One of the most often-reported parameters about a waterfall is its height
How often do you see brochures or websites reporting that Angel Falls
is the tallest waterfall in the world at 898m (3,292ft), or some waterfall is X
times taller than Niagara Falls
, or Yosemite Falls
is one of North America's tallest at 2,425ft, etc. etc.?
Indeed, what is it about a waterfall's height that grabs our attention so much?
Does that number somehow give you an indication of the waterfall's scale and magnitude without having been there? Do you use that number to determine whether a waterfall is tall enough to be worth visiting?
And it's not just waterfall lovers who tend to notice waterfall height. Tour operators and tourism authorities have also noticed this. In fact, sometimes liberties have been taken with that number (i.e. they're usually exaggerated) to entice visitors to come (and spend money) or bring a little more publicity to their attraction.
In this page, we're going to discuss how you measure the height of a waterfall. But before you wonder why we're devoting a whole page to something that seems so obvious, realize that you don't always have safe access to the very top of the waterfall. So what else can you do to get some sense of a waterfalls' height?
Well, we've seen quite a few waterfalls during our travels and we think there are some things you can do without risking your life.
Let's go into the various methods, shall we?Have a comment or contribution?
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THE BRUTE FORCE METHODThe brute force method is nothing more than going right up to the top of the waterfall then dropping a line with a weight tied to the end of it. You continue dropping the line until the weight touches either the ground or the plunge pool.
When that happens, you mark on the line (at the top of the falls) so you can measure the distance between your marking and the weight where it's safer to do so. That distance represents the height of the waterfall.
The problems with this method primarily have to do with safety. First off, the edge of a waterfall (let alone a cliff) tend to be unstable and could give at any moment. Second, the method doesn't quite work if the waterfall drops at an angle. Third, access to the very brink of the waterfall usually isn't safe and requires off-trail scrambling which accelerates erosion.
Nonetheless, this has been accomplished for some waterfalls. One example that comes to mind was the authors of The Ultimate Kauai Guidebook who managed to measure Wailua Falls using this method.
A related method is the so-called gravity method where you toss a rock over a cliff and time how long it takes to reach the ground. Then, take that time measurement by utilizing a little physics math to arrive at a height. The problem with this method is that: a) you may injure someone below, b) it's usually so loud around a waterfall that you can't even hear when the rock lands, c) if the waterfall has any bit of slope, you have no way of visually telling when the rock has landed, d) if the falls is not tall, your time measurement could be way off.
But to be honest, I highly discourage using the brute force and/or gravity method. As you'll see later on, there's a much better and more accurate way of measuring waterfalls without risking your life.
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QUICK ESTIMATIONI call this the lazy person's method because it requires nothing more than a reference and a lot of judgment. Admittedly, this is the method we use since we're usually on holiday where time is very precious (both from a vacation hours standpoint and from the fact that travel is generally costly). Unfortunately, it's very inaccurate. But often times, we only care roughly how tall a waterfall is and leave the accurate measurement to academics.
The method goes like this.
If there's an object standing near or next to the waterfall, you can use that object as the reference. If it's a person, you can guess that the person is about 5 or 6ft tall. If it's a tree, you can guess that it's probably 30ft tall or so depending on the type of tree.
Then, you can extrapolate by estimating how many times that object would be stacked on top of each other to make up the height of the waterfall.
On the left is a photographic example where we utilized this principle.
As you can see by the estimation method, Pe'epe'e Falls is about 50ft tall.
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CONTOUR LINES OF TOPOGRAPHIC MAPSThis method involves looking at a topographic map and then following a watercourse over a waterfall and recording the difference in height from start to finish.
This is one method where you don't have to be in the field to make a reasonable guess as the height of a waterfall! It has been put to extensive use by the folks at the World Waterfall Database (often times debunking certain claims but at the same time possibly giving too much credit to waterfalls that don't quite stack up to their more famous counterparts).
Below is a screenshot of this principle being put to use within the Topo! California software. Keep in mind that this method may not be possible in all cases as topographic maps are hard to come by in many countries.
In this example, I chose Yosemite Falls. I traced Yosemite Creek from around the top of the falls all the way down to its base. At the bottom of the screen, Topo! was able to build a profile for me and show that the waterfall is roughly 2500ft tall (corroborating the 2425ft claim). However, if this profile feature isn't available, you'll have to manually read the contour lines (there are numbers representing elevation for each line) and do the subtraction and judgment call manually.
The big downside to this method (besides the availability of topo maps for the region of interest) is that you don't have the information gained from being in the field. Sometimes it's hard to tell where one waterfall begins and where one ends simply by looking at a topo map.
Nonetheless, like the lazy persons method stated above, the topo method is pretty effective in getting a good ballpark estimate of a particular waterfall.
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COMPLICATIONS TO WATERFALL HEIGHTSUnfortunately, all of the above methods have some serious drawbacks. One particularly annoying one is that all of the above (except the topo method) assumes that the waterfall drops vertically. But what if the waterfall is sloping?
If the waterfall is sloping (keeping in mind we're only interested in the overall vertical drop), the string method won't work because it will prematurely get caught on the ground (or any other foliage in the way for that matter!).
The lazy person's method becomes less accurate with waterfall slope because the bottom of the waterfall is at a significantly different distance than the top of the waterfall, and you won't be able to determine how far the waterfall has travelled horizontally over that stretch.
What if you have no reference near the waterfall? If you use a reference that is rather far from the waterfall then perspective becomes distorted. And if you have no reference at all, the height estimation degenerates into a wild guess.
Besides calling from experience and a judgment call, what can you do to mitigate these shortcomings?
Fortunately, there is an elegant way of safely measuring the height of a waterfall, which is derived from a method used in the field by authorities such as the US Forestry Service, US Geological Survey, and other governmental and private agencies, civil engineers, etc. who require accurate measurements of how tall something is for one reason or another. This is discussed in the next section.
However, there is one very interesting question that seriously complicates one's ability to measure the height of a waterfall. That question is: Where Does A Waterfall Begin And End?
Let's look at why this is such an interesting question.
First, you have to ask yourself if cascades above and below the main plunge of the waterfall count as part of the waterfall. Sure the main plunge is obvious, but where do you draw the line between what should count as part of the falls or not?
Take Norway's Vedalsfossen for example. Notice how it has a plunge near its top then a long series of cascades as it makes its way down to the Hjølmo River. Should those cascades count as part of the overall drop of the falls?
I think it's examples like this that Norwegian authorities tend to express waterfall heights in terms of their vertical plunge only. Thus, you'll frequently see waterfalls like Vettisfossen be tagged with the tallest singular Norwegian waterfall while we know there are other ones that are taller from a cumulative height such as Mardalsfossen.
In our opinion, we tend to count those cascades as part of the overall drop, but we'll also try to note the vertical plunge as well. Usually, we rely more on info in the literature then try to put on our BS meter to see if the claims hold up. Not perfect I know, but we're lazy.
Second, what happens if a waterfall consists of multiple waterfalls. Where does one begin and where does one end? Or should they all count together as one big cumulative drop?
Take the Giant Stairway (i.e. the Nevada Falls and Vernal Fall combo) for example. In this instance, the Merced River plunges in two distinct sections each separated by a significant distance if you're hiking, but looks together when viewed from above. Should this count as one big waterfall or two separate ones?
In our opinion, we think they're two separate waterfalls because they're far enough apart from each other that it'd be hard to see them together from the ground. You can see there are problems with this line of reasoning, which is why we're not commiting to a rule on this subject. Another famous example along this train of thought is the Yellowstone River dropping over both Upper Falls and Lower Falls.
On the other hand, examples where we think the waterfalls with multiple drops should count as one entity include: Yosemite Falls, Belmore Falls in Australia, Mitchell Falls in Australia, and Gullfoss in Iceland among others.
A related subject (though not necessarily pertinent to the height of the waterfall) is the question of whether a waterfall counts as a single entity or multiple entities when the stream splits. In other words, how far apart must a waterfall be in order to count as separate entities if they come from a common stream nearby? Ntumbachushi Falls in Zambia comes to mind in this regard.
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THE BEST IN-THE-FIELD METHOD, PERIOD!I'm kicking myself for not figuring this out earlier and practicing it on every waterfall we've seen.
So what is this best-in-the-field method?
It basically involves some trigonometry and the use of a couple of handy devices you can buy commecially - a clinometer
and a rangefinder
The basic principle is this.
Through the use of trigonometry (i.e. the relationships between the length and angles in a right triangle), you can determine missing pieces of information simply by determining the length of the hypotenuse (the longest leg) of the triangle and the angle. Actually, if you know just the angle and the length of any leg of the right triangle or the length of any two legs of the right triangle, you can figure out all the other missing parameters of the right triangle, but I digress.
The drawing below (Figure 1) illustrates this graphically for a situation where you're at the bottom of a waterfall.
Figure 1: Measuring the height of a waterfall from its bottom with the help of a clinometer and rangefinder and a little trigonometry
You can get the hypotenuse measurement by using the rangefinder, which tells you how far away something is that you see through the tool.
You can get the angle measurement by using the clinometer, which tells you the angle of our line of sight relative to the horizontal.
Given these measurements (and realizing that the sine of an angle is the ratio between the opposite leg of the triangle and the hypotenuse), the height is determined by the trigonometric formula:
height = hypotenuse * sin(angle)
Now, you also have to add to the height how high your eyes are off the ground (typically around 5ft or so depending on how tall you are). The final formula then becomes:
waterfall_height = hypotenuse * sin(angle) + eye_level
The above procedure assumes you're at the bottom of the waterfall.
What about if you're at the top of a waterfall (Figure 2)?
Figure 2: Measuring the height of a waterfall from its top with the help of a clinometer and rangefinder and a little trigonometry
Again, you can still use rangefinder to get the hypotenuse of the right triangle and the clinometer to get the adjacent angle of that triangle.
However, you now have to use a different formula because we're talking about different legs of the triangle (namely, the fact that the cosine of an angle is the ratio between the adjacent leg of the triangle and the hypotenuse). That is, the following trigonometric formula:
height = hypotenuse * cos(angle)
Now, you have to subtract from the height how high your eyes are off the ground because eye level is higher than the top of the waterfall. Thus, you end up with the final formula:
waterfall_height = hypotenuse * cos(angle) - eye_level
Now what happens if you're neither at the bottom nor top of the waterfall, but somewhere in between (Figure 3)?
Figure 3: What you do when you're neither at the top nor bottom of the waterfall
Well, this scenario can be solved by dividing up the waterfall in two where you're eye level is the dividing line.
Let's first focus on the upper part of the waterfall.
Focusing on an object at the top of the waterfall or the top of the waterfall itself (nontrivial to pull off the latter), use the clinometer to get the angle relative to eye-level and the rangefinder to get the hypotenuse length (just like the bottom-of-the-waterfall approach mentioned earlier). Then use trigonometry to get the height of the upper part of the waterfall.
This can be described by the following formula:
height1 = hypotenuse1 * sin(angle1)
Now, let's focus on the lower part of the waterfall.
Focusing on an object at the base of the waterfall or at the bottom of the waterfall itself (nontrivial to pull off the latter), use the clinometer to get the angle relative to eye-level and the rangefinder to get the hypotenuse length (once again applying the bottom-of-the-waterfall approach). Then use trigonometry to get the height of the lower part of the waterfall.
In mathematical terms:
height2 = hypotenuse2 * sin(angle2)
To get back the waterfall's height, add the two results:
waterfall_height = height1 + height2
Another way to think about this calculation is that you've got two right triangles back-to-back with each other sharing their horizontal leg (which happens to be eye level). Thus, you're applying the you're-at-the-bottom-of-the-waterfall calculation twice (where the bottom triangle is simply flipped about the eye-level axis).
There's still yet a fourth case that is quite common: you're standing at a spot that's higher than the top of the waterfall (Figure 4).
Figure 4: What you do when you're standing from a spot that's higher than the waterfall itself?
Once again, you take two angle and hypotenuse measurements with the clinometer and rangefinder, respectively.
Take the first angle and hypotenuse measurements by focusing at the bottom of the waterfall or some nearby object at the same level. Plug in your measurements into the following formula to get the height between your eye level and the base of the waterfall.
height1 = hypotenuse1 * sin(angle1)
Now take the second angle and hypotenuse measurements by focusing at the top of the waterfall or some nearby object at the same level. Plus in your measurements into the following formula to get the height between your eye level and the top of the waterfall.
height2 = hypotenuse2 * sin(angle2)
To get the desired waterfall height, perform the following subtraction:
waterfall_height = height1 - height2
Indeed, the beauty of this best-in-the-field method is that you can apply these methods to almost any situation. It doesn't matter whether the waterfall is sloped or tiered, because you only care about the overall vertical drop. Plus, you're only limited by how far the clinometer and rangefinder can see. In other words, you can measure the height of a waterfall that's far away just so long as it's within the range of the clinometer and rangefinder .
The only situations where I can see this method failing are:
- when there's not enough light to focus on the object you're seeing through the clinometer and rangefinder
- the line of sight is blocked by some obstacle that keeps you from seeing the object you want to focus on with the clinometer and rangefinder
Finally, I have to admit that since I have somewhat of a mathematical background, I'm ashamed to say that I still have yet to try it! However, there are a couple of waterfallers who have already utilized this method successfully. Check out Scott Ensminger's New York Waterfalls Survey and Ruth's Waterfalls, which run through a few examples while beautifully explaining the methodology on this page. They also have tables and spreadsheets if the trigonometry frightens you.
At some point in time, I do plan on shelling out some $$$ for a clinometer and rangefinder (maybe I can take an old one from my brother's since he's an avid golfer).
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CONCLUSIONSo you see, the question of how tall a waterfall is can be a surprisingly complicated subject.
And while you'll no doubt continue to see various claims about how tall a waterfall is (usually taller than the reality might be), numbers alone can't replace the beauty, benefits, and variety that waterfalls bring in general. Besides, we usually have our BS meter on and see how the numbers stack up to our gut feeling after seeing it in person.
Even though we may glance at a waterfall's reported height when we know little else about that waterfall during the course of our travel research, we generally care more about how we react to it (especially after seeing it in person) than the statistics.
In the end, it's really about what waterfalls do for you rather than how they statistically stack up. This is why our Top 10 Waterfalls List doesn't necessarily take into account a waterfalls' height. Sure there may be taller ones out there we've personally visited that didn't make the list, but in our minds, the Top 10 are the ones that exemplify the best of the best all around.
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