The Wild World of **Geodesy!** *Part 1: Datums*

Go to http://lyzidiamond.com /geodesy-pt-1 to follow along.

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**.

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."

"oblate ellipsoid."

(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.

Because we, as **cartographers** are engaged in *measuring* the Earth. We need to know **what goes where.**

How do we do that? *MATH!*

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.

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

Because, again, of the **irregular shape** of the Earth.

Some *ellipsoids* are better for **certain areas**.

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.*

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)

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**

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!*

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!)**