+If you are not interested in the theoretical background, just jump down to the +summary. +
+ ++When dealing with geographical data like cave locations, you will +inevitably run into a whole zoo of coordinate systems with names like +WGS84, UTM, BMN and so on. While a thorough introduction is probably +more appropriate for a full course in geodesy, I'll try to summarise the most +important bits as far as they are relevant to us and as far as I understand +them myself. +
+ ++In a first approximation the earth is a sphere. And unfortunately there are +some mathematical proofs showing that it's not possible to project the surface +of a sphere onto a 2D plane or map without distortions. People have still tried +hard and come up with a particular projection called the Transversal Mercator +projection, which has beneficial properties summarised as "locally there are +almost no distortions". +
+ ++The non-transversal, standard Mercator projection essentially takes a cylinder +aligned with the rotational axis of the earth from north to south and wraps the +cylinder around the equator of the earth. Next all the important +landmarks are projected onto the cylinder by casting rays from the centre of +the earth through its surface and onto the cylinder. Once everything is mapped, +the cylinder is cut open and unwrapped onto a flat table and ready is your map. +This map will be very accurate and have very little distortions around the +equator, but the closer you get to the poles the more distortions will become +noticeable. In particular think of where the north and south poles will be +projected to. +
+ ++The Transversal Mercator projection is very similar to the above, but instead +of aligning the cylinder with a north-south axis and intersecting earth along +the equator, it is tilted sideways, aligned with an east-west axis and +intersects earth in a circle for example along the 0-meridian through +Greenwich, through the poles, and somewhere through the Pacific. The rest is +done as before and once you cut the cylinder open and unwrap it, you'll get an +accurate map with little distortions exactly around the line of intersection, +which is called the "central meridian" of this particular Transversal Mercator +projection. Of course America and China would be heavily distorted with the +above choice of central meridian. So instead of doing just one of these +Transversal Mercator projections globally, the earth is divided into e.g. +60 zones and a different cylinder with a different central meridian is selected +for each zone. One particular definition of such zones has been internationally +standardised as Universal Transversal Mercator coordinates, but for the +entertainment of the local geodesists, different local coordinate systems and +"zones" have been defined for many countries. In Germany this is called +"Gauss-Krüger (GK)", in Austria there is a definition called +"Bundesmeldenetz (BMN)", and in the UK it is the "British National Grid (BNG)". +
+ ++One more thing. Once you have your unwrapped cylinder you'll +have to define coordinates on this cylinder surface, your map. These are +usually metric coordinates, i.e. they specify how many metres you have to walk +north and east on the cylinder surface starting from a given origin. And +typically one starts the "easting" at for example the western boundary of a +zone and the "northing" at the equator. For a national Austrian grid, it +doesn't make sense to start at the equator and therefore some +"false easting" and "false northing" have been defined by omitting some +of the leading digits. This saves repeatedly typing all the +same prefixes over and over again. +
+ ++Unfortunately the earth is not a sphere. A slightly more accurate +representation would be an ellipsoid, that is wider around the equator and +flatter at the poles. This has long been known and the Transversal Mercator +projection has been adapted to an ellipsoidal shape, so that it has even less +distortions. And of course, many clever people have come up +with many clever approximations of the ellipsoid. For example, the British +National Grid uses an ellipsoid defined by someone called Airy in 1830, and +Bessel has come up with a different ellipsoid in 1841. These were computed +by making accurate astronomical observations at different places within Europe. +In contrast, the more modern WGS84 ellipsoid has been defined by satellite +observations in more recent times. +
+ ++The different ellipsoids not only vary in their major and minor axes, but +also the centre of the ellipsoids can be offset or the whole +ellipsoid can be rotated by a bit. So these offset and rotation parameters have +to be specified as well, and getting the ellipsoid parameters wrong would +typically result in coordinates that are around 500m off, which is unacceptable +for locating a cave entrance on the plateau. So we can't just ignore the +ellipsoids but have to get their definitions right. +
+ ++Unfortunately the earth is not an ellipsoid either, but rather something like +a potato. This is not so important for defining east and north coordinates, +but it is very important for defining altitudes. While one sensible definition +of altitudes would simply be the "height above ellipsoid", it actually makes +quite a bit of sense to rethink this definition and come up with something +different, called geoids (not to be confused with ellipsoids!). +
+ ++Traditionally height was defined by "mean sea level", and in Austria they use +something called "Gebrauchshöhen Adria", which is meant to be the height +above the Adriatic sea. Unfortunately you can only measure the mean sea level +along the coast and it becomes a bit more difficult in the mountains. So +starting from a single point defined as the mean sea level in Trieste in 1875 +or so, the Austrians started to triangulate a grid of survey stations across +all of their empire. According to this triangulation they ended up with +several reference heights of certain peaks and so on, which is not necessarily +the real height above Adria anymore but includes some errors. Still, these +reference heights make up the "Gebrauchshöhe Adria", which literally means +something like "Used Height Adria". +
+ ++As clinos are affected by gravity, so are the Austrian +triangulations, and it turns out that the mass of the continental +plates does indeed affect gravity. So if you simply approximate the mean +sea level by a "simple" ellipsoid such as the "height above ellipsoid" does, +then you end up with a completely different set of altitudes compared to +the triangulation results. It turns out that relative to the ellipsoid the +"mean sea level" at some point in the alps would be about 40m above the mean +sea level at some point along the coast, just because the heavy continental +crust would attract more water. The "Gebrauchshöhen +Adria" have been defined with exactly this mass anomaly, and that's +what the Austrians use to this date. +
+ ++Nowadays geodesists have come up with something called geoids. These geoids +define the shape of equipotential surfaces, i.e. the shape of the surfaces +along which a reference body would have the same potential energy in the +gravity field of the earth. So in a sense, the Austrians defined a small +portion of a geoid by measuring the gravity field and defining their +"Gebrauchshöhen Adria" accordingly. In the meantime, some other geoids +have been defined and refined using satellite measurements and so on. There are +plenty of them available as huge "geoid height above ellipsoid"-tables in some +massive files (well, 4MB for the old, simple geoid models, 200MB for more +modern and accurate ones). +
+ ++Most modern GPS receivers, at least most Garmin ones, will nowadays compute a +"height above sea level", and not a "height above ellipsoid". Unfortunately +at least Garmin devices do not allow to change this, and the bad news is that +in fact no one outside the Garmin Corporation really seems to know, how they +managed to approximate the geoid in their tiny little units with not very much +memory and computation power. But the good news is that the +differences between various geoids are usually in the range of 25cm, and the +Austrian "Gebrauchshöhen Adria" make no difference there. In fact, as the +Bessel ellipsoid has been designed within Europe and adapted to the shape of +the alps, even the differences between the Bessel ellipsoid and the +"Gebrauchshöhen Adria" are below 3.5m for most parts of Austria and about +40cm on the Schwarzmooskogel. +
+ ++Luckily all of the above is so horribly complicated, that people have long come +up with computer programs for converting these coordinate systems back +and forth. You just have to find an appropriate suite of software and learn how +to use it. And particularly the using part can still be quite complicated. For +the reasons detailed in the "Geoids" section above, I'd recommend converting +only the horizontal coordinates and keeping the altitude measurements from the +GPS. +
+ ++I personally get along very well with Proj4, which is open source and free and +all that. It should also be packaged with all major Linux distributions and +installed on the expo computer. Unfortunately the current versions do not deal +very well with vertical datums (i.e. geoids), but we can ignore the geoids +anyway. To invoke it, you have to type in something like +
+ ++cs2cs +from [+some +magic +parameters] \ + +to [+some +more +magic +parameters] +
+Then you type in the coordinates in the source format and you'll get +coordinates in the destination system, sometimes with x and y swapped back +and forth. The following table is intended to help you choose the right magic +parameters for your coordinate system: +
+ +
+Latitude-Longitude in WGS84 datum with heights above WGS84 ellipsoid:
++proj=latlon +ellps=WGS84 +datum=WGS84+ |
+Latitude-Longitude in WGS84 datum with heights above EGM96 geoid[1]:
++proj=latlon +ellps=WGS84 +datum=WGS84 +geoidgrids=egm96_15.gtx+ |
+UTM coordinates in WGS84 datum with heights above EGM96 geoid[1]:
++proj=utm +zone=33 +ellps=WGS84 +datum=WGS84 \ + +geoidgrids=egm96_15.gtx+ |
+Austrian coordinates for our Loser data set[2]:
++proj=tmerc +lat_0=0 +lon_0=13d20 +k=1 +x_0=0 +y_0=-5200000 \ + +ellps=bessel +towgs84=577.326,90.129,463.919,5.137,1.474,5.297,2.4232+ |
[1] +Starting from version 4.8, the cs2cs program should have rudimentary support +for vertical datums. You might have to separately install the file egm96_15.gtx, +though. While this file strictly speaking only defines the EGM96 geoid, it can +serve as a good approximation to most other geoids, including the one used by +Garmin GPS receivers and the "Gebrauchshöhe Adria" +
+[2] +There are a few different versions of the "+towgs84" part of the Austrian +coordinate system, which specifies the offset and rotation of the used Bessel +ellipsoid with respect to the WGS84 ellipsoid. According to an old table found +on this expo website, it should read "575,93,466,5.1,5.1,5.2,2.5", which is +clearly a mistyped version of the more commonly found definition +"575,93,466,5.1,1.6,5.2,2.5". Both of these seem slightly less accurate than +the "577.326,90.129,463.919,5.137,1.474,5.297,2.4232" proposed by various +other sources, but in the end it will only make a difference of +about a metre or so. +
++For all practical purposes I'd say, set your GPS receiver to UTM coordinates, +WGS84 ellipsoid, WGS84 datum. It will +usually spit out rather unspecific "heights above sea level", which are within +about 25cm of the heights in our data set. To convert the horizontal +coordinates from UTM zone 33 to our data set coordinates, use: +
+ ++cs2cs +from +proj=utm +zone=33 +ellps=WGS84 +datum=WGS84 \ + +to +proj=tmerc +lat_0=0 +lon_0=13d20 +k=1 \ + +x_0=0 +y_0=-5200000 +ellps=bessel \ + +towgs84=577.326,90.129,463.919,5.137,1.474,5.297,2.4232 +
+As an exercise you can try to convert the following between +latitude-longitude, UTM and data set coordinates: +
+ +| Point | lat-long WGS84 | UTM WGS84 | data set |
|---|---|---|---|
| 161g | 13d49'35.982"E 47d41'1.807"N | 411941 5281827 | 37095.76 82912.23 |
| 204a | 13.82146667 47.69093333 | 411563 5282622 | 36700.78 83698.97 |
| 2001-06 | 13.81911639 47.67609556 | 411362 5280976 | 36534.63 82048.14 |
| 2011-01 | 13.82701861 47.69979611 | 411995 5283601 | 37111.31 84686.99 |
Olaf Kähler, September 2012
+If you want to read about the nitty gritty of converting GPS coordinates to -the ones used by the Kataster system, you can do no better than read Wookey's -Compass Points Article. Briefly, this -says "it's horribly complicated and we don't really know how to do it -properly". Things have improved a little since those days, particularly as -without the fog of the SA variation it's now easy to find out whether your GPS -is set up right by just GPSsing a known point and comparing the results. -However, the main point of having a GPS fix on an entrance is so we can find it -again and be sure it is the same one!
+the ones used by the Kataster system, you can do no better than read the +short introduction to coordinate systems, which briefly +says "it's horribly complicated and we use computer programs to do it properly". +(A rather outdated first attempt at this can also be found in Wookey's +Compass Points Article from 1996, which +briefly says "it's horribly complicated and we don't really know how to do it +properly".) Overall things have significantly improved since the early days, +particularly as without the fog of the SA variation it's now easy to find out +whether your GPS is set up right by just GPSsing a known point and comparing +the results. However, the main point of having a GPS fix on an entrance is +so we can find it again and be sure it is the same one!