A vertical datum is used a frame of reference for making vertical measurements in relation to things like elevation or altitude from the surface of the earth, essentially, or what we would think of as the surface of the Earth. If you're trying to describe a location of something there's the X coordinate and the Y coordinate, which typically could be the longitude and the latitude. But what about the Z coordinate? What about the vertical part of that? How high up is something? So, if we have the surface of the Earth, this is in profile, and we're trying to describe, well how high is this location? The key question here is, well how high in reference to what? What's our base level that we're measuring away from in terms of our heights? Now the one that probably comes to mind here in terms of that base level might be, is sea level, and local sea level. So if you're on the coast and look at the water and you say well, it's water, it settles to the lowest possible level. So that's a good base level to work from, and then we can do that. So this is our local sea level. [SOUND] There's a boat coming in. Fun with PowerPoint and Clip art. Okay, [LAUGH] so to continue is that well what if what we're trying to measure the height of isn't right at the water? Well we can actually think of it or imagine that sea level's extending under the land. If we just have that same reference level, we can measure the elevation from that reference sea level to the height of whatever it is that we're interested in. So it could be the top of a mountain or a lighthouse or wherever you're hiking or plane flying or whatever it happens to be. So what could be wrong with that? So we've got our local sea level, we're measuring heights away from that, everything's great, right? Well, not necessarily. Okay so if we have our sea level here, and we have the thing that we're trying to measure the height to, maybe it's the top of this hill here. Okay, so we have our sea level, we have the top of our hill, we have our nice little boat over here in the corner to show that it's sea level. The thing about sea level is that is assumes that water settles to a common level everywhere on Earth. And there is this assumption that, it's always the same. And it's just not. There are variations in sea level on any given day and over long periods of time. So it's not actually a very consistent baseline to measure things from. If your baseline is shifting, or going up and down, then you're going to introduce errors into your elevation measurements. It's not going to be exactly correct. So let's explore that a little bit. So what we could say is that, all right if water levels change from day to day, we have tides and things like that. Why don't we take an average and we could call that the mean sea level? Okay, so people have done that. They took the average water level for the same place over a 20 year period. Okay so they measured it all the time over and over again over 20 years and say, all right so now we have an average that's going to be more consistent. Remember the whole idea here is we just want to have a frame of reference for vertical measurements, or a baseline that's consistent, so maybe that would work. We could average out the high and low tides. The problem is that the mean sea level or MSL will still vary with location even along the same coastline, and that's a problem. Mean sea level varies with things like currents, air pressure, temperature, salinity, changes in the Moon's orbit. I won't go into the explanations as to how all of these affect sea level. For us at this point all we really need to do is accept the fact that they do affect our mean sea level. And so really what we need is a more consistent surface, we need something that's like sea level. That we can imagine is similar to sea level, but that doesn't have all of these inconsistencies or problems associated with it so that we can use it as the consistent frame of reference. So at this point, we try a little thought experiment. If the world was consistent, so there's no changes in terms of the composition of the Earth, or the shape of the Earth, it's just this nice, perfectly round sphere. It's all exactly the same material, then you could have water that would settle to one sea level. In other words, we're going to remove all of the factors that affect sea level like the moon's orbits, and tides, and all those these other things, salinity, currents. Pretend that they don't exist, this is part of our thought experiment. We're going to eliminate all of those variables, okay? So then, the sea level would be the same everywhere, even over land. So we'd have this kind of perfectly round Earth with a perfectly consistent sea level, and we could perfectly measure our elevations from that. So, then we could measure any elevation relative to this one sea level, and it just so happens, that's equivalent to the GRS80 ellipsoid. That's just sort of a side point here, but it is kind of useful information to keep in mind, as we go along. Okay, so let's just extend that a little bit. If we account for gravity, It turns out that there are parts of the Earth that have higher density rock. There are parts of the Earth that have lower density rock. And that affects the local gravitational pull at these locations on the surface of the Earth. And it turns out, that higher density rock will actually pull water towards that part of the Earth. And you'll get a bulge around that area, and water is drawn away from areas with a lower amount of gravity, with a lower density of rock. These are not huge amounts, but again, we want to try to take everything we can into consideration to increase the accuracy of the measurements that we're making. So, we can still measure our elevations from this baseline. All we're doing is modifying that baseline a little bit, and saying as long as we know that there's this difference at a particular location. So, it's a little bit, bulging out a little bit here, it's a little bit flatter there. As long as we have a model of that so we know what that is, we can still use that as a frame of reference to measure our elevations from. So now we have our hypothetical version of sea level that's taking gravity into consideration, and that gravity is being effected by the composition of different points inside the Earth itself. And so we have this undulations that are occurring, but we can still make our measurements for elevation based on this baseline. It's just that this baseline is being modified, it's a little bit higher here, it's a little bit lower there but that okay, don't let that kind of freak you out. It's just saying that, well, even if our baseline was slanted like this, as long as we know that it's slanted we can still take measurements here and here relative to our baseline. Or if it's like this or like that, as long as we know what it is, we can make those measurements correctly. So that's all that really comes down to, we've got a hypothetical simplified version of sea level that we can use to make measurements from. And this model of the Earth based on this idea of sea level is what we call the geoid. So this is a version of the geoid, this is a digital model of it. And it's important when you look at the color scheme of this geoid to understand what it is that we're looking at. This is not elevation. And this is something I think that people tend to want to think but it's not correct is when you see areas that are red here, that's not in itself a mountain range. And when you see blue areas, that's not in itself a low area in terms of elevation. What this is is related to gravity, okay? So we have areas that are above, the ellipsoid here and below the ellipsoid there. What am I talking about, is that think of it back to this idea of the ellipsoid. So this is before we took gravity into consideration okay? So if we didn't have gravity it would look like the ellipsoid, but what this is mapping is that you have areas that are a little bit below the ellipsoid? And so the areas that are blue are areas that are below the ellipsoid. You have other areas like over here where the gravity is stronger and the sea level is bulging above the ellipsoid, and that's what the red areas on this geoid are referring to. So these are the areas that are a little bit above the ellipsoid or a little bit below the ellipsoid. But this geoid, this model of the Earth, is what we can then use to measure elevations away from. So now if we're looking at something and saying how high is something, we can say in reference to a geoid. A geoid is just, yeah, a frame of reference I just love this model. This is a, I don't know what you want to call this, kind of a gold lame, disco version of a geoid. This is referred to as the Potsdam gravity potato. I am not kidding you, that is the official name for it. This is wildly exaggerated, as things often are, so we can see the differences better. But what this is showing is not the terrain or the topography of the Earth. This is showing where the geoid is higher than the ellipsoid or lower than the ellipsoid. And so you have areas that are below the ellipsoid here or above the ellipsoid over here and so on. So this is just another model, it's a frame of reference. Think of it as just a fancy version of sea level that we can use to make our elevation measurements from. So the Potsdam gravity potato. So to summarize, we have our geoid which is a surface with the same strength of gravity at sea level. And then we have the ellipsoid and they're going to differ at different locations. So this brings us back to our original question, is, how do we describe to somebody how high something is and in reference to what? Well we could use local sea level but now we have something better. We can take the Earth's gravity into consideration, take measurements from that, build a geoid, and then. Make our elevation measurements from that geoid. And so that gives us an answer to our question how high is this in so many meters above the geoid. Now that geoid will likely, at any given location, be different than the ellipsoid. And so we can also take into consideration the geoid height which is the difference between the ellipsoid and the geoid. And why do we do that? Because it's a lot easier to map locations using an ellipsoid. And we'll see this when we get into map projections and things like that is that if we want to simplify our calculations and make it easier to work with. We can take our elevation value that's based on the geoid and then adjust it, taking the geoid height into account. And then map it on the ellipsoid. And so we actually are still able to use the true height and we will know what that is. It's just that we've adjusted that number so that we can map it on the ellipse way, which is a much simpler version of the Earth. Imagine if you are trying to map things using the Potsdam gravity potato, which has this bumpy, crazy kind of surface. And you're trying to map elevations and xy locations as well on this kind of crazy surface. The calculations that you're going to be making in terms of areas, and distances, and directions and things like that is going to be really complicated. So what they do as a strategy is they take those coordinates, and they then move them onto the ellipsoid. Which is this nice, simple, mathematical surface that just has one variable really, which is the amount of flattening it has. And then most of the time maps are made from that, which uses a much simpler process. So that's why you have elevations made from geoid, but then their map using the geoid height on the ellipsoid. So some terminology for you there, make sure that this all clear in your head and they'll all kind of make sense, so that when you you are seeing this kind of data you can use it correctly. This is a really good illustration for geoid heights. So what this is showing is that we have areas that are blue that are below the ellipsoid so the geoid height is less than the ellipsoid. And the red area, just like the model I was showing you earlier, where the geoid height is above the ellipsoid. And what's kind of interesting here is that the total difference on the scale ranges from negative 100 to positive 100. Which means that over the entire surface of the Earth we're only talking about a possible difference of 200 meters. So like we were talking about with the horizontal datum and whether you could treat the Earth as a sphere or an ellipsoid. Here, we have to think of it as like, well how important is it to us that we have that 200 meter difference? If you're flying a plane, that's probably pretty important. But if you're just trying to drive down the street or you're mapping the location of a park or things like that. Often we don't even bother with vertical values. We'll just use x and y values and treat the Earth as if it's on this simple kind of flat ellipsoid and not even worry about the elevation. But if elevation is important to you, if there are situations where that is critical information, then you have to make sure that you specify the vertical datum. And the vertical datum just specifies which geoid is being used so that you're using the same frame of reference that was used to collect that vertical data to begin with, just like we did with the horizontal datum. Just to summarize the point I was making a minute ago in terms of the geoid and geoid heights and things like that. The geoid is the most accurate way to measure vertical position. The ellipsoid is much easier to make maps from than geoids, it's mathematically much simpler. So accurate measurements are made from the geoid, and then adjusted to fit on the ellipsoid. So that's just kind of quick summary of what I was trying to say earlier. Just to make sure that's clear for you. Okay, so that's our section on the vertical datum and geoids. Just think of it, just like with the horizontal datum. It's a frame of reference, it's kind of the standard if you want that you are making measurement from. And just like the horizontal one, it's that you need to know what datum was used to vertical datum to make vertical measurements and that when you bringing in the data you specify that so that you mapped correctly.
