN 3D-X,Y,Z-coordinates Datum-transformation, 3D-similarity transformation table 7 Table 6, column 1 EUREF-FIN 3D-X,Y,Z-coordinates EUREF-FIN geographic 3D-X,Y,Z > geographic JHS153, 5.2 GRS80 ellipsoid, table 9 EUREF-FIN geographic ETRS-based grid coordinates Transverse Mercator projection JHS154, app. 1 ETRS-based grid coordinates, table 8 ETRS-based grid coordinates EUREF-FIN geographic Transverse Mercator projection JHS154, app. 1 ETRS-based grid coordinates, table 8 EUREF-FIN geographic EUREF-FIN 3D-X,Y,Z-coordinates Geographic > 3D-X,Y,Z JHS153, 5.2 GRS80 ellipsoid, table 9 EUREF-FIN 3D-X,Y,Z-coordinates KKJ 3D-X,Y,Z-coordinates Datum-transformation, 3D-similarity transformation table 7 Table 6, column 1 KKJ 3D-X,Y,Z-coordinates KKJ geographic 3D-X,Y,Z > geographic JHS153, 5.2 Hayford ellipsoid, table 2 KKJ geographic KKJ grid-coordinates Transverse Mercator projection (Gauss-Krüger) JHS154, app. 1 KKJ-grid-coordinates, table 3

Conversion services onlineFinnish Geodetic Institute has created online conversion service for coordinate conversions between all coordinate reference systems used nationally in Finland.

About the conversion accuracyThe conversions between the 3D-Cartesian, geodetic and grid-coordinates very seldom cause considerable errors, but as explained above, due to the distortion in both scale and orientation in the current KKJ-system, the seven parameter similarity datum transformation with best parameters between KKJ and EUREF-FIN leaves residual errors of maximum two meters. Most handheld GPS devices and mapping and navigation programs use simpler three parameter similarity transformation, which leaves even greater residual errors (see table 6)

It is however worth noticing, that the conversion errors are only one part of the total error. The geodetic and cartographic base work, GPS-techniques and user's navigation activities are all measuring after measuring, and errors are by definition an inseparable part of all measuring. This applies even, when all activities are made in formally correct way; in addition to that errors are caused by misinterpretations, misunderstandings, operational errors etc. The total error is the sum of the errors made in different phases of a positioning or navigation act.

I want to thank Ph.D. Matti Ollikainen for his kind advice and for his corrections of some mistakes and inaccuracies in this article.

I also want to thank all other individuals, who have kindly commented this article, for their valuable input.

- Hirvonen, R.A., 1949: Die Gauss-Krügersche Projektion für breite Meridianstreifen auf dem Internationalen Ellipsoide. In Publication of the Finnish Geodetic Institute no 36 (in German)
- Ollikainen, M., 1993: GPS-koordinaattien muuttaminen Kartastokoordinaateiksi. Geodeettinen laitos, tiedote 8 (Converting GPS coordinates to Finnish National Coordinate System coordinates, Finnish Geodetic Institute, research note 8, in Finnish)
- Poutanen Markku, 1998, GPS-paikanmääritys - ISBN 951-9269-89-4, Publication of Ursa no 64 (GPS-positioning, in Finnish)
- Ollikainen, M., H. Koivula and Markku Poutanen, 2000. The densification of the EUREF network in Finland. The Publication of Finnish Geodetic Institute, no. 129. P.O. Box 15, FIN-02431 Masala
- Ollikainen, M., Koivula H., Poutanen M., 2001: EUREF-FIN koordinaatisto ja EUREF-pistetihennykset Suomessa, Geodeettinen laitos, tiedote 24 (EUREF-coordinates and EUREF-densification in Finland, Finnish Geodetic Institute, research note 24, in Finnish)
- Suomen kartasto, vihko 112 (Finnish mapping, book 112, in Finnish)
- Public Recommendation 153, JHS 153, Realization of the pan-European coordinate system ETRS89 in Finland
- Public Recommendation 154, JHS 154, Map projections and plane coordinates used with EUREF-FIN as well as accurate datum transformation methods
- Marko Ollikainen and Matti Ollikainen, 2004, The Finnish Coordinate Reference Systems. Published by the Finnish Geodetic Institute and the National Land Survey.