Eino Uikkanen's homepage > About the coordinate systems - updated 10.2.2023
This document is written by Eino Uikkanen and professor Martin Vermeer, and translated from Finnish to English by Eino Uikkanen. The document presents Finnish and global coordinate systems, and is targeted for anyone who wants to get a basic understanding of coordinate systems.
The Finnish version of this article: Oppijakso koordinaatistoista
For
more detailed information of the Finnish coordinate systems, please
visit: Finnish
coordinate systems
Geographical
coordinate systems provide the basis for expressing the exact position
of any geographical location as unique coordinate values. The most
widely used and oldest way of expressing the locations on the earth is
dividing the earth into parallels and meridians and expressing the
positions as latitude, longitude, and height. Other coordinate systems
used are, e.g.
- earth-centered three-dimensional coordinates and
- grid coordinates aka projected coordinates.
Earth-centered,
three-dimensional coordinates are used only in scientific work.
Grid
coordinates are used to present a limited geographical area with a
coordinate system, which approximates a rectangular grid. The UTM
coordinate system, for example, is a widely used grid coordinate system.
A
coordinate system is always based on a coordinate reference system,
i.e., the determination of how and on what basis the coordinate values
of the points in the coordinate system are determined and measured.
The
actual coordinate system consists of a selected set of fixed and
identifiable marked points, whose coordinate values have been measured
and marked according to the selected coordinate reference system. Such
a point defining the coordinate system can be, for example, a bolt
struck in the rock in the terrain or, a fixed GPS measuring station.
This set of points defining the coordinate system is called “coordinate
reference frame”. For example, the EUREF-FIN coordinate system
currently in use in Finland is defined by thousands of points measured
and marked in the terrain and many permanent GPS measuring stations.
The
earth is a challenging object for determining coordinate systems, as
the earth is unstable in many ways. The continental plates of the earth
move relative to each other at a rate of several centimeters, even 10
cm, per year. During the year, the position of the Earth's axis of
rotation wanders along an irregular circle of about 10 meters in width
as the sum of many different movement cycles. There are many other
smaller phenomena, which move parts of the earth with respect to each
other and occur in different cycles.
As
the movement of the continental plates significantly exceeds the
accuracy requirements of the coordinate systems in a relatively short
time, the coordinate systems intended for normal practical use must be
fixed to the continental plates. Therefore, the EUREF-FIN coordinate
system used in Finland and the other European coordinate systems are
fixed to the stable part of the Eurasian continental plate. Since the
coordinate points move with the continental plate, the movement of the
continental plate does not affect the coordinate systems.
In
earlier times, the instability of the earth was not a problem in the
coordinate system definitions, because the coordinate systems were
local and the requirements for the accuracy and compatibility of the
coordinate systems were much lower than today. Most countries had their
local coordinate systems, which could differ significantly. For
example, the coordinate values of the KKJ coordinate system, which was
used in Finland until the early 2000s, the coordinate values differ
from the current globally compatible EUREF-FIN coordinate system up to
nearly 200 meters.
Global,
cross-border functions and systems, e.g., satellite navigation systems,
require global coordinate systems alongside country-specific and other
local coordinate systems.
The
best-known and most widely used global coordinate system is the WGS84
coordinate system used by the GPS system. The WGS84 coordinate system
was created by the United States Department of Defense. In global
coordinate systems, the effect of the earth’s instability cannot be
eliminated by fixing the coordinate systems to continental plates. As a
result of that, the coordinate points are in constant motion to
different directions making the coordinate values dependent on time.
Therefore, the applications utilizing global coordinate
systems have either to consider the time dependence or to accept the
inaccuracy caused by the earth’s instability in the coordinate values.
As a result, the WGS84 coordinate system is not suitable for
use in mapping work or any high-precision tasks. However, global
coordinate systems like WGS84 are most suitable for positioning and
navigation purposes, where the accuracy requirements are lower.
The
most accurate and up-to-date information on the movements of the earth
and its surface is produced by an international scientific service
called “International Earth Rotation and Reference Systems Service”
(IERS). The IERS service is provided by an international
surveying-science organization called “International Association of
Geodesy” (IAG). This organization has produced a global coordinate
system called “International Terrestrial Coordinate Reference System”
(ITRS) and a set of corresponding coordinate frames called
“International Terrestrial Reference Frame” (ITRF). ITRF is based on a
dense network of measuring stations located around the globe. IERS
maintains coordinate data globally with scientific accuracy using
existing observational data. Because the coordinate points are in
constant motion, IERS maintains information about the direction,
velocity, and coordinate values of the coordinate points at certain
points in time.
Constantly
moving or changing coordinate values are ill-suited for everyday use.
Therefore, IERS regularly publishes coordinate values at specific
times. IERS names the resulting coordinate systems according to the
time epochs. For example, ITRF89 refers to the coordinate values of the
ITRF coordinate frame at time 1989, or epoch 1989.0. Correspondingly,
for example, the ITRF coordinate frames ITRF90, ITRF91, …, ITRF2005,
ITRF2008, and ITRF2014 have been published.
The
current Finnish coordinate system and most other European coordinate
systems are based on the European Terrestrial Reference System 89
(ETRS89). The ETRS89 coordinate system is coincident with ITRS at the
epoch 1989.0 and fixed to the stable part of the Eurasian Plate.
Various realizations of ETRS89, i.e., coordinate frames, have been
created at different times in different European countries. The name of
the Finnish national ETRS89 realization, i.e., the coordinate frame, is
EUREF-FIN.
At
the beginning of the 21st century, the current EUREF-FIN coordinate
frame, a national realization of the pan-European ETRS89 coordinate
frame, was introduced in Finland. This means that the points in the
EUREF-FIN coordinate frame are measured and determined according to the
ETRS89 coordinate frame.
The
EUREF-FIN reference frame consisted originally of 100 points
(benchmarks), which were measured and marked in the terrain, and of 12
permanent GPS measuring stations. Since then, the EUREF-FIN reference
frame has been hierarchically densified into thousands of points in
different phases and by different actors.
The
predecessor of the EUREF-FIN coordinate frame was the KKJ coordinate
frame, which was introduced in 1970. Although the transition from the
KKJ coordinate frame to the EUREF-FIN coordinate frame started in the
early 2000s, coordinates according to the KKJ coordinate frame continue
to appear in various lists, old documents, etc. for a long time to come.
To
convert KKJ coordinates to current EUREF-FIN coordinates, several
freely available conversion programs are available as web services. The
most comprehensive of these is the coordinate transformation service
developed at the Finnish Geodetic Institute. This service is currently
embedded in the Paikkatietoikkuna online map service: https://kartta.paikkatietoikkuna.fi/?lang=en
All
mapping and measurement work in Finland is carried out in the EUREF-FIN
coordinate system. The GPS system, on the other hand, uses the WGS84
coordinate system. EUREF-FIN and WGS84 are two different coordinate
systems: EUREF-FIN is local, fixed, and more accurate, WGS84 is global,
variable, and less accurate. However, the difference between EUREF-FIN
coordinates and WGS84 coordinates is so small that it can be ignored in
most applications used by average spatial data users, e.g., in
positioning and navigation applications.
EUREF-FIN
coordinates can be presented in several different formats. These
formats with respective coordinate value samples are listed in the
table below. For comparison, the coordinates of the same point in the
outdated KKJ coordinate system are included.
All
EUREF-FIN coordinate entries in the list are thus different
representations of the coordinate values of the same point in the same
EUREF-FIN coordinate system.
Coordinate
system |
Coordinate
format |
Latitude/
Northing |
Longitude/
Easting |
EUREF-FIN- Geographical coordinates |
|||
EUREF-FIN |
ddd
mm ss.sss… |
60
11 19 |
24
48 30 |
EUREF-FIN |
ddd
mm.mmmm… |
60
11.32 |
24
48.50 |
EUREF-FIN |
ddd.ddddd… |
60.188611 |
24.808333 |
EUREF-FIN
projected coordinates |
|||
EUREF-FIN |
ETRS-TM35FIN |
6674433.905 |
378465.407 |
EUREF-FIN |
ETRS-TM35 |
6674433.905 |
378465.407 |
EUREF-FIN |
ETRS-TM34 (*) |
6678508.217 |
711131.053 |
EUREF-FIN |
ETRS-GK25 |
6675102.149 |
489365.946 |
KKJ-coordinates
(KKJ is obsolete and is based on a different basis of the calculation
than EUREF-FIN) |
|||
KKJ |
KKJ universal coordinates in meters |
6677236.864 |
3378586.032 |
(*) =
Sample point is on UTM-zone TM35, outside UTM-zone TM34, but presented
as an example as UTM-zone TM34 coordinates.
Geographic
coordinates can be expressed in degrees, degrees and minutes, or
degrees, minutes and seconds. Using geographical coordinates when
transmitting coordinate information lowers the risk of
misunderstandings. It is also worth remembering that the EUREF-FIN
coordinate system and the WGS84 coordinate system differ so little,
that it seldom matters, whether we refer to EUREF-FIN or WGS84.
On
Finnish maps, geographical coordinates are presented in degrees and
minutes.
The
Emergency Response Centre Agency in Finland recommends that the
coordinates are given in degrees and minutes, as Emergency Response
Centre Agency's information system uses the format ddd ° mm.mmm, i.e.
degrees, minutes and decimals.
The
ETRS-TM35FIN coordinate format is a grid coordinate system covering
the entire Finland. Zone 35 of the global UTM
coordinate system coincides with the ETRS-TM35FIN coordinate system,
but the ETRS-TM35FIN extends beyond the UTM zone throughout Finland.
ETRS-TM35FIN
coordinates provide us with a coordinate system as close as possible to
a rectangular plane grid, where the unit is a meter. Because of the
curvature of the earth’s surface, this is not entirely possible, but in
a limited area, even in an area of the size of Finland, we get very
close. Therefore, ETRS-TM35FIN coordinates can, with reasonable
accuracy, be used to perform calculations as if they were rectangular
grid coordinates.
As
an example and demonstration of how close the ETRS-TM35FIN grid is to a
metric rectangular grid, we calculate the distance between two Finnish
cities Vaasa and Kotka using two methods:
- The actual shortest distance along the geodesic line or the “as the crow flies” distance
- An approximate value of the distance is calculated by the Pythagorean theorem as if the grid was a metric rectangular grid.
The
ETRS-TM35FIN-coordinates for these cities are in meters:
- Vaasa ETRS-TM35FIN coordinates: 7015316, 231624
- Kotka ETRS-TM35FIN coordinates: 6707100, 495422
The
difference between the northern coordinates is 308216 meters, and the
difference between the eastern coordinates is 263798 meters. The
distance calculated by the Pythagorean theorem is 405693 meters. The
actual shortest distance along the earth's surface is 405733 meters.
The difference between the results of these two calculations was only
40 meters. Between Helsinki and Sodankylä the distance calculated along
the earth's surface is 811755 meters and the distance calculated from
the ETRS-TM35 coordinates by the Pythagorean theorem is 811481 meters.
Thus, the difference between the results of the distance calculations
between Helsinki and Sodankylä will be 274 meters, which is 0.034% of
the total distance.
The
ETRS-TM35FIN coordinate system does not fully correspond to the
rectangular metric grid coordinate system but differs from it by an
amount called the projection error. However, this is not an actual
error but a difference that is known and can be accurately calculated.
It is worth noting that the projection error only affects the
properties of the projection, such as scale or area, and not the
coordinate values. Thus, coordinate values are not less accurate where
there is a larger projection error.
The
grids of the ETRS-TM35FIN coordinate system are indicated on the Finish
maps with black lines in the UTM zones 34 and 36 and with black crosses
in the UTM zone 35.
UTM
coordinate system zones 34, 35, and 36 do overlap the area of Finland
and are marked on the Finnish maps with purple lines. These
UTM-coordinates are based on EUREF-FIN and are thus distinguished from
standard UTM-coordinates with the prefix “ETRS-“; ETRS-TM34, ETRS-TM35,
and ETRS-TM36. ETRS-TM35 coincides with the ETRS-TM35FIN coordinate
system within the UTM zone width.
The
ETRS-GK coordinate system is used in applications that require a
projection error smaller than in the ETRS-TM35FIN coordinates. This is
achieved by using a narrow, one-degree zone width.
Therefore, 13 ETRS-GK zones, ETRS-GK19 - ETRS-GK31, are needed to cover
the entire area of Finland. Municipalities select the GK zone that best
covers the municipality's area. If the municipality's area extends to
several GK zones, the municipality may choose one GK zone and use it
with extended zone width (e.g. the city of Lahti).
ETRS-GK
coordinates are not marked on Finnish maps.
The
discussions of the theoretical differences between coordinate systems
and, for example, the magnitude of computational errors in
transformations between coordinate systems easily gives the impression
that the sources of the errors in the coordinate values are limited to
these sources. However, there are several other sources of errors in
the coordinate values and the biggest source of errors is human
processing of the coordinate values. For example, when determining
coordinate values from a paper map or an application, the thickness of
the pen or the resolution of the map application can considerably
exceed the errors that occur in other processing.
Basic
geodetic and cartographic work, GPS technology, and user navigation
work are all about making measurements, and whenever measurements are
made, errors are made too. The total error is accumulated from the
errors made at different stages. The steps listed below do inevitably
result in measurement or calculation errors, even if the operation
itself is error-free.
- Errors in measuring and marking the coordinates in the terrain
- Errors in map production
- Errors when the user determines the coordinate values from the map
- Errors in transformations between coordinate systems, possibly at several stages of the process
- Errors in the GPS system
- Other human errors - misunderstandings, labeling errors, interpretation errors, etc.
Until
recently, different countries and regions in the world have applied
different and mutually incompatible coordinate systems. Today, most
coordinate systems of different countries are as compatible as the
slightly unstable surface of our planet allows. Until the beginning of
the 21st century, Finland also applied a local coordinate system,
Finnish National Grid Coordinate System KKJ. KKJ differed significantly
from Finland's current EUREF-FIN coordinate system, which is compatible
with global coordinate systems.
Today,
different countries have largely compatible coordinate systems. The
development of coordinate systems to the current accuracy and
compatibility has been made possible by the development of measurement
and other technology, not least space technology, the use of
positioning satellites orbiting our planet. On the other hand, the same
development, as well as globalization, has required higher
compatibility of the coordinate systems.
The
current coordinate systems in most countries are somehow based on a
global coordinate system called the International Terrestrial Reference
System (ITRS). This coordinate system is maintained by an international
scientific service called International Earth Rotation and Reference
Systems Service (IERS). The coordinate system currently in use in
Finland is called EUREF-FIN. The EUREF-FIN coordinate system was
introduced in the early 2000s. EUREF-FIN is based on the common
European coordinate system ERTS89 and ETRS89 is based on the global
ITRS coordinate system.
The
Finnish EUREF-FIN coordinates can be presented as geographical
coordinates in different formats, as coordinates of the nationwide
ETRS-TM35FIN grid coordinate system, as UTM coordinates or as
coordinates of the 13-zone ETRS-GK coordinate system. The conversions
between the different representations are purely mathematical and can
thus be done to any desired accuracy. Even though these are different
representations of the same coordinate system, they may be called
coordinate systems.
The
GPS system uses the global WGS84 coordinate system. As a global system,
the WGS84 coordinate system is less accurate than coordinate systems
which are fixed to continental plates. However, the differences are so
small that they are irrelevant to the average user, for example in
navigation.
For
emergency messages and other urgent transmissions of coordinate data,
it is recommended to use geographical coordinates in the format ddd °
mm.mmm ', i.e. degrees, minutes, and decimals.
The
surface of the globe can not be accurately projected on a plane map;
only some properties of the spherical surface can be presented
accurately or with minor distortion on the plane while other properties
are presented with bigger distortion. Therefore, a large number of
different map projections, which preserve different properties
unchanged or almost unchanged, have been developed over time. For
example, a projection may correctly preserve shapes, angles or areas,
represent latitudes and/or longitudes in straight lines, or, for
example, present lines with constant bearing as straight lines.
When
choosing a suitable map projection, it is necessary to consider which
properties of the spherical surface are appropriate to preserve on this
particular map. The appropriateness of the projection depends on e.g.
the size and shape of the area to be described and the purpose of the
map.
For
example, the features of the quite commonly known Mercator-projection
support very well the ocean navigation, but show the areas near the
polar regions much larger than areas near the equator. The user of the
Mercator projection must either understand and accept this scale
distortion or choose another projection and give up the maritime
features of the Mercator projection - the map projection is always a
compromise.
With
thematic maps made to present some specific information, a projection
can be chosen that gives the map user the most accurate idea possible
of what is presented on the thematic map. Indeed, a projection that is
ill-suited to presenting a case may give the map researcher an
incorrect picture of the matter presented, even if the map and the
information presented on it are correct in themselves. This can and
will be used to deliberately mislead the map user.
The
map projection and the coordinate system can be selected independently.
Sometimes, however, it is appropriate to select a particular projection
with a particular coordinate system. For example, ETRS-TM35FIN or some
other large plane coordinate system should be presented in a similar
projection so that the grid formed by the coordinate lines is displayed
on the map regularly.