How to be in two (or more) places at once
Multiple coordinate systems are covered in this post.
In these busy, busy times, wouldn’t it be nice to be in more than one place at a time? Good news! You can! In fact you have been ! You’re soaking in it! “How?” you may well ask. All thanks to multiple coordinate systems. This ties in with some earlier discussions we’ve had about map projections. With every map projection we also get a coordinate system thrown in for good measure (sorry, pun intended…) – it’s the coordinate system, after all, that allows us to make measurements of area and length in real world units (like metres).
We saw earlier that most of our New Zealand data and maps have adopted New Zealand Transverse Mercator (NZTM) as their coordinate system. With NZTM I can specify any location within New Zealand with two elements: an easting (the x-coordinate) and a northing (the y-coordinate). So, for example, if I’m standing in front of the Forbes building,
I could tell you exactly where I am using the NZTM coordinates:
Easting: 1557067.60 Northing: 5167552.88
There’s one of my places.
An easy second one has to do with the fact that NZTM is a projection from the NZGD2000 datum (as we’ve seen), which is based on the GRS80 elipsoid and on that elipsoid, that same location has coordinates:
Longitude: 172.4677 ° E Latitude: 43.6438 ° S
(Note: these units are decimal degrees. In the Degrees/Minutes/Seconds format, those same coordinates are: 172° 28′ 3.66705”, -43° 38′ 37.60688”)
But wait, there’s more. While NZTM is what we currently use for maps and data, New Zealand Map Grid is what we used to use and the older 260 series of topographic maps had their own coordinates. In NZMG, that some location is at:
Easting: 2467062.15 Northing: 5729260.66
And NZMG is based on NZGD1949, which has coordinates:
Longitude: 172.4676 ° E Latitude: 43.6455 ° S
As a side note, the image below may not really make any sense, but it shows the NZ coastline (in light blue) in NZTM and the coastline in NZMG in darker blue. I edited the NZMG layer so that it doesn’t have any information on the layer’s projection, so it’s just placed it within the coordinate system of NZTM (I hope that made sense). This just gives you a sense of the two systems being in different places, even though they’re the same place (how very Inception-like):
But that’s not all. If we think about WGS84, the spheroid used by GPS, we get yet another set of coordinates.
Longitude: 172.4677 ° E Latitude: 43.6438 ° S
Quite similar to the second set above, which shouldn’t be too surprising as NZGD2000 almost exactly corresponds to WGS84.
Let’s throw another one in for good measure. In addition to NZTM, we also have a set of smaller, more local coordinate systems, mainly used by surveyors for marking out property boundaries. These are the local surveyors, or meridional circuits and there are 28 that cover New Zealand. Here’s how they are spread around the place:
For us, it’s the Mount Pleasant circuit so that same location also has coordinates:
Easting: 379081.80 Northing: 794053.88
So there you have it – six places at once. (No extra points for those who recognise that these all relate to the same place; but they are all different because they’re all in different coordinate systems.)
One of the fundamental characteristics of any GIS feature is where it is. All GIS data will contain a location based on some coordinate system. Best practice is that there are some additional data (metadata) that specify exactly which coordinate system. When you add a data layer to a map, the software pickups up the x, y coordinates and places that feature on the map. With the right information, ArcMap also knows what units the data are in (metres? cubits?). ArcMap also uses this information if you add a new data layer that’s in a different coordinate system. So if I’ve got data on a map in NZTM (the first layer added sets the coordinate system of the map) and then try and add a layer in WGS84, ArcMap projects the data (lingo alert) “on the fly”, meaning it knows where stuff should be and places it there. (Best practice would be to take my WGS84 layer and use the Project tool to convert it to NZTM) My two layers can live and play happily together on the same map because of this extra information. In the image of TM and MG above, if I had included the projection data, ArcMap would have arranged the two layers in the same place.
(By the way, there’s nothing exceptionally special about NZTM, apart from it makes it much easier to deal with GPS data. It’s just that we’ve all tacitly agreed to use it).
I hope that helps put you in your place.