Finland’s geographical centre has been an area of interest before. While some have suspended an analogue cardboard model, some have tried to find the centre using mathematics. Because the calculation is so simple, mathematical methods have usually started by defining the centre of a polygon in a selected projection. As a result, calculation methods have been as simple as possible.
However, a 2D projection distorts the surface area, even fairly significantly, depending on the projection selected. At its largest, the difference can be up to hundreds of square kilometres when doing calculations for Finland. So far, no calculation of the geographical centre calculated using a 3D coordinate system has been identified in literature
As pensioners with all the time in the world on our hands, we decided to get on with it and redefine Finland’s surface area and geographical centre in 2D and 3D coordinate systems.
Where are Finland’s boundaries?
Different sources offer various conceptions of Finland’s surface area. Google search gives the lowest estimate of 338,440 km2. According to statistics of the NLS, Finland is significantly larger at 390,908.62 km2 (figure determined in 2020). The difference depends on whether the land area alone is calculated or whether sea areas are also included. The surface area should always be furnished with metadata, which contains the proper definition of surface area and method of calculation.
How is the surface area defined? The ground rule is that those who define it have an identical and accurate idea of the country borders. As we were unable to find a single source that would have provided sufficiently reliable and accurate border coordinates, we determined a boundary polygon from several sources we considered best. The polygon that outlines Finland consists of roughly 28,109 corner points.
The outer boundary of Finland’s territorial waters has been defined in an act and decree. The border between Finland and Sweden at the Torne River was last verified in 2006. The Norwegian border was verified in 2000, and the Russian border in 2018. The coordinates of the border points are available on the NLS website.
In defining points for the geographical centre, we used Finland’s geoid model and the 128-metre elevation zone model in our calculations. They can also be found on the NLS website.
Table: Finland’s surface area and geographical centre in different projections, in an Earth ellipsoid and geoid, and the elevation model’s geographical centre.
Cannot wait to start calculating
We made our calculations using Excel, the Visual Basic for Applications programming language, QGIS software, and the Paikkatietoikkuna service (https://kartta.paikkatietoikkuna.fi/?lang=en). The algorithms we used can be found in the sources listed at the end of this article
We found out right away that it was not as easy as we had thought to find elevations in the 10-metre elevation model. No services were available for interpolating elevations with large volumes of data. Therefore, we decided to obtain approximate elevation data from the 128-metre elevation model.
Calculating the surface area using the projection plane was relatively easy using Excel. We started with the coordinates of the polygon’s corners. The geographical centre was fairly easy to calculate at the same time. The ellipsoid gave us a headache. Calculating the surface area using the ellipsoid was more challenging, but we succeeded using Excel’s macro functions. We applied Charles F. F. Karney’s algorithms, which are largely used in open data systems in the geospatial data sector.
To calculate the geographical centre, we divided Finland into 20-metre latitude zones. We identified the intersections of the zones and the nation’s border and calculated their coordinates.
Based on the intersections, we calculated geographical centres for each zone in the same way as for the arc of a circle, as well as averages for the geographical centres weighted by the length of the zones. This resulted in the 3D coordinates of the geographical centre of the ellipsoid surface.
We used the same zones in calculating the geographical centre of the geoid surface. We divided them into 20-metre grids, for which we obtained 3D coordinates from the geoid model. To have as accurate results as possible, we used almost a billion grids in our calculation.
Finally, we calculated the geographical centre of the surface model. We added elevation data to the grids formed in calculating the geoid model’s geographical centre. Another option would have been to obtain elevation data from the 10-metre elevation model, and this would have given us more accurate results. However, it was not possible to interpolate the elevation model with such large volumes of data.
The surface area is a question of definition
For us pensioners, the project was a fairly enjoyable and refreshing experience. It showed that the surface area is a question of definition. In calculations, we need to accurately define what we mean by the surface area and explain it using metadata. Because no metadata for the surface area is presented in national statistics, there can easily be misconceptions and differences in interpretation.
In addition, the method of interpolating the surface’s outlines affects the final outcome. The surface area outlined in an Earth ellipsoid or geoid surface is something completely different from the surface area of a polygon projected on a plane. Coordinates for the nation’s borders are available in various sources, and they are partly subject to interpretation – especially regarding the outer borders of territorial waters. Human errors in background information are also possible.
Defining the surface area accurately using an ellipsoid and geoid is slightly difficult, as not many geospatial data programs can do this. The accurate 3D calculation of the geographical centre requires a massive number of tiny surface area objects.
We hope that younger scientists will specify the location of the geographical centres with their more powerful computers.
The full description is available at https://napapiiri.webnode.fi/Suomen-keskipiste.
Terminology
Geoid: The shape of the potential of Earth’s gravitational field that best connects with the mean sea level either globally or locally
Geoid model: A numerical estimate of the geoid
Earth ellipsoid: A spheroid that represents the shape of Earth’s surface
Ellipsoidal height: The distance between a point and the Earth ellipsoid calculated along the Earth ellipsoid’s normal
Sources
- Public Administration Recommendation JHS 197, Appendix 2
- Helsinki University of Technology’s old handout no. 305/1972: R.A. Hirvonen, Mathematical geodesy
- Charles F. F. Karney: Algorithms for geodesics, J. Geodesy 87(1), Jan. 2013
Authors: After his brief career in the Land Survey Administration, Onni Kukkonen worked as an IT specialist (City of Helsinki, Tietotehdas Oy) and entrepreneur (Vegasoft Oy) before returning to his roots dating back nearly 50 years in this project. Email: firstname.lastname@vegasoft.com
Reino Ruotsalainen started his career in the Land Survey Administration in the 1970s, worked as a development manager at Finnmap Oy throughout the 1980s, worked briefly as a special education teacher at the Espoo–Vantaa Institute of Technology in the mid-1990s, and returned to the NLS, retiring in 2013. Email: firstname.lastname@kolumbus.fi
TAGS: SURVEYING AND MAPPING
