Waterflow Estimation

This is an untested methods for canyoneers wanting to guesstimate stream flow before descending canyons. If it works out like I think, just using the formula below should put you around the right flow, plus or minus 20% most of the time, but the flow could potentially be a little over 50% higher in some unusual situations. Below the formula is some explanation of how I came up with this, and some advice on how you can account for inaccuracies. My hope is that with a bit of practice, and some quick thoughts into what inaccuracies might be present, is that with a couple minutes of effort we can get the streamflow within + or – 10% of what it actually is.

Streamflow (cfs) = (w*d*v)/2

w= stream width d= maximum stream depth along width v= stream velocity at surface

Select a stream section: -This can be upstream or downstream from the canyon. Where ever is convenient! -Check for any major tributaries (ones that would have flow). If at all possible, do not select a section below any major tributaries that come in below your technical canyon, and do not select a section above any major tributaries that come in above your technical canyon. If this is not possible, you'll have to guess the flow of this tributary and account for it. -Look for a portion of the stream with visible current, but with as little hydraulics (eddies, holes, places where some water is moving upstream) as possible and hopefully not a lot of rocks or islands poking up. Also avoid undercut rocks as they can conceal flow. -Look for a portion of stream where the width and average depth appear to remain fairly consistent. -Ideally a floating object placed in this stream will take around 20 seconds to travel the length. If you can't find a long enough section, that's okay, but shoot for at least 5 seconds.

Measure stream width: Stretch a rope across the stream from one edge of the water to the other. Then determine the length of that rope in feet.

Measure maximum stream depth: Find the deepest point in the stream and stand in it. You can stand on the edge of your rope to get a length of rope to then measure, or you could take some time before going canyoning to figure out where certain depths would hit your body. For instance 1 foot is a little over halfway up my calf, two feet is right on top of my quad, and three feet is at waist level. If the water current is too strong to stand where you are measuring, you are likely either standing in a waterfall, or dealing with some serious flows, probably at least 50cfs and better have a good idea of what you're getting into. Still, you can guess the max depth, or try to find somewhere wider to get your flow.

Measure stream velocity: Measure out a length of stream where the width and depth appear to remain fairly consistent. Place a floating object (apple, orange, or partially filled water bottle is ideal) at the top of this section of stream, and time the object as it floats the length. Using a watch would be ideal, but counting out seconds is okay (Note that if the float gets stuck for any significant time in a hydraulic or eddy, you'll want to start over). Now do this again two more times, and take an average of those times (an approximate average is okay). The length of the stream segment divided by the average time it takes the object to travel is your velocity.

Now multiply your width, by your depth, by your velocity, and divide it by 2! This should be your approximate streamflow, but this estimate is made based off of some major assumptions. Depending on your section of stream, you may want to take some of those into consideration, and adjust your number a bit accordingly. Streamflow is the amount of water flowing down a stream (duh) and remains consistent despite the gradient, depth, and water velocity. The flow going through a waterfall is just the same as the flow through a pool that appears almost still downstream.

One way streamflow is calculated is to use a weir or another point where water is channelized into one falling stream, and to fill up a fixed volume, and measure the amount of time it takes it to fill. This volume divided by those seconds gives you the flow. So if you held your empty nalgene bottle up to a waterfall that contained the entire flow of a stream, and it took five seconds to fill up, the flow would be 1/5 of a liter per second or less than 0.007 cfs (cubic feet per second). It also wouldn't really be a class C canyon, so this method is not particularly helpful.

Other streamflow calculations are based on measuring the flow through a cross sectional area of the stream. So if the cross sectional area of a stream is 10 square feet, and the average water velocity through this area is 1 foot per second, then the area times the velocity gives us 10cfs of flow, which depending on the canyon could be fun or deadly!

Our problem lies with coming up with an easy way to get that cross sectional area, and the velocity flowing through it. Let's start with the cross sectional area. Easy enough. Width times depth gives us our area. And width we can figure out with little to no issue. Stretch your rope across the stream, find the distance between one edge of the water to the other, and use whatever canyoneering rope measuring techniques you prefer.

Depth is a bit more tricky. Scientific protocol is to measure out intervals across your cross section and to measure many times across the stream then get an average. You could certainly do this if you wanted to be more accurate, but I wanted to make this a quick process. So the idea is to assume a general shape for the streambed. Here's the shape I decided would work out nicely (note it can be a variety of widths and depths):

This is admittedly kind of a big assumption, but if we think about it, a lot of stream beds look kind of like this, smoothing out the cobbles on the bottom which is essentially what taking an average does anyway. It is also conveniently the shape that makes our “divide by 2 to get cfs” part work out! The area of this shape is two thirds of the width times depth of our stream. You can look at the section of stream you are sampling, and say “the sides are sloped down about one third of the way from either stream edge, the middle is flat, this works!” and use that calculation. But lets look at some situations where your stream bed isn't quite the same.

Here one bank is steep and one is quite shallow. But if we look at the area cut off and the area added to our original shape, the cross section is still more or less the same area. No problem, same calculation!

Say at your deep point it gets immediately shallower and slopes up to the sides to either bank. Our cross section is now only one half of depth times height, which is 76% (round up to 80%) of our assumed area. All that means, is that when we get our flow from the simple calculation, we can assume the actual flow is about 80% of that.

In this case we have some steeper cutbanks down to a fairly flat bottom, giving us approximately half of an oval for our cross section. The area is then width/2 times depth time pi, all divided in half. This area is 19% (round to 20%) higher than our assumed cross section, so our final flow should be 120% of what we calculated. So another 20% of the calculated flow on top of that to get our final.

In this case our stream is box shaped, which is pretty weird, but if the banks of your stream are nearing this steep, you certainly need to be careful. The cross sectional area is width times depth which is 150% of our flow. The stream flow will be half again as much as we calculated in our estimate.

So hopefully based off of that information, you can look at your stream section, guess whether or not the cross sectional area is close enough to our assumed trapezoid, and if not, adjust your final streamflow accordingly. All of this should only take a few seconds, and be easy enough to estimate in your head.

The next part of this is getting the streamflow, which it turns out is pretty easy. You may have guessed that the flow on the surface which we can calculate with your improvised float is not the same as the flow all the way through the stream. Actually the flow 40% below the surface works out to be the nice average, which is unfortunately hard to measure. But, thanks to hydrologists we know that the surface flow is around 120% faster than the average streamflow and gives us a correction factor. This number varies a bit with what the bottom of the stream looks like. For cobbly rocky streams the surface velocity times a correction factor of .8 gives us our average flow. For smooth bottom the correction factor is .9.

As in most streams above canyons that I know of there are cobbles along the bottom, I went with the .8 correction factor. But you should know, that if the bottom of the stream section your measuring is granite bed rock, silt, or sand or something else unobstructive, that the flow will be 10% higher than the calculation with your calculation and you should adjust.

So that's what I have for now. Please try it out, especially if you have somewhere where you can verify with an online guage, and let me know what you think, or if you have ideas for improvements. Certainly don't trust your life to the numbers you come up with.

And if you're wondering where the formula came from, it's pretty simple.

Cross section area of trapezoid= .66*w*d (The trapezoid is basically 2 out of 3 squares, one of the squares cut in half to make triangles on either end of the first square... if that makes any sense.) Water velocity= .8*v (.8 is the correction factor) Then we multiply the cross section by the velocity... .66*w*d*.8*v=0.528*w*d*v And a little bit of rounding we get: (w*d*v)/2