Tag Archives: coordinate systems

UTM

In a couple of previous posts we have examined latitude and longitude in some detail, and explored in what format the numbers might be displayed on your handheld GPS unit. Here we will explore another commonly used coordinate system: UTM.

Latitude and longitude work well, but since they are all based upon circles, and because degrees are divided into groups of 60, the calculations required to work with them are unwieldy. It is frequently useful to have coordinates based upon plane rectangular geometry in our normal base 10 system. This can work well if the area in question is not too large, because then we can discount the curvature of the Earth. Over just a section of the Earth, the curve does not make a huge difference in error.

In order to do this, we must “flatten” the Earth to a plane, and when we do we can use the Cartesian coordinates that we all used in high school geometry class. It would be like flattening the peel of an orange. If you try to flatten the whole peel it makes a very irregular shape. But if you flatten a small piece it does fine. Then you can think of the x and y axes as east-west and north-south.

The familiar Cartesian coordinate system showing how points can be assigned a distance along two axes from the origin point.

As you recall, every point on this plane can be described by two coordinates, one along each axis. And you can see in the illustration that some of the points have negative values with respect to the origin (point 0,0). However, we can control how we place the coordinate system, and with the origin point outside of our area of interest all the points can be positive (east, north)—in the upper right-hand quadrant.

State of Kansas laid on top of a Cartesian coordinate form

The State of Kansas placed on the rectangular grid so that every point in the state will be positive with regard to the origin.

UTM coordinates, or Universal Transverse Mercator coordinates, are a rectangular plane system in metric units. Cartographers have taken swaths of each state and mathematically flattened them into a plane, assigned an origin southwest of each section, and laid out the resulting grid. Some of the smaller states are covered in a single swath, but the larger states must be broken into several zones so that the curvature of the Earth does not distort each map too much.

So, UTM coordinates have two components: their easting and northing values from the origin point in meters, and which state zone you are referring to. You can see a map of the zones here.

I have used UTM coordinates to good effect in my scientific work. When mapping a paleontological excavation, for example, we make all measurements in metric units. Since we are already measuring in metric units, every point in the dig site can easily be assigned its real-world UTM coordinate, instantly relating all points in the dig to any other point on the globe.

This means we can accurately and quickly plot the location of any fossil site, or even individual fossils, on a real-world map.

Latitude and longitude 2

In the first discussion of latitude and longitude, we investigated how the latitude-longitude grid was established. In this post we will look at how that relates to the display on your handheld GPS unit.

If I stand outside with my GPS and direct the unit to display my position, it may do so in a couple of different ways. First, it might show my position on a map background, pinpointing my location with regard to other features such as streets, buildings, or landforms. This shows me my location as if I were walking around on the map.

I might want to know my latitude and longitude coordinates. Perhaps I want to record them so I can return to this spot in the future. (You can understand why a “bone digger” would want that!) In most handheld GPS units you can save your location as a waypoint. (See my review of the best GPS units.)

A really useful thing to be aware of about has to do with the format of latitude and longitude number displays. These numbers can be expressed in several ways, and you must know which format the numbers are in or risk making errors. After GPS units first came out, I used one to locate some fossil sites where I collected. I happily recorded the coordinates for the fossils I picked up, and dutifully wrote them in my field book. Only later did I realize that I was not perfectly clear which form the coordinates were in, making the records almost useless!

Most handheld GPS units allow you to display the coordinates in several formats. You could show the form degrees-minutes-seconds, sometimes denoted as DMS. This might look something like 38°53’22.49″N, 99°17’58.73″W. Latitude is given as degrees north or south from the equator, and longitude is given as degrees east or west from the prime meridian.

But we could also give these same numbers in another format which would look like: 38° 53.375’N, 99° 17.979’W. This format is in the form of degrees, minutes, and decimal minutes, or DMM.

Finally, we could show these coordinates as full decimal degrees (DDD) and it would look like: 38.889583°, -99.299650°. Note that in this form, the positive or negative form of the number is important as that gives the direction. Positive latitude numbers are north, and negative longitude numbers are west.

Notice that these forms are all equal: 1° 30′ 30″ (DMS); 1° 30.5′ (DMM); 1.5083° (DDD). And you can see if you just wrote down numbers on a page, and were not very clear about which form the numbers were in, you could be very far off the mark in terms of location.

There is another common coordinate form called UTM which we will examine in another post. Bonus points to anyone who can tell me what is at the coordinates used in this post.

Latitude & Longitude

Thought question: when you are standing at the North Pole, which direction are you looking?

A topic that I think people find a bit confusing is the coordinate systems commonly used in their handheld GPS units. The handheld GPS can tell you your exact location, and this is because cartographers have partitioned the surface of the Earth so that one point can be located with regard to any other point. However, over time they have developed a variety of different coordinate systems to meet various needs.

The most commonly used coordinate system is probably the latitude and longitude grid. This system is based on two 360 degree circles that are envisioned to circle the planet. The first great circle spans the planet from “head to toe,” or along the axis of rotation. The second great circle goes around the “waist” of the planet, at right angles to the axis of rotation, and along the planet’s midline. We call this great circle the equator.

You no doubt learned that a circle can be divided into 360 degrees. The circle of the equator can likewise be divided, but where should we start? The line projected from the North Pole through Greenwich, England, through the equator to the South Pole is the prime meridian. Here, “prime” means “first” or “initial.” The point where it crosses the equator is the starting point for dividing the equatorial circle.

Why Greenwich, England, you ask? This standard was really only recently set, in 1884, when delegates from 25 nations met in Washington, D.C. for the International Meridian Conference. They adopted the meridian passing through the Transit Instrument at the Greenwich Observatory as the “prime” one. You have to start somewhere!

From the prime meridian, we can measure around the circle of the equator east and west up to 180 degrees, covering the full circle. This establishes the lines of longitude (running from the pole to pole) and defines the directions “east” and “west.”

We can divide the prime meridian into its 360 degrees also, and we find it useful to start at the equator and count 180 degrees from pole to pole. So, you can go from zero to 90 degrees in both directions, north and south, and this establishes lines of latitude, and defines “north” and “south.”

Notice that lines of latitude do not converge on a spot—they remain parallel to each other on the globe. However, lines of longitude do converge, at the poles. What this means is that the distance on the ground remains the same between degrees of latitude. But the degrees of longitude get closer together as you approach the poles. In other words, one degree of longitude at the equator is a longer physical distance on the ground than one degree of longitude farther to the north, say in Greenland. This is just an interesting complication of living on a sphere.

And it is because of that complication that I know exactly which direction you are looking when you are standing on the North Pole—no matter how you turn your body, you are by definition looking south. At 90 degrees north there is so other way to go but down (in latitude, that is).

Boneblogger: Science and the outdoors

Exploring the natural world

Tag Archives: coordinate systems

UTM

Latitude and longitude 2

Latitude & Longitude