In this section, I want to talk about grid coordinate systems in a popular example of that which is UTM, which stands for Universal Transverse Mercator. So, there's two different ideas going on here. We're going to talk about a particular type of coordinate system and a particular type of projection and how those two things work together. UTM is really useful, it's very popular and so I want to make sure that you're aware of it and what it does and why you may want to use it. With the Mercator projection, we know that there's distortion that takes place with it. If we look at the T-cells indicator c's here, so these are the circles. That the circles are still circles as we move north and south but they're increasing in size and so areas are being distorted. So, you may think, "Well, why are we talking about that in this section?" Because UTM is based on Mercator and that may not seem intuitive to begin with, but let's just follow the logic here with the strategy that was used to design UTM and how this works. So, what if, if we know that distortion is minimal right around the standard lines. So in this case, in this projection, the standard line is at the equator. That's where the scale factor equals one, there is no distortion and the areas that are directly around that will have pretty small amounts of distortion as well. So, what if we just made a map for that small area just around the standard line? Well, then we actually have a map that will maintain all of the properties that we're interested in well enough that we can use them. So, distance, direction, shape and area. The strategy that was used to design the Universal Transverse Mercator projection was to use a transverse projection and that's what we see here. What I was just showing you is the typical Mercator projection which is done with a normal aspect where the standard line is along the Equator. What happens with the transverse is that the standard line is along a meridian. So, that means that remember, I've said this before, but the scale factor equals one, there is no distortion and right near that standard line, the distortion is pretty minimal and very acceptable. So, what they did was they said, "Well, what if we turn that cylinder sideways? Have it along a meridian and then we just map areas that are near that meridian and that will give us really good acceptable levels of small distortion." Then you say "Okay, fine, but that's only for that one line." So, you can make a map of say, this area right here, but what about the rest of it? Well, all they did was they said, "Okay. We'll make a map projection that's customized for just this zone here and then we'll rotate that cylinder a few degrees and then we'll make another map projection for that next slice of the earth. Then we'll rotate the projection again and do the next slice of the earth." So, they created these customized zones for every part of the earth as we'll see. But I'm getting a little ahead of myself. The main thing I want you to see here is that the standard line is along a meridian because it's a transverse projection. So we've taken that Mercator, we've modified it in a way that's useful for our purposes. So, one UTM zone is six degrees wide, this is what I'm showing here. So, you can see how they've customized this where you only make a map with this zone inside that red area. It's not meant to be used for really large areas, it's only meant to be used for really small areas or what we would call large map scales. So, here's our transverse version where the standard line is touching along a meridian and the strategy they used, as I said, is that they just rotated the cylinder. So, here's our cylinder and there's the zone that's customized for that one part of the world. Then they rotated the cylinder and made another one. Rotated the cylinder again, made another one. They continue to do that until they've created these UTM zones for every part of the world and they numbered them. So how this works is, that wherever you're working in the world, as long as the area that you're mapping will fit inside a zone, then you can use the UTM projection. You just need to know which zone you're in. So, it could be zone 17 or zone 18 because you're telling the software, remember these are different projections. There's one customized for each zone, so, you tell it which projection you're using, which version of UTM for that particular zone. So, that's the strategy for the projection that was developed for UTM. If we look at that projection for that one particular zone, this is what the map of the world ends up looking like. Now it's not meant to be shown as a whole map of the world, I'm using this to show how extreme it looks and now you're really only meant to use it for this one part of the world. The other thing I want you to recognize is that the graticule for the lines of latitude and longitude, they're warp, they're distorted just like they would be on any map because they're meant to be converging at the polls and things like that. So, the second part of the UTM system is- the first part was the projection, the second is to come up with a consistent coordinate system, a grid coordinate system. If we zoom in here, you can see that this is our 3D coordinate system. It's a geographic coordinate system which is fine if you're working with longitude and latitude and you're not projecting something, but it's not consistent or very useful in terms of measuring things like distances or areas on a flat projected map. So, the designers of the UTM system decided to place a regular coordinate system, Cartesian coordinate system on top of the projected version of the UTM map. So, this is much easier to work with now. Instead of working with degrees and minutes and seconds or something like that, we're just working with meters and we have a very consistent way of measuring distances in any direction we want to. Remember, as long as you're mapping inside that zone. So, the grid coordinate system is just like any other regular Cartesian coordinate system. If we want to describe the location of something, we do it in relation to two axes or an x and y axis. So, that forms a grid and we just say how many units over in the x, is it? In this case, it would be four units and how many units up or down from on the y-axis, is it? And now it will be three. We always list the x first and then the y and so that would give us a Cartesian coordinate of four and three. So, the origin where these meet is zero, zero, and of course we have the axes are extended in negative directions as well. So, that's a regular Cartesian coordinate system. The thing about that is that if we have coordinates to this side of the x-axis, you'll notice that we get negative numbers. Down here we actually get to negative numbers, one for the x and one for the y. We get a positive here and a negative there. So, this is the different quadrants. So, we have the first quadrant, second, third and fourth there. So, the thing is, is that when they were designing the UTM coordinate system, they said, "You know what? It would be really convenient if we could avoid having negative values. If we could only have positive values." So, what they did was, if this was the area that they were mapping, without this new system that they came up with, part of the mapped area is here with positive coordinates, part of it's over here with some negative coordinates and here and here. So, if it happens to go over more than one of these different quadrants, you've got this whole mixture of positive and negative values. So, what they wanted to do was avoid that. So, all they did was they shifted the entire thing over. So, that the x and y-axis are such that they're at the one side of the zone, so that anything that you're mapping inside that UTM zone will be positive. It'll be positive in this direction and positive in that direction. So, here is our UTM grid coordinate system. Now, before this adjustment, the origin would normally be right in the middle of the grid, correct? So, that would be zero, zero and then we would have the problem of having negative values. So, all they did was they shifted everything over so that this becomes the origin, that's zero, zero. When you're recording coordinates in the UTM system, you record them as so many meters east of the edge of the zone, so that's called the easting, and so many meters north of the Equator, that's called the northing. In the southern hemisphere, instead of having negative values, they set x-axis down here near the South Pole that became zero meters. So, you still have eastings and northings and then all you have to specify is whether you're in the northern hemisphere or the southern hemisphere but otherwise all of the coordinates are still in meters and they're all positive, which is just more convenient and easier to work with. So, if we compare the two, the blue lines here are the geographic coordinate system, this is the graticule from longitude and latitude and the red lines are the UTM grid coordinate system that have been superimposed on top of it and you can see how it's much more uniform, predictable, easy to work with. This is an example of a national topographic system map from the Canadian government and they actually use both systems, latitude and longitude and UTM. So, you can see here that in this corner, they have an easting and a northing. So, the coordinates for this corner are actually 621,000 meters east of the edge of the zone and 4,845,000 meters north of the equator in zone 17, north. Meaning it's in the northern hemisphere. So, that's how you would correctly record and show UTM coordinates. They're in meters, they have these numbers that are eastings from the edge of the zone and you have them as northings north of the equator. So, the coordinates in UTM for the CN Tower would be 630,084 meters east, 4,833,438 meters north, zone 17 north. So, it's just an example of what UTM coordinates look like. If you see numbers that look like this or in this range and you're not sure what they are, more than likely they're UTM. It's one of the most popular coordinate systems and projections that you'll see. So, just to finish this section off, I want to make sure that it's clear that we're talking about two different things at the same time here, is that UTM is a great example of a strategy that was used to customize a projection, so that if you're working at these kinds of scales, like say within a city, that all the projection properties so, size, shape, distance, and direction are all maintained well enough that they're within acceptable tolerances that you can use them. So the things I mentioned before about distortion are true, when you're talking about a country or the world, but within the range of one UTM zone, it's acceptable to be able to use that. So, that's one part is the projection that was used that's a strategy. The second part is that as with projected coordinate systems in general, it's not just the UTM one, is that a regular grid has been superimposed on top of that projection, so that you can measure things in predictable unit. So, here it's in meters, some other ones may use miles or feet or there's other systems out there, but this is a good example of a grid coordinate system and an interesting strategy for developing and projection. If you're curious, this shows the size of UTM zone. So, this is Ontario just to give you some sense of the size of them. Inevitably, when you're mapping, you may find that the area that you want to map falls into two different UTM zones. I've explained to you this whole section the idea that you want to stay inside one zone. So, is this forbidden? Are you not allowed to do this? You can still do it. It's not crazy to do. Remember, the whole idea of a UTM strategy is that you have a standard line running down the middle of the UTM zone. That's where the scale factor is one and there's no distortion and the distortion is increasing away from that, but if you stay inside that one zone, the distortion is small enough that it's quite acceptable. So, if you want to map something that falls a little bit outside of that zone, let's say it was an area like that, then that's okay because remember really, your standard line is here, it's still a relatively small distance away and so the amount of distortion that you're going to get is probably still fairly minimal. I mean I can't tell you what's the right decision in your particular circumstance but I'm just saying in general. A good guideline is that if it's sort of I don't know maybe halfway across other zone, then it's probably okay. If you're getting a little bit beyond that, then really you're probably wanting to look at a different type of projection besides UTM. Incidentally, if you're wondering how the software handles this is that, if most of your areas inside one's own exceeds zone 17 here, and it just goes a little beyond into another zone, that the software is smart enough to just extend the grid coordinate system into that next zone and pretend that it's all- let me just do the other lines here too- that it's all part of the same UTM zone. So, it's much simpler than trying to have one map that spans two different zones and having two different projections it's really difficult to do. So, what the software does is it just pretends that this extra area over here is inside zone 17.