The Wild World of Geodesy! Part 1: Datums
PLEASE interrupt if you have questions!
Go to http://lyzidiamond.com /geodesy-pt-1 to follow along.
(Use left and right arrows to navigate. Links have a purple background.)
What is geodesy?
Wikipedia says: the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space.
:-/
Let's break it down.
We can all agree: the Earth is three-dimensional.
Yes. :)
But the Earth is not a sphere. It is its own fancy shape.
We measure and describe that shape in a few ways.
First: the geoid.
"Lumpy Earth"
The geoid is the shape of the Earth without land masses, tides, and wind. It assumes that all locations have the same gravitational potential.
Gauss described it as "the mathematical figure of the Earth."
But the lack of uniformity makes it hard to use as a reference for measurement.
Shapes with lots of different angles and irregular protrusions make for very difficult math equations.
Enter the reference ellipsoid.
or

"oblate ellipsoid."
A reference ellipsoid is mathematically defined: you can read more about that here.
(Also, the equation that makes up our most-commonly-used reference ellipsoid actually changes over time and with different use cases!)
The important part of the Earth ellipsoid is that the short (polar) axis is roughly aligned with the rotation axis of the Earth.
Why is it important to have a mathematically defined shape for the Earth?
Because we, as cartographers are engaged in measuring the Earth. We need to know what goes where.
How do we do that? MATH!
Hooray! Now we get to talk about coordinate systems and datums!
So we now know that the reference ellipsoid for Earth is a significant approximation of the geoid, which is itself a significant approximation of the real shape of the Earth.
(I found a lot of illustrations for this.)
But the reference ellipsoid is super helpful to us when it comes to knowing where things are in relation to each other.
It enables the creation of a geodetic datum: a coordinate system and set of reference points that are used to locate places on the Earth.
A datum provides starting points for measurement.
Horizontal datums measure positions on the Earth's surface. Vertical datums measure elevations.
Let's walk through an example.
You and I are giants standing at the same spot on the earth.
We're having an argument. You're trying to tell me the earth is curved, and I am insisting that it is flat.
(Ignore for the moment that we are both giants and can clearly see that it's a curved surface.)
You decide to prove it to me. You tell me, walk ten steps forward.
Then you turn on your jet pack and walk ten steps forward yourself, straight out. (Oh yeah, you have a jet pack.)
We walked the same distance but ended up in different places. And this is why datums are important.
We tend to think about measuring space in a Cartesian fashion.



Cartesian coordinate system
But remember: the Earth is three-dimensional and lumpy, even in the reference ellipsoid.
If you looked at our relative positions on and next to the earth from above, it will seem as though one of us traveled further.
But we didn't.
A datum takes this into account and makes a coordinate system that (roughly) reflects it.


Not perfect, but at least not flat.
Notice in that image where it says Local Datum?
There are many different datums that refer to many different reference ellipsoids.
For example, a datum may define a location for the Equator, but that location may be different for a different datum.


An even better example
Why so many?
Because, again, of the irregular shape of the Earth.
Some ellipsoids are better for certain areas.
The National Geodetic Survey manages the US's national datums: NAD83 and NAVD88.
One widely-used datum is WGS84, or the World Geodetic System of 1984.
WGS84 is a vertical and horizontal datum.
This is the datum that is used by the Global Positioning System (GPS).
Let's look at a different example. Let's say we're going from one side of this hill to the other.
If I used my GPS to get to a point on the other side of the hill, it would give me a different estimated distance if I was going over the hill than if I was going beside the hill.
Using WGS84, it knows the relationship between distance on the earth and relative location.
But even if there wasn't a hill, this would still be necessary. Why?
Because the Earth is three-dimensional.
Cartesian distance becomes flawed on a curved surface.
(Remember when we were giants?)
And our job as cartographers is to take this three-dimensional thing and represent it on a two-dimensional plane.
Because a map fits in our pockets much more easily than a globe.
And imagine how big that globe would have to be to be useful in a city!
So let's take a look at how datums are used in the wild.
As we mentioned before, national datums are managed by the NOAA National Geodetic Survey.
The first US datum was North American Datum of 1927. It was based on the Clarke Ellipsoid of 1866.
It is based on a single reference point in Lucas, Kansas.



(Former) geodetic center of North America!
Now we have hella advanced survey technology, and we have a new datum.
NAD 83!!!
Some translation is necessary.
And NGS is defining a new datum to come out in 2022.
NGS used to mark datum waypoints with survey markers.
Let's watch a video they made about datums.
So how relevant is this knowledge?
Does it apply to web maps?
... not so much
99% of web maps are in web mercator projection and use a geographic coordinate system.
Latitude, longitude... you know the drill.
But datums are hugely important when it comes to precise measurements.
And many many others.
There's a lot more we could go into but teaching geometry is not my strong suit.
So let's look at this puppy...
... and talk about what we learned today.
We learned about the science of geodesy!
We learned about geoids and reference ellipsoids!
We learned about datums and coordinate systems!
We learned that this is a HARD PROBLEM.
Pat yourself on the back! You are a champion!!!
There is so much I didn't cover. A quick Google search will yield so much more.
Keep learning! It just gets more fun!
Next geodesy lesson will be about PROJECTIONS OMG.
Extra credit: Watch more of NOAA's great videos on understanding datums.
Thanks!
My name is Lyzi! I am on Twitter at @lyzidiamond! (NAD27 never forget!)