So just to reiterate, here's our definition of a geographic coordinate system. And you'll see here that I said that the ellipsoid is part of the definition of the datum, which is part of the definition of the geographic coordinate system. And so I can't emphasize this enough. Since the datum is part of the definition, if you change the datum, you're changing the geographic coordinate system, so your coordinates will change. This is the key thing here. And when we talk about coordinates changing, what I mean is, if you have a location on the surface of the Earth, like an absolute exact location of something, and you store coordinates for that. The numbers that you're storing will actually be different for that same object depending on which datum you use. And so if that happens, then that's where you can run into problems with things shifting or not being mapped correctly. Because the frame of reference that you're using to describe that location is changing, okay, hope that makes sense. Let me just illustrate how this works. If you're trying to determine the latitude for a point location on the surface of the earth, and you measure that using a geocentric latitude, and you get an angle of 45 degrees. That angle is the coordinate that you're using to describe that location. You may remember in the section on longitude and latitude, I talked about the fact that these are angular measures. That they're not just numbers, they're angles, and this is where this really comes into play. So that's an angle of 45 degrees that's being used to describe a location. If that sphere changes to an ellipsoid, That actual location of that object that you're trying to map, that hasn't moved on the surface of the earth. That tree is still where it always was, but the frame of reference we're using has changed, and so now, that point is no longer at 45 degrees latitude. So changing the shape of the earth also changes the angle, and that angle is the coordinate. And that's why when you change the ellipsoid and you change the datum, you're changing the number that's being used to describe a location for that coordinate. If we want to put this another way, if this is the true location, but we use the 45 degree number to map that location, you will actually map it incorrectly. It'll put it somewhere else on the surface of the earth. Now, as I've mentioned before, the difference is not that great. We're only talking about less than 1%, so that shift, depending on where you are, may not be that much, but it could be important. Do you really want to have less accurate locations for something? If it's something critical or where it's really important you have exact numbers, it may be really important for you to make sure that you're using the correct ellipsoid and the correct datum, so that those points are being mapped in the correct location. You can see here that the true location using a different ellipsoid will give us a different angle, which might be 35 degrees, and so that's a different coordinate. Now, I'll just say this one more time, these are wildly exaggerated, I'm just doing this so it's easy to see. The numbers in reality would only be off by a very small amount. I'm kind of taking some liberties here, but I'm hoping that this helps illustrate the point. So if you change ellipsoids, you have the same thing as going from a sphere to an ellipsoid. because if you have one ellipsoid where you've mapped a location using an angle of 35 degrees, if you change that to a different ellipsoid, that angle has changed again. And so that coordinate will have changed again. So it's not just going from a sphere to an ellipsoid, it could be going from one ellipsoid to another. Remember, they're all just different models of the shape of the earth, they all have slightly different versions of the amount of flattening that's taking place. That means that the angles that are being used to describe the location are going to be slightly different. That means it's going to have an affect on where things are located when you're mapping them. So with geographic coordinates, the datum, and therefore, the ellipsoid, is the frame of reference of the coordinates. When you map angular coordinates, you must use the same datum that was used to originally measure them, okay? So this is critically important. All this really means is that is that if you're downloading a GIS dataset from a website or you're getting it from some other source, you need to know, what was the frame of reference? What was the datum that was used to create those points and to create those coordinates? And when you tell the software what the datum was, then it knows how to bring those in using the correct frame of reference. Once they're in there, you can change them, and you can do that consciously and accurately. After that, you can transform them if you want, but when you bring them in, you have to use the same datum that was used to create them originally. So just to summarize, the same location will have different coordinates on a sphere versus an ellipsoid, and from one ellipsoid to another. And if you change datums, you actually will change the actual coordinate values. So this is just to illustrate this point, as this is for a location in Redlands, California. It's the same location but using two different datums. One is NAD 27, one is NAD 83, and of course, what I'm trying to show you here is that the numbers actually change. They're angles, they're different angles for the same location. And so if you use the wrong datum, you'll have the wrong angles, the wrong coordinates for that location, and it will shift them. I love this example. This is an old example from a guy named Peter Dana from the Geographer's Craft, which was this website that was generated or created back in 1994. It's still available, you can still refer to it. I think it's a really valuable source of information, so I thank Peter Dana for that, and I'm borrowing his example here. I kind of updated it slightly, but basically it's the same example. And what he came up with was this idea of mapping the top of the star being held by the statue on the top of the Texas State Capitol building in Austin, Texas. So at the top of this building there's a statue that's holding a star, and he mapped the location of the point, the tip of the point of that star. So in other words, the tip of that point is not moving. It's not shifting in any different location but what he wanted to illustrate was what happens if you use the wrong datum or a different datum to map that location. If this red star represents the star on the statue that's being held by the Goddess of Liberty, and we map it using the same datum that was used to create the coordinates, which in this case was NAT83, then it will be mapped correctly. But if you use a different datum, such as the Pulkovo 1942, there will be a difference, there'll be a discrepancy. This will actually be off from where it's supposed to be. If you use the European Datum 1950, that's where it will be located, so that's almost 500 meters away from the true location. Then there are some other ones. There's an Indian datum, an Australian one, South American, CAPE, Ordnance Survey, Indian, one for Tokyo. So remember, these are all the same location, the same star, the same tip of the star, but using these different datums, this is trying to illustrate how far off you can be with these. So these are where they would be mapped on your map. So they could be off by almost a kilometer for that location if you use the wrong datum. So I'm hoping this is a good way of illustrating the consequences of not knowing what a datum is, or not choosing the correct coordinate system based on the correct datum. And I put together this little example. So this is the same road network data for part of Toronto. And the blue is the NAD 83, so that's the correct location of this, and then I used the Tokyo datum to map the same data, and you can see that there's this shift here. So it may not seem that dramatic. I actually haven't measured it, but I'm going to guess that it's off by, I don't know, maybe 10 or 20 meters. Again, maybe that's important, maybe it isn't. But if you happen to bring in a dataset that doesn't seem to line up correctly, or it doesn't end up where you thought it should be, then one of the first things you should probably check is to make sure that you brought it in using the correct geographic coordinate system, using the correct datum. This is a great illustration of how far off you can be between NAD 27 and NAD 83. So these are not the only two datums out there, but these are ones that are very commonly used. And I really like this illustration of it, and it may not be obvious to you to begin with, so I've put together this little version here. If the blue line is NAD 83 and the red is NAD 27, you'll see that they're both versions of flattening of the earth, and there are parts where they are quite different from one another. So for example here and here, but its likely or it's going to happen that there will be a location where they happen to intersect. So if you're mapping a location where they intersect, just by dumb lucky really, they will map correctly. Because that's where those two versions of the earth happen to be the same, and so there's no difference or discrepancy between them. And you'll probably not even notice if you don't know what you're doing, and you'll say, everything looks great. But if you're trying to map something over here, you could be off by quite a bit, and so that's what this map is trying to show. Is that, I've got a little PowerPoint version here, is that so here's where they intersect. This is where there's no difference between the two. And what these numbers are trying to indicate here, so the 20, the 40, the 60, is the number of meters difference. Or how far off you would be if you were using NAD 27 when you were supposed to be using NAD 83. So that's what's being shown here, is that this difference is as you move farther away from where they intersect. Hopefully, this is making sense to you. This is where they intersect, somewhere out here, but as you move away, the differences become greater and greater. And so if you're out in, say, California, then the difference could be 80 or 90 meters, maybe close to even 100 meters from the true location. So that's not going to be great for anybody, it's not a really good way to be able to map things. So I just really like this as a visual illustration of what can happen, or the consequences of using the wrong datum. All of this is to say that if you're acquiring data, so you're downloading it from a website, you're getting it from another agency, or whatever it happens to be. That you have to know the datum that was used to create that data, and if you use the wrong datum, you'll have measurement errors, and your objects will not line up properly. I am hoping that by the end of the segment that this makes sense to you, you can see why it's happening. You have to kind of think about the fact we're modeling the earth in a certain way. There's flattening that's taking place, we're trying to describe that flattening with an ellipsoid. The ellipsoid is described using the datum, and so on. And so I kind of see it as sort of maybe a chain or sequence of ideas, that you have to make sure you can connect the dots between then. And if you can, then this will all make sense to you and all be clear, and then you won't have any problems with it. So I hope that's what's happening. I hope this is all starting to gel in your mind, and that this makes sense. And really, all of that comes down to this very practical thing that if you don't use the right one, your stuff won't look right, it won't line up correctly, and you'll have problems.
