Education and Outreach - Tutorial: Elevation Correction and the Geoid

### Elevation Correction and the Geoid

The GPS receiver uses a model to calculate the elevation which requires a correction before it is truly your elevation above sea level. We have prepared this explanation for both teachers and students. Please use these webpages to help you learn more about accuracy, scientific models, and how GPS receivers work.

Much of the information in this section of our website will be new to you, but please don't be discouraged. Please feel free to ask questions about anything that you don't understand, or that you would like explained in more detail.

### The Shape of the Earth: An Introduction to the Ellipsoid

The Earth is not a perfect sphere, but is instead more like a slightly squashed sphere called an ellipsoid. We say "more like an ellipsoid" because the Earth isn't a perfect ellipsoid either due to the mountains and valleys on the surface. However, it is close to an ellipsoid, so we are going to talk about what an ellipsoid is.

Imagine that an ellipsoid looks like a basketball when someone is sitting on it. What would that look like? Instead of being perfectly round in all directions, it is squished down from top to bottom, and squished out from side to side.

 NOT SQUISHED SQUISHED! Basketball image from http://www.nba.com

You use a GPS receiver to find your latitude, longitude and elevation. The receiver that found your coordinates uses an ellipsoid model called a reference ellipsoid to calculate this elevation.

There are many different reference ellipsoids, but all GPS receivers use the same one, and it is called the WGS-84 Reference Ellipsoid. Below is a picture of this ellipsoid with some lengths in meters for:

1. The distance from the North Pole to the Center
2. The distance from any point on the Equator to the Center

Notice that the Semi Major Axis (a) is LONGER than the Semi Minor Axis (b), or the distance from side to side on the Earth is LONGER than from top to bottom. It is just like the squished basketball! The lengths shown in the image define the exact shape of this ellipsoid, and are used by the GPS receiver to help it calculate elevation.

### The GPS Receiver and the Reference Ellipsoid Model

So now we know what a reference ellipsoid is, and we want to know how the GPS receiver uses those numbers that define the WGS-84 Reference Ellipsoid to find an elevation? The receiver has to know 3 things to find your coordinates:

1. The GPS receiver has to remember where the satellites are in space.
2. The GPS receiver has to remember what time it is.
3. The GPS receiver has to remember the shape of sea level for the Earth.

Even though there is a computer inside the GPS receiver, this is a lot of information that the receiver has to know to do its job. The reference ellipsoid is a simplified model of the shape of sea level that makes it very easy for the receiver to do the third part of its job. Essentially, the reference ellipsoid is a map of sea level.

A map is a MODEL. A map of your town shows where all the streets are, but it doesn't show buildings, and it doesn't show your house. Does that mean the map isn't useful? Of course the map is useful. If you had a map that showed every single building in your town it would have to be a very big map! It would be hard to carry and unfold because it would have to be almost as big as the town itself and then nobody could use it.

Maps, including the reference ellipsoid, are a simplified version of the world around us. They are very useful, they help us find our way around, and they don't have to show us everything to work. This is the idea behind all MODELS.

As we mentioned before, the GPS receiver needs to know the shape of sea level for the Earth. This is because we talk about elevation as the vertical distance from a point down to sea level. When you look at a topographic map, and it says your elevation is 1600 meters, it means 1600 meters above sea level! When the GPS receiver figures out where you are, it reports your height above the reference ellipsoid rather than above real sea level.

Now you are probably wondering why the GPS receiver doesn't just use the real sea level. Remember how we decided that a map that showed every building in every town would have to be a really big map? Well, the same thing is true for a map of sea level. The real sea level for the Earth is SO complicated that it is too big to fit in the GPS receiver. This is why the GPS receiver uses the reference ellipsoid.