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USGS topographic quadrangles are maps produced by the U.S.Geological Survey. They can be accessed in
digital or paper form. For purposes of this video tutorial I’ll be using this digital version of the
Pyramid Peak topographic quadrangle. Pyramid Peak is in the Desolation Wilderness in California.
The borders of USGS quadrangles are latitude and longitude lines. We can identify the value
of those lines by studying the corners of the quadrangle. Here at the top left corner, we see a
vertical longitude line and a horizontal latitude line and their corresponding measurements,
identified from the mess of numbers that exist here by their location and their units: degrees,
minutes, and seconds. The rest of these numbers are part of a national grid or state plane
coordinate system. We are not going to discuss or use those numbers in this video tutorial.
That means we have to ignore most of these numbers and focus only on those that are latitudes
and longitudes. How do we find them? Look for numbers with minutes and seconds as their unit.
Back to the left corner: the latitude line moves across the top, so we should find the same
latitude measurement on both top corners: 38° 52’ 30”. Of course all latitude lines must also have a
direction: north or south of the equator. So let’s look at the bottom corners to help us determine
direction for this quadrangle . Down here in the lower right and lower left, we see the bottom
latitude: 38° 45’ 00”. The map doesn’t provide us direction or even include seconds when those are
equal to zero because the map makers felt the reader could understand for themselves these
abbreviations and fill in the missing information. Abbreviations reduce the amount of text required
to be on the map. But we’re going to fill in the abbreviations for our records to ensure our
information is complete. Notice that the latitude numbers get larger as we move north. That is true
only if we are north of the equator, so we can add the letter N after all these latitude lines.
Now let’s look at the longitude borders. Here on the top right corner, at the top above this
vertical border, we find the number 120° 7’ 30”, which matches the number that sits below the line
in the bottom right corner. Is it west or east of the prime meridian? Let’s look at the left
side of the map. Here we see the number 120° 15’ 00”. Since these numbers grow larger as we move
westward, we must be west of the prime meridian, so we add W or West to each of our border numbers.
Comparing the two latitude borders with each other, we see that there are a total of 7’ 30”
of latitude covered by this map -- 45’ + 7’ 30” = 52’ 30”. And there are also 7’ 30” of longitude.
7’30” + 7’30” = 15’. So there are equal angles of measurement for all sides.
That makes this map a 7’ 30” or 7.5’ quadrangle.
Though we can see that the map is not square shaped. Equal angles are not the same as
equal distances. Its width and height are not identical distances, just identical angles.
Remember: latitude lines are parallel and cover roughly the same distance between them regardless
of where they are on the planet. In other words, a 7.5’ quadrangle will always be this tall.
However, longitude lines converge as they approach the poles, so a 7.5’ quadrangle
will get narrower and narrower the further north or south of the equator we get. That
just means this quadrangle covers and displays less terrain width wise than it does height wise.
Now let’s look at the rest of the borders on this map. Somewhere in there amongst all these
extra grid system numbers are subdivisions of the latitude and longitude. Here we see an abbreviated
latitude: 47’ 30” that is matched on the opposite side of the map. That tells us it’s the latitude
line 38° 47’ 30” North. Continuing up we find a measurement that says 50’ meaning 38° 50’
00” Noth. So now we can see four latitude lines breaking up the quadrangle into a grid system.
Similarly there are 4 longitude lines -- with subdivisions of 120° 10’ 00”
W -- and 120° 12’ 30” W. So we could estimate the latitude and longitude of any location on this map
by estimating where it sits between these grid lines and adding the appropriate error. Example:
This star here is in the middle of these grid lines.
The grid lines, themselves, are separated by 2’30” -- half of which is 1’15”.
So if we add 1’15” to this longitude and to this latitude, we will find the latitude and longitude
of this point in the middle. I’ll also add 15” of error to handle the fact that it’s an estimation
Now let’s study the rest of the map. Here in the top right corner we find the name of the map
and we see it identified as being part of a 7.5 minute series.
Our measurements of the latitude and longitude borders confirm that.
We also see this other name in parentheses going off at an angle. That is the name of
the 7.5 minute quadrangle that would cover the terrain that meets this quadrangle at that corner.
All the edges and corners of this map will have names of the adjoining maps.
Let’s move to the bottom center of the map to see another example.
The quadrangle that would adjoin this map to the south is called Tragedy Springs.
Also, notice under the map here we see three scale bars -- one for miles, one for feet,
and one for kilometers. Notice that for each scale bar, the zero is not on the left side,
but somewhere in the middle. Let’s look more closely at the kilometer scale bar.
The zero is in the center, and we have 1 kilometer measured on the right
and 1 kilometer measured on the left but with 0.1 kilometer subdivisions.
How do we use these scale bars? Let’s zoom out again and imagine we have two locations we want
to measure the distance between. We can lay down a piece of paper between those two locations on our
map or on our screen if we’re on a computer and make tick marks on our paper to represent that
length. The we move the paper down to the scale bar and lay the left tick mark on the zero and
look across to the right. We’ll tick off the first kilometer here and then move the paper along this
scale bar, ticking off 1 kilometer at a time until we find ourselves with less than a kilometer left.
For this example, we have 2 full kilometers and one partial. Now we move the remainder of our
line over to the left, line it up with zero to determine how many tenths of a kilometer we have
left. In this case, it looks like 0.85 kilometers. So we add them all up for our final distance
measurement and add in the appropriate error. That error comes from a combination of the user
and the method that we used. In this case I fell confident that my measurement is within 0.1 km.
What else can be seen down here at the bottom of the map? These arrows here
tell us the magnetic declination at this location when the map was made.
The star in this case points true north. GN is grid north -- related to the numbers of
the grid system we’re ignoring, so we’ll ignore this as well. The MN refers to
magnetic north -- the direction magnets pointed in this location in 1994 when this map was made.
The angle between those two (from true north to magnetic north) is a bearing or orientation.
An oceanographer would write it simply as 15.5°, meaning 15.5° clockwise from north.
A geologist would write it as N15°E, meaning start facing north, and then rotate 15° to the east.
Now let’s return to the scale bar. Just underneath we can read the contour interval for this
map -- 40 feet. What does that mean? Notice that throughout the map itself we find brown lines.
These lines connect points of equal elevation above sea level and are called
contour lines. Each one is 40 feet higher or lower than the one next to it.
And the numbers get higher as wemove up peaks.
Other maps, called nautical charts, have lines called isobaths that connect points of equal depth
below sea level, and in that case the numbers get bigger as we go deeper under sea level.
Let’s look at another example. Here is an exaggerated terrain model showing peaks and
valleys and lines of equal elevation. The corresponding map looks like this. Notice
the contour interval noted at the bottom is 20 feet. Here is what the same map
would like like if the lines were isobaths instead and the terrain were underwater.
For contours, the numbers get bigger as we move up to the peak here. But for the nautical chart,
underwater, the numbers get smaller, because we’re moving closer to sea level.
Now let’s return to the Pyramid Peak quadrangle, which is above sea level, so we call the lines
contours and they get bigger as we move up. Zooming in to the upper right of this quadrangle,
we find Pyramid Peak, the mountain that gives this quadrangle its name.
Notice that the contour lines come in two types -- a light brown and a dark brown.
Each contour line is separated by 40 feet, but the dark brown lines appear
after every 5th contour and thus group the contour lines into 200 feet sections.
These darker lines are called index contours, and they should have a
number marked along them somewhere making it easier for us to tell their elevation.
For example, moving up this valley here on the left, we see a 7600 contour line, then 7800,
then 8000, then what we know must be 8200, 8400, 8600, and then no more index contours, but four
more regular contours before we reach the peak of Blue Mountain. The black number written across the
contour lines near the peak is the measured value or benchmark of the highest point on the peak.
Notice that each of these peaks has an x marked at the highest spot and a number indicating the
peak height. Measured benchmarks will appear at other locations as well, such as here at the
spillway to Lake Aloha, noted at the time this map was made to be 8116 feet above sea level.
Whether an isobath or a contour line, remember that only the points on the line have that exact
value for elevation or depth. Either side of the line will be greater or smaller.
As we get comfortable reading contour lines or isobaths and recognizing shapes of hills
and canyons, one useful tool for visualizing the relief in an area is to draw a topographic
or bathymetric profile. These are especially useful if we plan to hike in an area and want
to know how steep the slopes are. I’ll demonstrate using this simple topographic map here that shows
a hill that gets taller and reaches a peak. The contour interval is 20 feet, so this is 400 feet,
and this is 520 feet. And everything inside this circle will be higher than 520 feet but
less than 540 feet. First step in building a profile is to draw a profile line on my map.
I draw my line so that it cuts across the peak and right through the two different types of hills.
Second step: on a piece of graph paper, I draw a Y-axis to represent the elevations I’ll be
drawing. In this case the smallest would be 400 feet and the highest would be 540 feet.
Notice that each division is equally separated by 20 feet. I could also draw it so each division
was separated by 40 feet or 10 feet or 100 feet, whatever you choose, just be consistent in each of
your subdivisions. Next I lay the graph paper down along the cross-section line. Everywhere a contour
line intersects the cross-section line, I note the elevation and transfer that to my profile.
This spot is 400 feet. This spot is 500 feet. Once I have all of my elevations transferred,
I connect the dots with a smooth line. What do I do at the peak? I continue as best I can
the two slopes on either side and smooth them to a peak that sits between 520 and 540 feet.
And now I can see the differences in slopes between the west and east sides of this hill.
Final step is to tell my audience how much I exaggerated this topographic profile,
since the scale for the X-axis is not the same as that for the Y-axis.
What we’ve done is taken something that would look a lot flatter in reality,
and we’ve stretched it out vertically so that we can exaggerate and see more
closely the differences. Now we have to tell our audience how much we did that.
I take this scale bar for the x-axis, which is 0.25 miles or 1320 feet,
and I lay that same length down on my Y-axis. Here it equals 100 feet.
1320 feet per line unit on the X-axis and 100 feet per line unit on the Y-axis.
The Y-axis is vertically exaggerated 1320/100 or 132 times! Note: that’s probably too precise
a calculation because the 100 foot measurement that I noted likely had an error of +/- 5 feet,
so the vertical exaggeration might more realistically be rounded to 130 times.
We use topographic or bathymetric profiles
to exaggerate the terrain and better see the slopes and shapes above and below sea
level so that we can turn our 2-dimensional maps into more 3-dimensional renderings.
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