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# Making Waves: Episode 85 (October 13, 2011)

You're listening to Making Waves from NOAA's National Ocean Service. I'm Troy Kitch.

Figuring out the exact location of a point on the Earth's surface in three dimensions is what the science of geodesy is all about. Thanks to the network of satellites in space known as the Global Positioning System, we can determine latitude and longitude with great accuracy. Heights, however, are a trickier business to nail down.

Today, we're going to hear how scientists are using measurements of the Earth's gravity to refine a complex mathematical model of the Earth's shape that's known as the geoid. When this new model is ready for business in about ten years, it's expected to revolutionize how we measure heights. Once the new geoid model is rolled out, the hope is that we'll be able to use a GPS receiver to get our current elevation in most places across the nation within an accuracy of two centimeters or less.

Now, this may seem like overkill to you, but it's critical to know elevations as accurately as possible. A difference of just a few centimeters, after all, can make all the difference in which direction water flows over land. If you live in a flood-prone place, you know how important this is.

I recently sat down with chief geodesist Dru Smith of NOAA's National Geodetic Survey to learn more about how heights are measured today and how geodesists are now creating a better geoid model to help us determine more accurate elevations in the future.

A good place to start is by understanding what the geoid is and how it's used. Dru said that a good way to think of it is as an idealized version of mean sea level.

"Back into pre-history, humans have intuitively thought of the ocean as a place of zero elevation. So we talk about height above sea level. It's a very common term to use. And so it's sort of in our nature to think of it that way."

The problem is that sea level isn't level at all.

"The sea level is unfortunately a dynamic surface. There's tides, there's currents, there's lots of things going on, and it goes up and down. Sea level is rising now. So it's not a perfect surface to choose, and sea level in one part of the world is not the same as sea level in another. So what the geoid is, if you can conceive of letting the sea surface itself settle down, not have tides, not have currents, and that the only thing giving it any sort of shape are the very small fluctuations in gravity around the world."

The Earth's gravity varies around the globe because the Earth is not a round, uniform globe. It's very lumpy and irregular and it's made up of lots of different stuff that all has different densities. The key thing to understand is that water tends to pool up in places of strong gravity and flow away from areas of low gravity. So minus the tides and currents and other things that affect the ocean, imagine what the ocean surface would look like if it was only affected by gravity. It wouldn't be flat. It would have these smooth, gradual up and down undulations around the planet.

"That's exactly what the geoid is. It's that perfect surface. And the beauty of that is, that that is a surface that doesn't have to exist only at the oceans. The shape that the ocean would take under those perfect conditions is entirely ruled by the gravity field. And that surface has a known shape underneath the continents, too. So it's not just height above sea level literally out at the sea. I could talk about the height above the geoid anywhere in the world."

This kind of height is known to geodesists as an orthometric height. It's the type of elevation readings that you find on a topographic map or a FEMA floodplain map. For about 150 years, scientists have known that the way to figure out the geoid is to take measurements of the Earth's gravity at points all over the globe. But there are two important considerations that make this a difficult thing to do. For one, gravity changes because the Earth is an incredibly dynamic place. Also, there are many different types of matter on the planet. The rocks that make up the Himalayas, for instance, are different from the rocks that make up the Rocky Mountains. So figuring out the shape of the geoid is a formidable task. It's a science that relies on how much we know about the Earth, how good our measuring equipment is, and how good our mathematical models are.

And that brings us back to what the National Geodetic Survey is all about. The mission of the agency is to provide 'geodetic control' through what's known as the National Spatial Reference System.

"We have to provide that to all the federal agencies that make maps, do surveying, do any sort of geodetic spatial positioning. To give you a practical idea, we need to make sure that FEMA floodplain maps, U.S. Geological Survey topological maps, Corps of Engineers levee surveys, that they all use the same coordinate system. They're all using the same latitude, longitudes, and heights. And you do that through providing control points. We tell people, 'here's a really well known point that you start with,' and when I say a 'point,' literally for hundreds of years it was a mark in the ground, a disk, mounted in the ground with a pinpoint right in the top of it, and a well-calculated coordinate for what that point is on the Earth. And then everybody who needed to make a map could start at those points, know what their starting coordinate is -- latitude, longitude, height -- and make their map off of that, so everybodies maps would line up because of that. "

So the National Geodetic Survey doesn't make any maps, but they make maps possible. Today, geodesists rely less and less on physical disks in the the ground and decades-old surveys and more and more on the space-based Global Positioning System and a vast network of ground receiver stations. While this provides very accurate latitude and longitude measurements, elevations calculated with GPS aren't as accurate. That's because GPS uses a rough approximation of the geiod which is basically a simpler mathematical model of mean sea level. It's called the ellipsoid. What geodesists are trying to do now is create a really good geoid model that can be added to the Global Postioning System so that a handheld GPS receiver can calculate serve up both orthometric and ellipsoid heights for any location.

"There's a hundred ways to measure height. Orthometric heights are really a very useful and commonly used type of height because they have some physical meaning about the gravity field. A high orthometric height and a low orthometric height, generally speaking, water will flow from the high to the low . Ellipsoidal heights, they don't follow that rigor. So you can get a simple ellipsoid height out of GPS, and you can get it quickly and accurately. But it doesn't tell you that useful physical information about where water will flow. But if you mix in a geoid model -- that undulating surface that sort of idealizes sea level -- if I know that, I can add that information to the ellipsoid height that GPS gives me and right away I get a brand new, very accurate orthometric height anywhere I like out of my GPS receiver. No need to go to a passive mark, no need to rely on surveys that are 50 years old. The problem is to do this, and to do it right, we really have to have nailed the geoid model that we're going to give to people, because we already know GPS is fast and accurate, we want to give them that accurate geoid model on top of it, so now they can get orthometric heights wherever they like."

And that's one of the big projects that scientists at the Survey are working on now. Part of providing the new geoid model involves getting new data. That means taking new airborne gravity surveys over the entire nation to replace gravity surveys that are decades old and out of date. They're also improving the complex theories and mathematics that underlie how the model is created. Dru said they think they're on the right path for delivering more accurate heights, but there's only one way to find out. They have to prove it.

"So even if we think we're making a very accurate geoid model, we need some independant verification that, whatever accuracy we're shooting for, we're actually achieving it."

To do that, teams from NGS just wrapped up an incredibly detailed survey along a 200-mile stretch of land between Corpus Christi and Austin, Texas. They started back in July and have braved drought conditions, smoke from nearby giant wildfires, and a multi-week heat wave during which the temperature never dipped below 105 degrees. Over the summer, the surveyors measured the shape, or slope, of the geoid along this one small section of land using three different methods that don't rely on gravity measurements.

"We'll use those three different technologies and compare them -- hopefully, they'll agree with each other, of course -- and then they will serve as a calibration against which we will check the modeled geoid values coming out of all of our gravity surveys. So it'll help us know is our theory improved, is the gravity data we're collecting good, have we driven those approximations down to some small level."

If this seems like a lot of work to you, it is. The new geoid model isn't expected to be completed until 2022, and that's if all goes well. Dru said that the expectation is that, within about ten years, both GPS technology and the model of the geoid will have greatly improved. The goal is to get a system in place that will allow anyone with a GPS receiver to get a reading for any location that's accurate to within just a few centimeters. He added that there are some places in the interior of the country where this likely won't be possible within this timeframe because of limits on what we know about the densities of some landmasses ... for example, in places like the Rocky Mountains. But he does think it's achievable along the nation's coastal areas. And this is where accurate heights are needed more than anywhere.

" It's very critical to know differences in elevation from one point to another, predominantly because it helps us deal with flooding issues. And these are pretty high profile things like with Katrina -- all the hurricane problems we've had -- the interior floodings that have occured out in the Great Plains in the last couple of years. Our job is to make sure that FEMA has the right starting elevations to do their surveys, to build floodplain maps so homeowners have the right insurance. Are you in a floodplain? Are you not? And it all comes back to how these surveys are done."

"Well, we're playing catch-up. There is a problem with how we give out heights today and that's that it's with these passive control discs that haven't been checked in a long time. So consider if you will how flat most of the coastal regions are. You have about 50% of the nation that lives within about 50 miles of the coast. And so you've got a lot of people with a lot of real estate invested in these very flat coastal areas, and very slight errors in the heights of those flat areas could mean that you think you're in a floodplain, but you're not ... Or vice-versa. So the idea of having accurate heights is being driven by the fact that we want to make sure that people can save lifes, save property, save money in the insurance industry, because accurate heights mean accurate knowledge of where water is going to flow when there's some sort of disaster."

That was Chief Geodesist Dru Smith with NOAA's National Geodetic Survey. If you like to learn more about this topic as well as the many other missions and projects of the National Geodetic Survey, check our show notes for links.

And that's all for this episode. If you have any questions about this week's podcast, about the National Ocean Service, or about our ocean, send us an email at nos.info@noaa.gov.

Let's bring in the ocean....

This is Making Waves from NOAA's National Ocean Service. See you in two weeks.

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