Intro to coordinate systems and UTM projection

hi everybody welcome to a quick video about coordinate systems so what are coordinate systems and why are they important in GIS well one motivating question is to just ask how would you describe your location to someone and of course we all know we would use latitude and longitude so 44 degrees north 72 degrees west for example but we think about coordinate systems we need to think about what is that latitude and longitude referenced to and how did that how was that grid established and moreover how do you actually know what your latitude and longitude are especially if you don't have a GPS in hand well of course in the pre GPS days you would read that from a map and mapmakers new latitude and longitude relative to a bunch of benchmarks of known locations so in this video we'll go through a little bit about how this lat/long grid is established what the role of the benchmarks is and how coordinate systems have changed over time so most coordinate systems have four parts an ellipsoid a geographic coordinate system a datum and then sometimes a projected coordinate system so we'll look at each of these in turn so if you want to break earth into a grid of lat/long the first thing you do is you have to decide what the surface of Earth looks like and agree on that shape and that's done using what's called a reference ellipsoid which defines the major and minor axis of Earth and the ellipsoid is basically defined by the geoid the geoid is an imaginary surface of gravity equipotential so it's a surface of constant gravity and gravity of course depends on topography and then the ellipsoid is simply the average of that geoid in most cases so now that we know the size and shape of earth how do we break it into an evenly spaced grid of course this is done with lines of latitude and longitude but like any grid or coordinate system the origin needs to be defined in this case the origin of this grid is given by the intersection of the Greenwich meridian which runs through Greenwich England and is a line of zero longitude and where that intersects the equator which is defined as zero degrees latitude and so this is really the zero zero point of the global coordinate system but from there we have an even thorny er problem which is in the old days surveying is required to actually then determine where exactly each of these lines of latitude and longitude fall on earth it's easy to draw this in a cartoon representation but to actually put your finger on the exact spot where 22 and 1/2 degrees longitude is is a lot trickier in part because it basically has to be all measured relative to for example the origin or to some other known point like Greenwich England so the the way this is done is using datums and datums are networks of benchmarks that have a known latitude and longitude so in the early days of surveying you know the hundreds of thousands of man hours were spent surveying the actual distance between points and actually pounding in benchmarks into Rock such that the actual latitude and longitude of that point would be known and then any subsequent surveys could be done off of that particular benchmark which had a known latitude and longitude so that worked well and datums gave us the ability to kind of draw out or lay out the lat/long but of course over time surveying techniques improve and it may be that the early surveys weren't exactly right maybe they were off by 5 10 20 meters so in the subsequent years new datums have been introduced and if you look at a list of datums you'll find dozens of them two of the most common datums are wgs84 and nad83 so these are two that are really commonly used global datums in in GIS so how different are these datum shifts when people redo the surveying a good example is the shift from the North American datum nad83 versus the original nad27 so we can see that the difference is about 20 meters if you're in the Midwest it's up to a hundred meters if you're out in California that may actually be in feet I'm not positive but the key point is that the benchmarks themselves didn't move the surveying was simply redone and it was determined that that benchmark wasn't actually at its original Latin long it was actually 40 feet off of where it was thought to be before so kind of just refining this latitude and longitude grid but what's critically important is that whenever you determine your latitude and longitude today say with the GPS it's being determined relative to a datum so you're basically saying look I'm some place on earth I have to describe that with a latitude or longitude number and that lat lawn number has to be relative to a datum so you always have to specify which datum you are locating yourself relative to and that's why it's so critical not to confuse these you have to always specify that if you get it wrong you're going to be off by this much 20 feet 100 feet etc so what's so if we've talked now basically about geographic coordinate systems datums relative position let's finish up by talking about projected coordinate systems and this is a bit of a problem because the coordinate system we described before the Latin long lines were basically circles they were circles that were transcribing the sphere that we live on but most of the way we view maps is actually on a flat surface so we're effectively always trying to view a curved surface of the earth on a flat map projection and a simple way to think about this is if this is Earth and if you're trying to draw a map of Earth on a flat surface you effectively have to unwrap this circular surface and spread it onto a flat surface now mathematically the way this is done is with a projection and we can visualize that by basically in this case it's a nomic projection so we can imagine a point of light on the inside of the earth and with those rays of light or vectors going through the surface and then intersecting a plane out here and so this point on the surface of Earth gets projected to this point on the map this point to this one and this point to this one so what we see is that depending where the plane is relative to the sphere points will their linear distances apart will not be preserved in the projection so we can see that example here if this is the plane we're trying to project on to here and we've got four points on the sphere a B D and E we can see that points B and D end up getting projected so they end up further apart than they are in reality whereas points a and B end up getting projected so they're actually closer together than they are in reality so depending on the projection relationships those those distances and areas are not preserved during the act of projection onto a flat surface now to minimize the warping effect it's best to have the surface upon which you're projecting most closely approximate the circular surface and there's a lot of tricky ways to do this and there's a lot of different types of projections in this video we're only going to talk about transverse Mercator projections and the way this typically works is there's a sphere earth and we fit that sphere inside of a cylindrical tube ok so earth is a ball that's been slid into this tube and again it's a projection from the inside of the ball out to the surface of the tube and there's one point of contact running up and down the line of longitude or the central meridian of Earth and then to convert it into a flat map we would slice this tube and unroll it into a flat surface okay so first we do the projection then we slice the tube and unroll it the result of course is that the part along the meridian that actually was directly touching the inside of the tube is not distorted at all there was no no movement or distortion between where the point was on the sphere and where it comes out on the unrolled cylinder but any place off of that meridian over in this area or over here is a bit distorted in this map attempts to show that distortion if you imagine these circles were roughly this size to begin with and those circles were roughly that size on the spirit surface they've now been blown up to be that big on the edges or they've been shrunken and elongated if you're up near the poles so the main point here is that these circles represent a shape the relative locations of a bunch of points that enclose an area and the relative locations are distorted in the projection the shape gets bigger the points get further away and all projections have that problem of distorting the geometric relationships as you go from a circular surface to a flat surface so one other common Mercator projection is a state plane coordinate system and what this does is it gets around the problem you can see when we try to project the whole earth onto a single projection obviously the the earth doesn't really approximate a flat surface at all so we end up with terrible distortion state plane gets around that by using a series of much smaller footprint projections so each state might have one or several or many actual individual meridians and the idea is that the plane of projection actually pretty closely approximates the flat surface and by using smaller footprint areas you don't really have to deal with the curvature of the earth or the effect of the Earth's curvature is greatly minimized so this is a huge advantage because the distortion is very very limited and you don't have to worry too much about distortion of geometric relationships the disadvantage is that it's a small footprint it's only relevant to data in this part of Minnesota in this case and it won't work sensibly with a global data set the most common transverse Mercator projection is called the universal transverse Mercator or UTM and this is basically a series of 60 different Mercator projections each one has a central Meridian that is basically a line of longitude so it runs north to south in this case and we know that there should be almost no distortion in the transverse Mercator projection along this line of longitude right we know we can unwrap that and that particular line has no distortion so the idea is that UTM coordinate system is that you've got a whole series of lines and then each one is kind of narrow has a narrow width so that you encounter less distortion because you're moving only a limited distance away laterally so again this system works very well it's a global system the only drawback to it is that you have to always specify which UTM zone you're in so you have to always any coordinates have to be referenced to this central meridian of a given UTM zone so here's a map of the United States we span nine of these UTM zones 10 to 19 Vermont is in zone 18 n here and so let's look at how the actual coordinates are given in a UTM system so first off the coordinates are always in meters they're not in degrees now the origin of this coordinate system is defined as 0 meters 0 meters and each UTM zone has an arbitrary origin in this case it's defined actually outside of the UTM zone someplace off to the west of the UTM zone so in terms of east-west coordinates zero is at that origin and then the central meridian of the zone is always at 500,000 okay so it's always going to be at 500,000 the central meridian so the the easting coordinate or the east-west coordinate in here is going to be some number in the hundreds of thousands and it's always going to be positive now when we think about the northern coordinate the origin is always at the equator so it's zero at the equator and positive numbers go up to the north and positive numbers also go up to the south so you go from zero up to four million nine hundred thousand in the north direction and you could also go positive in the south direction so the kicker there is that in addition to defining your UTM zone number like eleven you also have to say whether you're in the North or South Zone and that's what's going to tell you whether you want to be counting positively to the north or counting positively down to the south so in that case both your easting and your northing are always positive numbers and you're always counting from some false origin UTM zones of course also have the added benefit that you're already working in units of meters which are super intuitive and easy to use in measurements instead of degrees which really are only useful when you're talking about angles so meters are a great unit for actual life but most coordinates are in degrees so let's wrap this up why do projections matter who cares well a couple reasons one your computer screen is actually showing a projection it is a flat screen and it's trying to show you something that is circular so anytime you're envisioning data it's being projected into something flat that you can see and if you happen to be visited in looking at two different images in two different projections that you're over that you're over lying they may not overlap correctly if you have them in different projections so a point on one might not match the point that is showing to be directly beneath it now in arcmap it usually projects data on the fly so in fact even if your data are in different projections you're usually going to see them correctly render on your screen and a final reason projections are super important is for any kind of spatial calculation keep in mind that when you project things they get distorted so if you measure a distance on a projected image it might be wrong because what you really want is the distance on that curved surface so it's important to use projections that minimize distortion so that if you measure a distance on a flat surface it's pretty close to the same answer as what you get on a curved surface so anytime you're doing calculations an area or distance you want to be really careful about what projections you're using now of course just a little advice about arcmap every layer that you load into arcmap has some native coordinate system sometimes this will be projected already sometimes it will be unprojected now the arc project itself also has a coordinate system which usually is taken from the first data layer that you load it usually adopts that coordinate system and it's very important that all the layers have the same coordinate system in your arcmap project it may not matter a lot for display but it matters a lot if you start to do calculations where you're extracting values from things or computing areas of things so keep that in mind going forward the end thanks for listening everybody

Channel: Middlebury Remote Sensing

Views: 118,094

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Id: HnWNhyxyUHg

Length: 18min 51sec (1131 seconds)

Published: Fri Apr 08 2016